Pseudodifferential operators and Banach algebras in mobile communications

We study linear time-varying operators arising in mobile communication using methods from time–frequency analysis. We show that a wireless transmission channel can be modeled as pseudodifferential operator Hσ with symbol σ in or in the modulation space (also known as weighted Sjöstrand class). It is then demonstrated that Gabor Riesz bases {φm,n} for subspaces of L2(R) approximately diagonalize such pseudodifferential operators in the sense that the associated matrix [〈Hσφm′,n′,φm,n〉]m,n,m′,n′ belongs to a Wiener-type Banach algebra with exponentially fast off-diagonal decay. We indicate how our results can be utilized to construct numerically efficient equalizers for multicarrier communication systems in a mobile environment.