On the Minimax Capacity Loss under Sub-Nyquist Universal Sampling

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

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper investigates the information rate loss in analog channels, when the sampler is designed to operate independent of the instantaneous channel occupancy. Specifically, a multiband linear time-invariant Gaussian channel under universal sub-Nyquist sampling is considered. The entire channel bandwidth is divided into n subbands of equal bandwidth. At each time, only k constant-gain subbands are active, where the instantaneous subband occupancy is not known at the receiver and the sampler. We study the information loss through an information rate lossmetric, that is, the gap of achievable rates caused by the lack of instantaneous subband occupancy information. We characterize the minimax information rate loss for the sub-Nyquist regime, provided that the number n of subbands and the SNR are both large. The minimax limits depend almost solely on the band sparsity factor and the undersampling factor, modulo some residual terms that vanish as n and SNR grow. Our results highlight the power of randomized sampling methods (i.e., the samplers that consist of random periodic modulation and low-pass filters), which are able to approach the minimax information rate loss with exponentially high probability.

Original languageEnglish (US)
Article number7903620
Pages (from-to)3348-3367
Number of pages20
JournalIEEE Transactions on Information Theory
Volume63
Issue number6
DOIs
StatePublished - Jun 1 2017

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Sampling
Bandwidth
Low pass filters
Modulation
recipient
regime
lack

All Science Journal Classification (ASJC) codes

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

Keywords

  • Channel capacity
  • concentration of spectral measure
  • log-determinant
  • minimax sampling
  • non-asymptotic random matrix

Cite this

Chen, Yuxin ; Goldsmith, Andrea J. ; Eldar, Yonina C. / On the Minimax Capacity Loss under Sub-Nyquist Universal Sampling. In: IEEE Transactions on Information Theory. 2017 ; Vol. 63, No. 6. pp. 3348-3367.
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On the Minimax Capacity Loss under Sub-Nyquist Universal Sampling. / Chen, Yuxin; Goldsmith, Andrea J.; Eldar, Yonina C.

In: IEEE Transactions on Information Theory, Vol. 63, No. 6, 7903620, 01.06.2017, p. 3348-3367.

Research output: Contribution to journalArticle

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