Initialization and prefiltering techniques for adaptive equalizers

Abstract

The thesis investigates initialization problem and prefiltering techniques for adaptive equalizers. First, an equalizer initialization problem is considered for adaptive equalizers that can operate in a decision-directed mode during the training period. The clustering problem which groups similar channel vectors into a subset and optimizes the corresponding equalizer weight vector is formulated and sub-optimal solution to this optimization is developed based on generalized Lloyd algorithm (GLA) in vector quantization. The performance of proposed equalizer initialization algorithm (EIA) is examined through an application to the initialization of decision feedback equalizer (DFE) in 1000BASE-T systems. The experimental results shows that set of weight vectors with size two can cover channels with cable length up to 100 m and arbitrary initial timing errors. Second part of the thesis is devoted to investigate the worst-case performance bound of adaptive equalizers in the presence of modeling errors. For this end, a procedure for finding the worst-case MSE bound is developed under the assumption that norm of modeling error in auto-correlation matrix and that of cross-correlation vector in Wiener-Hopf equation are bounded. Application to linear equalization indicates that the worst-case performance loss in MSE increases as the MSE of equalizer without modeling errors decreases. Finally, we consider optimization of prefilter in baud-rate timing recovery to enhance equalizer performance. It is shown that prefiltering the received signal can improve the performance of a digital equalizer. The procedure for the optimal design of such a prefilter is developed under the assumption that the channel impulse response and desirable timing phase, at which point the equalizer performs best, are known. Application to Gigabit Ethernet system demonstrates that prefiltering can improve receiver performance.