Reliability-Based Splitting Algorithms for Time-Constrained Distributed Detection in WSNs

We consider distributed detection applications for a fusion center that has a limited time to collect, weight and fuse local decisions to produce a global decision in a wireless sensor network that uses a random access protocol. When this time is not long enough to collect decisions from all nodes in the network, a strategy is needed for collecting those with the highest reliability. This is accomplished by incorporating a reliability-based splitting algorithm into the random access protocol: the collection time is divided into frames and only nodes with a specified range of reliabilities compete for the channel within each frame. Nodes with the most reliable decisions attempt transmission in the first frame; nodes with the next most reliable set of decisions attempt in the next frame; etc. To ensure that the results we derive are lower bounds on the detection performance that would be seen in practice, the local decisions that arrive within a frame are assigned the smallest reliability in the range associated with that frame. Two performance measures are used: Detection Error Probability (DEP) and Asymptotic Relative Efficiency (ARE) of the proposed scheme relative to a TDMA-based scheme. We then show how to minimize the DEP by determining the reliability intervals that define which nodes attempt to transmit in each frame. Intervals that maximize the channel throughput will often, but not always, minimize the DEP of the proposed scheme. Necessary conditions for the optimality of the maximum throughput intervals are thus derived. Numerical results indicate that these conditions are often sufficient when the observation noise is Gaussian. From the ARE, we determine when the proposed scheme asymptotically outperforms a TDMA-based scheme.