Jointly optimal transmission power control and remote estimation over aninfinite horizon is studied. A sensor observes a dynamic process and sends itsobservations to a remote estimator over a wireless fading channel characterizedby a time-homogeneous Markov chain. The successful transmission probabilitydepends on both the channel gains and the transmission power used by thesensor. The transmission power control rule and the remote estimator should bejointly designed, aiming to minimize an infinite-horizon cost consisting of thepower usage and the remote estimation error. A first question one may ask is:Does this joint optimization problem have a solution? We formulate the jointoptimization problem as an average cost belief-state Markov decision processand answer the question by proving that there exists an optimal deterministicand stationary policy. We then show that when the monitored dynamic process isscalar, the optimal remote estimates depend only on the most recently receivedsensor observation, and the optimal transmission power is symmetric andmonotonically increasing with respect to the innovation error.
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