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Multipath signal propagation is the defining characteristic of terrestrial wireless channels. Virtually all existing statistical models for wireless channels are implicitly based on the assumption of rich multipath, which can be traced back to the seminal works of Bello and Kennedy on the wide-sense stationary uncorrelated scattering model, and more recently to the i.i.d. model for multi-antenna channels proposed by Telatar, and Foschini Gans. However, physical arguments and growing experimental evidence suggest that physical channels encountered in practice exhibit a sparse multipath structure that gets more pronounced as the signal space dimension gets large (e.g., due to large bandwidth or large number of antennas). In this paper, we formalize the notion of multipath sparsity and discuss applications of the emerging theory of compressed sensing for efficient estimation of sparse multipath channels.