Sparsity in time-frequency representations

TL;DR

This paper demonstrates that sparse time-frequency representations in finite-dimensional signals can be reliably recovered using Basis Pursuit, especially in wireless communication channel estimation, under certain sparsity conditions.

Contribution

It establishes probabilistic guarantees for recovering sparse Gabor representations with random unimodular windows, linking compressive sensing theory to practical applications.

Findings

Recovery of S-sparse Gabor representations with high probability

Applicable to wireless channel estimation

Validates measurement matrices for compressive sensing

Abstract

We consider signals and operators in finite dimension which have sparse time-frequency representations. As main result we show that an $S$-sparse Gabor representation in $\mathbb{C}^n$ with respect to a random unimodular window can be recovered by Basis Pursuit with high probability provided that $S\leq Cn/\log(n)$. Our results are applicable to the channel estimation problem in wireless communications and they establish the usefulness of a class of measurement matrices for compressive sensing.