Pseudodifferential operators and Banach algebras in mobile communications

Abstract

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 H σ with symbol σ in F L w 1 or in the modulation space M w ∞ , 1 (also known as weighted Sjöstrand class). It is then demonstrated that Gabor Riesz bases { φ m , n } for subspaces of L 2 ( R ) approximately diagonalize such pseudodifferential operators in the sense that the associated matrix [ 〈 H σ φ m ′ , n ′ , φ m , 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.