LINEAR MULTIUSER RECEIVERS FOR ASYNCHRONOUS MC-CDMA SYSTEMS Tiziano Bianchi, Fabrizio Argenti, and Enrico Barsali Dipartimento di Elettronica e Telecomunicazioni, University of Florence Via S. Marta 3, 50139, Firenze, Italy phone/fax: +39 055 4796485, email: {bianchi, argenti, barsali}@lenst.det.unifi.it ABSTRACT In this paper, we propose a linear multiuser receiver for asyn- chronous MC-CDMA systems. The proposed receiver con- sists of two stages, namely a bank of MRC receivers and a MMSE multiuser detector, and it relies both on channel and delay estimation. The performance of the receiver is greatly improved with respect to the simple MRC approach. More- over, the additional complexity is moderate, so that the pro- posed approach is well suited for practical applications. 1. INTRODUCTION The next generation of wireless communications must pro- vide a larger capacity physical layer to satisfy the require- ments of bandwidth consuming services such as data and video transmission. For this purpose, the combination of Orthogonal Frequency Division Multiplexing (OFDM) and Code Division Multiple Access (CDMA) seems one of the best solutions [1]. OFDM and CDMA can be combined ac- cording to two different schemes, MC-CDMA and MC-DS- CDMA, in which either a frequency-domain spreading or a time-domain spreading is implemented, respectively. In the case of the transmission from one access point (AP) to several mobile terminals (MTs) over a frequency- selective channel, usually MC-CDMA shows better perfor- mance than both MC-DS-CDMA and DS-CDMA, since it is able to fully exploit the frequency diversity of the channel. However, when considering the reverse link, MC-CDMA re- quires more complicated receiver structures [2]. Multiuser detection (MUD) techniques can sensibly improve the per- formance of CDMA systems in the uplink. In particular, lin- ear MUD [3] is well suited for practical applications due to its tractable complexity. In this paper, we propose a reduced complexity linear multiuser receiver that is based on two stages. The first stage uses a bank of maximal-ratio combining (MRC) sin- gle user receivers synchronized with the user of interest that produces a vector of temporary decision variables. The ap- proach is similar to the MRC receiver proposed in [4], even if our method considers an all digital MC-CDMA system with a cyclic prefix. The second stage refines the MRC decision variables by means of a linear minimum mean squared error (MMSE) multiuser detector. The main difference from the classical linear MMSE receiver proposed in [5] is that our approach requires the inversion of an N u × N u matrix, where N u is the number of active users, whereas the receiver in [5] would require the inversion of a 2M × 2M matrix, where M is the number of subcarriers, even for a single active user. 2. ASYNCHRONOUS MC-CDMA The MC-CDMA modulated signal of a generic user indicated by the index ℓ can be expressed by the samples x ℓ (iN + m)= 1 √ N M−1 ∑ k=0 s ℓ,k b ℓ (i)e j2π km M , 0 ≤ m < M (1) where b ℓ (i) is the ith transmitted bit, s ℓ,k are the chips of the spreading sequence associated with the ℓth user and M in- dicates the number of subcarriers. The transmitted signal is periodically extended by means of a cyclic prefix of L sam- ples, i.e., x ℓ (iN + m)= x ℓ (iN + M + m) for −L ≤ m < 0, re- sulting in a symbol length of N = M + L samples. If we let n = iN + m, then the transmitted waveform is x ℓ (t )= +∞ ∑ n=−∞ p(t − nT − τ ℓ )x ℓ (n) (2) where T is the system sampling period, p(t ) indicates the response of the pulse shaping filter and τ ℓ is the delay of the ℓth user. The received waveform after matched filtering is given by y(t )= ∑ ℓ∈U +∞ ∑ k=−∞ φ ℓ (t − kT − τ ℓ )x ℓ (k)+ w(t ) (3) where U is the set of the active users, φ ℓ (t )= p ∗ (−t ) ∗ g ℓ (t ) ∗ p(t ), g ℓ (t ) models the effects of both the antennas and the multipath channel relative to the ℓth user and w(t ) models the thermal noise. If we express the users’ delay as τ ℓ = D ℓ T + δ ℓ and we sample y(t ) with period T , then a full digital transmission model can be obtained as y(n)  y(nT )= ∑ ℓ∈U +∞ ∑ k=−∞ h ℓ (n − k − D ℓ )x ℓ (k)+ w(n) (4) where h ℓ (n)  φ ℓ (nT − δ ℓ ) represents the equivalent discrete time channel impulse response of the MC-CDMA system rel- ative to the ℓth user and w(n)  w(nT ). In particular, we assume that the length of h ℓ (n) is less than L. 2.1 Block Representation Let x ℓ (i)=[x ℓ (iN), ..., x ℓ (iN + N − 1)] T be the vector of transmitted samples relative to the ith bit of the ℓth user. It can be expressed in a compact form as (see Fig. 1) x ℓ (i)= ΞW H M s ℓ b ℓ (i) (5) where the vector s ℓ =[s ℓ,0 ,..., s ℓ,M−1 ] T represents the spreading sequence associated to the ℓth user, W M is the