Distributed estimation with constant modulus signals over multiple access channels

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. When the distributions of the sensing noise are not identical, the existence of a bound on the variances is shown to establish strong consistency. The estimator is shown to be asymptotically normal with an asymptotic 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, and simulations are shown to corroborate our analytical results.