Mean square convergence of adaptive envelope-constrained filtering

A new type of adaptive filtering scheme for solving an envelope-constrained filter design problem in a stochastic environment has been presented. The steady-state stochastic analysis of the adaptive scheme is established in the sense of the mean square. It is shown that if a given initial point is in a neighborhood of the origin, the adaptive scheme with a fixed step-size produces a filter that converges in the mean square sense to within an upper boundary of the noise-free optimum filter. Numerical examples involving pulse compression and channel equalization are presented to illustrate the convergence characteristics of the adaptive scheme operating in a stochastic environment.