Multi-bit Distributed Decision Fusion Rules for Multi-hop Multi-relay Wireless Sensor Networks

The multi-bit distributed decision fusion rules for the multi-hop multi-relay Wireless Sensor Networks (WSNs) is investigated. Specifically, the binary information of interest is observed and quantized into multi-bit data at the local sensor and then received by the fusion center through multi-relay forwarding. We first give the optimal fusion rule using the log-likelihood ratio (LLR), which involves the instantaneous channel state information (CSI) and the Hamming distance between the received signal and all multi-bit quantized signals. Secondly, we give three suboptimal decision fusion methods, each characterized by lower complexity. Our results suggest that the dependence of the optimal fusion rule and the instantaneous CSI can be relaxed. Our results also suggest that the simplified suboptimal fusion rule is only related to the Hamming distance between the signal received and the source quantization signal when the local channel is ideal or the signal-to-noise ratio (SNR) of the relay channel is low. Moreover, when the SNR of the relay channel is high, the fusion center only needs the detection probability and false alarm probability of the local sensor to complete the extraction of the fusion statistics, which make the fusion rule to be easy to implement. In addition, we have provided the exact expression for the detection error probability (DEP) when the quantization degree is set to 2. The final simulation results are consistent with the performance analysis.