Decision fusion rules in multi-hop wireless sensor networks

The decision fusion problem for a wireless sensor network (WSN) operating in a fading environment is considered. In particular, we develop channel-aware decision fusion rules for resource-constrained WSNs where binary decisions from local sensors may need to be relayed through multi-hop transmission in order to reach a fusion center. Each relay node employs a binary relay scheme whereby the relay output is inferred from the channel impaired observation received from its source node. This estimated binary decision is subsequently transmitted to the next node until it reaches the fusion center. Under a flat fading channel model, we derive the optimum fusion rules at the fusion center for two cases. In the first case, we assume that the fusion center has knowledge of the fading channel gains at all hops. In the second case, we assume a Rayleigh fading model, and derive fusion rules utilizing only the fading channel statistics. We show that likelihood ratio (LR) based optimum decision fusion statistics for both cases reduce to respective simple linear test statistics in the low channel signal-to-noise ratio (SNR) regime. These suboptimum detectors are easy to implement and require little a priori information. Performance evaluation, including a study of the robustness of the fusion statistics with respect to unknown system parameters, is conducted through simulations.