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In contrast to the prevalent assumption of rich multipath in informationtheoretic analysis of wireless channels, physical channels exhibit sparsemultipath, especially at large bandwidths. We propose a model for sparsemultipath fading channels and present results on the impact of sparsity onnon-coherent capacity and reliability in the wideband regime. A key implicationof sparsity is that the statistically independent degrees of freedom in thechannel, that represent the delay-Doppler diversity afforded by multipath,scale at a sub-linear rate with the signal space dimension (time-bandwidthproduct). Our analysis is based on a training-based communication scheme thatuses short-time Fourier (STF) signaling waveforms. Sparsity in delay-Dopplermanifests itself as time-frequency coherence in the STF domain. From a capacityperspective, sparse channels are asymptotically coherent: the gap betweencoherent and non-coherent extremes vanishes in the limit of large signal spacedimension without the need for peaky signaling. From a reliability viewpoint,there is a fundamental tradeoff between channel diversity and learnability thatcan be optimized to maximize the error exponent at any rate by appropriatelychoosing the signaling duration as a function of bandwidth.

Non-Coherent Capacity and Reliability of Sparse Multipath Channels in the Wideband Regime