Universal Distributed Estimation Over Multiple Access Channels With Constant Modulus Signaling

A distributed estimation scheme where the sensors transmit with constant modulus signals over a multiple access channel is considered. The proposed estimator is shown to be strongly consistent for any sensing noise distribution in the i.i.d. case both for a per-sensor power constraint, and a total power constraint. When the distributions of the sensing noise are not identical, a bound on their variances is shown to establish strong consistency. The estimator is shown to be asymptotically normal with a variance ( AsV) that depends on the characteristic function of the sensing noise. Optimization of the AsV is considered with respect to a transmission phase parameter for a variety of noise distributions exhibiting differing levels of impulsive behavior. The robustness of the estimator in the sense of degrading gracefully when the sensing noise deviates from the Gaussian distribution to impulsive sensing noise distributions such as those with positive excess kurtosis, or those that do not have finite moments is shown. The proposed estimator is favorably compared with the amplify and forward scheme under an impulsive noise scenario. The effect of fading and phase error at the sensors are shown to not affect the consistency of the estimator, but to degrade the asymptotic variance by terms that depend on the fading and phase error distributions. Simulations corroborate our analytical results.