A frequency domain Conjugate Gradient algorithm and its 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 autocorrelation matrix is used for the estimation of the gradient vector and the correlation quantities are updated on a block by block basis. Due to this formulation, the algorithm can be implemented in the frequency domain (FD) using the fast Fourier transform (FFT). Efficient recursive relations for the frequency domain quantities updated on a block by block basis have been derived and an appropriate decoupling of the direction vector has been applied. The applicability of the new algorithm to the problem of adaptive equalization is studied. The proposed algorithm exhibits superior convergence properties as compared to existing CG techniques, offering significant savings in computation complexity.