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