Ber analysis of the box relaxation for BPSK signal recovery

Type
Conference Paper

Authors
Thrampoulidis, Christos
Abbasi, Ehsan
Xu, Weiyu
Hassibi, Babak

Online Publication Date
2016-06-24

Print Publication Date
2016-03

Date
2016-06-24

Abstract
We study the problem of recovering an n-dimensional BPSK signal from m linear noise-corrupted measurements using the box relaxation method which relaxes the discrete set {±1}n to the convex set [-1,1]n to obtain a convex optimization algorithm followed by hard thresholding. When the noise and measurement matrix have iid standard normal entries, we obtain an exact expression for the bit-wise probability of error Pe in the limit of n and m growing and m/n fixed. At high SNR our result shows that the Pe of box relaxation is within 3dB of the matched filter bound (MFB) for square systems, and that it approaches the (MFB) as m grows large compared to n. Our results also indicate that as m, n → ∞, for any fixed set of size k, the error events of the corresponding k bits in the box relaxation method are independent.

Citation
Thrampoulidis C, Abbasi E, Xu W, Hassibi B (2016) Ber analysis of the box relaxation for BPSK signal recovery. 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Available: http://dx.doi.org/10.1109/icassp.2016.7472383.

Acknowledgements
This work was supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASAs Jet Propulsion Laboratory through the President and Directors Fund, by King Abdulaziz University, and by King Abdullah University of Science and Technology. Xu’s work is supported by Simons Foundation, Iowa Energy Center, KAUST, and NIH 1R01EB020665-01.

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

Journal
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Conference/Event Name
41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016

DOI
10.1109/icassp.2016.7472383

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