MMSE equalizers and precoders in turbo equalization.

Thesis (M.Sc.Eng.)-University of Natal, Durban, 2003.Transmission of digital information through a wireless channel with resolvable multipaths or a bandwidth limited channel results in intersymbol interference (1SI) among a number of adjacent symbols. The design of an equalizer is thus important to combat the ISI problem for these types of channels and hence provides reliable communication. Channel coding is used to provide reliable data transmission by adding controlled redundancy to the data. Turbo equalization (TE) is the joint design of channel coding and equalization to approach the achievable uniform input information rate of an ISI channel. The main focus of this dissertation is to investigate the different TE techniques used for a static frequency selective additive white Gaussian noise (AWGN) channel. The extrinsic information transfer (EXIT) chart is used to analyse the iterative equalization/decoding process and to determine the minimum signal to noise ratio (SNR) in order to achieve convergence. The use of the Minimum Mean Square Error (MMSE) Linear Equalizer (LE) using a priori information has been shown to achieve the same performance compared with the optimal trellis based Maximum A Posterior (MAP) equalizer for long block lengths. Motivated by improving the performance of the MMSE LE, two equalization schemes are initially proposed: the MMSE Linear Equalizer with Extrinsic information Feedback (LE-EF (1) and (U)). A general structure for the MMSE LE, MMSE Decision Feedback Equalizer (DFE) and two MMSE LE-EF receivers, using a priori information is also presented. The EXIT chart is used to analyse the two proposed equalizers and their characteristics are compared to the existing MAP equalizer, MMSE LE and MMSE DFE. It is shown that the proposed MMSE LE-EF (1) does have an improved performance compared with the existing MMSE LE and approaches the MMSE Linear Equalizer with Perfect Extrinsic information Feedback (LE-PEF) only after a large number of iterations. For this reason the MMSE LE-EF is shown to suffer from the error propagation problem during the early iterations. A novel way to reduce the error propagation problem is proposed to further improve the performance of the MMSE LE-EF (I). The MAP equalizer was shown to offer a much improved performance over the MMSE equalizers, especially during the initial iterations. Motivated by using the good quality of the MAP equalizer during the early iterations and the hybrid MAP/MMSE LE-EF (l) is proposed in order to suppress the error propagation problem inherent in the MMSE LE-EF (I). The EXIT chart analysis reveals that the hybrid MAP/MMSE LE-EF (l) requires fewer iterations in order to achieve convergence relative to the MMSE LE-EF (l). Simulation results demonstrate that the hybrid MAP/MMSE LE-EF (I) has a superior performance compared to the MMSE LE-EF (I) as well as approaches the performance of both the MAP equalizer and MMSE LE-PEF at high SNRs, at the cost of increased complexity relative to the MMSE LEEF (I) receiver. The final part of this dissertation considers the use of precoders in a TE system. It was shown in the literature that a precoder drastically improves the system performance. Motivated by this, the EXIT chart is used to analyse the characteristics of four different precoders for long block lengths. It was shown that using a precoder results in a loss in mutual information during the initial equalization stage. However" we show by analysis and simulations that this phenomenon is not observed in the equalization of all precoded channels. The slope of the transfer function, relating to the MAP equalization of a precoded ISI channel (MEP), during the high input mutual information values is shown to play an important role in determining the convergence of precoded TE systems. Simulation results are presented to show how the precoders' weight affects the convergence of TE systems. The design of the hybrid MAP/MEP equalizer is also proposed. We also show that the EXIT chart can be used to compute the trellis code capacity of a precoded ISI channel