Distributed Detection with Consulting Sensors and Communication Cost: The Gaussian Case

The problem of distributed detection with consulting sensors is formulated and solved when there is a communication cost associated with any exchange of information (consultation) between the sesnors. We consider a system of two sensors, S1 and S2, in which S1 is the primary sensor responsible for the final decision u0, while S2 is a consulting sensor capable of relaying its decision u2 to S1 when requested by S1. In the scenario that is considered, the final decicion u0 is based either on the raw data available to S1 only, or, it may, under certain request conditions, also take into account the decision u2 of sensor S2. Random and non-random request schemes have been analysed and numerical results for both request schemes are presented for a slowly fading Rayleigh channel.