Decision fusion for multi-route and multi-hop Wireless Sensor Networks over the Binary Symmetric Channel

Abstract

The decision fusion for multi-route and multi-hop Wireless Sensor Networks (WSNs) is studied, wherein a discrete memoryless channel model, i.e., the Binary Symmetric Channel (BSC), is considered to characterize the relay transmission of each hop from the local sensor to the fusion center. In particular, we first develop the optimal log-likelihood ratio (LLR) based decision fusion rule, wherein the fusion center is assumed to have perfect knowledge of both the local sensor performance indices and the Channel State Information (CSI), i.e., crossover probability for each BSC. Secondly, we derive the suboptimum and robust fusion rules for two cases. In the first case, channel condition from the source to the local sensor is considered to be ideal. In the second case, the crossover probability for each BSC is assumed to be relatively large or small. Our result show that our suboptimum fusion detectors require less or no a priori information about crossover probability and/or the local sensor performance indices, and thus are easy to implement. We also show that the simple decision fusion statistic, i.e., the counting-based statistic, can be directly derived from the optimal LLR-based statistic for both cases. These suboptimum fusion rules are clearly desired for applications, wherein perfect estimation of the local sensor performance and CSI is complexity-intensive or unachievable. Furthermore, the optimal LLR-based scheme for joint decision fusion and CSI estimation is proposed. We uniformly quantize the equivalent crossover probability into discrete status, and thus give a suboptimum but more computationally practical scheme. The performance evaluation is finally developed both analytically and through simulation.