Non-Coherent Capacity and Reliability of Sparse Multipath Channels in the Wideband Regime (0705.2848v1)

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