A Class of Frequency-Domain Adaptive Approaches to Blind Multi- Channel Identification

In this technical memorandum we extend previous studies on blind channel identification from the time domain into the frequency domain. A class of frequency-domain adaptive approaches, including the multi-channel frequency-domain LMS(MCFLMS) and constrained/unconstrained normalized multi-channel frequency- domain LMS (NMCFLMS) algorithms, are proposed. By utilizing the FFT and overlap-save techniques, the convolution and correlation operations that are computationally intensive when performed by the time-domain multi-channel LMS (MCLMS)or multi-channel Newton (MCN) methods are efficiently implemented in the frequency domain and the MCFLMS is rigorously derived. In order to achieve independent and uniform convergence for each filter coefficient and therefore accelerate the overall convergence, the coefficient updates are properly normalized at each iteration and the NMCFLMS algorithms are developed. Simulations show that the frequency-domain adaptive approaches perform as well as or better than their time-domain counterparts and the cross-relation (CR) batch method in most practical cases. It is remarkable that, for a three-channel acoustic system with long impulse responses(256 taps in each channel) excited by a male speech signal, only the proposed NMCFLMS algorithm succeeds in determining a reasonably accurate channel estimate which is good enough for applications such as time delay estimation.