New Steady-State Analysis Results of Variable Step-Size LMS Algorithm With Different Noise Distributions

The step-size in well-known variable step-size least mean square (VSSLMS) is updated as μ_n+1 = αμ_n + γe_n² with , γ > 0, and μ_n+1 is set to μ_min or μ_max when it falls below or above these lower and upper bounds, respectively. It provides fast convergence at early stages of adaptation while ensuring small steady-state misalignment. This paper considers the steady-state performance of the VSSLMS in non-Gaussian noise environments. The contribution of the paper to the VSSLMS is threefold; (1) when γ ≪ 1 - α, the VSSLMS has low steady-state misalignment. (2) when α ≪ 1, the VSSLMS achieves different steady-state misalignments for different noise distributions. (3) In theory, there are different optimal values α for different noise distributions, i.e., 0.17 (Gaussian distribution), 0.21 (Student distribution), 0.38 (Laplace distribution), 0 (Binary and Uniform distributions). Analytical results are compared with simulations and are shown to agree well.