Block adaptive filtering algorithms based on conjugate gradient method

Abstract

In this dissertation work, we are concerned with both improving the convergence performance and achieving the computational efficiency of block adaptive filtering algorithm for finite impulse response (FIR) adaptive digital filters (ADF``s). The rapid convergence rate is achieved by employing the nested iteration technique and the preconditioning technique. The computational efficiency is achieved by using the fast convolution technique and the fast deconvolution technique based on an approximation of the autocorrelation matrix. Using these techniques, several block adaptive filtering algorithms are proposed. First, to introduce a new updating procedure called the nested iteration technique that can update the filter tap weights several times for each data block, we define an estimate of the block mean-square error (BMSE) as an objective function. Based on the BMSE estimate, the block least mean-square (BLMS) and optimum block adaptive (OBA) algorithms are reformulated and the frequency-domain BLMS (FBLMS) and frequency-domain OBA (FOBA) algorithms are reviewed as frequency-domain implementations of the BLMS and OBA algorithms, respectively. In derivation of these algorithms, we assume that the direction vector is based on the steepest descent method and the descent process is terminated after only one iteration for each block. Second, we propose the nested OBA (NOBA) algorithm as a fast version of the OBA algorithm by employing the nested iteration technique, in which the direction vector is based on the steepest descent method as a descent method. In formulation of the algorithm, we assume that the BMSE estimate is time-invariant since the processed data blocks are disjointed rather than overlapping, in contrast to the optimum block adaptive shifting (OBAS) algorithm, where the data block can be shifted by some samples. Thus, for each iteration, a descent direction is given by the negative gradient of the BMSE estimate, and a time-varying step size is determi...