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This paper proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results are provided, and show that the proposed method is very accurate.

In this paper, we consider the problem of recovering a binary phase shift keying (BPSK) modulated signal in a massive multiple-input-multiple-output (MIMO) system. The recovery process is done using the box-relaxation method, in which the discrete set {±1} n is relaxed to the convex set [−1, +1] 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.

In this paper, we consider the problem of recovering an unknown sparse signal x 0 ∈ R n from noisy linear measurements y = Hx 0 +z ∈ R m . A popular approach is to solve the ℓ 1 -norm regularized least squares problem which is known as the LASSO. In many practical situations, the measurement matrix H is not perfectely known and we only have a noisy version of it. We assume that the entries of the measurement matrix H and of the noise vector z are iid Gaussian with zero mean and variances 1/n and σ 2 z . In this work, an imperfect measurement matrix is considered under which we precisely characterize the limiting behavior of the mean squared error and the probability of support recovery of the LASSO. The analysis is performed when the problem dimensions grow simultaneously to infinity at fixed rates. Numerical simulations validate the theoretical predictions derived in this paper.

In this letter, we consider the problem of recovering an unknown sparse signal from noisy linear measurements, using an enhanced version of the popular Elastic-Net (EN) method. We modify the EN by adding a box-constraint, and we call it the Box-Elastic Net (Box-EN). We assume independent identically distributed (iid) real Gaussian measurement matrix with additive Gaussian noise. In many practical situations, the measurement matrix is not perfectly known, and so we only have a noisy estimate of it. In this work, we precisely characterize the mean squared error and the probability of support recovery of the Box-Elastic Net in the high-dimensional asymptotic regime. Numerical simulations validate the theoretical predictions derived in the paper and also show that the boxed variant outperforms the standard EN.Index Terms-Elastic Net, squared error, measurement matrix uncertainties, probability of support recovery, box-constraint.