Near Optimal Online Resource Allocation Scheme for Energy Harvesting Cloud Radio Access Network with Battery Imperfections

Abstract

In energy harvesting wireless networks, the energy storage devices are usually imperfect. In this paper, we investigate dynamic online resource allocation scheme for Energy Harvesting Cloud Radio Access Network (EH-CRAN) by jointly considering the EH process, data admission, and a practical battery model with finite battery capacity, energy charging and discharging loss. We use Lyapunov optimization technique and design data queue and energy queue to formulate a stochastic optimization problem, and decompose the formulated problem into three subproblems, including data scheduling, power allocation and routing scheduling. Based on the solutions of these subproblems, an online resource allocation algorithm is proposed to maximize the user utility while ensuring the sustainability of RRHs. Furthermore, this algorithm does not require any prior statistical information of the system, e.g., channel state, data arrival and EH process. Both performance analysis and simulation results demonstrate the proposed algorithm can achieve close-to-optimal utility.

Appendix

Proof of Theorem 1

Squaring both sides of the queueing equation in (5), and using the fact that $([Q-b]^+ +a)^2 \le a^2+b^2+2Q(a-b)$, we can have:

$$\begin{aligned} \frac{1}{2}&\left( [Q_{n,m}(t+1)]^2-[Q_{n,m}(t)]^2\right) \nonumber \\&\le \frac{1}{2}(\theta _{\max }^2+A_{\max }^2) -Q_{n,m}(t)[\sum _{n\,\in \,\mathcal {N}}\sum _{m\,\in \,\mathcal {M}}\theta _{n,m}(t)-A_{n,m}(t)] \end{aligned}$$

(24)

similarly, we can also derive

$$\begin{aligned} \frac{1}{2}&([B_n(t+1)-\varUpsilon _n]^2-[B_n(t)-\varUpsilon _n]^2) \nonumber \\&\le -\frac{1}{2}(1-\eta ^2)[B_n(t)-\varUpsilon _n]^2 +\frac{1}{2}\left[ \frac{\sum _{m\,\in \,\mathcal {M}}P_{n,m}(t)}{\lambda }-\lambda b_n(t)+(1-\eta )\varUpsilon _n\right] \nonumber \\&\le \frac{1}{2}\max \left\{ [\frac{P_{\max }}{\lambda }+(1-\eta )\varUpsilon ]^2,[- \lambda b_{\max }+(1-\eta )\varUpsilon _n]^2\right\} \nonumber \\&-\frac{\eta }{\lambda }(B_n(t)-\varUpsilon _n)[\lambda b_n(t)-(1-\eta )\varUpsilon _n] \end{aligned}$$

(25)

Proof of Theorem 2

We prove Eq. (21) by inductions. Since Eq. (21) holds at $t=0$, we show that if Eq. (21) holds at slot t, i.e., $Q_{n,m}(t)\le \gamma _{\max } V+A_{\max }$, then it also holds at slot $t+1$. If $Q_{n,m}(t)\le \gamma _{\max } V+A_{\max }$, then it is easy to see that $Q_{n,m}(t+1)\le V \gamma _{\max } +A_{\max }$ according to the data availability constraint (3). Suppose $Q_{n,m}(t) \ge V \gamma _{\max }$, we prove Eq. (21) by showing that the objective function of DA problem monotonically increases with $A_{n,m}(t)$. Therefore, the $A_{n,m}^*(t)=0$ is the optimal solution for the DA problem. Taking derivative of the objective function in the DA problem w.r.t. $A_{n,m}(t)$ yields $Q_{n,m}(t)-V U'(\sum _{n\,\in \,\mathcal {N}}A_{n,m}(t))$. Recalling the $\gamma _{\max }$ denotes the upper bound of the first derivative of the user utility, it can be found that the derivative of the objective function is larger than 0. Therefore, minimizing the objective function yields $A_{n,m}^*(t)=0$, which proves Eq. (21).

The proof of Eq. (22) is similar.