Published in IET Communications Received on 22nd January 2008 Revised on 21st June 2008 doi: 10.1049/iet-com:20080046 ISSN 1751-8628 Precoding in downlink multi-carrier code division multiple access systems using expectation maximisation algorithm A. Haghbin P. Azmi Electrical Engineering Department, Tarbiat Modares University, Tehran, Iran E-mail: pazmi@modares.ac.ir Abstract: The presence of multiple access interference and hardware complexity of the mobile terminal are two major burdens for multi-carrier code division multiple access schemes. Both burdens can be overcome in downlink by precoding the transmitted signal using the knowledge of the channel state information. In multi- user precoding techniques, the transmitter is optimised to combat channel impairments through the use of new spreading sequences that are obtained by solving an optimisation problem based on some criterion. Among these optimisation problems, the problem based on maximum likelihood is hard and complex to solve. In the proposed precoding scheme, the well-suited expectation maximisation algorithm is used to solve this problem. The proposed precoding technique is simulated and its performance is analysed and compared with some other precoding and detecting techniques. The results show that the proposed scheme considerably outperforms the previous precoding schemes. 1 Introduction The advantages of both code division multiple access (CDMA) and orthogonal frequency division multiplexing (OFDM) techniques are combined in multi-carrier CDMA (MC-CDMA) systems [1, 2]. However, MC- CDMA systems suffer from multiple access interference (MAI) that occur in the presence of fading. Multi- user detection (MUD) techniques [2, 3] are effective in mitigating MAI, but because of their high complexity and excessive power consumption at the mobile stations (MS), they are unattractive for implementation on the downlink. Instead of MUD, precoding techniques can be employed at the downlink transmitter to mitigate MAI and channel distortions. Precoding requires channel state information (CSI) of all users at the transmitter or base station (BS). This information is accessible to the transmitter in, e.g. time division duplex (TDD), owing to the reciprocal behaviour of uplink and downlink channels [4]. In frequency division duplex (FDD), CSI can be transmitted from receiver to transmitter via a feedback channel. Recently, several linear and nonlinear precoding schemes for downlink MC-CDMA systems have been proposed. In [5], two types of linear transmitter precoders, namely pre- equal gain combiner (PRE-EGC) and pre-maximum ratio combiner (PRE-MRC), have been proposed for downlink MC-CDMA systems. These techniques have lower performances relative to corresponding decorrelating-EGC and decorrelating-MRC detectors but with lower complexity in the receiver. In [6], a nonlinear precoding technique, based on the conclusions of Costa’s dirty-paper coding paper [7] for downlink MC-CDMA system has been proposed. This technique, in combination with single-user EGC or single-user MRC detectors in the receiver, has performance better than or near that of the minimum mean square error (MMSE) detector but with lower complexity of the system especially in MS. This technique, with the use of very simple, pure despreading detector in the receiver, has lower performance than that of the MMSE detector. By using proper precoding the transmitter can combat channel impairments such as MAI, inter-carrier IET Commun., 2008, Vol. 2, No. 10, pp. 1279–1288 1279 doi: 10.1049/iet-com:20080046 & The Institution of Engineering and Technology 2008 www.ietdl.org