Channel Capacity under Sub-Nyquist Nonuniform Sampling

TL;DR

This paper characterizes the capacity of linear Gaussian channels under sub-Nyquist nonuniform sampling, showing that optimal sampling extracts the highest SNR spectral components and that irregular sampling offers no capacity advantage over uniform sampling.

Contribution

It provides a closed-form capacity characterization for a broad class of sampling methods, revealing that irregular nonuniform sampling does not improve capacity over uniform sampling with proper preprocessing.

Findings

Optimal sampling extracts highest SNR spectral sets

Irregular nonuniform sampling does not increase capacity

Aliasing does not provide capacity gain

Abstract

This paper investigates the effect of sub-Nyquist sampling upon the capacity of an analog channel. The channel is assumed to be a linear time-invariant Gaussian channel, where perfect channel knowledge is available at both the transmitter and the receiver. We consider a general class of right-invertible time-preserving sampling methods which include irregular nonuniform sampling, and characterize in closed form the channel capacity achievable by this class of sampling methods, under a sampling rate and power constraint. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest signal-to-noise ratio among all spectral sets of measure equal to the sampling rate. This can be attained through filterbank sampling with uniform sampling at each branch with possibly different rates, or through a single branch of modulation and filtering followed by uniform sampling. These results reveal that for a large class of channels, employing irregular nonuniform sampling sets, while typically complicated to realize, does not provide capacity gain over uniform sampling sets with appropriate preprocessing. Our findings demonstrate that aliasing or scrambling of spectral components does not provide capacity gain, which is in contrast to the benefits obtained from random mixing in spectrum-blind compressive sampling schemes.