New error bounds and optimum quantization for multisensor distributed signal detection

The binary signal detection problem is considered, when a distributed system of sensors operates in a decentralized fashion. Local processing at each sensor is performed. Using Chernoff´s large deviation theorems, the author considers as a criterion the rate of convergence of the error probability to zero. It is shown that the optimum quantizer of blocks of data under the above criterion is the likelihood ratio quantizer. A lower bound to the error probability is also developed. The question of how many coarsely quantized sensors can replace the infinitely quantized one is also answered. The main result given is the structure of the optimum quantizer, consisting of the calculation of the likelihood ratio concatenated by a scalar quantizer