Distributed Detection of A Deterministic Signal in Correlated Gaussian Noise Over MAC

Distributed detection of a deterministic signal in correlated Gaussian noise in a one-dimensional sensor network is studied in this paper. In contrast to 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 and transmitted simultaneously to the fusion center. Using a large deviation approach, we demonstrate that 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. Finally, we derive an upper bound on the performance loss due to the lack of perfect synchronization over MAC, and show that the performance degradation is negligible when the phase mismatch among sensors is sufficiently small