location-awareness of mobile wireless systems in indoor areas, which require accurate

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2 To my wfe

3 Abstract Recently, there are great nterests n the locaton-based applcatons and the locaton-awareness of moble wreless systems n ndoor areas, whch requre accurate locaton estmaton n ndoor envronments. The tradtonal geolocaton systems such as the GPS are not desgned for ndoor applcatons, and cannot provde accurate locaton estmaton n ndoor envronments. Therefore, there s a need for new locaton fndng technques and systems for ndoor geolocaton applcatons. In ths thess, a wde varety of techncal aspects and challengng ssues nvolved n the desgn and performance evaluaton of ndoor geolocaton systems are presented frst. Then the TOA estmaton technques are studed n detals for use n ndoor multpath channels, ncludng the maxmum-lkelhood technque, the MUSIC superresoluton technque, and dversty technques as well as varous ssues nvolved n the practcal mplementaton. It s shown that due to the complexty of ndoor rado propagaton channels, dramatcally large estmaton errors may occur wth the tradtonal technques, and the super-resoluton technques can sgnfcantly mprove the performance of the TOA estmaton n ndoor envronments. Also, dversty technques, especally the frequency-dversty wth the CMDCS, can further mprove the performance of the super-resoluton technques. The CRLB derved wth the snglepath AWGN channel model for the tradtonal applcatons s not applcable n ndoor

4 multpath channels. In ths thess, computer smulatons based on the frequency-doman channel measurement data, collected wth a standard channel measurement system n typcal ndoor applcaton envronments, are employed to evaluate the performance of varous TOA estmaton technques. Our smulaton results provde a clear nsght nto the achevable performance n ndoor applcaton envronments. The smulaton method presented n ths thess can be used n practce to convenently establsh emprcal performance benchmarks when desgnng the super-resoluton TOA estmaton systems for ndoor applcatons.

5 Acknowledgements I am deeply ndebted to my advsor Professor Kaveh Pahlavan for a lot more than hs help, encouragement, and advce, and for a lot more than sklls and knowledge that I learned from hm. He has been much more than an advsor to me. Hs words of wsdom, nsght, and phlosophy are among the best thngs that I have learned. Thanks are due to Professor Allen Levesque for hs knd help over the last few years, to Professor Kevn Clements, Professor Wllam Mchalson, and Dr. Robert Tngley for ther valuable comments as my thess commttee members, and to many professors at WPI from whom I have learned greatly. I am also thankful to many frends for ther help n the last few years, especally those n the CWINS, ncludng Dr. Jacques Beneat, Duan Wang, Jeff Fegn, Barda Alav, and Emad Zand, who have provded hearty help n many dfferent ways and shared numerous pleasant hours n the lab. Words cannot express my gratefulness to my dear famly for ther care and support, especally to my grandma, my parents, and my wfe, whose love s the source of my happness and strength.

6 Table of Contents Abstract Acknowledgements Table of Contents Lst of Fgures v v Chapter Introducton. Indoor Geolocaton. Obectves of the Thess 4.3 Contrbutons of the Thess 7.4 Outlne of the Thess Chapter Techncal Aspects of Indoor Geolocaton 3. Introducton 4.. Geolocaton Methods 4.. System Archtecture 8. Channel Characterstcs for Indoor Geolocaton.. Impacts of Channel Characterstcs.. Measurement and Modelng of Indoor Channels 4.3 Locaton Sensng Technques 8.3. Receved Sgnal Strength RSS 9.3. Angle of Arrval AOA Tme of Arrval TOA 33.4 Postonng Algorthms Tradtonal Technques Pattern Recognton Technques 39.5 Summary and Conclusons 4 v

7 Chapter 3 TOA Estmaton for Indoor Geolocaton Maxmum Lkelhood Estmaton of TOA Cramer-Rao Lower Bound for TOA Estmaton TOA Estmaton n Multpath Channels Estmaton of TDOA TOA/TDOA Measurement Methods TOA/TDOA Measurement Methods for Overlad Systems Summary and Conclusons 77 Chapter 4 Super-resoluton TOA Estmaton Technques 8 4. Introducton 8 4. Super-resoluton Technques Issues n Practcal Implementaton Improved Estmaton of Correlaton Matrx wth Lmted Measurement Data Determnaton of Parameters L and L p Egenvector Method 4.4 Dversty Technques 4.5 Summary and Conclusons 8 Appendx 4.A Dervatons of Correlaton Coeffcents 4.A. Correlaton Coeffcents usng Forward Estmaton Method 4.A. Correlaton Coeffcents usng Forward-backward Estmaton Method 4.A.3 Correlaton Coeffcents wth Frequency Dversty 4 Chapter 5 Performance Evaluaton Based on Channel Measurements 6 5. Frequency-Doman Channel Measurement 7 5. Performance Evaluaton Method 5.3 Performance of Super-resoluton Technques Comparson of Super-resoluton and Conventonal Technques Effects of Tme Dversty Effects of Frequency Dversty Summary and Conclusons 39 v

8 Appendx 5.A Measurement Stes and Scenaros 4 5.A. Descrptons of Measurement Stes 4 5.A. Descrptons of Measurement Scenaros 45 Appendx 5.B Cumulatve Dstrbuton Functons of the Rangng Errors 49 Chapter 6 Conclusons and Future Work Conclusons Future Work 63 Bblography 65 v

9 Lst of Fgures. Dstance-based geolocaton method. The radus of the dotted-lne crcle s the real dstance between the MT and the RP; the radus of the sold-lne crcle s the estmated dstance between the MT and the RP.. Drecton-based geolocaton method. The accuracy of the drecton measurement s ± θ. s.3 Functonal block dagram of wreless geolocaton systems. 8.4 Smulaton result of ndoor rado propagaton usng ray-tracng software. The locaton of transmtter s desgnated by a crcle mark, and the locaton of recever by a cross mark. 3.5 Multpath profle of ndoor rado propagaton channel. 6.6 Rado transmsson n the envronment of a macrocell and b mcrocell. All prmary scatters, whch cause multpath transmsson, are assumed located nsde the regon of scatters. 3.7 Phasor dagram for narrowband sgnalng on a multpath channel The ML estmaton of tme delay by cross-correlaton Numercal results of the CRLB of TOA estmaton errors wth dfferent values of bandwdth and the product of bandwdth and observaton tme wth respect to sgnal-to-nose power rato SNR. The carrer frequency s zero Power delay profles wth dfferent channel profles. a Snglepath channel wth propagaton delay D = Tc ; b two-path channel wth sgnal attenuaton parameters α = α, and propagaton delays = Tc and = 5 Tc ; c two-path channel wth sgnal attenuaton parameters α =. 6 α, and propagaton delays = Tc, and =. 5 Tc. 3.4 Inter-frame spacng and medum access prortes. 7 6 v

10 3.5 Uncast data transfer mode for IEEE GRP-based TDOA method for IEEE 8. wreless LAN Fragmentaton mode of IEEE The functonal block dagram of the recever of super-resoluton TOA estmaton systems. H ˆ f s the estmated channel frequency response, whch s defned n The tme-doman MUSIC pseudospectrum, obtaned wth a sample frequency-doman channel measurement data. The estmate of the TOA corresponds to the frst peak of the pseudospectrum, marked by a small crcle sgn as shown on the plot. 4.3 The functonal block dagram of super-resoluton TOA estmaton algorthms. Rˆ xx s the estmated correlaton matrx, L p s the estmated total number of multpath components defned n 4., and S s the tme-doman pseudospectrum defned n Correlaton coeffcents of forward and forward-backward correlaton matrces, wth f = MHz, = 5ns, θ θ =, f = 9 MHz, and L = Correlaton coeffcents of forward and forward-backward correlaton matrces, wth the parameters M = 9, f = MHz, θ θ =, f = 9 MHz, and L = General structure of TOA estmaton wth dversty technques, general dversty combnng scheme GDCS. 4.7 Estmaton of correlaton matrx wth dversty technques for super-resoluton TOA estmaton, correlaton matrx based dversty combnng scheme CMDCS. 4.8 Correlaton coeffcent wth frequency dversty, wth parameters = 5ns, θ θ =, and f c = GHz. 4.9 Correlaton coeffcents of FCM and FBCM wth and wthout frequency dversty, wth parameters f = MHz, = 5ns, θ θ =, f c = GHz, L = 3, and F = MHz. 4. Correlaton coeffcents of FCM and FBCM wth and wthout frequency dversty, wth parameters M = 9, f = MHz, θ θ =, f c = GHz, L = 3, and F = MHz v

11 5. Block dagram of the frequency-doman channel measurement system. 5. Frequency-doman channel measurement data obtaned usng the measurement system n Fg Mean of rangng errors usng the MUSIC and EV algorthms wth the forward FCM and forward-back FBCM estmaton of correlaton matrx. The vertcal lne corresponds to plus and mnus one standard devaton of the rangng errors about the mean. 5.4 Normalzed tme-doman channel responses obtaned usng three dfferent technques. The vertcal dash-dot lne denotes the expected TOA. The estmated TOA s marked on the tme-doman channel response for each of the three technques. 5.5 Mean of the estmaton errors usng three dfferent technques. The vertcal lne corresponds to plus and mnus one standard devaton. 5.6 Percentages of the measurement locatons where absolute rangng errors are smaller than 3 meters wth three dfferent TOA estmaton technques. 5.7 Mean and standard devaton of rangng errors wthout tme dversty EV/FBCM, wth tme dversty usng the CMDCS EV/FBCM/TD4-CMDCS and GDCS schemes EV/FBCM/TD- GDCS. 5.8 Cumulatve dstrbuton functon of the absolute rangng errors for a bandwdth of MHz wth frequency dversty A. A snapshot of Plant 7, Norton Co., Worcester, MA A. A snapshot of the Fuller Laborotores, WPI, Worcester, MA A.3 A snapshot of Schussler house, WPI, Worcester, MA A.4 Buldng layout wth transmtter and recever locatons at the 46 ground level of Plant 7, Norton Co., Worcester, MA. 5.A.5 Buldng layout wth transmtter and recever locatons at Fuller 47 Laboratores, WPI, a for ndoor-to-ndoor and outdoor-to-ndoor scenaros, b for outdoor-to-second floor scenaros. 5.A.6 Buldng layout wth transmtter and recever locatons at Schussler house, WPI, a for ndoor-to-ndoor and outdoor-to-ndoor scenaros, b for outdoor-to-second floor scenaros x

12 Chapter Introducton. Indoor Geolocaton In recent years, wth the fast advancement of wreless communcaton technologes and the ever ncreasng penetraton level of moble computng devces nto the people s daly lfe, there are ncreasng nterests n the locaton-based applcatons and the locaton fndng systems for ndoor areas, that s, nsde and around buldng envronments [Bac97, Wer98, Bah, Wan, Pahb]. The avalablty of the locaton nformaton of moble computng devces wll enable the creaton of a large number of new locaton-based applcatons. In commercal applcatons, there s an ncreasng need for locaton fndng systems n ndoor areas to track people wth specal needs, such as the elderly and chldren who are away from vsual supervson, to navgate the blnd, to locate n-demand personnel and equpments n hosptals, and to fnd people and specfc tems n large buldng complex, such as shoppng mall and warehouses, among many other smlar applcaton scenaros. In publc safety and mltary applcatons, locaton fndng systems are needed to track nmates n prsons and to navgate polcemen, frefghter, and solders to complete ther mssons nsde and around buldngs. In addton, locaton-awareness has been wdely accepted as a key

13 feature of the next generaton wreless systems. Wth the accurate locaton nformaton of the users of moble devces, such as laptop computers, cellular phones, and handheld PDAs, servce provders may provde locaton-senstve bllng, locaton-specfc advertsement, and the lke locaton-aware servces. The next generaton locaton-aware moble devces, beng a powerful communcaton and/or computng devces carred by users at all tme, wll be often used n ndoor envronments. Therefore, t s mportant to employ the locaton fndng technques that can perform accurate locaton estmaton n ndoor envronments. The exstng geolocaton systems such as the Global Postonng System GPS and wreless enhanced 9 servce system E-9 also address the ssue of locaton fndng [[Kap96, Caf98], but these technologes are not desgned for ndoor applcatons, and they cannot provde accurate locaton nformaton n ndoor envronments. For example, the GPS s desgned for locaton fndng applcatons n the open envronments where drect vsual contact exsts between the GPS recever devce and at least four GPS satelltes, and the GPS sgnals are not desgned to penetrate nto most of the constructons on the ground. Also, ndoor geolocaton systems are very dfferent from the tradtonal locaton fndng systems such as the GPS and the E-9 n many aspects, ncludng applcaton scenaros, operatng envronments, system requrements, and performance requrements. Therefore, there s a need for new locaton fndng technques to provde accurate locaton estmaton n ndoor envronments, whch are specfcally desgned for ndoor applcatons to cope wth the unque challenges and to

14 explot the unque features theren. The ndoor geolocaton s emergng as a new mportant feld for research and development. In the past a few years, many researchers have worked on varous aspects of the ndoor geolocaton. Wth the wde spread use of the tradtonal geolocaton systems such as the GPS, locaton fndng technques have been studed for many years and now there s a rather rch lterature on ths subect. But very few of the exstng studes on the locaton fndng technques are specfc to ndoor applcatons. Also, a large amount of research work has been conducted on the applcaton layer aspects of ndoor geolocaton n the context of locaton-awareness and context-awareness of moble computng devces by researchers wth computer scence background wthout too much concern about the underlyng locaton fndng systems, such as [Bac97, Ban]. Many relevant references n the lterature related to varous aspects of the ndoor geolocaton wll be surveyed n detals and referred n later chapters where t s approprate. In addton to the ever ncreasng nterests n ndoor geolocaton n research communty, a varety of the frst generaton ndoor locaton fndng products have been emergng nto the market, such as those reported n [Wer98, Fon] search wth Google for more relevant products wth key words such as ndoor geolocaton and local postonng. In [Pah98], t was shown that the rado propagaton channel characterstcs have tremendous effects on the accuracy of the locaton estmaton n ndoor envronments, whch necesstates a devoted study on the locaton fndng technques for ndoor applcatons. To help the growth of the emergng ndustry of the ndoor geolocaton, 3

15 there s a need for a scentfc framework to lay a foundaton for the desgn and performance evaluaton of such systems. Ths thess s concerned wth accurate locaton fndng technques and systems for applcatons n ndoor envronments, where the tradtonal geolocaton systems cannot operate properly to provde accurate locaton estmaton. In ths thess, we ntend to conduct an n-depth study of the locaton fndng technques and systems, especally the tme-of-arrval TOA estmaton technques, n order to provde a fundamental understandng of varous ssues related to ndoor geolocaton, and to provde a basc foundaton for the desgn and performance evaluaton of ndoor geolocaton systems. Detaled descrpton of the obectves of ths thess s presented n the next secton.. Obectves of the Thess As dscussed n last secton, the ndoor geolocaton system has dfferent applcaton scenaros and dfferent system requrements than the tradtonal systems, and the tradtonal geolocaton systems such as the GPS do not work properly n ndoor envronments. Also some unque features of ndoor applcatons can be exploted to develop new technques, whch can be used to sgnfcantly mprove the performance of the locaton fndng systems n ndoor envronments. Therefore, there s a need for new and nnovatve technques to handle the locaton fndng problems n ndoor envronments. However, the ndoor geolocaton s a new emergng research feld, and there s stll no scentfc framework to apply for the desgn of ndoor locaton fndng 4

16 systems. As part of the research proect Indoor Geolocaton Scence funded by the Natonal Scence Foundaton NSF, the prncpal goal of ths work s to provde a fundamental understandng of the ssues related to the ndoor geolocaton technques and systems, and to establsh a foundaton for the desgn and performance evaluaton of ndoor geolocaton systems. More specfcally, three obectves are dentfed for ths research work as explaned n detals n the followng. The frst obectve s to conduct a systematc study of the locaton fndng technques and systems to dentfy the unque features and the challengng ssues related to ndoor geolocaton, and to provde a fundamental understandng of ths new emergng feld. The research work presented n ths thess s only concerned wth radolocaton systems. In radolocaton systems, the locaton coordnate of a target moble unt s estmated from the locaton related characterstcs of the rado sgnals communcated between spatally separated unts. As a result the rado propagaton channel has sgnfcant mpacts on the performance of the locaton fndng technques and systems. To acheve the frst obectve, the system archtectures and radolocaton technques that can be used for ndoor applcatons wll be studed as well as the effects of ndoor rado propagaton channel characterstcs on the performance of the locaton fndng technques and systems. As we wll present n Chapter, a locaton fndng system conssts of three functonal modules, ncludng locaton sensng, postonng, and dsplay elements or locaton-based applcatons. The locaton sensng devces measure the locaton metrcs such as the tme of arrval TOA and the angle of arrval AOA drectly from the 5

17 receved rado sgnals, whch are related to the relatve poston of a moble termnal wth respect to a remotely located reference pont wth known locaton coordnate. As the second obectve of ths thess, we ntend to conduct comprehensve study of the techncal aspects of the TOA-based locaton sensng technques and ther applcablty to ndoor applcatons. The TOA estmaton technques have been wdely used n a number of tradtonal locaton fndng systems such as radar, sonar, and the GPS. In ths thess, we frst examne the exstng TOA estmaton technques and study the applcablty of these technques to ndoor applcatons. As we wll present n ths thess, the unque characterstcs of ndoor rado propagaton channels make t very challengng to accurately estmate the TOA wth the tradtonal estmaton technques n ndoor envronments. Therefore, sgnfcant amount of efforts have been devoted n ths thess to explore new sgnal processng technques to accurately estmate the TOA n ndoor envronments, ncludng super-resoluton technques and dversty technques. The super-resoluton TOA estmaton technques are desgned by applyng the superresoluton spectrum estmaton algorthms to the estmated frequency response of the multpath ndoor rado propagaton channels. The dversty technques are used to further mprove the performance of the super-resoluton TOA estmaton technques n ndoor envronments. Performance study, ncludng comparatve performance study and performance benchmarkng among others, s one of the most mportant ssues encountered n the desgn of sgnal processng technques and systems. The performance study of the TOA estmaton technques n the realstc applcaton scenaros provdes an nsght nto the 6

18 achevable accuracy of ndoor geolocaton system. Therefore, as another obectve we explore the channel measurement data based smulaton methods to compare the performance of varous TOA estmaton technques presented n ths thess and to provde a performance benchmark of varous technques that can be acheved n typcal ndoor applcaton envronments. The channel frequency response can be readly measured wth a frequency-doman channel measurement system so that the channel measurement data based smulaton method presented n ths thess provdes a convenent means to establsh performance benchmarks when desgnng superresoluton TOA estmaton based ndoor locaton fndng systems..3 Contrbutons of the Thess The ndoor geolocaton s a new emergng research feld, and s concerned wth accurate locaton fndng technques and systems n ndoor envronments, where the tradtonal geolocaton systems do not work properly. The orgnal work presented n ths thess has made contrbutons to the lterature of ths new emergng feld n the followng aspects. Frst, an overvew of a wde varety of techncal aspects and challengng ssues of ndoor geolocaton s presented, whch provdes a basc foundaton for the desgn and performance evaluaton of ndoor geolocaton systems, and forms a bass for further research work n ths feld. The orgnal work n ths regard s presented n Chapter and has been publshed n [Pahb]. Second, the tradtonal TOA and TDOA tme-dfference-of-arrval estmaton technques are presented, and the mpacts of ndoor rado propagaton channels on the 7

19 performance of tradtonal technques are studed n detals. It s shown that due to the complexty of the multpath ndoor rado propagaton channels, dramatcally large estmaton errors may occur wth the tradtonal estmaton technques, and the Cramer- Rao lower bound CRLB derved for the tradtonal applcaton scenaros s no longer applcable n ndoor envronments. Our research provdes a fundamental understandng of the challengng ssues nvolved n the TOA estmaton n ndoor envronments. Relevant results are presented n Chapter 3, and have been publshed n [L]. Thrd, for the dedcated geolocaton systems, the TOA can be easly measured wth a synchronzed transcever method or a round-trp TOA method, but drect applcaton of these smple methods s dffcult for overlad systems. A nonsynchronzed method s desgned to measure TOA/TDOA wth the WLAN wreless local-area network sgnals, whch s presented n Chapter 3 and has been publshed n [La, Lb]. Such a method can be used to overlay the geolocaton functonalty onto the exstng wreless LANs wthout sgnfcant modfcaton to the exstng nfrastructure and sgnalng formats. Forth, the super-resoluton spectral estmaton technques are appled to the TOA estmaton n the multpath channels on the bass of the frequency-doman representaton of the multpath channel models. The ssues n the practcal mplementaton of the super-resoluton TOA estmaton technques are studed and several mprovement technques ncludng dversty technques are proposed to mprove the performance of the super-resoluton technques. Dversty technques and two dversty combng schemes are presented and studed for use wth the super-resoluton 8

20 technques. The effects of the frequency dversty technques are analyzed, and t s shown that frequency dversty can further mprove the performance of the superresoluton technques. The orgnal work n ths regard s presented n Chapter 4, and has been publshed n [La, Lb]. Ffth, a channel measurement data based performance evaluaton method s proposed and employed n ths thess to compare and benchmark varous TOA estmaton technques n typcal ndoor applcaton envronments. There s no sutable ndoor rado propagaton channel model avalable n the lterature to evaluate the performance of the TOA estmaton technques n ndoor envronments. In our research, the super-resoluton and the dversty technques are evaluated and compared wth the tradtonal technques usng the computer smulatons based on the emprcal channel measurement data. Our smulaton results provde a clear nsght nto the achevable performance of varous TOA estmaton technques n the realstc ndoor applcaton envronments, whle the CRLB performance bound obtaned for the tradtonal applcatons cannot be used to benchmark the performance of the TOA estmaton technques n ndoor envronments due the exstence of the no-lne-of-sght NLOS stuatons. The measurement data based smulaton method that we employed can be used n practce to establsh emprcal performance benchmarks for the real mplementaton of the super-resoluton TOA estmaton based ndoor geolocaton systems. The relevant results n ths regards are presented n Chapter 5 and have been publshed n [Lb, L]. 9

21 .4 Outlne of the Thess The rest of the thess s organzed as follows. In Chapter, we present a bref overvew of a wde varety of the techncal aspects and challengng ssues nvolved n the desgn and performance evaluaton of ndoor geolocaton systems, whch provdes a fundamental understandng of ndoor geolocaton systems, and forms a bass for the research work presented n the later chapters. In Secton., an ntroducton of geolocaton methods and system archtectures s frst presented. Then the techncal aspects, challengng ssues, and potental research topcs related to rado propagaton channels, locaton sensng technques, and postonng algorthms for ndoor geolocaton applcatons are dscussed n detals n the followng three sectons, respectvely. Ths thess s manly concerned wth the TOA-based radolocaton technques and systems for ndoor applcatons so that startng from Chapter 3 we wll focus on the TOA estmaton technques. In Secton 3. and 3., we frst present the maxmum lkelhood TOA estmaton technques and the CRLB, respectvely, whch are derved for the tradtonal applcatons by modelng the rado propagaton channel as the snglepath AWGN channels. Snce the ndoor rado propagaton channel s known as severe multpath channel, n Secton 3.3 we study the effects of the multpath propagaton on the performance of the TOA estmaton technques n ndoor envronments. The TDOA s another tme delay-based locaton metrcs that can be used n place of the TOA. In tradtonal applcatons both locaton metrcs have smlar estmaton technques and performance. Therefore, n Secton 3.4 we also brefly study the estmaton technques

22 as well as the performance of the TDOA estmaton n sngle-path and multpath channels. Our prelmnary analyss wll show that the TDOA becomes less approprate than the TOA n the multpath channels. At last, n Secton 3.5, the ssues nvolved n the practcal measurement of the TOA wth spatally separated moble unts are dscussed and the technques for synchronzng and coordnatng the remotely located transmtter and recever to measure the TOA/TDOA are presented for both dedcated and overlad locaton fndng systems. In Chapter 4, we study the super-resoluton technques that can be used n the multpath ndoor rado propagaton channels to more accurately estmate the TOA than the tradtonal technques. In ths chapter, the background and theoretcal development of the MUSIC super-resoluton TOA estmaton technque are frst presented n Secton 4. and 4., respectvely. Then n Secton 4.3 we present the ssues n the practcal mplementaton of the super-resoluton technques, and analyze the effects of several technques that can be used n practce to mprove the performance of the superresoluton technques. At last, n Secton 4.4 dversty technques and dversty combng schemes are ntroduced and analyzed. From the analyss t s shown that the frequency dversty technque can sgnfcantly enhance the performance of the superresoluton TOA estmaton technques. To keep the presentaton of ths chapter concse and easy to follow, some detaled mathematcal dervaton s omtted from the man content, but presented n the appendx at the end of the chapter. In Chapter 5, we evaluate the performance of varous TOA estmaton technques presented n Chapter 3 and 4 wth the computer smulatons based on

23 channel measurement data, whch s collected n typcal ndoor applcaton envronments. The channel measurement system s frst ntroduced n Secton 5., followed by a descrpton of the performance evaluaton method employed n ths thess. In Secton 5.3, several super-resoluton technques presented n Chapter 4 are evaluated and compared wth smulaton results. In Secton 5.4, to demonstrate the usefulness of the super-resoluton technques, the super-resoluton technques are compared wth two conventonal TOA estmaton technques. At last, the effects of the tme and frequency dversty technques are evaluated n Secton 5.5 and 5.6, respectvely. A descrpton of the measurement stes and scenaros are presented n Appendx 5.A, and the cumulatve dstrbuton functons of the rangng errors wth dfferent TOA estmaton technques are presented n Appendx 5.B for the reference purposes. At last, the thess s concluded wth conclusons and a dscusson of future work n Chapter 6.

24 Chapter Techncal Aspects of Indoor Geolocaton In recently years, there are ncreasng nterests n locaton-based applcatons n ndoor envronments. Locaton fndng systems such as the GPS have been wdely used for many years. The tradtonal geolocaton systems are not desgned for ndoor applcaton, and they cannot provde accurate locaton estmaton n ndoor envronments. As compared wth the tradtonal systems, the ndoor geolocaton systems have dfferent applcaton scenaros, operatng envronments, system requrements, and performance requrements, among many others. Currently, there exsts a rch lterature on locaton fndng technques. But unfortunately, very few of the exstng studes on ths subect are specfc to ndoor applcatons. The ndoor geolocaton s emergng as a new mportant feld for research, whch deserves a devoted n-depth study. In ths chapter we present a bref overvew of a wde varety of the techncal aspects and challengng ssues nvolved n the desgn and performance evaluaton of ndoor geolocaton systems, whch provdes a fundamental understandng of ndoor geolocaton systems, and forms a bass for the research work presented n the 3

25 later chapters. In Secton., we frst present an ntroducton of geolocaton methods and system archtectures. Then techncal aspects, challengng ssues, and potental research topcs related to rado propagaton channels, locaton sensng technques, and postonng algorthms for ndoor geolocaton applcatons are dscussed n detals n the followng three sectons, respectvely.. Introducton.. Geolocaton Methods The geolocaton method, that s, the method used by geolocaton systems to fnd the locaton of a moble termnal MT, can be classfed nto three categores: deadreckonng, proxmty method, and radolocaton method [Caf99]. The dead-reckonng method s based on accurate measurement of the MT s acceleraton, velocty, and drecton of movements usng varous nertal sensors of the MT, ncludng gyroscopes, accelerometers, and magnetc compasses among others. Gven a known startng poston of the MT, the traectory of the MT can be easly determned wth contnuous accurate measurement of the acceleraton, velocty, and movement drecton of the MT. Snce the dead-reckonng method reles on accurate update of the MT s locaton coordnates wth respect to the prevous locaton estmates, the estmaton error tends to accumulate. Wth proxmty locaton method, the MT s locaton s roughly determned to the proxmty of the nearest fxed reference ponts RP. The detecton of proxmty to a fxed RP can be accomplshed through a large varety of technques ncludng magnetc sensors and conventonal rado transmtters and recevers. The performance 4

26 of the proxmty method depends on the coverage of each fxed RP as well as the densty of the RP nfrastructure network. The radolocaton system estmates the MT s locaton by measurng varous characterstcs, such as receved sgnal strength RSS, angle of arrval AOA, and tme of arrval TOA that we wll dscuss later n ths chapter, of the rado sgnals transmtted between the MT and a number of fxed RPs. Ths thess s manly focused on the radolocaton related technques and systems for ndoor geolocaton applcatons. d RP MT d RP RP 3 d 3 Fgure.: Dstance-based geolocaton method. The radus of the dotted-lne crcle s the real dstance between the MT and the RP; the radus of the sold-lne crcle s the estmated dstance between the MT and the RP. The radolocaton method can be further categorzed nto two classes: dstancebased method and drecton-based method. The dstance-based method reles on the 5

27 estmaton of the dstance between the MT and a number of fxed RPs. As shown n Fg.., each dstance measurement wll geometrcally determne a crcle, centered at the RP, whch ndcates possble locaton of the MT. Accurate dstance measurements from the MT to a mnmum of three RPs provde a poston fx and gven the locaton coordnates of the RPs, the MT s locaton coordnate can be easly determned. Usually, the dstance estmates based on the TOA measurements n radolocaton system are larger than the true dstance between the transmtter and the recever [Mor95], n whch case three dstance measurements determne a regon of the possble MT locatons as depcted n Fg.., whch s known as the regon of uncertanty [Tek98]. Otherwse, f the estmated dstance s smaller than the real dstance, three dstance measurements may not be able to provde a poston fx nor a regon of uncertanty. As a result, more than three RPs are normally needed to mprove the locaton accuracy. RP α θ s MT RP α Fgure.: Drecton-based geolocaton method. The accuracy of the drecton measurement s ± θ s. 6

28 The drecton-based radolocaton method uses smple trangulaton to locate the transmtter as shown n Fg... Each RP measures the arrval drecton of the receved sgnals,.e., the angel of arrval AOA, from the MT, whch s ndcated by the dashed lne connectng the MT and the RP n the dagram n Fg... Accurate drecton measurements from the MT to a mnmum of two RPs provde an exact poston fx and gven the locaton coordnates of the RPs, the MT locaton coordnate can be easly determned. If the accuracy of the drecton measurement s ± θ s, AOA measurement at the RP recever wll restrct the MT poston nsde the beam around the dashed lne-ofsght LOS sgnal path wth an angular spread of θ s. The AOA measurements at two RP recevers wll provde a poston fx wthn the overlappng regon of the two beams as llustrated n Fg... We can clearly observe that gven the accuracy of the AOA measurement, the accuracy of poston estmaton degrades wth ncreasng dstance between the RP and the MT. On the other hand, the accuracy of the poston estmaton depends upon the MT poston wth respect to the RPs. For example, when the MT les between the two recevers, two AOA measurements wll not be able to provde a poston fx. As a result, more than two RPs are normally needed to mprove the locaton accuracy. The technques and the performance of the TOA-based dstance estmaton and the AOA-based drecton estmaton wll be further dscussed later n ths chapter n Secton.3. 7

29 Receved RF sgnal Locaton Sensng Locaton metrcs: TOA, AOA, RSS, Locaton coordnates x, y, z Postonng Algorthm Dsplay System Locaton Sensng Fgure.3: Functonal block dagram of wreless geolocaton systems... System Archtecture Fgure.3 llustrates the functonal block dagram of a wreless geolocaton system. The man elements of the system are a number of locaton sensng devces that measure/estmate the metrcs related to the relatve poston of a gven MT wth respect to a known RP, a postonng algorthm that processes the metrcs reported by locaton sensng elements to estmate the locaton coordnate of the MT, and a dsplay system that llustrates the locaton of the MT to users. The locaton metrcs may ndcate the approxmated arrval drecton of the sgnal or the approxmated dstance from the MT to the RP to be used n the drecton-based or the dstance-based geolocaton methods, respectvely, whch are dscussed n the prevous secton. The angle of arrval s the common metrc used n the drecton-based systems. The receved sgnal strength, the carrer sgnal phase, and the tme of arrval of the receved sgnal are the metrcs used for the estmaton of the dstance. As the measurement of the metrcs becomes less relable, the complexty of the postonng algorthm ncreases. The dsplay system can 8

30 smply show the coordnates of the MT or t may dentfy the relatve locaton of the MT n the layout of an area. Ths dsplay system could be a software resdng n a prvate PC or a moble locaton-fndng unt, or a locally accessble software n a local area network LAN or a unversally accessble servce on the web. Obvously, as the horzon of the accessblty of the nformaton ncreases the desgn of dsplay systems becomes more complex. The overall archtectures of geolocaton systems can be generally grouped nto two categores: moble-based archtecture and network-based archtecture. For both cases, multple RPs are needed to geometrcally locate a MT based on the measurements of relatve dstance or drecton from the MT to the RPs as we presented n the prevous secton. Wth moble-based archtecture, the MT performs all three functons shown n Fg..3,.e., locaton sensng, postonng, and dsplay. The MT extracts locaton metrcs from the receved rado sgnals that are transmtted by the RPs, calculates ts own locaton coordnate, and then dsplays t to the MT user. The moblebased archtecture s used when the locaton nformaton s manly used by the MT user as n most of the GPS-based applcatons. But f needed, the MT s locaton coordnate can also be forwarded to a central ste, such as Geolocaton Control Staton GCS, to provde other locaton-based applcatons and servces. Wth network-based archtecture, the RP performs locaton sensng by measurng receved rado sgnal from the MT. Then the RPs report locaton metrcs to the GCS, where the MT s locaton coordnate s estmated usng a postonng algorthm. The selecton of the geolocaton system archtecture depends on where the geolocaton nformaton s needed,.e., n the 9

31 MT or n the GCS, and some other mplementaton consderatons for specfc applcaton scenaros. For example, wth network-based archtecture, the MT can be mplemented much smpler than wth moble-based archtecture snce the MT does not need to perform locaton sensng and postonng functons wth the network-based archtecture. There are two basc approaches to desgn a wreless geolocaton system. The frst approach s to develop new sgnalng system and network nfrastructure of the locaton sensors focused prmarly on locaton-fndng applcatons. The second approach s to use an exstng wreless network nfrastructure to locate the MT. The advantage of the frst approach s that physcal specfcaton, and consequently the qualty of the locaton sensng results, s under the control of desgners. Wth ths approach, the MT can be desgned as a very small wearable tag or a stcker and the densty of sensor nfrastructure can be adusted to the requred accuracy of locatonfndng applcatons. The advantage of the second approach s that t avods the expensve and tme-consumng deployment of the sensor nfrastructure, and no sgnfcant change to the physcal layer hardware component s needed. Such a system, however, needs to use more ntellgent postonng algorthms at the applcaton layer to compensate for the low accuracy of the measured locaton metrcs. Both approaches have ther own markets, and desgn work on both technologes has been pursued n the past a few years [Caf98, Paha, Wer98, Bah]. From the Fg..3, we can observe that the performance of wreless geolocaton systems, that s the accuracy of the estmate of locaton coordnates, are determned by

32 the qualty of the receved rado sgnal, the performance of the locaton sensng elements, and the performance of the postonng algorthms n sequence. The ndoor rado propagaton channel characterstcs are very dfferent from that of the channels encountered by the tradtonal wreless geolocaton systems ncludng the GPS, sonar, radar, and etc. Thus the locaton sensng technques used n the tradtonal wreless geolocaton systems may not provde the optmum performance n ndoor envronments and on the other hand, the rado propagaton channel models used n developng locaton sensng technques for the tradtonal applcatons are not sutable for ndoor applcatons. To desgn optmum locaton sensng technques and to examne the performance of dfferent sgnalng technques and geolocaton approaches, the ndoor rado propagaton channel needs to be studed and modeled through emprcal channel measurements. As we ust mentoned, the performance of locaton sensng elements s largely determned by the rado propagaton channel characterstcs. Thus n ndoor applcaton envronments the estmates of locaton metrcs, that s the output of locaton sensng elements, show dfferent statstcal characterstcs as compared wth the tradtonal geolocaton systems. As a result, tradtonal postonng algorthms may not provde optmum performance n ndoor envronments, whch necesstates the desgn of new postonng algorthms for ndoor geolocaton systems. In the next three sectons, we address wth more detals the techncal ssues related to channel measurement and modelng, locaton sensng technques, and postonng algorthms, respectvely, for wreless ndoor geolocaton systems.

33 . Channel Characterstcs for Indoor Geolocaton In order to desgn better technques and evaluate system performance, we need to study, by measurement and modelng, how channel characterstcs would affect the accuracy of locaton sensng elements and postonng algorthms. In ths secton we brefly revew the effects of ndoor rado propagaton channel characterstcs on the estmaton of locaton metrcs, and the methods for measurement and modelng of ndoor rado propagaton channels for geolocaton applcatons. More detaled dscusson about the effects of channel characterstcs on the estmaton of locaton metrcs s deferred and wll be presented n Secton.3... Impacts of Channel Charactrstcs The ndoor rado propagaton channel s normally characterzed as severe multpath, low avalablty of lne of sght LOS sgnal propagaton path between the transmtter and the recever, and ste-specfc [Pah95]. Fgure.4 shows a smulaton result of ndoor rado propagaton usng raytracng software. In ray-tracng smulatons of rado propagaton channels, the rado sgnal s modeled as rays as n the study of optcs. Rays of rado sgnal emanated from the transmtter reach the recever after transmsson through and reflecton from walls, or other sgnal scatterng obects, whle scatterng obects have dfferent sgnal attenuaton parameters for transmsson and reflecton. As a result a large number of rays of rado sgnal wll arrve at the recever wth varyng arrval tme and sgnal power

34 through dfferent propagaton path. Ths propagaton phenomenon s known as multpath propagaton. Fgure.4: Smulaton result of ndoor rado propagaton usng ray-tracng software. The locaton of transmtter s desgnated by a crcle mark, and the locaton of recever by a cross mark. In geolocaton applcaton, we are only nterested n estmatng the arrval tme or the arrval drecton of the sgnal arrvng through the drect lne-of-sght DLOS rado propagaton path for dstance-based or drecton-based geolocaton methods, respectvely, whch were dscussed n Secton.. But n severe multpath propagaton condtons, the multpath components wll nterfere wth the DLOS sgnal, whch makes the accurate measurement of locaton metrcs a very challengng task. Normally large estmaton errors of locaton metrcs are resulted from multpath nterferences. When 3

35 the DLOS s not detectable, whch s known as no-los NLOS stuatons, dramatcally large errors occur n locaton sensng results snce the arrval tme of a multpath component s detected erroneously as the arrval tme of the DLOS sgnal. The NLOS stuaton can be resulted from a number of dfferent condtons. For example, f the DLOS sgnal path between the transmtter and the recever s obstructed when measurng the TOA, low recever senstvty and small recever dynamc rage may easly result n the NLOS stuaton [Pah98]. Thus two maor sources of errors n the measurement of locaton metrcs n ndoor envronment are the multpath nterference and the NLOS stuaton. In addton, the ste-specfc nature and the tme dependent fadng effect, whch s caused by random movement of scatterng obects such as people n the applcaton envronment, of the ndoor rado propagaton channels make t dffcult to model and smulate the channel and also makes the geolocaton sensor network nfrastructure ad hoc n nature. The ste-specfc sensor network nfrastructure s generally dffcult to deploy, whch necesstates an n-depth study of the system archtectures and the practcal deployment methods and rules for the ad hoc sensor networks n ndoor applcaton envronment... Measurement and Modelng of Indoor Channels Emprcal channel measurement s essental to study and model the rado propagaton channel and to check the valdty of the modelng results. In the lterature varous measurement results of ndoor rado propagaton channel have been reported for 4

36 frequences from to 6 GHz for telecommuncatons applcatons [Pah95]. The same channel measurement systems can be used for geolocaton applcatons, but the measurement results collected for telecommuncatons applcatons cannot be used drectly for geolocaton applcatons because they do not have a well-calbrated estmate of the AOA, RSS, and/or TOA of the DLOS sgnal, and an accurate measurement of the physcal drecton and/or dstance from the transmtter to the recever. A new set of short-range wde-band measurement data of ndoor rado propagaton channel has been collected and calbrated n CWINS for the TOA-based geolocaton applcatons [Ben99], whch s used n ths thess to evaluate the performance of the TOA estmaton technques. More ndoor rado propagaton channel measurements are needed to study and model the channel for wreless ndoor geolocaton systems usng dfferent locaton sensng technques ncludng the RSS, TOA, and AOA as well as dfferent combnatons of these technques. Rado propagaton channel models are developed to provde a means to analyze the performance of a wreless recever. Performance crtera for telecommuncaton and geolocaton systems are qute dfferent as dscussed n [Pah98]. The performance crteron for telecommuncaton systems s the bt error rate BER of the receved data stream whle for geolocaton systems performance measure s the accuracy of the estmated locaton coordnates. The accuracy of locaton estmaton s a functon of the accuracy of locaton sensng and the accuracy of postonng. Thus channel models for geolocaton applcatons have to reflect the effects of channel behavor on the estmated 5

37 value of the locaton metrcs at recevers, such as the RSS, TOA, AOA, or any combnaton of these metrcs. DLOS path strength and relatve strengths of the other paths used for geolocaton RMS delay spread used for telecommuncatons Multpath profle Fgure.5: Multpath profle of ndoor rado propagaton channel. Whle we do not have any good models for the multpath characterstcs of the ndoor rado propagaton channels for geolocaton applcatons, three classes of recent statstcal modelng approaches can be employed to develop relable models n the future, whch are the wdeband D multpath modelng, the 3D geometrcal statstcal modelng, and the 3D measurement-based statstcal modelng [Pahb]. In the measurement-based D statstcal modelng, the measurement data are used to defne a dscrete multpath profle smlar to the one shown n Fg..5, whch s expressed mathematcally n the followng form L p k= h = α δ,. k k where L p s the number of multpath components, and k α k = α k e φ and k are the complex ampltude and the propagaton delay of the kth path, respectvely. The 6

38 measurement systems for ths approach are the same as the measurement systems used for telecommuncaton applcatons [Pah98, Ben99]. However, these systems are calbrated for accurate measurement of the arrval tme of the DLOS sgnal path and for each measurement the physcal dstance between the transmtter and the recever s accurately recorded. Prelmnary measurement and modelng work n ths feld s reported n [Kr99, Ben99]; larger calbrated measurement databases and more practcal multpath models need further nvestgaton. In the 3D modelng, the mathematcal model of the multpath rado propagaton channel s represented by L p k= h, θ = α δ, θ θ,. k k k where θ k s the arrval drecton of the kth path [Tn]. Whle n the D modelng each path was assocated wth an arrval tme, n the 3D modelng each path s assocated wth an arrval tme and an arrval drecton. The 3D models can be developed ether based on the geometrcal statstcal analyss of the arrval paths from dfferent drectons or based on emprcal 3D channel measurement data. The 3D geometrcal statstcal models, developed for smart antenna applcatons, use an analytcal approach to relate propagaton parameters to the structure of scatterng n the applcaton envronment [Has]. In ths approach, a mathematcal descrpton of rado propagaton based on statstcal buldng features and a geometrc optcs approxmaton of Maxwell s equatons s employed to derve the relevant rado propagaton models such as the dstrbutons of the arrval tme, drecton, and strength of arrvng paths. Further research n ths area s needed to develop statstcal models for the arrval tme of the 7

39 DLOS path and ts relaton wth respect to other paths to make them useful for the performance analyss of geolocaton systems. In the 3D measurement-based statstcal modelng, results of the measured characterstcs of rado propagaton channels are used to develop models sutable for the performance evaluaton of the geolocaton systems based on the AOA, TOA and RSS. The maor challenge for ths approach s the mplementaton of a system to measure the 3D characterstcs of rado channels. Recently, two technques have been studed for ths purpose. Usng the frst technque, a drectonal antenna s mechancally rotated to measure the strength of the sgnal arrvng from dfferent drectons, whle usng the second technque, a set of eght channel mpulse responses are measured usng an antenna array and the AOA are calculated usng sgnal processng technques [Tn]. Prelmnary 3D modelng of an ndoor rado propagaton channel usng a lmted database n a buldng s avalable n [Tn]. More extensve measurement and modelng n ths feld are needed to develop relable channel models for ndoor geolocaton applcatons..3 Locaton Sensng Technques As we dscussed n Secton., the locaton sensng elements measure the RSS, AOA and TOA as locaton metrcs. The ndoor rado propagaton channel suffers from severe multpath propagaton and heavy shadow fadng condton so that the measurements of the RSS and AOA provde a less accurate metrcs than that of the TOA [Paha]. As a result, smlar to the GPS systems, ndependent systems desgned 8

40 for ndoor geolocaton normally employ the more accurate TOA as the locaton metrc. Systems usng exstng nfrastructures nstalled for wreless LAN or the 3G ndoor systems may use the measurements of RSS, AOA, TOA, or any combnaton of these metrcs to fully explot the exstng hardware/software mplementaton desgned for the tradtonal telecommuncaton applcatons [Bah]. For example, n wreless communcaton systems, the RSS nformaton s usually easly accessble, thus t makes sense to fnd ways to explot the RSS nformaton to further mprove the geolocaton performance. As a result, although ths thess s focus on the TOA-based geolocaton technques, ssues related to the estmaton of the RSS and AOA are brefly dssucssed n the followng together wth the sssues related to the estmaton of the TOA..3. Receved Sgnal Strength RSS The receved sgnal strength RSS,.e., the receved sgnal power, can be easly measured at the recever. The RSS s related to the dstance between the transmtter and the recever mathematcally n the form of path loss models [Pah95]. The path loss model characterzes the sgnal power attenuaton level as the sgnal travels from the transmtter to the recever. Assumng the path loss model s known a pror, wth the knowledge of the transmtted sgnal power at the recever the dstance between the transmtter and the recever can be calculated at the recever from the known path loss model by measurng the receved sgnal strength. Such a dstance estmaton method s known as the RSS-based rangng technque. The same as the TOA-based geolocaton method that we presented n Secton., the RSS-based estmaton of the dstances 9

41 between a moble termnal and a mnmum of three reference ponts can be employed to estmate the poston of the moble termnal. A wde varety of path loss models have been developed for dfferent envronments, each wth dfferent values of model parameters or dfferent parameters and mathematcal functon forms [Pah95]. In ndoor envronment the path loss model s hghly ste-specfc. For example, the value of power-dsatnce gradent, whch s a parameter of path loss models, vary n a wde range between 5- db/decade and a value as hgh as 7 db/decade [Pah95]. Also the receved sgnal strength of rado sgnals demonstrates fast-fadng phenomenon caused by multpath propagaton wth for example as large as 3 dbm fluctuaton n small local movement, and tme-dependent fadng phenomenon caused by dynamcally changng channel condtons, such as random movement of people over tme n the applcaton envronments, wth for example as large as dbm fluctuaton n seconds [Ber99]. As a result of the complexty of the ndoor rado propagaon channel, n practce usng the RSS-based geolocaton method necesstates the estmaton of the path loss model of the specfc applcaton envronment durng the system nstallaton or the ntalzatn phase to compensate for the ste-specfc nature of the ndoor rado propagaton channel, and frequent reestmaton of the path loss model to cope wth the dynamcally changng envronment. Thus an mmdate concluson s that the RSS-based geolocaton method s not a sutable choce for accurate ndoor locaton fndng systems. Some authors have studed varous technques to mprove the performance of the RSS-based geolocaton method ncludng the fuzzy logc algorthms [Son94] and 3

42 the premeasurement-based pattern regnton technques [Bah]. In essence, all these mprovement technques try to mprove the locaton accuracy by desgnng more ntellegent yet more complex postonng algorthms to combat the large dstance estmaton errors resulted from the RSS-based rangng technque. More detals on the ntellegent RSS-based geolocaton methods wll be presented later n ths chapter n the context of postonng algorthms..3. Angle of Arrval AOA The AOA s usually measured usng drectonal antennas or more often tmes usng antenna arrays. In moble rado systems, the antenna arrays are typcally located only at base statons BS, because of the dffcultes to employ antenna arrays n a moble staton or moble handset. Therefore, the AOA locaton metrc s normally employed n network-based locaton fndng systems. A varety of sgnal processng technques are avalable for AOA estmaton usng antenna arrays, ncludng maxmum lkelhood estmator, mnmum varance method, and super-resoluton sub-space technques; detals of these technques can be found n [Caf99, Tn] and many other references theren. 3

43 regon of scatters Tx Tx receved sgnals Rx Rx a b Fgure.6: Rado transmsson n the envronment of a macrocell and b mcrocell. All prmary scatters, whch cause multpath transmsson, are assumed located nsde the regon of scatters. In general, the accuracy of the AOA estmaton largely depends upon the rado propagaton envronments. Fgure.6 llustrates two scenaros of rado transmsson,.e., the transmsson n macrocell envronment and the transmsson n mcrocell envronment, respectvely. The prmary scatterng obects,.e., the scatters, whch cause multpath transmsson, are assumed all located nsde the regon of scatters shown n the dagram [Jak94]. Then for macrocell envronment where the prmary scatters are located around the transmtter and far away from the recevers, the AOA method can provde acceptable locaton accuracy [Caf99] snce the receved sgnal roughly all comng from the drecton of the transmtter. But n mcrocell stuaton where the prmary scatters are located around the recever, receved sgnals could be 3

44 comng from any drecton around the recever. Thus n mcrocell envronment, dramatcally large AOA estmaton errors wll occur f the LOS sgnal path s blocked and a scattered sgnal component s used for the AOA estmaton. The ndoor rado propagaton envronment, where the LOS sgnal path s usually blocked by surroundng obects or walls, can be readly modeled as the mcrocell envronment. Even when a strong LOS sgnal s detectable n ndoor envronments, strong multpath sgnals may ntroduce consderable nterference to the AOA estmaton, resultng n large AOA estmaton errors. As a result, the AOA-based geolocaton method s not preferred n ndoor severe multpath envronments for accurate ndoor locaton fndng systems..3.3 Tme of Arrval TOA In ndoor areas, due to the obstructon and the scatterng of rado sgnals by walls, celngs, or other obects, the DLOS propagaton path s not always the strongest path and even n some occasons, for example the NLOS codtons, the DLOS sgnal may not be detectable wth a specfc recever mplementaton [Pah98]. In such cases, dramatcally large errors occur n the TOA estmaton. To accurately estmate the TOA n ndoor areas, we need to resort to dfferent and more complex sgnalng formats, frequency of operaton, and sgnal procssng technques that can resolve the problems. The TOA-based systems measure the dstance based on an estmate of the sgnal propagaton delay,.e., the TOA, between a transmter and a recever snce n free space or n ar, rado sgnals travel at the constant speed-of-lght see Secton 3. for more rgorous defnton of the TOA estmaton problem. The TOA can be measured ether 33

45 by measurng the phase of the receved narrowband carrer sgnal or by drectly measurng the arrval tme of a wdeband pulse. The wdeband pulases for measurng the TOA can be generated ether drectly wth the ultra-wde band sgnals [Fon] or by usng spread spectrum sgnals [Wer98]. In the followng subsectons, we present these technques n three classes: narrowband, wdeband, and ultra wdeband technques Narrowband Sgnals and Phase Measurement for TOA Estmaton In narrowband rangng technque, the phase dfference between the receved and the transmtted carrer sgnals s used to measure the dstance between the transmtter and the recever. The phase of a receved carrer sgnal, φ, and the TOA of the sgnal,, are related by = φ / ωc, where ω c s the carrer frequency n radan. In applcaton scenaros of the GPS where the DLOS sgnal path s always present, measurement of carrer phase may be helpful to mprove the locaton accuracy. But n the ndoor geolocaton envronments, the severe multpath propagaton condton causes substantal errors n the narrowband phase measurements. When a narrowband carrer sgnal s transmtted n a multpath envronment, the composte receved carrer sgnal s the sum of a number of carrers, arrvng along dfferent paths, of the same frequncy but dfferent ampltude and phase. The frequency of the composte receved sgnal remans unchanged but the phase wll be dfferent from that of the DLOS sgnal as shown n Fg..7 [Pah95]. An mmedate concluson s that the phase-based dstance measurement usng narrowband carrer sgnal cannot provde accurate estmate of the dstance n the heavy multpath ndoor envronments. 34

46 Composte receved sgnal φ multpath sgnals φ φ r φ DLOS sgnal Fgure.7: Phasor dagram for narrowband sgnalng on a multpath channel Wdeband Sgnals and Super-resoluton Technques for TOA Estmaton The drect-sequence spread-spectrum DSSS wdeband sgnal has been used n rangng systems for many years [Kap96]. In such a system, a sgnal coded by a known pseudo-reandom PN sequence s transmtted by a transmtter. Then a recever crosscorrelates the receved sgnal wth a locally generated PN sequence usng a sldng correlator or a mathched flter [Wer98, Kap96]. The dstance between the transmtter and the recever s determned from the arrval tme of the frst correlaton peak. Because of the processng gan of the correlaton process at the recever, the DSSS rangng system performs much better than other competng systems n supressng nterference from other rado systems operatng n the same frequency band. More detals of the wdeband sgnal-based TOA estmaton technques wll be presented n Chapter 3. 35

47 Due to the scarcty of the avalable bandwdth n practce, n some ndoor geolocaton applcatons, the DSSS rangng systems may not be able to provde adequate accuracy. On the other hand, t s always desrable to acheve hgher rangng accuracy usng the same bandwdth. Inspred by hgh resoluton spectram estmaton technques, a number of researcheres have studed super-resoluton technques for tmedoman analyss such as [Pal9]. A frequency-doman super-resoluton technque can be used to determne the TOA wth hgh resoluton from the estmted frequency channel response. In ths thess, Chapter 4 s devoted to the super-resoluton TOA estmaton technques ncludng the basc theores and the ssues n practcal mplementaton Ultra Wdeband UWB Approach for TOA Estmaton As we mentoned earler, the sgnal bandwdth s one of the key factors that affect the TOA estmaton accuracy n the multpath propagaton envronments. The larger the bandwdth, the hgher the rangng accuracy. The UWB system, whch explots bandwths n excess of one GHz, have attrracted consderable attenton as a means of accurately measurng the TOA for ndoor geolocaton applcatons [Fon]. Due to the hgh attenuaton assocated wth the hgh-frequency carrer, the frequency band consdered for UWB system s typcally focued on - 3 GHz on the unlcensed bass. Wth results of propagaton measurement n a typcal modern offce buldng, t has been shown that the UWB sgnal does not suffer multpath fadng [Wn98], whch s desrable for accurate TOA estmaton n ndoor areas. The actual deployment of the UWB systems n the US s subect to the FCC approval. The man concern of the FCC 36

48 authortes s the nterference of the UWB devces to, among other lcensed servces, the GPS systems that operate approxmately at.5 GHz frequncy band. Smlar to the spread spectrum sgnals, the UWB sgnal has low, flat, and nose-lke power spectrum. But gven the weak satellte sgnals that must be processed by the GPS recevers, the nose-lke UWB sgnal s stll harmful to the GPS systems n close vcnty. A sgnfcant amount of research work s under way to assess the effect of the UWB nterference on the GPS recevers..4 Postonng Algorthms As we dscussed before, the measurement accuracy of the locaton metrcs n ndoor areas depends on the accuracy of the locaton sensng technologes and the stespecfc ndoor rado propagaton channel condtons. Due to the mperfect mplementaton of the locaton sensng technques, the lack of bandwdth, and the complexty of the multpath ndoor rado propagaton channels among other factors, there are always varyng errors assocated wth the measurements of the locaton metrcs. To acheve hgh postonal accuracy when the measurements of locaton metrcs are unrelable, the errors encountered n the locaton sensng process have to be mtgated n the postonng process. In the next two subsectons we dscuss the tradtonal postonng algorthms used wth the relable measurements of the locaton metrcs and the more ntellgent pattern recognton technques that can be used to mprove the postonng performance when the measurements of the locaton metrcs are unrelable. 37

49 .4. Tradtonal Technques In ndoor rado propagaton channels, t s dffcult to accurately measure the AOA, RSS and carrer sgnal phase so that most of the ndependent ndoor postonng systems manly use the TOA-based technques. Wth the relable TOA-based dstance measurements, smple geometrcal trangulaton methods can be used to fnd the locaton of the MT as presented n Secton. [Caf98]. But due to the estmaton errors of the dstances at the RP recevers, caused by the naccurate TOA measurement, the geometrcal trangulaton technque can only provde a regon of uncertanly, nstead of a sngle fx of poston coordnates, for the estmated locaton of the MT. To obtan an estmate of the locaton coordnates n the presence of the measurement errors of the locaton metrcs, a varety of drect and teratve statstcal postonng algorthms have been developed to solve the problem by formulatng t nto a set of non-lnear equatons [Caf98]. In some ndoor geolocaton applcatons, the purpose of the postonng systems s to provde a vsualzaton of the possble moble locatons nstead of an estmate of the locaton coordnates [Wer98]. On the other hand, the postonal accuracy s not constant across the area of coverage and the poor geometry of relatve poston of the MT and the RP can lead to a hgh geometrc dluton of precson [Tek98]. The output of the statstcal methods s an estmate of the moble locaton coordnates, and the changes of the shape of the regon of uncertanty are not revealed by ths method. 38

50 When the regon of uncertanty nformaton as well as the estmate of the locaton s needed, both the geometrc and the statstcal trangulaton algorthms are used [Tek98]. For the tradtonal outdoor geolocaton systems, the ntellgent technques, such as the Kalman flter based technques for trackng and fuson of multple metrcs, are normally used to mprove the postonng performance [Kap96]. In essence, these technques are readly applcable to ndoor geolocaton systems. However, ndoor applcaton envronments have some unque features, dscussed n the next secton, whch makes the tradtonal postonng algorthms less attractve. On the other hand, the unque features of ndoor applcatons enable the desgn of the ntellgent postonng algorthms that can sgnfcantly mprove the postonng performance n ndoor areas..4. Pattern Recognton Technques For ndoor geolocaton applcatons, the servce area s restrcted to the nsde and the close vcnty of a buldng whle nowadays the buldng floor plan s normally accessble as an electronc document. The avalablty of electronc buldng floorplan s one of the features of ndoor applcatons that can be exploted n the postonng algorthms. For example, whle trackng a moble termnal n buldngs, wth the ad of the buldng floorplan, the stuatons nvolvng crossng the walls or umpng through the floors can be easly dentfed and elmnated. Another unque feature of ndoor applcatons s that the sze of the coverage area s much smaller than outdoor applcatons. Ths makes t possble to conduct comprehensve study and plannng of 39

51 the deployment of the sensor nfrastructure network. Careful plannng of the sensor nfrastructure network can sgnfcantly reduce the estmaton errors of the locaton metrcs caused by the NLOS propagaton condton. The structural nformaton of the sensor network can also be easly employed n the ntellgent postonng algorthms n a way smlar to the use of buldng floorplans. The small coverage of ndoor geolocaton systems, as compared wth outdoor systems, also makes t possble to convenently conduct extensve pre-measurement n the areas of nterest for deployment. As a result, the pre-measurement based locaton pattern recognton, also known as locaton fngerprntng, technque s attractng sgnfcant attenton for ndoor applcatons [Bah]. On the other hand, n most of the ndoor applcatons, ncludng fndng the equpments n-demand or locatng the personnel n crtcal condton such as unconscous frefghter nsde the buldng on fre, the MT to be located s usually n quas-statonary stuatons. For such quas-statonary applcaton scenaros, the pattern recognton algorthms are more promsng than the tradtonal technques and the Kalman flter based trackng technques. The basc operaton of the pattern recognton postonng algorthms s smple. Each buldng s unque n ts sgnal propagaton characterstcs; each locaton spot n a buldng would have a unque sgnature n terms of the RSS, TOA, and/or AOA, observed from dfferent sensors n the buldng. A pattern recognton system determnes the unque pattern features,.e., the locaton sgnature, of the area of nterest n an ntal tranng process, and then ths knowledge s used to develop the rules for recognton. The challenge for such algorthms s to dstngush the locatons wth 4

52 smlar sgnature. To buld the sgnature database, a termnal s carred through the servce area transmttng sgnals to a montorng ste through the locaton sensng elements of all reference ponts. The servce area s dvded nto the non-overlappng zones or grds, and a pattern recognton tranng algorthm analyzes and comples the receved sgnal patterns n terms of the RSS, TOA, AOA, or any combnaton of these metrcs to derve a unque locaton sgnature for each zone. For quas-statonary applcatons, the smplest way for pattern recognton s usng the nearest-neghbor method on the bass of premeasurement and tranng. Wth such a method, a locaton sgnature database s frst developed; then n regular operaton the Eucldean dstance measure s calculated between the measured metrcs, RSS, TOA, or AOA and all enttes n the sgnature database. The locaton estmate s determned to be the one assocated wth the mnmum Eucldean dstance [Bah]. Expermental results are avalable n the references [Bah, Pahb]. A smple experment conducted n the Center for Wreless Communcatons, the Unversty of Oulu, Fnland, shows that the standard devaton of the postonng errors, usng the nearest-neghbor pattern recognton method, s.4 m and at about 8% locatons the postonal error was less than 3 m [Pahb]. But t s worth to note that due to the ste-specfc and the dynamcally varyng nature of ndoor rado propagaton envronments as we dscuss n Secton., the performance result reported may not appled to other applcaton envronments or for other tme perod n the same buldng. When the area of coverage becomes large and a large number of sensors are nvolved, the sze of the locaton sgnature database ncreases dramatcally, whch 4

53 makes the use of the smple nearest-neghbor pattern recognton technque computatonally cumbersome. More complex algorthms, ncludng the fuzzy logc, neural network, subspace technques, and hdden Markov model based technques among others, are beng nvestgated to reduce the overall computatonal complexty and to mprove the performance. When the 3G systems usng the spread spectrum sgnals and the RAKE recevers are employed for ndoor geolocaton, t s possble to use the measured tme and sgnal strength of all fngers n place of RSS to mprove the postonng performance. Even though buldng and updatng the sgnature database are much easer n ndoor envronments than n wde urban areas, the maor drawback of the pattern recognton technques stll les n the substantal efforts needed n the generaton and mantenance of the sgnature database n the vew of the fact that the applcaton envronments of ndoor geolocaton systems are dynamcally changng constantly..5 Summary and Conclusons Indoor geolocaton s an emergng research and engneerng feld that needs a scentfc foundaton. In ths chapter we presented a bref overvew of a wde varety of the techncal ssues nvolved n the desgn and performance evaluaton of ndoor geolocaton systems. To provde a scentfc foundaton for ndoor geolocaton, sgnfcant research work needs to be conducted n all aspects of ths new feld. We need to characterze the ndoor rado propagaton channels that mpact the performance of the ndoor geolocaton systems, based on the RSS, AOA, TOA, or any combnaton 4

54 of these locaton metrcs, through emprcal channel measurement and modelng; we need to desgn new locaton sensng technques to provde accurate estmate of the locaton metrcs n the complex ndoor multpath envronments; we need to desgn new postonng algorthms to compensate for the erroneous estmates of the locaton metrcs resulted from the multpath propagaton, to fuse the measurements of several locaton metrcs to mprove the postonng performance, and to explot the unque features of ndoor applcatons; we also need to study the system archtectures and the practcal deployment methods and rules for locaton sensor nfrastructure networks to acheve the optmum system performance n the ad hoc ndoor applcaton envronments. Two classes of ndoor geolocaton systems are emergng nowadays. The frst class has the dedcated nfrastructure for locaton fndng applcatons, employ complex sgnalng formats, locaton sensng technques and postonng algorthms, such as the wdeband and the UWB sgnals, and the super-resoluton technques. The challenge for such systems s to develop a sgnalng system and nfrastructure that s nexpensve to desgn and deploy, comples wth the frequency regulatons, and provdes a comprehensve coverage for the accurate rangng. The second class system overlays the locaton fndng functonalty onto the exstng wreless systems deployed for the telecommuncaton and broadband data applcatons, ncludng the wreless LAN systems and the cellular networks. The overlad system can only obtan less relable estmate of locaton metrcs usng the exstng physcal layer sgnalng format and nfrastructure networks, but mproves postonng performance by employng the premeasurement data and the complex postonng algorthms at the hgher applcaton 43

55 layer such as the pattern recognton technques. In general, both technques demonstrate promsng postonng performance for emergng markets for ndoor geolocaton applcatons. In the next chapter we present the TOA estmaton technques n detals. 44

56 Chapter 3 TOA Estmaton for Indoor Geolocaton The TOA estmaton technques have been wdely used for many well-known tradtonal locaton fndng applcatons, ncludng the GPS, radar, and sonar systems. In essence the same TOA estmaton technques developed for the tradtonal applcatons can be appled to the emergng ndoor locaton fndng systems. However, because the severe multpath ndoor applcaton envronment s very dfferent from that of the GPS, radar, or sonar systems, the performance of the tradtonal TOA estmaton technques degrades sgnfcantly when appled to ndoor systems. In ths chapter we frst present the maxmum lkelhood technque for the TOA estmaton, whch was derved for the tradtonal locaton fndng applcatons, and the Cramer-Rao lower bound for the TOA estmaton errors, whch provdes a means to predct and bound the accuracy of the TOA estmaton technques. Then we wll study n detals the mpacts of ndoor multpath rado propagaton channel on the performance of the TOA estmaton technques. The tme-dfference-of-arrval TDOA s another tme delay based locaton metrc that can be used n place of the TOA n locaton fndng systems. 45

57 In tradtonal applcatons, the estmaton technques as well as the performance of the TDOA and the TOA are very smlar, but n the multpath ndoor rado propagaton channels the TDOA locaton metrc becomes less approprate than the TOA due to an nherent ambguty n the estmaton technque. So we wll brefly look nto ths ssue by studyng the mpacts of multpath propagaton on the TDOA estmaton technques. At last, the ssues n the practcal measurement of the TOA locaton metrc wth spatally separated moble unts are dscussed and technques for synchronzng and coordnatng the remotely located transmtter and recever to measure the TOA and the TDOA are presented. 3. Maxmum Lkelhood Estmaton of TOA The tme delay estmaton problem s defned as follows. A known rado sgnal s emanated from a transmtter and the sgnal s montored at a spatally separated recever. The recever estmates the arrval tme of the rado sgnal,.e., the tme-ofarrval TOA, arrvng from the transmtter. Assumng the transmtter and the recever are synchronzed n tme and the transmsson tme of the rado sgnal s known to the recever, the recever can easly convert the arrval tme estmaton to the tme delay estmaton,.e., the propagaton delay of the sgnal from the transmtter to the recever. Then snce n free space the rado sgnal propagates at the well-known constant speedof-lght, the propagaton delay of the rado sgnal can be easly converted to the dstance between the transmtter and recever, whch s used n the dstance-based geolocaton method, presented n Secton., for locaton fndng purposes. In the lterature as well 46

58 as n ths thess for the ease of analyss t s usually assumed that the spatally separated transmtter and recever are synchronzed, and the transmsson tme of the rado sgnal s known to the recever f not declared otherwse, even though t needs specal treatment to acheve n practce. Thus the acronym TOA, whch s the arrval tme of rado sgnal n strct sense, often also refers to the propagaton delay of rado sgnal from transmtter to recever where actual meanng should be clear from the context. Issues and technques to synchronze or coordnate the spatally separated transmtter and recever to measure the TOA locaton metrc are dscussed n Secton 3.5. The estmaton of TOA falls nto the feld of sgnal parameter estmaton. The sgnal parameter estmaton concerns wth fndng the optmum measurement of a set of unknown parameters ψ = ψ, ψ,..., ψ ] contaned n a sgnal s t; ψ by observng [ M the sgnal n the presence of the addtve nose n t. Usually, for the ease of analyss, the addtve nose n t s assumed to be addtve whte Gaussan nose AWGN wth two-sded power spectral densty N /. The observed sgnal x t s expressed as, x t = s t; ψ + n t. 3. There are bascally two crtera that are wdely used n sgnal parameter estmaton: maxmum-lkelhood ML crteron and maxmum a posteror probablty MAP crteron. In the MAP crteron, the sgnal parameter vector ψ s modeled as a vector of random varables, and characterzed by a ont a pror probablty densty functon PDF p ψ. In the ML crteron, the sgnal parameter vector ψ s treated as determnstc but unknown [Pro95]. 47

59 By performng an orthonormal expanson of x t usng N orthonormal functons { t, l N}, we may represent x t by a vector of coeffcents f l x = x, x,..., x ]. The ont PDF of the random varables x, x,..., x } n the [ N { N expanson can be expressed as p x ψ. Then the ML estmate of ψ s the value that maxmzes p x ψ. On the other hand, the MAP estmate s the value of ψ that maxmzes the a posteror PDF of ψ p x ψ p ψ p ψ x =. 3. p x We note that f there s no pror knowledge of the parameter vector ψ, we may assume that t s unformly dstrbuted over a gven range of the values of the parameters. In such a case, the value of ψ that maxmzes p x ψ also maxmzes p ψ x so that the MAP and the ML estmates are dentcal. In our treatment of the parameter estmaton gven below, we vew the parameters as unknown, but determnstc. Hence, we adopt the ML crteron for estmaton of these parameters. In the ML estmaton of the sgnal parameters, we requre that the recever extract the estmate by observng the receved sgnal over a tme nterval T, whch s called the observaton nterval. The estmates obtaned from a sngle observaton nterval are sometmes called one-shot estmates. In practce, however, the estmaton s performed on a contnuous bass by usng trackng loops ether analog or dgtal that contnuously update the estmates. If we assume the addtve nose n t s whte and zero-mean Gaussan 48

60 the ont PDF p x ψ can be expressed as n t ~ N, σ, 3.3 n p x ψ = = N l= p x πσ n N l ψ exp σ n N l= [ x l s ψ] l 3.4 where xl = s ψ = l T T x t f s t; ψ f l t dt l t dt 3.5 and T represents the ntegraton nterval n the expanson of x t and s t; ψ. We note that by substtutng 3.5 nto 3.4, we can easly derve that N [ x ] = [ ; ] l sl ψ x t s t ψ dt σ N T n l= 3.6 where N = s the two-sded power spectral densty of the whte nose n t. / σ n Now, the maxmzaton of p x ψ wth respect to the sgnal parameter ψ s equvalent to the maxmzaton of the lkelhood functon Λ ψ = exp [ x t s t; ψ] dt 3.7 T N or the log-lkelhood functon ln Λ ψ = [ x t s t; ψ] dt. 3.8 N T To apply the ML estmator to the tme delay estmaton, we frst assume that the rado propagaton channel between the transmtter and recever s sngle-path and 49

61 5 dsturbed only by addtve whte Gaussan nose, whch s usually referred to as the AWGN channel. Ths means that the receved sgnal encounters a constant propagaton delay D, whch s the TOA to be estmated, and a constant sgnal strength attenuaton α so that the rado propagaton channel between the transmtter and recever s modeled by D t t h = δ α, 3.9 and the receved sgnal s gven by t n D t s t n t h t s t x + = + = α 3. where t n s addtve whte Gaussan nose. To obtan the maxmum lkelhood tme delay estmate, the functon to be maxmzed s the lkelhood functon gven n 3.7 or equvalently 3.8 wth the tme delay parameter substtuted for ψ, that s = Λ ] [ ln T dt t s t x N. 3. Followng the necessary condton for a maxmum ln ˆ = Λ = ML D d d, 3. we can obtan that ' ' ˆ ˆ ˆ = = = = = = ML ML ML D T D T D T dt t s d d dt t s d d dt t s t x d d 3.3

62 reflectng the fact that the translaton of the ntegrand on the rght-hand sde does not render the ntegral a functon of and hence the rght-hand sde equals to zero. The correlaton functon of the receved sgnal and the transmtted sgnal s defned as r xs = x t s t dt T 3.4 = α r D + v ss where r s the auto-correlaton functon of the transmtted sgnal and v s the ss addtve nose term gven by rss = v = T T s t s t dt n t s t dt. 3.5 By substtutng 3.4 nto 3.3 d d r xs Dˆ = ML =, 3.6 we can observe that the ML estmate of the propagaton delay can be obtaned by fndng the value of that maxmzes the correlaton functon r as shown n Fg. 3.. The receved sgnal s cross-correlated wth a delayed verson of the transmtted sgnal and a varety of possble delay values Dˆ are tred untl the peak detector detects a peak. The correlaton functon r, whch s a functon of delay, s referred to as xs xs delay profle whle the functon r xs s referred to as power delay profle. In practce, the delay profle can be measured at recever usng a sldng correlator or a matched flter [Pah95]. If the transmtter and the recever are synchronzed to the same 5

63 tme reference, the propagaton delay can be estmated by measurng the delay of the peak of the delay profle or the power delay profle wth respect to the tme reference. Tme delay estmaton can also be accomplshed usng trackng loops, whch contnuously update the estmates [Pro95]. The tme synchronzaton between spatally separated transmtter and recever s hard to acheve n practce. The alternatves of the TOA measurng methods are presented n Secton 3.5. The next secton dscusses the performance of the TOA estmaton n the AWGN channels. rt s t Dˆ T dt Peak Detecton Dˆ ML Delay st Fgure 3.: The ML estmaton of tme delay by cross-correlaton. 3. Cramer-Rao Lower Bound for TOA Estmaton The qualty of a sgnal parameter estmate s usually measured n terms of the estmate bas and ts varance. In order to defne these terms, we assume that there s a data vector T x = [ x, x,..., x N ], wth the condtonal PDF p x ψ, from whch we extract an estmate of a parameter ψ. The bas of an estmate ψˆ s defned as bas = E [ ψˆ x] ψ, 3.7 5

64 where ψ s the true value of the parameter. When E [ ψ ˆ x] = ψ, we say that the estmate s unbased. The varance of the estmate ψ ˆ x s defned as σ ψ ˆ = E[ ψˆ x E[ ψˆ x] ]. 3.8 = E[ ψˆ x ] { E[ ψˆ x]} In general σ ψˆ may be dffcult to compute. However, a well-known result n parameter estmaton s the Cramer-Rao Lower Bound CRLB on the mean square error defned as [Van68] d d E [ ψˆ x ψ ] E[ ψˆ x] E ln p x ψ. 3.9 dψ dψ When the estmate s unbased, that s E [ ψ ˆ x] = ψ, the numerator of 3.9 s unty and the bound becomes a lower bound on the varance σ of the estmate ψ ˆ r,.e., ψˆ σ ψ ˆ = d E ln p x ψ dψ. 3. d E ln p x ψ dψ snce d d E ln p x ψ = E ln p x ψ [Van68]. To further smplfy 3. dψ dψ consder that ln p x ψ dffers from the log-lkelhood functon ln Λ ψ by a constant factor ndependent of ψ. Thus t follows that 53

65 54 Λ = Λ ln ln ˆ ψ ψ ψ ψ σ ψ d d E d d E. 3. Ths lower bound provdes a benchmark for the varance of any practcal estmate. Any estmate that s unbased and whose varance attans the lower bound s called an effcent estmate. In general, effcent estmate s rare. When they exst, they are maxmum lkelhood estmates. The Cramer-Rao lower bound CRLB of the varence of TOA estmaton errors about the true tme delay can be derved by assumng T as follows, + = = + = = = = = Λ dw w S w N dw w S w S w N dw dw w S w S w w w N dt dw dw e w S w S w N dt t s d d t s N dt t s d d t x E N dt t s t x N d d E d d E T t w w T T T ] [ ] [ ln π π πδ π π 3.

66 where S w s the Fourer transform of the sgnal s t. For the ease of analyss, here we assume α = n the sgnal model n 3., or equvalently assume the sgnal attenuaton factor are estmated before the cross-correlaton operaton so that the sgnal s t s the sgnal at the nput of the recever nstead of the transmtted sgnal. Thus, σ Dˆ = w = ρ β d E ln Λ d π N S w dw 3.3 where ρ β = = N E s / w S w S w dw dw 3.4 and E s = S w dw = s t dw π s the energy of the sgnal. As shown n [Rae97], t can be proved that the varance of the ML estmate of the delay estmaton n the neghborhood of the true delay value attans the CRLB as the observaton tme T tends to nfnty. If we assume that the sgnal spectrum s two sded and extends from f to f Hz and also from f to f Hz wth constant energy spectral densty S / W/Hz, the CRLB n 3.3 can be smplfed as follows [Qua8]. Wth the aforementoned assumptons, 55

67 f π f π S df f β = f π S df f 3.5 4π = 3 f + f f + f and 3 σ ˆ, 3.6 D 8 π T SNR f f 3 3 where the sgnal energy E = s Ps T, P s s the mean sgnal power, T s the observaton tme, the mean nose power,.e., the varance of the nose, σ = N f f snce the n power spectral densty of the whte nose s N /, and the sgnal-to-nose power rato SNR SNR = P / σ. Equaton 3.6 may also be wrtten n terms of the sgnal s n bandwdth B and the center frequency f as σ ˆ D 8 π SNR BT f + B / 3.7 where B = f f and f / = f + f. We can observe that the bound s nversely proportonal to the SNR, the product of sgnal bandwdth, and the observaton tme, and s nversely related to the square of the carrer frequency and the sgnal bandwdth. 56

68 Standard devaton σ D ns - B=MHz, BT= B=MHz, BT=8 B=6MHz, BT= B=6MHz, BT= SNR db Fgure 3.: Numercal results of the CRLB of TOA estmaton errors wth dfferent values of bandwdth and the product of bandwdth and observaton tme wth respect to sgnal-to-nose power rato SNR. The carrer frequency s zero. Fgure 3. shows some numercal results of the CRLB of the TOA estmaton errors obtaned from 3.7 wth dfferent values of bandwdth and the product of bandwdth and observaton tme wth respect to the sgnal-to-nose power rato whle assumng the frequency s zero,.e., the cross-correlaton s performed n baseband. The ML estmate of the TOA s unbased and the varance of the estmaton errors s lower bounded by the CRLB. So far the maxmum lkelhood estmaton of tme delay, determned by 3.6, and the CRLB of the varance of tme delay estmaton errors gven by 3.3 and 3.6 are all derved for the sngle-path AWGN channels. But the ndoor rado propagaton 57

69 channel s multpath channel. As shown n the next secton, the multpath propagaton of rado sgnals has tremendous mpacts on the performance of the TOA estmaton. In ndoor multpath envronments, the TOA estmaton technques derved for the snglepath AWGN channel model can no longer acheve good performance and the CRLB presented n ths secton no longer closely bounds the TOA estmaton errors n multpath channels. 3.3 TOA Estmaton n Multpath Channels In dervng the ML estmaton method, we assumed the rado propagaton channel between the transmtter and the recever s sngle-path and dsturbed only by the addtve whte Gaussan nose. In such a channel, the receved sgnal s gven by 3., whch s x t = α s t D + n t, 3.8 where the parameter D s the sgnal propagaton delay, α s the complex sgnal strength attenuaton parameter, and n t s the addtve whte Gaussan nose. And the delay profle s gven by 3.4 r = α r D v, 3.9 xs ss + where r s the auto-correlaton functon of the transmtted sgnal and v s the ss addtve nose term gven by 3.5. However, when the sgnal s transmtted through a multpath channel whch s mathematcally modeled as h t = L p k = α δ t, 3.3 k k 58

70 where L p s the number of multpath components, α k and k are the complex ampltude and propagaton delay of the kth path, respectvely, the receved sgnal becomes x t = s t h t + n t = L p k = α k s t k + n t. 3.3 For geolocaton applcatons, the propagaton delay of the DLOS path needs to be estmated. So that n ths thess the term TOA s used to only refer to the propagaton delay of the DLOS path n multpath channels f not declared otherwse. Usng the same correlaton recever shown n Fg. 3., the delay profle measured n multpath channels s gven by r xs = x t s t dt T T L p = α r + v k = k ss k 3.3 We note that n contrast to that n the sngle-path channels, n the multpath channels the measured delay profle s a weghted sum of multple shfted auto-correlaton functons of the transmtted sgnal. In general, the same correlaton technque can be used for the TOA estmaton n multpath channels. As dscussed n [Pah98], whether the propagaton delay of the DLOS s detectable or not largely depends on the nstantaneous channel profle between the transmtter and the recever and the characterstcs of the rangng systems such as the sgnal bandwdth, the recever senstvty, and the recever dynamc range. The recever senstvty specfes the mnmum power level of a sgnal that can be detected and the recever dynamc range 59

71 defnes the dfference n the power level of the strongest and the weakest detectable sgnals. Accordng to the detectblty of the DLOS path, the rado propagaton channel profles are classfed nto three categores for the TOA estmaton n ndoor geolocaton applcatons [Pah98]. The frst category s the domnant drect path DDP case, n whch the DLOS path s detectable by measurement systems and t s the strongest path n the channel profle. The second category s the non-domnant drect path NDDP case, where the DLOS path s detectable by measurement systems but t s not the domnant path n the channel profle. The thrd category s the undetected drect path UDP case where measurement systems cannot detect the DLOS path. The channel profles can also be grouped smply nto DLOS and NLOS no-los cases accordng to whether the DLOS path s detectable or not [Pah]. In general, sgnals of any format can be employed for the TOA estmaton usng the ML estmaton technque. But the wdeband DSSS sgnal s wdely used for the TOA-based rangng systems because of several advantages as compared wth other alternatves. From 3.7, we note that the performance of the TOA estmaton mproves as the bandwdth ncreases. As a result, one advantage of usng the DSSS sgnal for the TOA estmaton s ts large bandwdth, whch also helps to resolve multpath sgnals as we present n the followng. Another advantage s that because of the processng gan of the correlaton process n the recevers, the DSSS sgnal-based rangng system performs much better than the competng systems n suppressng nterference from other rado systems operatng n the same frequency band. The same ML estmator can be used n the mplementaton of the TOA estmaton systems usng 6

72 DSSS sgnalng, where the delay profle s frst measured and then the TOA s determned by fndng the delay value that maxmzes the measured delay profle / Tc Fgure 3.3: Power delay profles wth dfferent channel profles. a Sngle-path channel wth propagaton delay D = Tc ; b two-path channel wth sgnal attenuaton parameters α = α, and propagaton delays = Tc and = 5 Tc ; c two-path channel wth sgnal attenuaton parameters α =. 6 α, and propagaton delays = Tc, and =. 5 Tc. Fgure 3.3 presents the power delay profles obtaned usng DSSS sgnals wth three dfferent channel profles. In measurng the delay profles usng DSSS sgnals, a 6

73 maxmal-length shft regster sequence m-sequence s commonly used as a PN sequence. The auto-correlaton functon of the m-sequence s a trangular functon smlar to the one shown n Fg. 3.3a wth a spread of ± Tc around the correlaton peak, where T c s the chp nterval of the sequence. The spread of the correlaton peak depends on the sgnal bandwdth snce the bandwdth of the baseband DSSS sgnals equals to /Tc wthout pulse shapng. When the channel has a sngle-path profle gven by 3.9, the propagaton delay D can be determned usng the ML estmator by fndng the delay value that corresponds to the peak of the power delay profle shown n Fg. 3.3a and the varance of the estmate s bounded by the CRLB n 3.3. When a rado sgnal s passed through a multpath channel, the delay profle conssts of multple copes of the delayed verson of the auto-correlaton functon of the transmtted sgnal as gven by 3.3. Fgure 3.3b shows the power delay profle obtaned n a two-path channel. We can observe that when the dfference between the adacent path delays s greater than Tc, clearly separated correlaton peaks appear n the power delay profle so that the delay of the DLOS can be determned by fndng the delay value that corresponds to the frst peak. When the frst peak s the strongest one of the delay profle, the channel belongs to the DDP category. When the frst peak s not the strongest one but t s detectable wth the gven recever senstvty and recever dynamc range, t falls nto the NDDP case. If the strength of the frst peak s below the recever senstvty or the dfference between the strength of the frst peak and the strongest peak exceeds the recever dynamc range, the DLOS path s not detectable so 6

74 that the channel profle falls nto the UDP category. In ths case, dramatcally large TOA estmaton errors may occur. When the dfference between the adacent delays s smaller than Tc, the two delayed correlaton functons overlap. Due to the constructon and deconstructon effects between the two overlapped correlaton functons, as shown n Fg. 3.3c large delay estmaton error occurs f the TOA s estmated by detectng the frst peak of the power delay profle. Increasng sgnal bandwdth reduces the spread of the correlaton peak and helps to resolve the DLOS path. However, t s practcally mpossble to ncrease the sgnal bandwdth freely due to the regulatons on frequency spectrum usage posed by the FCC. An alternatve way of ncreasng the resoluton les n the applcaton of advanced sgnal processng technques, whch s the man subect of Chapter 4. From the prevous dscusson we can conclude that f the same ML estmator desgned for the AWGN channels s used n the multpath channels, the performance of the TOA estmaton degrades sgnfcantly, dependng on the characterstcs of the rangng system and the nstantaneous channel profle that the rado sgnal encounters. In summary, the followng general prncples can be used to mprove the TOA estmaton n multpath channels: Increase the recever dynamc range and the recever senstvty, Increase the resoluton of estmaton technques by ncreasng the sgnal bandwdth or by employng advanced sgnal processng technques, 63

75 Place the rangng transmtter and recever, or deploy the reference ponts of ndoor geolocaton systems, n a way to mnmze the occurrence of the NLOS propagaton scenaros between the transmtter and the recever. The CRLB n 3.3 s derved for the sngle-path AWGN channel and t s the varance of the ML delay estmate n the neghborhood of ts true value. However, n multpath channels the CRLB s not drectly applcable because dramatcally large TOA estmaton errors occur when the DLOS path s undetectable. There are no sutable ndoor rado propagaton channel models for performance evaluaton of the TOA estmaton technques. Consequently, n the lterature, n desgnng the TOA estmaton technques for multpath channels, the performance evaluaton s usually conducted by studyng the resoluton of the estmaton technques based on computer smulatons wth a smple two-path channel model [Pal9]. As we dscussed prevously, n addton to the resoluton of the estmaton technques, the rado channel characterstcs has tremendous effects on the performance of the TOA-based rangng systems n real applcaton scenaros. So that n ndoor areas, performance of TOA estmaton technques can be measured more approprately by computer smulatons based on channel measurements, by conductng feld measurement usng prototype systems, or by usng the ray-tracng software to smulate the ste-specfc ndoor rado channels. Due to the complexty of the ndoor rado propagaton channels, the performance study based on these methods reveals much more realstc statstcal results than the resoluton study of the estmaton technques wth the smple theoretcal channel models. 64

76 3.4 Estmaton of TDOA The tme-dfference-of-arrval TDOA s an alternatve locaton metrc, whch s a tme delay based locaton metrc smlar to the TOA. Instead of measurng the arrval tme, or equvalently the dstance, as n the TOA-based approach, n the TDOAbased approach the tme dfference of arrval, or equvalently the dstance dfference, from a MT to two RPs are measured. A mnmum of two TDOA measurements, whch requres a mnmum of three RPs, can be used to provde a poston fx of the MT smlar to the dstance-based geolocaton method presented n Secton.. In ths thess detals of TDOA-based locaton method s not dscussed; nterested readers are referred to [Caf99, Kap96] and references theren. In tradtonal locaton fndng applcatons, the estmaton technques as well as the performance of the TDOA and the TOA are closely related and very smlar, but n the multpath ndoor rado propagaton channels the TDOA locaton metrc becomes less approprate than the TOA due to an nherent ambguty n the estmaton technque. In ths secton we wll brefly look nto ths ssue by studyng the mpacts of multpath propagaton on the TDOA estmaton technques, whch s closely related to the delay estmaton technque used for the TOA estmaton. The problem of the TDOA estmaton s generally modeled as follows. A sgnal s transmtted from a remote source and s montored at two spatally separated recevers. When the rado propagaton channel between the transmtter and the recever s assumed to be sngle-path and dsturbed only by the addtve whte Gaussan nose, the receved sgnals at the two recevers can be mathematcally represented by 65

77 x t = s t + n t x t = α s t + D + n t 3.33 where α s the ampltude rato of the sgnals observed at the two recevers and D s the dfference n the arrvng tme of the sgnals observed at the two recevers. The noses n and n are ontly ndependent statonary random process, and the transmtted t t sgnal s t s assumed to be uncorrelated wth the noses. The recevers are synchronzed n tme so that the TDOA to be estmated s the tme delay D. Normally a cross-correlaton technque, smlar to the one that s used n estmatng the TOA, s used to estmate the TDOA. Frst the delay profle, whch s the cross-correlaton functon of the two receved sgnals, s obtaned, r = x t x t dt T T 3.34 = α r ss D + v where the T represents the observaton tme nterval, the auto-correlaton functon of the transmtted sgnal r s the same as n 3.5, and the addtve nose term s gven by ss v = T T T n t n t dt + s t n t dt + T T T α n t s t + D dt Then the TDOA s estmated by fndng the value of the delay that maxmzes the delay profle n A generalzed correlaton method can also be used n estmatng the TDOA, where each of the two receved sgnals s pre-fltered. Wth proper choce of 66

78 67 the pre-flters, the estmaton of the TDOA can be mproved usng the generalzed correlaton method presented n [Kna76]. The CRLB can be derved for the varance of the TDOA estmate about the true value [Kna76, Qua8]. Wth some smplfcaton assumptons smlar to those used n dervng 3.6, at low SNR SNR<< the CRLB for the TDOA estmaton can be determned as [Qua8] 3 3 ˆ SNR 8 3 f f T D π σ 3.36 whle at hgh SNR SNR>> t s gven by [Qua8] 3 3 ˆ SNR 4 3 f f T D π σ Comparng 3.36 and 3.37 wth 3.6, we note that n general the estmate of the TDOA s less accurate than that of the TOA. Ths observaton can be ntutvely ustfed snce n the case of the TDOA estmaton, both sgnals are corrupted by nose, but n the case of the TOA estmaton a clean reference sgnal s avalable for correlaton. When the transmtted sgnal t s s propagated through multpath channels, the receved sgnals at the two recevers are gven by, t n t s t x t n t s t x p p L l l l L k k k + = + = = = α α 3.38

79 where the two sets of parameters { L p, α k, k }, k L p, and { L p, α l, l}, l L p, defne the multpath channels between the transmtter and the two recevers, respectvely. Then the cross-correlaton functon of the two receved sgnals becomes r L p L p = k = l= α k α lrss k l + v 3.39 where the addtve nose term s gven by v = T + T T n t n Lp l= α l t dt + T T n t s t l Lp k = α k dt. T s t n k t dt 3.4 We can observe that smlar to the case of the TOA estmaton n multpath channels, the delay profles for the TDOA estmaton conssts of multple copes of the autocorrelaton functon of the transmtted sgnal wth dfferent delays. In multpath channels, the TDOA to be measured s the tme dfference between the propagaton delays of the two DLOS paths TDOA =. 3.4 From 3.39 we can observe that the TDOA cannot be detected by fndng the delay value that corresponds to the frst peak of the delay profle snce the frst occurrng correlaton functon n the delay axs does not necessarly corresponds to the delay value. On the other hand, followng a dscusson smlar to that n secton 3.3, we can deduce that n multpath channels, the delayed copy of the correlaton functon correspondng to the delay value s not necessarly the strongest one n the delay profle gven by Ths means that n multpath channels there s 68

80 ambguty n detectng the TDOA from the delay profles snce the correlaton peak to be detected s nether the strongest one nor the frst one for sure. An ntutve concluson followng ths fact s that n multpath channels the estmaton of the TDOA s much harder than the estmaton of the TOA. Moreover, the CRLB n 3.36 and 3.37 are no longer applcable for the estmate of the TDOA for the same reason dscussed n Secton 3.3 for the TOA estmaton, and dramatcally large errors occur n the TDOA estmaton due to the complexty of the multpath ndoor rado propagaton channels. Snce n geolocaton applcatons, the rangng sgnal s t transmtted by a MT s usually known to the RPs, a more obvous method of estmatng the TDOA for the sgnal receved by two spatally separated RP recevers s to calculate the dfference of the TOA estmates measured by the two recevers. Ths method avods the ambguty n estmatng the TDOA from the delay profle 3.39 that we ust mentoned, but t requres the synchronzaton between the transmtter and both of the recevers whle the drect measurement of TDOA by the cross-correlaton method only requres the synchronzaton between the two recevers. More ssues n the measurement methods of the TOA and the TDOA wll be dscussed n the next secton. 3.5 TOA/TDOA Measurement Methods In essense, the TOA estmaton technques that we dscussed n the prevous sectons, concern wth the estmaton of the arrval tme of a rado sgnal. To convert the arrval tme estmaton to the sgnal propagaton delay estmaton for the purpose of 69

81 geolocaton, the spatally seperated transmtter and recever need to be synchronzed n tme and the transmsson tme of the rado sgnal needs to be known to the recever. Thus the process of the TOA measurement nvoles coordnaton between a par of the spatally separated tranmter and recever. In ths secton, we dscuss the coordnaton methods that are needed to form a TOA or a TDOA estmate from the arrval tme estmaton. In general, there are two basc measurement methods to measure the TOA from rado sgnals: the synchronzed transcever method and the round-trp TOA method. To measure the TOA usng the synchronzed transcever method, the remotely located transmter and recever are synchronzed to a common tme reference. If the transmsson tme of the rado sgnal s sent to the recever as a tmestamp whle the arrval tme of the sgnal s estmated at the recever, the TOA can be easly calculated as the dfference of the arrval tme and the transmsson tme of the sgnal. The accurate synchronzaton between remotely located termnals are usually very dffcult to acheve n practcal applcaton scenaros where they are physcally separated and randomly located. To avod the synchronzaton requrement, a roundtrp TOA method can be employed to measure the TOA. Usng the round-trp TOA method, a termnal A sends a rado sgnal to a second termnal B. Then termnal B smply echoes the receved sgnal back to termnal A usng a dfferent carrer frequency, or usng the same carrer frequency but after watng for a known tme perod, for proper operaton of the two RF transcevers. Termnal A measures the arrval tme of the sgnal receved from termnal B. The tme delay between transmsson tme t and 7

82 the arrval tme t of the sgnal at termnal A ncludes the round-trp propagaton delay,.e. the round-trp TOA, and a processng delay p that s encountered n the two transcevers. The processng delay p can be easly measured durng the system ntalzaton or calbraton perod and can be readly compensated. Consequently, the TOA estmate s obtaned as TOA = [ t t p ]. 3.4 There are two basc ways to measure the TDOA: the drect cross-correlaton method and the ndrect TOA-based method. Wth the drect method, two recevers are synchronzed to a common tme reference. The synchronzed recevers receve a rado sgnal from a transmtter, then the receved sgnal s dgtzed and forwarded to a central staton to perform cross-correlaton to estmate the TDOA as presented n Secton 3.4. Wth the ndrect method, transmtter needs to be synchronzed to the same tme reference of the recevers. Each recever measures the TOA ndependently and the estmates of the TOA are forwarded to a central staton to form an estmate of the TDOA. It s noted that both methods requre the synchronzaton among several physcally separated termnals. In the next secton, we present a non-synchronzed TDOA measurement method whch explots the archtecture and sgnalng system of wreless LAN WLAN systems based on IEEE 8. standards. For the dedcated geolocaton systems, the smple approaches that we ust dscussed can be easly appled. But for the overlad geolocaton systems, the drect applcaton of these methods s challengng because the geolocaton functon s overlad 7

83 onto a wreless network wthout sgnfcant modfcatons to the exstng nfrastructure and hardware as well as the physcal layer sgnalng formats. In the followng we explore the TOA/TDOA measurement methods for the overlad geolocaton systems TOA/TDOA Measurement Methods for Overlad Systems Wth the wde deployment of the wreless LAN systems n ndoor areas, mplementng geolocaton functons n the WLANs has receved consderable attenton n the recent years [Pahb, La, Lb, Bah]. The geolocaton functons and servces can be ether ntegrated nto the next generaton WLANs or overlad n the exstng systems. In ths secton we focus on the TOA/TDOA measurement methods that can be used n the overlad systems wthout concernng about the sgnal format and the detaled tme delay estmaton technques. DIFS DIFS PIFS medum busy SIFS contenton next frame t Fgure 3.4: Inter-frame spacng and medum access prortes. As we wll descrbe n detals shortly, some features of the MAC layer protocols of the IEEE 8. standards can be exploted n measurng the TDOA for geolocaton purposes. To ease the dscusson, some relevant materals of the standard are brefly revewed frst. Three basc access mechansms are defned n the 8. MAC layer 7

84 specfcatons: the mandatory basc method based on the CSMA/CA, an optonal RTS/CTS method to avod the hdden termnal problem, and a contenton-free pollng method for the tme-bounded servce [Iee99]. There are three mportant parameters for controllng the watng tme before accessng the medum,.e. the SIFS Short nterframe spacng, the PIFS PCF nter-frame spacng and the DIFS DCF nter-frame spacng. These three parameters defne the prortes of the medum access as shown n Fg The medum can be busy due to the transmsson of data frames or other control frames. Durng a contenton phase, several nodes try to access the medum. The parameter SIFS denotes the shortest watng tme and thus the hghest prorty for medum access. The DIFS s used for asynchronous data servce, the PIFS s used for a tme-bounded servce and the SIFS s defned for the short control messages such as acknowledgements for data packets or pollng responses. The uncast data transfer mode defned n the standard s llustrated n Fg A termnal accesses the medum and transmts a data frame. Once the recever receves the data, t reples drectly wth a short acknowledgement message ACK after watng for a short SIFS duraton. Snce the watng tme SIFS s the shortest and other statons can only access the medum after a longer watng perod, no other statons can access the medum n the meantme to cause a collson. Ths mechansm ensures the proper transmsson and recepton of the ACK message. If the tme duratons of the SIFS and the data frame are known accurately, the round-trp TOA method can be easly appled by measurng the tme nterval between the transmsson tme of a data frame and the arrval tme of the ACK frame. However, 73

85 accordng to the standard, n a real mplementaton, the accuracy of the tme spacng between frames that are defned to be separated by a SIFS tme s only wthn µ s, whch corresponds to a maxmum rangng error of 6m. Apparently, ths method s not approprate for ndoor geolocaton applcatons snce the coverage of WLANs s usually below m for most of the applcaton scenaros. But f sgnfcant modfcatons are made n the desgn of moble termnals and access ponts to ensure accurate estmate of the tme delays, ths method s stll applcable. sender DIFS data recever SIFS ACK other statons DIFS data watng tme contenton t Fgure 3.5: Uncast data transfer mode for IEEE 8.. Instead of measurng the TOA, the TDOA can be measured n the overlad systems as shown n Fg Here we assume the overlad geolocaton system conssts of a Geolocaton Control Staton GCS and a number of Geolocaton Reference Ponts GRP operatng around the AP of the WLAN networks. The geolocaton servce s frst ntated by a MT or the GCS. Suppose the AP sends a data frame to the MT at the 74

86 tme t and MT reples wth an ACK message after t receves the data. Meanwhle the GRPs montor the communcaton traffc between the AP and the MT to measure the tme delays between the arrvng tme of the data frame and the ACK message,.e., and shown n Fg The GRP and GRP receve the data frame at t and t, and ACK message at t and t, respectvely. The duratons and denote the propagaton delays from the AP to GRP and GRP whle and denote the propagaton delays from the MT to GRP and GRP, respectvely. Snce the dstance from the AP to each of the GRP can be assumed known a pror, the propagaton delays from the AP to the GRPs, and, can be accurately estmated. Therefore, the TDOA from the MT to the GRP and the GRP can be obtaned as follows: TDOA = = [ + ] [ + ] = Usng ths method, the GCS acts as a master that collects the measurements of the tme delays and to form the estmate of the TDOA. Snce the measurement at each GRP s the tme delay not the tmestamp wth respect to a common tme reference, the GRPs are not necessarly to be synchronzed. Thus ths method can also be referred to as non-synchronzed TDOA measurement method. But t s worth to note that the GRPs need to be able to estmate tme delay accurately. 75

87 AP t data GRP receved data receved ACK t t GRP receved data receved ACK t t MT ACK t Fgure 3.6: GRP-based TDOA method for IEEE 8. wreless LAN. The non-synchronzed TDOA measurement method can be used for systems usng the optonal RTS/CTS mechansm. Utlzng RTS/CTS for geolocaton purpose mght be a more approprate choce than usng the uncast mode of the mandatory CSMA/CA mechansm snce the RTS message can also act as a request for geolocaton servces to reserve a tme perod for geolocaton only. Furthermore, the fragmentaton mode defned by the standard shown n Fg. 3.7 can be used to mprove the performance n measurng the TDOA by averagng multple consecutve measurements. 76

88 Sender RTS frag frag SIFS SIFS SIFS SIFS SIFS Recever CTS ACK ACK t Fgure 3.7: Fragmentaton mode of IEEE 8.. Another maor WLAN standard s the HIPERLAN standards, whch s a collectve reference name to the hgh performance rado local area networks standards developed by ETSI European Telecommuncatons Standards Insttute proect BRAN Broadband Rado Access Networks. The same non-synchronzed TDOA measurement method can be used n the overlad geolocaton systems n the HIPERLAAN/ WLANs as dscussed n detals n [La]. 3.6 Summary and Conclusons The TOA-based rado rangng technque has been wdely employed n the tradtonal locaton fndng or postonng and trackng systems, ncludng radar, sonar, and the GPS. As a result, a large amount of research work has been devoted n the study of the TOA estmaton technques. The maxmum-lkelhood TOA estmaton technque was derved for the applcatons where the rado propagaton channel can be smply modeled as sngle-path AWGN channel. The CRLB of the TOA estmaton errors about the true tme delay provdes a benchmark for the varance of any practcal 77

89 estmator. In practce, the performance of the ML TOA estmaton technque n the tradtonal locaton fndng systems s qute closely bounded by the CRLB. However, n ndoor geolocaton applcatons, due to the complexty of the multpath ndoor rado propagaton channels, dramatcally large TOA estmaton errors may occur and the CRLB derved for the tradtonal applcaton scenaros s no longer sutable for benchmarkng the performance of practcal ndoor geolocaton systems. In general, n multpath channels, the performance of the TOA estmaton can be mproved by ncreasng the recever dynamc range and the recever senstvty; ncreasng the tmedoman resoluton of the estmaton technques; placng the rangng transmtter and recever n a way to mnmze the occurrence of the NLOS scenaros. Whle the CRLB cannot drectly apply to ndoor envronments, the performance of the TOA estmaton can be benchmarked usng the computer smulatons based on emprcal channel measurement data; conductng feld measurement wth prototype systems; and usng the computer smulatons based on ray-tracng software to smulate the ste-specfc ndoor rado propagaton channels. The tme dfference of arrval TDOA s another tme delay-based locaton metrc that can be used n place of the TOA. In the sngle-path AWGN channels, the technques and the performance of the TDOA estmaton are very smlar to that of the TOA estmaton. But as explaned n ths chapter, n multpath channels, the TOA s more approprate due to an ambguty n the TDOA estmaton wth the ML crosscorrelaton technque. 78

90 For the dedcated geolocaton systems, the smple synchronzed transcever method or round-trp TOA method can be easly employed. But for the overlad geolocaton systems, the drect applcaton of these methods s challengng because the geolocaton functon s overlad onto a wreless network system wthout sgnfcant modfcatons to the exstng nfrastructure and hardware as well as physcal layer sgnalng formats. A non-synchronzed TDOA measurement method s desgned for overlayng the geolocaton functonalty onto the exstng wreless networks such as the WLAN systems. In the next chapter, the super-resoluton TOA estmaton technques wll be presented, whch can be used to mprove the performance of the TOA estmaton n the multpath ndoor rado propagaton channels. 79

91 Chapter 4 Super-Resoluton TOA Estmaton Technques In last chapter we have shown that the TOA estmaton technques derved for the tradtonal locaton fndng applcatons s not sutable for ndoor applcatons snce the rado propagaton channel of the tradtonal applcaton envronment can be readly modeled as the sngle-path AWGN channel whle the applcaton envronment of ndoor geolocaton systems s severe multpath channel. The two maor sources of the TOA estmaton errors n ndoor envronment are the multpath nterference and the NLOS condton. As dscussed n Secton 3.3 one way to mprove the performance of the TOA estmaton n ndoor multpath envronment s to ncrease the resoluton of the estmaton technques by ncreasng the sgnal bandwdth or by employng advanced sgnal processng technques. In ths chapter, we present an nvestgaton of the frequency-doman super-resoluton TOA estmaton technque desgned by applyng the super-resoluton spectrum estmaton technques to the frequency-doman channel response, whch can be modeled as a harmonc sgnal model. In the followng we frst present the theoretcal background and the development of the basc algorthm for the 8

92 TOA estmaton. Then we present and evaluate the ssues and technques, ncludng dversty technques, whch should be consdered n the practcal mplementaton of the algorthm for ndoor geolocaton applcatons. Two dversty combnng schemes for the super-resoluton TOA estmaton technques are presented and the effects of the dversty technques are analyzed based on these two schemes. The quanttatve performance evaluaton of the super-resoluton technques s deferred untl next chapter, where the emprcal channel measurement data based computer smulaton method s used to compare and evaluate the performance of varous TOA estmaton technques presented n ths chapter. 4. Introducton Wth the emergence of the locaton-based applcatons and the next generaton locaton-aware wreless systems, locaton fndng technques are becomng ncreasngly mportant [Paha]. As dscussed n the precedng chapters, locaton fndng based on the TOA s the most popular method for accurate postonng systems. The basc problem n TOA-based technques s to accurately estmate the propagaton delay of the rado sgnal arrvng from the transmtter through the drect lne-of-sght DLOS rado propagaton path. However, as presented n Chapter and 3, n ndoor envronments due to the severe multpath condton and the complexty of rado propagaton, the DLOS sgnal cannot always be accurately detected [Pah98, Pah]. Among other technques presented n Secton 3.3, ncreasng the tme-doman resoluton of the channel response to resolve the DLOS path mproves the performance of the locaton 8

93 fndng systems employng the TOA estmaton technques. Thus n ths chapter we develop and nvestgate the super-resoluton as well as the dversty technques that can be used to mprove the tme-doman resoluton of the channel response. The super-resoluton algorthms have been wdely studed n the feld of the model-based parametrc spectral estmaton for a varety of applcatons [Man]. Recently, a number of researchers have appled the super-resoluton spectral estmaton technques to the tme-doman analyss for dfferent applcatons. These applcatons nclude electronc devces parameter measurement [Bey, Yam9] and multpath rado propagaton studes [Lo94, Mor98, Pal9, Dum94, Saa97]. In [Lo94], the superresoluton technque was employed n the frequency doman to estmate the multpath tme dsperson parameters such as the mean excess delay and the RMS delay spread. A smlar method was used n [Mor98] to model ndoor rado propagaton channels wth the parametrc harmonc sgnal models. Here we address the applcaton of the superresoluton technques to the accurate TOA estmaton for ndoor geolocaton applcatons. In the lterature, the tme delay related estmaton problems have been studed wth a varety of super-resoluton technques, such as the mnmum-norm [Pal9], the root-music [Dum94] and the TLS-ESPRIT [Saa97]. It s worth to note that whle the super-resoluton technques can ncrease the tme-doman resoluton as well as the locaton fndng performance, t also ncreases the complexty of the system mplementaton. But the studes of the complexty and the cost of the practcal mplementaton of the super-resoluton technques are beyond the scope of ths research. Here we focus on the development of the theoretcal foundaton of the super-resoluton 8

94 TOA estmaton technques, and ssues as well as technques to address the lmtatons posed by ndoor geolocaton applcatons, whch s dfferent from the spectral estmaton applcatons. Also n ths chapter we study the dversty technques and the dversty combnng schemes for the super-resoluton technques to further mprove the performance of the TOA estmaton n ndoor geolocaton applcatons. 4. Super-Resoluton Technques The multpath ndoor rado propagaton channel s normally modeled as a complex, low-pass equvalent mpulse response gven by., that s h t = L p k k = α δ t, 4. k where L p s the total number of multpath components, and α k k = α k e θ and k are the complex attenuaton and the propagaton delay of the kth path, respectvely. The multpath components are ndexed so that the propagaton delays k, k Lp, are n ascendng order. As a result, the parameter n the model denotes the propagaton delay of the shortest path,.e., the DLOS path, and t needs to be detected for the purpose of the TOA estmaton. Takng Fourer transform of 4., the frequencydoman channel response can be obtaned as H f = L p k = α. 4. e πf k k When modelng the multpath ndoor rado propagaton channels, the parameters α k and k are random tme-varant functons because of the moton of people and other 83

95 obects n and around buldngs. However, snce the rate of ther varatons s very slow as compared wth the measurement tme nterval, these parameters can be treated as the tme-nvarant random varables [Sal87]. The phase of the complex attenuaton θ k s normally assumed random from one snapshot to another wth a unform probablty densty functon PDF U, π [Pah95]. On the other hand, these parameters are frequency-dependent snce they are related to the rado sgnal characterstcs such as the transmsson and reflecton coeffcents. However, as shown n [Yan94], for the frequency bands used n ths paper these parameters can be assumed frequencyndependent. In practce, the dscrete samples of the frequency-doman channel response can be obtaned by sweepng the channel at dfferent frequences [How9], by usng a mult-carrer modulaton technque such as OFDM, or n a DSSS system by deconvolvng the receved sgnal over the frequency band of hgh sgnal-to-nose rato [Pal9, Dum94, Lo94, Saa97]. In ths thess, we consder the super-resoluton TOA estmaton based on the frequency-doman measurement of ndoor channel response. In Chapter 5, we wll study the performance of the super-resoluton TOA estmaton technques wth the computer smulatons based on emprcal frequency-doman channel measurement data, whch were obtaned by sweepng the channel at dfferent frequences wth a standard frequency-doman channel measurement system. If we exchange the role of the tme and the frequency varables n 4., we can observe that t becomes the harmonc sgnal model 84

96 L p k = H = α, 4.3 e πf k k whch s well known n the model-based parametrc spectral estmaton feld [Man]. Consequently, n essence any spectral estmaton technques that are sutable for the harmonc sgnal model can be appled to the frequency response of the multpath ndoor rado channel to perform the tme-doman analyss. In ths secton, we apply the MUSIC algorthm, whch was frst ntroduced n [Sch8], as an example of the superresoluton algorthms, to the TOA estmaton for ndoor geolocaton applcatons. The dscrete measurement data are obtaned by samplng the channel frequency response or frequency-doman channel response H f at L equally spaced frequences. Consderng the addtve whte nose n the measurement process and representng the estmated channel frequency response n nose wth H ˆ f, the sampled dscrete frequency-doman channel response s gven by x l = Hˆ f = Lp k = l α e = H f k l + w l + w, π f + l f k l 4.4 where l =,,..., L - and w l denotes the addtve whte measurement nose wth the mean zero and the varance σ w. We can then concsely wrte the sgnal model n 4.4 n the followng vector form where x = H + w = Va + w,

97 x = [ x x... H = [ H f H f w = [ w w... x L ]... T H f w L ] L T ] T V = [ v a = [ α ' α ' v... α... Lp v '] T Lp ] and v = [ k α ' = α e k k e π f k π f k,... e π L f k ] T and the superscrpt T denotes the matrx transpose operaton. The MUSIC super-resoluton technques are based on the egen-decomposton of the auto-correlaton matrx of the precedng sgnal model n 4.5, R xx = E{ xx = VAV H H } + σ, wi 4.6 where H A = E{ aa }, 4.7 and I s the dentty matrx whle the superscrpt H denotes the conugate transpose operaton,.e., the Hermtan, of a matrx. Snce the propagaton delays k n 4. can be readly assumed all dfferent, the matrx V has full column rank,.e., the column vectors of V are lnearly ndependent. If we assume the magntude of the parameters α k s constant and the phase s a unform random varable n [, π ], the L p Lp covarance matrx A s non-sngular. Then from the theory of lnear algebra, t follows that assumng L > L p, the rank of the matrx H VAV s L p, or equvalently, the L Lp 86

98 smallest egenvalues of R are all equal to σ w. The egenvectors correspondng to xx L L p smallest egenvalues of R xx are called nose egenvectors whle the egenvectors correspondng to the L p largest egenvalues are called sgnal egenvectors. Thus the L-dmensonal subspace that contans the sgnal vector x can be splt nto two orthogonal subspaces, known as sgnal subspace and nose subspace, by the sgnal egenvectors and the nose egenvectors, respectvely. Assumng the egenvectors are all normalzed, we have where H Q w Q w = I, 4.8 Q w [ q q +... q ] = L L L p p and q, k L, are the nose egenvectors. Then the proecton matrx of the k L p nose subspace can be readly determned as see the defnton of the proecton matrx n the reference [Man] P w = Q = Q w w Q Q H w H w. Q w Q H w 4.9 Snce the vector v, k L, must le n the sgnal subspace and the sgnal k subspace s orthogonal to the nose subspace, we have p P v =, 4. w k that s, the vector v, k L, must be orthogonal to the nose subspace. k p Thus the multpath delays k, k Lp, can be determned by fndng the delay values at whch the tme-doman MUSIC pseudospectrum, defned as 87

99 S MUSIC = = H H Pwv v Pw Pwv = = H H v P v Q v = L k = L q p H k w v w 4. acheves the maxmum value. The dervaton n 4. s apparent by notcng that P H w P w = Q = Q = P w w w, Q Q H w H w Q w Q H w = Q w IQ H w.e., the proecton matrx s dempotent [Man]. Receved sgnal Hˆ f Estmaton of channel frequency response Super-resoluton algorthm Pseudospectrum S Detecton of TOA Estmate of TOA Fgure 4.: The functonal block dagram of the recever of super-resoluton TOA estmaton systems. H ˆ f s the estmated channel frequency response, whch s defned n 4.4. Fgure 4. shows a functonal block dagram of the recever of the superresoluton TOA estmaton systems. The receved sgnal s frst used to estmate channel frequency response, whch s modeled as 4.4 and 4.5. Then a superresoluton algorthm, such as the MUSIC algorthm presented n ths secton, s used to 88

100 transform the channel frequency response to the tme-doman pseudospectrum, whch s defned n 4.. The estmate of the TOA s then obtaned by detectng the frst peak of the pseudospectrum along the delay axs. f: Normalzed tme-doman pseudospectrum delay ns Fgure 4.: The tme-doman MUSIC pseudospectrum, obtaned wth a sample frequency-doman channel measurement data. The estmate of the TOA corresponds to the frst peak of the pseudospectrum, marked by a small crcle sgn as shown on the plot. Fgure 4. shows a sample result of the tme-doman MUSIC pseudospectrum obtaned by applyng the MUSIC algorthm to an emprcal frequency-doman channel measurement data. The smulaton method as well as the descrptons of the channel measurement system and the measurement data s presented n Chapter 5. The TOA s 89

101 estmated by searchng for the frst peak of the pseudospectrum, whch corresponds to the arrval tme of the sgnal arrvng from the DLOS path. In geolocaton applcatons, we are only nterested n the arrval tme of the frst DLOS sgnal path, but f needed the arrval tmes of all the paths n the multpath channel model n 4. can be estmated by dentfyng delay values correspondng to all the sgnfcant peaks of the pseudospectrum usng peak detecton algorthms. It should be emphaszed here that there s no quanttatve relatonshp between the magntude of the peaks of the pseudospectrum and the values of the attenuaton parameters of the multpath channel model, that s, the attenuaton parameters of the multpath channel model cannot be estmated from the magntude of the pseudospectrum peaks. The attenuaton parameters of the multpath channel model s normally estmated from the measured tme-doman or frequency-doman channel response and the estmates of arrval tmes usng least-square algorthms [Pal9, Man94, Mor98]. In the next secton ssues n the practcal mplementaton of the super-resoluton TOA estmaton technques are presented. 4.3 Issues n Practcal Implementaton Note that n the analyss n last secton, whch led to the MUSIC TOA estmaton algorthm, we consdered the theoretcal or the true correlaton matrx R xx. In practce, the correlaton matrx must be estmated from the measured data samples. Fgure 4.3 llustrates a functonal block dagram of the super-resoluton TOA estmaton algorthms. The nput data vector,.e., the estmate of channel frequency response 9

102 gven n 4.5, s frst used to estmate the correlaton matrx R xx. Then the egenvalues as well as the correspondng egenvectors of the correlaton matrx are computed. The parameter L p s determned through the analyss of the egenvalues and egenvectors of the correlaton matrx, whch s dscussed n detals later n ths secton. Fnally, the pseudospectrum s obtaned usng 4.. If we have P snapshots of the measurement data, the estmate of the correlaton matrx s obtaned from P k k H x x P k= R ˆ =. 4. xx But f only one snapshot of the measurement data of length N s avalable, the data sequence s dvded nto M consecutve segments of length L and then the correlaton matrx s estmated as where M k= ˆ H R xx = x k x k, 4.3 M x k = [ x k... x k + L ] and M = N L +. In ths secton we wll focus on the second method, where only one snapshot of measurement data s used n estmatng the data correlaton matrx as n 4.3. Methods based on multple snapshots wll be dscussed n the next secton for applcaton wth the dversty technques. T 9

103 Input data vector x Rˆ xx Egenvalues and egenvectors S Estmaton of correlaton matrx Egen decomposton Estmate Lp L p Compute pseudospectrum Fgure 4.3: algorthms. The functonal block dagram of super-resoluton TOA estmaton Rˆ xx s the estmated correlaton matrx, L p s the estmated total number of multpath components defned n 4., and S s the tme-doman pseudospectrum defned n 4.. As we mentoned earler, for the super-resoluton TOA estmaton technques, the measurement data vector x s obtaned by samplng channel frequency response unformly over a gven frequency band. In order to avod alasng n the tme doman, smlar to the tme-doman Nyqust samplng theorem, the frequency-doman samplng nterval f s determned so as to satsfy the condton / f max, where max s the maxmum delay of the measured multpath rado propagaton max = L p channel. For example, for ndoor geolocaton applcatons, the frequency samplng nterval f s normally set to be MHz, whch accommodates applcaton scenaros where the maxmum delay max s less than 5 ns or equvalently the maxmum length of the multpath sgnal propagaton path s less than 5 m. Thus wth a bandwdth of MHz, the length of one measurement data sequence s, whch s far too short to accurately estmate the correlaton matrx. Ths s very dfferent from the stuaton n 9

104 the spectrum estmaton applcatons, where the super-resoluton algorthms are wdely used. In the spectrum estmaton applcatons, the super-resoluton algorthms are used to convert the tme-doman measurement data of a random sgnal to frequency doman to estmate the spectrum of the sgnal. Thus n the spectrum estmaton applcatons, more measurement data or longer measurement data vector x, whch s the nput of the super-resoluton algorthms and s used to estmate the correlaton matrx, can be obtaned by smply extendng the observaton tme of the random sgnal. Wth longer measurement data, the correlaton matrx can be estmated more accurately usng 4.3, whch leads to better performance of the super-resoluton algorthm. But n the TOA estmaton applcatons, the super-resoluton algorthm s used to convert the measurement data, whch s the estmate of channel frequency response, from frequency doman to tme doman as llustrated n Fg. 4. to estmate the arrval tme of the DLOS sgnal. Thus, n TOA estmaton applcatons, the length of the measurement data equals to the rato of the measured sgnal bandwdth and the frequency samplng nterval. Wth the frequency samplng nterval fxed, determned by the samplng theorem that we ust dscussed, ncreasng the length of the measurement data means an ncrease n the sgnal bandwdth. In practce, the natonal/nternatonal frequency usage regulaton rules, such as regulatons by the Federal Communcatons Commsson FCC, pose a lmtaton on avalable sgnal bandwdth. As a result, n applyng the super-resoluton algorthms to the TOA estmaton applcatons we wll face the ssue of havng short lmted length measurement data that we cannot ncrease freely. Thus n the TOA estmaton applcatons t s mportant to fnd ways to ensure the proper 93

105 operaton of the super-resoluton algorthms wth short lmted measurement data. As presented n the followng a number of technques can be used to mprove the performance, ncludng the forward-backward estmaton method for correlaton matrx estmaton and the egenvector method n ths secton, and the dversty technques n the next secton. In ths secton methods to estmate the total number of multpath components are also presented n detals Improved Estmaton of Correlaton Matrx wth Lmted Measurement Data The measurement data x n 4.5 and Fg. 4.3 are normally assumed statonary. Thus the correlaton matrx of the data R xx s Hermtan,.e., conugate symmetrc, and Toepltz,.e., havng equal elements along all dagonals. However, n practce the estmate of the correlaton matrx Rˆ xx based on the actual measurement data of small fnte length N s not Toepltz. The estmate of the correlaton matrx can be mproved usng the followng forward-backward correlaton matrx FBCM, = Rˆ ˆ xx JR xxj 4.4 ˆ FB * xx + R where the superscrpt * denotes conugate, superscrpt FB stands for the forwardbackward estmaton, and J s the L L exchange matrx, defned as L M N J =. N N M L 94

106 It can be easly shown that the matrx ˆ FB R xx s persymmetrc, that s J Rˆ =, 4.5 FB ˆ FB* xx J R xx and ts elements are conugate symmetrc about both man dagonals. Ths technque s wdely used n the spectral estmaton applcatons wth the name modfed covarance method [Man], n the lnear least-square sgnal estmaton wth the name forwardbackward lnear predcaton FBLP [Man], and n the antenna array sgnal processng wth the name modfed spatal smoothng preprocessng [Wl88, Yam9]. In contrast to the forward-backward correlaton matrx n 4.4, here we call the correlaton matrx n 4.3 the forward correlaton matrx FCM. In our development of the basc theores, we assumed that the magntude of the parameters α, k L p, n 4. are constant and the phase θ k, k L p, k are ndependent unformly dstrbuted random varables. Wth such assumptons t can be shown that the correlaton matrx A, defned n 4.6, s full-rank,.e., non-sngular. But f the phase θ k, k L, are non-random, whch s true f only one snapshot p of the measurement data s used n estmatng the correlaton matrx R xx, the rank of the correlaton matrx A tends to degrade to and the matrx tends to sngular. In such a stuaton, the MUSIC algorthm does not work properly. But fortunately, for the sgnal model n 4.4, the estmaton of data correlaton matrx usng 4.3 has decorrelaton effects as explaned below. The decorrelaton effects n forward and forward-backward correlaton matrces were analyzed n [Red87, Wl88, Yam9]. Followng the defnton n [Red87], the correlaton coeffcent for the forward 95

107 estmaton method n 4.3 between α ' and α ',.e., the th and th element of the multpath model parameter vector a defned n 4.5, can be derved as ρ FCM = A A A = Ke φ, 4.6 where and A s the sn[ Mπ f ] K = M sn[ π f ] φ = θ θ + πf + π M f,, th element of the parameter correlaton matrx A defned n 4.7. From 4.6 t s noted that the decorrelaton effects of the forward estmaton method depend on the number of segments M, the frequency samplng nterval f, and tme delay dfference. Smlarly, the correlaton coeffcent of the forwardbackward estmaton method n 4.4 can be readly derved as ρ FBCM ψ / = K cos φ + ψ / e, 4.7 where ψ = π L f, and K and φ are the same as n 4.6. Detaled dervaton of 4.6 and 4.7 can be found n the Appendx 4.A. From 4.7 t s clear that the correlaton coeffcent of the forward-backward estmaton method depends on the length of the segments L, the phase dfference of parameters θ θ, and the lowest frequency of the spectrum f, n addton to M, f, and as n

108 .9.8 FCM.7.6 FBCM ρ number of segments M Fgure 4.4: Correlaton coeffcents of forward and forward-backward correlaton matrces, wth f = MHz, = 5ns, θ θ =, f = 9MHz, and L = 3. From 4.6 and 4.7 t can be readly shown that FBCM FCM ρ = ρ cos φ + ψ /. 4.8 Thus we can clearly observe that the forward-backward correlaton matrx has better decorrelaton effect than the forward correlaton matrx, that s, ρ 4.9 FBCM FCM ρ snce cos φ +ψ /. Fgure 4.4 and Fg. 4.5 show examples of the decorrelaton effects, calculated from 4.6 and 4.7, versus the number of segments and the delay dfference, respectvely. The results n Fg. 4.4 and 4.5 clearly verfy the relaton n 97

109 4.9, that s, the forward-backward correlaton matrx has better decorrelaton effect than the forward correlaton matrx. The better decorrelaton effect leads to potentally better performance of the super-resoluton algorthm. In Chapter 5 we compare the performance of the forward and the forward-backward estmaton methods wth computer smulaton results. In next secton we address the ssue of the estmaton of L p n practce,.e., the total number of the multpath components..9 FCM.8 FBCM.7.6 ρ ns Fgure 4.5: Correlaton coeffcents of forward and forward-backward correlaton matrces, wth the parameters M = 9, f = MHz, θ θ =, f = 9MHz, and L = 3. 98

110 4.3. Determnaton of Parameters L and L p If we use only one measurement data snapshot of N samples to estmate the TOA usng super-resoluton algorthms, the frst step s to determne the value of L for the estmaton of Rˆ xx as n 4.3. Wth large values of L, the potental for hgher resoluton of the MUSIC algorthm ncreases, whch s smlar to that n array sgnal processng where ncreasng L means an ncrease n subarray aperture and thus an ncrease n resoluton capablty [Tuf8, Kr96]. On the other hand, from 4.3, we can see that for a fxed value of N, the value of M decreases as L ncreases. The decrease n M ncreases fluctuatons n the matrx Rˆ xx resultng n large perturbatons of the egenvalues and egenvectors of Rˆ xx, and reduces the number of coherent α k that can be detected [Kr96, Lb99]. Consequently, the value of L needs to be selected so that t provdes a balance between resoluton and stablty of the algorthm. Dfferent values of L have been used n the lterature, for example [Lan8] used N / and N / 3, [Tuf8] used 3N / 4, and [Pal9] adopted 3N / 5. In ths paper we use a value of N / 3, whch was determned through computer smulatons. Another parameter that needs to be determned n usng a super-resoluton technque s the total number of multpath components L p. If the true correlaton matrx R xx s avalable, L p can be easly determned by observng egenvalues of the correlaton matrx snce n theory, the w L Lp smallest egenvalues of R xx are all equal to σ, and the remanng L p egenvalues are all larger than σ w. But n practcal 99

111 mplementaton, especally when the correlaton matrx s estmated from a lmted number of data samples, the nose egenvalues are all dfferent, whch makes t challengng to clearly dstngush sgnal egenvalues and nose egenvalues. In [Wax85], the nformaton theoretc crtera for model selecton, ncludng Akake nformaton theoretc crtera AIC and Rssanen Mnmum Descrptve Length crtera MDL, are appled to ths problem. The MDL crteron for estmaton of L p s used n ths paper, whch s gven n [Wax85] MDL k = log L / Lk λ = k L λ Lk = k M Lk + kl klog M, 4. where λ, L, are the egenvalues of correlaton matrx n descendng order. The estmate of L p s determned as the value of k [, L ] for whch the MDL s mnmzed. In the reference [Xu94], authors showed that when the forward-backward estmaton method s used, the MDL crtera n 4.7 cannot drectly apply and the second term of the crtera must be modfed to / 4 kl k + log M, that s MDL k FB = log L / Lk λ = k L λ Lk = k M Lk + kl k + log M Egenvector Method One mplct assumpton n the MUSIC method s that the nose egenvalues are k σ w all equal,.e., λ = for k L, that s, the nose s whte. However, as we L p ust dscussed, when the correlaton matrx s estmated from a lmted number of data

112 samples n practce, the nose egenvalues are not equal. A slght varaton on the MUSIC algorthm, known as the Egenvector EV method, can be used to account for the potentally dfferent nose egenvalues [Man, Joh8]. The pseudospectrum of the EV algorthm s defned as S EV = L k= Lp λ k q H k v, 4. where λ k, L p k L, are the nose egenvalues. In effect, the pseudospectrum of each egenvector s normalzed by ts correspondng egenvalue. If the nose egenvalues are equal, the EV method and the MUSIC method are dentcal. The performance of the MUSIC and EV methods were compared n [Joh8] and t was shown that the EV method s less senstve to naccurate estmate of the parameter L p, whch s hghly desrable n a practcal mplementaton. As presented n the next chapter, the EV method s shown by computer smulatons to have slghtly better performance than the MUSIC method. In the next secton, we nvestgate dversty technques that can be used to further mprove the performance of super-resoluton TOA estmaton technques. 4.4 Dversty Technques Dversty technques such as tme dversty, space dversty, and frequency dversty are wdely utlzed n wreless communcaton systems to mprove lnk performance [Pah95, Rap96, Paha]. Dversty technques take advantage of the

113 random nature of the rado propagaton channel by fndng and combnng uncorrelated sgnal paths. In essence, all dversty technques used for wreless communcaton systems can be used for TOA estmaton systems wth the general structure shown n Fg. 4.6, where the dversty system has P dversty branches. The TOA s estmated ndependently at each dversty branch of recever, and then a combnng algorthm s used to process the TOA estmates from all branches to obtan an optmum estmate. A varety of dfferent combnng algorthms can be desgned for dfferent dversty technques. The smplest one s the equal-gan combnng algorthm gven by ˆ. 4.3 P k = ˆ P k = In some cases, more complex varable-gan combnng s also possble, where the estmate of each dversty branch s weghted wth a coeffcent that reflects the qualty of tme delay estmaton at each branch. More research work s needed to desgn optmum combnng algorthms for dversty technques for TOA estmaton applcatons. ˆ ˆ ˆ P Combnng Algorthm ˆ Fgure 4.6: General structure of TOA estmaton wth dversty technques, general dversty combnng scheme GDCS.

114 For the super-resoluton TOA estmaton technques presented n ths paper, dversty technques can also be appled as shown n Fg Instead of combnng ndependent tme delay estmates as n Fg. 4.6, the measurement data at dversty branches are combned to estmate the correlaton matrx usng the formula n 4.. For the convenence of referencng, we call the structure n Fg. 4.6 a general dversty combng scheme GDCS, and the structure n Fg. 4.7 a correlaton matrx-based dversty combng scheme CMDCS. In super-resoluton TOA estmaton technques, the maor computatonal load s n the egen-analyss,.e., computaton of the egenvalues and egenvectors, of the correlaton matrx. As a result, CMDCS s computatonally superor to GDCS snce the CM-based scheme performs egen-analyss only once, but the general scheme needs to perform ndependent egen-analyss P tmes. x x x P Estmaton of Correlaton Matrx Rˆ ˆ xx Super-resoluton TOA Estmaton Fgure 4.7: Estmaton of correlaton matrx wth dversty technques for superresoluton TOA estmaton, correlaton matrx based dversty combnng scheme CMDCS. On the other hand, by applyng the CMDCS scheme, the underlyng assumpton concernng the rado propagaton channel s that the ampltude attenuaton and the tme 3

115 delay for each path, and the number of sgnal paths are the same from the transmtter to all dversty branches of the recever. Ths restrcts CMDCS to only quas-statonary scenaros, where the channel structure remans unchanged whle the P dversty measurement data are collected. Ths s one dsadvantage of the CM-based scheme as compared wth the general scheme, whch has no such restrcton n applcaton. Ths condton for applcablty also makes t challengng to use CMDCS for space dversty snce n space-dversty stuatons, the rado propagaton channel from the transmtter and dversty branches of the recever are most lkely not the same. Smlarly, CMDCS s not sutable for tme dversty. As we dscussed n the precedng secton, the superresoluton technque cannot work properly when the phase of each sgnal path remans unchanged together wth the ampltude attenuaton and tme delay for each path, and the total number of sgnal paths. For quas-statonary scenaros, t s unknown whether the phase s random or not for repeated measurements whle the number of sgnal paths and the ampltude attenuaton and tme delay for each path all reman unchanged. But smulaton results based on measurement data collected on ndoor rado channels, whch wll be presented n the next chapter, show that tme-dversty wth CMDCS yelds almost no mprovement over non-dversty technques. In contrast, frequency-dversty can be well ftted nto CMDCS. By usng frequency-dversty, the k th measurement data vector k x, k P, are obtaned usng k th carrer frequency. A quanttatve relatonshp between the mprovement of TOA estmaton accuracy and frequency dversty s not known, but the effects of frequency dversty can be convenently 4

116 analyzed usng the correlaton coeffcents smlar to the way by whch we analyzed the forward and the forward-backward correlaton methods n the last secton. For frequency dversty, f the carrer frequency f s unformly dstrbuted,.e. f ~ U fc F /, fc + F /, 4.4 where f c s center frequency and F s the range of the frequency dstrbuton, the correlaton coeffcent between α ' and α ' can be derved as ρ FD sn π F = e π F = snc π F e [ θ θ π fc ] [ θ θ π fc ] 4.5 where the superscrpt FD stands for frequency dversty, and the snc functon s defned as snc x = sn x / x. Smlarly, f the frequency dversty method s used for the forward correlaton matrx, the correlaton coeffcent becomes ρ FCM, FD φ ' = K' e, 4.6 where sn π F K' = K π F = ρ FD ρ FCM = K snc π F φ' = θ θ + π f c + π M f and that for forward-backward correlaton matrx becomes ρ ψ FBCM, FD ψ / = K 'cos φ' + e, 4.7 5

117 where K ' and φ ' are the same as n 4.6. Detals of the dervaton of 4.5, 4.6, and 4.7 are presented n Appendx 4.A. We notce that by usng the frequency dversty method, the coherence between multpath components s decoorrelated accordng to the snc fncton as F and absolute value of delay dfference ncrease FD.5 ρ F MHz Fgure 4.8: Correlaton coeffcent wth frequency dversty, wth parameters = 5ns, θ θ =, and f c = GHz. Fgure 4.8 shows an example of the decorrelaton effect of frequency dversty, calculated from 4.5, versus the range of the frequency dstrbuton. Fgure 4.9 and Fg. 4. shows correlaton coeffcents of forward and forward-backward correlaton matrces wth frequency dversty, calculated from 4.6 and 4.7, usng the same 6

118 parameters as n Fg. 4.4 and Fg We can clearly observe that the frequency dversty technque further mproves the decorrelaton effects n both forward and forward-backward correlaton matrces. In Chapter 5, we compare and evaluate the performance of dversty technques usng computer smulatons based on emprcal frequency-doman ndoor rado propagaton channel measurement data..9.8 FCM.7 FBCM.6 ρ FBCM, FD FCM, FD number of segments M Fgure 4.9: Correlaton coeffcents of FCM and FBCM wth and wthout frequency dversty, wth parameters f = MHz, = 5ns, θ θ =, f c = GHz, L = 3, and F = MHz. 7

119 FCM FBCM FCM, FD.6 FBCM, FD ρ ns Fgure 4.: Correlaton coeffcents of FCM and FBCM wth and wthout frequency dversty, wth parameters M = 9, f = MHz, θ θ =, f c = GHz, L =3, and F = MHz. 4.5 Summary and Conclusons In ths chapter, we have presented super-resoluton TOA estmaton technques. The super-resoluton spectral estmaton algorthms are appled to the TOA estmaton applcatons on the bass that the frequency representaton of the multpath rado propagaton channel model can be vewed as the harmonc sgnal model, whch s well known n the spectral estmaton feld. After formng the sgnal model based on the frequency-doman channel response, the MUSIC super-resoluton TOA estmaton algorthm s derved n the same way as n the spectral estmaton applcatons. 8

120 In the TOA estmaton applcatons, the super-resoluton algorthm s used to convert the measurement data, whch s the estmate of the channel frequency response, from frequency doman to tme doman to estmate the arrval tme of the DLOS sgnal n contrast to the spectrum estmaton applcatons, where the super-resoluton algorthms are used to convert tme-doman measurement data of a random sgnal to frequency doman to estmate the spectrum of the sgnal. Thus n spectrum estmaton applcatons, more measurement data can be obtaned by smply extendng the observaton tme of the random sgnal, whle n the TOA estmaton applcatons ncreasng the length of the measurement data means an ncrease n the sgnal bandwdth. Wth longer measurement data, the correlaton matrx can be estmated more accurately, whch leads to the better performance of the super-resoluton algorthm. The practcal lmtaton on the avalable sgnal bandwdth poses a lmtaton on the length of the channel measurement data n the TOA estmaton applcatons. Thus n ths chapter several technques are presented, ncludng the forward-backward estmaton of correlaton matrx, egenvector method, and dversty technques, whch can be used to mprove the performance of the super-resoluton TOA estmaton algorthms when the length of the frequency-doman channel measurement data s short. Also n ths chapter, the effects of the forward estmaton of correlaton matrx, the forward-backward estmaton of correlaton matrx, the frequency dversty technques, the FCM wth frequency dversty, and the FBCM wth frequency dversty technques are analyzed wth the correlaton coeffcents. The detaled dervaton of the correlaton coeffcents s presented n the appendx of ths chapter. From the analyss 9

121 we can conclude that the forward-backward estmaton method has better decorrelaton effects, whch leads to the better performance of the super-resoluton TOA estmaton technques, and dversty technques, especally the frequency dversty technque, further mprove the decorrelaton effects of the correlaton matrx. Two dversty combnng schemes,.e., the GDCS and CMDCS dversty combnng schemes, are proposed for the super-resoluton TOA estmaton technques. It s shown that the CMDCS s computatonal superor than the GDCS, and the CMDCS s well suted for the frequency dversty technques, whch can sgnfcantly mprove the decorrelaton effects of the correlaton matrx of the channel measurement data. In the next chapter we compare and evaluate the performance of varous superresoluton TOA estmaton technques presented n ths chapter wth the computer smulatons based on emprcal frequency-doman channel measurement data.

122 Appendx 4.A Dervaton of Correlaton Coeffcents In order to keep the man content of ths chapter concse and easy to follow, the detaled dervaton of the correlaton coeffcents n 4.6, 4.7, 4.5, 4.6, and 4.7 s presented n ths appendx. 4.A. Correlaton Coeffcents usng Forward Estmaton Method The parameter correlaton matrx of the multpah channel model s defned n 4.5 as } { H E aa A =. 4.A. whle the parameter vector a s defned n 4.5. Thus usng the forward estmaton method defned n 4.3, the th, element of the correlaton matrx A can be obtaned as ] sn[ ] sn[ } ' ' { * * * * * f M f f f M f M k f k f M k f k f f k f f M f M e e e e e M e e M e e M E A π π α α α α α α α α α α π π π π π π π π π = = = = = = = A. and t easly follows that A α = 4.A.3

123 where α = α e θ as defned n 4.. From the defnton of the correlaton coeffcent between th and th parameters, defned as [Red87], we can easly obtan that where sn[ Mπ f ] K = M sn[ π f ] ρ φ = θ θ + πf A = = Ke, 4.A.4 A A FCM φ + π M f. 4.A. Correlaton Coeffcents usng Forward-backward Estmaton Method The forward-backward correlaton matrx s defned n 4.4, = Rˆ ˆ xx JR xxj 4.A.5 ˆ FB * xx + R where Rˆ and J R ˆ * J are forward and backward correlaton matrces, respectvely. xx xx The backward correlaton matrx can be equvalently calculated usng 4.3 wth the data vector H x = [ x L x L... x ] 4.A.6 whch s reversed verson of the orgnal data vector defned n 4.5, so that the element of the parameter vector a defned n 4.5 becomes α k * π f + L f k ' = α e. 4.A.7 k

124 3 Thus usng the backward estmaton method, the th, element of the parameter correlaton matrx can be obtaned as * * * * * * * B ] sn[ ] sn[ f L f M f L f f f M f L f M k f k f L f M k f L f k f f L f k f e A f M f M e e e e e M e e M e e M A π π π π π π π π π π π π α α α α α α α α + + = + = = = = = = 4.A.8 where A s gven by 4.A.. Then the th, element of the parameter correlaton matrx usng the forward-backward estmaton method can be obtaned as B FB A A A + =. 4.A.9 Fnally the correlaton coeffcent between th and th parameters can determned by / FB FBCM / cos ψ ψ φ φ ψ φ α α ρ e K Ke Ke A + = + = = + 4.A. where f L π ψ =, and K and φ are the same as n 4.A.4.

125 4 4.A.3 Correlaton Coeffcents wth Frequency Dversty For frequency dversty, we assume the carrer frequency s unformly dstrbuted as gven n 4.4. The elements of the parameter correlaton matrx are derved as follows: ] sn[ } ' ' { * / / * * FD f F f F f f F F e df e F E A c c c π π α α α α α α π π = = = + 4.A. and the correlaton coeffcent s easly obtaned:, snc sn ] [ ] [ FD FD c c f f e F e F F A π θ θ π θ θ π π π α α ρ = = = 4.A. where the snc functon s defned as x x x / sn snc =. The correlaton coeffcents of forward estmaton methods, gven n 4.6 are easly obtaned by notcng that { } { } ' ] [ ] [ ] [ FCM FD FCM, ' ] sn[ } { φ π θ θ π π θ θ π π π θ θ π π ρ ρ f M f f M f f M f e K Ke F F e Ke e E Ke E E c c c = = = = = 4.A.3

126 5 where ' snc sn ' FCM FD c f M f F K F F K K π π θ θ φ ρ ρ π π π + + = = = = and the statstcal expectaton } { E s performed wth respect to the unformly dstrbuted carrer frequency f, whch s defned n 4.4. Smlaryly, the correlaton coeffcents of forward-backward estmaton methods, gven n 4.7 are obtaned as follows, { }. ' 'cos / ' cos sn } { / cos } { / / ] / [ ] / [ / / FBCM FD FBCM, ψ ψ ψ π π θ θ ψ π π θ θ ψ ψ ψ φ ψ φ π π ψ π π θ θ ρ ρ f M f f M f c e K F F Ke e e E Ke e f M f K E E c c + = + = + = = = A.4 where ' K and ' φ are the same as n 4.A.3, and ψ s the same as n 4.A..

127 Chapter 5 Performance Evaluaton Based on Channel Measurements In the prevous chapters we have presented the tradtonal TOA estmaton technques, developed for the sngle-path AWGN channels, and the super-resoluton TOA estmaton technques as well as the dversty technques developed on the bass of the frequency-doman representaton of the multpath rado propagaton channel models. The super-resoluton technques can ncrease the resoluton of the tme-doman channel response n multpath channels, whch helps to accurately estmate the arrval tme of the DLOS sgnal, and thus mproves the performance of the TOA estmaton n ndoor multpath rado propagaton channels for geolocaton applcatons. In Chapter 4, the performance of varous super-resoluton and dversty technques has been evaluated and compared theoretcally by comparng the correlaton coeffcents of the estmated channel parameter correlaton matrx snce better decorrelaton effect n the channel parameter correlaton matrx leads to better performance of the super-resoluton technques. However, there s no theoretcal way to quanttatvely compare the performance of varous super-resoluton technques, and the super-resoluton technques 6

128 wth the tradtonal TOA estmaton technques. As a result, n ths chapter we further nvestgate the performance of super-resoluton and dversty technques for TOA estmaton applcatons by the computer smulatons based on the measured frequencydoman response of ndoor rado propagaton channels. In ths chapter, the channel measurement system and measurement scenaros are descrbed frst n Secton 5., followed by a descrpton of the performance evaluaton methodology n Secton 5. that s employed n our research. Then varous super-resoluton technques are evaluated and compared based on computer smulaton results n the rest of ths chapter. For reference purposes, a descrpton of the measurement stes and scenaros are presented n Appendx 5.A, and the cumulatve dstrbuton functons of the rangng errors wth dfferent TOA estmaton technques are presented n Appendx 5.B. 5. Frequency-Doman Channel Measurement The frequency response of ndoor rado propagaton channel can be drectly measured wth a frequency-doman channel measurement system reported n [How9, Pah95]. Fgure 5. shows the block dagram of the frequency-doman channel measurement system. The man component of the measurement system s a network analyzer that generates a swept frequency sgnal and analyzes the resultng receved sgnal to estmate the ampltude and phase fadng effects of the rado propagaton channel of nterest at each specfc frequency. The network analyzer s controlled by a laptop through the HP s verson of a general purpose nstrumentaton bus GPIB. The laptop ntalzes the network analyzer precedng each measurement, and collects the 7

129 data at the completon of each measurement. The magntude and phase of the measured channel frequency response are stored for each measurement. A varety of sgnal processng technques can be appled to the frequency-doman channel measurement data collected wth ths measurement system to obtan the tme and frequency responses of the rado propagaton channel, to estmate varous channel characterstcs, and to conduct statstcal channel modelng as presented n [How9, Pah5]. TX RX Power amplfer Attenuator Preamplfer HP-8547A S-Parameter Test Set Laptop Computer HP-8753B.3-6 MHz Network Analyzer GPIB Bus Fgure 5.: Block dagram of the frequency-doman channel measurement system. The ndoor rado propagaton channel measurement data reported n [Ben99], collected wth the measurement system shown n Fg. 5., s used n our research to evaluate the performance of super-resoluton TOA estmaton technques as explaned n detals n the next secton. The magntude and phase measurements of rado 8

130 propagaton channel were performed at the center frequency GHz wth a bandwdth of MHz. The measurements were conducted at three dfferent buldngs that represent hghly lkely places for deployment of ndoor geolocaton systems, ncludng a manufacturng buldng at the Norton Co., Worcester, MA, a modern academc buldng, the Fuller Laboratory at WPI, and a resdental house, the Schussler House at the WPI. Thrty locatons were selected at each ste for measurement at the places where ndoor geolocaton systems wll be lkely used. At each recever locaton, four consecutve snapshots of rado propagaton channel were taken whle preventng movement around the vcnty of the antennas of the transmtter and recever. Durng the measurement, the transmtter antenna was fxed at one locaton whle the recever antenna was moved around. The measurement locatons were dstrbuted so as to nclude three dfferent rado propagaton scenaros, that s, ndoor-to-ndoor, outdoor-tondoor, and outdoor-to-second floor communcatons. For each measurement locaton, the physcal dstance between the antennas of the transmtter and recever were determned and recorded ether drectly or ndrectly from the blueprnt of the buldng floorplans. The detaled descrpton of measurement stes and measurement locatons are presented n Appendx 5.A. After the measurement process, the frequency doman measurement data were calbrated to remove the effects of the system and antenna gans and delays as descrbed n the reference [How9]. 9

131 5. Performance Evaluaton Method The super-resoluton TOA estmaton technques are developed on the bass of the frequency-doman representaton of the multpath rado propagaton channel model, whch can be equvalently vewed as the harmonc sgnal model that s well known n parametrc spectral estmaton feld. As presented n Secton 4. and 4.3, the nput of the super-resoluton algorthm n the TOA estmaton s the estmated dscrete channel frequency response. The frequency response of ndoor rado propagaton channel can be drectly measured wth a network analyzer as descrbed n Secton 5.. Thus n ths thess, we evaluate the super-resoluton TOA estmaton technques wth emprcal frequency-doman channel measurement data as the nput of the algorthm, wthout concernng about ssues n the channel frequency response estmaton n the practcal mplementaton of the TOA estmaton systems. The technques and performance of channel frequency response estmaton,.e., the frst functonal block n Fg. 4., deserves a separate study and s beyond the scope of ths thess. The purpose of the performance evaluaton n ths chapter s to compare varous TOA estmaton technques, and to evaluate and benchmark the perormance of superresoluton technques n realstc ndoor applcaton envronments. As we dscussed n Chapter 3, the CRLB presented theren s derved for the sngle-path AWGN channels and t s the varance of the ML delay estmate n the neghborhood of ts true value. However, n multpath channels the CRLB s not drectly applcable because dramatcally large TOA estmaton errors occur when the DLOS path s undetectable. The effects of channel characterstcs on the performance of the TOA estmaton has not

132 yet been well studed and modeled. There are no sutable ndoor multpath rado propagaton channel models avalable n the lterature for the performance evaluaton of the TOA estmaton technques. Consequently, n desgnng TOA estmaton technques for multpath channels, the performance evaluaton s usually conducted by studyng the resoluton of the estmaton technques based on computer smulatons wth a smple equal-gan two-path channel model as used n [Pal9]. In addton to the resoluton of the estmaton technques, the rado channel characterstcs such as multpath fadng and shadow fadng aomong others have tremendous effects on the performance of the TOAbased rangng systems n real applcaton scenaros as we dscussed n Chapter 3. The two-path channel model does not ncorporate any of the complex characterstcs of ndoor rado propagaton channels. Therefore, whle the two-path channel model s useful n prelmnary study of the multpath-resolvng capablty of the TOA estmaton technques, t s mpossble to compare the tradtonal TOA estmaton technques and the super-resoluton technques, and to provde performance benchmarks n real applcaton envronments wth the smple two-path model. In ndoor envronments, the performance of the TOA estmaton technques can be measured and benchmarked more approprately by the computer smulatons based on emprcal channel measurement data, by conductng feld measurement usng prototype systems, or by usng the ray-tracng software to smulate the ste-specfc ndoor rado propagaton channels. The performance study based on these methods reveals much more realstc statstcal results than the resoluton study of the estmaton technques wth the smple two-path channel model. On the other hand, as noted n the begnnng of ths secton,

133 the frequency-doman channel measurement data can be readly ncorporated n the super-resoluton TOA estmaton technques. As a result, n ths chapter we evaluate the performance of varous TOA estmaton technques, nlcudng tradtonal technques, super-resoluton technques, and dversty technques, through computer smulatons based on emprcal frequency-doman ndoor rado propagaton channel measurement data, whch can be obtaned wth the frequency-doman channel measurement system presented n Secton 5.. Such a measurement-based smulaton method can be employed n practce to convently establsh emprcal performance benchmarks when desgnng the TOA estmaton systems. Extensve channel measurement data are colleted at spacally wdely dstrbuted locatons where ndoor geolocaton systems are most lkely deployed and used. Durng the measurement, the physcal dstance between the transmter and recever antennas of the measurement system s measured ether drectly or ndrectly from the blueprnt of buldng floorplans, to determne the expected TOA for each measurement locaton. Through the computer smulatons based on channel measurement data, the statstcal results of rangng errors are determned such as mean, standared devaton STD, and cumulatve dstrbuton functon CDF. Varous TOA estmaton technques are compared based on these statstcal smulaton results obtaned from the same set of measurement data descrbed n Secton 5. and Appendx 5.A. It s mportant to note that due to the ste specfc nature and the complexty of ndoor rado propagaton channels, as presented n Chapter and 3, the computer smulatons based on dfferent set of channel measurement data may reveal varyng statstcal results so that the

134 quanttatve peformance comparson of dfferent TOA estmaton technques s meanngful only wth the same set of measurement data. The sgnal bandwdth s one of the key factors affectng the accuracy of the TOA estmaton n the multpath propagaton envronments as pesented n Chapter 3 and the reference [Pah]. Therefore, n ths chapter we comapre dfferent TOA estmaton technques wth varous bandwdths to observe the effect of sgnal bandwdth. To study the performance of the TOA estmaton usng sgnals of varous bandwdths, n our smulatons we use only a segment of each frequency-doman measurement data to reflect the band-lmtaton effects. For example, wth a MHz frequency-doman samplng nterval, a data segment of samples of each measurement data, centered at GHz, s used n the smulatons for a sgnal bandwdth of MHz. In the followng sectons, varous perforamnce evaluaton results are presented, whch are obtaned from the channel measurement data based smulatons that are outlned n ths secton, to evaluate and to benchmark the performance of varous TOA estmaton technques n ndoor applcaton envronments. 5.3 Performance of Super-resoluton Technques The purpose of ths secton s to compare the performance of varous superresoluton TOA estmaton technques presented n Secton 4. and 4.3 wth the measurement data based smulatons outlned n Secton 5.. As dscussed n Secton 5., nstead of estmatng from the receved sgnal as shown n Fg. 4., the channel 3

135 frequency response s drectly obtaned usng the frequency-doman channel measurement system shown n Fg. 5.. A sample measured channel frequency response s shown n Fg. 5., whch s obtaned at the center frequency of GHz wth a frequency bandwdth of MHz and a frequency samplng nterval of MHz. The super-resoluton TOA estmaton algorthm shown n Fg. 4. s mplemented to estmate the TOA. In ths secton the nput data correlaton matrx R xx s estmated usng the forward estmaton technque gven n 4.3 and the forward-backward estmaton technque gven n 4.4 whle n Secton 5.5 and 5.6 the correlaton matrx s estmated usng the dversty technques gven n 4. together wth the forward and forward-backward estmaton technques. In our smulatons, as dscussed n Secton 4.3. the length of segments L = N / 3 number of the multpath components, whch s defned n 4.3, and the total L p s determned usng the MDL crtera gven n 4. and 4. for forward and forward-backward estmaton methods, respectvely. As we dscussed earler n Secton 4.3.3, the Egenvector EV method s a varant of the MUSIC method and t s preferred when the correlaton matrx s estmated from a lmted number of data samples. To compare the performance of the EV and MUSIC methods, both algorthms are appled to the same set of the measured data descrbed n Secton 5. and Appendx 5.A, wth the forward-backward estmaton of the correlaton matrx. In Secton 4.3., we have theoretcally analyzed the forward FCM and forward-backward FBCM estmaton technques for super-resoluton TOA estmaton through the decorrelaton effects n the estmated correlaton matrx. Snce there s no analytcal way to quanttatvely relate the mprovement n the accuracy of the 4

136 TOA estmaton to the correlaton matrx estmaton technques, n ths secton we also compare these two methods usng statstcal smulaton results. -7 no: Magntude db frequency MHz Fgure 5.: Frequency-doman channel measurement data obtaned usng the measurement system n Fg. 5.. Fgure 5.3 presents the mean of the rangng errors versus sgnal bandwdth usng varous super-resoluton TOA estmaton technques. The vertcal lne corresponds to plus and mnus one standard devaton about the mean. To clearly relate the results to geolocaton applcatons, tme delay s converted to dstance d by the relaton 8 d = c, where c = 3 m/s s the constant speed-of-lght n free space. The results for dfferent technques are slghtly shfted n the x-axs for better observaton. From the results n Fg. 5.3, we can observe that both mean and standard devaton of the 5

137 rangng errors decrease as the bandwdth ncreases for all technques. The statstcal performance of the MUSIC and EV algorthms wth the FBCM,.e., MUSIC/FBCM and the MUSIC/FCM, s very close to each other. However, the EV method has slghtly better performance than the MUSIC for low sgnal bandwdth n terms of smaller standard devaton of estmaton errors. Wthout further comparson of the MUSIC and EV algorthms, n the followng we use the EV algorthm for further nvestgaton of the FCM, FBCM, and the dversty technques. 8 MUSIC/FBCM EV/FBCM EV/FCM Mean of rangng errors m bandwdth MHz Fgure 5.3: Mean of rangng errors usng the MUSIC and EV algorthms wth the forward FCM and forward-back FBCM estmaton of correlaton matrx. The vertcal lne corresponds to plus and mnus one standard devaton of the rangng errors about the mean. 6

138 Fgure 5.3 also presents the smulaton results for the EV algorthm wth the FCM EV/FCM. Comparng the EV/FBCM and the EV/FCM, t s clear that the FBCM based method performs much better than the FCM based method n terms of smaller mean and standard devaton of the estmaton errors for the same smulaton scenaros, whch s consstent wth the analyss n Secton For example, the EV/FBCM has about m s smaller mean and about m s smaller standard devaton than the EV/FCM for a bandwdth of MHz. It s also noted that both technques have smlar performance when the sgnal bandwdth s large, e.g., when the bandwdth s larger than MHz. 5.4 Comparson of Super-resoluton and Conventonal Technques In order to demonstrate the usefulness of the super-resoluton technque, we compare ts performance wth two conventonal tme delay estmaton technques. In the frst of the other two technques, the frequency-doman channel response s converted drectly to tme doman usng the nverse Fourer transform IFT and then the propagaton delay of the DLOS sgnal s detected. Snce ndoor rado propagaton channels have lmted multpath delay spread and here we are only nterested n the arrval tme of the DLOS sgnal, partal tme-doman channel response wll suffce for the TOA estmaton. If partal tme response s desred when convertng the frequency response to tme doman, the chrp-z transform CZT s preferred that provdes flexblty n the choce of tme-doman parameters wth the cost of longer 7

139 computatonal tme as compared wth the IFFT [Ulr86]. The tme-doman resoluton wth the CZT s the same as wth the nverse FFT. On the other hand, a proper wndow functon s needed to avod leakage and false peaks by reducng the sdelobes of the tme-doman response, whch s resulted from fnte bandwdth, wth the cost of reduced tme-doman resoluton. In our smulatons, we employ the CZT wth the Hannng wndow to convert frequency channel response to tme doman, though on the fgures of our smulaton results such a technque s stll denoted by IFT. The second technque uses the tradtonal cross-correlaton technque wth the drect-sequence spread-spectrum DSSS sgnals, desgnated as DSSS/xcorr on the fgures of the smulaton results. To smulate the DSSS sgnal-based cross-correlaton technque usng the frequency-doman channel measurement data, the frequency response of a rased-cosne pulse wth a rolloff factor of.5 s frst appled to the frequency channel response as a combned response of the band-lmtaton pulseshapng flters of the transmtter and the recever. Then the resultant frequency response s converted to tme doman usng the nverse Fourer transform for the TOA estmaton. The use of such a smulaton technque s easly ustfed snce the delay profle obtaned usng the DSSS sgnal-based rangng technque s the channel mpulse response convolved wth the pulse shape of a sngle chp of the spread spectrum sgnal. Interested readers can refer to the references [Rap96, Cox7] for more detaled dscusson on ths ssue. 8

140 no: IFT DSSS/xcorr EV/FBCM Normalzed tme-doman response delay ns Fgure 5.4: Normalzed tme-doman channel responses obtaned usng three dfferent technques. The vertcal dash-dot lne denotes the expected TOA. The estmated TOA s marked on the tme-doman channel response for each of the three technques. Fgure 5.4 shows the normalzed tme-doman channel responses obtaned from the smulatons usng three dfferent technques,.e., the IFT and DSSS/xcorr technques descrbed n ths secton and the EV/FBCM descrbed n Secton 5.3, usng a sample frequency-doman channel measurement data wth a bandwdth of 4 MHz. The vertcal dash-dot lne on the fgure denotes the poston of the expected TOA obtaned by measurng physcal dstance between the transmtter and recever antennas and the estmated TOA s marked on the tme-doman channel response for each of the estmaton technques. We can clearly observe that the EV/FBCM super- 9

141 resoluton technque shows much hgher tme-doman resoluton than the other two technques and t accurately detects the arrval tme of the DLOS path wth.7 ns estmaton error, whle the other two show much larger estmaton errors of about 35 ns. Fgure 5.5 presents the mean and the standard devaton of rangng errors versus sgnal bandwdth usng the same technques as n Fg Fgure 5.6 presents the probabltes of the channel measurement locatons where the absolute rangng errors are smaller than 3 m. From these results we can observe sgnfcant dfference between the super-resoluton technque and the other two TOA estmaton technques, especally when the sgnal bandwdth s relatvely small. Wth a sgnal bandwdth of MHz, the mean of rangng errors wth the super-resoluton technque s about m s smaller than that of the DSSS/xcorr technque, and about 4 m s smaller than that of the IFT technque. On the other hand, wth MHz bandwdth, usng the super-resoluton technque we can estmate dstance wthn 3 m s accuracy at about 5% more locatons than by usng the other two technques. It s also noted that the performance dfference decreases as the sgnal bandwdth ncreases. From the smulaton results presented above, we can conclude that n general, the super-resoluton technque has the best performance and t s especally preferred when the sgnal bandwdth s small. On the other hand, t should also be noted from the smulaton results that whle usng the super-resoluton technque and larger bandwdth can mprove the statstcal performance of the TOA estmaton, t cannot elmnate large estmaton errors at some locatons. For example, from Fg. 5.6 we can observe that even wth a bandwdth of 6 MHz there are stll around 5% of the total measurement 3

142 locatons showng larger than 3 m s rangng errors. Ths s because of the hgh probablty no-los NLOS stuaton n ndoor envronments between the transmtter and recever antennas that we dscussed prevously n Secton 3.3. The large TOA or dstance estmaton errors due to the NLOS condton need to be dealt wth n the postonng process to acheve hgh postonal accuracy n ndoor geolocaton systems as presented n Secton 3.3 and Secton IFT DSSS/xcorr EV/FBCM Mean of rangng errors m bandwdth MHz Fgure 5.5: Mean of the estmaton errors usng three dfferent technques. The vertcal lne corresponds to plus and mnus one standard devaton. 3

143 Percentage of absolute rangng errors < 3 m IFT DSSS/xcorr EV/FBCM bandwdth MHz Fgure 5.6: Percentages of the measurement locatons where absolute rangng errors are smaller than 3 meters wth three dfferent TOA estmaton technques. The exact comparson of our smulaton results wth the CRLB presented n Secton 3. s not possble because our smulaton results show the mean and standard devaton of the TOA estmaton errors over a larger number of dfferent locatons but the CRLB s the lower bound of the TOA estmaton errors caused by addtve whte nose at one locaton. However, snce the CRLB s the lower bound of the varance of TOA estmaton errors about the true tme delay, the exstence of the NLOS stuatons, whch s apparent from our smulaton results, makes t mpossble to benchmark the performance of the TOA estmaton technques n ndoor envronments wth the CRLB. For the same reason, the TOA estmaton n the multpah ndoor rado propagaton channels has non-zero mean of estmaton errors, that s, the estmaton s based as 3

144 shown n the Fg. 5.5; and the varance of the TOA estmaton errors s much larger than the CRLB obtaned wth the sngle-path AWGN channel shown n Fg EV/FBCM EV/FBCM/TD4-CMDCS EV/FBCM/TD-GDCS Mean of rangng errors m bandwdth MHz Fgure 5.7: Mean and standard devaton of rangng errors wthout tme dversty EV/FBCM, wth tme dversty usng the CMDCS EV/FBCM/TD4- CMDCS and GDCS schemes EV/FBCM/TD-GDCS. 5.5 Effects of Tme Dversty In Secton 4.4 we have dscussed dversty technques for the TOA estmaton applcatons, ncludng tme, space, and frequency dverstes. In ths secton we study the effects of tme dversty wth the two dversty combnng schemes that we presented n Secton 4.4,.e., the GDCS and CMDCS dversty combnng schemes. In our channel measurement data based smulatons, the tme dversty s smulated by 33

145 runnng smulatons wth the four snapshots of the channel frequency response collected consecutvely at each locaton whle stoppng movement n the vcnty of the transmtter and recever antennas durng the measurement. Ths represents the stuaton n whch the system s used for quas-statonary applcatons wth four tme dversty branches. Fgure 5.7 shows smulaton results for the EV/FBCM technque wth tme dversty usng two dfferent dversty combnng schemes,.e., usng the CMDCS EV/FBCM/TD4-CMDCS and usng the GDCS EV/FBCM/TD-GDCS. The smulaton results for the EV/FBCM method wthout tme dversty are also presented on the fgure as a reference for comparson and t s referred to as non-dversty method n the followng. From the results, we can observe that there s no sgnfcant dfference n the mean of the rangng errors wth the three technques for all bandwdth values. But the CMDCS based method has slghtly worse performance n terms of larger standard devaton of rangng errors than the non-dversty method, whch ustfes the analyss and concluson n Secton 4.4 that the CMDCS dversty combnng scheme s not sutable for the tme dversty technques. However, the GDCS based method has consstently better performance than the non-dversty method for all bandwdth values n terms of smaller standard devaton of rangng errors. For example, as compared wth the non-dversty technque the GDCS based method has m s smaller standard devaton of rangng errors wth MHz bandwdth, and about.5 m s smaller standard devaton wth 4 MHz bandwdth. Therefore, the same as n Secton 4.4 we can conclude that the GDCS dversty combnng scheme can be used n tme dversty 34

146 systems to mprove the performance of the TOA estmaton, whle the CMDCS dversty combnng scheme s not sutable for the tme dversty technque. In the next secton, we evaluate the performance of frequency dversty technques wth smulaton results. 5.6 Effects of Frequency Dversty Through the analyss of the correlaton coeffcents of the estmated channel parameter correlaton matrx, t s shown n Secton 4.4 that the CMDCS dversty combnng scheme s well suted for the super-resoluton TOA estmaton technques wth frequency dversty technque. The frequency dversty wth the CMDCS can sgnfcantly reduce the correlaton coeffcents of the estmated channel parameter correlaton matrx, and thus mproves the performance of the super-resoluton algorthms. But the theoretcal quanttatve relaton between the mprovement n the TOA estmaton results and the parameters of frequency dversty technque, such as the number of the dversty branches, s not known. Therefore, n ths secton we evaluate the effect of frequency dversty on the super-resoluton TOA estmaton technques wth the channel measurement data based smulaton results. The use of frequency dversty technque s smulated by runnng smulatons wth a number of dfferent segments of data samples from one snapshot of the frequency-doman channel response n a way smlar to the data segmentaton method used n 4.3. Each frequency-doman channel measurement data,.e., each snapshot of the frequency-doman channel response, s dvded nto a number of equally spaced 35

147 segments, so that each segment of the data has dfferent center frequency. Snce the measurement data at each locaton are of MHz bandwdth, to avod overlappng among dversty segments, the effect of frequency dversty s evaluated only for a bandwdth of MHz n ths secton. But t should be noted that n real mplementaton, overlappng segments can be used for frequency dversty. In our smulatons, the overlappng s avoded only n order to avod the correlaton between measurement noses n the overlappng segments snce the segments are obtaned from the same snapshot of the frequency-doman channel response. Four equally spaced segments are frst used for each measurement data sequence to compare the frequency and tme dversty technques usng the same number of dversty branches. Both the GDCS and CMDCS dversty combnng schemes are used for the EV/FBCM wth frequency dversty,.e., the EV/FBCM/FD4-GDCS and the EV/FBCM/FD4-CMDCS as shown n Fg. 5.8a, and the results are compared wth that of the non-dversty technque EV/FBCM and the tme-dversty technque EV/FBCM/TD-GDCS. Snce we only have smulaton results for one bandwdth values, here we could use the cumulatve dstrbuton functon CDF of the absolute rangng errors for comparson, whch provdes much more performance nformaton than the mean and the standard devaton measures. From Fg. 5.8, we can observe that all three dversty technques perform better than the non-dversty technque EV/FBCM and the CMDCS-based frequency dversty technque EEV/FBCM/FD4-CMDCS has the best performance. In order to examne the effects of the number of dversty branches, we ncrease the number of dversty branches to, whch s the maxmum number of segments of 36

148 MHz bandwdth that we can acheve from MHz channel measurement data wthout overlappng segments. The smulaton results of the GDCS and the CMDCS based frequency dversty technques wth dversty branches are compared,.e., the EV/FBCM/FD-GDCS and the EV/FBCM/FD-CMDCS n Fg. 5.8b, respectvely, wth that of the non-dversty technque EV/FBCM and the frequency dversty technque EV/FBCM/FD4-CMDCS, the latter of whch has the best performance n Fg. 5.8a. From the results, t s clear that the EV/FBCM/FD-CMDCS technque has the best performance and even the EV/FBCM/FD4-CMDCS technque has slghtly better performance than the EV/FBCM/FD-GDCS technque, although t has a smaller number of dversty branches. Consequently, from the smulaton results we can conclude that frequency dversty technques can sgnfcantly mprove the rangng performance and for frequency dversty, the CMDCS dversty combnng scheme s strongly preferred to the GDCS scheme by consderng the computatonal superorty, dscussed n Secton 4.4, that the CMDCS-based super-resoluton technques has over the GDCS-based super-resoluton technques. 37

149 BW = MHz EV/FBCM EV/FBCM/FD4-GDCS EV/FBCM/TD-GDCS CDF EV/FBCM/FD4-CMDCS absolute rangng errors m a BW = MHz.9.8 EV/FBCM/FD-CMDCS CDF EV/FBCM EV/FBCM/FD-GDCS EV/FBCM/FD4-CMDCS absolute rangng errors m b Fgure 5.8: Cumulatve dstrbuton functon of the absolute rangng errors for a bandwdth of MHz wth frequency dversty. 38

150 5.7 Summary and Conclusons The super-resoluton TOA estmaton technque needs to frst estmate channel frequency response and then convert the channel frequency response to tme doman to estmate the arrval tme of the frst peak of the tme-doman pseudospectrum. Therefore, the emprcal frequency-doman channel measurement data can be very convenently ntegrated nto the super-resoluton technques to study the performance of the TOA estmaton n ndoor envronments. In ths chapter we have evaluated the performance of varous super-resoluton TOA estmaton technques, whch are presented n Chapter 4, wth the computer smulatons based on a set of measured channel frequency response. The ndoor rado propagaton channel measurement data s collected wth a frequency-doman channel measurement system. From our smulaton results, t s clearly observed that the super-resoluton technques can sgnfcantly mprove the performance of the TOA estmaton n ndoor multpath channels as compared wth the conventonal technques ncludng the drect IFT and the DSSS sgnal-based cross-correlaton technques. The mprovement technques can further mprove the TOA estmaton performance, ncludng the EV method, the forward-backward estmaton of the correlaton matrx, tme dversty technques, and frequency dversty technques. Two dversty combnng schemes,.e., the GDCS and CMDCS schemes, are studed for the tme and frequency dversty super-resoluton technques. The smulaton results show that for the tme dversty technques the GDCS dversty combnng scheme s preferred whle for the frequency dversty technques the CMDCS s strongly preferred. 39

151 It s also observed from the smulaton results presented n ths chapter that the sgnal bandwdth has great mpacts on the performance of the TOA estmaton technques n the multpath ndoor rado propagaton channels. For each of the technques, the larger the bandwdth s, the better the performance. Ths observaton s consstent wth our analyss presented n Chapter 3. Also the super-resoluton TOA estmaton technques and the mprovement methods for the super-resoluton technques all provde sgnfcant performance mprovement when the sgnal bandwdth s small, but as the bandwdth ncreases there tends to be less sgnfcant dfference between dfferent estmaton technques. It s also noted that because of the possblty of the NLOS condton between the transmtter and recever antennas n ndoor envronments, usng the super-resoluton technque and the large sgnal bandwdth cannot elmnate the large rangng errors at some locatons. The large TOA estmaton errors due to the NLOS condton need to be dealt wth n the postonng process, whch follows the process of the TOA estmaton, to acheve good performance of the locaton fndng systems. It s worth to menton that due to the ste specfc nature and the complexty of ndoor rado propagaton channels, the smulatons based on channel measurement data may reveal varyng statstcal results so that quanttatve performance comparson between dfferent TOA estmaton technques s meanngful only wth the same set of measurement data. There s no sutable multpath channel model avalable n the lterature for the performance evaluaton of the TOA estmaton technques n ndoor envronments. The CRLB derved for the tradtonal applcatons s not applcable for ndoor applcatons 4

152 due to the exstence of the NLOS stuaton, whch can be easly verfed wth our smulaton results. The results obtaned from the emprcal channel measurement data based smulatons provde an nsght nto the achevable performance n realstc ndoor applcaton envronments. The measurement data based smulaton methods presented n ths chapter can be used n practce to convenently establsh the performance benchmarks of the TOA estmaton systems n ndoor applcaton envronments. In the next chapter we conclude ths thess wth a summary of conclusons, and dscussons of future work. 4

153 Appendx 5.A Measurement Stes and Scenaros Descrptons of the measurement stes and measurement scenaros are presented n ths secton for the ease of reference, more detals can be found n [Ben99c]. The measurements were conducted at three dfferent buldngs, ncludng a manufacturng buldng at the Norton Co., Worcester, MA, a modern academc buldng, the Fuller Laboratory at WPI, and a resdental house, the Schussler House at WPI. Thrty locatons were selected at each ste for measurement, ncludng ndoor-to-ndoor, outdoor-to-ndoor, and outdoor-to-second floor communcaton scenaros. 5.A. Descrptons of Measurement Stes Norton company s a manufacturer of weldng equpment and abrasves for grndng machnes. The buldng selected for measurement s Plant 7 that s a large buldng wth dmensons on the order of a few hundred meters. Ths buldng s connected to a fve floor brck buldng and to another manufacturng floor through a long corrdor. The rest of Plant 7 s manly surrounded by open areas and small buldngs. The buldng s used for manufacturng abrasves and nsde the buldng are huge ovens, grndng machnes, transformers, cranes and other heavy machnery. The buldng ncludes a set of parttoned offces wth brck external walls, metallc wndows and doors attached to the man huge open manufacturng area wth steel sheet walls of a heght of around seven meters and small metallc wndows close to the celng. In addton to the fluorescent lghts, many utlty ppes and metallc support beams hang from the celng. A snapshot of the nteror vew of the buldng s shown n Fg. 5.A.. 4

154 Fgure 5.A.: A snapshot of Plant 7, Norton Co., Worcester, MA. Fuller Laboratores at WPI s a modern buldng that houses the Computer Scence department at WPI and has been selected as the ste for measurements related to offce areas. The dmensons of ths buldng are on the order of a few tens of meters. It s surrounded on two sdes by older WPI buldngs the Atwater Kent Laboratores and the Gordon Lbrary and by roads on the other two sdes. One of the road s an nternal WPI campus road on the other sde of whch s the Salsbury Laboratores. The other road s a man road wth an open park on the other sde. The external walls of Fuller Laboratores are made of brck wth some alumnum sdng on two sdes, metallc wndow frames and doors. Wthn the buldng are several computer labs, department offces, offces of faculty and graduate students, lecture halls, and classrooms. The walls are made of sheetrock and n some offces, soft parttons dvde the room nto cubcles. Most of the rooms have furnture such as tables, chars and desks as well as computers. Some conference rooms have glass walls mounted n metallc frames. Fgure 5.A. shows an exteror vew of the buldng. 43

155 Fgure 5.A.: A snapshot of the Fuller Laborotores, WPI, Worcester, MA. Schussler house s a part of the resdences avalable at WPI for vstors. Ths s a farly bg resdental house wth wooden exteror walls and sheetrock nteror walls. The house s however very old and some portons of the external walls are made of stone as shown n Fg. 5.A.3. The house s located n a farly open area wth a few buldngs of smlar features located nearby. Some trees and a parkng lot surround other sdes of the house. Insde, there are several rooms that are furnshed wth couches, tables, chars etc.. Some rooms have brck freplaces. Rooms have dmensons on the order of a few meters. Fgure 5.A.3 A snapshot of Schussler house, WPI, Worcester, MA. 44