Channel capacity under sub-Nyquist nonuniform sampling

Yuxin Chen, Andrea J. Goldsmith, Yonina C. Eldar

Research output: Contribution to journalArticle

13 Scopus citations

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 includes 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 grid employed 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 are typically complicated to realize in practice, 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 in this scenario, which is in contrast to the benefits obtained from random mixing in spectrum-blind compressive sampling schemes.

Original languageEnglish (US)
Article number6814945
Pages (from-to)4739-4756
Number of pages18
JournalIEEE Transactions on Information Theory
Volume60
Issue number8
DOIs
StatePublished - Aug 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • Beurling density
  • Nonuniform sampling
  • channel capacity
  • irregular sampling
  • sampled analog channels
  • sub-Nyquist sampling
  • time-preserving sampling systems

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