Analysis and design of a signed regressor LMS algorithm for stationary and nonstationary adaptive filtering with correlated Gaussian data

A least mean square (LMS) algorithm with clipped data is studied for use when updating the weights of an adaptive filter with correlated Gaussian input. Both stationary and nonstationary environments are considered. Three main contributions are presented. The first, corresponding to the stationary case, is a proof of the convergence of the algorithm in the case of a M-dependent sequence of correlated observation vectors. It is proven that the steady state mean square misalignment of the adaptive filter weights has an upper bound proportional to the algorithm step size μ. The second contribution, also belonging to the stationary case, is the derivation of the expressions of convergence time N_c and steady state mean square excess estimation error ε. It is shown that N _c is proportional to 1/(μλ), with λ being the minimum eigenvalue of the input covariance matrix. It is also shown that the product N_cε is independent of μ. For a given ε, the convergence time increases with the eigenvalue spread of the input covariance matrix and the filter length, as well as its input noise power. The range of μ that achieves tolerable values of N_c and ε is determined. The third contribution is concerned with the nonstationary case. It is shown that the mean square excess estimation error is the sum of the two terms with opposite dependencies on μ. An optimum value of μ is derived