Bayesian Fusion Performance and System Optimization for Distributed Stochastic Gaussian Signal Detection Under Communication Constraints

The problem of decentralized detection and fusion of a Gaussian signal is considered under the assumption of analog relay-amplifier local processing. It is shown that under an average global (system) power constraint, there always exists an optimal number of nodes that achieves the best possible performance under both orthogonal and nonorthogonal sensor-to-fusion center communication. Any increase in the number of nodes beyond the optimal value leads to degraded performance. This implies that each node needs to maintain a certain minimum received power level at the fusion center in order to make a useful contribution to the final decision. This is contrasted with the monotonic performance improvement observed under individual node power constraints as well as in the case of deterministic signal detection under a global power constraint. Three communication scenarios are studied in detail: 1) orthogonal; 2) equicorrelated; and 3) random signaling waveforms. In each case, error exponents and resulting bounds for Bayesian fusion performance are derived. A sensor system optimization method based on Bhattacharya error exponent, that leads to simple rules for determining the optimal number of nodes under a global average power constraint is also proposed