Box-Relaxation for BPSK Recovery in Massive MIMO: A Precise Analysis under Correlated Channels

In this paper, we consider the problem of recovering a binary phase shift keying (BPSK) modulated signal in a massive multiple-input-multiple-output (MIMU) system. The recovery process is done using the box-relaxation method, in which the discrete set {±I}
ⁿ
is relaxed to the convex set [-I,+I]
ⁿ
and solved by a convex optimization program followed by hard thresholding. We assume that the system has a Gaussian channel matrix with one sided left correlation. The entries of the noise vector are assumed to be independent and identically distributed (iid) zero-mean Gaussian. In this work, we precisely characterize the mean squared error (MSE) and the bit error rate (BER) of the box-relaxation decoder in the asymptotic regime where both dimensions grow simultaneously large at a fixed ratio. Numerical simulations validate the theoretical expressions derived in this paper.