Performance of Updated NLMS Algorithm in Rayleigh Channel

In this paper, we have developed a new normalized least mean square (NLMS) algorithm using past coefficient vectors and regularization parameter for nonstationary Rayleigh channel. The proposed algorithm modifies the minimization of the mean square deviation (MSD) of recently updated coefficient vector and past coefficient vectors using the regularization parameter. The existing conventional NLMS method suffers from low convergence speed in nonstationary channel. The MSD of the modified NLMS algorithm is evaluated for various values of regularization parameter from zero to one. The result shows that the convergence rate increases, as the regularization parameter decreases. Thus improved NLMS algorithm achieves significant improvement in the convergence rate, in the nonstationary environment. We have used random walk model to incorporate the nonstationary Rayleigh channel. The performance of the improved NLMS algorithm is compared for various values of SNR and the result shows that the value of MSD decreases as the value of SNR increases. Thus the modified NLMS algorithm shows lower misalignment as the value of SNR increases. It has also been shown that proposed NLMS algorithm is a generalized case of conventional NLMS algorithm.