# Robust Distributed Estimation over Multiple Access Channels with Constant Modulus Signaling

## TL;DR

This paper introduces a robust distributed estimation method over multiple access channels using constant modulus signals, which is consistent, asymptotically normal, and resilient to impulsive noise and fading effects.

## Contribution

It proposes a novel constant modulus signaling estimator that is strongly consistent under various noise distributions and optimizes asymptotic variance considering impulsive noise.

## Key findings

- Estimator is strongly consistent for i.i.d. noise
- Estimator remains consistent under non-identical noise variances
- Robust to impulsive noise and fading effects

## Abstract

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.