Type-Based Decentralized Detection in Wireless Sensor Networks

Abstract

Distributed detection strategies for wireless sensor networks are studied under the assumption of spatially and temporally independent and identically distributed (i.i.d.) observations at the sensor nodes. Both intelligent (with knowledge of observation statistics) and dumb (oblivious of observation statistics) sensors are considered. Two types of communication channels are studied: a parallel access channel (PAC) in which each sensor has a dedicated additive white Gaussian noise (AWGN) channel to a decision center, and a multiple-access channel (MAC) in which the decision center receives a coherent superposition of the sensor transmissions. Our results show that the MAC yields significantly superior detection performance for any network power constraint. For intelligent sensors, uncoded (finite duration) communication of local log-likelihood ratios over the MAC achieves the optimal error exponent of the centralized (noise-free channel) benchmark as the number of nodes increases, even with sublinear network power scaling. Motivated by this result, we propose a distributed detection strategy for dumb sensors-histogram fusion-in which each node appropriately quantizes its temporal data and communicates its type or histogram to the decision center. It is shown that uncoded histogram fusion over the MAC is also asymptotically optimal under sublinear network power scaling with an additional advantage: knowledge of observation statistics is needed only at the decision center. Histogram fusion achieves exponential decay in error probability with the number of nodes even under a finite total network power. In principle, a vanishing error probability at a slower subexponential rate can be attained even with vanishing total network power in the limit. These remarkable power/energy savings with the number of nodes are due to the inherent beamforming gain in the MAC