Optimality of Rate Balancing in Wireless Sensor Networks

TL;DR

This paper investigates the optimality of rate balancing in distributed binary hypothesis testing within wireless sensor networks, especially when the number of sensors is limited and the sum rate constraint is considered.

Contribution

It extends previous work by providing conditions under which rate balancing is optimal when sensors are limited, not necessarily matching the sum rate constraint.

Findings

Rate balancing is optimal under certain conditions.

Explicit models satisfy the sufficient conditions.

Analysis extends to practical sensor network scenarios.

Abstract

We consider the problem of distributed binary hypothesis testing in a parallel network topology where sensors independently observe some phenomenon and send a finite rate summary of their observations to a fusion center for the final decision. We explicitly consider a scenario under which (integer) rate messages are sent over an error free multiple access channel, modeled by a sum rate constraint at the fusion center. This problem was previously studied by Chamberland and Veeravalli, who provided sufficient conditions for the optimality of one bit sensor messages. Their result is however crucially dependent on the feasibility of having as many one bit sensors as the (integer) sum rate constraint of the multiple access channel, an assumption that can often not be satisfied in practice. This prompts us to consider the case of an a-priori limited number of sensors and we provide sufficient condition under which having no two sensors with rate difference more than one bit, so called rate balancing, is an optimal strategy with respect to the Bhattacharyya distance between the hypotheses at the input to the fusion center. We further discuss explicit observation models under which these sufficient conditions are satisfied.