Efficient distributed estimators in wireless sensor networks

The problem of distributed estimation of an unknown parameter in noise is revisited. To meet the stringent bandwidth and energy constraints in practical wireless sensor network (WSN) applications, a one-bit quantization scheme is adopted to compress local sensor observations. Imperfect communication between local sensors and the fusion center is considered and modeled as a flat fading channel. Due to its simple form and practicality for WSN applications, in this paper, we consider linear estimators and derive the optimal form, i.e., the linear minimum variance unbiased estimator (LMVUE). This estimator turns out to be the average received signal power normalized by the average channel power gain, which does not require channel state information or channel estimation. It achieves near MLE performance especially for relatively low channel SNR. To further improve the performance in the high SNR regime, a two-step estimator which decodes the transmitted information bits before estimation is also proposed. It can be shown that for relatively high channel SNR, this estimator based on the average of decoded signals achieves near MLE performance.