Distributed consensus in wireless sensor networks with quantized information exchange

In this paper we analyze the impact of quantization on the performance of a discrete-time distributed algorithm aimed at computing the average of an initial set of values in a wireless sensor network. We modify a well-known consensus model and propose a simple scheme where the transmitted data is quantized due to bandwith and/or power constraints. Conversely to existing models that include quantization noise, a closed-form expression for the residual mean square error of the state can be derived for the proposed model. This expression depends on general network parameters and provides therefore an a priori quantitative measure of the effects of quantization on the consensus.