Noise Robust Multichannel Frequency-Domain LMS Algorithms for Blind Channel Identification

A number of multichannel least mean square (LMS)-type algorithms have been proposed in the literature to identify single-input multi-output finite impulse response channels. All of these algorithms share the common characteristic of good initial convergence followed by a rapid misconvergence in the presence of noise. This misconvergence characteristic is due to the nonuniform spectral attenuation of the estimated channel coefficients as reported in some research results. In this letter, we formulate a novel cost function that inherently oppose such spectral attenuation resulting from the noisy update vector. We show analytically that the gradient of the proposed penalty term enforces uniform distribution of the estimated channel spectral energy over the entire frequency band and thus contribute to ameliorating the misconvergence of these multichannel algorithms in the presence of noise. The robustness of the proposed algorithm is verified using numerical examples for different channels in a wide range of signal-to-noise ratios.