A Low Communication Rate Scheme for Distributed Detection

In a practical distributed detection application a large number of resolution cells are continually being tested. A key observation is that most resolution cells will be empty and obviously so, and hence transmission, depending on the coarseness of quantization either of many local "no" decisions or of low-valued local likelihood ratios, is wasteful both of communication bandwidth and of fusion center attention. Here we consider a new scheme based on a "send/no-send" idea. The local sensors are assumed to "censor" their observations such that data about a cell deemed (locally) to be uninformative is simply not transmitted. The main result is that with conditionally-independent sensor data and under a communication rate constraint, in order to minimize the probability of error, transmission should occur if and only if the local likelihood ratio value observed by the sensor does not fall in a single interval. With an appropriate redefinition of the average communication rate, a similar result can be derived under the Neyman-Pearson criterion. For low prior probabilities of a target's presence in a given resolution cell, generally the most applicable case (and also, by symmetry, the case of a prior probability close to unity), the degradation in performance as measured against centralized decision-making is generally insignificant.