Blind Equalisation for Space-Time Coding over ISI Channels

Multi-input multi-output (MIMO) channels are known to increase the capacity of a transmission link. This can be exploited to increase either the multiplexing gain or the diversity gain, which leads to a higher data throughput or a better resilience of the link to fading, respectively. This thesis is concerned with the diversity gain, which, in a flat fading channel, can be maximised by Alamouti’s space-time block coding (STBC) scheme and a number of derivative techniques. For frequency selective fading, i.e. dispersive, MIMO channels, a few solutions have been reported in the literature including MIMO-OFDM, where the channel is decomposed into a number of narrowband problems, and a technique known as time-reversal STBC. For the latter, a number of blind adaptive algorithms have been derived, implemented and tested in order to avoid the requirement of explicit knowledge of the channel. The above diversity scheme for broadband MIMO are invariable block-based and often assume stationarity of the channel over the duration of one block. Therefore, non-block based approaches appear useful where tracking of fast changing channels is required.  In this thesis, a non-block-based constant modulus receiver is designed for the equalisation of STBC over channels with Inter Symbol Interference (ISI). Assuming the transmitted symbols have a single modulus, known at the receiver, a trivial extension of the Constant Modulus Algorithm (CMA) can be used at the receiver to combat the temporal dispersion. The equaliser adapts its coefficients by forcing the outputs to have the same modulus. The proposed algorithm adds a new term to the cost function of the standard MIMO-CMA to minimize the cross correlation between the outputs and prevent extraction of the same source at multiple outputs. Simulation results will show that the derived algorithm outperforms the block-based scheme over time-varying channels.  Due to the slow converging nature of the CMA, this report explores the use of fast converging implementations such as: Newton’s method, the Conjugate Gradient method, and the matched PDF scheme. A thorough evaluation is carried out taking into consideration the complexity of each implementation in terms of multiply-accumulate (MAC) operations required per iteration. A concurrent CM and Decision Directed (DD) equaliser is also developed in order to speed up the convergence and correct the phase rotation of the recovered signals. Fractionally spaced equalisation (FSE) is also investigated in this thesis. Computer simulations have been performed to evaluate the performance of the proposed set of algorithms.  A blind CM based scheme is also developed for the equalisation of a multi-user STBC system based on Space-Time Spreading (STS). The algorithm minimises the error at a matched-filtered version of the output taking advantage of the implicit orthogonality inherent in the CDMA spreading.