Distributed Detection in Wireless Sensor Networks Using A Multiple Access Channel

Distributed detection in a one-dimensional (1-D) sensor network with correlated sensor observations, as exemplified by two problems-detection of a deterministic signal in correlated Gaussian noise and detection of a first-order autoregressive [AR(1)] signal in independent Gaussian noise, is studied in this paper. In contrast with the traditional approach where a bank of dedicated parallel access channels (PAC) is used for transmitting the sensor observations to the fusion center, we explore the possibility of employing a shared multiple access channel (MAC), which significantly reduces the bandwidth requirement or detection delay. We assume that local observations are mapped according to a certain function subject to a power constraint. Using the large deviation approach, we demonstrate that for the deterministic signal in correlated noise problem, with a specially chosen mapping rule, MAC fusion achieves the same asymptotic performance as centralized detection under the average power constraint (APC), while there is always a loss in error exponents associated with PAC fusion. Under the total power constraint (TPC), MAC fusion still results in exponential decay in error exponents with the number of sensors, while PAC fusion does not. For the AR signal problem, we propose a suboptimal MAC mapping rule which performs closely to centralized detection for weakly correlated signals at almost all signal-to-noise ratio (SNR) values, and for heavily correlated signals when SNR is either high or low. Finally, we show that although the lack of MAC synchronization always causes a degradation in error exponents, such degradation is negligible when the phase mismatch among sensors is sufficiently small