On the optimality of finite-level quantizations for distributed signal detection

Distributed multisensor detection problems with quantized observation data are investigated for cases of nonbinary hypotheses. The observations available at each sensor are quantized to produce a multiple-bit sensor decision which is sent to a fusion center. At the fusion center, the quantized data are combined to form a nal decision using a predetermined fusion rule. Firstly, the necessary conditions for Bayes optimum sensor decision rules are described. Then it is demonstrated that there is a maximum number of bits that should be used to communicate the sensor decision from a given sensor to the fusion center. This maximum is based on the number of bits used to communicate the decisions from all the other sensors to the fusion center. If more than this maximum number of bits is used, the performance of the optimum scheme will not be improved. In some special cases of great interest, the bound on the number of bits that should be used can be made signiicantly smaller. Finally, the optimum way to distributed a xed number of sensor decision bits across the sensors is described for two-sensor cases. Illustrative numerical examples are presented at the end of this paper.