Adaptive envelope-constrained filter design

A new type of adaptive scheme was proposed recently for designing a deterministic envelope-constrained (EC) filter such that the generated sequence of filters converges to the optimum filter. Previous results at this level of generality linked convergence only to within a neighborhood of the optimum filter. Based on the adaptive scheme, two new theorems are established in a stochastic environment for which the adaptive EC filter converges in mean square sense and with probability one to the noiseless optimum filter for a fixed step-size and a decreasing sequence of step-sizes, respectively. Numerical examples involving pulse compression Barker-coded signal are studied for solving the EC filtering problem.