Energy-Efficient Estimation of Correlated Data in Wireless Sensor Networks

In this paper, we study the energy-efficient distributed estimation problem for a wireless sensor network where a physical phenomena that produces correlated data is sensed by a set of spatially distributed sensor nodes and the resulting noisy observations are transmitted to a fusion center via noise-corrupted channels. We assume a Gaussian network model where (i) the data being sensed at different sensors are correlated and the correlation structure (in the form of a correlation matrix) is known at the fusion center, (ii) the links between the local sensors and the fusion center are subject to multipath fading plus AWGN, and the fading gains are available to the receiver node, and (iii) the central node uses the squared error distortion metric. We first determine the optimum power-distortion regions assuming (i) a multiple-letter, and (ii) a single-letter square distortion characterization. Next, for the two distortion characterization, we investigate the performance of an uncoded transmission approach where the noisy observations are only amplified-and-forwarded to the fusion center. At the fusion center, two different estimators are considered: (i) minimum mean-square error estimator (MMSE) that exploits the correlation, and (ii) best linear unbiased estimator (BLUE) that does not require or exploit the knowledge of the correlation matrix. For both estimators, we solve for the optimal power allocation that results in a minimum total transmission power while satisfying some distortion level for the estimate (for both multiple-letter and single-letter distortion metrics). The numerical comparisons between the two schemes indicate that the MMSE requires less power to attain the same distortion provided by the BLUE. Furthermore, comparisons between power-distortion region achieved by the theoretically optimum system and the uncoded system indicates that the performance gap between the two system becomes small for low level of correlation between the sensor observations. If observations at all sensor nodes are uncorrelated, the uncoded system attains the theoretically optimum system performance.