Optimal Sensor Rules and Unified Fusion Rules for Multisensor Multi-hypothesis Network Decision Systems with Fading Channels

In this paper, we firstly present optimal sensor rules with fading channel for a given fusion rule, in which sensor observations are not necessarily independent of each other. Then as a preliminary result to solve the unified fusion rule problem for multisensor multi-hypothesis network decision systems with fading channels, we propose the unified fusion rule for a specific l sensors parallel binary Bayesian decision system under assumption that the ith sensor is required to transmit a certain number ri of bits via fading channel while the fusion center can receive its own observation. Since the communication pattern at every node including the fusion center in the multisensor multi-hypothesis decision network are the same as the above parallel binary Bayesian decision system, the above unified fusion rule results can be extended appropriately to more general multisensor multi-hypothesis network decision systems with fading channels, such as the tandem and tree network. More precisely speaking, for these network decision systems, a unified fusion rule is proposed. People only need to optimize sensor rules under the proposed unified fusion rule to achieve global optimal decision performance. More significantly, the unified fusion rule does not depend distributions of sensor observations, decision criterion, and the characteristics of fading channels.Finally, several numerical examples support the above analytic results and show a interesting phenomenon that the two points (0, 0) and (1, 1) may not be the beginning and end points of ROCs when all channels are fading channels, while in ideal channel case they are the start and end.