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

TL;DR

This paper investigates how sparsity in multipath channels affects their capacity and reliability in wideband regimes, revealing that sparse channels become effectively coherent at large scales and highlighting a tradeoff between diversity and learnability.

Contribution

It introduces a model for sparse multipath channels and analyzes their non-coherent capacity and reliability, showing asymptotic coherence and optimizing signaling strategies.

Findings

Sparse channels have sub-linear degrees of freedom growth.

Asymptotic coherence in sparse channels reduces the capacity gap.

Tradeoff exists between diversity and learnability for reliability.

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.