Asymptotic optimality of likelihood ratio threshold tests in decentralized detection

Two distributed systems are considered for discriminating between two finite-alphabet bivariate memoryless sources and for detecting a known signal in stationary bivariate additive Gaussian noise. Each system comprises two sensors, M-ary local quantizers and a fusion center which makes decisions based on quantized source observations. The problem of asymptotically optimal quantization is considered in detail for the binary (M=2) case. It is shown that optimality is achieved by quantizing a locally computed likelihood ratio wherein one distribution is in general different from the appropriate source marginal. For the problem of detection in Gaussian noise, it is further demonstrated that the optimal distributed system attains the same asymptotic performance as the optimal centralized system for appropriate choice of M