Optimal power allocation for an energy harvesting estimation system

Optimal transmit power allocation strategies are proposed for an energy harvesting estimation system, where energy can be harvested from the environment and buffered in a battery for future use. With the aim of minimizing the mean squared error at the receiver, two types of side information (SI) available to the transmitter are considered: causal SI (energy harvested in the past) and non-causal SI (energy harvested in the past, present and future). For the case where non-causal SI is available and battery storage is unlimited, it is shown that the optimal power allocation can be attained by a simple water-filling-like procedure, where the water level follows a non-decreasing staircase function. Dynamic programming is used to optimize the allocation policy when causal SI is available. The issue of unknown transmit power at the receiver is also addressed.