  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 the 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 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 is shown
to not affect the consistency of the estimator, but to scale the asymptotic
variance by a constant fading penalty depending on the fading statistics.
Simulations corroborate our analytical results.
