An efficient conjugate gradient method in the frequency domain: Application to channel equalization

In this paper, a new block adaptive filtering algorithm, based on the conjugate gradient (CG) method of optimization, is proposed. A Toeplitz approximation of the auto-correlation matrix is used for the estimation of the gradient vector and the involved quantities are updated on a block by block basis. Due to this formulation, the algorithm can be efficiently implemented in the frequency domain (FD). To this end, recursive relations for the FD quantities updated on a block by block basis have been derived. Different ways of accelerating convergence based either on the use of a preconditioner or on an appropriate decoupling of the direction vector are described. The applicability of the new algorithm to adaptive linear equalization (LE) and decision feedback equalization (DFE) has been studied. The proposed LE and DFE algorithms exhibit superior convergence properties as compared to existing adaptive algorithms, offering significant savings in computational complexity.