Joint Power Allocation for Remote State Estimation With SWIPT

In this paper, we consider remote state estimation with simultaneous wireless information and power transfer (SWIPT). A remote estimator receives the state estimate transmitted by a sensor and sends an acknowledgment (ACK) signal to the sensor via a feedback wireless channel. The sensor has no other energy supply except that it can harvest wireless energy from the received ACK signal, which carries information and energy simultaneously. Since the symbol error rate of the state estimate transmitted by the sensor depends on the sensor's transmission power allocation, there exists a tradeoff between the accuracy of the state estimate received by the remote estimator and the transmission power consumption of the sensor. Moreover, the sensor's transmission power is restricted by the remaining energy level in its battery, which is decided by the amount of the harvested wireless energy. Therefore, we jointly optimize the transmission power allocation of the remote estimator and the sensor and formulate the optimization problem into an infinite time-horizon average cost Markov decision process (MDP). We first prove the existence of the optimal stationary power allocation policy, and then present the monotonic structures of the optimal policy. Simulation results are provided to verify and illustrate the main results.