TY - JOUR
T1 - On the Minimax Capacity Loss under Sub-Nyquist Universal Sampling
AU - Chen, Yuxin
AU - Goldsmith, Andrea J.
AU - Eldar, Yonina C.
N1 - Funding Information:
Manuscript received April 28, 2013; revised May 7, 2015; accepted December 17, 2016. Date of publication April 18, 2017; date of current version May 18, 2017. This work was supported in part by the NSF under Grant CCF-0939370 and Grant CIS-1320628, in part by the AFOSR through MURI under Grant FA9550-12-1-0215, and in part by BSF Transformative Science under Grant 2010505. This paper was presented at the 2013 IEEE International Symposium on Information Theory. (Corresponding author: Yuxin Chen.) Y. Chen is with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail: yuxin.chen@princeton.edu).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2017/6
Y1 - 2017/6
N2 - 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.
AB - 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.
KW - Channel capacity
KW - concentration of spectral measure
KW - log-determinant
KW - minimax sampling
KW - non-asymptotic random matrix
UR - http://www.scopus.com/inward/record.url?scp=85028318365&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85028318365&partnerID=8YFLogxK
U2 - 10.1109/TIT.2017.2695541
DO - 10.1109/TIT.2017.2695541
M3 - Article
AN - SCOPUS:85028318365
SN - 0018-9448
VL - 63
SP - 3348
EP - 3367
JO - IRE Professional Group on Information Theory
JF - IRE Professional Group on Information Theory
IS - 6
M1 - 7903620
ER -