PRE-RAKE DIVERSITY WITH GENERALIZED ORTHOGONAL CODES AND IMPERFECT CHANNEL CONDITIONS FOR FDD/DS-CDMA SYSTEMS

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1 VOL. 4, NO. 7, SEPTEMBER 9 ISSN Asian Research Publishing Networ (ARPN). All rights reserved. PRE-RAKE DIVERSITY WITH GENERALIZED ORTHOGONAL CODES AND IMPERFECT CHANNEL CONDITIONS FOR FDD/DS-CDMA SYSTEMS C. Subhas, K. Rama Naidu and Y. Venatarami Reddy 3 Department of Electronics and Communication Engineering, Sree Vidyaniean Engineering College, Tirupati, A. P., India Department of Electronics and Communication Engineering, JNTU College of Engineering, Anantapur, A. P., India 3 Andhra Pradesh Public Service Commission, Hyderabad, A. P., India schennapalli@gmail.com ABSTRACT The Pre-Rae diversity combining technique decreases e complexity, size and cost of e mobile unit while achieving e same inter symbol interference (ISI) mitigation effects of conventional Rae receiver for direct sequence code division multiple access (DS-CDMA) systems. The technique is based on preprocessing of signal at e transmitter relying on nowledge of e channel state information. This a priori information is available in time division duplex (TDD) mode due to channel reciprocity. In frequency division duplex (FDD) mode e channel has to be estimated at mobile unit (MU) for e downlin and fed to base station to predict e channel for downlin time slot. In is paper, we compare e performance of Pre-Rae system wi different spreading codes. We will also propose a meod for channel prediction in FDD mode and evaluate e system under ideal and predicted channel conditions using generalized orogonal (GO) and Walsh codes rough analytical and computer simulations for DS-CDMA downlin. Keywords: channel prediction, DS-CDMA, FDD, ISI, pre-rae, rae. INTRODUCTION In recent years, direct sequence code division multiple access (DS-CDMA) has become more and more important for modern wireless communications. One interesting feature of DS-CDMA systems is e use of Rae receivers in multipa environment to achieve multipa diversity gain []. Rae diversity combining, a receiver-based technique, will effectively combat self interference (SI) or inter symbol interference (ISI) and increases data roughput. However, is meod requires channel state information (CSI) and complex signal processing at e mobile unit (MU) in e downlin which mae e MU more buly, expensive and unreliable. Hence, for e downlin, one can transfer e signal processing for interference suppression from e MU receiver to e base station (BS) transmitter by using Pre- Rae diversity combining technique, ereby reducing complexity of e MU (only a matched-filter to e own spreading sequence is required) wi equal performance for bo e single-user and multiuser systems employing orogonal codes []. The Pre-Rae system wi generalized orogonal (GO) codes outperforms e one wi oer spreading codes []. In time division duplex (TDD) mode because e uplin and downlin transmissions share e same frequency channel wi different time slot, it can be assumed at e uplin and downlin undergo e same channel fading. For operation in frequency division duplex (FDD), e downlin channel has to be predicted at e BS after obtaining CSI from MU rough feedbac. In very few papers in e literature, e Pre-Rae system s performance using various modulation schemes is evaluated wi orogonal codes under imperfect channel conditions [-5] at too in TDD mode. GO codes are applied to e Pre-Rae system to suppress system interference in is paper. The generalized orogonality describes e zero correlation zone (ZCZ) or orogonal zone property of GO codes, instead of e zero in-phase correlation property owned by traditional orogonal codes such as Walsh sequences [6, 7]. The leng of e orogonal zone Z cz represents e degree of e generalized orogonality. Because, in e DS-CDMA system, e multiple access interference (MAI) and e SI are determined by e cross and autocorrelation functions, respectively [], e concept of e orogonal zone, in fact, opens a new direction in spreading sequence design. In is paper, we evaluate e performance of multiuser Pre-Rae system [] using BPSK for various spreading sequences including GO codes. We extend our study of Pre-Rae technique in FDD mode for e DS-CDMA downlin. Since for FDD operation, e downlin channel needs to be predicted to compensate inherent feedbac delay involved in receiving its CSI from MU, we will propose a very effective prediction meod for obtaining CSI. MULTIPATH CHANNEL MODELING We utilize e simplified tapped delay line multipa channel model of []. The up-lin channels are assumed to be statistically independent for all users. Also, wi e utilization of up-lin power control we assume at all channels are statistically identical, even if e MU s are at different distances from e BS. The complex low-pass impulse response of e channel of user is given by h ( t) = L l l, exp( jγ l, ) δ( t lt ) =, () c 64

2 VOL. 4, NO. 7, SEPTEMBER 9 ISSN Asian Research Publishing Networ (ARPN). All rights reserved. Where L is e number of channel pas, e pa gains l, are independent identically distributed (i.i.d.) Rayleigh random variables (r.v. s) for all and l, e angles γ are i.i.d. uniformly distributed in [, π ], and l. T c is e chip duration. Wiout any loss of generality we can tae e normalization E[ ]. In a TDD system, = l under slow fading conditions, which are typical for portable communication systems, we assume at h () t does not change during two successive up and down time slots. In particular, when a slot is received at e BS rough h () t, BS estimates h () t for use in its own Rae receiver. The h () t might change due to time variability when e BS transmits during e next time slot to e MU of user. GENERALIZED ORTHOGONAL CODES It is well nown at in DS-CDMA system, e MAI is mainly caused by e discrete periodic and aperiodic correlation properties between e spreading sequences []. Therefore, e discrete correlation functions of GO sequences [] are presented briefly in is section before furer discussion. ( ) For e GO code set { a n, n =,... N; =,,..., M -} of family size M and leng N, e discrete periodic correlation function can be written as ( ) () i θ () l = N, n an a i = n+ l Nforl=, = i = forl= o, i foro< l Zcz, i Where Z cz is e orogonal zone which represents e degree of e generalized orogonality. It should be noted at e traditional orogonal codes, such as Walsh- Hadamard codes and orogonal variable spreading factor (OVSF) codes, can be treated as GO codes wi Z = cz. In oer words, e traditional orogonal code set is only a special case of e GO code set. In e following sections, e discrete aperiodic correlation function given below is used N l ( ) ( i) n an a n, l N = + ( ) ( i) C () l = N l a a, N l i, + n= n n +, l N (Instead of θ () l i, ) to evaluate e system performance. However, notice at when l = N, from () and (3), () (3) θ () (), l i C i, l can be obtained. Thus, for GO codes, we have C () l i, for l Z cz. The GO codes wi required leng and orogonal zone can be generated using e following recursive relation [7]. ( n ) ( n ) ( n ) ( n ) ( n) ( ) = ( n ) ( n ) ( n ) ( n ) ( ) Where - denotes e matrix e ij negation of, and ij (4) entry of which is e denotes e matrix e ij entry of which is e concatenation of e ij entry of () and e ij entry of. The starter is 4x4 Hadamard matrix. PERFORMANCE ANALYSIS OF PRE-RAKE SYSTEM WITH GO CODES In a multipa fading channel, conventionally a Rae receiver is used. It consists of a matched filter (MF) at is matched to e chip waveform of e spreading code, followed by a number of Rae fingers. Each Rae finger is synchronized to one of e channel pas. The Rae receiver fingers provide matching to e channel impulse response. Each Rae finger despreads e spread spectrum (SS) signal on its assigned channel pa. Using Rae combining, e despread signals on all fingers are multiplied wi e time reversed complex conjugate of e pa gains and all outputs are en added [3]. Hence, e receiver in bo BS and MUs must be equipped wi sufficient Rae fingers and e corresponding channel estimation process. In TDD mode, we can utilize e fact at for a period of slot time e channel impulse response is e same for e up and down lins. Hence, only e BS needs to estimate it. As shown in Figure-, to Pre-Rae e Figure-. The pre-rae diversity combination process wi ideal channel. down-lin signal of a user, e BS convolves is signal wi e time reversed complex conjugate of e uplin channel impulse response of at user. Estimation of e uplin multipa complex gains can be practically achieved using pilot symbols aided techniques. The BS receiver extracts e pilot symbols and uses em to estimate e uplin channel impulse response. Alternate 65

3 VOL. 4, NO. 7, SEPTEMBER 9 ISSN Asian Research Publishing Networ (ARPN). All rights reserved. meod is to use dedicated pilot channels. Channel estimation errors cause performance degradation in bo e Pre-Rae and e conventional Rae systems. For ideal channel, e conventional transmitted signal wiout Pre- Rae wi binary phase-shift eying (BPSK) modulation is given by s ( t) = Pb ( t) a ( t) exp( jωt), (5) Where P is e transmitted power, ω is e carrier frequency, and b () t is e data stream for user consisting of a train of i.i.d. data bits wi duration T. The current bit is denoted by b while next or previous bits are denoted by adding or subtracting e superscript by one. a () t is e PN code of user wi chip duration of T and code leng N = c TTc. Now, in a Pre-Rae system, instead of (5) e downlin transmitted signal will be P () L s t = L, l b( t ltc) U l=. a ( t lt ) exp( jω( t lt ) jγ ) c c, L l Where U is a normalizing factor at eeps e instantaneous transmitted power constant regardless of e number of pas, and is given by U (6) = L n= n, (7) Based on e analysis of e study in [3], assuming a DS- CDMA system wi K users, e received signal of user i during e downlin time slot can be written as r () t = n() t + Re K L j i, js( t jtc)exp( jγi, j) i = = Where n(t) is e zero-mean additive white Gaussian noise (AWGN) wi two-sided power spectral density N /. From (6), (8), and Figure-, it is shown clearly at e desired part of e received signal is e strongest pea among e L- pas. Because, in e Pre-Rae system, e receiver no longer processes e pa combination, e remaining L- pas should be treated as e interference to user i and e oer users. Wiout loss of generality, we assume at user is e desired user. The output of e correlation receiver of user can be written as ( L ) Tc + T Z = ( L ) r() t a( t ( L ) T c ) Tc.cos[ ωt ωt ( L )] dt = D + S + A+ η c Where D is e desired part of received signal, S is e SI, A is e MAI, and η is e zero-mean AWGN wi variance TN /4. (8) (9) As shown in Figure-, e desired part of e received signal can be obtained from (9) when j = L--l P D = b T U () Where b denotes e current bit of user. By employing Gaussian approximation, S and A can be treated as independent zero-mean Gaussian r.v s, and to estimate e bit error performance, e variances of S and A conditioned on,j are discussed in e following parts. Self Interference (SI) Because of multipa propagation, e SI exists even in a single-user system. In (6) and (8), when j L--l and =, which means e undesired part of user, termed as e SI, S can be obtained as P S = L L,, j, m cos[ T ( j m) ] U j= m= j ω + γ γ c, m, j. T b ( t ( j m ) T c) a [ t ( j m ) T c] a ( t ) dt () S can be divided into two parts: S m j Z CZ and S m j >Z CZ. Because e aperiodic autocorrelation value of GO codes is almost equal to zero wiin e orogonal zone, e SI contributes by pas arriving wiin e zero zone can be eliminated. After some manipulations, S can be furer written as, P S T c U L Z. cz L j= {,, cos[ T ( j m) m j j m c, m, j Zcz ω + γ = + + γ ] -.[( b + b ) C ( N - m+ j) + b C ( m- j)]} () Where C ( m ) = ( ) C, m is e discrete aperiodic autocorrelation function of e code. For any value of j and m, e mean of S is zero, and all terms in () are uncorrelated due to e independent phase shifts. When GO codes are considered, e variances of S conditioned on,j can be obtained as ES [ { }] = PTc, j U. L Zcz L { j=, j, m EC [ ( N m+ j)] m= j+ + Z cz where + EC [ ( m j)]} = PTc [ N µ ] U χ (3) L χ = Zcz L j= m j Z cz, j = + +, m and L Z µ = cz L j =, j, m ( m j). m= j+ + Zcz 66

4 VOL. 4, NO. 7, SEPTEMBER 9 ISSN Asian Research Publishing Networ (ARPN). All rights reserved. Multiple access interference (MAI) In e Pre-Rae system, because e transmitted signal has been Pre-Rae processed according to e channel impulse response, e received signal has more pa components and stronger MAI an e conventional Rae system. Based on (6) and (8), when, e MAI can be obtained as P K L L, j, m A =.cos[ ωtc( j m) + γ, m γ, j] = j= m= U. T b [ t ( j m ) T c] a [ t ( j m ) T c] a ( t ) dt (4) A can be divided into two parts: A m j Z CZ and A m j >Z CZ. When codes GO are used, because e aperiodic cross-correlation value of GO codes is almost equal to zero wiin e orogonal zone, A m j Z CZ can be obtained. Therefore, after some manipulations, A can be written as, P K L Zcz L A = = j= m= j+ + Zcz.cos[ ωt ( j m) + γ γ ] c, m, j.[ bc ( ), j m+ bc,( N+ j m)] +, m, jcos[ ωtc( m j) + % γ, j γ, m].[ b C ( m j N) + b C ( m j)]},, T c { U, j m, (5) Furermore, e variances of A conditioned on,j can be obtained as EA [ { }], j T c P ( K ) L Z { [ [ cz L, EC, ( j m)] 4L j= j + m= j+ + Zcz EC [ ( )]] [, N+ j m +, m EC, ( m j N)] + UPNT ( )( ) [ ( )]]} c K L EC m j =, 4L (6) Probability of error [Bit error rate (BER)] The signal to interference and noise ratio (SINR) can be written as, D D Y = = Var( Z ) [ Var( A) + Var( s) + Var( η)] (7) Where Var (Z) is e variance of r.v. Z. Based on (3), (6), and (7), it is not hard to get L 4χ µ ( K )( L ) Y = + + γbu NU NL N U (8) Where γ = PTL/N b is e average received signal to AWGN ratio. All items in (5) and (6) are assumed to be zeromean Gaussian r.v. The conditioned probability of error can be written as, P( e { }) =.5 erfc( Y), j (9) For GO codes, however, it is hard to obtain e analysis results of E [C,,j(m)]. To evaluate e error performance, e value of E [C,j(m)] would be obtained by numerical computation for certain GO codes. Therefore, by randomly generating e Rayleigh r.v.,j, j =,,..., L-, Y can be evaluated according to (8), and e conditioned error probability can be obtained based on (9). Averaged on more an millions of conditioned error probability, e averaged error probability P (e) can be obtained. CHANNEL PREDICTION In is section, we discuss e procedure for prediction of fading channel impulse response at MU for e downlin using Burg s algorim assuming ideal channel conditions as inputs in order to estimate e performance of e system in FDD mode. In our wor, we predict e channel information for e next time slot based on ideal channel samples of e previous slots at e MU. We assume at predicted channel information is available at BS rough control channel fed by MU. We also assume at e feedbac delay corresponds to one time slot duration which would be optimistic. The objective of e prediction operation is to forecast future values of e fading channel coefficients ahead. To accomplish is tas, a linear prediction meod based on e autoregressive model (AR) of fading is proposed [8]. Assume at e equivalent complex Rayleigh fading process ht () is sampled at e rate f s = Ts, where f is at least twice e maximum s Doppler shift. The linear MMSE prediction of e future channel sample hn ( ) based on its G previously estimated channel samples { hn ( ), hn ( ),..., hn ( G)} can be determined as hn ˆ( ) = G j= ag ( jhn ) ( j ) () Where a ( j)' s are e coefficients of e prediction G filter and G is e order of e predictor [8]. The optimum values of ese coefficients are computed using Burg's meod. This meod can be viewed as an order-recursive least squares lattice meod, based on e minimization of e forward and bacward errors in linear predictors wi e constraint at ese coefficients satisfy e Levinson- Durbin recursions [8]. The Burg's algorim is summarized as follows: Step. Initialize e forward and bacward prediction errors wi e estimated channel coefficients. 67

5 VOL. 4, NO. 7, SEPTEMBER 9 ISSN Asian Research Publishing Networ (ARPN). All rights reserved. Step. For m =,, 3,.., Where Here, K m is e f ( n) = q ( n) = h( n), () G, compute e following: f ( n) f ( n) K q ( n ), m = m + m m * q ( n) K f ( n) q ( n ) m = m m + m ( ) * M n= m f m n q m ( n ) K = m.5 M [ f ( ) ( ) n= m m n + qm n ] m () (3) (4) reflection coefficient of e lattice filter. M is e number of channel estimates used as an input for estimating e lattice filter. The denominator of e above equation is e least square error. This is minimized by computing e prediction coefficients such at, ey satisfy e recursive equation given by * a ( ) = a ( ) + K a ( m ) m m m m for m (5) The a ( j)' s obtained from e above algorim are G substituted in () to obtain e predicted channel sample at time n. SIMULATION RESULTS To see e performance of e Pre-Rae diversity combining under channel estimation errors, we consider a Parameter Table-. Parameters used in simulation. Value Bit rate 65 bits/sec Spreading code types Random, Walsh, and GO codes Process gain 64 Modulation Doppler frequency Number of pas Power delay profile Frame leng Number of slots 5 Feedbac delay BPSK 5,, 5 Hz As per IEEE standards ms.667 ms ( time slot) DS-CDMA system wi time varying Rayleigh fading channel. The absolute pa gains are i.i.d. Rayleigh random variables and angles are i.i.d. uniformly distributed in[, π ]. The channel tap weight vector is normalized such at h =. Simulation parameters used in simulation are given in Table-. Subsections on results are organized as follows: First, we compare and discuss e performance of e multiuser Pre-Rae system wi various spreading sequences under ideal channel conditions. Subsequently, e system is evaluated under imperfect channel conditions in FDD mode. Multiuser pre-rae system wi various spreading sequences In Figure-, e BER versus Eb/No performance of e Pre-Rae system is compared wi at of Rae system for random, orogonal and GO codes under ideal channel conditions. Clearly, when GO codes are used, ere is substantial improvement in e performance of bo e systems which can be explained by e fact at e SI and MAI arriving wiin e orogonal zone are eliminated when compared wi oer two codes, wi Rae receiver performing better an e Pre-Rae. However, e difference is marginal, and e use of Pre- Rae is still justified to reduce e cost and size of e MU. Next, e performance of bo e systems is moderate wi orogonal codes and bo e systems perform similarly at higher values of Eb/No. At lower side, e difference is not much and hence use of Pre-Rae is again justified. At Eb/No of 3 db, e BER is approximately 6 x -4 for GO codes and - for orogonal codes. When random codes are used, e Pre- Rae receiver greatly over performs e Rae receiver since e latter maximum ratio combines e interference as well along wi desired signal. BER BER plot for Prerae Ideal Channel - - random code (prerae) -3 walsh code (prerae) GO code (prerae) random code (rae) walsh code (rae) GO code (rae) Eb/No(dB) Figure-. BER performance of ideal multiuser pre-rae system wi various spreading sequences. The system parameters are N=64, L=, K=6 and Z cz =. Multiuser pre-rae system wi predicted channel in FDD mode In FDD mode, e channel is predicted at e MU for e current slot wi lattice filter of leng, G=8 and fed to e BS. We have considered one time slot feedbac 68

6 VOL. 4, NO. 7, SEPTEMBER 9 ISSN Asian Research Publishing Networ (ARPN). All rights reserved. delay which is typically used in 3G standards. In Figure-3, BER versus Eb/No performance of e system wi predicted channel is compared wi at of ideal channel using bo orogonal and GO codes. Figure-4 shows e BER versus number of user s performance of e Pre-Rae system using bo types of codes. System performance saturates as e number of users increases. In bo e graphs, e system performance wi predicted channel has coincided wi at of ideal channel showing at our prediction meod is more effective. However, in bo e cases, e performance wi GO codes is much better due BER BER plot for Prerae System Ideal Channel(walsh code) Predicted Channel(walsh code) Ideal Channel(GO code) Predicted Channel(GO code) Eb/No(dB) Figure-3. BER performance of pre-rae system versus Eb/No wi predicted channel in FDD mode. The system parameters are N=64,L=, K=6, and Z cz =. BER - BER plot for Prerae System - -3 complex an e conventional Rae system, which introduces more interference at e receiver. The generalized orogonal codes will help e Pre-Rae system to reduce e self and multiple access interference effectively because of eir zero correlation zone property. It is shown at e performance of e system has improved significantly wi generalized orogonal codes as compared to at wi e conventional orogonal codes. An effective meod for channel prediction is presented and e performance of e system under predicted channel conditions wi generalized orogonal codes is compared to at wi conventional orogonal codes for FDD/DS-CDMA systems. It is shown at e performance wi predicted channel is close to at of ideal channel for bo e codes which indicates at e prediction meod we have proposed is effective and can be applied in realistic scenario. At BER of x -, Eb/No is better by about db and at 6 users BER is better by times when GO codes are used. REFERENCES [] Ke Wan Li Hao and Pingzhi Fan. 7. Performance Analysis of Pre-Rae Diversity wi Generalized Orogonal Codes for DS-CDMA. IEEE Trans. on Vehicular Technology. 56(4): [] Essam E. Sourour, Tamer A.Kadous and Said E. El- Khamy The Performance of TDD-CDMA Systems Using Pre-Rae Combining wi Different Diversity Techniques and Imperfect Channel Estimation. nd IEEE symposium on computers and communications. pp July. [3] Said E. El-Khamy, Essam E. Sourour and Tamer A. Kadous Wireless Portable Communications using Pre-Rae CDMA/TDD/QPSK Systems wi Different Combining Techniques and Imperfect Channel Estimation. 8 IEEE intl. Symposium on PIMRC. : September. -4 Ideal Channel(walsh code) Predicted Channel(walsh code) Ideal Channel(GO code) Predicted Channel(GO code) Number of users Figure-4. BER performance of pre-rae system versus number of users wi predicted channel in FDD mode. The system parameters are N=64, L=, andz cz =. to e reason given in Section 6.. At BER of x -, Eb/No is better by about db and at 6 users BER is better by times when GO codes are used. CONCLUSIONS To simplify e complexity of MU, Pre-Rae processing at e BS maes e transmitted signal more [4] Yue Song and Yang Xiao.. The Performance of Prerae Diversity Combining Under Imperfect Channel Estimation based on QPSK Modulation in TDD CDMA System. Proceedings of IEEE TENCON. pp [5] Norharyati binti Harum, Yuh Tamura, Sigit P. W. Jarot, Ria Esmailzadeh and Masao Naagawa. 5. Analysis of Performance Degradation due to Channel Estimation Error in Pre-Rae TDD/CDMA. IEICE Trans. Comm. Vol. E88-B. No.6. June. [6] Pingzhi Fan. 4. Spreading Sequence Design and Theoretical Limits for Quasi-synchronous CDMA Systems. EURASIP Jr. on wireless comm. and networing. pp

7 VOL. 4, NO. 7, SEPTEMBER 9 ISSN Asian Research Publishing Networ (ARPN). All rights reserved. [7] Rainaumar and A.K. Chaturvedi. 4. Mutually Orogonal Sets of ZCZ Sequences. Electronics Letters. 4(8): September. [8] C. Subhas, K. Rama Naidu and Y. Venatarami Reddy. 9. Performance Degradation due to Imperfect Channel Conditions in Pre-Rae DSSS Systems. International Journal of Systemics, Cybernetics and Informatics. Pentagram Research Publications, Hyderabad, India. ISSN pp April. 7