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
Abstract
This paper investigates the problem of recovering an n-dimensional BPSK signal x <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> ∈ {−1, 1} <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> to ℝ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> and the box constrained case where the relaxation is to [−1, 1] <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">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.
BibTeX
@inproceedings{icassp2017_beranalysisofreg,
title = {BER analysis of regularized least squares for BPSK recovery},
author = {Ismail Ben Atitallah and Christos Thrampoulidis and Abla Kammoun and Tareq Y. Al-Naffouri and Babak Hassibi and Mohamed-Slim Alouini},
booktitle = {ICASSP 2017},
year = {2017}
}