Adaptive algorithms for envelope-constrained filtering with bounded noise

The problem of designing adaptive filters subject to output envelope constraints in the presence of bounded noise at the input channel is investigated. The bound on the noise is used to form the input mask that contains all possible input signals corrupted by noise. The optimal envelope-constrained filter is designed with respect to the entire input mask. A cubic smoothing function is applied to implement the constraint approximation, which paves the way for establishing adaptive algorithms. The adaptive envelope-constrained filter thus designed achieves guaranteed satisfaction of the output envelope constraints as long as it has converged. Computer simulations that support the theoretical findings are given