Distributed estimation using binary data transmitted over fading channels

We study the parametric distributed estimation problem using a wireless sensor network (WSN) where each sensor observes an unknown scalar parameter, quantizes its observation and sends its quantized observation to a fusion center via fading and noisy communication channels. We propose to incorporate channel statistics rather than the instantaneous channel state information (CSI) into the maximum likelihood (ML) formulation and show that the resulting likelihood function is strictly log-concave almost surely with a change of variable provided that at least one of the communication channels between the sensors and the fusion center has nonzero capacity. We also investigate the effects of channel layer on the sensor threshold design and show that the threshold design problem is coupled with the channel layer and the sensor signal-to-noise ratio (SNR) only for nonsymmetric channels. Our formulation is very general in the sense that no assumptions are made about the physical layer in terms of the modulation schemes and the reception techniques.