Precoding optimization for the sparse MC-CDMA downlink communication

Abstract

We introduce a novel Multi-Carrier Code Division Multiple Access (MC-CDMA) system, where random sparse signatures are deployed in the frequency domain. Data symbols transmitted from base station (BS) to mobile stations (MSs) are drawn from discrete finite alphabets, such as M-QAM constellations. Transmitter-based precoding is introduced so as to allow simple despreading followed by single-user detection at MSs. A power-efficient non-linear precoding optimization problem is formulated by imposing minimum Symbol Error Probability (SEP) targets at MSs. We first elaborate on how to translate the SEP targets into exact constraint regions on noiseless received components at MSs. With relaxation on the exact regions, a tractable convex problem is obtained. A dual- decomposition-based algorithm is then developed to accommo- date parallel processors to perform precoding calculation. The signature sparsity turns out to be vital to reduce interprocessor communication overhead and computational complexity for pre- coding. The scheme proposed offers considerable transmit power reduction compared with the conventional zero-forcing precoder. I. INTRODUCTION Multi-Carrier Code Division Multiple Access (MC-CDMA) is a multi-access scheme based on the Orthogonal Frequency Division Multiplexing (OFDM) method. In this paper, we introduce a novel MC-CDMA that uses sparse signature sequences. Sparse signature sequences have been used in uplink CDMA analyses (1)-(3) but have not so far been considered for downlink systems. In the uplink papers, sparsity is exploited to provide a distributed, message-passing approach to the uplink multi-user detection problem. In particular, the belief-propagation algorithm has been proposed for such a system, an algorithm that has a natural implementation using parallel processors, and one that is fast and accurate, provided that the graphs are asymptotic cycle-free (2), (3). In this paper, we formulate a different problem, appropriate for the downlink, but one that also has a natural implemen- tation using parallel processors. The solution to the problem provides an algorithm for precoding at the base station (BS). As with the earlier uplink results, the algorithm is implemented at the BS, and the mobile stations (MSs) use conventional single-user matched filters and standard symbol detection. We compare the performance of our algorithm with standard lin- ear, zero-forcing (ZF) precoding, and show that considerable savings in transmit power are achievable using our approach. MC-CDMA naturally integrates the advantages of CDMA with the robustness to frequency selectivity offered by OFDM. Since its invention (4), MC-CDMA has attracted broad inter- est, see, e.g., (5), (6), and it serves as one of the promising candidates to provide reliable high data-rate communication. One main advantage of MC-CDMA as compared to Or- thogonal Frequency Division Multiplexing Access (OFDMA) is a reduced requirement in terms of the coordination required amongst the users. Rather than require all intracell users to be perfectly orthogonal, random signature sequences can be used which do not have to be precisely orthogonal to each other. On the other hand, there is a resulting loss in spectral efficiency, and an increased complexity in the signal processing required. On the uplink, the complexity is in the multi-user detection. On the downlink, the complexity is in the nonlinear precoding that we propose in this paper. Analogous to the known results for the uplink, we show that, with sparse signature sequences, the downlink problem that we propose is tractable, being a straightforward convex optimization problem. The use of sparse signature sequences has not received much attention, but we show in this paper that sparsity can be exploited to reduce the complexity of the precoding, as compared to MC-CDMA with full-length signature sequences. We also believe it has attractive features in terms of channel measurement, since each user only occupies a small number of subcarriers, and the chance of two (newly arriving) users having overlapping subcarriers is minimal, which aids the channel access and channel measurement process 1 . Another attractive feature of CDMA is the robustness to out- of-cell interference. To achieve the same level of robustness