Distributed estimation based on measurements from multiple wireless sensors is investigated. It is assumed that a group of sensors observe the same quantity in independent additive observation noises with possibly different variances. The observations are transmitted using amplify-and-forward (analog) transmissions over nonideal fading wireless channels from the sensors to a fusion center, where they are combined to generate an estimate of the observed quantity. Assuming that the best linear unbiased estimator (BLUE) is used by the fusion center, the equal-power transmission strategy is first discussed, where the system performance is analyzed by introducing the concept of estimation outage and estimation diversity, and it is shown that there is an achievable diversity gain on the order of the number of sensors. The optimal power allocation strategies are then considered for two cases: minimum distortion under power constraints; and minimum power under distortion constraints. In the first case, it is shown that by turning off bad sensors, i.e., sensors with bad channels and bad observation quality, adaptive power gain can be achieved without sacrificing diversity gain. Here, the adaptive power gain is similar to the array gain achieved in multiple-input single-output (MISO) multiantenna systems when channel conditions are known to the transmitter. In the second case, the sum power is minimized under zero-outage estimation distortion constraint, and some related energy efficiency issues in sensor networks are discussed.
Bibliographical noteFunding Information:
Manuscript received February 11, 2006; revised December 7, 2006. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Sergio Barbarossa. Part of this work was presented at the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)’05, Philadelphia, PA, March 18–23, 2005, and the International Conference on Communications (ICC)’06, Istanbul, Turkey, June 11–15, 2006. This research was supported in part by funds from the University of Arizona Foundation, the National Science Foundation under grants No. CCR-02-05214 and No. DMS-0312416, the U.S. Army MURI under award No. W911NF-05-1-0246, the Intel Corporation, and the DOD Army under grant No. W911NF-05-1-0567.
- Distributed estimation
- Energy efficiency
- Estimation diversity
- Estimation outage