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BER analysis of regularized least squares for BPSK recovery

Atitallah, Ismail Ben and Thrampoulidis, Christos and Kammoun, Abla and Al-Naffouri, Tareq Y. and Hassibi, Babak and Alouini, Mohamed-Slim (2017) BER analysis of regularized least squares for BPSK recovery. In: 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE , Piscataway, NJ, pp. 4262-4266. ISBN 978-1-5090-4117-6. http://resolver.caltech.edu/CaltechAUTHORS:20171222-075024697

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Abstract

This paper investigates the problem of recovering an n-dimensional BPSK signal x_0 ∈ {-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 ℝ^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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ICASSP.2017.7952960DOIArticle
http://ieeexplore.ieee.org/document/7952960/PublisherArticle
Additional Information:© 2017 IEEE. 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.
Funders:
Funding AgencyGrant Number
King Abdullah University of Science and Technology (KAUST)URF/1/2221-01
Subject Keywords:BER analysis, box relaxation, regularized least squares, MMSE, high dimensions
Record Number:CaltechAUTHORS:20171222-075024697
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20171222-075024697
Official Citation:I. Ben Atitallah, C. Thrampoulidis, A. Kammoun, T. Y. Al-Naffouri, B. Hassibi and M. S. Alouini, "BER analysis of regularized least squares for BPSK recovery," 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, 2017, pp. 4262-4266. doi: 10.1109/ICASSP.2017.7952960. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7952960&isnumber=7951776
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84013
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:22 Dec 2017 16:07
Last Modified:22 Dec 2017 16:07

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