Joint power scheduling and estimator design for sensor networks across parallel channels

This paper addresses the joint estimator and power optimization problem for a sensor network whose mission is to estimate an unknown parameter. We assume a two-hop network where each sensor collects observations from the source that transmits the quantity to be estimated, then amplifies and forwards its observations to a fusion center. The fusion center combines the observations using a Linear Minimum Mean Squared Error (LMMSE) estimator. We study the scenario where multiple parallel channels are available between the source and each sensor as well as between the sensors and the fusion center. We find the global optimal power allocation and estimator design for this network model. We present two practical scenarios of interest that utilize spatial and temporal diversity for which this solution applies, namely, a clustered network model and a single cluster model with an ergodic fading channel.