Data recovery with sub-Nyquist sampling:fundamental limit and a detection algorithm  

作　　者：Xiqian LUO Zhaoyang ZHANG 

机构地区：[1]College of Information Science and Electronic Engineering,Zhejiang University,Hangzhou 310027,China

出　　处：《Frontiers of Information Technology & Electronic Engineering》2021年第2期232-243,共12页信息与电子工程前沿（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.61725104 and 61631003);Huawei Technologies Co.,Ltd.(Nos.HF2017010003,YB2015040053,and YB2013120029)。

摘　　要：While the Nyquist rate serves as a lower bound to sample a general bandlimited signal with no information loss,the sub-Nyquist rate may also be sufficient for sampling and recovering signals under certain circumstances.Previous works on sub-Nyquist sampling achieved dimensionality reduction mainly by transforming the signal in certain ways.However,the underlying structure of the sub-Nyquist sampled signal has not yet been fully exploited.In this paper,we study the fundamental limit and the method for recovering data from the sub-Nyquist sample sequence of a linearly modulated baseband signal.In this context,the signal is not eligible for dimension reduction,which makes the information loss in sub-Nyquist sampling inevitable and turns the recovery into an under-determined linear problem.The performance limits and data recovery algorithms of two different sub-Nyquist sampling schemes are studied.First,the minimum normalized Euclidean distances for the two sampling schemes are calculated which indicate the performance upper bounds of each sampling scheme.Then,with the constraint of a finite alphabet set of the transmitted symbols,a modified time-variant Viterbi algorithm is presented for efficient data recovery from the sub-Nyquist samples.The simulated bit error rates(BERs)with different sub-Nyquist sampling schemes are compared with both their theoretical limits and their Nyquist sampling counterparts,which validates the excellent performance of the proposed data recovery algorithm.

关 键 词：Nyquist-Shannon sampling theorem Sub-Nyquist sampling Minimum Euclidean distance Under-determined linear problem Time-variant Viterbi algorithm 

分 类 号：TN911.72[电子电信—通信与信息系统]