one time frame to another, whereas the amount of energy demanded, $p(i)$, is a stochastic process[^4], and its parameters[^5] are pre-determined by the transmitter. When setting $p(i)$, the transmitter regards certain constraints and performance requirements, e.g., energy overflow and outage probability constraints, which will be defined below. The energy level in the battery at the end of the $i^{\text{th}}$ time frame, denoted by $e(i)$, $i\in\mathbb{Z}^{+}$, is governed by the following update rule: $$\label{actual_capacity_2}
e(i)=\min\{[e(i-1)+u(i)-p(i)]^{+},e_{\max}\},$$ where $[\cdot]^{+}\triangleq\max\{0,\cdot\}$, $e_{\max}$ denotes the battery capacity, and $e(0)$ is the initial energy level of the battery. As seen from (\[actual\_capacity\_2\]), the energy harvested in the $i^{\text{th}}$ time frame, $u(i)$, is ready for consumption in the same time frame. If $e(i-1)+u(i)-p(i)>e_{\max}$, we will have an *energy overflow* in the $i^{\text{th}}$ time frame, wasting some of the harvested energy. On the other hand, when $e(i-1)+u(i)<p(i)$, we will have an *energy outage*.

While $p(i)$ is the rate of the energy demanded by the transmitter, the battery may not be always able to provide energy at this level. When there is enough energy in the battery, i.e., $e(i-1)+u(i)\geq p(i)$, the battery satisfies the energy demand completely. Otherwise, the battery provides what is left in it for the transmission of 