Power Control for Multi-sensor Remote State Estimation over Interference Channel

In this paper, we investigate a multi-sensor transmission power control problem for remote state estimation over interference channel. Assume that there are N sensors, which measure a dynamic process in a networked system at the same time, and send their measurements to a remote state estimator for data fusion through a shared packet-dropping channel. Since the communication process of each sensor may be affected by the interference power from other sensors, we consider a signal-to-interference-and-noise-ratio (SINR)-based channel model to describe the simultaneous transmission process. As such, the transmission power used by different sensors needs to be jointly designed to achieve an optimal state estimation performance. We formulate such a power control problem into a stochastic programming problem, and obtain its certainty-equivalent problem to tackle the difficulties brought by the implicit expression of the objective function and the non-linearity/non-convexity of the original problem. Then, a sub-optimal solution to the optimal power control problem is obtained by solving a standard convex optimization problem. An event-based power controller and a heuristic power controller are also provided. We also discuss the power control problem with a threshold-based channel model. Performance analysis of the sub-optimal controller and the comparison with other power controllers are demonstrated.