An energy efficiency optimization jointing resource allocation for delay-aware traffic in fronthaul constrained C-RAN

Abstract

The Cloud Radio Access Network (C-RAN) with centralized processing features achieves efficient and unified resource management to meet the quality of service (QoS) requirements, while results in an increment of energy consumption. To reach a tradeoff between energy efficiency and QoS, jointly considering baseband unit (BBU) computing resource, remote radio head (RRH) power, and fronthaul (FH) link capacity optimization for delay-aware traffic is an NP-hard problem. In this paper, we propose a system energy efficiency optimization model jointing multiple resources allocation for C-RAN downlink transmission. The end-to-end delay (De) in the proposed model is formulated by the established user data queue model, which satisfies the strict Lyapunov stability. Then, based on defining an improved Drift-Plus-Penalty function $F_{DPP}$ to transform the proposed original problem into two sub-problems which are BBU service rate allocation and RRH power control problems. The optimal BBU service rate and RRH transmission power of a single slot are obtained through solving a linear equation and applying a convolution neural network (CNN), respectively. Further, we propose an iterative-based optimization algorithm to achieve the optimal resource allocation for each slot. The simulation results show that the proposed optimization algorithm effectively reaches the balance between energy efficiency and QoS, and achieves better energy efficiency compared with the decomposition allocation method based on heuristic algorithm and BBU scheduling based on first-fit-decreasing (FFD) algorithm with lower computational complexity.

Appendix A Proof of the Throrem 2

For the update equation of user queue, the two sides of the equation are squared. By applying the inequality

$$\begin{aligned} \begin{aligned} {\left[ {\max \left( {x + y - z,0} \right) } \right] ^2} \le {x^2} + {y^2} + {z^2} + 2x\left( {y - z} \right) - 2yz,\\\mathrm{{ }}\forall x,y,z \in {\mathcal {R}} \end{aligned} \end{aligned}$$

(A1)

we can obtain

$$\begin{aligned} & \Delta L\left( {{Q_n}\left( t \right) } \right) = \frac{1}{2}E\left[ {\sum \limits _{n = 1}^N {Q_n^2\left( {t + 1} \right) } - \sum \limits _{n = 1}^N {Q_n^2\left( t \right) } } \right] \\ &\quad= \frac{1}{2}E\left[ {\sum \limits _{n = 1}^N {{{\left( {{Q_n}\left( t \right) + {\mu _n}\left( t \right) - {R_n}\left( t \right) } \right) }^2} - \sum \limits _{n = 1}^N {Q_n^2\left( t \right) } } } \right] \\ &\quad= \frac{1}{2}E\left[ {\sum \limits _{n = 1}^N {\left[ {Q_n^2\left( t \right) + \mu _n^2\left( t \right) + R_n^2\left( t \right) } \right] } } \right] \\ &\qquad + \frac{1}{2}E\left[ {\sum \limits _{n = 1}^N {\left[ {2{Q_n}\left( t \right) \left[ {{\mu _n}\left( t \right) - {R_n}\left( t \right) } \right] } \right] } } \right] \\ &\qquad - \frac{1}{2}E\left[ {\sum \limits _{n = 1}^N {\left[ {2{\mu _n}\left( t \right) {R_n}\left( t \right) } \right] } } \right] - \frac{1}{2}E\left[ {\sum \limits _{n = 1}^N {Q_n^2\left( t \right) } } \right] \\ &\quad\le \frac{1}{2}E\left[ {\sum \limits _{n = 1}^N {\left[ {Q_n^2\left( t \right) + \mu _n^2\left( t \right) + R_n^2\left( t \right) } \right] } } \right] \\ &\qquad + \frac{1}{2}E\left[ {\sum \limits _{n = 1}^N {\left[ {2{Q_n}\left( t \right) \left[ {{\mu _n}\left( t \right) - {R_n}\left( t \right) } \right] } \right] } } \right] \\ &\qquad - \frac{1}{2}E\left[ {\sum \limits _{n = 1}^N {Q_n^2\left( t \right) } } \right] \\ &\quad= \frac{1}{2}E\left[ {\sum \limits _{n = 1}^N {\left[ {\mu _n^2\left( t \right) + R_n^2\left( t \right) + 2{Q_n}\left( t \right) \left[ {{\mu _n}\left( t \right) - {R_n}\left( t \right) } \right] } \right] } } \right] \\ &\quad= \frac{1}{2}E\left[ {\sum \limits _{n = 1}^N {\left[ {\mu _n^2\left( t \right) + R_n^2\left( t \right) } \right] } } \right] \\ &\qquad + \sum \limits _{n = 1}^N {E\left[ {{Q_n}\left( t \right) \left[ {{\mu _n}\left( t \right) - {R_n}\left( t \right) } \right] } \right] } \\ &\quad= E\left[ {B_{lya}\left( t \right) } \right] + \sum \limits _{n = 1}^N {E\left[ {{Q_n}\left( t \right) \left[ {{\mu _n}\left( t \right) - {R_n}\left( t \right) } \right] } \right] } \end{aligned}$$

(A2)

where $B_{lya}\left( t \right) = \frac{1}{2}\sum \limits _{n = 1}^N {\left( {\mu _n^2\left( t \right) + R_n^2\left( t \right) } \right) }$.

Because of the capacity limitation of the fronthaul link ${\mu _n}\left( t \right) \le {R_{n\max }}$ and the maximum data transmission rate of the downlink ${R_n}(t) \le R_{\max }^n$, $B_{lya}$ satisfies the inequality,

$$\begin{aligned} E\left[ {B_{lya}\left( t \right) } \right] \le B_{lya} \end{aligned}$$

(A3)

where $B_{lya} = \frac{1}{2}\sum \limits _{n = 1}^N {\left[ {{{\left( {{R_{n\max }}} \right) }^2} + {{\left( {R_{\max }^n} \right) }^2}} \right] }$. By inserting (A2) and (A3) into the ${F_{DPP}}$ (24), Theorem 2 can be proved.