Noise robust frequency-domain adaptive blind multichannel identification with ℓ_p-Norm constraint

Blind multichannel identification is a challenging problem in many domains. The normalized multichannel frequency-domain least-mean-square (NMCFLMS) algorithm was developed to blindly identify a single-input multiple-output acoustic system, which can yield good performance in noise-free environments. However, the robustness of this algorithm to noise has been shown to be problematic. One way to improve the robustness is by applying a constraint on the spectral flatness of the channel impulse responses, which led to the development of the so-called robust normalized multichannel frequency-domain least-mean-square (RNMCFLMS) algorithm. This spectral flatness constraint, however, may not be always proper or reasonable in realistic acoustic environments. In this paper, we develop an ℓ_p-norm constraint based robust normalized multichannel frequency-domain least-mean-square (ℓ_p-RNMCFLMS) algorithm. The ℓ_p-norm constraint is introduced into the NMCFLMS algorithm to control the effect of different ℓ_p-norm penalties on the adaptive filter for the impulse responses with different degrees of sparseness. Numerical and realistic experiments justify the effectiveness of the proposed ℓ_p-RNMCFLMS algorithm.