# RF Energy Harvesting Wireless Communications:
## 4 Power Management in RF-EHWC
### Design Principles of Power Management in RF-EHWC
#### 4.1.2 Limited Data Storage  
Due to the cost and the size constraints, the maximum capacity of the data storage component (i.e., data buffer) in an RF-EHWC system is limited. Therefore, the collected data may overflow from the data buffer if they cannot be sent out timely. The optimal power management with the consideration of limited data storage is to seek an energy harvesting strategy to transmit the data timely at the minimum energy cost. A dedicated energy source is usually needed to charge the RF-EHWC device in a fully controlled manner. In [56], the authors developed a dual-tunnel strategy to solve this problem. In Step (a) of the dual-tunnel strategy, it calculates the least energy that the RF-EHWC system needs to send the collected data subject to the limited capacity of data storage. We can formulate the objective of the first step as the following optimization problem:  
\[ \begin{array}{ll}\textbf{P2:}&\operatorname*{arg\,min}_{p(t)}\int_{0}^{t_ {i}}p(t)\,\mathrm{d}t,\\ \textbf{s.t.}&\textbf{C1:}&\int_{0}^{t_{i}}r(t)\,\mathrm{d}t\, \leq\sum_{j=1}^{t_{j}\leq t_{i}}D_{j},&i=1,\ldots,N+1,\\ &\textbf{C2:}&\sum_{j=1}^{t_{j}\leq t_{i}}D_{j}-\int_{0}^{t_{i}}r(t)\, \mathrm{d}t\,\leq D_{max},&i=1,\ldots,N+1,\end{array}  \tag{2}\]  
where \(D_{i}\) and \(t_{i}\) are the size and the arrival time of data packet \(i\), respectively; \(D_{max}\) is the maximum capacity of the data storage; and the transmission rate is represented by \(r(t)\), which is related to the transmission power through a power-rate function, \(p(t)=f(r(t))\). Constrains **C1** and **C2** represent the data causality constraint and the maximal data capacity constraint, respectively. Here, Problem **P2** is to minimize the energy consumption of the EHD on transmitting all data, subject to the limited data storage. As shown in Figure 14a, a feasible data tunnel is constructed based on the cumulative data arrival and constraint of data storage capacity. By comparing Problems **P2** and **P1**, it can be realized that managing the transmission power in a feasible data tunnel is similar to the optimization problem introduced in Section 4.1.1. Thus, the optimal transmission power in a feasible data tunnel must have the following three properties:  
**Property 4**. : _The optimal transmission power does not change until the data buffer is either full or empty._  
**Property 5**. : _The optimal transmission power decreases if the data buffer is completely filled or increases if the storage is empty._  
**Property 6**. : _The optimal power management keeps the longest stretches of constant power periods in the feasible data tunnel._  
The optimal transmission power solved in Step (a) forms an energy tunnel, as shown in Figure 14b. The lower bound is the least required energy calculated in the first step. The width of the tunnel is the maximum capacity of the battery. If the profile of cumulatively requested energy (the red line in Figure 14) is below the lower bound, the harvested energy will be insufficient for a timely data transmission and will cause data overflow; if it is over the upper bound, the requested energy will be larger than the battery's capacity and will result in energy overflow. In Step (b) of the dual-tunnel strategy, it seeks an energy request strategy within the feasible energy tunnel to minimize the energy cost at the energy source. A path-oriented approach is proposed in [57] for the optimal energy request. The new feasible energy tunnel is divided into multiple grids, forming a graph with a set of \"vertices\" and \"edges\", as depicted in Figure 14. A horizontal edge means no energy charging and generates no cost at the energy source. The vertical edge indicates an energy replenishment, which produces an associated cost for the energy request. Eventually, the optimal energy requesting strategy in the path-oriented approach is converted to finding a route from the source to the destination that has the minimum sum-cost along the path in a directed and weighted graph.