Optimal sensor power control via a correlated block fading channel

This paper considers the scenario that a power-limited sensor transmits the states of a physical plant to a remote estimator through a correlated block fading communication channel. From the perspective of the system operator, it is of importance to design a proper sensor power control strategy to gain desirable state estimation quality at the remote estimator side and save the power cost at the sensor side concurrently. To achieve this objective, an optimization problem is constructed to minimize the weighted sum of the average remote estimation error and the average power cost in an infinite time horizon. Then a Markov decision process framework is adopted to show that the optimal sensor power control strategy exists. Unfortunately, owing to an implicit part existing in its expression, the optimal solution cannot be used directly. In order to approximate the optimal solution, we derive the analytical expression of optimal solution when the sensor power control policy is restrained. Drawing support from it, we present a suboptimal power control strategy with the explicit expression. Finally, a simulation example is presented to demonstrate the effectiveness of our proposed sensor power control strategy.