BER analysis of regularized least squares for BPSK recovery

Ismail Ben Atitallah, Christos Thrampoulidis, Abla Kammoun, Tareq Y. Al-Naffouri, Babak Hassibi, Mohamed-Slim Alouini

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

11 Scopus citations


This paper investigates the problem of recovering an n-dimensional BPSK signal x0 {’1, 1}$^{n}$ 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}$^{n}$ to „ $^{n}$ and the box constrained case where the relaxation is to [’1, 1]$^{n}$. 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.
Original languageEnglish (US)
Title of host publication2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages5
ISBN (Print)9781509041176
StatePublished - Jun 20 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): URF/1/2221-01
Acknowledgements: 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.


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