Distributed SNR estimation with power constrained signaling over Gaussian multiple-access channels

A sensor network is used for distributed signal-to-noise ratio (SNR) estimation in a single-time snapshot. Sensors observe a signal embedded in noise, and each observation is phase modulated using a constant-modulus scheme and transmitted over a Gaussian multiple-access channel to a fusion center. At the fusion center, the mean and variance are estimated jointly, using an asymptotically minimum-variance estimator. It is shown that this joint estimator decouples 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. The estimators are evaluated in terms of asymptotic variance, which are then used to evaluate the performance of the SNR estimator with Gaussian and Cauchy sensing noise distributions in the cases of total transmit power constraint as well as a per-sensor power constraint. For each sensing noise distribution, the optimal phase transmission parameters are also determined. The asymptotic relative efficiency of the 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.