Application of compressive sensing to sparse channel estimation

TLDR

Compressive sensing has attracted significant attention in applied mathematics and signal processing, and is widely used in imaging, radar, speech recognition, data acquisition, and is accepted for sparse channel estimation in communications. The article aims to highlight the fundamental concepts of compressive sensing and provide an overview of its application to pilot‑aided channel estimation. The authors illustrate the framework by applying compressive sensing to multicarrier underwater acoustic communications, where sparse arrivals with distinct delay and Doppler scales are modeled, and discuss practical modifications such as adapting the channel model detail and pilot‑data mixing to reduce estimation error. They show that the common assumption of sparsity in the equivalent baseband representation has pitfalls, and that using over‑complete dictionaries yields much sparser channel representations and better estimation performance.

Abstract

Compressive sensing is a topic that has recently gained much attention in the applied mathematics and signal processing communities. It has been applied in various areas, such as imaging, radar, speech recognition, and data acquisition. In communications, compressive sensing is largely accepted for sparse channel estimation and its variants. In this article we highlight the fundamental concepts of compressive sensing and give an overview of its application to pilot aided channel estimation. We point out that a popular assumption - that multipath channels are sparse in their equivalent baseband representation - has pitfalls. There are over-complete dictionaries that lead to much sparser channel representations and better estimation performance. As a concrete example, we detail the application of compressive sensing to multicarrier underwater acoustic communications, where the channel features sparse arrivals, each characterized by its distinct delay and Doppler scale factor. To work with practical systems, several modifications need to be made to the compressive sensing framework as the channel estimation error varies with how detailed the channel is modeled, and how data and pilot symbols are mixed in the signal design.