Channel Capacity under General Nonuniform Sampling

TL;DR

This paper establishes the fundamental limits of channel capacity under sub-Nyquist sampling, showing optimal sampling strategies extract the highest SNR frequencies and that irregular sampling offers no capacity advantage over uniform sampling with proper preprocessing.

Contribution

It derives the capacity limits for general nonuniform sampling methods and characterizes optimal sampling structures for maximizing channel capacity.

Findings

Optimal sampling extracts highest SNR spectral sets.

Capacity is a monotone increasing function of sampling rate.

Irregular nonuniform sampling does not outperform uniform sampling with preprocessing.

Abstract

This paper develops the fundamental capacity limits of a sampled analog channel under a sub-Nyquist sampling rate constraint. In particular, we derive the capacity of sampled analog channels over a general class of time-preserving sampling methods including irregular nonuniform sampling. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest SNR among all spectral sets of support size equal to the sampling rate. The capacity under sub-Nyquist sampling can be attained through filter-bank sampling, or through a single branch of modulation and filtering followed by uniform sampling. The capacity under sub-Nyquist sampling is a monotone function of the sampling rate. These results indicate that the optimal sampling schemes suppress aliasing, and that employing irregular nonuniform sampling does not provide capacity gain over uniform sampling sets with appropriate preprocessing for a large class of channels.