数据采集与处理  2018, Vol. 33 Issue (4): 722-731 PDF

1. 池州学院机电工程学院, 池州, 247000;
2. 华东交通大学信息工程学院, 南昌, 330013;
3. 东南大学信息科学与工程学院, 南京, 211189

Design of QoS-Aware User Association for Load Balancing in Heterogeneous Cellular Networks
Qian Yewang1,3, Zhou Tianqing2,3, Yang Lüxi3
1. Mechanical and Electronic Engineering Department, Chizhou University, Chizhou, 247000, China;
2. School of Information Engineering, East China Jiaotong University, Nanchang, 330013, China;
3. School of Information Science and Engineering, Southeast University, Nanjing, 211189, China
Abstract: Considering that the conventional associations may not be appropriate due to the special characteristics of heterogeneous cellular networks (HCNs), some novel associations that can balance the network loads should be designed. To reflect the resource consumption levels of users and balance loads, a QoS-aware user association is proposed for load balancing in HCNs. In the association, the load is defined as the amount of consumed resources, which can reflect the resource consumption levels of users. Finally, this scheme is formulated as a network-wide weighted utility maximization problem. That is a nonlinear mixed-integer optimization problem, and obtaining its optimal solutions is very challenging (especially for large-scale problems). To solve the problem, a distributed algorithm is designed using dual decomposition. Numerical results show that, compared with the best power association and range expansion association, the proposed scheme has higher load balancing levels and lower call blocking probabilities.
Key words: heterogeneous cellular networks    load balancing    user association    interference management

1 系统模型与问题描述

 图 1 两层异构蜂窝网络 Fig. 1 Two-tier HCNs

 ${\rm{SIN}}{{\rm{R}}_{nk}} = \frac{{{p_n}{g_{nk}}}}{{\sum\limits_{j \in N/\left\{ n \right\}} {{p_j}{g_{jk}}} + {W_{{\rm{prb}}}}{N_0}}}$ (1)

 $\begin{array}{l} \mathop {\max }\limits_x \sum\limits_{n \in N} {\sum\limits_{k \in K} {{x_{nk}}{s_{nk}}{U_{nk}}\left( {{E_{nk}}} \right)} } \\ {\rm{s}}.\;{\rm{t}}.\;\;\;\;{C_1}:\sum\limits_{k \in K} {{x_{nk}}{s_{nk}}} \le {S_n}\;\;\;\;\;\;\forall n \in N\\ \;\;\;\;\;\;\;\;{C_2}:\sum\limits_{n \in N} {{x_{nk}}} = 1\;\;\forall k \in K\\ \;\;\;\;\;\;\;\;{C_3}:{x_{nk}} \in \left\{ {0,1} \right\}\;\;\;\;\forall n \in N,\forall k \in K \end{array}$ (2)

 $\begin{array}{*{20}{c}} {\mathop {\max }\limits_x \sum\limits_{n \in N} {\sum\limits_{k \in K} {{x_{nk}}{s_{nk}}\left\{ {\log {r_{nk}} - \log \sum\limits_{j \in K} {{x_{nj}}{s_{nj}}} } \right\}} } }\\ {{\rm{s}}.\;{\rm{t}}.\;\;\;\;{C_1},{C_2},{C_3}} \end{array}$ (3)

 $\begin{array}{l} \mathop {{\rm{Max}}}\limits_{x,y} F\left( {\mathit{\boldsymbol{x}},\mathit{\boldsymbol{y}}} \right) = \sum\limits_{n \in \left\{ N \right\}} {\sum\limits_{k \in \left\{ K \right\}} {{x_{nk}}{s_{nk}}\log {r_{nk}}} } - \sum\limits_{n \in \left\{ N \right\}} {{y_n}\log {y_n}} \\ {\rm{s}}.\;{\rm{t}}.\;\;\;\;{C_2},{C_3}\\ \;\;\;\;\;\;\;\;{C_4}:\sum\limits_{k \in \left\{ K \right\}} {{x_{nk}}{s_{nk}}} = {y_n}\;\;\;\;\;\forall n \in \left\{ N \right\}\\ \;\;\;\;\;\;\;\;{C_5}:0 < {\mathit{y}_n} \le {S_n}\;\;\;\;\forall n \in \left\{ N \right\} \end{array}$ (4)

2 算法设计与分析

2.1 分布式算法设计

 $L\left( {\mathit{\boldsymbol{x}},\mathit{\boldsymbol{y}},\mu } \right) = \sum\limits_{n \in N} {\sum\limits_{k \in K} {{x_{nk}}{s_{nk}}\log {r_{nk}}} } - \sum\limits_{n \in N} {{y_n}\log {y_n}} + \sum\limits_{n \in N} {{\mu _n}\left( {{y_n} - \sum\limits_{k \in K} {{x_{nk}}{s_{nk}}} } \right)}$ (5)

 $G\left( \mu \right) = \left\{ \begin{array}{l} \mathop {{\rm{Max}}}\limits_{x,y} \left( {\mathit{\boldsymbol{x}},\mathit{\boldsymbol{y}},\mu } \right)\\ {\rm{s}}.\;{\rm{t}}.\;{C_2},{C_3},{C_5} \end{array} \right.$ (6)

 $\mathop {{\rm{Min}}\;G}\limits_\mu \left( \mu \right)$ (7)

 $H\left( \mu \right) = \left\{ \begin{array}{l} \mathop {{\rm{Max}}}\limits_x \sum\limits_{n \in N} {\sum\limits_{k \in K} {{x_{nk}}{s_{nk}}\left\{ {\log {r_{nk}} - {\mu _n}} \right\}} } \\ {\rm{s}}.\;{\rm{t}}.\;{C_2},{C_3} \end{array} \right.$ (8)
 $I\left( \mu \right) = \left\{ \begin{array}{l} \mathop {{\rm{Max}}}\limits_y \sum\limits_{n \in N} {{y_n}\left\{ {{\mu _n} - \log {y_n}} \right\}} \\ {\rm{s}}.\;{\rm{t}}.\;{C_5} \end{array} \right.$ (9)

 ${n^ * } = \arg \mathop {{\rm{Max}}}\limits_{n \in N} \left\{ {{s_{nk}}\left( {\log {r_{nk}} - {\mu _n}} \right)} \right\}\;\;\;\;\;\forall k \in K$ (10)

(1) If t=0

(2) 根据来自所有基站的导频信号估计r

(3) Else

(4) 用户k接收来自所有基站的广播信息μ，并根据规则(10)选择基站n*

(5) 反馈接入信息xn*k=1给基站n*

(6) End If

 $y_n^t = {\rm{Min}}\left\{ {\exp \left( {\mu _n^t - 1} \right),{S_n}} \right\}\;\;\;\;\;\forall n \in N$ (11)

 $\mu _n^{t + 1} = \mu _n^t - {\xi ^t}\left( {y_n^t - \sum\limits_{k \in K} {{s_{nk}}x_{nk}^t} } \right)\;\;\;\;\;\forall n \in N$ (12)

 ${\xi ^t} = {\omega ^t}\left( {G\left( {{\mu ^t}} \right) - {{\tilde G}^t}} \right)/{\left\| {G\left( {{\mu ^t}} \right)} \right\|^2}\;\;\;\;0 < \underline \omega \le {\omega ^t} \le \bar \omega < 2$ (13)

 ${{\tilde G}^t} = \mathop {{\rm{Min}}}\limits_{i = 0, \cdots ,t} G\left( {{\mu ^i}} \right) - {\varepsilon ^t}$ (14)

 ${\varepsilon ^{t + 1}} = \left\{ {\begin{array}{*{20}{c}} {\alpha {\varepsilon ^t}}&{G\left( {{\mu ^{t + 1}}} \right) \le {{\tilde G}^t}}\\ {{\rm{Max}}\left\{ {\beta {\varepsilon ^t},\underline \varepsilon } \right\}}&{其他} \end{array}} \right.$ (15)

(1) If t=0

(2) 初始化步长ξtμt

(3) Else

(4) 对任意用户kK，接收来自该用户的反馈信息xnkt=1。

(5) 根据式(11)计算负载ynt+1，并利用规则(12)更新乘子μnt+1

(6) 广播信息μnt+1至所有用户。

(7) End If

yμ的更新规则来看，不难发现，它们发生于基站端，即组成了基站端算法，其详细描述可参考算法2。

2.2 算法收敛性与复杂度分析

 $\mathop {\inf }\limits_t G\left( {{\mu ^t}} \right) \le {G^ * } + \varepsilon$ (16)

 $\frac{{\partial G}}{{\partial {\mu _n}}}\left( \mu \right) = {y_n}\left( \mu \right) - \sum\limits_{k \in K} {{s_{nk}}{x_{nk}}\left( \mu \right)}$ (17)

3 仿真结果与分析

 $J = {\left( {\sum\limits_{n \in N} {{\kappa _n}} } \right)^2}/\left( {N\sum\limits_{n \in N} {\kappa _n^2} } \right)$ (18)

 图 2 用户数对网络负载平衡水平的影响 Fig. 2 Impact of NU on LBI

 图 3 用户实际速率需求对网络负载平衡水平的影响 Fig. 3 Impact of user′s PR on LBI

 图 4 用户数对呼叫阻塞概率的影响 Fig. 4 Impact of NU on CBP

 图 5 用户实际速率需求对呼叫阻塞概率的影响 Fig. 5 Impact of user′s PR on CBP

 图 6 QAA算法的收敛性 Fig. 6 Convergence of algorithm QQA

4 结束语