Adaptation of Weyl-Heisenberg frames to underspread environments

Abstract

Underspread environments provide an operator theoretic framework for slowly time-varying linear systems with finite memory and for the second-order modeling of quasistationary random processes. We consider the adaptation of continuous and discrete Weyl-Heisenberg (WH) frames to trace-class underspread operators in the sense of approximate diagonalization. The atom optimization criteria are formulated in terms of the ambiguity function of the atom and the spreading function of the operator. The theoretical results are demonstrated by a numerical experiment.