Design and Detection Process in Chipless RFID Systems Based on a Space-Time-Frequency Technique

Transcription

1 Desig ad Detectio Process i Chipless RFID Systems Based o a Space-Time-Frequecy Techique REZA REZAIESARLAK Dissertatio submitted to the faculty of the Virgiia Polytechic Istitute ad State Uiversity i partial fulfillmet of the requiremets for the degree of Doctor of Philosophy i Electrical Egieerig Majid Mateghi, Chair William A. Davis Gary S. Brow Jeffrey H. Reed Werer E. Kohler APRIL 7, 15 BLACKSBURG, VIRGINIA Keywords: Atea, Chipless RFID, Detectio, Scatterig, Short-time Matrix Pecil Method (STMPM), Time-Frequecy Aalysis, Trasiet Aalysis, Ultra Widebad. Copyright 15 REZA REZAIESARLAK

2 Desig ad Detectio Process i Chipless RFID Systems Based o a Space-Time-Frequecy Techique Reza Rezaiesarlak ABSTRACT Recetly, Radio Frequecy Idetificatio (RFID) techology has become commoplace i may applicatios. It is based o storig ad remotely retrievig the data embedded o the tags. The tag structure ca be chipped or chipless. I chipped tags, a itegrated IC attached to the atea is biased by a oboard battery or iterrogatig sigal. Compared to barcodes, the chipped tags are expesive because of the existece of the chip. That was why chipless RFID tags are demaded as a cheap cadidate for chipped RFID tags ad barcodes. As its ame expresses, the geometry of the tag acts as both modulator ad scatterer. As a modulator, it icorporates data ito the received electric field lauched from the reader atea ad reflects it back to the receivig atea. The scattered sigal from the tag is captured by the atea ad trasferred to the reader for the detectio process. By employig the sigularity expasio method (SEM) ad the characteristic mode theory (CMT), a systematic desig process is itroduced by which the resoat ad radiatio characteristics of the tag are moitored i the pole diagram versus structural parameters. The atea is aother compoet of the system. Takig advatage of ultra-widebad (UWB) techology, it is possible to study the time ad frequecy domai characteristics of the atea used i chipless RFID system. A ew omi-directioal atea elemet useful i widebad ad UWB systems is preseted. The, a ew time-frequecy techique, called short-time matrix pecil method (STMPM), is itroduced as a efficiet approach for aalyzig various scatterig mechaisms i chipless RFID tags. By studyig the performace of STMPM i early-time ad late-time resposes of the scatterers, the detectio process is improved i cases of multiple tags located close to each other. A space-time-frequecy algorithm is itroduced based o STMPM to detect, idetify, ad localize multiple multi-bit chipless RFID tags i the reader area. The proposed techique has applicatios i electromagetic ad acoustic-based detectio of targets.

3 To my parets, Fakhri ad Hamid iii

4 ACKNOWLEDGEMENTS First ad foremost, I would like to thak my parets ad sisters for their ivaluable support ad sacrifices durig my educatio. There are so may people who cotributed to my educatioal life. I remember the ames of may of them ad have forgotte some of them. I am grateful to all of them from my first grade teacher to my PhD advisor. I would like to express my gratitude to my supervisor, Dr. Majid Mateghi, for his woderful metorship, ecouragemet, costructive criticism ad discussios, ad providig me a friedly scietific atmosphere throughout my PhD studies. I would like to thak Dr. William A. Davis, Dr. Gary S. Brow, Dr. Jeffrey H. Reed, ad Dr. Werer Kohler for servig o my committee. I really appreciate their support, patiece ad commets i every step of the way, durig my PhD educatio. Special thaks to my great frieds i Blacksburg, especially Haif Livai, Mohse Salehi, ad Reza Arghadeh for their precious helps ad all the fu we had together. I additio, I have to thak my colleagues at Virgiia Tech Atea Group (VTAG), Rodrigues Blaco, Taeyoug Yag ad Shyam Mabiar for their precious time, discussios ad suggestios. iv

5 TABLE OF CONTENTS ABSTRACT... ii Dedicatio...iii ACKNOWLEDGEMENTS... iv TABLE OF CONTENTS... v LIST OF FIGURES... vii LIST OF TABLES... xiv 1 INTRODUCTION RFID Systems Passive RFID tags Near-field RFID Far-field RFID Chipless RFID System Dissertatio Outlie... 7 Mathematical Represetatio of Scattered Fields from Chipless RFID Tags [8] (Chapter used with permissio of Spriger sciece ad busiess media, 15) Sigularity Expasio Method (SEM) Altes Model SEM-Based Equivalet Circuit of Scatterer SEM Represetatio of Currets o a Dipole Eigemode Expasio Method Example: Eigemode Expasio of Currets o a Dipole Characteristic Mode Theory Mathematical Formulatio of the Characteristic Mode Theory Characteristic Mode Aalysis of Dipole Desig of Chipless RFID Tags [8] (Chapter used with permissio of Spriger sciece ad busiess media, 15) Complex Natural Resoace-Based Desig of Chipless RFID Tags Desig of Chipless RFID Tag Based o Characteristic Mode Theory UWB Atea i Chipless RFID Systems Lik Equatio i Frequecy Domai... 7 v

6 4. Time-Domai Sigal Lik Characterizatio Atea Effective Legth Atea Characteristics i Time Domai New Atea Prototype for Widebad ad Ultra-widebad Applicatios Time-Frequecy Techiques for Aalyzig Trasiet Scattered Sigal from Targets [8] (Chapter used with permissio of Spriger sciece ad busiess media, 15) Short-Time Fourier Trasform (STFT) Resolutio Wavelet Trasform Re-assiged Joit Time-Frequecy (RJTF) Short-Time Matrix Pecil Method (STMPM) Matrix Pecil Method (MPM) [68] STMPM i Late-Time STMPM i Early Time Performace of STMPM Agaist Noise Applicatio of STMPM i Widebad Scatterig from Resoat Structures [7] Detectio, Idetificatio, ad Localizatio i Chipless RFID Tags [8] (Chapter used with permissio of Spriger sciece ad busiess media, 15) Detectio of Chipless RFID Tags Space-Time-Frequecy Ati-Collisio Algorithm for Idetifyig Chipless RFID Tags [8] Space, Time ad Frequecy Resolutios Separatig the Early-Time ad Late-Time Resposes for Detectio, Idetificatio, ad Localizatio of Chipless RFID Tags Measuremet Results Localizatio of Chipless RFID Tag [88] Coclusio ad Future Work Summary of Dissertatio Suggestios for Future Work Refereces vi

7 LIST OF FIGURES Figure 1.1 Two passive RFID tags.... Figure 1. Block diagram of ear-field passive RFID tag Figure 1.3 Far-field commuicatio mechaism i RFID systems Figure 1.4 Gamma-matched atea Figure 1.5 A 6-stage full-wave rectifier voltage multiplier Figure 1.6 Chipless RFID system Figure.13-bit tag illumiated by a icidet plae wave Figure.3-bit tag illumiated partly by a icidet plae wave Figure.3(a) Trasversal ad (b) modified filter model of the early-time respose.... Figure.4 Measuremet setup to measure a UWB pulse scattered from a metal object.... Figure.5 Excitatio pulse ad its derivative with respect to time Figure.6 Received electric field from the metal object for differet distaces (a) d = cm, (b) d = 3 cm, (c) d = 1 cm, ad d = 13 cm Figure.7 Received electric field from the metal plate for d = cm ad d = 13cm Figure.8 (a) A tag illumiated by a icidet plae pulse, ad (b) SEM-based equivalet circuit of chipless RFID tag... 6 Figure.9 Geometry of the dipole illumiated by a icidet field Figure.1 Pole diagram of the dipole, represetig the resoat frequecy ad dampig factor of the CNRs... 9 Figure.11 (a) Real ad (b) imagiary parts of the first three atural currets of the dipole Figure.1 Real ad imagiary parts of the first three eigemodes of the dipole Figure.13 Eigevalues of the characteristic modes versus frequecy Figure.14 (a) Modal sigificace ad (b) characteristic agle of the characteristic modes versus frequecy Figure.15 First three characteristic modes of the dipole at (a) f = 13 MHz, (b) f = 8 MHz, (c) f = 3 MHz, ad f = 43 MHz Figure 3.1 Schematic view of a surface acoustic wave tag Figure 3. Dispersive delay structures [4] (With permissio, Copyright 11 IEEE) Figure 3.3 Chipless RFID system based o DDSs [4] (With permissio, Copyright 11 IEEE) Figure 3.4 Assiged resoat frequecies for a chipless RFID tag Figure 3.5 Spectral-based chipless RFID tags usig (a) dipole resoators [43] (Copyright 5 IEEE) (b) fractal Hilbert curve [44] (Copyright 6 IEEE) (c) slot resoators [45]. (Copyright 7 IEEE) (d) Resoat circuitry attached to the trasmittig/receivig ateas as a chipless RFID tag [46] (Copyright 9 IEEE) (e) chipless RFID tag based o highimpedace surface [47] (Copyright 13 IEEE) (f) 4-bit tag usig quarter-wavelegth slot resoators [4] (With permissio, Copyright 14 IEEE) Figure 3.6 Sigle-bit tag with structural dimesios Figure 3.7 Curret distributio o the tag for differet time istaces [33] (With permissio, Copyright 15 IEEE) Figure 3.8 (a) Frequecy-domai ad (b) time-domai backscattered field from the sigle-bit tag [33] (With permissio, Copyright 15 IEEE) Figure 3.9 Pole diagram of the sigle-bit tag [33] (With permissio, Copyright 15 IEEE).. 5 vii

8 Figure 3.1 Curret distributio o the tag at (a) f = 5.54GHz ad (b) 8.8 GHz [4] (With permissio, Copyright 14 IEEE) Figure 3.11 Resoat frequecy of the slot versus L. W =.3mm [4] (With permissio, Copyright 14 IEEE) Figure 3.1 Dampig factor of the CNR of the slot versus d for differet values of a. W =.3 mm [4] (With permissio, Copyright 14 IEEE)... 5 Figure 3.13 Dampig factor of the CNR of the slot versus d for differet values of a. W =.3mm [4] (With permissio, Copyright 14 IEEE) Figure 3.14 (a) Resoat frequecy ad (b) dampig factor of the CNR of the tag versus dielectric costat. A = 1mm, d =.8mm, t =.3mm Figure 3.15 Sigle-bit tag above a metallic plate Figure 3.16 Percetage variatios i the (a) resoat frequecy ad (b) dampig factor of the CNR of the tag versus distat to the metallic plate. A = 1mm, d =.8mm, t =.3mm Figure 3.17 Schematic view of the 4-bit tag [4] (With permissio, Copyright 14 IEEE). 56 Figure 3.18 Radar cross-sectios of the 4-bit tags [4] (With permissio, Copyright 14 IEEE) Figure 3.19 Sigle-bit tag illumiated by icidet plae wave Figure 3. Eigevalues of the characteristic modes versus frequecy Figure 3.1 Modal sigificaces of the characteristic modes versus frequecy Figure 3. Characteristic agle of the characteristic modes versus frequecy Figure 3.3 Characteristic modes of the tag at two resoat frequecies [33] (With permissio, Copyright 15 IEEE) Figure 3.4 Variatio of the resoat frequecies of the tag versus d1 [33] (With permissio, Copyright 15 IEEE) Figure 3.5 Variatio of the resoat frequecies of the tag versus d [33] (With permissio, Copyright 15 IEEE) Figure 3.6 Scattered far-field electric field radiated from the tag. d1 = 6 mm, a = 1 mm, d =.8 mm, W =.3 mm [33] (With permissio, Copyright 15 IEEE) Figure 3.7 Quality factor of the CNR of the tag versus d [33] (With permissio, Copyright 15 IEEE) Figure 3.8 Far-field electric fields radiated from the tag for (a) d =.8 mm ad (b) d =.4 mm [33] (With permissio, Copyright 15 IEEE) Figure 3.9 Schematic view of the desiged 4-bit tag. Uits: mm [33] (With permissio, Copyright 15 IEEE) Figure 3.3 The simulated backscattered electric field from 4-bit tags [33] (With permissio, Copyright 15 IEEE) Figure 3.31 Pole diagram of the simulated backscattered fields from the tags [33] (With permissio, Copyright 15 IEEE) Figure 3.3 Two 4-bit fabricated tags (a) d = 3 mm ad (b) d = 7 mm [33] (With permissio, Copyright 15 IEEE) Figure 3.33 Measured RCS of the tags [33] (With permissio, Copyright 15 IEEE) Figure 3.34 Pole diagram of the measured backscattered fields from the tags [33] (With permissio, Copyright 15 IEEE) Figure 4.1 FCC mask for outdoor ad idoor UWB applicatios Figure 4. Moo-static chipless RFID system Figure 4.3 Gai ad power cosideratios i chipless RFID systems viii

9 Figure 4.4 Schematic of the bio-static set-up for measurig the impulse respose of the tag Figure 4.5 Measuremet set-up for measurig trasfer fuctio of the atea Figure 4.6 (a) UWB Moopole disk ad (b) Narrowbad moopole atea Figure 4.7 (a) Amplitude ad (b) phase of the S1 for θ = ad φ =, (c) Amplitude ad (d) phase of the atea effective legth i frequecy domai, (e) atea effective legth i time domai, ad (f) pole-diagram of the atea Figure 4.8 (a) Moopole atea above a groud plae (b) its reflectio coefficiet Figure 4.9Radiated Eθ versus the distace from the moopole atea Figure 4.1 Normalized impulse respose of the UWB moopole atea alog with aalytic evelope Figure 4.11 Variatio of Eθ versus distace from the atea i (a) ear field ad (b) far field of the atea Figure 4.1 Group delay of UWB moopole atea Figure 4.13 (a) Bowtie atea as a frequecy-idepedet atea, (b) a self-complemetary atea, (c) TEM hor as a travellig-wave atea, ad (d) Log-periodic atea as a multiple resoace atea Figure 4.14Two examples of UWB small ateas Figure 4.15 Amplitude of the curret alog the moopole ad its directio at differet frequecies Figure 4.16 Radiatio gai of the moopole atea at differet frequecies Figure 4.17 Variatios of CNRs of the moopole atea versus (a) atea legth, L ad (b) atea radius, r Figure 4.18 (a) Moopole atea above a groud plae, (b) its pole diagram for differet values of r Figure 4.19 (a) Reflectio coefficiet of the moopole atea, ad (b) time-domai radiated field from the atea Figure 4.Curret distributio o the moopole atea at differet resoat frequecies Figure 4.1 Radiatio gai of the moopole atea at differet resoat frequecies. (Solid lie: φ = ad dashed lie: φ = 9 ) Figure 4. A moopole atea surrouded by short cylider as a widebad /UWB elemet.. 91 Figure 4.3 Reflectio coefficiet of the atea for differet values of h Figure 4.4The curret distributio o the atea at three resoat frequecies Figure 4.5 The curret distributio o the moopole atea at its coaxial mode resoace for two differet values of h, (b) resoat ad radiatio modes of curret Figure 4.6 Reflectio coeffiect of the atea for differet values of s Figure 4.7 The gai of the atea versus elevatio agle at differet frequecies for h=8 mm Figure 4.8 Reflectio coefficiet of the atea for two differet desigs. Desig 1: s = 11 mm, W = mm, h = 5.5 mm, d = 18 mm, Desig 1: s = 9 mm, W = mm, h = 5.5 mm, d = 18 mm.. 95 Figure 4.9 Gai of the atea at (a) f = 4 GHz, (b) f = 6 GHz, (c) f = 8 GHz, ad (d) f = 1 GHz Figure 4.3 (a) The radiatio field ad (b) ormalized radiatio field of the atea i far field Figure 4.31 (a) amplitude ad (b) phase of S1 betwee two similar ateas whe they are spaced 4 cm far from each other, (c) amplitude ad (d) phase of the atea effective legth for θ = 9 ad φ = ix

10 Figure 4.3 (a) Fabricated tag, ad (b ) Atea coected to the etwork aalyzer Figure 4.33 Measured reflectio coefficiet of the atea Figure 4.34 Co- ad cross polar radiatio patter of the atea at (a) f =.7 GHz, (b) f = 4.8 GHz, (c) f = 6.9 GHz, ad (d) f = 9 GHz at xz ad yz plaes Figure 5.1Time-domai sigal Figure 5. Spectrogram of the sigal for (a) δ =.8e-9, ad (b) δ = 4e Figure 5.3 Time ad frequecy resolutios i wavelet trasform Figure 5.4 Wavelet trasform of the sigal Figure 5.5 Some practical wavelets Figure 5.6 Time-frequecy represetatio of sigal by RJTF ad δ =.6e Figure 5.7 Time-domai sigal with movig widow Figure 5.8 (a) Time-domai sigal, (b) time-frequecy, (c) time-dampig factor ad (d) timeresidue diagrams of the sigal... 1 Figure 5.9 Miimum widow legth for distiguishig two resoaces of the sigal versus frequecy distace [7] (With permissio, Copyright 15 IEEE) Figure 5.1 Time-frequecy represetatio of the sigal by applyig (a) STMPM ad (b) RJTF Figure 5.11 (a) Sigal i time domai, Time-frequecy represetatio of sigal for (a) TW = 1.1 s, p =, (b) TW = 4 s, p =, ad (c) TW = 1.1 s, p = 4 [7] (With permissio, Copyright 15 IEEE)... 1 Figure 5.1 Gaussia pulse ad its first derivative with respect to time Figure 5.13 Pole diagram of the Gaussia pulse fuctio Figure 5.14 Four extracted damped siusoidal modes by applyig STMPM to the Gaussia pulse Figure 5.15 Gaussia pulse ad recostructio oe from Fourier trasform ad CNRs Figure 5.16 Pole diagram of the Gaussia pulse for differet values of τ Figure 5.17 Recostructed pulse sigal for (a) τ =.5 s, p = 4, (b) τ = 1 s, p = 4, (c) τ = 1 s, p = 8, (d) τ = 1.5 s, p = Figure 5.18 Pole diagram of the derivative of Gaussia pulse for differet values of τ Figure 5.19 Derivative of the Gaussia pulse ad recostructio oe from Fourier trasform ad CNRs Figure 5. Extracted dampig factor versus the ceter of the slidig widow for (a) pulse, ad (b) its derivative Figure 5.1 (a) Backscattered electric field from the scatterer, (b) pole diagram of the sigal for differet slidig times, (c) extracted dampig factors with respect to the ceter of the slidig widow, (d) backscattered electric field from two scatterers, (e) extracted dampig factors with respect to the ceter of the slidig widow, ad (f) recostructed early-time ad late-time resposes Figure 5. (a) Backscattered electric field, (b) Time-frequecy diagram, (c) Time-dampig factor, ad (d) Time-residue diagram of the sigal [69] (With permissio, Copyright 14 IEEE) Figure 5.3 (a) Time-dampig factor of the sigal, (b) Time-residue diagram of the sigal for SNR = 15 db [69] (With permissio, Copyright 13 IEEE) Figure 5.4 Scatterig mechaisms i time-frequecy aalysis. (a) Scatterig ceter. (b) Resoat behavior. (c) Structural dispersio. (d) Material dispersio [7] (With permissio, Copyright 15 IEEE) x

11 Figure 5.5 (a) Ope-eded circular cavity excited by icidet plae wave, (b) Backscattered sigal i time domai [7] (With permissio, Copyright 15 IEEE) Figure 5.6 (a) Time-frequecy diagram of the backscattered sigal from the cylider based o (a) STMPM ad (b) STFT [7] (With permissio, Copyright 15 IEEE) Figure 5.7 Time-frequecy diagram of the scattered field for TW = 1 s, p = 4 [7] (With permissio, Copyright 15 IEEE) Figure 5.8 Time-dampig factor represetatio of backscattered sigal from cavity Figure 5.9 Time-frequecy diagram of the sigal with (a) SNR=1dB, TW =.8s, p= ad (b) SNR=dB. TW =.8s, p=4 [7] (With permissio, Copyright 15 IEEE) Figure 6.1 Sigle-bit tag illumiated by a plae icidet field Figure 6. (a) Scattered electric field from the tag for two differet orietatios of receivig atea, (b) Group delay of the scattered field for two differet orietatios of receivig atea Figure 6.3 Multiple chipless RFID tags preset i the reader zoe [8] (With permissio, Copyright 14 IEEE) Figure 6.4 Flowchart of the proposed ati-collisio algorithm [8] (With permissio, Copyright 14 IEEE) Figure 6.5 (a) Two sigle-bit tags ad (b) two -bit tags spaced by R are illumiated by a plae wave. Uits i mm [8] (With permissio, Copyright 14 IEEE) Figure 6.6 (a) Time-domai backscattered sigal from two tags spaced by R=cm (b) timefrequecy represetatio of the sigal by applyig STMPM with T =.5s. (c) time-residue diagram of the sigal. (d) Separated resposes of the tags i frequecy-domai [8] (With permissio, Copyright 14 IEEE) Figure 6.7 (a) Time-frequecy ad (b) time-residue represetatio of the sigal by applyig STMPM with T=.5s. (c) Separated resposes of the tags i frequecy-domai (d) spacefrequecy respose after SFMPM [8] (With permissio, Copyright 14 IEEE) Figure Time-residue diagram for differet polarizatios [8] (With permissio, Copyright 14 IEEE) Figure 6.9 (a) Time-domai sigal (b) frequecy-domai respose (c) time-frequecy diagram after STMPM (d) space-frequecy diagram after SFMPM [8] (With permissio, Copyright 14 IEEE) Figure 6.1 Schematic view of the tags. (a) ID1:111, (b) ID: 11[8] (With permissio, Copyright 14 IEEE) Figure 6.11 Pole diagram of the 3-bit tag [8] (With permissio, Copyright 14 IEEE) Figure 6.1 (a) Time-domai backscattered sigal from two tags spaced by R=cm (b) frequecy-domai respose (c) time-frequecy represetatio of the sigal by applyig STMPM with T=.5s. (d) Time-residue diagram of the sigal [8] (With permissio, Copyright 14 IEEE) Figure 6.13 (a) Time-residue diagram of the backscattered sigal (b) separated resposes of the tags i frequecy-domai [8] (With permissio, Copyright 14 IEEE) Figure 6.14 Miimum required widow legth as a fuctio of Δ for differet SNRs [8] (With permissio, Copyright 14 IEEE) Figure Backscattered sigal from two sigle-bit tags [8] (With permissio, Copyright 14 IEEE) Figure 6.16 A 4-bit chipless RFID tag located 3 cm away from the atea xi

12 Figure 6.17 Reflectio coefficiet of the atea loaded by tag i (a) frequecy domai, (b) time domai, (c) Time-dampig factor diagram ad (d) Time-frequecy diagram of the S Figure 6.18 (a) Time domais ad (b) Time-dampig factor diagrams of the backscattered sigal from two tags Figure 6.19 Set-up for the measuremet of backscattered sigal from two tags [8] (With permissio, Copyright 14 IEEE) Figure 6. (a) Time-domai backscattered sigal from the tags, (b) Time-frequecy represetatio of the backscattered sigal [8] (With permissio, Copyright 14 IEEE) Figure 6.1 Time-residue represetatio of the backscattered sigal [8] (With permissio, Copyright 14 IEEE) Figure 6. (a) Real ad imagiary parts of the measured backscattered sigal, (b) Spacefrequecy diagram of the measured respose [8] (With permissio, Copyright 14 IEEE) Figure 6.3 Ragig error versus SNR [88] (With permissio, Copyright 14 IEEE) Figure 6.4 System cofiguratio for localizig chipless RFID tags i the reader area [88] (With permissio, Copyright 14 IEEE) Figure 6.5 Flowchart of proposed localizatio algorithm [88] (With permissio, Copyright 14 IEEE) Figure 6.6 Cofiguratio of the 3-bit fabricated tag [88] (With permissio, Copyright 14 IEEE) Figure 6.7 Simulated ad measured RCS of the tag whe the icidet electric field is perpedicular to slot legth [88] (With permissio, Copyright 14 IEEE) Figure 6.8 Normalized received power at the atea versus frequecy [88] (With permissio, Copyright 14 IEEE) Figure 6.9 Measured time-domai respose from the tag for differet distaces [88] (With permissio, Copyright 14 IEEE) Figure 6.3 (a) Frequecy-domai, (b) time-domai, (c) time-frequecy ad (d) time-residue represetatio of measured backscattered sigal from the tag [88] (With permissio, Copyright 14 IEEE) Figure 6.31 (a) Real ad (b) imagiary parts of the measured backscattered sigal from the tag[88] (With permissio, Copyright 14 IEEE) Figure 6.3 Space-frequecy diagram of measured backscattered respose from the tag for differet cases [88] (With permissio, Copyright 14 IEEE) Figure 6.33 (a) Two -bit tags illumiated by a icidet electric field. (b) Frequecy-domai respose of the backscattered electric field from two tags, time-domai respose from the tags for (c) φ = º ad (d) φ = 3º [88] (With permissio, Copyright 14 IEEE) Figure 6.34 Space-frequecy diagram of the backscattered respose from the tags [88] (With permissio, Copyright 14 IEEE) Figure 6.35 Simulatio set-up i FEKO [88] (With permissio, Copyright 14 IEEE) Figure 6.36 Measuremet set-up for localizig the chipless RFID tag [88] (With permissio, Copyright 14 IEEE) Figure 6.37 (a) Measured time-domai sigals from the tag located at the ceter of the uit cell, (b) Positio of the tag extracted from the proposed techique compared to real positio [88] (With permissio, Copyright 14 IEEE) Figure 6.38 Backscattered sigals from two tags at the atea ports [88] (With permissio, Copyright 14 IEEE) xii

13 Figure 6.39 (a) Time-frequecy respose of the received sigal at the first atea, (b) Positios of the tags extracted from the proposed techique compared to real positio [88] (With permissio, Copyright 14 IEEE) xiii

14 LIST OF TABLES Table 3-1. The resoat frequecy, quality factor, ad residue of the CNR of the slot for differet cases Table 5-1 Percetage error of estimatig of real ad imagiary parts of the domiat poles of the tag calculated from direct matrix pecil method (MPM) ad short-time-matrix-pecil-method (STMPM) xiv

15 1 INTRODUCTION Today s ever icreasig demad for wireless trackig ad idetificatio of objects ad targets has attracted may people i idustry to move toward the applicatio of RFID systems. Compared to Barcodes, the RFID tags ca be detected i loger distaces ad o-lie-of-sight view of the reader atea. It eables the sellers ad maagers to moitor differet objects ad persoel remotely. Nowadays, they are widely beig used i differet applicatios such as: advertisig, trasportatio systems, passports, aimal ad huma idetificatio, libraries, hospitals ad healthcare systems, museums ad so o [1]. The cocept of radio frequecy idetificatio (RFID) is relatively old ad back to World War II []. Idetificatio, fried or foe (IFF) is a idetificatio system eables the radar to detect the closig target as friedly or ot. I fact, it is the first RFID system used i practice. I 1948, the idea of modulatio of the reflected sigals i time domai was itroduced [3]. The device modulated huma voice o reflected light sigals. I 1963, a breakthrough was happeed by itroducig the passive RFID traspoder developed ad pateted by Richardso. Later o, iductive couplig betwee iterrogator ad tag was used for chargig the passive RFID tags by Vidig. May available chipless RFIDs i the market are workig based o the same idea proposed i I 1975, Koelle, Depp ad Feyma at Loss Alamos Scietific Laboratory (LASL), itroduced the idea of traspoder atea load modulatio [4]. I 198s ad 199s, may compaies aroud the world started commercializig RFID systems i various applicatios such as trasportatio ad persoel access i Uited States ad Europe. I 1987, first RFID tollcollectio system was employed i Alesoud, Norway. Because of the widespread use of RFIDs i commercial applicatios, some orgaizatios such as the Iteratioal Stadards Orgaizatio (ISO) ad the Iteratioal Electrotechical Commissio (IEC) coducted some stadardizatio activities [5]. Recet advaces i silico techology eabled the itegratio ad miiaturizatio of efficiet RFID tags [6]. I Jue 3, Wall-Mart Ic. itroduced the RFID i the ear future for all its suppliers at the Retail system coferece, which led to the release of first EPCglobal stadard [5, 7]. 1

16 1.1 RFID Systems I geeral, RFID systems ca be divided ito three classes: active, passive ad semi-passive. Active tags eed a power supply to power RF commuicatio. This power supply implemetatio eables active tags to trasmit iformatio of loger distaces. I passive RFID tags, there is o oboard power supply attached to the tag. Istead, it receives its power from a illumiatig electromagetic field luched from the reader atea. Hece, they are usually used i shorterrage commuicatio with smaller data capacity compared to active tags. Figure 1.1 shows some passive RFID tags. These RFID tags are lighter ad cheaper tha active RFID tags. Compared to active tags where a battery is directly used for geeratig RF power, the oboard battery i semi-passive RFID tags are employed oly to provide power for supportig eablig circuits, ot for geeratig RF power. Figure 1.1 Two passive RFID tags. 1. Passive RFID tags Because of lower price of passive tags, they are commoly used i idetificatio systems. As metioed before, passive tags are powered by a iterrogatig electromagetic field. The tag itroduces modulatio o the scattered field, depedig o the ID of the illumiated tag. These tags ca be categorized by two groups of ear-field ad far-field tags.

17 1..1 Near-field RFID I ear-field RFID systems, the electromagetic fields radiated from the reader atea are coupled to the tag by a iductive couplig mechaism. Based o Faraday s priciple, a large alteratig curret o the reader coil geerates a alteratig magetic field aroud the atea. The time-varyig magetic field ca produce a small voltage across the tag if they are located i the reactive ear-field of the tag. The voltage is rectified ad used for powerig the tag chip. The basic block diagram of the ear-field RFID is show i Figure 1.. The aalog frot-ed icludes a limiter, rectifier ad regulator. The regulated voltage powers up the digital uit icludig microcotrollers, Iput/output ad memory. It also has to meet the commuicatios protocol ad geerate the required serial data to be trasmitted to the reader [8]. Near-field tags are usually desiged at low frequecies, commoly 18 KHz (LF) ad MHz (HF). The most problematic aspect with these tags is the large size of the atea coils. As aother drawback, the power chages with 1/r 6 (r is the distace from atea) i the ear field of the atea leadig to a fast decay of the power with respect to distace. The low data rate is aother dowside of ear-field tags [5, 9]. Demodulator RX Serial Data TX Serial Data Digital Atea Limiter Rectifier Regulator Power Supply Uit Clock Geerator Clock Figure 1. Block diagram of ear-field passive RFID tag. 3

18 1.. Far-field RFID The fields i the far-field of ateas are radiative i ature. Figure 1.3 illustrates the commuicatio mechaism i far-field RFID systems. The atea illumiates the tag located i its far-field. Part of the icidet field is modulated by a mismatchig load coected to the atea. This icorporates some data o the scattered field which ca be used for idetificatio purpose. Far-field tags usually operate at higher frequecies, MHz (UHF bad) or.45 GHz (Microwave). Compared to ear-field tags, the employed ateas i these tags are smaller. The essetial parts of the tag are atea, voltage multiplier, modulator, ad digital uit [6, 1]. Trasmissio sigal Reflected sigal Tag Atea Voltage multiplier Digital Modulator Uit Reader Biary tag ID Figure 1.3 Far-field commuicatio mechaism i RFID systems. Atea. Amog various ateas proposed for RFID tags, the Gamma-matched dipole has bee used i more UHF tags [8]. As Figure 1.4 shows, the atea is attached to a chip. By loadig the atea with differet impedaces, a ASK modulatio, based o iformatio stored i the digital uit, is performed o the scattered electric field ad reflected back to the reader. Voltage-multiplier. Although higher power trasfer efficiecy is possible i ear-field RFID systems, they are used i short-rage commuicatio. I UHF RFID tags, the tag is located i the far-field of the atea. Based o radar equatio, the maximum detectable rage of the tag ca be writte by R max 4 P G G reader reader tag (1.1) P mi 4

19 Figure 1.4 Gamma-matched atea. AC GND DC AC Figure 1.5 A 6-stage full-wave rectifier voltage multiplier. where λ is the wavelegth, Preader represets radiated power of the trasmitig sigal, Greader ad Gtag are the gai of the reader atea ad tag atea, respectively, ad Pmi is miimum power required by the tag to tur o. Accordig to FCC regulatio [11], the equivalet Isotropically Radiated Power (EIRP) for a reader at ISM bad, 9 98 MHz, must be less tha 4 W. Assumig db gai for the tag atea ad Pmi = -15 dbm, the maximum read rage will be Rmax = 3 m at 915 MHz by igorig polarizatio mismatch. I perfect matchig coditio betwee atea ad attached chip, the voltage o the chip port will be 41 mv, which is ot sufficiet for powerig up the tag circuitry. A full-wave rectifier voltage multiplier show i Figure 1.5 ca be used to power up the tag circuitry. The umber of stages ad type of diodes determies the multiplicatio costat [8]. Modulator. Based o the radar equatio, the received power (Pr) by the reader atea is give by GreaderGtag Pr Preader 3 4 (1.) tag 4 R 5

20 The radar cross-sectio (RCS) of the tag, tag, depeds strogly o the loadig of the atea. Hece, by loadig the atea cosistet with the embedded data i the digital memory, the RCS of the tag is chaged. The demodulator ca be a simple evelope detector which provides required power for digital uit. Digital Uit. The digital uit is resposible for geeratig various trasmit data based o the EPC G protocol. It is composed of a few sectios icludig cotroller, memory, EPROM, clock geerator, ad so o. The voltage multiplier provides the required power to power up the digital uit [8]. 1.3 Chipless RFID System I chipless RFID systems, the tag does ot cotai ay microchip. This reduces the price of the fabricatio process of tag i idustrial level. I these tags, the structure acts as both scatterer ad modulator. The overall cofiguratio of chipless RFID system is depicted i Figure 1.6. Three importat parts of the system are tag, atea ad reader. The frequecy of operatio is UWB rage, GHz. The UWB atea illumiates the reader area. The icidet wave iterrogates the chipless RFID tags preseted i the reader area. The iduced currets o the tags depeds strogly o the tag geometry ad size, polarizatio, directio ad positio of the tag relative to the reader atea. The iformatio o the tag must be aspect-idepedet ad do ot chage by directio ad positio of the tag. These parameters are complex atural resoaces (CNRs) of the tag. By embeddig some resoat circuitry o the tag structure, the CNRs ca be used as the ID of the tag. The reflected field is modulated by the tag structure, correspodig to embedded resoat circuitry, ad reflects back to the atea reader. After frot-ed of the receiver, the received sigal is processed i the reader i order to extract the iformatio of the tag. The most importat part of the system is the reader ad the employed detectio algorithm. The received sigal by the atea icludes the oise ad reflectios from backgroud objects (clutter) i additio to the scattered sigal from the tags. These iterfereces itroduce some difficulties i extractig the required iformatio from the received sigal. 6

21 Atea Iterrogatio impulse Tag Reader Backscattered waveform Figure 1.6 Chipless RFID system. 1.4 Dissertatio Outlie This dissertatio addresses three importat parts of chipless RFID systems: chipless tag, atea, ad detectio techique. Before startig the desig ad implemetatio of chipless RFID compoets, a theoretical backgroud o the scatterig mechaism i chipless RFID systems is required. Chapter is devoted to the theory of the sigularity expasio method (SEM), the eigemode expasio method (EEM), ad the characteristic mode theory (CMT). After studyig the theoretical issues, some importat features of the aforemetioed methods applicable i the desig of chipless RFID systems are addressed. The theory itroduced i chapter is used i the desig of chipless RFID tags i chapter 3. Sice the tag structure acts as both scatterer ad modulator, the radiatio ad resoat behaviors of the tag are studied versus structural parameters based o SEM ad CMT. Takig advatages of SEM ad CMT, the resoat frequecies, quality factors, ad radiatio characteristics of tag are ivestigated i terms of geometry ad dimesios i a pole diagram. This helps the desiger to easily assig the resoat frequecies ad desired dampig factors of the resoators for meetig requiremets. These specificatios are the read-rag of the tag, data desity (umber of bits), ad tag size. I some applicatios, all aforemetioed specificatios caot be satisfied simultaeously ad trade-off are eeded i the desig procedure. As a example, for embeddig a high desity of data o a small tag, the quality factors of the resoaces must be very high. O the other had, by icreasig the quality factor, the radiatio fields decrease, leadig to a smaller radar cross-sectio of the tag. Hece, the read-rage of the tag becomes shorter. I chipless RFID sesors, the radar cross-sectio of the tag or equivaletly the stregth of the received sigal is very importat. 7

22 Systematic desig procedures itroduced i chapter 3 provide some useful iformatio ad isight of the electromagetic behavior of the tags. I chapter 4, atea structures applicable i UWB systems are reviewed. Because of the employmet of UWB techology i chipless RFID systems, oe eeds to study both time-domai ad frequecy-domai characteristics of UWB ateas. Frequecy-domai parameters of ateas are the iput impedace ad radiatio patter of the atea. Likewise, the time-domai parameters of the atea are the dispersio characteristics such as rigig, aalytic evelope ad group delay of the atea. After a summary of these parameters, a small omi-directioal atea elemet useful i widebad ad UWB applicatios is proposed. The time ad frequecy domai characteristics of the atea are ivestigated i more detail i this chapter. The ext chapters of the dissertatio are devoted to the detectio process i chipless RFID system. I multiple multi-bit tags preseted i the reader area, the time, frequecy ad spatial iformatio of the tags are importat i the detectio, idetificatio ad localizatio processes, respectively. The accuracy of the employed approach depeds strogly o the resolutio i time, frequecy ad space. Sice the IDs of the tags are icluded i the spectral domai of the scattered sigal ad its locatio ca be obtaied from its time-domai respose, chapter 5 itroduces some time-frequecy represetatios of the received sigal. After a review o short-time frequecy trasform (STFT), wavelet, ad re-assiged joit time-frequecy (RJTF) techiques, a ew timefrequecy aalysis approach, called short-time matrix pecil method (STMPM) is explored i detail. By addressig the effective parameters of STMPM o resolutio i time ad frequecy, it is applied to some scattered sigals from scatterers. It will be show that various scatterig mechaisms such as resoace, scatterig ceter, ad dispersio characteristics of the scatterers ca be detected i time-frequecy represetatio of the sigal. The effect of oise i the calculatio of CNRs extracted from matrix pecil method (MPM) is studied ad improved by STMPM. The, the pole diagram ad dampig factors of the extracted CNRs of the sigal are studied whe the slidig widow is located i the early-time ad late-time resposes of the scatterer. Fially, a efficiet techique is itroduced for separatig the early-time ad late-time resposes of the scatterers. Chapter 6 is dedicated to detectio, idetificatio ad localizatio of chipless RFID tags. First, a space-time-frequecy algorithm is itroduced by which the locatios ad IDs of the tags are obtaied i the reader. Assumig the reader area as a scatterig medium, the tags act as the 8

23 scatterig ceters of the media. Based o Altes model itroduced i chapter, the scatterig ceters are calculated by applyig NFMPM (dual of SMPM) to the frequecy-domai respose. I detectio process, the umber of tags preseted i the reader area is obtaied. I the cases where the tags are close to each other, the detectio process is costraied to the rage resolutio. The rage resolutio is proportioal to the iverse of the badwidth of the icidet pulse. I chipless RFID systems, the frequecy bad of operatio is i the rage of GHz, leadig to the resolutio of cm. It meas that the tags distaced farther tha cm ca be detected i the reader. I most radar applicatios, the idea of matched filter is used i the detectio process. I chipless RFID systems where the iformatio of the tags are icluded i the late-time resposes, the earlytime of the secod scatterer might be hidde i the early time of the former illumiated target, which complicates the detectio of the tags. This sceario is more complicated whe the tags are located i close proximity of each other. By applyig STMPM to the time-domai sigal ad moitorig the poles of the widowed sigal i the pole diagram or the zero-crossig poits i time-dampig factor diagram of the sigal, the locatios of the tags ca be obtaied with a better accuracy. After detectio of the tags, the idetificatio process is performed by extractig the resoat frequecies of the tags. I circumstaces whe multiple tags are preset i the reader area, a ati-collisio algorithm is required i order to assig the extracted CNRs to the preseted tags. Usig three ateas spaced i the reader area, the positios of the tags ca be calculated relative to a referece poit. This procedure is called tag localizatio. Some scearios are simulated ad measured i the laboratory to cofirm the validity of the proposed algorithm. Fially, chapter 7 presets a overall summary, coclusios, cotributios ad followed by a short discussio ad suggestios o the possibilities for future work. 9

24 Mathematical Represetatio of Scattered Fields from Chipless RFID Tags [8] (Chapter used with permissio of Spriger sciece ad busiess media, 15) I scatterig scearios whe a icidet electric field impiges a scatterer, the scattered fields ca be mathematically represeted by a ier product of the dyadic Gree s fuctio of the structure ad equivalet iduced currets o the scatterer. The iduced currets ad equivaletly, the scattered fields ca be expaded i differet ways. I sigularity expasio method (SEM), the iduced currets are expaded versus the atural resoat modes of the scatterer. The atural modes are defied as the correspodig currets o the scatter surface at complex atural resoaces (CNR), the zeroes of the metricized Gree s fuctio of the scatterer. Istead, the iduced currets ca be expaded versus the eigemodes of the Gree s fuctio. Compared to the atural modes of the scatterer which are idepedet of frequecy, the eigemodes ad correspodig eigevalues of the scatterer are fuctios of frequecy. For some special geometries, the structure is perfectly coicided with a special coordiate system. I such cases, the eigemodes are i-phase o the scatterer surface. This is ot valid for arbitrary shaped geometries. The characteristic modes of the scatterer are defied as the curret modes whose correspodig scattered fields are i-phase o the surface of the scatterer. These modes are the eigemodes of a geeralized eigevalue equatio. I this chapter, after studyig the mathematical descriptios ad the physical iterpretatio of the aforemetioed curret represetatios, a simple dipole is cosidered as a scatterer. By employig SEM ad usig electric-field itegral equatio (EFIE), the CNRs ad correspodig atural modes o the dipole are calculated. As a secod method, the eigemodes ad eigevalues of the dipole are calculated by applyig method of momet to the EFIE represetatio of the scatterer. Fially, the characteristic modes ad equivaletly, their scattered fields are calculated for differet frequecies..1 Sigularity Expasio Method (SEM) As a example, a 3-bit chipless RFID tag show i Figure.1 is illumiated by a icidet field (E ic, H ic ), lauched from a trasmittig atea. The surroudig medium is assumed to be free 1

25 space with permittivity ԑ ad permeability µ. The ID of the tag is set ito the resoat frequecies of the structure, which ca be embedded ito some resoat-based circuitry o the tag. I practical applicatios, it is beeficial to desig the tag o a metallic surface i order to maximize the radiatio efficiecy of the scatterer. Assumig the iduced curret o the tag as J, the scattered field is obtaied from either a electric-field itegral equatio (EFIE) or a magetic-field itegral equatio (MFIE) [1]. Here, the former case is cosidered for simplicity i formulatios. Therefore, the scattered electric field is writte i the Laplace domai as [13] s 1 E ( r; s) s G, ; s ; sds AI r r k J r (.1) where I xx ˆˆ yy ˆˆ zz ˆˆ, s = α+jω is the complex frequecy, k = s/c represets the propagatio costat of the fields i the complex frequecy domai, ad A is the surface of the tag. The primed ad uprimed coordiates represet the source ad observatio poits, respectively. The quatity G is the scalar Gree s fuctio i free space. G rr, ; s jk rr e 4 r r (.) ic H ic E Iduced currets Figure.13-bit tag illumiated by a icidet plae wave. 11

26 where G satisfies the Sommerfeld radiatio coditio as lim r jk G rr, ; s (.3) r r The scattered field i (.1) ca be writte as the ier product of the dyadic Gree s fuctio ad curret distributio o the structure as s s E ( r; s) G r, r ;, J r (.4) where the dyadic Gree s fuctio is defied as 1 G( r, r; s) s I G ( r, r ; s) (.5) k The associated radiatio coditio for G is r ad <.> i (.4) is defied by ˆGr r (.6) lim r jkr, ; s r A, B AB da (.7) a Assumig the tag is a perfect electric coductor (PEC), the boudary coditio o the tag surface is give by where ic s ˆ. ; ; t E r s E r s r A (.8) tˆ deotes the uit vector tagetial to the tag surface. As a result, the electric-field itegral equatio (EFIE) is writte by ic G( r, r), J r E r r A (.9) r t It is assumed that the itegral i (.9) is doe as a fiite-part itegral. Subscript t i (.9) idicates the tagetial compoets of the fields o the tag surface. The method of momet (MoM) ca be used to solve equatio (.9). By discretizig the surface of the tag ito N isolated meshes ad applyig method of momets (MoM), oe ca rewrite (.9) as 1

27 J I (.1) m The matrix equatio i (.1) should be i some sese a accurate represetatio of the itegral equatio i (.9). Oe importat criterio of such accuracy is the covergece of the solutio obtaied from (.9) to the real curret distributio as N tag is obtaied from [14]. The curret distributio o the J I (.11) 1 m Accordig to (.11), the sigularity poles of the tag are the zeroes of the determiat of the coefficiet matrix as k det s k =1,, 3 (.1) These sigularity poles are the complex atural resoaces (CNRs) of the tag at which the curret distributio o the tag shows damped oscillatig behavior after the icidet source field crosses through the tag. The basis of the SEM is that the curret distributio is assumed to be a aalytic fuctio i the complex s-plae, except at CNRs such as ( ; s) J r a r J r (.13) ( ; s) e( ; s) s s where s = α+jω is the th CNR of the tag. Sice the time-domai respose is a real-valued sigal, the for simple complex poles ad couplig coefficiets, oe ca write s s (.14a) * - a ( r; s ) [ a ( r ; s)] (.14b) * * J ( r; s ) [ J ( r ; s)] (.14c) e * * e Equatio (.13) eeds some more iterpretatio. Accordig to Mittag-Leffler s theorem [1], a etire fuctio i the s-plae is required for each pole i the ifiite series to guaratee the covergece of the series [15]. This etire fuctio is represeted by Je(r; s) i (.13). The other importat part of the series is the weightig fuctio a(r; s), which is assumed separable i the spectral-spatial form of 13

28 a ( r; s) R ( s) J ( r ) (.15) Here, J(r) is the atural mode of the tag at the th resoat frequecy, ad R(s) is the correspodig frequecy-depedet residue of the pole. By isertig (.15) i (.13), the curret distributio close to s is writte by R ( s) J ( r) J r J r (.16) ( ; s) e( ; s) s s It will be show that for class-1 couplig coefficiets, R is idepedet of complex frequecy. By expadig G ad the icidet source field, E ic, i a power series aroud s = s as m 1 G( r, r; s) m G r, r ; s ( s s) (.17) m m! s s s ic t m m ic t m m m! s s s 1 E ( r; s) m E r ; s ( s s ) (.18) ad isertig (.17) ad (.18) i (.9), oe ca write G( r, r; s) R ( s ) J ( r) G r r J r (, ; s) ( s s), e( ; s) s s s s s ic ic Et ( r; s) Et ( r; s ) ( s s ) s s s r (.19) By balacig the two sides of (.19) accordig to powers of (s-s), some importat expressios are obtaied. The coefficiet of the (s-s) -1 term at s = s gives G( r, r; s ), J ( r) (.) r Equatio (.) provides some importat features of the CNRs ad correspodig atural modes. By covertig (.) to matrix form, it is see that the determiat of the coefficiet matrix should be zero at CNRs i order to have otrivial solutios. As aother sigificat poit, these poles are completely depedet upo the dyadic Gree s fuctio of the structure ad as (.) illustrates, they are source-free ad aspect-idepedet parameters of the tag. This is the reaso that these parameters are ofte used i idetificatio applicatios. For each CNR, s, there is a otrivial 14

29 atural mode, J(r), which is the solutio of (.). Correspodig to (.), oe ca defie the couplig factors as the solutios to the followig homogeous equatio M ( r), G( r, r; s ) (.1) r By equatig the coefficiets of (s-s) i both sides of (.19), oe has G( r, r; s) G( r, r; s ), J ( r; s) R ( s ), J ( r) E ( r ; s ) (.) ic e t r s s s r The ier products i the left-had side of (.) are performed o the rʹ parameter. Thus, both sides of the equatio are fuctios of r. By takig the ier products of the two sides of (.) by M(r), the couplig coefficiets ca be foud at resoat frequecies as R ( s ) M ( r), E ( r; s ) ic t G( r, r; s) M( r),, J( r) s s s r r r (.3) For electric-field itegral equatios (EFIE), where symmetric matrices are ecoutered, the couplig vectors ad atural mode vectors are the same [1], so that (.3) is writte by R ( s ) J ( r), E ( r; s ) ic t G( r, r; s) J( r),, J( r) s s s r r r (.4) It is see i (.4) that the couplig coefficiets at resoat frequecies deped o the icidet electric field as well as the atural mode distributio at the correspodig resoat frequecy. I ic the cases where J r), E ( r; s ), the related mode will ot be excited by the icidet electric ( t r field. The couplig coefficiets i (.4) are just obtaied at CNRs of the tag. There is o straightforward way to obtai the etire fuctio added to the resoat respose of the scatterer i (.13). Mathematically, this is ecessary to guaratee covergece of the series. However, more explaatio is eeded i order to uderstad the physical cocepts behid the theory of SEM. As the equatio (.4) shows, the couplig coefficiets at the resoat frequecies of the structure 15

30 deped o the atural modes, dyadic Gree s fuctio of the structure, ad icidet field at those frequecies. For other complex frequecies, s, differet represetatios ca be chose as the couplig coefficiet, which affects the etire fuctio added to the series. I the late-time respose of the scatterer, we have just the damped siusoidals correspodig to the CNRs of the tag. Hece, the etire-fuctio cotributio comes ito the early-time respose, which rises ad falls faster tha the late-time sigals. I order to cover other complex frequecies, differet couplig coefficiets have bee itroduced, where class 1 ad class represetatios are most commo i literature [1]. For a class 1 represetatio, which is the simplest oe, the couplig coefficiets of the atural modes are defied as R ( s) e R ( s ) (1) ( ss) t e ( ss) t J ( r), E ( r; s ) ic t G( r, r; s) J( r),, J( r) s s s r r r (.5) By isertig (.5) i the series part i (.13), the time-domai respose is give by j( r; t) U( t t)re R j ( r) e st je ( r ; t) (.6) 1 where U(.) is the Heaviside step fuctio defied as 1 U( t t) t t t t (.7) ad the iverse Laplace trasform is defied as st j( r; t) e J( r ; s) ds (.8) Br which causality esured by havig the Bromwich itegratio cotour Br passig above all sigularities i the s-plae. Tur-o time might be the time at which the icidet wave is first applied aywhere o the tag. Although class 1 form of the couplig is more useful i the aalyticalbased formulatio of SEM, it shows some covergece issues i earlier times of the respose i 16

31 umerical calculatios [16]. For computatioal purposes, the class form is more efficiet. I this form, the frequecy depedecy of the couplig coefficiets is held i the icidet electric field as R () () s J ( r), e E ( r; s) ( ss) t ic t G( r, r; s) J( r),, J( r) s s s r r r (.9) The effect of these couplig coefficiets o the curret distributio ca be better illustrated i the time domai. For more simplicity, the followig icidet electric field is cosidered. where the vector ˆr ic t s rr ˆ. ( ; s) e c E r E (.3) is the propagatio vector, E icludes the polarizatio vector ad amplitude of the icidet wave, ad c is the speed of light i free space. By isertig (.9) ad (.3) i (.3), the curret distributio i the Laplace domai is writte as s ( ss) t rr ˆ c e J ( r), E J ( r) r J( r; s) Je( r; s) G( r, r; s) s s J ( r),, J ( r) s s s r r (.31) By applyig the iverse Laplace trasform defied i (.8) to (.31), the curret distributio i time domai is writte as j r s rr ˆ rr c J ( r), Ee U ( t t ) J ( r) c r st ; t Re e je ( r; t) 1 G( r, r; s) J( r),, J( r) s s s ˆ r r (.3) The covergece difficulties i the class 1 form of couplig coefficiets are alleviated i the class represetatio, where a time-varyig regio of itegratio covers that part of the object surface, which has already bee illumiated by the icidet field [16]. Whe the icidet wave completely passes through the tag, both class 1 ad class represetatios are similar. For better illustratio, 17

32 Figure. shows the regio of itegratio at t = t o the surface of the tag for class couplig coefficiets whe the icidet plae wave passes through a part of the tag. illumiated regio icidet plae wave ct Figure.3-bit tag illumiated partly by a icidet plae wave. By represetig the curret distributio o the tag as the summatio over the atural modes i the late-time respose accompayig a etire fuctio as the early-time respose, the scattered field is obtaied from the itegral equatio i (.4) as R ( s) J ( r) ( ; s) (, ; s), ( ; s) s E r G r r Je r s s G( r, r; s), J ( s) R ( s) s s r r G( r, r; s), J ( r; s) e r (.33) The radiated field close to the th CNR is writte by 1 R s E ( r; s) si G r, r; s, Je( r ; s) (.34) k s s s J ( r) r I the far field, the field i (.34) ca be approximated by ˆˆ s R J ( r) E ( r; s) μs I rr G r, r, μs I rr G r, r, J ( r; s) ˆ R s ss ˆˆ e s s ss r jk rr r jk rrrˆ e J( r) e μs I rr ˆˆ, μs I rr ˆˆ, Je( r; s) 4πr s s 4πr r r r (.35) 18

33 As (.35) expresses, i the far-field regio, the scattered fields i the time domai are approximately proportioal to the first derivative of the curret distributios o the tag. I cotrast, i the ear field, the field distributio is mostly affected by the spatial derivatives of the currets. By applyig the iverse Laplace trasform to the scattered field i (.33), the fields i the time domai are writte as s e t U t t R e t ee t t ( ; ) ( ) cos( ) ( ; ) r r (.36) where the class 1 form of couplig coefficiets is assumed i (.36). Accordig to (.36), the scattered field from a tag is affected by two differet pheomea. Early-time respose, which is depicted by ee(r;t) i (.36), is affected by the specular reflectios from the scatterig ceters of the tag. The early-time respose is followed by the series of damped siusoidals with some weightig coefficiets. The CNRs of the tag, show by s = α+jω, are aspect-idepedet parameters of the tag, ot depedet o the directio, polarizatio, or distace to the tag s observatio poit. For this reaso, they are well-suited to be used as the tag s ID..1.1 Altes Model Though the late-time respose of the tag ca be compactly cast ito a series-form formulatio, it is ot as easy to predict the behavior of the early-time impulse respose. This is because it depeds o the spatial variatios of the scatterer ad observatio poit. Based o (.33), the early-time respose is formulated by 1 Ee( r; s) s I G r, r ; s, e( ; s) k J r (.37) where the first part of the dyadic Gree s fuctio is more proouced i the far zoe ad the secod term is domiat i the ear zoe of the scatterer. Because of the fast variatios of the early-time currets, the scattered field icludes pulse-shape impulses reflected from the scatterig ceters of the tag. Assumig a scatterer cotaiig M scatterig ceters is illumiated by a icidet plae wave with pulse fuctio p(t), the backscattered sigal i the early time ca be modeled as the summatio of the delayed pulses from the scatterig ceters as [17] 19

34 Trasmitted sigal t1 A A 1 t Tapped Delay Lie AM t M Adder Scattered sigal (a) Trasmitted sigal Tapped Delay Lie t 1 t M N times itegratio A1 ( N ) A N..... N times itegratio AM ( N ) A M A AMN Adder Adder Adder Scattered sigal (b) Figure.3(a) Trasversal ad (b) modified filter model of the early-time respose. M e ( r; t) A p( t t ) (.38) e m m m1 where Am ad tm are the amplitude ad time delay related to the m th scatterig ceter. This earlytime represetatio is modeled i Figure.3a as a tapped delay lie (t1, t,, tm) with M multipliers ad a adder. Based o physical optics approximatios, some fuctios other tha impulses must be added to the series i (.38) i order to completely model the early-time respose of the scatterer. The model see i Figure.3a, which icludes the parallel combiatios of the itegrators ad differetiators, ca be described with the well-accepted model i Figure.3b by assumig that some of the delay differeces tm+1-tm are very small compared to the smallest wavelegth of the impigig sigal. If two eighborig scatterig ceters have opposite sigs, ad their delay differece (d= tm+1-tm) is very small, d << 1, oe ca write

35 A ( p( t t ) p( t t )) m m+1 m dp() t dt t t m (.39) This compoet is proportioal to the differetiated sigal at t = tm. Similarly, weightig factors ca result i a retur compoet as kd p( t) p( t d) p( t kd) p( t) dt (.4) I order to perfectly model the early-time respose of the scatterer, oe must cosider both the itegrators ad differetiators i the model, i additio to the replica of the icidet pulse. This model is formulated as the covolutio of the icidet pulse with the impulse resposes of the scatterig ceters. M ( ) e m m m1 e ( r; t) p( t) A ( r; t t ) (.41) I (.41), the impulse respose of the m th scatterig ceter is summed over the itegrals ad derivatives of the Dirac-delta fuctio. Here, the egative ad positive values of refer to the th itegral ad derivative of the delta fuctio with respect to time. I the Laplace domai, the earlytime respose is writte by E ( r; s) A s P( r; s) e e M m1 M m1 B m m ( r; s) e stm stm (.4) where Bm Am s P( r; s) (.43) For scatterig from edges, fractioal = ±.5 must be cosidered i Bm [18]. By comparig (.4) with (.36), it is iferred that there is a duality betwee early-time respose i the Laplace domai ad late-time respose i the time domai. I the former, the respose is expaded over the expoetial fuctios of delay times, while i the latter, the time-domai respose is expaded versus expoetial fuctios of complex resoaces of the tags. This duality will be helpful i the idetificatio process of chipless RFID tags, preseted i Chapter 6. 1

36 I simple scatterers such as chipless RFID tags, the reflectio from the first illumiated part of the tag is strog eough to be cosidered as the early-time respose of the tag. But i the complex scatterers such as a airplae, the impulse resposes of the multiple scatterig ceters of the target should be cosidered i the respose. Therefore, the early-time respose from the simple scatterers ca accurately be approximated by just oe term of the series show i (.4). This part is strogly depedet o the polarizatio ad directio of the icidet electric field. This is because of the depedecy of the scatterig ceters o the polarizatio ad directio of the icidet wave. Additioally, the shape of the early-time respose chages from the ear field of the scatterer to its far field. I the ear field, the scattered field is mostly similar to the icidet pulse, but i the far field, the scattered field is limited to the first time-derivative of the icidet field [19], [].As a example, the scattered field from a rectagular metal plae with size of 15 cm 15 cm illumiated by a icidet pulse is cosidered. The measuremet set-up is show i Figure.4. A rectagular metal plae is located 6 cm above a optical table. A TEM hor atea is coected to a digital samplig oscilloscope i order to calculate the backscattered sigal from the tag at differet distaces. Aother measuremet without the presece of the metal is performed ad the results are subtracted from the earlier sigal to cacel the effects of backgroud objects. Time averagig is applied to the received pulses i order to improve the sigal-to-oise ratio (SNR). The excitatio pulse ad its derivative with respect to time are show i Figure.5. I Figure.6, the backscattered sigal from the plate is show whe it is located at four differet distaces d = cm, 3 cm, 1 m ad 1.3 m away from the atea aperture. UWB Atea Metal plate 6cm d Optical table Digital samplig oscilloscope Figure.4 Measuremet setup to measure a UWB pulse scattered from a metal object.

37 I the cases where d = cm ad 3 cm, the observatio poit is i the ear-field of the scatterer ad as ca be see, the scattered sigal is similar to the icidet pulse. I these two cases, the scattered sigal is followed by a tail, which is related to the impulse respose of the atea. By locatig the plate ad the atea i the far- field of each other, the scattered sigal iclies to the first derivative of the icidet pulse. By icreasig the distace betwee the atea ad scatterer, the amplitude of the scattered sigal decreases. I Figure.7, the ormalized resposes are plotted for d = cm ad d = 13 cm. Accordig to the results, the scattered field is similar to the icidet field i the ear-field ad similar to the first derivative of the icidet pulse i the far-field of the scatterer. 1 v(t) dv(t)/dt Normalized amplitude Time (s) Figure.5 Excitatio pulse ad its derivative with respect to time..1. SEM-Based Equivalet Circuit of Scatterer I previous chapters, the mathematical represetatio of the scatterig modes was studied. The early-time respose of the scatterer was formulated i (.41) by the time covolutio of the icidet pulse with the summatio over localized impulse resposes of the scatterig ceters of the tag. Based o the wavefrot represetatio [1-3], the iteractios betwee the local resoaces i the early time geerate global resoaces. Accordig to the sigularity expasio method, these global resoaces are modeled i the time domai as the summatio over damped siusoidals correspodig to the complex atural resoaces of the scatterer with some weightig residues as the couplig coefficiets. Although the CNRs are aspect-idepedet, depedig oly o the geometry ad material of the scatterer, the couplig coefficiets are strogly aspect- 3

38 1 E (mv/m) 5 E (mv/m) 1 E (mv/m) Time (s) (a) E (mv/m) Time (s) (b) Time (s) (c) Figure.6 Received electric field from the metal object for differet distaces (a) d = cm, (b) d = 3 cm, (c) d = 1 cm, ad d = 13 cm Time (s) (d) 1 d=cm d=13cm.5 Normalized amplitude Time (s) Figure.7 Received electric field from the metal plate for d = cm ad d = 13cm. 4

39 depedet. I the scatterig aalysis, it is usually more desirable to model the scatterig process with a equivalet-circuit represetatio. This equivalet circuit is helpful i the desig process of the scatterer. I order to cosider the effects of polarizatio i the scatterig process, a geeral situatio, show i Figure.8a, is assumed. Assumig the icidet ad scattered electric fields as E ic ad E s with polarizatio vectors defied as â ic ad â s, the scatterig trasfer fuctio of the tag is s E r s ( ; ) Ht ( aˆ ˆ ic, as; s) ic E ( r; s) (.44) Assumig the icidet electric field as a Dirac-delta fuctio, the trasfer fuctio of the tag is related to the scattered electric field. The equivalet circuit of the scatterer is depicted i Figure.8b. The iput ad output voltages are defied at the trasmittig ad receivig atea ports, respectively. The icidet field is coupled to the CNRs by couplig coefficiets (i) ic i=1,,., N, which deped o the directio ad polarizatio of the icidet electric field. Each CNR is represeted by a parallel RLC circuit i series with a delay lie, which models the tur-o times of the CNRs. The excited atural curret modes are coupled to the scattered field with couplig coefficiets (i) s i=1,,., N. The quatity Ze represets the early-time respose of the tag, which is aspect-depedet. The trasfer fuctio of the tag as defied i (.44) is coverted to the ratio of output to iput voltages. With some mathematical maipulatio, the trasfer fuctio ca easily be writte as H ( s) H ( s) H ( s) e l A A N He() s 1 s s s s (.45) The first term is the early-time part ad the secod term, icludig the complex atural resoaces, is the late-time part. Although i reality, N is ifiity, for umerical computatios, N is usually trucated to a fiite value. 5

40 ... (a) (b) Figure.8 (a) A tag illumiated by a icidet plae pulse, ad (b) SEM-based equivalet circuit of chipless RFID tag.1.3 SEM Represetatio of Currets o a Dipole I this sectio, scattered fields from a dipole are formulated based o the SEM i order to illustrate the applicatio of the SEM i umerical computatios [4]. A sigle dipole of legth L = 1m is aliged with the z-axis (Figure.9) ad illumiated by a icidet plae wave propagatig i the directio formig a agle θ with the z-axis. The icidet wave is assumed to be a step fuctio, strikig the scatterer at t =. By formulatig the curret distributio usig the SEM, it is possible to obtai the curret distributio ad scattered fields i the time domai. By eglectig the effects of the ed caps o the wire ad φ variatios of the currets o the wire, a Pockligto equatio ca be writte for the axially-directed curret o the dipole. Assumig s = α+jω, the Pockligto equatio is writte as [4] where K is give by / ic, L, s s Et z s I z s K z, z ; sdz L/ z c (.46) ic Et is the tagetial compoet of the icidet electric field alog the dipole ad the kerel Here, a is the radius of the wire ad 6 1 exp sr / c K z, z; s ad a (.47) 4R

41 ic E z L x Figure.9 Geometry of the dipole illumiated by a icidet field. 4 si / 1/ R z z a (.48) The icidet tagetial electric field alog the dipole is writte by ic ic sz Et z, s E scos exp c si (.49) For the step-fuctio icidet wave, we have E ic E (.5) s s By discretizig the legth of the dipole ito N segmets, the itegral equatio i (.46) is coverted to the equatio Z I V (.51) where [Z] is a N N matrix referred to as the system impedace matrix, [I] is a N 1 respose vector ad [V] is a N 1 vector correspodig to the icidet field. Accordig to (.), at CNRs of the scatterer, the followig equatio holds Z s I s (.5) 7

42 The CNRs of the dipole are obtaied from s det Zs (.53) The CNRs ca be calculated by employig differet searchig algorithms. Oe easy way is to expad Δ(s) i a complex Taylor series about s as s s s s s (.54) Keepig the first two terms of the series, the CNR, s, is obtaied from s s s (.55) s where s is the iitial guess of the resoat frequecy. More accurate values for s ca be obtaied by repeatig this procedure. Figure.1 shows the pole diagram of the dipole. It is see that the poles, s=α+jω, are located i differet layers i the s-plae. The poles situated i the first layer are more domiat i the time-domai respose because they have lower dampig factors tha those located i the further layers. The atural curret modes o the dipole are the solutios of equatio (.5). I 1 Z V Y V s (.56) I Figure.11, the real ad imagiary parts of the first three modes of the dipole located i the first layer are depicted. By possessig the atural modes ad CNRs of the dipole, the curret distributio ca be cast to the form s 1 Y I Z V V (.57) where R is the residue of the th pole, obtaied from (.4). The time-domai respose is obtaied by applyig a iverse Laplace trasform alog the appropriate Bromwich cotour. exp i t R s t J (.58) 8

43 Frequecy (MHz) (s -1 ) x 1 9 Figure.1 Pole diagram of the dipole, represetig the resoat frequecy ad dampig factor of the CNRs. Real part mode 1-1 mode mode z (m) Imagiary part mode 1 mode mode z (m) (a) Figure.11 (a) Real ad (b) imagiary parts of the first three atural currets of the dipole. (b). Eigemode Expasio Method Returig to scatterig from the chipless tag show i Figure.1, the icidet electric field iduces a curret distributio o the tag, which ca be calculated by applyig boudary coditios o the tag surface as 9

44 ic G( r, r; s), J r E r; s r A (.59) where Ĝ i the followig formulatios is the electric-type dyadic Gree s fuctio ad A represets the surface of the tag. The eigevalue equatio associated with (.59) is writte by r r G( r, r; s), J r; s s J r; s r A (.6) where J(r; s) ad λ(s) are th eigemode ad eigevalue of G, respectively. By applyig the method of momet (MoM), the itegral equatio i (.59) is coverted to the followig matrix equatio t s s s Γ J I e (.61) ad the eigevalue equatio correspodig to (.61) is writte by s s s s Γ J J (.6) I order to have otrivial solutios, the determiat of the coefficiet matrix must be zero as C det Γ s s I (.63) C, is called the characteristic equatio ad I, is a uit matrix. Assumig Γ to be a square matrix of rak N, oe ca write s N 1 s det( Γ ) (.64) The eigevalues may or may ot all be distict. It is clearly see from (.63) ad (.64) that the CNRs of the scatterer are the zeroes of the eigevalues. Each eigevalue may cotai a ifiite umber of CNRs. For each square matrix, two sets of eigemodes, right-side ad left-side, are defied. I (.6), the right-side eigemodes are itroduced, which are represeted by followig. The left-side Eigemodes are defied as [5] L s s s s L R J i the J Γ J (.65) The orthogoality ad bi-orthogoality relatios betwee eigemodes ca be summarized as 3

45 J s J s (.66a) L L m m J s J s (.66b) R R m m J s J s (.66c) L R m m where m 1 m m The curret distributio ad icidet electric field i (.6) ca be expaded versus the eigemodes as R Js aj s (.67) 1 I b J s (.68) R e 1 Substitutig (.67) ito (.63) ad usig (.68), oe arrives at R R 1 1 e s a Γ s J s a s J s I (.69) By takig a ier product of the two sides of (.69) with L s J ad usig the orthogoality relatio i (.66), oe ca write a L J L R J J 1 s I s s s s (.7) Therefore, the curret distributio o the tag is writte by J s L J s L R 1 J J s 1 I s s s J R s (.71) 31

46 By defiig the ormalized dyadic fuctios as d R L J s J s R L J sj s (.7) the curret distributio i (1.71) ca be expressed by By comparig (.61) ad (.73), oe ca write 1 J s d si s (.73) s 1 s 1 Γ d (.74) s It shows that the sigularity poles of the scatterer are the zeroes of the Eigevalues. Similarly, Therefore, s s Γ d (.75) 1 s s Γ Γ d δ (.76) I some scatterig problems, the geometry of the scatterer is perfectly matched to a specific coordiate system. As a example, whe the icidet electric field illumiates a perfectly electric coductig (PEC) sphere or a ifiite cylider, the scattered fields or equivaletly the iduced currets o the scatterer ca be easily expaded versus the eigemodes of the structures. For arbitrary geometries, which are ot ecessarily compatible with ay specific coordiate system, the umerical evolutio of the eigemode equatio (.6) ca be used i order to fid the eigemodes, eigevalues ad, cosequetly, the complex atural resoaces of the scatterer...1 Example: Eigemode Expasio of Currets o a Dipole Assumig the dipole see i Figure.9, the eigemodes ad eigevalues of the dyadic Gree s fuctio of the scatterer ca be calculated from (.6). The real ad imagiary parts of the first 3

47 three eigemodes of impedace matrix of the dipole are represeted i Figure.1 at frequecies f = 133 MHz ad f = 4 MHz. Compared to the real part of the eigemodes, the imagiary part chages sigificatly by frequecy. Real part mode 1 mode mode z (m) Imagiary part 5 x mode 1-1 mode mode z (m) (a) Real part at f = 133 MHz (b) Imagiary part at f = 133 MHz Real part mode 1 mode mode z (m) Imagiary part mode 1 mode mode z (m) (c) Real part at f = 4 MHz (d) Imagiary part at f = 4 MHz Figure.1 Real ad imagiary parts of the first three eigemodes of the dipole..3 Characteristic Mode Theory For structures whose geometry coicides perfectly with a special coordiate system, the eigemodes of the structure are i-phase o the surface of the scatterer. As a example, assumig a perfectly coductig sphere of radius a is illumiated by a icidet plae wave, the scattered fields ca be writte by 33

48 E Α h rr P cos e H B m, m m m j (.77) where h is the secod kid spherical Hakel fuctio ad m P represets the associated Legedre fuctio of first kid, θ is the agle measured from z-axis ad φ is the agle measured from xz-plae. Sice the sphere is assumed as PEC, the iduced currets o its surface ca be obtaied from J ˆ H (.78) Fields i (.77) satisfy the followig Maxwell equatio as E k E H H (.79) which ca be writte as three separate eigevalue equatio. The iduced currets ad the scattered fields i (.77) ad (.78) are i-phase o the surface of the sphere. The same result is see for cylidrical mode expasio aroud a ifiitely log cylider located alog the z-axis. I such special cases where the geometry of the structure is perfectly matched to a special coordiate system, the boudary coditios ca be easily satisfied o just oe spatial compoet of the fields. The idea of characteristic modes is how to expad the currets ad fields versus the basis fuctios (or characteristic modes) which are i-phase o the scatterer surface. This theory was first itroduced by Garbacz i 1971 for coductig bodies of arbitrary shapes [6]. His proposed approach was based o diagoalizig the scatterig matrix of the scatterers. He preseted a ew class of eigemodes o a scatterer that are real ad their correspodig scattered fields have costat phase over the surface of the body. Although the proposed method was used i some cases, its implemetatio was ot easy for a arbitrarily-shaped scatterer. I [7], Harrigto proposed a alterative viewpoit for diagoalizig a operator. This techique relates the curret distributio to the tagetial electric field o the body. He defied a particular weighted eigevalue equatio, which gives the same eigemodes defied by Garbacz, but with a simpler approach. Ever sice, this proposed techique has bee widely employed i the desig ad modelig of ateas ad scatterers [8-33]. Similar to atural resoat modes, the characteristic modes are idepedet of source fields ad deped oly o the geometry ad shape of a scatterer. 34

49 .3.1 Mathematical Formulatio of the Characteristic Mode Theory Referrig to Figure.1, it is assumed that a icidet plae wave illumiates the scatterer. The first step i formulatig the eigevalue equatio, which defies the characteristic modes of the tag, is the applicatio of the electric-field itegral equatio (EFIE) o the tag surface as L J G( r, r; s), J r E ic t r; s r (.8) where G is defied i (.5) ad the itegratio is performed over the surface of the tag. Sice the operator L(.) i (.8) has the dimesios of impedace, it is more coveiet to itroduce the otatio Z(J)=L(J) (.81) where Z is a symmetric operator as C B C B, Z Z, (.8) Oe ca write Z i terms of its real ad imagiary compoets 1 where R Z Z ad 1 Z R jx (.83) X Z Z. Sice the radiated power from a curret distributio J o j the tag is give by P J,RJ (.84) it follows that R is positive semi-defiite. The startig step i defiig the characteristic modes of the tag is the followig eigevalue equatio Z J MJ (.85) where γ ad J are the th eigevalue ad eigemode of the equatio ad M is a weightig operator. Choosig M = R esures orthogoality of the radiatio patters of the curret modes i the far zoe. Itroducig 35

50 1 j (.86) ito (.85), the eigevalue equatio is coverted to X J RJ (.87) Sice R ad X are real symmetric operators, both the eigevalues ad the correspodig characteristic modes, J, must be real. I additio, the eigemodes satisfy the orthogoality relatioships where J J J, R J (.88a) m m, X J (.88b) m m J, Z 1 j (.88c) m m 1 m m m The electric ad magetic fields produced by a eigemode J o the surface of the tag are called characteristic fields, ad are referred to as (E, H). Oe importat property of the characteristic fields is their orthogoality i the far zoe. Based o Poytig s Theorem, the mutual power couplig betwee the curret modes J ad Jm distributed o the surface of the tag ca be writte as follows P m S Jm, Z J J, R J J, X J (.89) j m m E H ds j H H H H dv m v m m Here, Sʹ is ay surface eclosig the tag ad v is the regio eclosed by Sʹ. Accordig to the orthogoality relatios i (.88), we have P 1 j (.9) m m 36

51 If Sʹ is chose to be a sphere at ifiity, the the characteristic fields i the far zoe ca be expressed by E rˆ H j e 4 r jkr F, (.91) where / is the itrisic impedace of space, rˆ is the uit radial vector perpedicular to Sʹ, (θ, φ) are the agular coordiates of the positio o Sʹ ad F is the patter of the field. Isertig the far-zoe fields i (.89), the real ad imagiary parts of the radiated power ca easily be separated as E S m H d s m (.9) v H H E E dv m m m (.93) Relatio (.9) expresses the orthogoality of the characteristic fields i the far-zoe regio. For a sigle characteristic mode, (.93) is writte by v H H E E dv (.94) From (.94), it is see that at resoat frequecies where the electric ad magetic eergies are equal, the correspodig eigevalues are zero. At frequecies where, the fields are iductive ad for, the fields are capacitive. Accordig to (.87), at resoat frequecies, we have X( J ) (.95) By applyig MoM ad covertig equatio (.95) ito matrix equatio, the determiat of the reactace matrix should be zero at the resoat frequecies of the structure i order to have otrivial solutios. The curret distributio o the tag ca be expaded i terms of the characteristic curret modes as 37

52 J aj (.96) 1 where J is the th characteristic mode ad a is the ukow coefficiet i the expasio series. Substitutig (.96) i (.8) ad cosiderig the liearity of the operator, we have ic az J Et (.97) By takig a ier product of the two sides of (.97) with Jm ad usig the orthogoality relatios i (.88), oe ca write a ic ic Et, J Et, J J, Z J 1 j (.98) It is see that the ukow coefficiets are strogly depedet o the couplig betwee the characteristic modes ad the icidet electric field. By substitutig (.97) i (.95), the curret distributio o the tag is give by J 1 E ic t, J 1 1 j V J 1 j J (.99) where V E, J (.1) ic t is the couplig coefficiet betwee th characteristic mode ad icidet electric field. The electric ad magetic fields scattered from the tag ca be writte by V E E (.11) 1 1 j V H H (.1) 1 1 j 38

53 The variatio of eigevalues, curret distributio, ad correspodig fields versus frequecy provides some useful iformatio about the scatterig properties of the tag structure. The modal expasio of the curret i (.99) is iversely depedet o the eigevalues as MS 1 1 j (.13) This parameter is called the modal sigificace. This parameter depeds oly upo the geometry ad dimesios of the tag, ad does ot vary with the icidet excitatio. Aother parameter, which is very useful i calculatig the quality factor of the scatterer at resoat frequecies, is the characteristic agle defied as 18 ta (.14) 1 This parameter models the phase agle betwee a characteristic curret, J, ad the associated characteristic field, E. It is clear from (.13) ad (.14) that at the resoat frequecies of the tag, the characteristic agle is equal to zero ad the modal sigificace has a maximum value of oe. These parameters are very useful i calculatig the quality factor of the tag respose at resoat frequecies. I computig the radiatig badwidth of the modes, we eed to kow the frequecies at which the radiated power is half of that at resoat frequecies. From (.13), at the frequecies where λ = 1 or λ = -1, the correspodig modal sigificace is.77, ad the correspodig characteristic agles are 135 ad 5. Labellig these frequecies fl ad fh, the quality factor of the characteristic mode at resoat frequecy ca be calculated from the expressio f Q f f H L (.15) This approximatio is oly valid for high-q resoators. There have bee umerous formulae for calculatig the quality factor of a scatterer. I our applicatio where we try to implemet resoators with high quality factor, all the proposed formulae give approximately the same results with slight variatios. Aother simple formula useful i calculatig the quality factor of the resoators embedded o chipless RFID tags is give by the expressio 39

54 Q d d (.16) which was proposed by Harrigto [34]. 3 1 mode 1 mode mode 3 Eigevalue Frequecy (MHz) Figure.13 Eigevalues of the characteristic modes versus frequecy..3. Characteristic Mode Aalysis of Dipole Assumig the dipole of legth L = 1m see i Figure.9, the variatios of eigevalues of the dipole are show i Figures.13. The first three resoat frequecies of the dipole are located at f1= 133 MHz, f = 8 MHz ad f3 = 43 MHz at which the correspodig eigevalues are zero. The mode is capacitive at frequecies lower tha its correspodig resoat frequecy ad is iductive at frequecies above it. Accordig to Figure.14a, the modal sigificace is equal to 1 at the resoat frequecies of the dipole. The quality factor of the dipole at the resoat frequecies are equal to Q1 = 4.3, Q = 5.34 ad Q3 = 6.. The characteristic agle of the characteristic modes is equal to 18 at the resoat frequecies, as Figure.14b shows. The first three characteristic modes of the dipole are show i Figure.15 at resoat frequecies. The characteristic modes are sorted based o their correspodig eigevalues. The actual curret o the dipole is the summatio of the characteristic modes weighted by couplig coefficiets, which deped o the icidet electric field. 4

55 MS Frequecy (MHz) (a) Frequecy (MHz) (b) Figure.14 (a) Modal sigificace ad (b) characteristic agle of the characteristic modes versus frequecy. Characteristic agle Characteristic mode mode 1 mode mode 3 Characteristic mode mode 1 mode mode z (m) (a) z (m) (b) 1 Characteristic mode mode 1 mode mode z (mm) (c) z (mm) (d) Figure.15 First three characteristic modes of the dipole at (a) f = 13 MHz, (b) f = 8 MHz, (c) f = 3 MHz, ad f = 43 MHz Characteristic modes mode 1 mode mode 3 41

56 3 Desig of Chipless RFID Tags [8] (Chapter used with permissio of Spriger sciece ad busiess media, 15) Oe key elemet of a chipless RFID system is the tag. Sice it is chipless, it acts both as the scatterer ad ecoder. As the scatterer, it eeds to reradiate the icidet field as much as possible i order to maximize sigal-to-oise ratio (SNR) i the reader. As the ecoder, it eeds to ecode a high desity of data o the backscattered sigal. There are some challeges i attaiig all desired characteristics of the tag as the scatterer ad ecoder altogether. Although may desigs have bee proposed as chipless RFID tags, they ca be categorized ito two geeral groups [35]. I the first group, called time-domai reflectometry-based (TDR) desig, the tag icludes some discotiuities alog a log trasmissio lie. The positios of the discotiuities ecode the data by a trai of pulses shifted correspodig to the positios of the discotiuities. Surface acoustic wave (SAW) tags are a example of this category. The schematic view of a SAW RFID tag is show i Figure 3.1. It icludes a atea, piezoelectric surface, ad multiple reflectors which ecode the data o the sigal [36]. The icidet electromagetic pulse received by the atea is coverted to the acoustic wave through the piezoelectric substrate. The SAW is affected by a umber of reflectors, which create a umber of shifted pulses correspodig to the positios of the reflectors. Although SAW tags are owadays used i some commercial applicatios, there are still some issues to be addressed to make them compatible for RFID applicatios. Reductio i size ad loss, ad icrease i data capacity ad readig rage are some of these issues. Additioally, due to the costly process of makig the SAW ad attachig it to the atea, this type of RFID tag is more expesive tha the silico-based tags [37]. The same idea was employed by utilizig delay lie istead of piezoelectric substrate, icorporated by some discotiuities istead of reflectors [38, 39]. I [4], a chipless RFID tag based o group delay egieered dispersive delay structures is proposed. The tag employs trasmissio-type all-pass dispersive delay structures (DDSs, show i Figure 3.) to assig the pulse positio modulatio (PPM) code oto the iterrogatig sigal. The proposed chipless RFID system based o DDSs is show i Figure 3.3. The iterrogatig sigal icludes three pulses modulated with three differet frequecies. Depedig o the frequecy of the icidet pulse, the structure itroduces the required phase shift correspodig to bits or 1. As a example, the pulses ca be positioed i the first half or the secod half of a bit iterval to ecode a bit or a bit 1, respectively. 4

57 Figure 3.1 Schematic view of a surface acoustic wave tag. I practical applicatios, TDR-based tags are loaded with a atea, which icreases the size. I additio, the log trasmissio lie icluded i these structure itroduces some loss i the trasmissio path of the sigal. I the secod group of chipless RFID tags, which is called spectral-based tags, the ID of the tag is icorporated ito the spectral respose of the scattered sigal. I these desigs, the frequecy bad of operatio is divided ito N sectios, correspodig to N bits. Accordig to Figure 3.4, the presece ad absece of resoace at each sectio of the frequecy bad is associated with bits 1 ad, respectively. By icreasig the umber of bits o the tag, the coupligs betwee the resoaces are icreased [41]. Hece, by removig a specific resoace, the coupligs betwee the other resoators are chaged ad as a result, the resoat frequecies of the other resoaces are altered. Therefore, we eed to icrease the quality factor of the resoator i order to decrease the couplig betwee them [4]. The first spectral-based desig is show i Figure 3.5a. It is a 11-bit tag icludig 11 dipoles, each correspodig to oe bit [43]. I order to decrease the couplig betwee the dipoles, they are placed far from each other, which icreases the size of the tag. Aother drawback of the tag is the low quality factor of the dipoles, which is ot suitable for high desity of data. I 6, a chipless RFID tag based o the fractal Hilbert curve was proposed [44]. The cofiguratio of the proposed tag is depicted i Figure 3.5b. From a electromagetic poit of view, such a curve provides a structure that ca resoate at a wavelegth much loger tha its physical size. For high desities of data where we eed to pack the resoaces ito a limited frequecy bad, this structure ivolves some difficulties i the fabricatio process. 43

58 Figure 3. Dispersive delay structures [4] (With permissio, Copyright 11 IEEE). Figure 3.3 Chipless RFID system based o DDSs [4] (With permissio, Copyright 11 IEEE). Scattered sigal f1 f f 3 f4 N 1 f f N Figure 3.4 Assiged resoat frequecies for a chipless RFID tag. 44

59 I 7, a simple structure based o the slot resoator was proposed [45]. By isertig quarterwavelegth slot resoators o a metallic plae as see i Figure 3.5c, the ID of the tag is adjusted by the resoat frequecies of the slots. Later o, this structure was used as a basis for desigig compact multi-bit chipless RFID tags. Figure 3.5d shows aother chipless RFID tag i which a receivig atea is attached to a resoat circuitry that ecodes data o the sigal ad the trasmits the ecoded sigal through a trasmittig atea [46]. The ateas are placed i differet polarizatios for trasmittig ad receivig purposes. Compared to the spectral-based chipless RFID tags i which the structure acts both as the scatterer ad ecoder, the tag show i Figure 3.5d has larger size with higher loss. Hece, this desig is ot suitable for compact chipless RFID tags. Figure 3.5e shows a chipless RFID tag desiged based o high impedace surfaces. I this tag, by employig a multi-resoat HIS uit cell, several bits ca be stored i the structure [47]. The states total reflectio ad total absorptio ecode bits ad 1, respectively. The groud plae of the microstrip participates i the resoat mechaism of the structure, which makes the tag bulky i some applicatios. The 4-bit tag represeted i Figure 3.5f cotais 4 quarter-wavelegth slots, each resoatig at the specified frequecy [4]. Besides all aforemetioed desigs proposed as chipless RFID tags, there is a eed for a systematic desig, which icludes all effective structural parameters i the desig process. As the ecoder, we eed to cosider the quality factor ad resoat frequecy tuability of the embedded resoators. As the scatterer, the residue of the poles ad radar cross sectio of the tag ad their depedecy o polarizatio ad directio should be cosidered i the desig process. I this chapter, two desig approaches based o sigularity expasio method (SEM) ad characteristic mode theory (CMT) are preseted. First, complex atural resoace-based desig of chipless RFID tags is itroduced. By moitorig the effects of structural dimesios o the dampig factor ad resoat frequecy of the resoators, the process of ecodig the data oto the tag is preseted. I the followig, aother desig process of the tag based o the theory of characteristic modes is itroduced, which provides the resoat frequecy, quality factor, ad additioally the itesity of the characteristic fields i the far-zoe regio [48]. Although the desig procedure is geeral ad ca be used for ay arbitrary resoat-based structure, the quarter-wavelegth slot resoators is used as the resoat circuitry i the preseted desig procedure. This structure exhibits some desired features compared to other proposed resoat structures [4, 49]. Its low profile, ease of fabricatio, ad lightess are the importat features of the proposed tag. 45

60 (a) (b) (c) (d) (e) (f) Figure 3.5 Spectral-based chipless RFID tags usig (a) dipole resoators [43] (Copyright 5 IEEE) (b) fractal Hilbert curve [44] (Copyright 6 IEEE) (c) slot resoators [45]. (Copyright 7 IEEE) (d) Resoat circuitry attached to the trasmittig/receivig ateas as a chipless RFID tag [46] (Copyright 9 IEEE) (e) chipless RFID tag based o high-impedace surface [47] (Copyright 13 IEEE) (f) 4-bit tag usig quarter-wavelegth slot resoators [4] (With permissio, Copyright 14 IEEE). 46

61 3.1 Complex Natural Resoace-Based Desig of Chipless RFID Tags As metioed i Chapter, the impulse respose of the tag ca be writte as the summatio over the CNRs combied with a etire-domai fuctio icludig the early-time respose of the tag as R H s H s s s e (3.1) As metioed before, the residues (R) ad etire-domai fuctio (He(.)) deped strogly o the polarizatio ad directio of the trasmittig ad receivig ateas, while the CNRs of the tag (s) are aspect-idepedet. Although the series icludes a ifiite umber of poles, we cosider just N fudametal high-q CNRs of the tag, which are excited strogly by the icidet electric field. A sigle-bit scheme of the tag is show i Figure 3.6 with its structural dimesios. I order to perceive a ituitive descriptio of the scatterig modes, the tag show i Figure 3.6 is illumiated by a y-polarized electric field propagatig i the x-directio. The curret distributio o the tag is illustrated i Figure 3.7 at differet time istaces. At t=.s, the impigig wave hits the leadig edge of the tag. The curret o the tag at t=.4s is show i Figure 3.7b. At this time, the icidet wave illumiates part of the tag ad as the figure shows the iduced curret is strogly depedet o the source field. At t =.6 s, the icidet field crosses through the tag ad afterward the curret distributio ca be writte by the summatio over the atural modes of the tag. Although each scatterer has ifiite CNRs, the domiat resoaces s x W a L Figure 3.6 Sigle-bit tag with structural dimesios. y d 47

62 excited by the icidet field are related to the fudametal resoat frequecy of the slot ad metal parts. Accordig to the curret distributio at t =.4 s ad t =.6 s, it is explicitly see that the curret distributio o the tag is the summatio of the atural currets related to the fudametal resoace of the slot ad metal. At t =.4s, the curret is domiated by the atural modes related to the slot ad metal resoat frequecies. At t =.6s ad thereafter, the slot s fudametal atural mode is more domiat, because it has a low dampig factor compared to other CNRs of the tag. Assumig W =.3 mm, S = 3 mm, d =.8 mm, ad L = 1.6 mm, the time-domai ad frequecy-domai backscattered field from the tag are depicted i Figure 3.8. The icidet electric field is polarized i the y-directio ad propagates i the z-directio. As the frequecy-domai respose of the backscattered field shows, two excited resoat frequecies of the structure are located at f = 5.54 GHz ad f = 8.35 GHz. The pole diagram of the tag is show i Figure 3.9. It depicts the resoat frequecies of the tag versus their correspodig dampig factors. The residues of the poles are depicted beside them. The high-q resoace at f = 5.54GHz is related to the fudametal frequecy of the slot resoator, ad the low-q resoat frequecy at f = 8.35GHz is associated with the metallic part of the tag. Although the CNR of the slot has a lower dampig factor tha the CNR of the metal, its residue is five times weaker. Sice the fudametal resoat frequecy of the slot is used i ecodig the data oto the tag, the resoat frequecy of the metal should be cosidered i the desig procedure ad distiguished i the applied detectio techique. I Figure 3.1, the curret distributio o the tag is show for two resoat frequecies. As it shows, at the resoat frequecy of the slot, the curret o the arms of the slot are i opposite directios while at f = 8.35GHz, which correspods to the half-wavelegth resoace of the metal, the curret o the arms is mostly i the same directio. Based o these curret distributios, it ca be iferred that the resoat frequecy of the slot is mostly sesitive to the slot legth L ad that the resoat frequecy of the metal ca be chaged by L+S. I practical applicatios, the fudametal CNR of the slot rather tha the metal is used for ecodig the data oto the tag because of its higher quality factor. I Figure 3.11, the resoat frequecy of the slot is plotted versus slot legth for two differet values of d. As ca be see, icreasig the slot legth shifts dow its resoat frequecy. I additio, for larger values of d, as a result of slightly icreasig the electrical legth of the slot, its resoat frequecy decreases. Therefore, the resoat frequecy ca be easily adjusted by the slot legth (L). Aother importat parameter to be cosidered i the 48

63 (a) t =. s (b) t =.4 s (c) t =.4 s (d) t =.6 s Figure 3.7 Curret distributio o the tag for differet time istaces [33] (With permissio, Copyright 15 IEEE). E (dbv/m) E (V/m) Frequecy (GHz) Time (s) (a) (b) Figure 3.8 (a) Frequecy-domai ad (b) time-domai backscattered field from the sigle-bit tag [33] (With permissio, Copyright 15 IEEE). 49

64 8.5 8 R= f (GHz) R= (s -1 ) x 1 9 Figure 3.9 Pole diagram of the sigle-bit tag [33] (With permissio, Copyright 15 IEEE). desig procedure is the dampig factor of the resoaces. I order to icorporate more resoat frequecies ito a relatively arrow frequecy bad, it is ecessary to desig the poles with low dampig factors or equivaletly high quality factors. I Figure 3.1, the dampig factor of the slot s fudametal CNR is plotted versus the width of slot (W). As it shows, by icreasig the slot width ad cosequetly icreasig the parasitic fields at the ope-eded edge of the slot, its dampig factor slightly icreases. Due to the limitatio i prototypig of slots with widths below.mm, this parameter caot be used effectively to lower the dampig factor of the slot resoator. Assumig slot width of W =.mm, the dampig factor of the slot is depicted i Figure 3.13 i terms of d. As it shows, by decreasig d, the dampig factor is sigificatly decreased. Accordig to the curret distributio o the tag as see i Figure 3.1a, by decreasig d, the currets o the edges of the resoator are placed closer to each other ad as a result, backscattered radiatio decreases drastically. By reducig the radiated power, accordig to the defiitio of the quality factor Q E P stored (3.) radiatio the quality factor of the resoator icreases which leads to a lower dampig factor at that resoat frequecy. The quatities ω, Estored, ad Pradiatio are the radia frequecy, stored eergy aroud the tag, ad radiatio power from the tag, respectively. By decreasig the radiatio fields the radar 5

65 cross-sectio (RCS) of the tag is decreased, which makes the idetificatio process of the tag more challegig especially i the presece of oise ad clutter. Assumig a sigle-bit tag as see i Figure 3.6, the late-time respose correspodig to fudametal resoace ca be writte by t Re cos t s t (3.3) (a) (b) Figure 3.1 Curret distributio o the tag at (a) f = 5.54GHz ad (b) 8.8 GHz [4] (With permissio, Copyright 14 IEEE) d=.8mm d=.4mm f (GHz) L (mm) Figure 3.11 Resoat frequecy of the slot versus L. W =.3mm [4] (With permissio, Copyright 14 IEEE). 51

66 -.6 x (s -1 ) W (mm) Figure 3.1 Dampig factor of the CNR of the slot versus d for differet values of a. W =.3 mm [4] (With permissio, Copyright 14 IEEE). x (s -1 ) a=1mm a=1mm a=8mm d (mm) Figure 3.13 Dampig factor of the CNR of the slot versus d for differet values of a. W =.3mm [4] (With permissio, Copyright 14 IEEE). where R ad φ are the amplitude ad phase of the sigal resoatig at the radia resoat frequecy of ω ad atteuatig with dampig factor α. The eergy of the sigal is defied by 5

67 Es s t dt t R R 4 4 e (3.4) For the CNRs with low dampig factor as ω>>α, assumig φ=, the eergy of the sigal i (3.4) is summarized as E s R 4 (3.5) It is see that the eergy of the sigle-pole sigal is proportioal to the square of its amplitude ad iverse of its dampig factor, whe its dampig factor is much smaller tha radial frequecy. For this reaso, it is crucial i the idetificatio process of the scattered sigal from chipless RFID tag to use resoaces with a low dampig factor. I practical applicatio, the tag structure is usually desiged o a thi dielectric substrate. Because of the existece of the lossy dielectric, both the resoat frequecy ad dampig factor of the CNRs chage. I Figure 3.14, the variatio of the CNRs versus dielectric costat of the substrate is show. The thickess of the substrate is assumed.7874 mm ad the dimesios of the structure are a = 1mm, d =.8mm, W =.3mm. As it shows by icreasig the dielectric costat of the lossless substrate, the resoat frequecy ad the dampig factor of the CNR decrease. Based o the scalig relatioship, whe a tag is located i a lossy dielectric with dielectric costat ԑ ad coductivity δ [5], s fs s (3.6) where fs s ad s are the th -CNR of the tag i free space ad i the lossy dielectric. I the case where the tag is located o the dielectric substrate from oe side, eglectig the loss of the dielectric, we have fs s s (3.7) eff 53

68 9 8 Frequecy (GHz) Dielectric costat (a) x 18-1 (s -1 ) Dielectric costat (b) Figure 3.14 (a) Resoat frequecy ad (b) dampig factor of the CNR of the tag versus dielectric costat. A = 1mm, d =.8mm, t =.3mm. Accordig to (3.7), the dampig factor ad resoat frequecy of the tag attached to the dielectric substrate decrease by icreasig the dielectric costat of the substrate (accordig to Figures 3.13 ad 3.14). As the Figure 3.14 shows, whe the dielectric costat of the substrate is betwee ad 3, the dampig factor of the CNR icreases. I this regio, the resoat frequecy of the slot is 54

69 close to the resoat frequecy of the metal. Therefore, the couplig effect betwee these two resoat mechaisms icreases the dampig factor of the slot s CNR. Aother importat parameter i chipless RFID tags is the sesitivity of the CNRs to backgroud objects i the eviromet. For this purpose, a sigle-bit chipless RFID tag is assumed above a metallic plate as the Figure 3.15 shows. The percetage variatios of the resoat frequecy ad dampig factor i terms of the distace betwee tag ad plate are illustrated i Figure Accordig to the figures, as a result of couplig, the dampig factor of the pole is much more sesitive to the evirometal objects tha the resoat frequecy. This is the reaso why the dampig factor of the poles is ot usually used i the idetificatio process. The sigle-bit tag see i Figure 3.6 ca be used i the desig of multi-bit chipless RFID tags. The couplig betwee resoaces plays a critical role i the desig of chipless RFID tags. The presece ad absece of a resoace at a specific resoat frequecy represets bit 1 or, respectively. Therefore, the structure should be desiged i such a way that by ullig oe resoat frequecy, the resoat frequecies of the other resoators do ot chage. A 4-bit tag show i Figure 3.17 is desiged based o the quarter-wavelegth slot resoators o a Rogers RT/Duroid /587 (r =.) with a thickess of.78mm. The legths of the slots are tued i order to adjust the resoat frequecies of the slots accordig to the ID of the tag. By fillig the slot surface with metal or isertig some stubs alog the slot, the correspodig bit is 1mm Figure 3.15 Sigle-bit tag above a metallic plate. 55

70 ulled. Therefore, 4 tags with uique IDs ca be ecoded with 4 slots. As a example, i the secod tag, the secod ad fifth bits of the tag are ulled by isertig some stubs alog the slot. The radar cross-sectios of the tags are depicted i Figure It is see that the secod ad fifth bits of the tag are ulled without ay cosiderable chage i the positios of the other resoaces. Frequecy chage (%) Distace (mm) (a) Dampig-factor chage (%) Distace (mm) (b) Figure 3.16 Percetage variatios i the (a) resoat frequecy ad (b) dampig factor of the CNR of the tag versus distat to the metallic plate. A = 1mm, d =.8mm, t =.3mm Figure 3.17 Schematic view of the 4-bit tag [4] (With permissio, Copyright 14 IEEE). 56

71 3. Desig of Chipless RFID Tag Based o Characteristic Mode Theory I the previous sectio, the effects of various structural dimesios of the tag o the CNRs were studied. The scattered field radiated from the atural curret mode depeds strogly o its distributio o the tag surface. We eed to calculate the CNRs ad correspodig atural modes o the tag by employig some umerical techiques such as method of momet (MoM). Aother approach for moitorig the effects of structural parameters o the scattered respose is characteristic mode theory (CMT). As metioed i Chapter, by decomposig the curret distributio o the tag ito its characteristic modes, the resoat ad radiatio characteristics of the tag ca be studied easily at each frequecy. I some commercial software such as FEKO, the characteristic modes of the structure ad the variatios of the eigevalues, modal sigificaces, ad radiated power ca be easily moitored versus frequecy. This isight is useful i the desig of chipless RFID tags. A sigle-bit tag with the dimesios show i Figure 3.19 is cosidered. Two parameters d1 ad d are show i Figure 3.19, which are iitialized at the y-axis i order to study the effects of the metal ad slot resoaces more accurately. The eigevalues of the first two characteristic modes of the tag are illustrated i Figure 3. versus frequecy for d =.8 mm, W =.3 mm, d1 = 3.5 mm, d =, a = 1 mm, ad L = 1.1 mm RCS (dbm ) ID 1 Figure 3.18 Radar cross-sectios of the 4-bit tags [4] (With permissio, Copyright 14 IEEE) Frequecy (GHz) 57 ID

72 W d d 1 a L x y d Figure 3.19 Sigle-bit tag illumiated by icidet plae wave. The resoat frequecies of the tag are the frequecies at which the eigevalues are equal to zero. I this case, the resoat frequecies of the tag i the 3-1GHz bad are located at f1 = 5.7GHz ad f = 8.6GHz. Figure 3.1 illustrates the modal sigificaces of the characteristic modes, which are calculated from MS 1 1 j (3.8) Accordig to Figure 3.1, the first resoace of the tag has a much higher quality factor tha the secod. For high-q resoaces which are usually used i the desig of chipless RFID tags, the quality factor of the CNRs ca be calculated from the modal sigificace (MS) of the modes. Assumig fl ad fh as the frequecies at which the MS is.77, the quality factor ca be calculated from f Q f f H L (3.9) where f is the resoat frequecy of the tag. The quality factor of the resoaces ca also be calculated from the characteristic agles of the modes. The characteristic agle of a characteristic mode is obtaied from 18 ta 1 (3.1) 58

73 6 Mode 1 Mode 3 Eigevalue Frequecy (GHz) Figure 3. Eigevalues of the characteristic modes versus frequecy. 1.8 Modal sigificace.6.4. Mode 1 Mode Figure 3.1 Modal sigificaces of the characteristic modes versus frequecy. As ca be see from (3.1), the characteristic agle is 18 at the resoat frequecy ad is 135 ad 5 at fl ad fh, respectively. The characteristic agles of the modes are show i Figure 3. versus frequecy. The first resoat frequecy at f1 = 5.7 GHz is correspodig to the quarterwavelegth resoat of the slot ad the resoat frequecy at f = 8.6 GHz is related to the halfwavelegth resoace of the metal Frequecy (GHz) 59

74 The first two characteristic modes of the tag at two resoat frequecies are depicted i Figure 3.3. As the figures show, the currets o the arms of the slots oppose each other at f = 5.7 GHz which is associated to the slot s resoace. The first characteristic mode of the tag at f=8.6 GHz agrees with the curret distributio at the half-wavelegth resoace of the tag, while it is ot the same for the secod characteristic mode. The actual curret o the tag is the superpositio of the characteristic modes weighted with coefficiets proportioal to the couplig coefficiets ad modal sigificaces. Takig advatage of the characteristic mode theory (CMT) i the desig procedure, the variatios of the resoat frequecy ad quality factor of the CNRs ad field itesity ca be moitored easily. Accordig to the curret modes, it is see that the resoat frequecy of the slot is depedet strogly upo the slot legth ad the resoace of the metal is proportioal to the metal legth. Kowig this, two parameters d1 ad d show i Figure 3.19 are used to chage the legths of the slot ad metal o the tag structure. I Figure 3.4, the variatios of the first ad secod resoat frequecies of the tag are show versus d1. It is see that by icreasig d1 ad cosequetly decreasig the slot legth, its resoat frequecy icreases without cosiderable chage i the resoat frequecy of the metal. Figure 3.5 shows the variatios of the resoat frequecies of the slot ad metal versus d. By alterig d, the resoat frequecy of the metal chages without cosiderable variatios i the resoat frequecy of the slot. It is very useful i Characteristic agle (degree) Mode. 1 Mode Frequecy (GHz) Figure 3. Characteristic agle of the characteristic modes versus frequecy. 6

75 J1 at f = 5.7GHz J at f = 5.7GHz J1at f = 8.6 GHz J at f = 8.6 GHz Figure 3.3 Characteristic modes of the tag at two resoat frequecies [33] (With permissio, Copyright 15 IEEE). the desig of the tag to be able to tue the resoat frequecies of the structure separately. Sice the resoace of the slot is usually utilized for ecodig the ID oto the tag, it is ecessary to place the resoace of the metal outside the frequecy bad of operatio or to distiguish it from the slot resoaces i the detectio process. Whe the resoat frequecy of the slot is located close to the resoat frequecy of the metal, by icreasig the couplig betwee these two resoat frequecies the quality factor of the slot resoator decreases. I Figure 3.6, the backscattered respose from the sigle-bit tag with dimesios d1 = 6 mm, a = 1 mm, d =.8 mm, W =.3 mm is show for three differet values of d. By keepig the value of d1 = 6mm ad chagig d, the resoat frequecy of the slot chages, but ot the metal s resoat frequecy. The quality factor of the CNRs of the tag is show i Table 1 for three cases. It is see that i the secod case where the resoat frequecies are located i close proximity to each other, the quality factor of the slot s CNR decreases more tha 1 times. The quatity R i the table is the residue of the correspodig 61

76 CNR of the tag i the late time. I the secod case, the slot s CNR has higher residue, which is very importat i the detectio process. Based o (3.3), the eergy of the CNR is directly proportioal to the square of the residue ad iversely to the dampig factor of the CNR. I Chapter 5, the effects of residue ad dampig factor o detectio of a sigal i the presece of oise will be show. I some applicatios such as chipless RFID sesors where few bits are used i the sesig process i the lossy media, the stregth of the late-time respose is critical i the detectio of a sigal. I tags with high desity of data, a low dampig factor is desirable, decreasig the couplig betwee resoators. As metioed before, the quality factor of the resoaces of the tag ca be cotrolled by d. The variatio of the quality factor of the slot is show i Figure 3.7 versus d. By icreasig the arm width d, the quality factor of the slot s resoace decreases, which agrees with the discussio i sectio 3.. By decreasig d ad icreasig the quality factor of the CNR, more eergy is localized i the reactive ear-field of the tag, which leads to a decrease i the radiatio from the tag. Therefore, the RCS of the tag decreases. As a example, the far-field radiatio patter of the tag is see i Figure 3.8 for d =.8 mm ad d =.4 mm. The maximum radiatio itesity of the far-zoe electric field is 33uV/m for d =.8 mm, compared to 84uV/m for d =.4mm. By followig the aforemetioed desig procedure ad moitorig the effects of 11 Resoat frequecy (GHz) f 1 f Figure 3.4 Variatio of the resoat frequecies of the tag versus d1 [33] (With permissio, Copyright 15 IEEE) d 1 (mm) 6

77 Resoat frequecy (GHz) f 1 f d (mm) Figure 3.5 Variatio of the resoat frequecies of the tag versus d [33] (With permissio, Copyright 15 IEEE) E (dbv/m) d =8mm d =5.5mm d =3mm frequecy (GHz) Figure 3.6 Scattered far-field electric field radiated from the tag. d1 = 6 mm, a = 1 mm, d =.8 mm, W =.3 mm [33] (With permissio, Copyright 15 IEEE). 63

78 Table 3-1. The resoat frequecy, quality factor, ad residue of the CNR of the slot for differet cases [33] (With permissio, Copyright 15 IEEE). d(mm) Qslot Qmetal (R) fslot(ghz) fmetal(ghz) structural dimesios o the resoat frequecy, quality factor, ad itesity of the backscattered field from the tag, two 4-bit tags are desiged. The schematic view of the tag is show i Figure 3.9. The slot resoators embedded o the metallic plae are used for ecodig the data. Two differet cases of d = 3 mm ad d = 7 mm are cosidered. By illumiatig the tag with a icidet plae wave polarized i the x-directio ad propagatig i the z-directio, the backscattered respose from the tag is show i Figure 3.3 for two values of d. The pole diagram of the tag is depicted i Figure 3.31 for two differet cases. The resoace of the metal is located out of the frequecy bad of the slot s resoaces for d=3mm. By icreasig d sufficietly, the resoace of the metal ca be withi the frequecy bad of the slot s resoaces. I this case, the dampig factor of the slot s resoaces icreases as a result of couplig, which leads to a lower quality factor. This must be avoided i the desig of the tags with high desity of data i order to pack may resoat frequecies i a arrow frequecy bad. Two fabricated tags are show i Figure Q from (8) from (1) d (mm) Figure 3.7 Quality factor of the CNR of the tag versus d [33] (With permissio, Copyright 15 IEEE). 64

79 (a) d =.8 mm (b) d =.4 mm Figure 3.8 Far-field electric fields radiated from the tag for (a) d =.8 mm ad (b) d =.4 mm [33] (With permissio, Copyright 15 IEEE). y x.5.3 Figure 3.9 Schematic view of the desiged 4-bit tag. Uits: mm [33] (With permissio, Copyright 15 IEEE) The tags were desiged o a Rogers RT/Duroid /33 (r =3) with a thickess of.7874mm. Assumig the icidet electric field directed i x ad propagatig i z, the measured backscattered electric field from the tags is depicted i Figure Although the data are icorporated as four resoat frequecies of the slots, five resoat frequecies are see i the backscattered sigal from the tags. I these circumstaces, the resoat frequecy of the metal shall be distiguished from the slot resoaces i the detectio process of the tag. The pole diagram of the tags is show 65

80 i Figure 34 based o the measured backscattered sigal. It is see that the CNRs of the tags calculated from the measuremet data are i good agreemet with the simulatio results E (dbv/m) -4-5 d =3mm d =7mm Figure 3.3 The simulated backscattered electric field from 4-bit tags [33] (With permissio, Copyright 15 IEEE) Frequecy (GHz) 7 Frequecy (GHz) d =3mm d =7mm Dampig factor (Np/s) x 1 9 Figure 3.31 Pole diagram of the simulated backscattered fields from the tags [33] (With permissio, Copyright 15 IEEE). 66

81 (a) (b) Figure 3.3 Two 4-bit fabricated tags (a) d = 3 mm ad (b) d = 7 mm [33] (With permissio, Copyright 15 IEEE) RCS (dbm ) d =3mm d =7mm Frequecy (GHz) Figure 3.33 Measured RCS of the tags [33] (With permissio, Copyright 15 IEEE). 67

82 6.5 6 Frequecy (GHz) d =3mm d =7mm Dampig factor (s -1 ) x 1 9 Figure 3.34 Pole diagram of the measured backscattered fields from the tags [33] (With permissio, Copyright 15 IEEE). 68

83 PSD (dbm/mhz) 4 UWB Atea i Chipless RFID Systems This chapter is devoted to the scatterig process i chipless RFID systems. Whe a atea illumiates a scatterer, the backscattered sigal received by the atea is aalyzed i the reader to extract the required iformatio of the scatterer. Therefore, the iteractio betwee atea ad scatterer plays a importat role i the detectio process of data. The atea eeds to cover a wide rage of frequecies ad its frequecy respose strogly affects the received sigal. Differet atea types ca be used for this purpose providig some pros ad cos. Sice the locatio ad ID of the tag are calculated based o time-domai ad frequecy-domai sigals, respectively, both time ad frequecy domai properties of atea must be cosidered i the systematic desig of chipless RFIDs [51]. The Uited States of America was the first coutry to release a regulatory framework for the use of UWB techology. This framework defies UWB trasmitters as: A itetioal radiator that, at ay poit i time, has a fractioal badwidth equal to or greater tha. or has a UWB badwidth equal to or greater tha 5 MHz, regardless of the fractioal badwidth [11]. The available spectrum for ulicesed UWB commuicatios is betwee 3.1 GHz to 1.6 GHz with a maximum power emissio limit of dbm/mhz. The FCC mask for outdoor ad idoor UWB applicatios i USA is show i Figure 4.1. Assumig the FCC regulatio, some attetios must be draw i the desig process of chipless RFID systems. Accordig to the radar equatio i the Idoor Outdoor Frequecy (GHz) Figure 4.1 FCC mask for outdoor ad idoor UWB applicatios. 69

84 frequecy domai, the power of received sigal depeds o the trasmitted power, path loss, radar cross sectio (RCS) of the tag, ad atea gais. Sice these parameters are frequecy-depedet, oe eeds to study their frequecy depedecy i the desired frequecy bad of operatio. I this chapter, first a mathematical represetatio of the scatterig process i betwee the atea ad scatterer is preseted ad the, some importat parameters of the atea i time domai are reviewed. Various UWB ateas are studied i summary ad fially, a ew atea elemet applicable i widebad ad UWB is itroduced. 4.1 Lik Equatio i Frequecy Domai As metioed, the received sigal by the atea is a fuctio of may parameters. Assumig a moo-static case see i Figure 4. ad based o the radar budget equatio, the power of the received sigal ca be writte as P r f P t f Ga f Ga f f R f (4.1) where R is the read-rage distace from the scatterer to the atea, Pt ad Ga are the power of the trasmitted sigal ad atea gai respectively, λ is the wavelegth ad δ(f) represets the radar cross-sectio (RCS) of the scatterer. All these parameters are frequecy-depedet. It is assumed that the atea ad scatterer are located i the far field of each other. High-gai ateas cocetrate eergy ito a arrower solid agle tha omi-directioal oes ad are usually used so as to reduce the effects of the iterfereces ad backgroud objects i the scatterig media. I cotrast, the omi-directioal ateas ca receive sigal from ay directio. These ateas have relatively lower gai ad a wider field of view. Regulatory costrais require trasmitted power to be decreased whe usig a high-gai atea i order to meet the same maximum radiated emissio limit show i Figure 4.1. Sice the regulatory limits are defied i terms of equivalet isotropically radiated power (EIRP), Pt.Ga, the trasmitted sigal is egieered based o the atea gai to meet the FCC costrais for short-rag UWB applicatios. The term λ /(4π) 3 R 4 is referred as roudtrip path loss. The frequecy depedecy of the path loss comes from the defiitio of the atea gai ad atea effective aperture i the frequecy domai as [5, 53] 7

85 P t f R G a f P r f f Figure 4. Moo-static chipless RFID system. f 4A eff Ga f (4.) For large directive ateas, the effective aperture is comparable to the physical area of the atea. For omidirectioal small ateas, the effective aperture may be sigificatly larger tha the physical area of the atea. It meas that although a very small atea may have egligible RCS, it is a effective receiver or radiator. Two groups of ateas as costat-gai ad costat-aperture are cosidered here [5]. I omi-directioal small ateas which are beig widely used i short-rage applicatios, the gai of the atea is approximately costat i the frequecy bad of operatio leadig to the variatio of the aperture by 1/ f. I Figure 4.3a, the frequecy variatios of the sigal power ad atea gai are show i the receiver ad trasmitter sides. I the cases where a costat-gai atea is used i the etwork, the trasmitter power is desiged to be costat i the frequecy rage to meet costat EIRP i the trasmitter side, result f i the received power rollig off as / f i bad. O the other had, i costat aperture ateas which are large compared to the wavelegth of the sigal, the gai of the atea icreases by f (Figure 4.3b). Hece, the trasmitter gai should chage by 1/ f ad the power of the received sigal chages by δ(f) i this case. I other UWB ateas, the variatios of the gai ad effective aperture is betwee these two cases. I resoat-based detectio applicatios, the resoat frequecies of the scatterer are preset i the frequecy bad of operatio. These resoaces might itroduce some variatios i the power of the received sigal i the desired frequecy bad. 71

86 Trasmitted power Frequecy Atea Gai Frequecy Received power Trasmitted power Atea Gai Received power Omi-directioal atea i the lik Frequecy (a) Omi-directioal atea i chipless RFID system. Directioal atea i the lik Frequecy Frequecy Frequecy (b) High-gai directioal atea i chipless RFID system. Figure 4.3 Gai ad power cosideratios i chipless RFID systems. 4. Time-Domai Sigal Lik Characterizatio As a geeral case, a bi-static set-up comprised of two UWB ateas is depicted i Figure 4.4. The trasmitter atea, TX, is excited with a icidet voltage atx(t) ad the radiated field from the trasmitter at the scatterer positio is E ic (r, t). The iduced curret o the surface of the scatterer re-radiates a electric field, E s (rrx, t) at the positio of the receivig atea, RX. The scattered field geerates a voltage voc(t) across the receivig port. The trasmissio coefficiet 7

87 betwee two ateas is defied as the ratio of the received voltage wave brx(s) to the icidet voltage wave, atx(s), i the Laplace domai. As the first step, we itroduce the impulse respose of a scatterer located at the origi as the â -compoet of the scattered field at r, i the far zoe of the scatterer, for a impulsive icidet plae wave of 1 a ˆ t as 1 rˆ, r ˆ,t. I the geeral case, â 1 ad â 1 rr ˆ. c are fuctios of time. The impulse respose of the scatterer is a dyad, which icludes all the scatterer iformatio for a particular rˆ, rˆ,t 1 aa ˆˆ r 1. The ext step is computig the icidet field versus the effective legth of the trasmittig atea ad the iput sigal. The atea ca be characterized i the far-zoe by its equivalet effective legth as [54, 55] rˆrˆ hrˆ; t ; t ˆ/ cds I J r r r (4.3) S at a where Sat idicates the atea surface, J is the electric curret o the atea surface, rˆ is the uit vector to the observatio poit, Ia is the iput curret, ad c represets the speed of light i free space. The primed ad uprimed coordiates idicate the source ad observatio poits, respectively. If the iput impedace of the atea is assumed as Zr ad ZTX is the impedace of the matchig circuit, the the reflectio coefficiet at the trasmitter, STX, i the frequecy domai is give by S TX Z Z TX TX Z Z * r r (4.4) Figure 4.4 Schematic of the bio-static set-up for measurig the impulse respose of the tag. 73

88 The realized effective legth of the atea is defied i time domai as [55] R 1 stx t h rˆ; t h r ˆ; t (4.5) TX where stx(t) is the iverse Fourier trasform of STX. Usig the defiitio of the realized effective legth of the trasmittig atea, the icidet electric field E ic for a icidet voltage wave of atx(t) is computed from TX ic 1 atx t R rtx TX; t ˆ E r htx TX; t r (4.6) rtx t R c TX where RTX is the resistace of the trasmitter ad µ is the permeability of the free space. Usig the defiitio of the impulse respose of the scatterer, oe ca compute the received sigal at the receivig atea port as atx t R rtx RX R RX ˆ ˆ ˆ r ˆ ˆ b t htx rtx; t a1a rtx, rrx ; t hrx r ˆRX ; t (4.7) 8 rtxrrx t R c c RX RTX Equatio (4.7) ca be simplified if the impulse respose of the scatterer is computed for the case where â 1 ad â are i the same directio as R h TX ad R h RX, respectively. atx t R rtx RX R RX ˆ r ˆ ˆ b t htx rtx; t ΓrTX, rrx ; t hrx r ˆRX ; t(4.8) 8 rtxrrx t R c c RX RTX Applyig Laplace trasform to (4.8), the trasmissio coefficiet is defied as the ratio of brx(s) to atx(s). srtx rrx / c s e R R ˆ ˆ ˆ ˆ RT TX TX TX RX RX RX 8 rr RTX RRX ;, ; ; S s H r s r r s H r s (4.9) For the moo-static case where oe atea is used for both trasmittig ad receivig, the reflectio coefficiet is computed from S se 8 r R H rˆ; s r, r s sr RX / c 11 RX ; RX RRX (4.1) 74

89 The impulse respose of the scatterer is obtaied as rrx srrx / c 8 RRX e r, r; s S 11 (4.11) R s H rˆ; s Accordig to (4.1), the iformatio of the scatterer is icluded i S11 of the receivig atea multiplied by the square of impulse respose of the atea. As (4.11) shows, the impulse respose of the tag ca be calculated by kowig the effective legth of the atea ad the distace betwee the atea ad the scatterer, rrx. RX 4.3 Atea Effective Legth As (4.11) shows, oe eeds to have the effective legth of the atea i order to extract the impulse respose of the tag i the measuremet set-up. As (4.3) shows, the effective legth of the atea is defied i the far field ad is related to the far-field electric field by jkr e E() rˆ j I ˆ ah r (4.1) 4 r A bi-static set-up, see i Figure 4.5, ca be used i order to measure the effective legth of the atea. It is assumed that both ateas are similar to each other. I bi-static case, the effective legth of the atea ca be calculated from Atea 1 Atea d Network Aalyzer Figure 4.5 Measuremet set-up for measurig trasfer fuctio of the atea. 75

90 S 4S 1 1 S 11 j H TX H RX e R jkd RX d (4.13) where S1 is the trasmissio coefficiet betwee two ateas, S11 represets the reflectio coefficiet of the ateas, HTX ad HRX are the effective legth of the trasmittig ad receivig ateas, ad d is distace betwee the ateas. I order to measure the effective legth of the atea, it is ecessary to kow the distace d betwee the ateas. Ultra widebad ateas usually do ot have a well-defied phase ceter ad this provides some difficulties i calculatig the phase of the atea effective legth. This also might be happe i calculatig the phase of the trasfer fuctio of the scatterer i (4.11). The phase respose of S i (4.13) ca be separated ito three terms: 9 due to the jω, twice of the phase of the atea impulse respose, ad the phase related to the spherical mode, liearly chages with kd. Assumig the atea as a miimum phase system, its phase respose ca be calculated from the Hilbert trasform of its magitude respose [56]. As (4.13) shows, the amplitude of S is proportioal to the amplitude of the square of the trasfer fuctio of the atea with coefficiet of ω/(πd). Hece, the miimum phase fuctio φm(ω) ca be foud from l S l S m d (4.14) by assumig a omial distace d d. The liear part of the phase i S1 is calculated from L S (4.15) The correctio distace ca be calculated from the liear phase part as c dl d (4.16) df By substitutig d d d i (4.13), the amplitude of ad phase of the trasfer fuctio of the atea is obtaied. As a example, two differet ateas (circular disk ad arrowbad moopole) show i Figure 4.6 are cosidered. Two circular disks with R = 1 cm are located 4 cm away from each other (face to face) ad the reflectio ad trasmissio coefficiets betwee 76 m

91 R the iput ports of the atea are measured. The S11 ad S1 betwee ateas are depicted i Figure 4.7a. As it shows the ateas are matched (S11 < -1dB) for frequecies i the rage of GHz. The phase of S1 is see i Figure 4.7b. Accordig to (4.1), the phase of the S1 is the combiatio of the three differet terms. By assumig the atea as a miimum phase system, the liear part of the respose ca be calculated from (4.15). This part is also depicted i Figure 4.7b. By usig the equatio (4.1) ad (4.14), the amplitude ad phase respose of the atea effective legth are show i Figure 4.7c ad 4.7d. By applyig iverse fast Fourier trasform (IFFT) to the atea effective legth, its effective legth i time domai is see i Figure 4.7e for θ = 9 ad φ =. It just represets the agular variatio of the patter of the atea i the far field. By applyig MPM to the late-time respose of the radiated field of the atea, its pole diagram show i Figure 4.7f. I arrowbad ateas, sice the atea ad propagatio characteristics are assumed costat over the desired frequecy bad, they are typically described i the frequecy domai. O the other had, i UWB ateas, ot oly the frequecy-domai characteristics of the atea ad chael should be cosidered, but their time-domai properties should also be take ito cosideratio, because they are usually realized i a impulse-based techology. 4.4 Atea Characteristics i Time Domai I order to evaluate the performace of a atea i time domai, some parameters eed to be defied as figure of merits. Sice the radiatio properties of the atea i the frequecy domai Groud plae y z x Figure 4.6 (a) UWB Moopole disk ad (b) Narrowbad moopole atea. 77

92 S 11, S 1 (db) Frequecy (GHz) - (a) S 11 S 1 phase (Degree) Frequecy (GHz) (b) S 1 L H a (m) Frequecy (GHz) (c) Phase (radia) Frequecy (GHz) (d).1 15 h (m) Frequecy (GHz) Time (s) (e) Figure 4.7 (a) Amplitude ad (b) phase of the S1 for θ = ad φ =, (c) Amplitude ad (d) phase of the atea effective legth i frequecy domai, (e) atea effective legth i time domai, ad (f) pole-diagram of the atea. are usually defied i the far-field, it is sigificatly ecessary to traslate the cocept of far-field ito time domai. IEEE defies the far field as The regio of the field where the ormalized agular field distributio is essetially idepedet of the distace from a specified poit i the atea regio. For a arrow bad atea, the far-field distace is defied as the distace from the atea phase ceter where the phase shift from the ray origiatig from atea maximum Dampig factor (s -1 ) x 1 1 (f)

93 L= cm dimesio ad oe from atea ceter is.5. I most arrowbad ateas, the followig rag is cosidered as the far-field [57]. D R (4.17) where D is the maximum atea dimesio i meter ad λ is the wavelegth of the sigal at the desired frequecy. As a example, Figure 4.8a shows a arrowbad moopole atea located above a groud plae. Differet probes are located at differet distaces from the atea. The reflectio coefficiet of the atea is see i Figure 4.8b. The first ad third resoaces of the atea are located at f = 3.6 GHz ad f = 1.8 GHz. I Figure 4.9, the θ-compoet of the electric field is depicted versus the distace from the atea at two resoat frequecies. Sice the fields i the far field chage iversely by distace, the real fields i the far field are approximated by A/r i Figure 4.9. At the distace where the variatios of electric field deflects from A/r, the ear-field of the atea starts. For example, the far-field regio starts from R = 4.5 cm ad R =1 cm at frequecies of f = 3.6 GHz ad f = 1.8 GHz, respectively, which are well matched with (4.17). For widebad ad UWB ateas, the far field seems frequecy-depedet ad oe eeds ew defiitio i time domai. Before defiig the far-field regio i time domai, it is required to calculate the aalytic evelope respose of the atea as h + (t) = h(t) + jh(h(t)) (4.18) r Moopole S 11 (db) -1 - Groud plae (a) Probes Frequecy (GHz) (b) Figure 4.8 (a) Moopole atea above a groud plae (b) its reflectio coefficiet. 79

94 E (V/m) E at f=3.6 GHz E=15/r E at f=1.8 GHz E=17/r R (cm) Figure 4.9Radiated Eθ versus the distace from the moopole atea. Normalized Impulse respose 1.5 FWHM Rigig h(t) h + (t) Figure 4.1 Normalized impulse respose of the UWB moopole atea alog with aalytic evelope. where h (t) is the impulse respose of the atea ad H(.) is the Hilbert trasform. The dispersio characteristics of the atea ca be studied from the evelope of the aalytic impulse respose of the atea, h + (t) [51] Time (s) As a example, Figure 4.1 shows the impulse respose ad aalytic evelope of the UWB moopole atea at θ = 9 ad φ =. Some of the specific quatities usually used i characterizig the UWB ateas are summarized as followig. 8

95 as 1) Peak Value of the Evelope: It is defied as the maximum of the atea trasfer fuctio p, max h t,, (4.19) t It depeds strogly o the directivity of the atea ad its impedace badwidth [58]. ) Evelope Width (τfwhm): It shows the wideig of the radiated impulse from the atea. It defies as the full width at the half maximum (FWHM) of the aalytic evelope of the atea. This parameter is depicted i Figure 4.1. The lower values of evelope width esures the trasmissio of high data rate through the atea. I [59], the far-field of the atea i time domai is defied as the rage where the arrival of the closest ray ad the arrival of the farthest ray is small compared to evelope width. Assumig d1 ad d as the distaces of the closest ad farthest dimesios of the atea to the observatio poit, the far field of the atea is the rage where [59] d d 1 FWHM (4.) c v where c is the speed of light i free space ad v is a umber betwee 3 to 5 for large ateas. For smaller ateas i the dimesios comparable with λ, larger value of ν must be used. I geeral, there is ot a uique closed-form formula for fidig the far-field of UWB ateas i time domai. A reliable way is moitorig the variatio of the field from ear field to far field. Figure 4.11 shows the variatio of the electric fields i the ear field ad far field of the UWB moopole atea with R = 1 mm at differet distaces of the observatio poit compared to the ceter of the atea. I the ear field, the shape of the field chages sigificatly versus distace, d. As Figure 4.11a shows, for larger distaces i the ear-field regio, ot oly the fields are shifted, but their shape also chages. O the other had, the shape of the radiated field does ot chage versus distace i the far field, as Figure 4.11b shows. 3) Rigig: A importat parameter which illustrates the dispersio properties of the atea is rigig, τr. Rigig origiates from the stored eergy aroud the atea or multiple reflectios from the atea structure. Quatity τr=α is defied as the time util the evelope is falle i a boud from its peak to α.p(θ,φ). For UWB applicatios such as ragig, oe eeds to lower the rigig of the atea less tha a few evelope width. 81

96 4) Group Delay: The frequecy depedecy of the phase respose of the atea impulse respose is defied as the group delay. g d (4.1) d where φ is the phase of the atea impulse respose. I o-distorted atea, the group delay is costat over the frequecy bad of operatio leadig to liearly varyig phase with frequecy. The oliearities of the group delay idicate the resoat behavior of the atea. I Figure 4.1, the group delay of the UWB atea see i Figure 4.6 is depicted. 4.5 New Atea Prototype for Widebad ad Ultra-widebad Applicatios Differet types of widebad ateas have bee itroduced ad employed i practical applicatios as Frequecy-idepedet ateas; Self-complemetary ateas; Travellig wave ateas; Multiple resoace ateas; Electrically small ateas; I frequecy-idepedet ateas, a scaled versio of the radiatig elemet is used for scaled wavelegth. I practice, oe eeds to trucate the atea structure. Bowtie atea (plaar versio of Bicoical atea) show i Figure 4.13a is a example of frequecy-idepedet ateas. It is importat to ote that idepedece from frequecy refers to the radiatio properties of the atea ot its iput impedace. Self-complemetary ateas are realized by a self-complemetary metallizatio. I these ateas, the metal ad dielectric ca be replaced without chagig the atea s cofiguratio. Based o Babie s priciple, the iput impedace is idepedet of frequecy as Zi=6π Ω (4.) 8

97 It does ot mea that the radiatio field is idepedet of frequecy as well. The atea structure see i Figure 4.13b is a example of the self-complemetary atea. I some applicatios where both radiatio characteristics ad iput impedace eed to be idepedece of frequecy for large badwidth, both techiques are combied. Two-arm logarithmic spiral atea is a example of the atea which combies two aforemetioed techiques together. Normalized felectric field d=.1 mm d=1 mm d= mm d=3 mm Time (s) (a) Normalized electric field d= cm d=4cm d=6 cm d=8 cm Time (s) (b) Figure 4.11 Variatio of Eθ versus distace from the atea i (a) ear field ad (b) far field of the atea. 83

98 g (s) Frequecy (GHz) Figure 4.1 Group delay of UWB moopole atea. I travellig-wave ateas, a travellig wave alog a guidig structure with size much larger tha wavelegth is used as the radiatig elemet. By travellig the wave alog the structure, it radiates progressively ad the reflected wave from the atea ed is usually very small compared to the iput sigal. TEM hor see i Figure 4.13c is a example of this type of ateas. The atea structure is tapered to match the atea impedace to the free space itrisic impedace for a wide rage of frequecies. Aother type of UWB ateas is realized by employig multiple resoaces i the atea structure. These ateas are combiatios of multiple ad arrow-bad radiatig elemets. Plaar log-periodic atea is a multiple resoace atea, see i Figure 4.13d. It icludes multiple dipoles with differet legths as (lu/lu+1) = costat. Differet arrowbad ateas elemets ca be used as a basis i the desig of multi-resoat UWB ateas. Electrically small ateas are ateas with dimesios far below the resoace regio. These ateas are poor i radiatio characteristics ad impedace matchig. Based o the physical limits of the radiatio, there is a relatioship betwee the size of the atea, its quality factor ad radiatio efficiecy [6, 61]. As a result, by decreasig the size of the atea, its radiatio efficiecy decreases i order to achieve wider badwidth. Some efforts have bee made i order to miiaturize the atea structures close to the physical limits. I these ateas the 84

99 (a) (b) + - (c) (d) Figure 4.13 (a) Bowtie atea as a frequecy-idepedet atea, (b) a self-complemetary atea, (c) TEM hor as a travellig-wave atea, ad (d) Log-periodic atea as a multiple resoace atea. (a) Figure 4.14Two examples of UWB small ateas. (b) 85

100 radiatio patter of the atea is very close to the radiatio patter of TM1 (ideal small dipole) or TE1 (ideal small loop). These ateas are very applicable for low frequecy applicatios (HF, VHF ad UHF frequecies) which the size of the atea is a critical issue. Figure 4.14a shows a typical rotatioal symmetric UWB moocoe atea with the height of about λ/5 [51]. I Figure 4.14b aother small atea of with maximum size of λ/1 more tha 1:1 badwidth, ad efficiecy of more tha 95 percet is depicted [6]. The proposed atea elemet i this chapter is based o simple moopole atea above a groud plae. By excitig the atea through a source termiated i betwee the groud ad atea, the odd-order resoaces ca be excited. Figure 4.8 depicts a moopole atea of legth L = mm ad its reflectio coefficiet for a wide rage of frequecy. The excited resoat frequecies of the atea are very close to the sharp ulls of the reflectio coefficiet. Assumig a ifiite groud plae, the curret distributio ad correspodig patter i the far-field are show i Figure 4.15 ad At the first resoace of the atea, f = 3.6 GHz, the curret distributio has its maximum o the feedig poit ad its ull at its ed. It produces a radiatio patter with maximum at θ = 9 ad ull at θ=. Sice the atea structure is symmetric aroud z-axis, its radiatio patter is omi-directioal. At f = 7 GHz, the curret distributio is tapered at the ed poits which makes the atea more directive at the broadside directio. At the third resoat modes, f = 1.8 GHz, the curret distributio has a ull o the atea legth. The curret chages its directio at the ull poit leadig to a ull i the radiatio patter of the atea. By icreasig the frequecy, the locatio of the ull shifts up from the voltage source, correspodig to the frequecy of the source. The impedace characteristics of the ateas ca be studied by moitorig the variatios of the CNRs as a fuctio of structural parameters i the pole diagram. I pole diagram, the resoat frequecies ad dampig factors of the excited CNRs of the atea are represeted together. I atea laguage, the quality factor of the CNRs is usually used i the desig procedure, istead of dampig factors. For high-q resoaces, the followig relatio exist betwee the quality factor ad dampig factor [19]. Q (4.3) 86

101 z z Curret Curret (a) f = 3.6 GHz z (b) f = 7 GHz z Curret Curret (c) f = 1.8 GHz (b) f = 1 GHz Figure 4.15 Amplitude of the curret alog the moopole ad its directio at differet frequecies. 1 Gai (dbi) f = 3.6 GHz f = 7 GHz f = 1.8 GHz f = 1 GHz (Degree) Figure 4.16 Radiatio gai of the moopole atea at differet frequecies. 87

102 Two structural parameters for chagig the resoat frequecy ad quality factor of the CNRs are the legth ad width of the moopole atea. The variatios of the CNRs versus the legth ad width of the moopole are show i Figure As it shows, ay icrease i the legth of the atea reduces the resoat frequecies with slightly icrease i dampig factors. O the other had, by icreasig the width of the moopole, the dampig factors icrease leadig to the wider badwidth of the atea at the resoat frequecies. The correspodig quality factors of the first three CNRs of the moopole atea are Q1 = 17.6, Q3 = 7.5, ad Q5 = 53.3 i the case of r =.5 mm ad L = mm. I order to obtai a wide iput impedace from the moopole atea, oe eeds to lower the quality factors of the CNRs eough ad at the same time adjust the resoaces of the atea at appropriate frequecies. Figure 4.18a shows a moopole atea with simply adjustable legth ad width as r1 ad r. Assumig r1 = 1 mm, the variatios of CNRs versus r is depicted i Figure 4.18b. For better illustratio, the reflectio coefficiet of the atea is see i Figure 4.19a. As the results show, by icreasig r, the first resoat frequecy of the atea does ot chage. While the higher order resoaces decrease slightly. Additioally, the quality factors of the CNRs decrease leadig to a widebad iput impedace. I Figure.19b, the radiated electric fields from the atea i time domai are show for r=.5 mm ad r= mm. As it shows, the atea is less dispersive for r = mm. As above metioed aalysis of UWB moopole atea showed, the resoat frequecies, dampig factors ad correspodig residues of the CNRs of the atea ca be desiged properly i order to have UWB iput impedace. The absolute value of the curret distributio o the atea surface for r1 = mm ad r = 1 mm is Frequecy (GHz) Dampig factor (s -1 ) x 1 9 (a) Figure 4.17 Variatios of CNRs of the moopole atea versus (a) atea legth, L ad (b) atea radius, r. L = cm L =.5 cm L = 3 cm Frequecy (GHz) r =.1 mm r =.5 mm r = 1 mm dampig factor (s -1 ) x 1 9 (b) 88

103 15 Groud plae x y z Frequecy (GHz) 1 r =.5 mm 5 r = 5 mm r = 1 mm r = 15 mm r = mm Dampig factor (s -1 ) x 1 1 (a) (b) Figure 4.18 (a) Moopole atea above a groud plae, (b) its pole diagram for differet values of r S 11 (db) r =.5 mm r = 5 mm r = 1 mm r = 15 mm r = mm Frequecy (GHz) (a) Figure 4.19 (a) Reflectio coefficiet of the moopole atea, ad (b) time-domai radiated field from the atea. depicted i Figure 4. at differet resoat frequecies of the atea. At lower frequecies, the curret distributio is very close to the curret distributio o moopole atea see i Figure By icreasig the frequecy, the curret is stroger o the edges of the ateas ad the stadig wave o the atea edges has more variatios which itroduces some variatios i the far-field radiatio fields. At some frequecies, depedig o the phase of the curret distributio o the tag, some dip ull might be itroduced i the radiatio patter. For example, the radiatio patter has a dip ull at θ = 9 ad frequecy f = 6 GHz. I aforemetioed UWB atea, the quality factors ad resoat frequecies of the atea are adjusted for wide iput impedace matchig by elargig the size of the moopole. I followig a simple atea elemet is 89 Normalized E Time (s) (b) r =.5 mm r = mm

104 (a) f = GHz (b) f = 4.9 GHz (c) f = 8.3 GHz (d) f = 11.7 GHz (e) f = 15.5 GHz (f) f = 18.6 GHz Figure 4.Curret distributio o the moopole atea at differet resoat frequecies. itroduced useful i widebad ad UWB applicatios. By isertig a short cylider aroud the moopole, as see i Figure 4., some ew CNRs are added to the atea structure. The resoat modes of the atea ca be totally categorized by coaxial ad moopole modes. The coaxial modes are the TEM resoat modes of the ope-eded coaxial lie comprised of the moopole as the ier coductor ad surroudig cylider as outer coductor. O the other had, the moopole modes are the resoat modes of the combiatio of moopole ad the groud plae. Figure 4.3 shows the reflectio coefficiet of the atea for a ifiitely thi moopole ad s=.4 mm, d= mm ad differet values of h. Comparig to the reflectio coefficiet of the moopole atea see i Figure 4.8b, there is a resoat frequecy i betwee the first ad third resoaces of the moopole. This resoace frequecy is strogly depedet o the legth (h) ad the width (s) of the cylider aroud the moopole. By icreasig the legth of the coax, h, its 9

105 correspodig resoat frequecy decreases. By choosig W = i our simulatios, it is possible to study the electric curret o the moopole more clearly (a) f = GHz (b) f = 4 GHz (c) f = 6 GHz (d) f = 8 GHz (b) f = 9 GHz (c) f = 1 GHz Figure 4.1 Radiatio gai of the moopole atea at differet resoat frequecies. (Solid lie: φ = ad dashed lie: φ = 9 ) Figure 4. A moopole atea surrouded by short cylider as a widebad /UWB elemet. 91

106 -5-1 S 11 (db) h=8 mm h=1 mm -3 h=1 mm h=14 mm Frequecy (GHz) Figure 4.3 Reflectio coefficiet of the atea for differet values of h. I Figure 4.4, the magitude of the curret o the moopole part of the atea is show at three resoat frequecies of the atea. At first ad third resoat frequecies, f = 3.7 GHz ad f = 11.1 GHz, the curret is well-matched with the curret distributio o the moopole atea (without surroudig cylider). While, the curret distributio at f = 7.1 GHz is affected by the presece of the cylider aroud it. As ca be see, there is a discotiuity i the curret distributio at z = 1mm, cylider height. The curret o the moopole at the resoat frequecy of the coaxial mode of the atea is depicted i Figure 4.5a for h = 8 mm ad h = 14 mm. This curret ca be separated ito two parts: resoat mode ad radiatio mode. These two modes are show i Figure 4.5b. The resoat mode is the quarter-wavelegth resoace of the coaxial trasmissio lie, as the figure shows. By cotiuig the curret, it crosses the z-axis at quarter wavelegth which is higher tha h due to the parasitic effects at the ed of the coax. As a example, the curret distributio (Figure 4.5a) for h = 8 mm, has a discotiuity exactly at z = 8 mm ad the resoat mode of the curret crosses the z-axis at z = 9 mm, which is associated with the resoat frequecy of f = 8.33 GHz. By icreasig the legth of the cylider to h = 14 mm, the crossig poit of the resoat mode of the curret with z-axis is z = 17 mm, which is associated with f = 6.4 GHz. 9

107 3 5 f = 3.7 GH f = 7.1 GHz f = 11.1 GHz J (ma/m ) z (mm) Figure 4.4The curret distributio o the atea at three resoat frequecies. J (ma) h=8 mm h=14 mm 15 curret 1 Resoat mode z (mm) (a) Figure 4.5 The curret distributio o the moopole atea at its coaxial mode resoace for two differet values of h, (b) resoat ad radiatio modes of curret. Accordig to Figure 4.3, ay chage i the resoat frequecy of the coaxial mode does ot chage the resoaces of the moopole sigificatly. Figure 4.6 shows the reflectio coefficiet of the atea for d = 1 mm, h = 1 mm, W = mm. The calculated S11 is depicted for differet values of s. By chagig the value of s, the itrisic impedace of the coaxial lie chages leadig to the chage i the iput impedace of the atea ad its quality factor at the resoat frequecy. As Figure. 4.6 shows, the badwidth of the atea is 3.5 GHz GHz for S11 < -1 db. The radiatio patter of the atea is see i Figure 4.7 at three frequecies for s = 1 mm. As it shows, the radiatio patter chages very slightly i the frequecy bad. I all cases, the groud 93 5 h (b) Radiatio mode z

108 plae is a circular plate of radius mm. By adjustig the resoat frequecies ad correspodig dampig factors of the CNRs, a ultra-widebad respose ca be achieved. Figure 4.8 depicts the reflectio coefficiet of the atea for two differet desigs S 11 db s = 1 mm s = 1 mm s = 14 mm Frequecy (GHz) Figure 4.6 Reflectio coeffiect of the atea for differet values of s. f = 3.5 GHz f = 4.5 GHz f = 5.5 GHz Figure 4.7 The gai of the atea versus elevatio agle at differet frequecies for h=8 mm. 94

109 -5 S 11 (db) Figure 4.8 Reflectio coefficiet of the atea for two differet desigs. Desig 1: s = 11 mm, W = mm, h = 5.5 mm, d = 18 mm, Desig 1: s = 9 mm, W = mm, h = 5.5 mm, d = 18 mm As ca be see, the atea is matched (S11 < -1 db) for wide rage of frequecies. For s = 11 mm, the atea has wider badwidth. The far-field gai of the atea for differet frequecies is depicted i Figure 4.9 for desig 1. Sice the curret has some variatios i its directio at higher frequecies, there are some ulls i the patter of the atea at those frequecies. The patter of the atea is omidirectioal because of the symmetry of the atea structure i φ directio. The radiatio field of the atea i time domai is show i Figure 4.3a for differet directios. The early-time ad late-time resposes are clearly visible i the time-domai respose. For better compariso, the ormalized value of the radiated field i far-field is see i Figure 4.3b for differet observatio agles. Although the CNRs of the fields do ot chage with observatio agle, but the dispersio characteristics of the atea chage slightly with directio. For higher elevatio agles, the atea is more dispersive. Additioally, there is some rigig origiatig from the resoat behavior of the atea. By placig two similar ateas 4 cm away from each other ad followig the equatios (4.13) to (4.16), the amplitude ad phase respose of S1 are show i Figure 4.31a ad 4.31b. The amplitude ad phase of the atea effective legth ca be extracted from S1 respose for θ = 9 ad φ =. The effective legth of the atea is useful i calculatig the impulse respose of the tag i chipless RFID systems. A atea prototype with dimesios of s = 11 mm, W = mm, h = 5.5 mm, d = 18 mm is fabricated i the VTAG atea lab Desig 1 Desig Frequecy (GHz) 95

110 (a) (b) (c) Figure 4.9 Gai of the atea at (a) f = 4 GHz, (b) f = 6 GHz, (c) f = 8 GHz, ad (d) f = 1 GHz. 7 (d) 3 E (V/m) Time (s) (a) = 9 = 45 = 5 Figure 4.3 (a) The radiatio field ad (b) ormalized radiatio field of the atea i far field. Normalized field Time (s) (b) = 9 = 45 = 5 Iput 96

111 -3 S 1 (db) Phase (S 1 ) (Degree) Frequecy (GHz) (a) Frequecy (GHz) (b) -3. H a (db) h a (m) Frequecy (GHz) (c) Time (s) (d) Figure 4.31 (a) amplitude ad (b) phase of S1 betwee two similar ateas whe they are spaced 4 cm far from each other, (c) amplitude ad (d) phase of the atea effective legth for θ = 9 ad φ =. The fabricated atea is show i Figure 4.3a. The atea is coected to Network aalyzer (Rohde & Schwarz, ZVA 5-series), as ca be see i Figure 4.3b. The measured reflectio coefficiet of the atea is depicted i Figure Based o the measured S11, the atea shows S11 < -1 db at the desired frequecy rage of GHz. The radiatio patter of the fabricated atea is measured i the chamber of Virgiia Tech Atea Group (VTAG). The co-polar ad cross-polar radiatio patter of the atea are show i Figure 4.34 at differet frequecies. 97

112 Figure 4.3 (a) Fabricated tag, ad (b ) Atea coected to the etwork aalyzer S 11 (db) Frequecy (GHz) Figure 4.33 Measured reflectio coefficiet of the atea. 98

113 (a) (b) (c) (d) Figure 4.34 Co- ad cross polar radiatio patter of the atea at (a) f =.7 GHz, (b) f = 4.8 GHz, (c) f = 6.9 GHz, ad (d) f = 9 GHz at xz ad yz plaes. 99

114 5 Time-Frequecy Techiques for Aalyzig Trasiet Scattered Sigal from Targets [8] (Chapter used with permissio of Spriger sciece ad busiess media, 15) Sice the scatterer is located at some distaces from the receivig atea, we eed a timefrequecy aalysis techique i order to extract desired spatial ad structural iformatio of the target. Oe importat parameter i time-frequecy aalysis of scattered fields is the resolutio of employed techique i time ad frequecy domais. I circumstaces where multiple scatterers or a scatterer with multiple scatterig ceters is located i the mai beam of the receivig atea, the resolutio i time domai is importat. While i the cases where the scatterer has multiple resoaces i close proximity of each other, the resolutio i the frequecy domai will be importat parameter [63]. Sometimes, we eed to employ a time-frequecy techique which provides acceptable resolutio i both time ad frequecy domais. As a example, whe multiple chipless RFID tags are preset i the reader area, good resolutio i the time domai improves the accuracy of the localizatio process ad o the other had, good resolutio i the frequecy domai ehaces the accuracy of the extracted iformatio from the scattered sigal. Based o Heiseberg ucertaity priciple, there is a restrictio o the product of time ad frequecy resolutios [64]. I this chapter, some practical time-frequecy techiques are studied. Startig with most practical oe, short-time Fourier trasform (STFT), the defiitios of time ad frequecy resolutio are preseted. The, the applicatio of wavelet trasform i scatterig process is preseted ad its drawbacks are discussed i detail. Re-assiged joit time-frequecy (RJTF) method is itroduced for improvig the frequecy resolutio. Fially, Short-time matrix pecil method (STMPM) is itroduced as a efficiet techique ad its correspodig resolutio i time ad frequecy is compared with other time-frequecy techiques. 5.1 Short-Time Fourier Trasform (STFT) Covetioal spectral aalysis of a sigal is based o Fourier trasform. The Fourier trasform of sigal x(t) is defied as j ft X f x t e dt (5.1) 1

115 This trasformatio is useful tool for aalyzig the spectral cotet of the statioary sigals ad it also simplifies some differetial equatios by covertig the itegratios ad derivatives to algebraic operatios i Fourier domai. The iverse Fourier trasform of sigal is writte by x t X f e jft df (5.) I practical applicatios, the sigal is ustatioary ad its spectral cotets chage with time. The most commoly used time-frequecy represetatio of sigal is STFT. I this techique, a slidig widow of fixed legth is moved alog the time axis of the sigal ad fast Fourier trasform (FFT) is applied to each time sapshot. Assumig h(t) as the widow fuctio, the STFT of the sigal x(t) is defied by STFT x t, f x h t X e H f jft e d j t d (5.3) The first equatio i (5.3) shows that STFT ca be thought of as a local spectral of the widowed sigal. The secod equatio shows that the widow ca be applied i the frequecy domai. I this view, STFT performs as a filter slidig i the frequecy domai. Oe useful widow fuctio usually used i practical applicatios is the Gaussia fuctio defied as h 1 t / t e (5.4) where δ is related to the stadard deviatio of the pulse. As a example, time-domai sigal i (5.5) is cosidered. x t Asi Asi 1t f 1t e 1t t t f te Bsif te 1 t t t t (5.5) This sigal ca be regarded as the scattered field from two sigle-resoace scatterers located at differet distaces from the atea, regardless of the early-time resposes. The sigal is show i Figure 5.1 for A = 3, α1 =.5e9, α =.8e9, B = 3, f1 = 6 GHz, ad f = 7 GHz. The spectrogram of the sigal is depicted i Figure 5. by applyig Gaussia widow defied i (5.4) to (5.5) for two values of δ. By chagig the variace of the Gaussia widow, its width chages, which leads 11

116 to the chage i the resolutio i time ad frequecy domais. By choosig δ = 1 (arrower widow i time domai), the time resolutio is improved ad as a result, the tur-o times of the resoat frequecies ca be see i the spectrogram; while the close resoat frequecies are ot distiguishable i the spectrogram. O the other had, by choosig δ = 1, the frequecy resolutio is ehaced at the expese of deterioratio of time resolutio. Hece, the resolutio of the trasformed sigal is strogly depedet o the widow fuctio. For better illustratio, the timedomai sigal of jf t is cosidered [65]. By applyig STFT with the Gaussia x t t t e fuctio of δ to the time-domai sigal, the trasformed sigal is give by STFT x 1 tt / jft f f j f f t t, f e e e e (5.6) The trasformed sigal see i (5.6) shows clearly the effect of δ o the resolutio i time ad frequecy. It is desirable the STFT to be cocetrated aroud t = t ad f = f, because the sigal icludes a impulse at time t ad a impulse at frequecy f. But, the STFT of the sigal has two pulses aroud t=t ad f=f. As (5.6) shows, ay icrease i δ improves the frequecy resolutio ad deteriorates the time resolutio ad vice versa. Therefore, by choosig δ i betwee these two limits, oe has limited resolutio i time ad frequecy Resolutio It is more desirable to quatify the cocept of the resolutio i time ad frequecy domais. The time resolutio, t of the widow fuctio, h(t) is defied by t t h dt t (5.7) h dt t It meas that two pulses ca be distiguished i time domai if they are more tha t apart [65]. Similarly, the frequecy resolutio is defied by H d H d (5.8) 1

117 3 1 Amplitude -1 - Figure 5.1Time-domai sigal Time (s) (a) (b) Figure 5. Spectrogram of the sigal for (a) δ =.8e-9, ad (b) δ = 4e-9 Two frequecies ca be discrimiated i the frequecy domai if they are more tha apart. There is a itrisic limitatio o the time ad frequecy resolutios, which is govered by Heiseberg priciple as 1 t (5.9) For Gaussia widow defied i (5.4), the time ad frequecy resolutios are as 1. t ad 13

118 5. Wavelet Trasform As aother time-frequecy techique, wavelet trasforms are widely beig used i sigal processig. I STFT aalysis of a sigal, the legth of the widow is fixed i whole time-frequecy plae leadig to fixed time ad frequecy resolutios. The wavelet trasform of x(t), a squareitegrable fuctio, is defied by W x s xt h t, dt (5.1) s, where asterisk deotes the complex cojugates. The wavelets are geerated from a mother wavelet, h, as h s 1 t, t h (5.11) s s where s ad τ are the scale ad traslatio factor. The dimesio of s is Hz. The wavelet trasform of sigal x(t) is the trajectory of the sigal ito the wavelet basis fuctios with differet traslatio ad scale factors. The wavelets are dilated as s > 1 ad are cotracted whe s < 1. By ormalizig the wavelet basis as (5.11), their eergy is equal to 1 for ay traslatio ad scale. The wavelet trasform of the sigal ca also be writte versus the Fourier trasforms of the sigal ad widow fuctio as W x s j, e d (5.1) s X H s where H is the Fourier trasform of h(t). I this view, the wavelet trasform ca be assumed as a bak of wavelet filters with differet scales ad shifts correspodig to e j. As (5.1) shows, the wavelet trasform of a sigal depeds o the wavelet basis, h. Various wavelet fuctios are itroduced for differet applicatios. There are some coditios which wavelets should satisfy amog them admissibility ad regulatory properties are the most importat. Satisfyig these two coditios, oe ca make his ow wavelet for a special applicatio. As a importat property, o iformatio should be lost durig the trasformatio. This ca be expressed by the followig resolutio of idetity for two arbitrary fuctios of f1 ad f [65]. 14

119 1 f1, hs, f, hs, d d c f1, f (5.13) s where f, h shows the ier product of fuctio f ad wavelet h ad c is a costat. It is easy to show that c H d (5.14) Relatio (5.14) implies that the itegratio of the ier products of h with f1 ad f over all the scalig ad traslatio parameters is proportioal to the ier of the two fuctios. By removig f from the two sides of (5.13), the iverse wavelet trasform ca be writte by x 1 c 1 t W s, h d d t 1 (5.15) s x s s Therefore, the time-domai sigal ca be recovered from its wavelet trasform. It implies that o iformatio will be lost durig the trasformatio process. The costat value of c implies that H() =, or equivaletly t dt h (5.16) The coditio (5.16) which guaratees the oscillatory behavior of the wavelet fuctio is called admissibility property. The weaker coditio o wavelet is regularity coditio, which implies that wavelet should be local i time ad frequecy domais. Assumig τ = ad expadig sigal x(t) ito the Taylor series at t =, oe has [65] W x N 1 t t t s x h dt Rt h dt, (5.17) s! s s where R is the remider of the Taylor series. The r-order momet of the wavelet is writte by t r M r t h dt (5.18) 15

120 By chage of variables i the itegrals i (5.17) ad usig (5.18), the wavelet trasform at τ = is writte by f 1 f 1 Wx s, xm s M1s M s O s (5.19) s 1!! Based o the admissibility property, M =. Therefore, the speed of coverge of the above series with decreasig s is determied by the first o-zero term i the series. The -order wavelet is oe which its first -order momets are zero. t or equivaletly i the Fourier domai, oe ca write M t h dt (5.) H (5.1) This coditio exhibits the smoothess of the wavelet at f =. For the wavelet of order, wavelet trasform is decayed by s +1/. Additioally, it has first +1 vaishig momets decayig by t -. Therefore, the wavelet trasform is a oscillatory fuctio which is localized i both time ad frequecy domais. I compariso to STFT, by choosig small value of the scale, the wavelet aalysis permits to aalyze the discotiuities, sigularities ad edges i more detail ad it gives the global view of the sigal for large scales. This property of the wavelet is depicted i Figure As it shows, for larger scales correspodig to low frequecies, the wavelet is dilated ad for smaller scales, it cotracted. The badwidth of wavelet at scale s is s Therefore, its quality factor is defied as H s d (5.) H s d s 1/ s 1 Q (5.3) s 16

121 1/s Figure 5.3 Time ad frequecy resolutios i wavelet trasform. τ Hece, the wavelet trasform is costat-q aalysis. For low frequecies, it has small badwidth or wider time widow. O the other had, for high frequecies (low scales), it adopts larger badwidth leadig to the smaller time widow. As a example, the sigal i (5.4) is cosidered. The wavelet trasform of the sigal is depicted i Figure 5.4 by usig Morlet basis fuctio. It is see that aroud s = 1 correspodig to the resoat frequecy of the sigal, the wavelet trasform has stroger value. I multi-resoat sigals whe the resoaces are close to each other, the detectio of the resoaces usig wavelet trasform is ot easy. However, i the processig of the scattered sigals from resoat-based targets, oe eeds much better resolutio i time ad frequecy i order to extract the required data from the sigal. Some wavelet families have bee itroduced for time-frequecy aalysis of differet types of sigals. Figure 5.5 shows some practical wavelets. Oe ca chose the desired wavelet based o the shape of the sigal. Some approaches such as Wiger-Vile, adaptive time-frequecy represetatio ad so o were itroduced for ehacig the resolutio i both time ad frequecy domais [63]. I most of the proposed techique, some iterfereces preseted i the time-frequecy which are ot suitable for aalyzig of scattered sigal from resoat-based structures. 17

122 s x Figure 5.4 Wavelet trasform of the sigal. 5.3 Re-assiged Joit Time-Frequecy (RJTF) I previous sectios, two commoly used techiques for time-frequecy aalysis of time-domai sigals were studied. I both techiques, as (5.3) ad (5.1) show, the trasformed sigal depeds o the characteristics of the widow fuctio. I these approaches, the amplitude of the trasformed sigal is plotted i a time-frequecy plae. I geeral, each time-varyig sigal ca be expressed i time ad frequecy by X x t at exp jt (5.4) f A f exp j f (5.5) where X is the Fourier trasform of x ad a ad A are real positive quatities. The istataeous frequecy ad the group delay of a sigal are oe-dimesioal trasformatios tryig to represet the temporal ad spectral sigal characteristics simultaeously. For the sigal show i (4.4) ad (.5), these parameters are calculated as f i t g 18 t 1 d (5.6) dt f 1 d (5.7) df

123 (a) Haar (b) Db (c) Coeflet (d) Sym (e) Morlet Figure 5.5 Some practical wavelets (f) Mexica Hat These time-frequecy represetatios provide some drawbacks for multi-resoat sigals. Assumig the followig sigal [66] 19

124 t x j f 1t jf t e e (5.8) With some mathematical maipulatios, it is easy to show that the istataeous frequecy of the sigal is (f1+f)/. Oe ca fid so may sigals with the same istataeous frequecy. I order to study the effect of widow fuctio, we start with some simple cases. I the first group which is called amplitude maximum of the spectrum (MS), a widow of legth Δt is moved alog the time axis ad the spectrum of the widowed sigal is calculated versus time idex. Assumig the rectagular pulse as the widow fuctio located at t=t, the the spectrum of the sigal is S t t / t, f at exp j t t t / jf dt (5.9) We cosider two limits of Δt i the calculatio of S. I the first case, t, the S t t / t, f at exp j t t t / jf dt (5.3) Therefore, quatity S is maximum at the frequecy for which the phase is statioary as 1 d f m (5.31) dt t which is the istataeous frequecy of the sigal. For t, St, f X f which is a lie parallel to the time axis i the time-frequecy plae. The secod case is related to the secod equatio see i (5.3), which is called the maximum evelope method (ME). I this method, a rectagular pulse of width f-δf/ to f+δf/ i the frequecy domai moves alog the frequecy axis ad iverse Fourier trasform (IFFT) is applied to each widowed sigal as t f f / t, f X f exp j ft S df (5.3) f f / For f, the time at which S has a maximum is give by t m f 1 d (5.33) df f 11

125 which is the group delay time as a fuctio of frequecy. For f, St, f xt is a lie parallel to the frequecy axis i the time-frequecy plae. Hece, it is see that i these two cases the trasformed sigal i the time-frequecy axis depeds strogly o the legth of the widow chose i time or frequecy domais. I the third case, the eergy distributio ca be calculated for (t,f). Assumig f f / t, f X f exp j ft S df (5.34) f f / The itegrated eergy distributio at (t,f) is distributio is idepedet of t for f X f f. It is easy to show that the eergy ad is equal to x(t) for f I all above metioed time-frequecy aalysis techiques icludig STFT, the trasformed sigal is writte by The origial sigal ca be recovered from * f xt h t X dt (5.35),, f. t X f h t d df x, s (5.36), There is a ifiity of maers for defiig h; here we chose Assumig s jf t t g te h, (5.37) t dt 1 g (5.38) By isertig (5.37) i (5.35), the trasformed sigal is give by X jf, f e xt g t j, f A, f e e jft dt (5.39) Hece, the origial sigal ca be recostructed as 111

126 x j f j ft f t A f g te,., d df (5.4) If the time variatios of A ad g are slow compared to phase variatios, the maximum cotributio to the itegral emaates from the regios close to the statioary coditios as j, f j ft f e (5.41) f e j, f j ft f (5.4) The statioary-phase poits are 1, f t (5.43) f f 1, f (5.44) which are related to group delay ad istataeous frequecy of the filtered sigal. I re-assiged joit time-frequecy (RJTF), the eergy desity S(τ,f) is assiged to the poit of coordiates t, f istead of (τ, f). Now, the effect of the widow legth o the trasformed sigal ca be explored with subject to (5.34). For f, usig (5.43) ad (5.44), oe obtais t 1 arg X f f (5.45) (5.46) f f which is correspodig to the group delay at the frequecy f ad for f, oe has t t (5.47) xt 1 arg f (5.48) t which is the istataeous frequecy at t = t. I RJTF, the distributio eergy chages from group delay to istataeous frequecy curves i the time-frequecy plae by chagig the widow legth from to +. Assumig the STFT of the sigal x(t) as 11

127 X xt t jf t, e e dt (5.49) i which the Gaussia pulse has bee used as the widow fuctio. The istataeous time ad frequecy ca be calculated from [67] f ic f 1 Im X (5.5) t ic t Im (5.51) X I Figure 5.5, the time-frequecy represetatio of the sigal see i (5.4) is depicted for A= 3, α1 =.5e9, α =.8e9, B= 3, f1 = 6 GHz, ad f = 7 GHz. As it shows, the resoat frequecies ad tur-o times of the resoaces ca be easily see from its time-frequecy represetatio Time (s) Frequecy (GHz) Figure 5.6 Time-frequecy represetatio of sigal by RJTF ad δ =.6e Short-Time Matrix Pecil Method (STMPM) Based o sigularity expasio method (SEM) expressed i sectio.1, the backscattered respose from scatterers ca be expaded versus the complex atural resoaces. For complex scatterers with multiple scatterig ceters ad multiple resoaces, differet resoat frequecies might have 113

128 differet tur-o times. Depedig o the polarizatio ad the directio of the icidet field compared to the scatterer, some resoaces might be excited stroger tha the others. I these applicatios, there are two importat factors eed to be cosidered i the time-frequecy represetatio of the sigal. First as metioed before, time ad frequecy resolutios should be improved i order to extract the positio of the scatterer ad its resoat frequecies. The other factor is the robustess of the employed approach i extractig the weak resoaces i the presece of the stroger oes. Recetly, aother time-frequecy method, called short-time matrix pecil method (STMPM), is proposed which shows good performace as a view of resolutio ad ability to extract low eergy resoaces. I reality, there is a uique dampig factor correspodig to each resoat frequecy. Therefore, istead of workig o the spectral cotet of the scattered sigal i Fourier domai, it is more iformative to work o complex atural resoaces (CNRs) i Laplace domai. I some scearios such as desig process of resoat-based scatterers, the kowledge of the dampig factors of the resoaces give some more iformatio about the structural dimesios ad electromagetic behavior of the scatterer. Takig advatage of STMPM, the dampig factors of the CNRs ca be obtaied from its scatterig respose. As metioed i sectio.4, the scatterig respose from the scatterer is affected by two differet pheomea: the early time is due to the specular reflectios from the scatterig ceters of the scatterer ad is followed by the-late time respose which is the radiatio fields from the atural modes of the scatterer. I geeral, the scattered field ca be writte as t t et R e cos t s 1 (5.5) where e(t) is the early-time respose ad the late-time respose is expaded versus the atural resoaces of the scatterer as s = α+jω with correspodig residue, s. I 199, matrix pecil method (MPM) is employed to extract the complex atural resoaces of the damped siusoidal sigals [68]. I this techique, by samplig the time-domai sigal, two matrices are itroduced, which the CNRs are the geeralized eigevalues of their associated pecil Matrix Pecil Method (MPM) [68] MPM is a techique used for extractig the CNRs of the damped siusoidal sigal. First, the late-time respose of the scatterer as the summatio over damped siusoidals is cosidered as 114

129 115 M m t s m m e R t y 1 (5.53) By samplig the sigal, the k th sample is M m t s m k k m e R t y 1 (5.54) where t s e z (5.55) Quatity M is the umber of the poles i the sigal, k=, 1,., N-1 is the sample idex ad Δt is the samplig iterval. Igorig the oise, two followig matrices are formed by samplig data. L L N N Y L N y L N y L y y y L y y y Y (5.56) L L N N Y L N y L N y L y y y L y y y Y (5.57) where L is a umber betwee N/3 ad N/. Two matrices i (5.56) ad (5.57) ca be decomposed for a arbitrary L<N-1 i the followig maer 1 1 Z R Z Y (5.58) 1 Z Z R Z Y (5.59) where [Z] ad [R] are diagoal matrices 1 N diag,,, Z z z z (5.6) 1 N diag,,, R R R R (5.61) ad

130 1 1 1 z1 [ Z1] z zm z 1 z z N L1 N L1 N L1 N N L N (5.6) 1 1 [ Z] 1 z L1 1 1 z z L1 M z z z L1 M NL (5.63) By costitutig the followig matrix pecil as Y Y Z R Z I (4.64) 1 1 Z where [I] is a N N idetity matrix, it is easy to show the i th row of Z I is zero for λ = zi (I = 1,, N). Therefore, zi is the geeralized eigevalue of the matrix pair [Y], [Y1]. Thus, the zis are calculated by solvig the followig ordiary eigevalue problem. Y Y I 1 (5.65) where [Y1] + is the Moore-Perose pseudo-iverse of [Y1]. For oisy data, some prefilterig must be used i order to remove extra poles resultig from oise. I this case, first the followig matrix is formed usig sampled data as Y y y y y1 yl 1 y yl 1 N L 1 yn L yn L N L L1 (5.66) As ca be see, [Y1] ad [Y] are obtaied from [Y] by removig the last ad the first colums, respectively. A sigular-value decompositio (SVD) of the matrix [Y] ca be writte as Y U V H (5.67) where [U] ad [V] are uitary matrices. The parameter M, estimated umber of CNRs i the sigal by MPM, is itroduced as a threshold ad the sigular values beyod M are set to zero. I theory 116

131 ad oiseless data, M is equal to the umber of CNRs cotaied i sigal. A appropriate way to choose M is through lookig at the ratio of the maximum sigular value to all other sigular values i the matrix. Cosiderig c as the sigular value such that max 1 c p (5.68) where p is the umber of sigificat decimal digits i the data. For istace, if the measuremet data is kow to be accurate up to three sigificat digits, the the sigular values for which the ratio i (5.68) are less tha 1-3 are the sigular values of measured oise. The chose value of p depeds strogly o the stregth of the weakest pole compared to the strogest oe. For low values of p, the weak poles ca ot be detected i the presece of the much stroger poles. By icreasig the value of p, the weak poles ca be extracted at the expese of arrival of poles from oise. The ext step is to costruct the filtered matrix domiat right-sigular vectors [V]. V V v, v,, v. It is costructed such that it cotais oly M (5.69) 1 M Now, by suppressig the sigularities correspodig to the oise, [Y1] ad [Y] ca be costructed. where V 1 ad V U V H Y 1 1 (5.7) U V H Y (5.71) are obtaied from [V] by removig the first ad last rows ad [ ] is obtaied from the M th colum of [ ], correspodig to the M domiat sigular values. Followig the same approach as i (5.64), the poles of the sigal ca be obtaied. Oce the poles ad M are kow, the residues Ri are foud from the followig least squares problem. 1 y R1 y z1 z z M R N 1 N 1 N 1 y N 1 z R 1 z zm M (5.7) 117

132 5.4. STMPM i Late-Time I STMPM, a slidig widow of legth TW is moved alog the time axis ad matrix pecil method is applied to each widowed sigal [69]. Figure 5. 7 shows a time-domai sigal alog with the slidig widow located at t = T. As a simple scatterer, cosider the late-time respose of the sigal see i (5.73). L t t R e cos t U t t 1 (5.73) where U is the step fuctio defied as 1 t t U t t (5.74) t t I (5.73), it is assumed that all CNRs of the scatterer start resoatig at the same time, t, called tur-o time. This is valid for simple scatterers such as chipless RFID tag. Meawhile, for complex scatterers such as airplae ad so o, each resoace might have its ow tur-o time. The turo times give some iformatio about the locatio of the scatterig ceters of the scatterer compared to the receivig atea. Accordig to Figure 5.7, a time-widow of legth TW is moved alog the time axis icremetally by the value of T. Poles ad residues of each slidig widow are computed usig MPM ad they are idexed by T to realize a time-frequecy represetatio. The widowed sigal ca be writte by i which N e t Re R e U t t T stt (5.75) W 1 R T R e st j T Re (5.76) I atural logarithmic scale, (5.76) is expressed by T L R L R T (5.77) 118

133 8 6 4 amplitude T T W Time (s) Figure 5.7 Time-domai sigal with movig widow. Equatio (5.77) idicates that i ormal logarithmic scale, residues liearly decrease versus T with slope α. The real part of the poles, α, calculated from MPM are very sesitive to oise. A alterative way of calculatig the dampig factors of the CNRs is to fid the slopes of the residues versus time i the ormal logarithmic scale as (4.76) shows. The simulatio results preseted i this sectio will show that the CNRs calculated from STMPM are more accurate tha those from MPM. By calculatig the poles ad residues, three differet diagrams (time-frequecy, timedampig factor, ad time-residue) ca be used i detectio ad localizatio of scatterers. As a simple case, the followig sigal is cosidered. s cos cos 1 t t t R e f t R e f t (5.78) Figure 5. 8a shows sigal s(t) versus time for R1 =, R = 1.5, α1 = 3e8, α = 5e8, f1 = 5e9, f = 7e9, φ1 = π/4, ad φ = π/3. By applyig STMPM to the time-domai sigal, its time-frequecy ad 4 5 Amplitude Time (s) T (s) Frequecy (GHz) 119

134 5 (a) 5 (b) 4 4 T (s) 3 T (s) (c) Figure 5.8 (a) Time-domai sigal, (b) time-frequecy, (c) time-dampig factor ad (d) timeresidue diagrams of the sigal. time-dampig plots are depicted i Figure 5.8b, 5.8c, ad 5.8d. Two resoat frequecies ad their correspodig dampig factors are see clearly i the Figure. Figure 5.8d shows the ormal logarithm of the residues of the CNRs versus time. The slope of the lies is associated to the dampig factors of the CNRs. Two importat parameters of STMPM are the filterig parameter p ad widow legth, TW. I practical applicatios, it is very importat to choose the optimum values of p ad TW to extract the time ad frequecy iformatio from oisy data. Frequecy resolutio deals with the miimum distace betwee two adjacet resoat frequecies of the sigal which ca be distiguished. Assumig sigal see i (4.77) with R1= R= 1, α1= α= 3e8, f1= 5 GHz ad Δ= f-f1, the miimum widow legth required for distiguishig two poles of the sigal is represeted i Figure 5.9 i terms of Δ= f-f1 for differet values of p. For lower Δ, larger TW is required. This is commo i all time-frequecy approaches. O the other had, by icreasig p, smaller widow eed to be used. Employig smaller widow legth meas improvig the time resolutio. Therefore, it is possible to improve the time ad frequecy resolutios by applyig STMPM with optimum values of p ad TW. For better compariso, the time-frequecy represetatio of the sigal see i (5.78) is show i Figure 5.1 by applyig STMPM ad RJTF techiques to the time-domai sigal. The legth of the applied widow i both methods is TW =.5s. Compared to STMPM result, there are some iterfereces i betwee two resoaces of the sigal whe we use RJTF with the same widow legth. Additioally, there are slight variatios i the resoat frequecies of the sigal at time istaces. Therefore, the proposed techique ca be useful whe high desity of data is places o the tags (s -1 ) x L( R ) (d)

135 7 6 5 p= p=3 p=4 p=5 T W (s) (GHz) Figure 5.9 Miimum widow legth for distiguishig two resoaces of the sigal versus frequecy distace [7] (With permissio, Copyright 15 IEEE). T (s) Time (s) Frequecy (GHz) (a) Frequecy (GHz) (b) Figure 5.1 Time-frequecy represetatio of the sigal by applyig (a) STMPM ad (b) RJTF. I order to study the ability of the proposed techique i extractig low power CNRs i the presece of the stroger oes, the sigal see i (5.78) is cosidered with R1 = 3, R= 1, α1 = α = 5e8, f1 = 5e9, f = 6e9, ad φ1 = φ =. The sigal ad its time-frequecy represetatio are depicted i Figure 5.11 for differet values of TW ad p. The residue of the first pole is 3 times stroger tha the first oe s. For TW = 1.1 s ad p =, the stroger resoat frequecy is detected by STMPM. By icreasig the time widow to TW = 4 s, agai the stroger resoace is detected. 11

136 While by icreasig filterig parameter to p = 4, ad keepig TW = 1.1 s, both resoaces are detected. This is very importat i scatterig processes where some poles are excited stroger tha the others. As the results show, by icreasig the value of p, ot oly is the resolutio i time ad frequecy domais improved, but the weaker CNRs of the sigal ca be detected i the presece of the stroger oes. Amplitude Time (s) (a) 8 6 T (s) Frequecy (GHz) (b) 8 6 T (s) 4 T (s) Frequecy (GHz) (c) Frequecy (GHz) (d) Figure 5.11 (a) Sigal i time domai, Time-frequecy represetatio of sigal for (a) TW = 1.1 s, p =, (b) TW = 4 s, p =, ad (c) TW = 1.1 s, p = 4 [7] (With permissio, Copyright 15 IEEE) STMPM i Early Time Matrix pecil method (MPM) was first itroduced as a techique to extract the CNRs of the damped siusoidal sigals. Accordig to the discussio i sectio.4, a etire-domai fuctio eeds to be added to the series of damped siusoidals i order to guaratee the covergece of the series. It meas that the received sigal icludes a early-time respose followed by the damped siusoidals i the late time. Now the questio is how STMPM works for early-time resposes of 1

137 the scatterers. I other word if oe ca expad a impulse sigal i terms of damped siusoidals. Based o Fourier series, each time-limited sigal i ca be expaded versus siusoidal sigals as t, T W x t A cos t TW (5.79) I theory, the series has ifiite umber of terms. But i practical applicatios, it is trucated to a fiite umber of siusoidals to achieve the desirable accuracy. I UWB applicatio, the early-time respose is a pulse-shaped sigal coverig all the excited frequecies. Depedig o the locatio of the observatio poit compared to the scatterer, it ca be expaded versus the icidet filed ad its itegratio ad derivatives with respect to time [17]. I simple scatterers such as chipless RFID tag where the scatterer is approximated by just oe scatterig ceter i the frequecy bad of operatio, the early-time respose is approximated by just oe term. I the ear-field of the scatterer it is very similar to the icidet field, while i the far field it iclied to the first time derivative of the icidet field. I complex scatterers with multiple scatterig ceters, more terms eed to be cosidered i the series. As a example, the followig Gaussia sigal is assumed. t exp t x / (5.8) The time-domai sigal see i (5.8) ad its first derivative with respect to time are depicted i Figure 5.1 for δ =.5e-9 ad τ =.15 s. The derivative of the sigal is ormalized to its maximum value. By applyig STMPM with TW = s ad p = 3 to the sigal, its pole diagram is depicted i Figure As it shows, the origial pulse is approximated by four damped siusoidal sigals. These four sigals are depicted i Figure By summig the four damped siusoidals, the recostructed sigal is depicted i Figure 5.15 alog with the recostructed sigal based o Fourier series of the pulse. As it shows, the recovered sigal by damped siusoidals is more accurate tha oe resulted from Fourier series with the same umber of terms, M = 4.Assumig the legth of widow as TW = s i Figure 5.1, the positio of the pulse is chaged i the widow. 13

138 1 Gaussia pulse first derivitive Normalized amplitude T W Time (s) Figure 5.1 Gaussia pulse ad its first derivative with respect to time Frequecy (GHz) (s -1 ) x 1 1 Figure 5.13 Pole diagram of the Gaussia pulse fuctio. 14

139 8 Amplitude 4 Amplitude Time (s) (a) Time (s) (b).1 Amplitude 1.5 Amplitude Time (s) (c) Time (s) (d) Figure 5.14 Four extracted damped siusoidal modes by applyig STMPM to the Gaussia pulse. Amplitude Gaussia pulse Recostructed from Fourier series Recostructed from CNRs Time (s) Figure 5.15 Gaussia pulse ad recostructio oe from Fourier trasform ad CNRs. 15

140 The pole diagram of the pulse is show i Figure 5.16 for differet values of τ. By movig the pulse from left to the right of the widow, the extracted CNRs move to the right side of the imagiary axis either. For τ < 1 s, the CNRs must be highly damped resoaces leadig to the poles located at the left had side of the pole diagram. O the other had, for τ > 1 s, costructive sigals must grow with time leadig to the CNR located at the right had side of the pole diagram. For τ =.5 s ad τ = 1.5 s whe the pulse is located at the same distace from the ceter, the poles are asymmetrically located at two sides of the imagiary axis. By movig the pulse away from the ceter of the widow, the poles move away from the imagiary axis ad whe it is at the ceter, they are o the imagiary axis. Whe the pulse is located at the ceter of the widow, τ = 1 s, the poles are located o the imagiary axis of the pole diagram with more terms. It meas that whe the pulse is at the ceter of the widow, the series of the CNRs iclies to the Fourier series of the sigal. Sice the poles are o-damped siusoidals, more terms are eeded to achieve the required accuracy. The recostructive sigals are depicted i Figure 5.17 for differet τs ad TW = s. For τ =.5 s, the recostructed sigal is zero for t > s either. I the case of τ = 1 s where the poles are close to the imagiary axis, Gibbs pheomeo is see at sharp variatios of the sigal. Accordig to Figure 5. 17c, by icreasig p i STMP, more terms are icluded i the series ad the accuracy of the recostructed sigal is improved. Sice the poles are ot perfectly located o the imagiary axis, there is a sharp discotiuity at the ed of the time widow. For τ = 1.5 s whe the pulse i the RHS of the widow, the recostructed sigal is similar to the origial oe i t[,e-9]. But it has very sharp variatios for larger time values. These sharp variatios emaate from the growig siusoidal sigal summed together. Based o the preseted results i Figures 5.15 to 5.17, it is see that the recostructed sigal approximates the origial oe for t [ T, T TW ]. The width of the early-time impulses is related to the badwidth of the icidet field. By icreasig the badwidth, the impulses become arrower. I far-field regio, the shape of the scattered field iclies to the derivative of the icidet field. Assumig the Gaussia pulse see i (5.8), its ormalized derivative with respect to time is show i Figure 5.1. By chagig the positio of the sigal i the time widow, the extracted poles are show i Figure 5.18 for differet values of τ. 16

141 Frequecy (GHz) =.5 s =.5 s =.75 s =1 s =1.5 s =1.5 s =1.75 s (s -1 ) x 1 1 Figure 5.16 Pole diagram of the Gaussia pulse for differet values of τ. 1.5 Amplitude.5 Amplitude Time (s) (a) Time (s) (b) 1 1 Amplitude Amplitude Time (s) (c) Time (s) (c) Figure 5.17 Recostructed pulse sigal for (a) τ =.5 s, p = 4, (b) τ = 1 s, p = 4, (c) τ = 1 s, p = 8, (d) τ = 1.5 s, p = 4. 17

142 Frequecy (GHz) 1-1 =.5 s =.5 s =.75 s =1 s =1.5 s =1.5 s =1.75 s (s -1 ) x 1 1 Figure 5.18 Pole diagram of the derivative of Gaussia pulse for differet values of τ. Agai, by movig the pulse to the RHS of the widow, the correspodig poles move to the RHS of the pole diagram. Whe the pulse is located at the ceter of the widow, the poles are very close to the imagiary axis of the pole diagram. Figure 5.19 shows the recostructed sigal based o Fourier series ad summatio over CNRs with M = 4 compared to the origial sigal. As ca be see, the origial sigal is accurately costructed by summig over CNRs. While it eeds more terms i Fourier series to achieve the desired accuracy. Accordig to above metioed discussio, the CNRs of the early-time respose move from the LHS to the RHS of the pole diagram whe the widow moves alog the time axis. This is very useful i detectig the early-time respose of the scatterers. I Figure 5., the extracted dampig factors of the Gaussia pulse ad its derivative located at τ =.15 s is depicted versus the ceter of the slidig widow by applyig STMPM to the time-domai sigal. As it shows the dampig factors are zero whe the pulse is located at the ceter of the widow. For the derivative of the pulse, there are two other zero crossig poits coicidet with the positio of the maximum ad miimum poits of the sigal i additio to the ceter of the pulse located at τ =.15 s. As aother example, the scattered sigal from a resoat structure is depicted i Figure 5.1a. By applyig STMPM with TW = 1 s to the sigal, the extracted poles of the scatterer is depicted i Figure 5.1b for differet slidig times. The earlytime respose of the scatterer is cetered at t = 1.55 s. As it shows, the extracted poles move from the RHS of the pole diagram to the LHS by slidig the widow alog the time. The CNRs of 18

143 1.5 Origial sigal Recostructed from Fourier series Recostructed from CNRs Amplitude -.5 Figure 5.19 Derivative of the Gaussia pulse ad recostructio oe from Fourier trasform ad CNRs Time (s).3.3 T+T W / (s)..1 T+T W / (s) (1/s) x 1 1 (1/s) x 1 1 (a) (b) Figure 5. Extracted dampig factor versus the ceter of the slidig widow for (a) pulse, ad (b) its derivative. the late-time respose are show i the figure. They do ot chage by slidig widow alog the late-time sigal. O the other had, the poles of the early-time respose vary as a fuctio of T. This ca be helpful i separatig the early-time respose from the late-time oe. I Figure 5.1c, the extracted dampig factors are show as a fuctio of widow s ceter time. The positio of the early-time respose is clearly see at t = 1.55 s where the dampig factors are zero. The dampig factor of the CNR i the late time respose is see i Figure 4.1c. I secod example, two scatterers are assumed 1 cm away from each other. The radar cross-sectio (RCS) of the secod scatterer is cosidered much smaller tha the first scatterer RCS. Figure 5.1d shows the 19

144 received scattered sigal from the scatterers by illumiatig them by a icidet electric field. The early-time respose of the first scatterer is followed by the late-time respose origiatig from the atural modes of the scatterer. The early-time of the secod scatterer is hidde i the late-time of the first target. Sice its dimesios are much smaller tha the lowest wavelegth of the icidet field, it does ot excite the CNRs of the secod target. By applyig STMPM to the time-domai sigal, the extracted dampig factors are show i Figure 5.1e versus the ceter of the slidig widow. The zero crossig of the dampig factors show the positio of the early-time resposes of the scatterers. By extractig the CNRs of the early-time ad late-time resposes, the recostructed early time ad late time are depicted i Figure 5.1f. The tur-o time of the resoace ad positio of the scatterers ca be accurately obtaied from the proposed techique. The locatio of the scatterers ca be calculated by kowig the ceters of the early-time resposes Performace of STMPM Agaist Noise Noise is ay uwated sigal which iterferes with the desirable sigal. Detectio i the presece of oise is very challegig whe the backscattered sigal is ot very strog. Because the ormal radiatio modes of the scatterer are damped siusoidals, the sigal to oise ratio decreases with respect to time. I commuicatio systems, the domiat oise is additive white Gaussia oise (AWGN). White oise is a radom sigal with a costat power spectral desity. Assumig the iput oise as AWGN, the received sigal is represeted as s t t et R e cos t t 1 (5.81) where e(t) is the early-time respose ad (t) is AWGN. The secod term is the late-time respose icludig the CNRs of the scatterer. For th CNR, the correspodig sigal is s t t R e cos t t xt t (5.8) With aforemetioed assumptios o oise, its power spectral desity ad correlatio fuctio are defied as N S N f (5.83) 13

145 Amplitude (mv/m) 4 - frequecy (GHz) 4 - T=.7 s T=1 s T=1.3 s T=1.6 s T=1.9 s Late-time CNRs Time (s) (a) (1/s) x 1 1 (b) T+T W / (s) (1/s) (c) x 1 9 Amplitude (mv/m) Time (s) (d) T+T W / (s) s s (1/s) x 1 1 (e) Amplitude (mv/s) Time (s) (f) Early time Late time Figure 5.1 (a) Backscattered electric field from the scatterer, (b) pole diagram of the sigal for differet slidig times, (c) extracted dampig factors with respect to the ceter of the slidig widow, (d) backscattered electric field from two scatterers, (e) extracted dampig factors with respect to the ceter of the slidig widow, ad (f) recostructed early-time ad late-time resposes. 131

146 S SNR S x N T TTW x t dt H f KT df c (5.86) where K= (m Kg s - K -1 ) is the Boltzma costat, Tc is the temperature i Kelvi, ad H(f) is the sice fuctio correspodig to the Fourier trasform of the rectagular pulse of width TW i time domai. After some mathematical maipulatios, the SNR i (5.86) is give by SNR e T 4KT T c e R TW 1 cos T si T 1 cos T T si T T W W W W (4.87) Accordig to (5.87), SNR is proportioal with the square of the residue of the CNR ad decreases with ay icrease i dampig factor. For log-read distaces, the residues decrease leadig to smaller SNRs. As it shows, by slidig the widow alog the time, the eergy of sigal decreases, while the eergy of oise does ot chage. Hece, higher SNR is accessible at the earlier times of the sigal. I scatterig from multi-resoat structures, oe eed a few umber of cycles i order to detect all the resoaces from the scattered sigal. O the other had, i scatterig from lossy media, the dampig factors of the CNRs might be large eough to atteuate the respose very fast. I such cases, the kowledge of the tur-o time of the CNRs is very useful. Because by placig the slidig widow just before the tur-o time, some CNRs from the early time respose might come ito the pole diagram of the sigal. I order to study the effect of oise o STMPM, the backscattered sigal from a 3-bit tag is see i Figure 5.a. The early-time ad late-time resposes are clearly see i the figure. By applyig the proposed method to the time-domai sigal, the time-frequecy, time-dampig factor ad time-residue of the sigal is depicted i Figure 5.b, 5.c, ad 5.d for TW =.8s ad p =. The poles of the early-time respose are coverged to the poles of the late time at tur-o times. Compared to resoat frequecies, there are some variatios i the extracted dampig factors. The tur-o time of the CNRs of the tag is show i the time-frequecy represetatio of the sigal as t =.65s. By addig oise to the sigal, the time-dampig factor ad time-residue of the sigal are show i Figure 5.3 for SNR = 15dB. As the results show, the dampig factor is very sesitive 13

147 Time (s) Time (s) Tw.5 P1 P P3 Electric field (mv/m) Scattered field (mv/m) T Time (s) T (s) tur-o time=.65 s (s) (a) Time (s) 4 frequecy 6 (GHz) (b) Frequecy (GHz) P1 P3 P.5 Time (s) T (s) T (s) P3 P P x 1 9 (c) L( R ) Figure 5. (a) Backscattered electric field, (b) Time-frequecy diagram, (c) Time-dampig factor, ad (d) Time-residue diagram of the sigal [69] (With permissio, Copyright 14 IEEE). (d) L ( R ) Time T (s) (s) T (s) P3 P P x (a) L( R ) L ( R ) Figure 5.3 (a) Time-dampig factor of the sigal, (b) Time-residue diagram of the sigal for SNR = 15 db [69] (With permissio, Copyright 13 IEEE). 133 (b)

148 Table 5-1 Percetage error of estimatig of real ad imagiary parts of the domiat poles of the tag calculated from direct matrix pecil method (MPM) ad short-time-matrix-pecil-method (STMPM) [69] (With permissio, Copyright 13 IEEE). SNR ω ω ω 3 MPM α α α 3 Slope of residues MPM Slope of residues MPM Slope of residues to oise. For later times, by decreasig the SNR, the detectio of the CNRs becomes challegig. I Figure 5.3b, the time-residue of the CNRs of the sigal are show. The slop of the lies are equal to the dampig factors of the poles. The calculated dampig factors i time-residue diagram is more accurate tha oes calculated from MPM. Table. 1 presets the average error of estimatig the real ad imagiary parts of the poles for 5 differet sets of oisy data with a specific SNR value. As the table shows, the proposed method gives more accurate results for dampig factors tha MPM. The reaso is that the calculatig dampig factor from the time-residue diagram is based o the residues of CNRs which is related to the eergy. 5.5 Applicatio of STMPM i Widebad Scatterig from Resoat Structures [7] As a time-frequecy approach, various scatterig mechaisms such as resoace, scatterig ceter, ad dispersio features of the scatterer ca be moitored i the time-frequecy diagram obtaied from STMPM [7]. I some applicatios such as radar, the CNRs of the airplae are used as the ID for detectio purposes [71]. I these applicatios, high-q resoaces are more effective for idetificatio purposes. These high-q resoaces are mostly geerated by cavity structures embedded o the scatterer. For example, the egie of the airplae makes a ope-eded cavity resoator whose correspodig CNRs participate effectively i the late-time backscattered respose from the airplae. Hece, the ID of the airplae ca be adjusted by chagig the resoat modes of the ope-eded egie cavity. These CNRs are usually affected by the dispersio characteristics of the structure. 134

149 Figure 5.4 idicated various scatterig-mechaism represetatios i the time-frequecy diagram [7]. A vertical lie represets a reflectio from a scatterig ceter while a horizotal lie itroduces a resoace mechaism i the scatterig mode. Ay slope i the time-frequecy diagram (as Figures 5.4c ad 5.4d show) represets a dispersive pheomeo. I order to gather all the above mechaisms ito oe example, a ope-eded cylidrical cavity see i Figure 5.5a is ofte cosidered i literature [1,, 73-77]. A icidet electric field polarized i x-directio ad propagatig i z directio illumiates the cavity. The backscattered field cotais reflectios from the rim ad bottom of the cavity ad dispersive iteral resoat modes of the cavity. As the time-domai respose i Figure 5.5b idicates, three pulse-shaped resposes at t = 1s, t = 4.3s ad t=5.4s are due to the specular reflectios from the rim, ad the exteral ad iteral back of the cavity, respectively. The time-frequecy diagram of the sigal is depicted i Figure 5.6 usig STMPM ad STFT. The parameters of STMPM are chose as Tw =.4s ad p =. Accordig to figure, there are two scatterig ceters ad three resoat modes. The modes with cut-off Frequecy Frequecy Frequecy Frequecy (a) Time (b) Time (c) Time Figure 5.4 Scatterig mechaisms i time-frequecy aalysis. (a) Scatterig ceter. (b) Resoat behavior. (c) Structural dispersio. (d) Material dispersio [7] (With permissio, Copyright 15 IEEE). (d) Time 135

150 .1.8 E (V/m) (a) Figure 5.5 (a) Ope-eded circular cavity excited by icidet plae wave, (b) Backscattered sigal i time domai [7] (With permissio, Copyright 15 IEEE). x Time (s) (b) 5 Time (s) Frequecy (GHz) (a) Figure 5.6 (a) Time-frequecy diagram of the backscattered sigal from the cylider based o (a) STMPM ad (b) STFT [7] (With permissio, Copyright 15 IEEE). (b) frequecies f = 5 GHz ad f = 13.8 GHz have bee excited more strogly tha the mode with cutoff resoace at f = 9.9 GHz. There are some poles parallel to the frequecy axis located aroud t = 1 s which emaate from the secod roudtrip travel of the pulse iside the waveguide cavity. The spectrogram of the sigal based o STFT is show i Figure 5.6b. As ca be see, because of the poor resolutio of STFT i both frequecy ad time domais, the scatterig ceters ad resoat frequecies of the cavity caot be accurately extracted from the spectrogram of the sigal. This is especially severe whe the resoaces are closer to each other. By icreasig the legth of the widow ad filterig parameter, p, ad cosequetly icreasig the frequecy resolutio as see i Figure 5.7, ot oly is the secod mode clearly visible, but there also exist 136

151 some extra resoaces higher tha 13.8 GHz. These frequecies result from the secod roudtrip travel of the pulse iside the cavity, which shows itself at later times. Here, i additio to the dispersive modes of the first roudtrip of the pulse iside the cavity, the modes correspodig to the secod roudtrip are visible with differet tur-o times which is exactly matched with the electrical legth of the cavity. The dispersio characteristics of the modes have bee highlighted with dashed lies. I order to extract the accurate times of the reflectios from the lid ad bottom of the cavity i the time-domai sigal, the dampig factors of the widowed sigal are show i Figure 5.8 versus the ceter of the widow for two values of TW, widow legth, ad p, filterig parameter. The zero-crossig poits i the dampig factors versus time are the time istaces of the multiples reflectios from the structure. Aother advatage of the proposed techique is that the local resoat frequecies of the scatterer are illustrated by discrete poles i the time-frequecy diagram rather tha cotiuous colors i wavelet ad STFT. Figure 5.9 shows the time-frequecy diagram of the sigal based o the proposed techique for SNRs of db ad 1dB. For lower values of SNR, we eed to decrease the value of p i order to avoid the presece of poles origiatig from oise. 5 Time (s) Figure 5.7 Time-frequecy diagram of the scattered field for TW = 1 s, p = 4 [7] (With permissio, Copyright 15 IEEE) Frequecy (GHz) 137

152 1 1 T+T W / (s) Dampig Factor (s -1 ) x 1 1 Figure 5.8 Time-dampig factor represetatio of backscattered sigal from cavity. 5 5 Time (s) 15 1 Time (s) Frequecy (GHz) (a) Frequecy (GHz) Figure 5.9 Time-frequecy diagram of the sigal with (a) SNR=1dB, TW =.8s, p= ad (b) SNR=dB. TW =.8s, p=4 [7] (With permissio, Copyright 15 IEEE). (b) 138

153 6 Detectio, Idetificatio, ad Localizatio i Chipless RFID Tags [8] (Chapter used with permissio of Spriger sciece ad busiess media, 15) I previous chapter, short-time matrix pecil method (STMPM) was itroduced as a efficiet time-frequecy aalysis techique. By improvig time ad frequecy resolutios, the resoat frequecies ad tur-o times of the CNRs are moitored i time-frequecy diagram. The ID of the tag is located i the spectral of the scattered field. The tur-o times of the CNRs are useful i calculatig the distace of the tag compared to the atea. I circumstaces where multiple chipless RFID tags are preset i the reader area, a space represetatio of the tags is eeded to localize their positios. Hece, oe eeds a space-time-frequecy represetatio of the sigal i order to detect, idetify ad localize the chipless tags i the reader area. The accuracy of the approach depeds o the resolutio i space, time ad frequecy. Whe multiples tags are i the mai beam of the atea, a collisio-avoidace algorithm is required to separates the IDs of the tags I this chapter, first a space-time-frequecy algorithm is itroduced by which the IDs ad locatios of the tags are calculated by applyig STMPM ad its dual, arrow-frequecy matrix pecil method (NFMPM) to time ad frequecy domai sigals, respectively. I some applicatios, multiple reflectios from the atea structure used i the RFID system or multiple reflectios from the dielectric material itroduce some impulses i the late-time respose of the resoat-based scatterers. I such cases, the impulses limits the slidig of the time widow alog the sigal. This problem ca be solved by separatig the early-time ad late-time resposes of the scatterer. As metioed i sectio 5.3 ad 5.4, by slidig the widow alog the time-domai sigal, the poles origiatig from the early time ca be distiguished from poles of the late-time respose, which facilitates the detectio, idetificatio ad localizatio of chipless RFID tags. 6.1 Detectio of Chipless RFID Tags The detectio process ca be performed based o time-domai or frequecy-domai sigal. I [46, 49, 78, 79], the absolute value of the backscattered sigal i the frequecy domai ad group delay of the received sigal are used i detectio process. Based o the sigularity expasio method 139

154 (SEM), the impulse respose of the scatterer for the icidet ad scattered fields directed i the ˆr 1 ad ˆr ca be expressed by N R rˆ ˆ 1, r rˆ, ˆ ; s e ˆ, ˆ 1 r r1 r ; s s s 1 (6.1) where the first term is the late-time respose, icludig the complex atural resoaces s ad correspodig residues R, ad the secod term is the early-time respose of the scatterer. Compared to the early-time respose ad residues, the complex atural resoaces (CNRs) are aspect-idepedet. Although each scatterer icludes a ifiite umber of CNRs, the series i (6.1) is trucated to N, the umber of fudametal resoaces excited by the icidet electric field. Compared to the CNRs, the residues R ad the early-time respose of the tag Γe deped strogly o the directio ad polarizatio of the trasmittig ad receivig ateas. As metioed i Chapter, the embedded CNRs of the tag are high-q resoaces. Assumig the tag is illumiated by a icidet pulse δ(t), the scattered field i close proximity of the th resoat frequecy is writte by N R R E m e (6.) j m j m m m 1 Although the late-time respose has its maximums at the resoat frequecies of the tag, it does ot ecessarily happe for the total field. The received sigal at the th resoat frequecy is E N R R m (6.3) m j e m m m 1 As (6.3) shows, the received sigal at ω = ω is separated ito three terms. The first term i (6.3) is the scattered field from the th resoat frequecy; the secod term is due to the couplig of the other resoators o the th resoator resoatig at ω = ω, ad the third term is the early-time respose of the tag at ω. As a importat ote here, the magitude of the scattered field at the th resoat frequecy is ot simply a maximum at ω. The couplig of the other poles, the secod term i (6.3), ad early-time respose ca chage the maximum peak of the total field i the frequecy domai to a miimum ull or may shift it to other frequecies. Sice the coupligs ad 14

155 the early-time respose of the tag are aspect-depedet, the magitude of the scattered field i the frequecy domai is aspect-depedet as well. The mai observatio is that the magitude of the impulse respose of the tag i the frequecy domai is ot sufficiet to extract the resoat frequecies of the tag. Similarly, i detectio techiques based o the group delay of the received sigal, the group delay is ot sufficiet for extractig the resoat frequecies of the tag. The group delay is defied as where s 11 g d s 11 (6.4) d is the phase respose of the tag. Agai, assumig high-q resoaces are embedded o the tag ad igorig the effect of the secod term i (6.4), the group delay of the received sigal ca be writte by 1 1 g d e d (6.5) where is the phase of the early-time part of the sigal, which is aspect-depedet. e Therefore, both the magitude ad phase of the impulse respose of the scatterer ca vary by chagig the source ad observatio poits. Igorig the early-time part of the sigal causes a misleadig result where the group delay shows its maximum value at the resoat frequecies of the tag. I the cases where the phase of the early-time part has stroger variatios tha the phase of the late-time part, the detectio of the resoat frequecies from the group delay is ot straightforward. As a example, Figure 6.1 shows a sigle-bit tag, located i the xy plae, illumiated by a icidet electric field. The scattered sigal i give two differet orietatios of the receivig atea is depicted i Figure 6.a. The resoat frequecy of the tag is f = 5.9 GHz, while the peaks ad ulls i the scattered sigal are slightly shifted aroud it. Hece, the locatios of ulls ad peaks i the backscattered respose from the tag are ot the exact values of the resoat frequecies of the tag. This is very importat i the idetificatio of a tag with high desity of data, i which case the resoat frequecies are close to each other. I Figure 6.3b, the 141

156 group delay of the received sigal for two differet cases is show. Although the first peak of the group delay is exactly located at the resoat frequecy of the slot, there are some other peaks correspodig to variatios i the early-time respose. Hece, the absolute value of the scattered sigal ad its group delay caot be used to accurately extract the ID of the tag. I cotrast to the absolute-value ad group-delay respose of the scattered field, the detectio ca be performed based o the time-domai respose. As metioed before, the time-domai respose of the tag is the combiatio of the early-time ad late-time resposes. The aspect-idepedet parameters of the tag, the complex atural resoaces (CNRs), are icluded i the late-time respose. This part of the respose must be separated from the early time, which cotais the specular reflectios from the tag. Figure 6.1 Sigle-bit tag illumiated by a plae icidet field. E (dbv/m) =,= =, =7 deg Frequecy (GHz) (a) g (s) 4 x =, = =, =6 deg Frequecy (GHz) (b) Figure 6. (a) Scattered electric field from the tag for two differet orietatios of receivig atea, (b) Group delay of the scattered field for two differet orietatios of receivig atea. 14

157 6. Space-Time-Frequecy Ati-Collisio Algorithm for Idetifyig Chipless RFID Tags [8] I Figure 6.4, the schematic view of multiple tags preseted i the mai beam of the reader atea is depicted. As it shows, the received backscattered sigal is composed of the reflected sigals from each tag. Assumig the cofiguratio i Figure 6.4, the scattered field ca be writte i the Laplace-domai as (6.6). E r G r r J r ds (6.6) s ( ) e(, ; s) s( ) The source poits are preseted i the primed coordiate ad the observatio poits are preseted usig uprimed coordiates. Quatity Ge is the electric dyadic Gree s fuctio [13] ad Js is the surface curret desity iduced o the scatterer. Here, the reader area is assumed as a scatterig medium with tags as the scatterig ceters. For the case of multiple tags, the curret desity ca be writte as the summatio of the currets o the tags as M J ( r) J ( r r ) (6.7) s sm m m1 i which M is the umber of tags, ad r m ad Jsm are the locatio ad iduced curret o the m th tag, respectively. Backscattered fields from the tags ca be deduced from the electric field itegral equatio (EFIE) as Tag #1 UWB Atea Tag #M Tag # Figure 6.3 Multiple chipless RFID tags preset i the reader zoe [8] (With permissio, Copyright 14 IEEE). 143

158 ic Ge( r, r; s) J ( ) ˆ s r r ds t E ( r) r S (6.8) i which ic E is the icidet electric field which emaates from the atea, ˆt represets the uit vector tagetial to the tag surface, ad s=α+jω is the complex frequecy. O the other had, based o sigularity expasio method (SEM), the curret i (6.7) ad (6.8) ca be expaded by a series of complex atural resoaces as A J ( rr) J ( r ; ) J ( r r ; s) (6.9) M Nm () ( ) M m sm m s s () m m m1 N ( s s m m ) m1 where () J sm ad () s m are the th atural-mode curret ad pole of the m th tag. Compared to complex atural resoaces, the residue coefficiets, () A m, are aspect-depedet, depedig strogly o the polarizatio ad icidet agle. The last summatio i (6.9) cotais the etire-domai fuctio icludig the early-time respose from the scatterers [81, 8]. The early-time respose origiates from the scatterig ceters of the scatterer [81, 83-85]. By isertig (6.9) i (6.8) ad applyig the method of momets, the iduced currets o the tags ca be obtaied. Assumig the frequecy bad of operatio covers all the atural resoaces of the tags, the backscattered sigal from iduced curret o the tags ca be writte i time domai as M Nm (m) s (m) s ( t tm) e ( r, t) em( r, t) ReR e (6.1) m1 1 i which tm represets the tur o time of the m th tag. It is assumed that CNRs of each tag have the same tur-o time. For complex scatterers, this assumptio might ot be accurate. Accordig to Altes model [17] metioed i Chapter, the early-time respose ca be approximated by a series of pulse resposes as ic (p) m t amp t tm p e (t) e ( r, ) ( ) (6.11) where tm is the delay time equal to the roudtrip time betwee the atea ad the m th tag. The impulse respose of the m th tag i (6.11) is summed over the itegrals ad derivatives of the Diracdelta fuctio. Here, the egative ad positive value of p refers to the p th itegral ad derivative of the delta fuctio. Therefore, (6.1) ca be writte i Laplace-domai as 144

159 s E ( r, s) a s E ( r, s) e M Nm () p ic stm m mp () m1 p N s s m m M Nm () stm m Am ( r, se ) () m1 N s s m m R R (6.1) i which the early-time summatio is summarized by Am. Comparig (6.1) with (6.1), there is a duality betwee late-time respose i time domai ad the early-time respose i Laplace domai [8, 84]. By applyig STMPM to (6.1), the complex resoaces of the tags ad their residues are foud at each sapshot of time. By shiftig the slidig widow by T i the late-time regio, the backscattered sigal ca be writte as i which M Nm () s T, sm ( t tm) elate-time ( r, t) ReR m e 6.13) m1 1 () () T, () m j m T R R (6.14) m me I ormal logarithmic scale, (6.14) ca be expressed as L R L R T (6.15) T, () m m m As ca be see i (6.15), the residues liearly decrease versus T with slope () m. By applyig Narrow-frequecy matrix pecil method (dual of STMPM) to the frequecy respose i (6.1), a space-frequecy represetatio is obtaied i which the scatterig ceters (here the tags) of the respose are depicted versus frequecy. I this diagram, the resoat frequecies of the tags i the late time are coverted to some ustable poles. I practical applicatios limited to the frequecy bad of GHz, whe some dese multi-bit tags exist i the reader zoe, the resoaces of the tag i the frequecy domai perturb the early-time respose. I these cases, by isertig the poles ad related residues i (6.1), the early-time part of the sigal is foud as s stm E ( r, s) A ( r, s) e (6.16) early-time M m1 m By applyig NFMPM to (6.16), the delay times (tm) are accurately obtaied. The flowchart of the proposed algorithm is illustrated i Figure 6.4. The aforemetioed techique is geeralized ad 145

160 Frequecy-domai respose IFFT Time-domai respose STMPM Poles & Residues from timefrequecy ad time-residue diagrams Early-time respose Tur-o times (locatios of the tags) Tag IDs ad locatios Figure 6.4 Flowchart of the proposed ati-collisio algorithm [8] (With permissio, Copyright 14 IEEE). ca be used for ay multi-resoace tag schemes. For better illustratio, Figure 6.5a shows a sceario i which two sigle-bit tags are illumiated by a plae wave. I the first case, the resoat frequecies of the tags are assumed at f1= 7.8 GHz ad f=9.8 GHz ad the tags are located R= cm away from each other. Each tag is characterized by a complex atural resoace (CNR) which is created by isertig a quarter-wavelegth slot o the tag surface [4, 45]. The approach is applicable for other types of tag icludig slot, trasmissio lie, or spiral resoators [41, 44-47, 86]. The time-domai respose is show i Figure6.6a. The early-time ad late-time resposes of the tags are illustrated by two differet lies. The slidig time ad widow legth are show by T ad TW =.5s. The time-frequecy represetatio of the respose is show i Figure 6.6b. Accordig to the figure, the ustable poles i the early-time part coverge to the CNRs at tur-o times (t1 ad t). The, after t=.4s, the respose cotais the backscattered sigal from both tags; whereas before t, the backscattered sigal cotais just the respose from the first tag. I cotrast to the time-frequecy 146

161 T (s) k k R 6. (a) (b) Figure 6.5 (a) Two sigle-bit tags ad (b) two -bit tags spaced by R are illumiated by a plae wave. Uits i mm [8] (With permissio, Copyright 14 IEEE). x E (v/m) T (s) t T (s) Time time (s) 3 4 (a) L(R) -8-7 (c) Frequecy frequecy Frequecy (GHz) (b) Figure 6.6 (a) Time-domai backscattered sigal from two tags spaced by R=cm (b) timefrequecy represetatio of the sigal by applyig STMPM with T =.5s. (c) time-residue diagram of the sigal. (d) Separated resposes of the tags i frequecy-domai [8] (With permissio, Copyright 14 IEEE). E (v/m) 4 t 1 8 x 1-5 tag #1 tag # frequecy Frequecy (GHz) (d)

162 represetatio of the sigal, i the time-residue diagram of Figure 6.6c, two poles ca be easily distiguished. The pole with tur-o time t1=1s is associated with tag #1 ad likewise, the pole with tur-o time t=.4s is related to the secod tag. Accordig to (6.15), the slopes of the lies i Figure 6.6c are equal to the dampig factor of the poles. By recostructig the backscattered sigal from the tags i the time domai, the cotributio of each tag i the late-time respose of the received sigal is show i Figure 6.6d.As ca be see, the amplitude of the backscattered sigal from the first tag is higher tha that of the secod tag. The amplitudes at the resoat frequecies are directly proportioal to the residues of the poles. I additio, the frequecy respose of each tag is depicted separately which simplifies the idetificatio process. As aother example, two similar sigle-bit tags are cosidered i Figure 6.5a resoatig at f1=7.7ghz. The time-frequecy ad time-residue represetatios of the sigal are show i Figures 6.7a ad 6.7b, respectively. Two tur-o times of the resoators are show i Figure 6.7a. By plottig the residues versus slidig time, there is a jump i the residue at the secod tur-o time. This jump comes from the resoat frequecy of the secod tag. Assumig the pole of the tags as s1=α1+jω1 ad the residues of the first ad secod tag s poles as R1 ad R, the the backscattered sigal after t ca be writte as ( ) 1 j1 ( tt) j tt j t j t j t R e R e e R e R e (6.17) Hece, the residue of the sigle pole R1 before t becomes the term i the paretheses i right-had side of (6.17) after t. Sice the poles of the tags have the same dampig factors, the slopes of the lies are the same. The late-time frequecy respose of the tags is show i Figure 6.7c. Although they share the same resoat frequecy ad quality factor, they have differet amplitudes at the resoat frequecy. By applyig NFMPM to the total frequecy-domai respose of the tags (without subtractig the late-time respose), the locatios of the tags are depicted i Figure 6.7d i a space-frequecy diagram. There are some ustable poles (betwee R=5cm to R=5cm) associated with the resoaces of the tags. These poles ca be suppressed by subtractig the latetime respose from the total respose i (6.1). I Figure 6.8, the time-residue of the backscattered sigal from the tags is depicted for differet polarizatios of tag. As ca be see whe the secod 148

163 T T (s) 4 t t frequecy Frequecy (GHz) (a) T (s) L(R) (b) E (V/m) (v/m) 1.5 x frequecy (GHz) Frequecy (GHz) (c) tag #1 tag # R (cm) (d) Figure 6.7 (a) Time-frequecy ad (b) time-residue represetatio of the sigal by applyig STMPM with T=.5s. (c) Separated resposes of the tags i frequecy-domai (d) spacefrequecy respose after SFMPM [8] (With permissio, Copyright 14 IEEE). Frequecy (GHz) F (GHz) 1 5 tag is rotated by 45 alog its axis, the electric field of the icidet wave is perpedicular to the slot s legth ad it excites the tag s pole more effectively. Accordig to Figure 6.8, the residue of the first tag does ot chage while the residue of the secod tag shifts proportioal to the polarizatio of the secod tag. Whe the slot s legth is i parallel with the icidet electric field (9 rotatio), the excited residue of the secod tag is small ad as ca be see i Figure 6.8, it produces a small shift at the secod tur-o time. I the third example as show i Figure 6.5b, two -bit tags are illumiated by a icidet plae wave. The first illumiated tag represets two resoat frequecies at f1 = 5.3 GHz ad f = 7.1GHz (ID = 11) ad the secod tag has o resoat frequecies (ID = ). I additio, the RCS of the secod tag is much smaller tha that of the first. The time-domai ad frequecy-domai 149

164 degrees degrees 45 degrees 1.1 T (s) L( R ) Figure Time-residue diagram for differet polarizatios [8] (With permissio, Copyright 14 IEEE). T (s) E (v/m) (V/m) x Time time (s) (a) frequecy Frequecy (GHz) (GHz) (c) frequecy Frequecy (GHz) (b) R (cm) 5 (d) Figure 6.9 (a) Time-domai sigal (b) frequecy-domai respose (c) time-frequecy diagram after STMPM (d) space-frequecy diagram after SFMPM [8] (With permissio, Copyright 14 IEEE). 15 E (dbv/m) E (dbv/m) Frequecy F (GHz) (GHz)

165 7.3 resposes are depicted i Figures 6.9a ad 6.9b. I this case, the early-time respose of the secod tag is obscured i the late-time respose of the first tag. By applyig STMPM ad NFMPM to the time-domai ad frequecy-domai resposes, the time-frequecy ad space-frequecy diagrams of the sigal are show i Figures 6.9c ad 6.9d. Similar to previous examples, if oe kows the tur-o times ad poles, the ID of each tag ca be foud by recostructig the backscattered sigal of each tag. Here, the presece of the secod tag caot be detected without the space-frequecy diagram. As aother example, two 3-bit tags are assumed cm apart. The cofiguratio ad dimesios of the tags are show i Figure 6.1. The tags represet ID1:111 ad ID:11. The presece ad absece of each assiged resoat frequecy represets bits 1 ad, respectively. The assiged resoaces are at f1= 6.GHz, f=8.7ghz, ad f3=1.9ghz. The simulatio is performed i CST Microwave Studio. The pole diagram of the three-bit tag is depicted i Figure The illumiatig plae wave first hits tag #1 ad the tag #. The time, frequecy, timefrequecy ad time-residue resposes of the backscattered field are show i Figure 6.1. Obviously, the idetificatio process caot be doe perfectly with backscattered frequecydomai respose. From the time-frequecy respose, it ca be iferred that the first tag represets three resoat frequecies. At t = 1.8 s, the illumiatig wave hits the secod tag with ID = 11. Accordig to Figure 6 1c, three resoat frequecies exist i the backscattered sigal after t = 1.8 s. I the simulatio results, the widow legth of TW=.5s is used. Aother importat parameter itroduced i matrix pecil method (MPM) is p which is the umber of sigificat decimal digits i the sampled data. It acts as a filterig parameter determiig the accuracy of the extracted poles (a) (b) Figure 6.1 Schematic view of the tags. (a) ID1:111, (b) ID: 11[8] (With permissio, Copyright 14 IEEE). 151

166 f r (GHz) Frequecy (GHz) (Np/s) x 1 9 1e-9 Figure 6.11 Pole diagram of the 3-bit tag [8] (With permissio, Copyright 14 IEEE). For oisy data, we usually use p 3. Here, p = 4 is used for more accuracy. For values less tha 4, just two poles of the secod tag after t = 1.8 s are represeted i the time-frequecy diagram. To idetify the ID of the secod tag, we use the time-residue diagram show i Figure 6.1d. As ca be predicted by the mathematical formulatio i (6.15) ad (6.17), the residues of the first ad third bits have jumps at the secod tur-o time whereas the residues of the secod bit are located i a straight lie without ay jump at the secod tur-o time. It cofirms that the secod resoat frequecy after t = 1.8s is related to the first tag s respose. Therefore the ID of the secod tag is ID = 11. The slopes of the poles i the time-residue diagram are related to the dampig factors of the poles i Figure As a example, the secod pole, which has the lowest dampig factor, has the steepest slope i Figure 61d. As a fial sceario, the icidet wave first illumiates tag # with ID = 11, the secod tag with ID1 = 111. The time-residue diagram of the backscattered sigal is show i Figure 6.13a. I this case, all the residues have a jump at the secod tur-o time. By obtaiig the residues ad poles of the sigal, the cotributio of each tag to the backscattered sigal is show i Figure 6.13b. 15

167 E (mv/m). -15 E (V/m) (v/m) E (dbv/m) E (dbv/m) time Time (s) (a) frequecy Frequecy (GHz) (b) 3 3 T (s) 1 T (s) T (s) frequecy Frequecy (GHz) (c) (R) L( R ) (d) Figure 6.1 (a) Time-domai backscattered sigal from two tags spaced by R=cm (b) frequecydomai respose (c) time-frequecy represetatio of the sigal by applyig STMPM with T=.5s. (d) Time-residue diagram of the sigal [8] (With permissio, Copyright 14 IEEE). T (s) T (s) L (R) ( R ) (a) Frequecy (GHz) frequecy (b) Figure 6.13 (a) Time-residue diagram of the backscattered sigal (b) separated resposes of the tags i frequecy-domai [8] (With permissio, Copyright 14 IEEE). E (mv/m)

168 6..1 Space, Time ad Frequecy Resolutios Similar to other time-frequecy aalysis methods such as wavelet trasforms, short-time Fourier trasform ad so o, time ad frequecy resolutios are key parameters i the proposed method. The resolutio i time ad frequecy domais is strogly depedet upo the legth of the slidig widow. The frequecy resolutio is related to the miimum distace i frequecy betwee two adjacet resoat frequecies which ca be idetified. We discussed about the effect of widow legth ad filterig parameter o the resolutio i chapter 5. Other importat parameter affectig the frequecy resolutio is oise. I order to study the effect of the widow legth o the frequecy resolutio, the time-domai sigal i (6.18) is cosidered as the backscattered sigal from a two bit tag. permissio, Copyright 14 IEEE). 154 t s( t) Ae si( f t) si( f t ( t) (6.18) 1 1 For more simplicity, the poles are assumed to have the same residue ad dampig factor ad (t) is the additive Gaussia white oise. Assumig f1 = 5 GHz ad α = 1e8 (1/s), the miimum required frequecy legth of widow for distiguishig the poles is show i Figure 6.14 as a fuctio of Δ for differet SNRs. As it shows, whe the resoaces of the tag are located closer to each other, we eed to icrease the widow s legth to distiguish the resoaces. Also, for lower SNR cases, a larger value of Tw is required to distiguish the poles. The filterig parameter i MPM (p) is directly related to SNR. For lower SNRs, a lower value of p should be employed i the algorithm T w (s) T (s) (GHz) (GHz) Figure 6.14 Miimum required widow legth as a fuctio of Δ for differet SNRs [8] (With SNR=dB SNR=5dB SNR=dB

169 .1 W p W p.5 T W cycles Figure Backscattered sigal from two sigle-bit tags [8] (With permissio, Copyright 14 IEEE). so as ot to allow the poles due to oise to come ito the picture. Here, the value of p is chose as 5, 4, ad 3 for SNR =, 5, ad db, respectively. By icreasig the legth of time-widow, frequecy resolutio is icreased which deteriorates the time resolutio. For example, the tur-o time i Figure 61c is located i betwee 1.5s ad s which causes a sigificat error i calculatig locatios of the tags. O the other had, the rage resolutio depeds o the pulse width of the icidet wave. Figure 6.15 shows the backscattered sigal from two sigle-bit tags. The early-time respose of the tags is a replica of the icidet wave whose width ca be approximated by [87] 1 1 W p.13s B ( ) GHz (6.18) where B is the operatioal badwidth of the icidet wave ( GHz). Hece, the rage resolutio ca be calculated as cw p R cm (6.) I practical applicatios, we usually eed a few cycles of the siusoidal sigals i the widow to extract the poles. Cosiderig the worst case as fmi = 3.1 GHz, the miimum rage resolutio at which the tags ad their IDs ca be distiguished usig the arrival times of the early-time resposes is betwee 7-15cm. 155

170 6.3 Separatig the Early-Time ad Late-Time Resposes for Detectio, Idetificatio, ad Localizatio of Chipless RFID Tags I previous sectio, the tur-o time ad IDs of the tags were obtaied by applyig STMPM ad NFMPM to the time-domai ad frequecy-domai backscattered sigal received by the atea. As metioed, i multi-tag applicatios, the resolutio i space, time ad frequecy plays a importat role i detectio, idetificatio ad localizatio of the tags. A few cycles of the late-time respose is required i order to place the slidig widow i the late time for extractig the poles of the tag. The detectio of the tags is also very challegig whe the tags are located less tha 1cm away from each other. I such cases, oe eeds wider badwidth i order to decrease the resolutio i space. Based o the algorithm proposed i Figure 6.4, i multi-bit tags with high quality CNRs, the late-time poles must be removed from the frequecy respose i order to extract the delay-times of the scatterers accurately by applyig NFMPM to the frequecy-domai respose. The accurate calculatio of amplitude ad phase of the residues is ot easy, especially i low-q resoaces of the tags. By employig a optimizatio process i the detectio procedure, the accuracy of the approach is improved which complicates the processig calculatios i the reader. Accordig to sectio 5.3, by slidig the widow alog the time-domai sigal, the positio of the impulses i the received sigal ca be distiguished by moitorig the zero-crossig poits i time-dampig factor diagram. This techique is very efficiet whe multiple reflectios exist i the sigal. As a example, Figure 6.16 shows a 4-bit tag located 3 cm away from a TEM hor atea. The dimesio of the atea is depicted i Figure The reflectio coefficiet of the atea, i the presece ad absece of the tag, is see i Figure 6.17a. The reflectio coefficiet of the atea i time domai is see i Figure 6.17b. After multiple reflectios from the feedig poit ad atea aperture, the radiated field iterrogates the tag. Sice the embedded resoaces of the tag have high quality factors, the late-time respose from the tag stays for log time. The multiple reflectios from the atea ad tag are located i the let-time respose of the tag. For better illustratio, by applyig STMPM to the time-domai reflectio coefficiet, the extracted dampig factors are show i Figure 6.17c versus the ceter of widow. The locatio of multiple reflectios from the atea aperture are located at zero-crossig poits of the dampig factors. The time- 156

171 frequecy represetatio of the sigal is show i Figure 6.17d. The resoat frequecies of the tag are stably located at f = 4.8 GHz, f = 5. GHz, f = 6GHz, ad f = 6.4 GHz. The proposed techique ca be efficietly used i detectig multiple tags located close to each other. As a example, Figure 6.18 depicts the time-domai ad time-dampig factor diagrams of the received sigal whe two 3-bit tags are located i the reader area. Three cases as d = cm, d = 1 cm ad d = 4 cm are cosidered here. Sice the early-time resposes of the tags are located very close to each other ad are followed by the late time resposes of the tags, the extractio of the scatterig ceters (here the tags) from the time-domai respose is very challegig; While, by applyig the proposed techique, the locatio of the tags ca be obtaied from the zero-crossig times i time-dampig factor diagram. 6.4 Measuremet Results Three 3-bit tags with IDs of ID1 = 11, ID = 111, ad ID3 = 11 are desiged based o the proposed techique i Chapter 3. The secod ad first bits of tags #1 ad #3 are respectively ulled by solderig a stub i the middle of the related slots. This maual solderig causes a small shift i the resoat frequecies which is egligible i our aalysis. Two measuremets are performed: First, accordig to Figure 6.19, two tags (ID1 ad ID) are located cm away from each other i frot of a UWB quad-ridge hor atea. The the third tag is located 15cm from the secod tag. The atea is coected to the etwork aalyzer ad the S11 is measured while the frequecy is swept from 1 MHz to 5 GHz. This wide frequecy rage is chose for better resolutio i the time domai. For practical applicatios, the stadard frequecy bad ( GHz) ca be used for measuremet. The data measured by the etwork aalyzer caot be used directly to extract the poles because it icludes udesired compoets such as the cotributio of TEM hors ad the scatterig from backgroud objects i additio to the tag respose. As a result, aother measuremet is performed without the presece of the tags to subtract the effect of the backgroud objects from the first measured data. The iput power is 18dBm. The time-domai backscattered sigal for two cases is show i Figure 6.a. By applyig STMPM to the time-domai respose, the time-frequecy diagram of the sigal is obtaied, show i Figure 6.b. The optimum values of p ad TW are used at each sapshot of time for extractig the poles. Here, we used p = 4 ad Tw=.5 s for 3.5s t 5.3s ad p = 5 ad Tw =.6 s for 5.3s t. 157

172 Tag 4.5 cm Figure 6.16 A 4-bit chipless RFID tag located 3 cm away from the atea. S 11 (db) S x Frequecy (GHz) (a) Time (s) (b) T+T W / (s) Dampig Factor (s -1 ) x 1 1 (c) T (s) Frequecy (GHz) (d) Figure 6.17 Reflectio coefficiet of the atea loaded by tag i (a) frequecy domai, (b) time domai, (c) Time-dampig factor diagram ad (d) Time-frequecy diagram of the S

173 E (mv/m) Time (s) T+T w / (s) Dampig factor (s -1 ) x 1 1 Time-domai sigal for d = cm Time-dampig factor for d = cm E (mv/m) Time (s) T+T w / (s) Dampig factor (s -1 ) x 1 1 E (mv/m) Time-domai sigal for d = 1 cm Time (s) Time-domai sigal for d = 4 cm Time-dampig factor for d = 1 cm T+T w / (s) Dampig factor (s -1 ) x 1 1 Time-dampig factor for d = 4 cm (a) (b) Figure 6.18 (a) Time domais ad (b) Time-dampig factor diagrams of the backscattered sigal from two tags. 159

174 These parameters are chose based o umber of resoaces i the sapshot of time ad SNR. Due to the limited time resolutio, the exact tur-o times caot be obtaied from this diagram. The exact tur-o time is crucial i recostructig the tag resposes because the time-domai recostructed sigal is very sesitive to phase (or tur-o times). As ca be see i Figure 6.18, the secod set of poles excited at t = 5.3s have differet residues tha the poles excited at t = 3.9s. Thus, the first ad secod tags represet two ad three resoat frequecies, respectively. At t = 6. s, the poles of the third tag are excited. The third tag is rotated 45 with respect to icidet electric field. The resoat frequecies ad ID of each tag ca be idetified from the timefrequecy ad time-residue diagrams. I Figure 6.a, the real ad imagiary parts of the backscattered sigal versus frequecy are show. Followig the algorithm preseted i the flowchart of Figure 6.4, by suppressig the late-time poles of the tags, the space-frequecy diagram of the respose is show i Figure 6.b for two cases. Here, the accurate tur-o times (or equivaletly locatios of the tags) are depicted i a space-frequecy diagram ID: 111 cm 3cm ID: 11 Figure 6.19 Set-up for the measuremet of backscattered sigal from two tags [8] (With permissio, Copyright 14 IEEE). 16

175 E (mv/m) E (mv/m) Time (s) time (a) 3 tags tags T (s) frequecy Frequecy (GHz) (b) Figure 6. (a) Time-domai backscattered sigal from the tags, (b) Time-frequecy represetatio of the backscattered sigal [8] (With permissio, Copyright 14 IEEE) T (s) T (s) L( R ) L(R) Figure 6.1 Time-residue represetatio of the backscattered sigal [8] (With permissio, Copyright 14 IEEE). 161

176 E (v/m) real imagiary frequecy Frequecy (GHz) (a) R (cm) Figure 6. (a) Real ad imagiary parts of the measured backscattered sigal, (b) Spacefrequecy diagram of the measured respose [8] (With permissio, Copyright 14 IEEE). T (s) Frequecy (GHz) tags tags (b) 6.5 Localizatio of Chipless RFID Tag [88] I trackig applicatios, it is desired to kow the precise locatio of the tag i the reader area. For example, by kowig the tag locatio, the reader atea ca direct the atea beam to the object, suppressig the iterferece sigals from backgroud objects [89]. I additio, by eablig this capability i covetioal chipless RFID systems, it ca be used i a wider rage of crucial applicatios such as health-care moitorig i hospitals. For example, i microwave hyperthermia of breast cacer [9], the accurate localizatio of the tumor is ecessary. Additioally, the localizatio techique is useful i the positioig of chipless RFID sesors placed i differet locatios of the medium i order to sese the desity of a particular gas [91] or the humidity of the medium [78]. I such cases, because of the ihomogeeity of the material uder cosideratio, multiple tags are used i differet places. Therefore, the accurate localizatio ad idetificatio of the tags is a essetial part of the measuremet set-up. Ragig techiques ca be categorized as time-based ragig ad received sigal stregthbased ragig [9]. The former is based o the time of arrival (TOA) of the sigal while later is based o the priciple that the greater the distace betwee two odes, the weaker their relative received sigals are. I practical applicatios, takig advatage of ultra-widebad techology i the detectio process, the first method shows better accuracy ad precisio tha the secod [9]. However, there are some factors which affect the performace of the ragig process i the reader. I ideal propagatio coditios, without cosiderig multipath ad iterferece pheomea i our 16

177 discussio, the ragig accuracy for SNR larger tha 15dB is limited to the Cramer-Rao (CR) boud as [9, 93] c ER { } (6.1) 8 SNR where E{.}1 is the mea square error (MSE), R accouts for the estimatio error, c is speed of light i free space ad β represets the effective badwidth of sigal [94]. For lower SNRs, the estimatio error is limited to a stricter boud, called the Ziv-Zakai boud [9]. The formulatio is more difficult for multipath effects. As the simplest case, we cosider the CR boud i (6.1). Accordig to (6.1), the ragig error is strogly depedet o the SNR ad the pulse shape. Figure 6.4 shows the ragig error as a fuctio of SNR for CR boud i the presece of AWGN oise. The frequecy badwidth is GHz. For SNRs lower tha 1dB, the Ziv-Zakai boud is more accurate which shows worse ragig error tha the CR boud. It is see that by decreasig SNR, the ragig error is icreased. This may happe whe the tag is located at larger distaces from the reader atea. I additio, the detectio techique plays a importat role i ragig calculatios. I most applicatios, classical matched filter (MF) TOA estimator is used to fid the time whe the sigal has its maximum peak [9]. This strategy might ot be the best method for localizig chipless RFID tags. The backscattered respose from the tag icludes early-time ad late-time resposes. I the cases where the early-time respose is much stroger tha the late-time respose, the aforemetioed techique works well. However i multi-bit tags, the late-time respose of the tag is composed of high-q siusoidals correspodig to the embedded poles o the tag. At time istaces whe some siusoidals are i-phase, their effect might be costructive eough to stregthe the late-time respose at those time istaces. Additioally, if two or more tags are located i the reader area, the early-time respose of the secod tag might be hidde i the late-time respose of the first illumiated tag. Also, for bi- static cases, there is o guaratee that the early-time respose is stroger tha the late-time respose. Although may efforts have bee made i the desig ad implemetatio of chipless tags, there is a demadig request for improved detectio techiques i the reader, especially for localizatio applicatios. I [95], a space-time-frequecy method has bee suggested for the localizatio of the tags. Later o, the proposed method i [95] was cofirmed by experimetal results i [89]. 163

178 Ragig error (cm) SNR (db) Figure 6.3 Ragig error versus SNR [88] (With permissio, Copyright 14 IEEE). The localizatio is based o the employmet of three ateas spaced at differet poits i the reader area. For larger spaces, the area ca be divided ito some uit cells covered by some atea arragemet. Although the authors i [89] did ot cosider the circumstaces where the late-time respose is stroger tha the early-time part ad also whe multiple multi-bit tags are preset i the reader area, the method performs well withi.1cm ad 3.5º error i distace ad agle for a sigle tag. Here, a ew techique is itroduced for accurate localizatio of chipless RFID tags i the reader area. Similar to [95], three ateas are used i the uit cell. Assumig the reader area as the scatterig area, the tags ca be regarded as the scatterig ceters of the medium. Based o Altes model, the early-time respose from the reader zoe ca be expaded versus the localized impulse resposes of the scatterig ceters. By applyig NFMPM, which is the dual of the short-time matrix pecil method (STMPM), to the frequecy-domai respose of the tag at each atea port, its locatio ca be easily foud by some mathematical maipulatios. The major advatages of the techique proposed herei are as follows: 1) A easy-to-implemet approach is proposed to qualitatively improve localizatio accuracy i chipless RFID systems. ) This techique is applicable for localizatio of multiple multi-bit tags i the reader zoe. 3) By obtaiig the accurate value of tur-o time of the tag, its ID ca be easily foud by applyig STMPM to the time-domai respose. 164

179 4) By takig advatage of the three-atea implemetatio i the uit cell, the effects of oise ad polarizatio issues i the idetificatio ca be reduced cosiderably. 5) The iterfereces from adjacet uit cells ca be strogly elimiated from the backscattered sigals. Figure 6.4 illustrates the system cofiguratio arraged for the localizatio of chipless RFID tags. The area uder cosideratio is subdivided ito uit cells. Each uit cell is covered by three ultra widebad ateas spaced by 1º with respect to the ceter of the uit cell. The frequecy of operatio is assumed to be GHz compatible with FCC requiremets. By employig three ateas at each uit cell ad obtaiig the tur-o time of the tag (or equivaletly the distaces from the tag to the ateas), the positio of the tag ca be calculated easily. I additio, this arragemet has some other beefits which improves the detectio ad idetificatio capability of the reader. By icreasig the distace betwee tag ad atea, the amplitude of both early-time ad late-time resposes decrease which leads to a decrease i SNR. This results i two differet drawbacks i the localizatio ad idetificatio of the tags. Accordig to (6.1), by degradig SNR of the received sigal, the ragig accuracy deteriorates. Also, by icreasig the distace ad addig extra oise to the sigal, the extractio of the embedded poles of the tag becomes extremely challegig. With a three-atea arragemet ad some power cosideratios, we ca esure that the SNR of the backscattered sigal from the tag is above a threshold for at least oe of the atea ports. Hece, we ca obtai the sigature of the tag by aalyzig the strogest backscattered received sigal from the tags. ANT. 1 Local reader Cetral reader y x 3 Ceter reader Chipless tag ANT. R ANT. 3 Figure 6.4 System cofiguratio for localizig chipless RFID tags i the reader area [88] (With permissio, Copyright 14 IEEE). 165

180 Furthermore, by receivig the backscattered sigal from three differet directios, the directio ad polarizatio depedecy of the tag ca be mitigated. I coclusio, a three-atea cofiguratio i a uit cell facilitates both localizatio ad idetificatio processes i the reader part. Accordig to Figure 6.4, three ateas i the uit cell are spaced at 1º o a circle of radius R. Assumig multiple multi-bit chipless RFID tags preset i the reader area, the backscattered resposes at the atea ports cotai the reflectios from the tags, ateas ad iterfereces from the adjacet uit cells. Cosiderig si(t) as the iput sigal at the i th atea port, the backscattered sigal ca be writte as the combiatio of early-time ad late-time resposes of the scatterig objects as N N M r ( t) e ( t) l ( t) e ( t) Re R e U t t t o m m s t (6.) i i i,i,i,i 1 m1 where e,i is the early-time respose of the th object at the i th atea port. The secod part i the bracket cotais the late-time resposes from the objects which based o sigularity expasio method (SEM) is summed over all atural resoaces ( m s ) with weightig residues ( m R ). U(.) is the Heaviside fuctio ad t,i is the tur-o time of the th scatterer at the i th atea port. Nt is assumed to be the umber of the tags i the cell, No is the umber of sigals other tha the tag s reflectios comig from backgroud objects ad iterfereces, ad M is the umber of bits embedded o the th tag. Based o Altes model, the early-time respose from each scatterer ca be expaded versus the impulse respose of the localized scatterig ceters as ( p),i i,p,i,i p e ( t) s ( t) a ( t t ) (6.3) where t,i is the delay-time from the i th atea to the th scatterer. The impulse respose of the th scatterer i (6.3) is summed over the itegrals ad derivatives of the Dirac-delta fuctio. Here, the egative ad positive values of p refer to the p th itegral ad derivative of the delta fuctio, respectively. For simple scatterers as i our case, oe term of the summatio might be eough. By isertig (6.3) i (6.), the received sigal i the Laplace domai ca be writte as R ( s) A ( s) e m N M st,i,i (6.4) i,p,i m 1 m1s s R 166

181 Frequecy-domai respose IFFT Time-domai respose Ati-collisio algorithm dm i space-frequecy diagram Triagulatio tm Positio of tag ID Figure 6.5 Flowchart of proposed localizatio algorithm [88] (With permissio, Copyright 14 IEEE). p i which A,p,i ( s) a s S( s). By employig the method proposed i Sectio 6., suppressig the,p,i late-time respose ad applyig the arrow-frequecy matrix pecil method (NFMPM) to the frequecy-domai of early-time respose, the accurate values of roudtrip time of the scatterig ceters, t,i, ca be obtaied. I this approach, a slidig-frequecy widow is moved alog the frequecy axis ad the matrix pecil method is applied to each widow. By covertig the extracted complex times to distace as dm = ctm/ ad plottig dm versus slidig frequecy, the distace from the tags to the atea ca be moitored i the space-frequecy diagram. Kowig the distace of a tag from the ateas, its locatio ca be calculated with respect to the referece poit at the ceter of the uit cell. After obtaiig the tur-o times of the tags, the time-widow ca be adjusted i the late-time respose of the tag i order to extract the correspodig poles of the tag. The flowchart see i Figure 6.5 summarizes the proposed localizatio techique. As a example, the 3-bit tag uder cosideratio is show i Figure 6.6. It cosists of three quarter-wavelegth slots resoatig at f1=5.1ghz, f=7.1ghz, ad f3=8.1ghz. The simulated ad measured RCS of the tag is depicted i Figure 5 whe the icidet electric field is perpedicular to slot legth. Based o the RCS of the tag ad sesitivity of the receiver, the iput power ca be adjusted so as to maitai a SNR above a certai threshold. For larger tags, the reflected sigal 167

182 7.5 mm 1.5 mm Figure 6.6 Cofiguratio of the 3-bit fabricated tag [88] (With permissio, Copyright 14 IEEE). is stroger which results i lower ragig error based o (). Accordig to [3], the miimum SNR at which the tag s ID ca be accurately idetified is about 15dB. Assumig the tag is located i the far field of the atea, the radar budget equatio ca be writte i the frequecy domai as Pr A ( f ) f (6.5) 4 P 4 c R t where Pr ad Pt are the received ad trasmitted power at the atea with the effective area of A. The quatity is the frequecy-depedet RCS of the tag as show i Figure 5, c is the speed of light i free space ad R is distace from tag to atea. A TEM-hor atea with a legth of 3 cm ad effective aperture surface area of 15 cm is coected to a etwork aalyzer to measure the backscattered sigal from the tag. Assumig Rmax = 1cm as the maximum detectable rage, the ratio of received to trasmitted power at the atea is show versus frequecy i Figure 6.8 The measured received oise by the atea i the laboratory eviromet is about -6 dbm. The peaks of the frequecy-domai respose i Figure 6.8 are associated with the resoat frequecies of the tag. As it shows, at the first resoat frequecy of aroud f = 5GHz, the value of Pr/Pt is -5dB. This value is the combiatio of the early-time respose ad the correspodig residue of the late-time respose of the tag at f = 5 GHz. For high-q resoaces, the late-time residue is effectively domiat. Assumig 1dB for the early-time respose ad polarizatio mismatch, trasmitted power should be adjusted to have Pt > 1 dbm i order to keep the SNR above 15 db. By choosig Pt = dbm, the backscattered respose from the tag is calculated by subtractig the resultat S11 at the atea port from the off-tag measured S11. I Figure 6.9, the measured backscattered electric field from the tag is depicted for differet distaces of the tag from the atea. For better compariso, the electric fields are shifted up alog E-axis. It is see that by 168

183 icreasig the distace, the backscattered respose becomes oisy. I order to extract the resoaces of the tag from the backscattered sigal, short-time matrix pecil method (STMPM) is applied to the time-domai sigal. As a example, the frequecy-domai, time-domai, timefrequecy, ad time-residue resposes of the backscattered sigal from the tag located at 3 cm from the atea are show i Figure 6.3. From the time-domai respose, it is see that t= s at which the sigal has its maximum amplitude ca be cosidered as the roudtrip time from the RCS (dbm ) RCS (dbm ) Figure 6.7 Simulated ad measured RCS of the tag whe the icidet electric field is perpedicular to slot legth [88] (With permissio, Copyright 14 IEEE). P r /P t (db) Figure 6.8 Normalized received power at the atea versus frequecy [88] (With permissio, Copyright 14 IEEE). P r /P t (db) frequecy Frequecy (GHz) 169 Measuremet Simulatio frequecy Frequecy (GHz)

184 E (mv/m) E (mv/m) 1-1 Figure 6.9 Measured time-domai respose from the tag for differet distaces [88] (With permissio, Copyright 14 IEEE) cm 3 cm 5cm 7 cm 9 cm time Time (s) tag to the atea. The time-domai respose is composed of early-time ad late-time resposes. The early-time part emaates from the scatterig ceters of the tag ad depeds strogly upo the icidet agle ad polarizatio. The late-time respose is the summatio of damped siusoidals correspodig to the slot poles. All the iformatio embedded o the tag is icluded i the latetime respose. The time-frequecy diagram of the respose shows the resoat frequecies (frequecy-domai data) ad also, the tur-o times (time-domai data) of the resoaces i time. Because of limited time resolutio i time-frequecy aalysis, the exact tur-o time caot be extracted, especially whe multiple tags are preset i the reader area. It also leads to cosiderable error i ragig calculatios. The real ad imagiary parts of the backscattered sigal are show i Figure 6.31 versus frequecy. By applyig NFMPM to the frequecy respose, the distace of the tag from the atea is illustrated for differet cases i a space-frequecy diagram i Figure 6.3. Accordig to this diagram, the scatterig ceters, which i this case are the tags, reflect the icidet pulse. The accuracy of the method is show for differet distaces from tag to atea. The proposed method is applied to the cases where multiple tags are located i the mai beam of the atea. 17

185 E (dbv/m) Real (E) Imagiary (E) E (dbv/m) frequecy Frequecy (GHz) (a) E (mv/m) E (mv/m) Time time (s) (b) T (s) T (s) 3.5 T (s) T (s) frequecy Frequecy (GHz) Frequecy L( R ) (GHz) (c) (d) Figure 6.3 (a) Frequecy-domai, (b) time-domai, (c) time-frequecy ad (d) time-residue represetatio of measured backscattered sigal from the tag [88] (With permissio, Copyright 14 IEEE)... Real(E) Imag(E) Frequecy frequecy (GHz) frequecy Frequecy (GHz) (a) (b) Figure 6.31 (a) Real ad (b) imagiary parts of the measured backscattered sigal from the tag[88] (With permissio, Copyright 14 IEEE). 171

186 Frequecy (GHz) Frequecy (GHz) R (cm) Figure 6.3 Space-frequecy diagram of measured backscattered respose from the tag for differet cases [88] (With permissio, Copyright 14 IEEE). As a example, two -bit tags with high-q resoators are spaced 5cm apart. The sceario ad dimesios of the tags are depicted i Figure 6.33a. A icidet electric field illumiates the tags ad the backscattered respose is retrieved i the reader. The frequecy ad time-domai resposes are depicted i Figures 6.33b-d for two rotatio agles of the secod tag. The tags carry two differet IDs of 1 ad 11, respectively. As the time-domai respose shows, for φ =, the early-time respose of the secod tag is hidde i the late-time respose of the tags. This pheomeo is more severe whe more tags with higher desity data are preset i the reader zoe. I Figure 34, the space-frequecy diagram of the backscattered respose is show for φ=, the worst-case sceario. Compared to the results show i Figure 6.9, the backscattered sigals from the tags are ormalized to the impulse respose of the atea. I the cases where the data is embedded i the spectral-domai respose of the tags, the localizatio caot be efficietly performed based o the time of arrival (TOA) or received sigal stregth (RSS) [89]. Meawhile, by employig the proposed algorithm as show i Figure 6.5, ot oly ca the locatio of the tags be obtaied but their IDs ca also be retrieved successfully. The aforemetioed algorithm ca be employed for fidig the positios of the tags i the reader area. Here, we just cosider oe uit cell covered by three TEM hor ateas as Figure 6.35 depicts. The ateas are iterspersed alog a circle of radius R=65cm. The simulatio is performed i FEKO. The measuremet set-up 17

187 E (V/m) ic E -3-4 E E (dbv/m) (dbv/m) = =3 E (v/m) E (V/m) (a) Time (s) time (c) frequecy Frequecy (GHz) (GHz) (b) Time (s) time (d) Figure 6.33 (a) Two -bit tags illumiated by a icidet electric field. (b) Frequecy-domai respose of the backscattered electric field from two tags, time-domai respose from the tags for (c) φ = º ad (d) φ = 3º [88] (With permissio, Copyright 14 IEEE). E (v/m) Frequecy (GHz) Tag 1 Tag Figure 6.34 Space-frequecy diagram of the backscattered respose from the tags [88] (With permissio, Copyright 14 IEEE) d (cm) 173

188 TEM hor Atea Tag z 15cm x y Figure 6.35 Simulatio set-up i FEKO [88] (With permissio, Copyright 14 IEEE). is show i Figure Three TEM hors are coected to the etwork aalyzer ad two measuremets i the presece ad absece of the tag are performed. By takig the differece betwee two sets of measuremets, the tag respose is retrieved at the atea ports. First, oe tag is cosidered i the reader zoe. By receivig the backscattered resposes at the atea ports ad applyig the proposed techique to the sigals, the distaces of the tag from three ateas are obtaied. The positio of the tag ca be obtaied via triagulatio. I the cases where three circles do ot itersect at a uit poit because of the limited accuracy of the method, the closest poit to the circles is cosidered as the tag positio. For simplicity, we express the positio of the tag i polar represetatio by (ρ, φ). Figure 6.37a shows the time-domai backscattered sigals at the atea ports whe the tag is located at the ceter of the reader area perpedicular to the y-axis. It is see that the stregthbased positioig is ot a accurate techique for localizatio of chipless RFID tags. Depedig o the polarizatio ad directio of the tag with respect to the atea, the stregth of the late-time ad early-time resposes may chage. Hece, at some times the late-time respose ca be stroger tha the early-time respose which makes the localizatio more difficult. Istead, by employig the proposed algorithm show i Figure 6.5, the positios ad IDs of the tags ca be extracted. The simulated, measured, ad real positios of the tag i the uit cell are depicted i Figure 6.37b 174

189 Figure 6.36 Measuremet set-up for localizig the chipless RFID tag [88] (With permissio, Copyright 14 IEEE). E (mv/m) E (mv/m) Time time (s) (a) At. 1 At. At. 3 (degree) (degree) (cm) (b) Real positio simulatio measuremet Figure 6.37 (a) Measured time-domai sigals from the tag located at the ceter of the uit cell, (b) Positio of the tag extracted from the proposed techique compared to real positio [88] (With permissio, Copyright 14 IEEE). for differet situatios. I each situatio, the ID of the tag ca be extracted from the closest atea port due to better SNR.As aother example, two tags are placed i the uit cell. Figure 6.38 shows the time-domai backscattered sigals at the atea ports whe the tags are located at (, 9 ) ad (, 1 ). It is see that for the first ad secod ateas where the secod tag is further from the atea, the tur-o time is ot clearly visible. However, by applyig the proposed techique, the positios of the tags ca be extracted accurately. By applyig short-time matrix pecil method (STMPM) to the time-domai respose received at the first atea port, the time-frequecy 175