Full Text:   <1913>

Summary:  <1038>

CLC number: TN911.72

On-line Access: 2021-02-01

Received: 2019-06-28

Revision Accepted: 2019-11-26

Crosschecked: 2020-10-20

Cited: 0

Clicked: 3529

Citations:  Bibtex RefMan EndNote GB/T7714


Xiqian Luo


Zhaoyang Zhang


-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2021 Vol.22 No.2 P.232-243


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

Author(s):  Xiqian Luo, Zhaoyang Zhang

Affiliation(s):  College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   ning_ming@zju.edu.cn

Key Words:  Nyquist-Shannon sampling theorem, Sub-Nyquist sampling, Minimum Euclidean distance, Under-determined linear problem, Time-variant Viterbi algorithm

Xiqian Luo, Zhaoyang Zhang. Data recovery with sub-Nyquist sampling: fundamental limit and a detection algorithm[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(2): 232-243.

@article{title="Data recovery with sub-Nyquist sampling: fundamental limit and a detection algorithm",
author="Xiqian Luo, Zhaoyang Zhang",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Data recovery with sub-Nyquist sampling: fundamental limit and a detection algorithm
%A Xiqian Luo
%A Zhaoyang Zhang
%J Frontiers of Information Technology & Electronic Engineering
%V 22
%N 2
%P 232-243
%@ 2095-9184
%D 2021
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1900320

T1 - Data recovery with sub-Nyquist sampling: fundamental limit and a detection algorithm
A1 - Xiqian Luo
A1 - Zhaoyang Zhang
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 22
IS - 2
SP - 232
EP - 243
%@ 2095-9184
Y1 - 2021
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1900320

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.





Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Anderson JB, Rusek F, Öwall V, 2013. Faster-than-Nyquist signaling. Proc IEEE, 101(8):1817-1830.

[2]Chen YX, Eldar YC, Goldsmith AJ, 2013. Shannon meets Nyquist: capacity of sampled Gaussian channels. IEEE Trans Inform Theory, 59(8):4889-4914.

[3]Domínguez-Jiménez ME, González-Prelcic N, Vazquez-Vilar G, et al., 2012. Design of universal multicoset sampling patterns for compressed sensing of multiband sparse signals. Proc IEEE Int Conf on Acoustics, Speech and Signal Processing, p.3337-3340.

[4]Fan JC, Guo SJ, Zhou XW, et al., 2017. Faster-than-Nyquist signaling: an overview. IEEE Access, 5:1925-1940.

[5]Feng P, Bresler Y, 1996. Spectrum-blind minimum-rate sampling and reconstruction of multiband signals. Proc IEEE Int Conf on Acoustics, Speech, and Signal Processing, 3:1688-1691.

[6]Forney GD, 1973. The Viterbi algorithm. Proc IEEE, 61(3):268-278.

[7]Goldsmith A, 2005. Wireless Communications. Cambridge University Press, Cambridge, USA, p.327-340.

[8]Hajela D, 1990. On computing the minimum distance for faster than Nyquist signaling. IEEE Trans Inform Theory, 36(2):289-295.

[9]Herley C, Wong PW, 1999. Minimum rate sampling and reconstruction of signals with arbitrary frequency support. IEEE Trans Inform Theory, 45(5):1555-1564.

[10]Landau HJ, 1967. Necessary density conditions for sampling and interpolation of certain entire functions. Acta Math, 117(1):37-52.

[11]Liveris AD, Georghiades CN, 2003. Exploiting faster-than-Nyquist signaling. IEEE Trans Commun, 51(9):1502-1511.

[12]Lu YM, Do MN, 2008. A theory for sampling signals from a union of subspaces. IEEE Trans Signal Process, 56(6):2334-2345.

[13]Luo X, Zhang Z, 2019. Data recovery from sub-Nyquist sampled signals: fundamental limit and detection algorithm. Proc 11th Int Conf on Wireless Communications and Signal Processing, p.1-6.

[14]Mazo JE, 1975. Faster-than-Nyquist signaling. Bell Syst Techn J, 54(8):1451-1462.

[15]Mazo JE, Landau HJ, 1988. On the minimum distance problem for faster-than-Nyquist signaling. IEEE Trans Inform Theory, 34(6):1420-1427.

[16]Mishali M, Eldar YC, 2009. Blind multiband signal reconstruction: compressed sensing for analog signals. IEEE Trans Signal Process, 57(3):993-1009.

[17]Mishali M, Eldar YC, 2010. From theory to practice: sub-Nyquist sampling of sparse wideband analog signals. IEEE J Sel Top Signal Process, 4(2):375-391.

[18]Mishali M, Eldar YC, Elron AJ, 2011. Xampling: signal acquisition and processing in union of subspaces. IEEE Trans Signal Process, 59(10):4719-4734.

[19]Scoular SC, Fitzgerald WJ, 1992. Periodic nonuniform sampling of multiband signals. Signal Process, 28(2):195-200.

[20]Sun HJ, Nallanathan A, Wang CX, et al., 2013. Wideband spectrum sensing for cognitive radio networks: a survey. IEEE Wirel Commun, 20(2):74-81.

[21]Tropp JA, Laska JN, Duarte MF, et al., 2010. Beyond Nyquist: efficient sampling of sparse bandlimited signals. IEEE Trans Inform Theory, 56(1):520-544.

[22]Venkataramani R, Bresler Y, 2001. Optimal sub-Nyquist nonuniform sampling and reconstruction for multiband signals. IEEE Trans Signal Process, 49(10):2301-2313.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2023 Journal of Zhejiang University-SCIENCE