Least-squares optimal variable step-size LMS for nonblind system identification with noise

This paper proposes a least-square optimal variable-step-size (LSVSS) least-mean-square (LMS) adaptive algorithm for nonblind identification of single-input single-output (SISO) finite impulse response systems. It is shown that the well-known normalized LMS (NLMS) and the LSVSS-LMS algorithms are mathematically equivalent for the noise-free case. The derivation of LSVSS is then extended for noisy measurements. The convergence analysis of the LSVSS-LMS is also presented. The performance of the proposed method is compared with conventional robust variable-stepsize LMS algorithms. Experimental results demonstrate improved performance of the proposed algorithm for nonblind system identification in both stationary and nonstationary environments.