Ber analysis of the box relaxation for BPSK signal recovery

Christos Thrampoulidis, Ehsan Abbasi, Weiyu Xu, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Scopus citations

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.
Original languageEnglish (US)
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages3776-3780
Number of pages5
ISBN (Print)9781479999880
DOIs
StatePublished - Jun 24 2016
Externally publishedYes

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