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Published March 2017 | public
Book Section - Chapter

BER analysis of regularized least squares for BPSK recovery


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.

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.

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October 18, 2023