Distributed estimation over binary symmetric channels in wireless sensor networks

The problem of estimating an unknown parameter in wireless sensor networks with a fusion centre (FC) is studied. Each sensor observation is quantised as a result of the bandwidth constraint and then each quantised observation is transmitted to the FC over a binary symmetric channel (BSC). Under this setting, some estimators have been proposed but the maximum likelihood estimator (MLE) as well as the impact of the parameters of BSCs on the estimation performance are rarely considered. Assuming that the same one-bit quantiser is adopted at every sensor, the MLE and the Cramér - Rao lower bound (CRLB) are derived based on the quantised observations transmitted over BSCs. The impact of the capacity and the crossover probability of BSCs on the performance of the MLE and the CRLB are highlighted. The results reveal that the capacity of BSCs greatly influences both the performance of the MLE and the CRLB. It is also shown that both the performance of the MLE and the CRLB have the symmetric property with respect to the crossover probability of BSCs.