Achievable distortion/rate tradeoff in a decentralized Gaussian parameter estimation problem

In this paper, we study the decentralized version of the classical rate constrained Gaussian parameter estimation problem referred to as the Central Estimation Officer (CEO) problem which we refer to as the Decentralized Estimation Officers (DEO) problem. Like in the CEO case, we consider a group of N sensors observing an independently corrupted version of an infinite i.i.d. sequence of samples from a Gaussian source, in additive Gaussian noise. Unlike the CEO case, the sensors in our study are also the estimation officers. They are uniformly deployed in a circular pattern of radius r and communicate over RF links with limited energy. Their task is to reconstruct the quantity of interest (the samples of the source), without a central fusion node, better than what they are capable of with their local observations. We find achievable scaling laws by structuring our communication protocol as an instance of the so called average consensus algorithm, a gossiping protocol used for averaging original sensor measurements via near neighbors communications. We derive how the Mean Squared Error (MSE) of the sensors' estimation scales with the network size, per node power and ring radius r. Moreover, we compare our results with scaling laws previously derived for the centralized case, i.e, the CEO problem in a comparable scenario.