Keywords Frequency-domain equalization, antenna diversity, multicode DS-CDMA, frequency-selective fading

Transcription

1 Joint Frequency-doain Equalization and Antenna Diversity Cobining for Orthogonal Multicode DS-CDMA Signal Transissions in A Frequency-selective Fading Channel Taeshi ITAGAKI *1 and Fuiyui ADACHI *2 Dept. of Electrical and Counication Engineering, Graduate School of Engineering, Tohou University 5 Aza-Aoba, Araai, Aoba-u, Sendai, Japan E-ail: *1 itagai@obile.ecei.tohou.ac.jp, *2 adachi@ecei.tohou.ac.jp Abstract Orthogonal ulticode direct sequence code division ultiple access (DS-CDMA) has a flexibility in offering various data rate services. However, in a frequency-selective fading channel, the bit error rate (BER) perforance is severely degraded since othogonality aong spreading codes is partially lost. In this paper, we apply frequency-doain equalization and antenna diversity cobining, used in ulti-carrier CDMA (MC-CDMA), to DS-CDMA in order to restore the code othogonality while achieving frequency and antenna diversity effect. It is found by coputer siulations that the joint use of frequency-doain equalization and antenna diversity cobining can significantly iprove the BER perforance of orthogonal ulticode DS-CDMA in a frequency-selective fading channel. Keywords Frequency-doain equalization, antenna diversity, ulticode DS-CDMA, frequency-selective fading 1. Introduction Orthogonal ulticode DS-CDMA is flexible in offering various data rate services by changing the nuber of parallel orthogonal spreading codes [1]. In a DS-CDMA obile counications syste, orthogonal ulticode DS-CDMA is used for the downlin; each spreading code is assigned to a different user. In DS-CDMA, the ultipath fading channel [2] is resolved by a ban of correlators (nown as the rae fingers) into any distinct paths for coherent rae cobining. Coherent rae cobining can exploit the channel frequency-selectivity to iprove the BER perforance through path diversity effect (siilar effect to antenna diversity) [3]. However, as the nuber of resolvable paths increases, the receiver coplexity increases due to increasing nuber of rae fingers. Furtherore, increased inter-path interference (IPI) resulting fro tie asynchronis of different paths offsets the perforance iproveent by rae cobining. Recently, ulti-carrier CDMA (MC-CDMA) has been attracting uch attention for broadband wireless ultiple access [4]. In MC-CDMA, any orthogonal subcarriers are used and the data sybol to be transitted is spread over several subcarriers using frequency-doain orthogonal spreading code. At an MC-CDMA receiver, the frequency-doain equalization is applied to the received signal for restoring the code orthogonality. Through frequency-doain equalization and despreading, frequency diversity effect is attained, resulting in significantly iproved BER perforance of MC-CDMA copared to that of DS-CDMA with coherent rae cobining [5]. Quite recentry, application of frequency-doain equalization to single-carrier (SC) transission has been attracting attention [6]. It is pointed out in [7] that the frequency-doain equalization can be applied to orthogonal ulticode DS-CDMA for iproving its BER perforance in a severe frequency-selective channel. In this paper, joint frequency-doain equalization and antenna diversity cobining is considered for the reception of the orthogonal ulticode DS-CDMA signals in a severe frequency-selective channel. Section 2 presents weights for joint frequency-doain equalization and antenna diversity cobining. Various frequency-doain equalization schees using axial ratio cobining (), equal gain cobining (EGC), orthogonal restoration cobining (ORC) and iniu ean square error cobining () [8] are considered. In Sect. 3, the achievable BER perforances are evaluated by coputer siulation. Soe conclusions and future wor are offered in Sect Joint Frequency-doain Equalization and Antenna Diversity Reception Transission syste odel of orthogonal ulticode DS-CDMA using frequency-doain equalization and antenna diversity cobining is illustrated in Fig. 1. { d i } MF Reoval of GI S/P { c ( Insertion of GI { c C 1( { c scr ( Scrable-sequence Walsh-Hadaard sequence (a) Transitter Fro other w () branches { c ( FFT S/P w (-1) P/S IFFT c scr { ( (b) Receiver Fig. 1 Transission syste odel c C { 1 ( P/S d ˆ } { i

2 2.1. Insertion of Guard Interval (GI) for Frequency-doain Equalization Fast Fourier transfor (FFT) is applied for decoposing the received DS-CDMA signal into the subcarrier coponents (the ter subcarrier is used although subcarriers are not used for data odulatio for frequency-doain equalization and antenna diversity cobining. At the receiver, the received DS-CDMA signal with spreading factor on each diversity antenna is sapled at the chip rate. The FFT windowsize is equal to the spreading factor. For applying FFT, the received signal wavefor ust be treated as a periodic function in tie with the repetition period of chips. Reebering that the wireless channel consists of any tie delayed paths [2], cyclic extension of the transitting wavefor needs to be applied; a copy of the last part of N g chips in the transitting signal wavefor is inserted into the beginning of the signal wavefor as a guard interval (GI) as in MC-CDMA (see Fig. 2). The GI length T g needs to be longer than the largest tie delay difference in the channel. Letting T c be the chip period, T g is T g =T c N g and the effective sybol length is T s =T c. Then, GI-inserted DS-CDMA signaling period is T=T s +T g. Hence, the data sybol rate decreases by a factor of (1+ T g /T s ) or (1+ N g /) ties copared to the no GI insertion syste (which uses rae cobining instead of frequency-doain equalizatio and also power penalty of (1+T g / T s ) or (1+ N g /) is produced. After joint one-tap frequency-doain equalization and antenna diversity cobining, the tie-doain signal wavefor is obtained by applying inverse FFT (IFFT) for data deodulation. Since the IFFT operation is the linear cobination of all subcarrier coponents, the well-nown frequency diversity effect can be attained in a frequency-selective fading channel. Insertion GI N g chips Spread signal chips -N g Fig. 2 Insertion of GI tie 2.2. Signal representation For siplicity, we consider the th signaling interval, i.e., a tie interval of =-N g -1. At the transitter, binary data sequence is transfored into quadrature phase shift eying (QPSK) sybol sequence {d i ; i=c-1}, each sybol is then spread using orthogonal spreading codes { c i ( ) = ± 1; i = C 1, = 1} of spreading factor. The resultant orthogonal C parallel chip sequences are added (i.e., code ultiplexed) and then ultiplied by a scrable sequence { c scr ( ) = ± 1; =, 1,,1, } for aing the transitting signal noise-lie. Throughout the paper, the chip-spaced discrete tie representation is used. The generated ulticode DS-CDMA signal wavefor s() can be expressed using the equivalent baseband representation as C 1 ( ) = 2 / s Ec Tc dici ( ) cscr ( ), = 1, (1) i= where E c represents the chip energy. The GI-inserted signal wavefor can be expressed as s ( ) = s( od ), = Ng 1, (2) which is transitted over a frequency-selective fading channel and received by M antennas at the receiver. The channel is assued to be coposed of L distinct propagation paths with different tie delays. The coplex path gain and tie delay of the lth path corresponding to the th antenna are respectively denoted by ξ,l and τ l. The signal wavefor received on the th antenna at tie ay be expressed as L 1 τ r ( ), s ( l = ξ l ) + η( ) T l= c, (3) where {η ( is the zero-ean coplex Gaussian process with variance 2N /T c due to the additive white Gaussian noise () having the one-sided power spectru density N. Bloc fading, where the path gains stay constant over one signaling period, is assued. After reoval of GI, the received signal is decoposed into subcarrier coponents { R ( ; n = 1} by applying -point FFT. R ( is given by 1 R ( = r = H = ( )exp( j2πn ( S( + η ( ), (4) where H ( and S( are the Fourier transfors of the channel ipulse response and the transitted ulticode DS-CDMA signal wavefor, respectively. In Eq.(4), η ( n ) represents the noise coponent at the nth subcarrier frequency. R ( is ultiplied by the weight w ( for joint frequency-doain equalization and antenna diversity cobining to obtain M 1 ( = R ( w ( = R. (5) The tie-doain signal wavefor { ( -point IFFT is given by 1 1 n ( ) = R( exp( j2 ) n= r π. (6) r obtained by Parallel despreading and descrabling operation is perfored on { r ( to obtain the soft decision saple sequence d ˆ } : { i 1 ˆ 1 = di r ( ) ci ( ) cscr ( ), i = C 1 (7) =

3 for succeeding data deodulation Weights for joint frequency-doain equalization and antenna diversity cobining In this paper, a heuristic approach is taen following the frequency-doain equalization used in MC-CDMA. Various frequency-doain equalization schees using, EGC, ORC and are considered to copare the achievable BER perforance in a frequency-selective fading channel. Joint frequency-doain equalization and diversity cobining weight described in [9] can be used: H(, H(, EGC H( H(, ORC M 1 w ( = 2,(8) H( = H(, M E + H ( C c = N where E c /N represents the average received chip energy-to- power spectru density ratio. The nth subcarrier coponent R ( n ) of Eq. (5) after joint frequency-doain equalization and antenna diversity cobining is now rewritten as M 1 M 1 R( = w ( H ( S( + w = = = H ( S( + η ( ( η(, (9) where the first ter is the signal coponent and the second the noise coponent. ORC can copletely restore the frequency nonselective channel (thus, orthogonality of spreading codes can be restored) but produces noise enhanceent. Restoration of frequency non-selectivity and noise enhanceent have a trade-off relationship. cannot copletely restore the frequency non-selectivity but iniizes the equalization error on each subcarrier. Propagation channel odel Bloc Rayleigh fading channel with L=132 paths No. of FFT saples 256 (=) No. of antennas M=14 Frequency-doain ORC, EGC,, equalization Channel estiation Ideal 3.1. Frequency-doain ORC, EGC,, and equalizations The average BER perforances with frequency-doain ORC, EGC,, and equalizations are plotted as a function of the average received signal energy per bit-to- power spectru density ratio E b /N in Fig. 3 for various values of C in the case of L=8 and M=1. E b /N is defined as E b /N =(+N g )E c /N. The and EGC can achieve the frequency diversity effect and there is no noise enhanceent. Hence, they provide very good BER perforances. However, this is only true for the single code case (C=1). For the ulticode case, the BER perforances of EGC and degrade and the BER floors are seen due to enhanced frequency-selectivity of the channel (the perforance is uch worse than the EGC perforance). On the other hand, the BER perforance of ORC is insensitive to the value of C because of perfect restoration of frequency-nonselectivity, but its BER perforance is even worse than those of EGC and for low code-ultiplexing order. This suggests that can only be used for frequency-doain equalization of DS-CDMA signals. It can be clearly seen in Fig. 3(b) that the always provides the best BER perforance aong the four equalization schees. Hence, in the following siulation, only is considered. 1.E+ 1.E-1 1.E-2 1.E-3,, C =1 ORC EGC 3. Coputer Siulation Siulation condition is shown in Table 1. A very slow L-path frequency-selective bloc Rayleigh fading channel having unifor power delay profile is assued. The tie delay τ l of the lth path is assued to be τ l =lt c. Table 1 Siulation condition Data odulation QPSK Multicode Spreading BPSK spreading odulation Spreading factor =256 No. parallel C=1256 codes Scrable code M-sequence with a period of 495 chips Guard interval T g =32T c 1.E-4 1.E Average received E b/n [db] (a) C=1

4 1.E+,, C =256 1.E+ Ideal Rae 1.E-1 1.E-1 1.E-2 1.E-3 1.E-2 1.E-3 1.E-4 1.E-5 ORC EGC E-4 1.E-5 C =16 C =32 C =64 C =128 C = Average received E b/n [db] Average received E b/n [db] (b) C=256 Fig. 3 Perforance coparison of frequency-doain ORC, EGC,, and equalizations for L=8 and M= Perforance coparison of frequency-doain equalization and rae cobining Perforance coparison of frequency-doain equalization and rae cobining for ulticode case is illustrated in Fig. 4. As C increases, the BER perforance with rae cobining significantly degrades due to increasing inter-code interference (ICI) resulting fro IPI and hence BER floors appear. However, the BER perforance with frequency-doain equalization provides uch better BER perforance due to the frequency diversity effect and no BER floor is present at the cost of slightly reduced data rate and power penalty. So far, we have assued L=8. How the nuber of propagation paths ipacts the required E b /N for BER=1-4 with frequency-doain equalization is plotted in Fig. 5 for M=1, 2, and 4. It is clearly seen that as L increases, the channel frequency-selectivity becoes stronger and increased frequency diversity effect can be obtained, thereby iproving the BER perforance with frequency-doain equalization as in the case of MC-CDMA. The frequency diversity gain is defined here as the reduced value in db of the required E b /N copared to the L=1 case. The frequency diversity gain of as large as about 2519dB is obtained for C=1256when L=32 and M=1, respectively. Although the frequency diversity gain becoes saller as M increases, a gain of 4.7(3.5) db can still be achieved for C=1(256) when M=4. Fig. 4 Perforance coparison between frequency-doain equalization and rae cobining for ulticode case. L=8. Required average received E b/n [db] for BER= C =256 C =1 M =2 M =4 M =2 M = Nuber L of paths Fig. 5 Ipact of nuber L of paths Perforance coparison of DS-CDMA and MC-CDMA It is interesting to copare the DS-CDMA perforance with MC-CDMA. Figure 6 illustrates the BER perforances with DS-CDMA and MC-CDMA both using frequency-doain equalization for the sae transission condition, i.e., the sae data rate and the sae spreading factor (spreading bandwidth), for an L=8-path frequency-selective channel and no antenna diversity (M=1). Also plotted is the result of OFDM using 256 subcarriers and the sae data rate. It is clearly seen that both DS-CDMA and MC-CDMA with frequency-doain

5 equalization can achieve alost the identical BER perforance because the sae frequency diversity effect is obtained. Figure 7 shows how antenna diversity iproves the BER perforance for C=1 and 256. As the nuber M of antennas increases, the BER perforances of both DS-CDMA and MC-CDMA with frequency-doain equalization consistently iproves. Again there is no perforance difference between DS-CDMA and MC-CDMA. When M=4, the BER=1-4 can be achieved at the average E b /N of as sall as 5dB even for C= E+ 1.E-1 1.E-2 1.E-3 1.E-4 1.E-5 DS-CDMA with MC-CDMA with C =1 C =16 C =32 C =64 C =128 C =256 OFDM Average received E b/n [db] Fig. 6 Perforance coparison of DS-CDMA and MC-CDMA both using frequency-doain equalization for no antenna diversity (M=1). L=8. 1.E+ 1.E-1 1.E-2 1.E-3 1.E-4 1.E-5 M =4 M =2 DS-CDMA with MC-CDMA with C =256 C = Conclusion In this paper, joint use of frequency-doain equalization and antenna diversity cobining was considered for iproving the DS-CDMA signal transission perforance in a frequency selective fading channel and the achievable BER perforance was evaluated by coputer siulation. In the case of rae cobining, as the nuber C of codes increases, the BER perforance with rae cobining significantly degrades and BER floors appear due to increasing IPI. However, the BER perforance with frequency-doain equalization provides uch better BER perforance due to the frequency diversity effect and produces no BER floors at the cost of slightly reduced data rate and power penalty. It was shown that both DS-CDMA and MC-CDMA with frequency-doain equalization can achieve alost identical BER perforance for any nuber of diversity antennas. In this paper, ideal channel estiation was assued. Pilot assisted channel estiation can be applied to estiate the channel gains. Pilot sequence design and the evaluation of the BER perforance using a practical channel estiation ethod is left for an interesting future study. References [1] F. Adachi, K. Ohno, A. Higashi, and Y. Ouura, Coherent ulticode DS-CDMA obile radio access, IEICE Trans. Coun., Vol. E79-13, pp , Sept [2] W. C., Jaes Jr., Ed., Microwave obile counications, Wiley, New Yor, [3] F. Adachi, M. Sawahashi, and H. Suda, Wideband DS-CDMA for next generation obile counications systes, IEEE Coun. Mag., Vol. 36, pp , Sept [4] S. Hara, and R. Prasad, Overview of ulticarrier CDMA, IEEE Coun. Mag., Vol. 35, pp , Dec [5] T. Sao and F. Adachi, Coparative study of various frequency equalization techniques for downlin of a wireless OFDM-CDMA syste,, IEICE Trans. Coun, Vol. E86-B, pp , Jan. 23. [6] D. Falconer, S. L. Ariyavistaul, A. Benyain-Seeyer, and B. Eidson, Frequency-doain equalization for single-carrier broadband wireless systes, IEEE Coun. Mag., Vol. 4, pp , April 22. [7] F. Adachi, T. Sao, and T. Itagai, Perforance of ulticode DS-CDMA using frequency doain equalisation in frequency selective fading channel Electronics Letters, Vol. 39, No.2, pp , Jan. 23. [8] A. Chouly, A. Brajal, and S. Jourdan, Orthgonal ulticarrier techniques applied to direct sequence spread spectru CDMA syste,, Proc. IEEE Globeco 93, pp , Nov [9] T. Sao and F. Adachi, On diversity reception of ultirate MC-CDMA signals, IEICE technical report, RCS22-24, pp.73-78, Nov. 22. Average received E b/n per antenna[db] Fig. 7 Perforance coparison of DS-CDMA and MC-CDMA both using frequency-doain equalization when antenna diversity is used. L=8.