Decentralized estimation over orthogonal multiple-access fading channels in wireless sensor networks--optimal and suboptimal estimators

Abstract

We study optimal and suboptimal decentralized estimators in wireless sensor networks over orthogonal multipleaccess fading channels in this paper. Considering multiple-bit quantization for digital transmission, we develop maximum likelihood estimators (MLEs) with both known and unknown channel state information (CSI). When training symbols are available, we derive a MLE that is a special case of the MLE with unknown CSI. It implicitly uses the training symbols to estimate CSI and exploits channel estimation in an optimal way and performs the best in realistic scenarios where CSI needs to be estimated and transmission energy is constrained. To reduce the computational complexity of the MLE with unknown CSI, we propose a suboptimal estimator. These optimal and suboptimal estimators exploit both signal-and data-level redundant information to combat the observation noise and the communication errors. Simulation results show that the proposed estimators are superior to the existing approaches, and the suboptimal estimator performs closely to the optimal MLE.

The Effect of Correlated Observations on the Performance of Distributed Estimation

“…The estimated signal quality is limited by both the imperfect observations (correlation model and noise) and the channel variations (fading and noise) as shown in (10). In this section, we explore the effect of the different correlation models on the estimation distortion.…”

“…The corresponding distortion becomes (9) The normalized distortion is then given by (10), shown at the bottom of the next page. Hereafter, we will refer to the normalized distortion simply as distortion for short.…”

“…Depending on the available information at the FC about the source statistics, different estimators can be used to achieve the MSE criterion. The Best Linear Unbiased Estimation (BLUE) [5], [6], Minimum Mean Squared Error (MMSE) estimator [7], [8], and Maximum Likelihood Estimator (MLE) [9], [10] are studied in literature. For these different estimators, both orthogonal MAC [11]- [13] and coherent MAC [14], [15] are considered for the distributed estimation problem.…”

On the effect of correlated measurements on the performance of distributed estimation

“…Depending on the available information about the source statistics, different estimators can be used to achieve the MSE criterion. The performance of the Best Linear Unbiased Estimation (BLUE) [3], Minimum Mean Squared Error (MMSE) estimator [4], [5], and Maximum Likelihood Estimator (MLE) [6], [7] are studied in literature. Both orthogonal MAC [8] and coherent MAC [9], [10] are considered in the distributed estimation problem.…”