Title Author(s) Citation Issue Date URL Rights A family of spread-sequences for CDMA system in a multipath fading channel Nallanathan, A; Chan, SC; Ng, TS The 49th IEEE V T S Vehicular Technology Conference Proceedings, Houston, Texas, USA, 16-20 May 1999, v. 3, p. 1814-1818 1999 http://hdl.handle.net/10722/46118 ©1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. zyxwvu zyxw A FAMILY OF SPREAD-SEQUENCES FOR CDMA SYSTEM IN A MULTIPATH FADING CHANNEL A.Nallanathan, S.C.Chan, T.S.Ng Department of Electrical and Electronic Engineering University of Hong Kong, Pokfulam Road, Hong Kong. zyxwvutsrqp zyxwvuts zyxwvut zy zyxwvuts zyxwvutsr e-mail: analla@eee.hku.hk, scchan@eee.hku.hk, tsng@eee.hku.hk Abstract - A new class of orthogonal code-division multiple access (CDMA) system is developed. The key characteristicof the system is that the data symbols are spreaded by a spread-sequence that is longer than the period of the symbol and hence overlapped with the neighboring symbols. Using this approach, temporal diversity is incorporated with other diversities. Due to the temporal diversity, the proposed CDMA system performs well in fading environment. In this paper, a method for designing such a spread-sequence using filter bank theory is presented. The length of the spreadsequence could be varied according to the requirement. Simulation results show that the proposed spreadsequence based system yields lower BER than the conventional gold codes based DSICDMA system. the sequence will assume integer values instead of binary values. The paper is organized as follows: Section 11 is devoted to the system model of the new class of CDMA system. The channel model is described in Section M. In Section IVYmethods for constructing spread-sequences will be discussed and a new class of spread-sequence will be introduced. Simulation results are given in section V. Finally, the conclusion is given in section VI. 11. SYSTEM MODEL The system model of the proposed orthogonal CDMA system is shown in Fig 1. The input data symbols, b,[n] , are assumed to be binary antipodal where m stands for the m th user. Each data symbols, bJn3 , is modulated onto a unique spread-sequence h,[n] of length pM ( p > l ) where p is an integer and Mis the chip length of conventional system. The modulated signal is transmitted within the total available bandwidth. We can view the modulation process as consisting of two stages. As depicted in Fig. 1, these stages correspond to upsampling by a factor of M followed by linear time-invariant filtering with the spread-sequence. The key motivation for using longer sequence is that they can lead to a greater temporal diversity. I. INTRODUCTION There has been increasing interest recently in using direct sequence spread spectrum O S - S S ) code division multiple access (CDMA) for commercial applications. DS/CDMA is proposed for cellular, microcellular, indoor and satellite communications [6].CDMA is also a candidate for high data rate applications, such as wireless local area network (LAN) and videophones. Very often the SS modulation is used to mitigate the different problems encountered in different communications media. Therefore it is desirable to have a flexible and efficient design method for this signal suit various communication channel conditions. In this paper, a class of orthogonal CDMA system using longer and overlapping spread-sequences is proposed. Since the sequences are lapped, a greater temporal diversity is achieved and the bandwidth of the system is maintained as the conventional DSICDMA system. In order to design spread-sequences with binary values, the length of the spread-sequence proposed in [8] increases exponentially with the number of users. This causes large system delay in transmission. To avoid the large delay, we propose a new structure for constructing spread-sequences with flexible length. This greatly widens the selection of spread-sequences to suit different system delay requirement. On the other hand, 111. CaANNEL MODEL Several multipath models have been proposed in the literature, varying from the very comprehensive model to the simple tapped delay line model [6]. It has been shown that the performance of the DS/CDMA system is robust with respect to channel models. In this paper, the multipath fading channel is modeled by a continuum and a fixed number of paths. Utilizing power control among the CDMA users, the channel is assumed to be statistically identical for all users. The lowpass equivalent impulse response of the pass band fading channel is &en by [6], 0-7803-5565-2/99/$10.00 0 1999 IEEE 1814 zyxwvutsrqpo zyxwvutsr zyxwvutsrqp zyxwvu zyxwvuts zyxwvutsrqponmlkjihg zyxwvutsrqp zyxwvutsr The orthogonality condition can be expressed as, where, Lp is the number of paths, f i I , 2, and are respectively the path gain, delay and phase of the I th path. The channel auto-covariance function is easily found to be, C 4 k - nM]hT[k - ZM] = 4t~ - l)I, LP PO) = I=' - o;:S<t TI 1 (4.2) k where I, denotes the identity matrix of appropriate size and b[n] denotes the unit impulse. The modulated signal can then be written as follows, (3.2) The unit energy constraint on the fading process covariance function implies that (4.3) (3.3) The design of such sequence sets is related to the theory of perfect reconstruction filter bank In what follows, it will be shown the orthogonality condition in (4.2) can also be interpreted as the PR condition of a multirak filterbank made up of hi[n]. Let's consider the z-transform of equation (4.1) as follows, where the variance, o;,for uniform and exponential multipath power profiles are given respectively by, (3.4) H(z) = ch[n]z-' The parameter L' decides the rate of power decay on the successive paths. Using (3.2) and (3.3) for the exponential profile and arbitrarily taking L' = Lp , one hi[n]z-' . where Hi (z) = gets, n Using type-1 polyphase decomposition [l], H(z) can be written in the following form, (3.5) IV. SPREAD-SEQUENCES In multiple access systems, the coded symbol stream of the m th user, b,(n) , is modulated onto a unique spread-sequence h, (n) to produce y , (n) which is transmitted within the available system bandwidth. In the conventional multiuser system the maximum number of users is equal to the chip length M . However we can use the lapped orthogonal spreadsequence with the length of integer multiple of A4 . A natural requirement of such systems is that, in the absence of fading and with perfect synchronization among users, there will be no intersymbol interference either within a user's stream or among users. This is equivalent to requiring that the sequence sets satisfy certain orthogonality conditions. A reasonable solution is to ensure that the sequence together with all their translates by integer multiples of Mconstitute an orthonormal basis. If the spread-sequences are written as a vector sequence, 1815 where Q(z) is the polyphase matrix and e(z) is the ztransform of the delay chain of order M ,i.e, For orthonormal sequence sets, the associated polyphase matrix satisfies the following property, where * and T denote complex conjugation and matrix transposition respectively. Equation (4.7) is equivalent to the PR condition of the filter bank consisting of h,[n] and matrices which satisfy (4.7) are r e f m d to as " paraunitary". The Auto- and cross-correlation characteristics of the spread-sequencesare two very important properties in a zyxwvuts zyxwvutsrqp zyxwv zy zyxw CDMA system. Indeed, the auto correlation characteristics generally affect, for example, the ability of the receiver to synchronize the transmission, while the cross-correlationcharacteristics generally affect the degree and nature of co-channel interference. Ideally, one would like the auto correlation of each sequence h,[n] to satisfy, maximally spread. The sequence set was obtained from a cascade structure using Hadamard matrix which has a very low implementation complexity. More precisely, cascading the polyphase matrix is obtained by r-ated of lower order polyphase matrix as follows, Q(')(z) =~ (4.8) and the cross correlation between sequences hJn] and h,[n] to satisfy, , i = 1,2...... ~ ( Z M " - )Q('-')(z) " where A(z)is the diagonal delay matrix whose diagonal is constructedfkom the elements of e(z) ,i.e, distinct zyxw h(z)= diug(e(z)) . However (4.8) and (4.9) are conflicting objectives for traditional sequence sets. This is also true for spreadsequence sets. In fact, it was shown in [8] that good auto-correlation characteristics can only be obtained at the expense of cross-correlation characteristics, and vice versa. At one extreme, the trivial signature set corresponding to TDMA systems has perfect autocorrelation characteristics,but the worst possible crosscorrelation characteristics. At the other extreme, the sequence sets correspondingto ideal FDMA system has perfect cross-correlation characteristics but poor autocorrelation characteristics. In practical CDMA system, a compromise between these extremes is generally sought. The auto-correlation and the cross-correlation characteristics constitute only one of the important issue in the design of good spread-sequence sets. It is also important that the sequence sets be effective in mitigating the effects of fading by spreading each symbol bits of a user over a range of time samples. The dispersion factor Dh which measures a sequence set's spreading capability is defined as [8], (4.12) (4.13) From (4.5) and (4.12), the spread-sequence sets are given by, - H(') ( z ) - ah(zM')H"-''(z). (4.14) Z is the ( M x M ) Hadamard matrix and Q(O'(z) is chosen to be the Hadamard matrix.i.e., Q"'(z) = E M . zyxwvu zy b. Proposed Spread-Sequence Set From (4.79, we notice that the design of orthonormal sequence set is equivalent to the determination of pmunitary matrix, Q ( z ) , that satisfies the PR condition. fn [8], the sequence set is constructed from (4.12), which yield sequence set that assumes binary values of +1 or -1. However the length of the constructed sequence set increases exponentially with M . ~nfact, the length of the signature set is M " , k=2,3 ...... To avoid the long system delay, spread sequence set can be derived fiom the general solution of (4.14). The length of such signature set is more flexible. i.e, M,2M, ...... .Onthe other hand, the values of the signature set will no longer be +I or -1. The complete factorization of paraunitary matrices has been studied previously in [1],[10]. Our proposed construction follows a related factorization of the paraunitary matrix derived in [101. Spread-sequence set with length L = p M is constructed from the following cascade structure, zyxwvutsrqp (4.10) where D,,, represents the dispersion in the sequence hJn1 ,i.e, / Q(z)= Kp-l(z)Kp-2(z) .......Kl(z)EM,(4.15) \-' (4.1 1) where Ki(Z) a. A Class of Spread-Sequence Set In [8], Wornell proposed a family of orthogonal sequence set that is optimal in the sense of being 1816 = Piqws2(Z)w, zy zyxwvu zyxwvut zyxwvutsrq zyxwvuts the spread-sequences can be achieved but the resulting spread-sequences become integer valued. Simulation results show that the BER performance of the proposed Spread-Sequence based CDMA system is better than the conventional DS/CDMA system. Such improvement also increases with the overlapping length of the spread signature set. (4.16) Ui, Vi can be any (M12)x (M/2) orthogonal matrices. For simlplicity of implementation, they are taken to be the Hadamard matrix Z,, . Pi is a random permutation matrix which is used to randomize the spread- sequences. ACKNOWLEDGEMENT This work is supported by the Hong Kong Research Grants Council and the CRCG of the University of Hong Kong. The first author would like to thank Dr.E.H.Li, Department of Electrical and Electronic Engineering, University of Hong Hong, for providing financial support to attend the conference. V. SIMULATION RESULTS In this section, the performance of the conventional DS/CDMA and the proposed Spread-Sequence based CDMA system is compared. Gold codes with length 32 are used for the simulation of the conventional DSICDMA system. The proposed sequence set with different overlapping factors is used for the spread sequence based CDMA system and they are obtained using equation (4.15). Fig2a and Fig.2b show the spectrum of two proposed spread-sequences for M = 32 with p = 4 . It can be seen that the proposed spread sequence set is neither frequency or time localized. The channel is assumed to be Rayleigh fading with exponential ‘power delay profile’ (2 rays). To evaluate the performance of the proposed system, BER performance against EbI No is simulated and compared with the conventional DSKDMA system. Throughout the simulation, the RAKE receiver (2-finger) is used. Fig.3 shows the BER performance of the two systems against EbI Nowhen the number of users is 20 for uplink (asynchronous system). Fig.4 shows the BER performance of the two systems against EbI Nowhen the number of users is 20 for down-link (synchronous system). The improvement of the proposed spreadsequence modulation can partially be explained by the incorporation of time diversity in addition to path diversity. In Practice, RAKE receiver implementation may be expensive and match filters can be employed at the expense of BER performance. zy zyxwvu zyxwvutsrqp zyxwvutsr zyxwvuts REFERENCES (1) Vaidyanathan, P.P., “Multirate systems and filter banks”. PTR Printice Hall,1993. (2) Nallanathan, A., Chan,S.C. and Ng,T.S., “Generalized Lapped Transform (GLT) based highspeed transmission for wireless communications”, Proc. IEEE VTC’98, pp 1409-1413, Ottawa, May 1998. (3) Nallanatban,A., Chan,S.C. and Ng,T.S., “Generalized lapped Transform (GLT) based codes for multi-user communications” in Proc. Fifth symposium on Communications and Vehicular Technology, Netherland, Oct 1997. (4) ChaaS.C., Nallauathan,A., and Ng,T.S., “ A Class of M-channel linear-phase biorthogonal filter banks and their applications to subband coding” to appear in IEEE Trans. on Signal Processing, February 1999. ( 5 ) Chan.S.C., “The Generalized lapped Transform (GLT) for Subband coding Applications, “Proc.IEEE ICASSP’95, pp 1508-1511, May 1995. (6) Prasad,R.,” CDMA for Wireless Personal communications. Artech House”. 1996. (7) Malvar,H.S., “ Signal Processing with lapped transform^'^, Artech House, 1992. (8) Wornell,G.W., “ Spread-Signature CDMA: Efficient Multiuser Communication in the Presence of Fading”, IEEE Trans on Information Theory, Vol 41, NOS,September 1995. (9) Wornell, G.W., “ Spread-Response precoding for Communicationover hdhg Channels “,IEEE Trans on Information Theory, Vol. 42, N0.2,March 1996. (10) Soman,A.K., Vaidyawthan,P.P., and Nguyen,T.Q., “ Linear Phase Paraunitary Filter Banks: Theory, Factorizations and Designs” IEEE Trans on Signal Processing, Vol41, N012, December 1993. VI. CONCLUSION A new class of spread-sequence based orthogonal code-division multiple access (CDMA) system is developed. A method for designing such a spreadsequence set is proposed using filter bank theory. It is derived f?om the factorization of the paraunitary matrices in [lo]. As compared with the s&pence set proposed in [8], more fkeedom in selecting the length of 1817 Pf*] zyxwvuts zyxwvut Receiver ~d*l Channel w Receiver Fig. 1 zyxwvutsrqponm zyxwvutsrqp 40 . 40 . B 20 . B I -60 0 0.1 03 0.2 -600- 05 0.4 20- 0:1 0.2 Normalizedfrequency 0.5 0.4 0.3 Normalizedfrequency Fig. 2a Fig. 2b SSCDMA ( p a ) users - 20 102 zyxwvutsrqponmlk 1 -5 0 10 15 20 25 30 -5 EbMo (in dB) 5 . 1 10 . I 15 * I 20 . , 25 Eb/No (in dB) Fig .3 BER versus EbMo (Uplink) Fig. 4 BER versus Eb/No (down link) 1818 . 30