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On the Minimax Capacity Loss Under Sub-Nyquist Universal Sampling

机译：亚奈奎斯特通用采样下的Minimax容量损失

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摘要

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.
机译：当采样器设计为独立于瞬时信道占用率运行时，本文研究了模拟信道中的信息速率损失。具体而言，考虑了通用亚奈奎斯特采样下的多频带线性时不变高斯信道。整个信道带宽被分为相等带宽的n个子带。每次只有k个恒定增益子带处于活动状态，而在接收器和采样器处，瞬时子带占用率未知。我们通过信息速率丢失度量来研究信息丢失，即由于缺乏瞬时子带占用信息而导致的可达到速率的差距。如果子带的个数n和SNR都很大，我们就可以描述亚奈奎斯特体制下的最小最大信息速率损失。 minimax极限几乎完全取决于频带稀疏性因子和欠采样因子，对一些残余项取模，这些残余项随着n和SNR的增长而消失。我们的结果突出了随机采样方法（即由随机周期调制和低通滤波器组成的采样器）的强大功能，该方法能够以极高的概率接近最小最大信息速率损失。

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