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

Distributed multiple sensor detection problems with quantized observations are investigated for cases of nonbinary hypothesis and possibly statistically dependent observations from sensor to sensor conditioned on the hypothesis. The observations available at each sensor are quantized to produce a multiple digit sensor decision which is sent to a fusion center. At the fusion center, the sensor decisions are combined to form a final decision using a predetermined fusion rule. First, it is demonstrated that there is a maximum number of digits 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 digits used to communicate the decisions from all the other sensors to the fusion center. If more than this maximum number of digits is used, the performance of the optimum scheme will not be improved. In some special cases of great interest, the upper bound on the number of digits that should be used can be made significantly smaller. Secondly, the optimum way to allocate a fixed overall number of digits across sensors is investigated. Illustrative numerical results are also presented in this correspondence.