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On the Minimax Capacity Loss under Sub-Nyquist Universal Sampling

Author(s): Chen, Y; Goldsmith, AJ; Eldar, YC

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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 , 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.
Publication Date: 18-Apr-2017
Citation: Chen, Y, Goldsmith, AJ, Eldar, YC. (2017). On the Minimax Capacity Loss under Sub-Nyquist Universal Sampling. IEEE Transactions on Information Theory, 63 (3348 - 3367. doi:10.1109/TIT.2017.2695541
DOI: doi:10.1109/TIT.2017.2695541
Pages: 3348 - 3367
Type of Material: Journal Article
Journal/Proceeding Title: IEEE Transactions on Information Theory
Version: Author's manuscript

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