Collision-aware distributed detection with population-splitting algorithms

We consider the design of distributed detection algorithms for single-hop, single-channel wireless sensor networks in which sensor nodes send their local decisions to a fusion center (FC) by using a random access protocol. There is also limited time to collect local decisions before a final decision must be made. We thus propose and analyze a modified random access protocol in which the FC combines slotted ALOHA with a population-splitting algorithm called population-splitting-based random access (PSRA) and collision-aware distributed detection according to an estimate-then-fuse approach. Under the PSRA, only sensor nodes whose observations fall in a particular range of reliability will send their decisions in a specific frame by using slotted ALOHA. At the end of the collection time, the FC applies the collision-aware distributed detection to make a final decision. Here, the FC will first observe the state of each time slot—idle, successful, collision—in each frame, use this information to estimate the number of sensor nodes participating in each frame, and, then, compute a final decision using a population-based fusion rule. An approximation of the optimal transmission probability of the slotted ALOHA is determined to minimize the probability of error. Numerical results show that, unlike slotted-ALOHA-based data networks, the transmission probability maximizing the number of successful time slots does not optimize the performance of the proposed distributed detection. Instead, the proposed distributed detection performs best with a transmission probability that induces many collisions.