Distributed parameter estimation in wireless sensor networks in the presence of fading channels and unknown noise variance

Parameter estimation is one of the most important research areas in wireless sensor networks. In this study, we consider the problem of estimating a deterministic parameter over fading channels with unknown noise variance. Owing to the bandwidth constraints in wireless sensor networks, sensor observations are quantized and subsequently transmitted to the fusion center. Two types of communication channels are considered, namely, parallel-access channels and multiple-access channels. Based on the knowledge of channel statistics, the power of the received signals at the fusion center can be described by the mode of the exponential mixture distribution. The expectation maximization algorithm is used to determine maximum likelihood solutions for this mixture model. A new estimator based on the expectation maximization algorithm is subsequently proposed. Simulation results show that this estimator exhibits superior performance compared to the method of moments estimator in both parallel- and multiple-access schemes. In addition, we determine that the parallel-access scheme outperforms the multiple-access scheme when the noise variance is small and it loses its superiority when the noise variance is large.