Ouline Roman Merz, Cyril Boeron, Pierre-André Farine Insiue of Microechnology Universiy of Neuchâel 2000 Neuchâel Workshop on UWB for Sensor Neworks, 2005
Ouline Ouline 1 Inroducion Moivaions and Goals Descripion TH-UWB Receiver Archiecure 2 Coheren Addiion No Timing Error Gaussian Jier Frequency Offse 3 Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference 4
Moivaions and Goals Inroducion Coheren Addiion Muliuser Inerference Moivaions and Goals Descripion TH-UWB Receiver Archiecure Moivaions Goals A WSN may conain many nodes UWB is an aracive physical layer echnology for WSNs Evaluaion of he applicabiliy of a code sequence as a spreading code Evaluaion during all receiver s operaing modes, including iniial synchronizaion phase
Impulse Radio Inroducion Coheren Addiion Muliuser Inerference Moivaions and Goals Descripion TH-UWB Receiver Archiecure No modulaion, no spreading T s = N f T f Time Hopping Spreading (TH-UWB) T s = N f T f T f = N c T c Symbol composed of Nf frames Each frame conains one pulse A frame is formed by N c chips Pulse posiion deermined by repeiive spreading code wih N f elemens.
Receiver Archiecure Inroducion Coheren Addiion Muliuser Inerference Moivaions and Goals Descripion TH-UWB Receiver Archiecure Subseq T f Code T s Ref Pulse A subsequence a he expeced ime of arrival of a pulse is acquired Several subsequences are added o increase SNR Furher processing (correlaion, demodulaion) is no considered The implemenaion may be in analog or digial domain
Receiver Archiecure Inroducion Coheren Addiion Muliuser Inerference Moivaions and Goals Descripion TH-UWB Receiver Archiecure Subseq T f Code Correlaor wih seq. of recangular emplaes T s Ref Pulse A subsequence a he expeced ime of arrival of a pulse is acquired Several subsequences are added o increase SNR Furher processing (correlaion, demodulaion) is no considered The implemenaion may be in analog or digial domain
No Timing Error Inroducion Coheren Addiion Muliuser Inerference No Timing Error Gaussian Jier Frequency Offse Pulse combining gain GPC (db) 45 40 35 30 25 20 15 10 5 Theoreical Measuremen 0 2 0 2 5 2 10 2 15 Number of coheren addiions N f No iming error: linear pulse combining gain G PC = N f Gaussian jier: linear pulse combining gain ( ) 5 n G PC = N f 2 n + σ 2 Frequency offse: non-linear pulse combining gain
Gaussian Jier Inroducion Coheren Addiion Muliuser Inerference No Timing Error Gaussian Jier Frequency Offse Pulse combining gain GPC (db) 45 40 35 30 25 20 15 10 5 0 2 0 2 5 2 10 2 15 Number of coheren addiions N f 0 ps 100 ps 200 ps 500 ps No iming error: linear pulse combining gain G PC = N f Gaussian jier: linear pulse combining gain ( ) 5 n G PC = N f 2 n + σ 2 Frequency offse: non-linear pulse combining gain
Frequency Offse Inroducion Coheren Addiion Muliuser Inerference No Timing Error Gaussian Jier Frequency Offse Pulse combining gain GPC (db) 45 40 35 30 25 20 1 ps 100 fs 15 10 5 0 2 0 2 5 2 10 2 15 1 fs 10 fs Number of coheren addiions N f No iming error: linear pulse combining gain G PC = N f Gaussian jier: linear pulse combining gain ( ) 5 n G PC = N f 2 n + σ 2 Frequency offse: non-linear pulse combining gain
Frame Synchronizaion Inroducion Coheren Addiion Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference Frame Synchronized and Code Synchronized T s δ w 1,k w 2,k w 3,k w 4,k Frame Synchronized User of ineres coheren addiion Serves as a reference scenario for he evaluaion Frame Non Synchronized Erroneous code (no user of ineres or wrong code phase) Parially coheren addiion Inerferer wih unrelaed iming
Frame Synchronizaion Inroducion Coheren Addiion Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference Frame Synchronized and Code Synchronized Frame Synchronized w 1,k w 2,k w 3,k w 4,k Frame Non Synchronized Coheren Addiion of he user of ineres Serves as a reference scenario for he evaluaion Erroneous code (no user of ineres or wrong code phase) Parially coheren addiion Inerferer wih unrelaed iming
Frame Synchronizaion Inroducion Coheren Addiion Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference Frame Synchronized and Code Synchronized Frame Synchronized Frame Non Synchronized w 1,k w 2,k w 3,k w 4,k Coheren Addiion of he user of ineres Serves as a reference scenario for he evaluaion Erroneous code (no user of ineres or wrong code phase) Parially coheren addiion Inerferer wih unrelaed iming
Disincion Coefficien Inroducion Coheren Addiion Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference W (a) w 1,k w 2,k w 3,k w 4,k Maximum absolue value User of ineres, synchronized Inerferers W (b,c) w 1,k w 2,k w 3,k w 4,k Erroneous code Inerferers Max (all configuraions)
Disincion Coefficien Inroducion Coheren Addiion Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference W (a) w 1,k w 2,k w 3,k w 4,k D = W (a) /W (b,c) W (b,c) w 1,k w 2,k w 3,k w 4,k
Disincion Coefficien Inroducion Coheren Addiion Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference W (a) W (a) = N f max q (n) () w 1,k w 2,k w 3,k w 4,k W (b,c) W (b,c) = S max max q (n) () D = W w 1,k w 2,k w 3,k w (a) /W (b,c) 4,k Insead of correlaing signals, couning he number of his S max. (Valid if duraion of he received pulse is shorer han a chip).
Resuls Inroducion Coheren Addiion Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference D 8 7 6 5 4 3 2 1 0 2 4 8 16 32 64 128 256 Code lengh N f LFSR RAND 4 bis 3 bis 2 bis 1 bi Fig: D for LFSR and random spreading codes, wihou MAI, in PC Disincion coefficien depends on he code lengh N f and he number of bis o represen one elemen of he code.
Disincion Coefficien Inroducion Coheren Addiion Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference W (a) w 1,k w 2,k w 3,k w 4,k Expeced value User of ineres, synchronized Frame non synchronized inerferers W (b,c) w 1,k w 2,k w 3,k w 4,k max over all expeced values mh user all users m
Resuls Inroducion Coheren Addiion Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference 4 3 D 2 1 0 1 2 4 8 16 32 64 Code lengh N f Fig: D for hree bis LFSR code, wih MAI, in PC. D 4 3 2 1 0 1 2 4 8 16 32 64 M = 1 M = 2 M = 3 M = 5 M = 9 M = 17 M = 1 M = 2 M = 3 M = 5 M = 9 M = 17 Code lengh N f Fig: D for a hree bis LFSR code, wih MAI, in CM3 channel model.
Disincion Coefficien Inroducion Coheren Addiion Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference W (a) w 1,k w 2,k w 3,k w 4,k Expeced value User of ineres, synchronized Frame synchronized inerferer W (b,c) max over all expeced values w 1,k w 2,k w 3,k w 4,k
Resuls Inroducion Coheren Addiion Muliuser Inerference Definiions Single User Frame Non Synchronized Inerference Frame Synchronized Inerference M = 1 4 D 3 2 1 M = 2 M = 3 M = 5 0 M = 9 M = 17 2 4 8 16 32 64 sync no sync Code lengh N f Fig: D for hree bis LFSR code, wih MAI, in PC. M = 1 4 D 3 2 1 M = 2 M = 3 M = 5 0 M = 9 M = 17 2 4 8 16 32 64 sync no sync Code lengh N f Fig: D for a hree bis LFSR code, wih MAI, in CM3 channel model.
Inroducion Coheren Addiion Muliuser Inerference Evaluaion of code properies under idealized condiions Numerical resuls for more realisic condiions User separaion vs. code lengh and he number of bis o represen one elemen of he code
Addiional Frames Bibliography Single User? 1 User of ineres exclusively Compare correc code vs. erroneous code phases Classical analysis: auocorrelaion of he generaed RF signal 2 One user only, bu no he user of ineres Compare correc code of user of ineres vs. he larges resul receiving he wrong signal Classical analysis: crosscorrelaion beween he correc RF signal and he received RF signal Is here a way o obain he resuls from he spreading code direcly insead of he RF signals?
Addiional Frames Bibliography Pulse Shape 1.0 0.5 0.0 A (V) 2nd derivaive Gaussian pulse n = 200 ps 1 pj a 50 Ω (ns) 0.5 0.5 0.0 0.5 1.0
Addiional Frames Bibliography Frequency Offse Pulse combining gain G PC = 42 n 3Nα 2 + ( ) ( 2N 3 42 n 3Nα 2 exp 1 4 N 2 α 2 ) where α is he ime offse of he emier and receiver clock accumulaed during he frame ime T f (in beween wo consecuive pulses). The maximum of he pulse combining gain depends on n /α. For a second derivaive Gaussian pulse, he maximum gain is 2 n which is obained for addiions. G PC, max 0.9564 n α N max 1.6102 n α
Addiional Frames Bibliography Bibliography T. Erseghe, Ulra wide band pulse communicaions, Ph.D. disseraion, Universià Degli Sudi Di Padova, 2001. R. Merz, C. Boeron, P.-A. Farine, and J. Farserou, Asympoical analysis of iming imperfecions in uwb receivers, in 2nd IEEE In. Conf. on Circuis and Sysems for Communicaions, 2004, Moscow. R. Merz, C. Boeron, and P.-A. Farine, Muliuser inerference during synchronizaion phase in uwb impulse radio, in Proc. In. Conf. on Ulra-Wideband, 2005.