Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Underwater acoustic communication channels: propagation models and statistical characterization
IEEE Communications Magazine
IEEE Transactions on Signal Processing
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Generalized reconstruction algorithm for compressed sensing
Computers and Electrical Engineering
Iterative estimation of the time-varying underwater acoustic channel using basis expansion models
Proceedings of the Eighth ACM International Conference on Underwater Networks and Systems
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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 overcomplete 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.