Correlated observations in distributed detection systems

We consider parallel binary distributed detection in a wireless sensor network, in which sensors send their binary phase shift keying (PSK) modulated decisions to the fusion center (FC) over communication channels, that are subject to Rayleigh fading and noise. The FC is tasked with detecting the presence of a Gaussian signal source. When it is present, sensors´ observations are spatially correlated samples of the signal source, corrupted by Gaussian noises. Using identical energy detectors as local decision rules, we derive a linear fusion rule that combines likelihood ratios of received signals at the FC and maximizes modified deflection coefficient. Our numerical results show that at high signal-to-noise (SNR) regime, this rule outperforms the linear fusion rule which only combines the outputs of wireless communication channels.