A Unified Conjugate Gradient Based Approach for Optimal Complex Block FIR Filtering

Abstract

This paper proposes a unified block based approach to generate two complex filtering algorithms. The proposed unified approach calculates the complex conjugate gradients as the orthogonal update directions for the adaptive filter coefficients at each iteration. Along each update direction, the time-varying convergence factors tailored for the adaptive filter coefficients are updated based on the complex Taylor series expansion. The general formulation leads to two classes of adaptive algorithms: the Complex Block Conjugate Least Mean Square algorithm with Individual adaptation of parameters, CBCI-LMS, and the Complex Block Conjugate Least Mean Square algorithm, CBC-LMS. The formulation shows that the CBCI-LMS algorithm achieves faster adaptation than the CBC-LMS technique at the expense of an increase in the number of computations per iteration. The performances of these two proposed algorithms are evaluated and compared to existing techniques. In addition, the implementation aspects are examined under a wide range of adaptive conditions. These two generated algorithms are then applied to channel equalization and adaptive array beamforming. Based on the obtained results, the proposed algorithms demonstrate excellent convergence characteristics, in terms of the adaptation speed and accuracy.