Distributed SNR Estimation using Constant Modulus Signaling over Gaussian Multiple-Access Channels

Abstract

A sensor network is used for distributed joint mean and variance estimation, in a single time snapshot. Sensors observe a signal embedded in noise, which are phase modulated using a constant-modulus scheme and transmitted over a Gaussian multiple-access channel to a fusion center, where the mean and variance are estimated jointly, using an asymptotically minimum-variance estimator, which is shown to decouple into simple individual estimators of the mean and the variance. The constant-modulus phase modulation scheme ensures a fixed transmit power, robust estimation across several sensing noise distributions, as well as an SNR estimate that requires a single set of transmissions from the sensors to the fusion center, unlike the amplify-and-forward approach. The performance of the estimators of the mean and variance are evaluated in terms of asymptotic variance, which is used to evaluate the performance of the SNR estimator in the case of Gaussian, Laplace and Cauchy sensing noise distributions. For each sensing noise distribution, the optimal phase transmission parameters are also determined. The asymptotic relative efficiency of the mean and variance estimators is evaluated. It is shown that among the noise distributions considered, the estimators are asymptotically efficient only when the noise distribution is Gaussian. Simulation results corroborate analytical results.