Joint optimization of communication scheduling and online power allocation in remote estimation

This paper studies a specific sequential decision making problem: joint optimization of power and communication decisions of a remote estimation problem over an additive noise channel. At each time, the sensor observes a sample from a one-dimensional stochastic process, and then decides whether to transmit its observation to the remote estimator or not, which takes place over an additive noise channel. The number of transmissions and the total power spent over a finite horizon are limited. If the sensor decides to transmit its observation, it sends the observation to the encoder. The encoder then sends an encoded message to the remote estimator over the communication channel. The remote estimator generates real time estimates on the source based on the information received from the encoder over the channel. While the prior work considered the average power case, we are interested here in a more general setting where the encoder has a constraint on the total encoding power over the time horizon, and hence can optimize power jointly, in a closed loop fashion, with the communication decisions. Under some technical assumptions, we obtain team optimal decision policies including threshold-based communication scheduling policies together with affine encoding and decoding policies. We demonstrate the effectiveness of our joint optimization approach via numerical computations.