Performance comparison of the blind multi channel frequency domain normalized LMS and variable step-size LMS with noise

The paper provides a comparative performance analysis of the normalized multichannel frequency-domain least-mean-squares (MCFLMS) and variable step size MCFLMS (VSS-MCFLMS) algorithms used in blind channel identification. Both the algorithms eliminate the need of a priori estimation of the step size parameter for rapid convergence to the desired solution. We perform the convergence analysis of the normalized MCFLMS (NMCFLMS) and show that even for a moderate SNR, the algorithm fails to converge to the eigenvector corresponding to the minimum eigenvalue of the data correlation matrix and hence misconverge to a fictitious solution. On the other hand, we show that the VSS-MCFLMS algorithm converges, both in noise-free and noisy conditions, to the eigenvector corresponding to the minimum eigenvalue and therefore more noise robust as compared to the NMCFLMS. The enhanced noise robustness of the VSS-MCFLMS algorithm over the NMCFLMS algorithm was verified using computer simulation results for a wide range of SNRs.