BER analysis of regularized least squares for BPSK recovery

Handle URI:
http://hdl.handle.net/10754/625622
Title:
BER analysis of regularized least squares for BPSK recovery
Authors:
Ben Atitallah, Ismail ( 0000-0002-1748-1934 ) ; Thrampoulidis, Christos; Kammoun, Abla ( 0000-0002-0195-3159 ) ; Al-Naffouri, Tareq Y. ( 0000-0003-2843-5084 ) ; Hassibi, Babak; Alouini, Mohamed-Slim ( 0000-0003-4827-1793 )
Abstract:
This paper investigates the problem of recovering an n-dimensional BPSK signal x<inf>0</inf> ∈ {−1, 1}<sup>n</sup> from m-dimensional measurement vector y = Ax+z, where A and z are assumed to be Gaussian with iid entries. We consider two variants of decoders based on the regularized least squares followed by hard-thresholding: the case where the convex relaxation is from {−1, 1}<sup>n</sup> to ℝ<sup>n</sup> and the box constrained case where the relaxation is to [−1, 1]<sup>n</sup>. For both cases, we derive an exact expression of the bit error probability when n and m grow simultaneously large at a fixed ratio. For the box constrained case, we show that there exists a critical value of the SNR, above which the optimal regularizer is zero. On the other side, the regularization can further improve the performance of the box relaxation at low to moderate SNR regimes. We also prove that the optimal regularizer in the bit error rate sense for the unboxed case is nothing but the MMSE detector.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Ben Atitallah I, Thrampoulidis C, Kammoun A, Al-Naffouri TY, Hassibi B, et al. (2017) BER analysis of regularized least squares for BPSK recovery. 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Available: http://dx.doi.org/10.1109/ICASSP.2017.7952960.
Publisher:
IEEE
Journal:
2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
KAUST Grant Number:
URF/1/2221-01
Conference/Event name:
2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Issue Date:
20-Jun-2017
DOI:
10.1109/ICASSP.2017.7952960
Type:
Conference Paper
Sponsors:
This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. URF/1/2221-01.
Additional Links:
http://ieeexplore.ieee.org/document/7952960/
Appears in Collections:
Conference Papers; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBen Atitallah, Ismailen
dc.contributor.authorThrampoulidis, Christosen
dc.contributor.authorKammoun, Ablaen
dc.contributor.authorAl-Naffouri, Tareq Y.en
dc.contributor.authorHassibi, Babaken
dc.contributor.authorAlouini, Mohamed-Slimen
dc.date.accessioned2017-10-03T12:49:30Z-
dc.date.available2017-10-03T12:49:30Z-
dc.date.issued2017-06-20en
dc.identifier.citationBen Atitallah I, Thrampoulidis C, Kammoun A, Al-Naffouri TY, Hassibi B, et al. (2017) BER analysis of regularized least squares for BPSK recovery. 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Available: http://dx.doi.org/10.1109/ICASSP.2017.7952960.en
dc.identifier.doi10.1109/ICASSP.2017.7952960en
dc.identifier.urihttp://hdl.handle.net/10754/625622-
dc.description.abstractThis paper investigates the problem of recovering an n-dimensional BPSK signal x<inf>0</inf> ∈ {−1, 1}<sup>n</sup> from m-dimensional measurement vector y = Ax+z, where A and z are assumed to be Gaussian with iid entries. We consider two variants of decoders based on the regularized least squares followed by hard-thresholding: the case where the convex relaxation is from {−1, 1}<sup>n</sup> to ℝ<sup>n</sup> and the box constrained case where the relaxation is to [−1, 1]<sup>n</sup>. For both cases, we derive an exact expression of the bit error probability when n and m grow simultaneously large at a fixed ratio. For the box constrained case, we show that there exists a critical value of the SNR, above which the optimal regularizer is zero. On the other side, the regularization can further improve the performance of the box relaxation at low to moderate SNR regimes. We also prove that the optimal regularizer in the bit error rate sense for the unboxed case is nothing but the MMSE detector.en
dc.description.sponsorshipThis publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. URF/1/2221-01.en
dc.publisherIEEEen
dc.relation.urlhttp://ieeexplore.ieee.org/document/7952960/en
dc.subjectBinary phase shift keyingen
dc.subjectBit error rateen
dc.subjectClosed-form solutionsen
dc.subjectDecodingen
dc.subjectDetectorsen
dc.subjectError probabilityen
dc.subjectSignal to noise ratioen
dc.titleBER analysis of regularized least squares for BPSK recoveryen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journal2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)en
dc.conference.date2017-03-05 to 2017-03-09en
dc.conference.name2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017en
dc.conference.locationNew Orleans, LA, USAen
dc.contributor.institutionDepartment of Electrical Engeeniring, Caltech, Pasadena, USAen
kaust.authorBen Atitallah, Ismailen
kaust.authorKammoun, Ablaen
kaust.authorAl-Naffouri, Tareq Y.en
kaust.authorAlouini, Mohamed-Slimen
kaust.grant.numberURF/1/2221-01en
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