Ber Analysis Of Regularized Least Squares For Bpsk Recovery - 2017


This paper investigates the matter of recovering an n-dimensional BPSK signal x0 ? -1, 1n from m-dimensional measurement vector y = Ax+z, where A and z are assumed to be Gaussian with iid entries. We tend to take into account two variants of decoders primarily based on the regularized least squares followed by arduous-thresholding: the case where the convex relaxation is from -1, 1n to Rn and the box constrained case where the relief is to [-1, one]n. For each cases, we tend to derive an precise expression of the bit error likelihood when n and m grow simultaneously large at a mounted ratio. For the box constrained case, we tend to show that there exists a crucial worth of the SNR, higher than which the optimal regularizer is zero. On the opposite 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 within the bit error rate sense for the unboxed case is nothing however the MMSE detector.

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