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    Ber analysis of the box relaxation for BPSK signal recovery

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    Type
    Conference Paper
    Authors
    Thrampoulidis, Christos
    Abbasi, Ehsan
    Xu, Weiyu
    Hassibi, Babak
    Date
    2016-06-24
    Online Publication Date
    2016-06-24
    Print Publication Date
    2016-03
    Permanent link to this record
    http://hdl.handle.net/10754/623517
    
    Metadata
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    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.
    Sponsors
    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
    ae974a485f413a2113503eed53cd6c53
    10.1109/icassp.2016.7472383
    Scopus Count
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    Publications Acknowledging KAUST Support

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