Distortion minimization in multi-sensor estimation using energy harvesting and energy sharing

This paper investigates an optimal energy allocation problem for multisensor estimation of a random source where sensors communicate their measurements to a remote fusion center (FC) over orthogonal fading wireless channels using uncoded analog transmissions. The FC reconstructs the source using the best linear unbiased estimator (BLUE). The sensors have limited batteries but can harvest energy and also transfer energy to other sensors in the network. A distortion minimization problem over a finite-time horizon with causal and noncausal centralized information is studied and the optimal energy allocation policy for transmission and sharing is derived. Several structural necessary conditions for optimality are presented for the two sensor problem with noncausal information and a horizon of two time steps. A decentralized energy allocation algorithm is also presented where each sensor has causal information of its own channel gain and harvested energy levels and has statistical information about the channel gains and harvested energies of the remaining sensors. Various other suboptimal energy allocation policies are also proposed for reducing the computational complexity of dynamic programming based solutions to the energy allocation problems with causal information patterns. Numerical simulations are included to illustrate the theoretical results. These illustrate that energy sharing can reduce the distortion at the FC when sensors have asymmetric fading channels and asymmetric energy harvesting processes