ABSTRACT 1. INTRODUCTION 2. CHAOTIC SEQUENCE GENERATION

Transcription

1 BLIND ADAPIVE MULIUSER DEECION IN CHAOIC SEQUENCE BASED SYNCHRONOUS DS-CDMA SYSEM S J hiruvengadam, M hirumalai umar, A R arthiean, V Abhaiumar Signal Proceing Laborator Department of Electronic and Communication Engineering hiagarajar College of Engineering Madurai jtece@ahoo.co.in ABSRAC In thi paper, a novel blind adaptive multiuer detector for nchronou DS- CDMA tem i propoed b combining the merit of ubpace proceing and alman filtering. Chaotic preading equence are ued in the place of PN equence in the DS- CDMA tem. Subpace proceing decompoe the received ignal pace into deired ignal ubpace and noie ubpace, thereb providing the poibilit of handling onl the deired ignal. alman filtering allow the optimal ue of apriori information available and it i ued to etimate the channel leading to blind adaptive multiuer detection. Hence the propoed receiver tructure require onl the ignature waveform of the deired uer.. INRODUCION Code Diviion Multiple Acce (CDMA) tem accommodate a number of imultaneou ignal tranmiion on the ame channel. In ingle uer detection, the baeband receiver conider the ignal from other uer a interference []. hi reult in near-far problem. On the other hand, in multiuer detection (MUD), all the uer cooperate b tranmitting nchronoul in time. Multiuer detection deal with the demodulation of digitall modulated ignal in the preence of multi-acce interference. Over the pat two decade, a number of MUD cheme and implementation method have been developed. Maximum-Lielihood detector, Decorrelator, Minimum Mean Square Error (MMSE), Multitage detector, Deciion feedbac detector, Succeive Interference Canceller are the mot popular MUD cheme [2]. he multiuer receiver now the preading equence of all uer and jointl demodulate and detect all uer ignal. Hence, the total capacit of the CDMA tem can exceed the capacit of DMA and FDMA tem ince it ha ver high ignal to interference & noie (SINR) ratio. However, it depend trongl on the correlation propert of the choen PN equence et. hu, the election of preading PN equence et i vital in CDMA tem. Practicall, a peudorandom equence i produced b viiting each tate of a equence generator once in a determinitic manner with a finite number of tate to viit the output equence which i necearil periodic. he inherent periodicit of peudorandom equence compromie the overall ecurit of the tem. he greater the length of peudorandom equence, the higher the level of ecurit. Recentl, there ha been much interet in utilizing chaotic ignal for pread pectrum communication. Unlie the PN equence, a chaotic equence i generated b viiting an infinite number of tate of a dnamic tem in a determinitic manner and hence the equence i aperiodic in nature [3][4]. In thi paper, a novel cheme baed on ubpace proceing and diverit concept i propoed to improve the performance of the chaotic equence baed DS-CDMA tem. Further the concept of alman Filtering i introduced to mae the chaotic equence baed nchronou DS-CDMA tem blind adaptive. 2. CHAOIC SEQUENCE GENERAION Chaotic ignal generated b a nonlinear dnamic tem which i highl enitive to the initial condition, maing the ignal recontruction hard and thereb increaing the ecurit. he real valued chaotic equence produced b nonlinear dnamic tem are converted into chaotic binar equence uing

2 appropriate threhold function. here i a poibilit of generating a large number of chaotic binar equence which could be ued for more number of uer within the allocated bandwidth for CDMA tem. It ha been reported that the chaotic binar equence derived from the chaotic time erie exhibit better orthogonalit than the conventional PN equence. Chaotic equence have advantage uch a eae of generation, random code choice, large famil ize and dnamic length control. he generation method and determinitic tem pla a major role in deciding the propertie of the chaotic equence. In thi paper, chaotic equence are generated uing Piece Wie Linear Onto map [5] which ue a one dimenional equation given b, x n + = R ( x n ) for n = 0,,.N- () where 0 < x n <, and R (.) i the nonlinear chaotic map. In the i th ubinterval the mapping function i defined a R i (x n ) = a i x n + b i (2) where a i > and b i i an contant. he piecewie linear onto map i defined a, ((2 a ) ( a ))x + ax (a ) / 2 R(x ) = ((2 a ) ( a ))(x ) for ( 0 x < ( 2) ( 2 a ) ) (( 2) ( 2 a ) x < ( 2) + ( 2 a ) ) (( 2) + ( 2 a ) x ) (3) he chaotic binar equence are obtained uing the threholding function θ t (.) from the real valued chaotic equence X n b appling the proper threhold t. he threholding function i defined a 0 x < t θ (x) = (4) t x t It i oberved that the chaotic equence exhibit better correlation propertie than the conventional PN equence. Further, more number of chaotic preading equence can be generated than the conventional PN equence for the ame length. 3. NOVEL BLIND ADAPIVE DS-CDMA RECEIVER FOR MULIUSER DEECION Conider a multiuer nchronou DS-CDMA tem ignalling through flat fading channel. B paing through a chip matched filter followed b a chip-rate ampler, the dicretetime output of the receiver during one mbol interval i modelled a, (n) = A bh(n)s (n) + σv(n) (5) = for n = 0,,... where i the number of uer, A i the received amplitude of th uer, b i the th uer data choen independentl and equall from the et {-,+}, h(n) i the channel impule repone, S (n) i the th uer ignature waveform that i aumed to have unit energ and i the mbol duration. he mbol duration i alo expreed a = N c where N i the length of ignature waveform (or) proceing gain and c i chip duration. σ 2 i the variance of the noie and v(n) i the Gauian Noie Sequence. he receiver tructure i hown in Figure (). (n) Subpace Proceing (n) alman Filtering r opt (n) Decorrelating Detector r opt (n) (n) Figure Blind Adaptive Multiuer Detection uing Subpace Proceing and alman filtering he auto-correlation matrix (R) of the received equence i defined a, R = (n) (n) (6) where (n) repreent the tranpoe of (n). R can alo be expreed a, R = R + R v (7) where R repreent the autocorrelation matrix of ignal and R v i autocorrelation matrix of noie. he ran of R i the number of uer in the tem and hence i t ha nonzero eigen value. R v i diagonal in nature and full ran. Since the ran of R i equal to, then R ha onl nonzero eigen value and all thee eigen value are greater than zero. herefore, the firt Eigen value of R are greater than

3 σ 2 and the remaining eigen value are equal to σ 2. hu the eigen value and eigen vector of R i divided into two group. he firt group coniting of eigen vector that have eigen value (λ ) greater than σ 2, are referred to a ignal eigen vector (u ) and pan a dimenional ubpace called the ignal ubpace (U ). he econd group, coniting of thoe eigen vector that have eigen value (λ v ) i equal to σ 2 are referred to a noie eigen vector (u n ) and pan a (N-) dimenional ubpace and called a noie ubpace (U v ). In thi algorithm, the received ignal component which are correlated with the ignal ubpace component are obtained uing H (n) = U U (n) (8) he reultant (n) i ued in the tate pace formulation of alman filtering and deciion maing proce. Auming uer a the deired uer, (8) i rewritten in vector form a (n) = A' b (n)s + A' b (n)s + σv (n) (9) = 2 where (n) = [ (0), (),...., (N-)] V (n) = [v (0), v (),..., v (N-)] A = [A h(0), A h(),.., A h(n-)] S = [ (0), (),......, (N-)] A linear detector r (n) i deigned uing the concept of generalized ide lobe canceller for the detection of data of uer. r (n) i defined a, r (n) = S C W (n) (0),null C,null pan the null pace of S uch that the inner product between S and C,null i zero. C,null i N x (N-) matrix and the content of the matrix i formed uing Gram-Schmidt orthonormalization procedure [6]. W (n) i adaptive part of r and converge to the optimal value W opt (n). he tate-pace model of the tem i developed uing thi concept a follow. he tate equation i defined a Wopt (n + ) = Wopt(n) () he meaurement equation i defined a ŷ(n) = d (n)wopt (n) + e opt (n) (2) where d(n) = C (n),null e opt opt = S (n) d (n)w (n) (3) A compared to the conventional notation of tate pace model X(n+) = F(n+,n)X(n) + v (n) (4) (n) = C(n) x(n) + v 2 (n) (5) Now, the tate tranition matrix F(n+,n) i an N x N Identit matrix, X(n) i W opt (n), the random noie equence V (n) i zero, the meaurement matrix C(n) i d (n) which i equal to (n) C,null and v 2 (n) i e opt (n). Uing thee aignment, the alman filtering algorithm i written a g(n) = (n, n )d(n)[d (n)(n, n )d(n) + ξ min ] (6) (n +, n) = (n, n ) g(n)d (n)(n, n ) (7) g(n)[ ~ ŵ opt(n) = ŵ opt(n ) = (n) d (n)ŵ opt(n )] (8) r (n) = S C,nullŴopt (n) (9) where g(n) i alman gain factor, (n,n-) i (N-) x (N-) correlation matrix of predicted tate error vector and ε min i equal to. he initial value W opt = 0 and (, 0) =. he optimal linear detector r opt (n) i expreed a r opt (n) = S C,null W opt (n) (20) Uing thi, the deciion on b (n) during n th mbol interval i given b (n) = gn( < ropt, > ) (2) which can be rewritten a (n) = gn(r opt (n)) (22) he advantage of thi algorithm i that it uppree the noie prior to filtering and detection procee reulting in fater convergence at the cot of additional computational complexit due to ubpace proceing. 4. MULIUSER DEECION WIH RECEIVE DIVERSIY A chaotic equence baed DS-CDMA tem uing alman Filter and Subpace proce propoed in the previou ection i provided with receive diverit o a to enhance the performance of the tem in a flat fading channel [7][8]. he baeband received equence at antenna m i repreented a, m (n) = A h m (n)b (n) + σ mv = for m =,2,..M, n = 0,,..N- m (23)

4 where m (n) i the received equence at m th antenna, A i the th uer received amplitude, h m (n) i the channel repone at m th antenna, σ m i the variance of the noie at m th antenna, M i the number of receiver antenna, N i the length of the ignature waveform, i the number of uer and S (n) i the th uer ignature waveform. In vector notation it can be written a, ' Ym = A m,b (n) + σ mv m (24) = Y m = [ m (0), m ().. m (N-)] A m, = [A h m (0), A h m ()... A h m (N-)] = [ (0), ()... (N-)] (n) Subpace Proceing (n) alman Filtering r opt (n) Decorrelating Detector r opt (n) (n) Figure 3 Performance of Snchronou DS-CDMA tem with Maximal Length Spreading Sequence uing the Propoed Receiver Structure (Spreading Sequence length: 3 Number of Uer: 3) 2 (n) Subpace Proceing 2 (n) Decorrelating Detector r opt2 (n) (n) r opt2 (n) alman Filtering Figure 2. Blind Adaptive Multiuer Detection uing Subpace Proceing and alman Filtering with Receive Diverit In the propoed receiver hown in the Figure 2, the incoming ignal from each antenna i proceed independentl b ubpace proceor, alman filter and decorrelating detector. he deciion i made uing the ummed output of all the receive antenna. 5. RESULS AND DISCUSSIONS he performance of the propoed receiver tructure for nchronou DS-CDMA tem are analed in flat fading channel. he reult i hown in Figure 3 for DS- CDMA tem with 3 uer. It i oberved that the propoed ubpace baed alman filtering tructure require onl db a compared to blind adaptive alman filtering Figure 4 Performance of Snchronou DS-CDMA tem with Chaotic Spreading Sequence uing the Propoed Receiver Structure (Spreading Sequence length: 3 Number of Uer: 6) algorithm which require 3 db to achieve the ame probabilit of error. Further, the receive diverit of order two require onl 5 db, which i 6 db le compared to ingle antenna tem. he performance of chaotic equence baed nchronou DS-CDMA tem with 6 uer and chaotic preading equence length of 3 i alo analed in flat fading channel and the reult are hown in Figure 4. he chaotic equence were generated uing piecewie linear ontomap method. A oberved in PN equence baed DS-CDMA tem, the propoed tructure require 7 db in ingle antenna tem, 3 db in two antenna tem, which are 2 & 6 db le compared to the blind

5 7. REFERENCES Probabilit of Error SNR in db Figure 5. Performance of Snchronou DS-CDMA tem with Maximal Length Spreading Sequence uing the Propoed Receiver Structure (Spreading Sequence length: 3 Number of Uer: 6) adaptive alman filtering algorithm repectivel. Moreover, the performance of the tem i far uperior to the performance of maximal length equence baed tem with 6 uer a hown in Figure CONCLUSION In thi paper, chaotic preading equence were ued in place of Peudo Noie equence in the nchronou DS-CDMA tem and it performance i analed in a flat fading channel. Novel ubpace baed blind adaptive alman filtering algorithm i propoed in ingle receive antenna and two receive antenna cae. alman filtering algorithm wa made blind adaptive uing the concept of generalized ide lobe canceller. In the receive diverit cae, the propoed tructure for the ingle antenna cae i extended in parallel and it i combined onl in the decorrelating detector output tage. It wa verified that the propoed receiver tructure how better performance than the conventional alman filtering algorithm baed receiver tructure in both the chaotic equence baed nchronou DS-CDMA baed tem and the conventional PN equence baed tem. [] John G Proai, Digital Communication, McGraw-Hill International Edition, Fourth Edition, 200. [2] Sergio Verdu, Multiuer Detection, Cambridge Univerit Pre: Cambridge, U, 998. [3] Gianluca Mazzini, Gianluca Setti and Riccardo Rovatti, Chaotic complex preading equence for anchronou DS- CDMA Part I: Stem Modeling and Reult, IEEE ranaction on Circuit and Stem, Vol.44, No.0, pp , Oct 997. [4] Gianluca Mazzini, Gianluca Setti and Riccardo Rovatti, Chaotic Complex preading equence for anchronou DS- CDMA Part II: Some theoretical performance Bound, IEEE ranaction on Circuit and Stem, Vol.45, No.4, pp , April 998. [5] Aio uneda, Daiaburou Yohioa, and aahiro Inoue, Deign of Maximal- Period Sequence with Precribed Auto- Correlation Propertie Baed on One- Dimenional Map with Finite Bit, Department of Electrical and Computer Engineering, umamoto Univerit, umamoto, Japan. [6] Xian-da Zhang and Wei Wei, Blind adaptive multi-uer detection baed on alman filtering, IEEE ranaction on Signal Proceing, Vol.50, No., Jan [7] S. Alamouti, A imple tranmit diverit technique for wirele communication, IEEE Journal on Selected Area of Communication, Vol. 6, No. 8, pp , Oct [8] X. Wang and H.V. Poor, Blind Adaptive Space-ime Multiuer Detection with Multiple ranmitter and Receiver Antenna, IEEE ranaction on Signal Proceing, Vol. 50, No.6, June 2002.

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