Sensor System Optimization for Bayesian Fusion of Distributed Stochastic Signals Under Resource Constraints

Recently there has been a significant interest in distributed detection and data fusion with analog-relay amplifier local processing under a global power constraint. In particular, it was shown in S.K. Jayaweera (2005) that the optimal fusion performance for a distributed stochastic signal detection is achieved by a finite number of sensors. In this paper, we propose a sensor system optimization method based on the Bhattachrya error exponent. In addition to the global power constraint we also consider the case in which the total available bandwidth may also be limited. Assuming an equi-correlated signalling model we derive the error exponents to the Bayesian fusion performance for asymptotically large systems. Again we optimize the sensor system size based on the Bhattacharya error exponent and provide simple rules that are valid for either the low or high observation SNR regimes