Minimax universal sampling for compound multiband channels

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

This paper considers the capacity of sub-sampled analog channels when the sampler is designed to operate independent of the instantaneous channel realization, and investigates sampling methods that minimize the worst-case (minimax) sampled capacity loss due to channel-independent (universal) sampling design. Specifically, a compound multiband channel with unknown subband occupancy is considered, when perfect channel side information is available to both the receiver and the transmitter. We restrict our attention to a general class of periodic sub-Nyquist samplers, which subsumes as special cases sampling with modulation and filter banks. Our results demonstrate that under both Landau-rate and super-Landau-rate sampling, the minimax sampled capacity loss due to universal design depends only on the band sparsity ratio and the undersampling factor, modulo a residual term that vanishes at high signal-to-noise ratio. We quantify the capacity loss under sampling with periodic modulation and low-pass filters, when the Fourier coefficients of the modulation waveforms are randomly generated (called random sampling). Our results highlight the power of random sampling methods, which achieve minimax sampled capacity loss uniformly across all channel realizations and are thus optimal in a universal design sense.

Original languageEnglish (US)
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Pages1032-1036
Number of pages5
DOIs
StatePublished - Dec 19 2013
Externally publishedYes
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: Jul 7 2013Jul 12 2013

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Other

Other2013 IEEE International Symposium on Information Theory, ISIT 2013
CountryTurkey
CityIstanbul
Period7/7/137/12/13

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Sub-Nyquist sampling
  • channel capacity
  • minimaxity
  • non-asymptotic random matrices
  • universal sampling

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