Variable step-size multichannel frequency-domain LMS algorithm for blind identification of finite impulse response systems
Mohammad Ariful Haque, Md. Kamrul Hasan · IET Signal Processing · 2007
The choice of step size is a critical factor in blind identification of single-input multi-output systems using adaptive multichannel frequency-domain least-mean-squares (MCFLMS) algorithm. The proper step size is dependent on the signal power and it influences the speed of convergence and the final misalignment error. Applying normalised MCFLMS (NMCFLMS) algorithm, the dependency of the step-size parameter on signal power can be eliminated; however, it is shown that even for a moderate signal-to-noise ratio, the algorithm fails to converge to the eigenvector corresponding to the minimum eigenvalue of the data correlation matrix and hence misconverges to a fictitious solution. A self-adaptive variable step-size MCFLMS (VSS-MCFLMS) algorithm that optimises the performance of the algorithm in each iteration in order to achieve minimum misalignment with the true channel impulse response is proposed. The convergence analysis of the proposed algorithm is performed and it is shown that the VSS-MCFLMS algorithm converges, both in noise-free and noisy conditions, to the eigenvector corresponding to the minimum eigenvalue and is therefore more noise robust when compared with the NMCFLMS. The algorithm also shows the optimal speed of convergence in a noise-free case and the proposed variable step size guarantees the stability of the algorithm. Simulation results are presented to demonstrate that the proposed VSS-MCFLMS algorithm gives lower final misalignment when compared with the NMCFLMS algorithm without sacrificing the speed of convergence and computational efficiency.