PAC vs. MAC for Decentralized Detection Using Noncoherent Modulation

In decentralized detection, local sensor observations have to be communicated to a fusion center through the wireless medium, inherently a multiple-access channel (MAC). As communication is bandwidth- and energy-constrained, it has been suggested to use the properties of the MAC to combine the sensor observations directly on the channel. Although this leads to an array-processing gain if the sensors´ transmissions combine coherently on the channel, it has been shown that this is not the case when they combine noncoherently. We review known results for the coherent case and then analyze the noncoherent case based on a simple on/off scheme combined with optimal sensor ldquocensoring.rdquo Since the optimal forwarding function is not available, we also bound the performance using an equivalent communication problem and a centralized estimator to verify trends. We find that for noncoherent modulation, there is no processing gain using the MAC for decentralized detection, but compared to parallel-access channels (PACs) the MAC avoids the noncoherent combining loss. Still the performance of the MAC approach is only of diversity one, as the output of the MAC is approximately a zero-mean complex Gaussian random variable for a large number of sensor. The MAC performance can be increased by using multiple independent channels, each used as a MAC by all sensors, which we term diversity-MAC. This approach always outperforms the PAC scheme on Rayleigh fading channels, where the output is exactly Gaussian, but has inferior performance across random phase channels when few sensors are used, as the PAC does not create ldquoartificialrdquo fading.