M-ary Distributed Decision Fusion for Multihop Relay Wireless Sensor Networks: Decision Fusion Rule, Implementation Framework, and Performance Analysis

The M-ary distributed decision fusion is studied for multihop amplify-and-forward wireless sensor networks (WSNs), the implementation framework is given, and the performance analysis is developed. In particular, we first propose an M-ary distributed decision fusion configuration, wherein the multihop relay network is involved, and the relay node only forward information from their neighbors. Furthermore, the optimal decision rule with the explicit and exact form is derived, and the implementation structure is depicted. Our results show that, the hamming distance (HD), which is well-known in information theory, is finally involved in the optimal decision metric. Then, we derive the suboptimal decision fusion algorithms for three scenarios. First, we achieve an interesting rule in the form of a maximum ratio combining (MRC), wherein the local channel is considered to be ideal. When the idea of equal gain combining (EGC) is directly followed, we propose the minimum HD summation (MHDS) rule. We also give a selective combining (SC) statistic, wherein only received observation with the optimal quality is selected for decision fusion, and we correspondingly term this criterion as the minimum HD (MHD) rule. Second, we achieve a Chair–Varshney rule when it is assumed that the crossover probability of relay binary symmetric channel (BSC) is small enough. The simple majority-based statistic is developed when the homogeneous multihop relay WSNs is considered. A statistic with the similar form of SC is also developed. Third, when each relay BSC’s crossover probability is relatively large, we also propose the suboptimum fusion statistic in an analog form to the MRC and EGC, respectively. Our results show that the MHDS rule can be achieved via optimum decision rule in the first or third scenarios. The performance assessment is determined both Monte Carlo simulation and analysis.