A User Satisfaction Maximization Algorithm Based on Access and Backhaul Integrated Small Base Station
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摘要: 针对接入与回传一体化小基站场景下用户个性化视频流业务需求问题，该文提出一种基于接入与回传一体化小基站的用户满意度最大化算法。该算法首先根据系统实际可达速率和用户满意度需求速率间的不匹配程度，动态调整下一周期队列传输所需频谱资源，并建立用户质量满意度最大化模型，其次运用Lyapunov优化方法把初始问题转化为Lyapunov偏移加罚项的优化，将溢出概率约束转化为关于自变量的不等式，最后基于拉格朗日对偶分解的用户接入带宽分配算法和基于内点法的回传和接入带宽分配算法进行求解。仿真结果表明，该算法提高了系统用户质量满意度，同时保证了系统稳定性。
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关键词:
- 接入与回传一体化小基站 /
- 视频流业务 /
- 用户质量满意度 /
- 李雅普诺夫优化方法
Abstract: To meet the personal quality requirement of video streaming service under the access and backhaul integrated small base station scene, a user satisfaction maximization algorithm is proposed. The algorithm adjusts dynamically the spectrum resources used for next-cycle queue transmission by analysis the mismatch degree between the actual system reachable rate and user satisfaction demand rate. The corresponding optimization model of the quality satisfaction of all users is established. Then, the Lyapunov stochastic optimization method is used to transform the initial problem into drift plus penalty, the overflow probability constraint is transformed into inequality of variables. Finally, using the proposed user access bandwidth allocation algorithm based on Lagrange dual decomposition and the backhaul and access bandwidth allocation algorithm based on interior point method. The simulation results show that the algorithm can improve the quality satisfaction of all users and ensure the system stability. -
表 1 基于拉格朗日对偶分解的用户接入带宽分配算法
算法1 基于拉格朗日对偶分解的用户接入带宽分配算法 步骤1 初始化 ${{{π}} ^{(0)}},{o^{(0)}},{\delta ^{(0)}},{\sigma ^{(0)}}$, $\beta = 0.1$，终止条件 ${\varDelta _1} = {10^{ - 2}}$； 步骤2 根据 ${\rm{P}}2.2$式(28)求计算UE接入带宽分配 ${\eta _{1,k}}$的表达式； 步骤3 判定式 $||{Y^{(n + 1)}}(t) - {Y^{(n)}}(t)|| \le {\varDelta _1}$，若满足，则执行步骤
6，否则执行步骤4；步骤4 根据梯度法更新对偶变量 ${{{π}} ^{(n)}},{o^{(n)}},{\delta ^{(n)}},{\sigma ^{(n)}}$； 步骤5 $n = n + 1$，将更新的拉格朗日乘子值代入 ${\rm P}2.2$式(28)中计
算，得到新的用户接入频带分配比例，并跳转步骤3；步骤6 获得UE接入带宽分配方案 ${\eta _{1,k}}\!\!\!\!^*\ $。 
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表 2 基于内点法的回传和接入带宽分配算法
算法2 基于内点法的回传和接入带宽分配算法
步骤1 取初始 ${\chi ^{\left( 0 \right)}},{\rho ^{\left( 0 \right)}},{\kappa ^{\left( 0 \right)}},{\omega ^{\left( 0 \right)}}$都>0，一般取各自初始值为1，
误差 ${\varDelta _2} = {10^{ - 3}} > 0$；
步骤2 用随机数生成法生成多个初始点，并选取满足约束条件的
初始点 ${\beta ^{(0)}}$，令 $n = 1$；
步骤3 构造惩罚函数 $\varphi \left( {\beta ,{\chi ^{(n)}},{\rho ^{(n)}},{\kappa ^{(n)}},{\varpi ^{(n)}}} \right)$，从 ${\beta ^{(n - 1)}}$点出发
用无约束优化方法求惩罚函数的极值点：
${\beta ^*}\left( {{\chi ^{(n)}},{\rho ^{(n)}},{\kappa ^{(n)}},{\varpi ^{(n)}}} \right)$
步骤4 检查迭代终止准则：如果满足
$\left|\frac{{\varDelta \varphi }}{{\varphi \left( {{\beta ^*},{\chi ^{(n - 1)}},{\rho ^{(n - 1)}},{\kappa ^{(n - 1)}},{\varpi ^{(n - 1)}}} \right)}}\right| \le {\varDelta _2}$
其中，
$\begin{align} \Delta \varphi =& \varphi \left( {{\beta ^*},{\chi ^{(n)}},{\rho ^{(n)}},{\kappa ^{(n)}},{\varpi ^{(n)}}} \right) \\ &- \varphi \left( {{\beta ^*},{\chi ^{(n - 1)}},{\rho ^{(n - 1)}},{\kappa ^{(n - 1)}},{\varpi ^{(n - 1)}}} \right) \\ \end{align} $
则停止迭代计算，并以 $\left( {{\beta ^*},{\chi ^{(n)}},{\rho ^{(n)}},{\kappa ^{(n)}},{\varpi ^{(n)}}} \right)$作为
目标函数P2.3的局部最优解，否则转步骤5；
步骤5 缩小惩罚因子， $n = n + 1$，转向步骤3。递减系数
${\omega _1},{\omega _2},{\omega _3},{\omega _4}$通常取值为0.1。
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表 3 基于接入与回传一体化小基站的用户满意度最大化全局算法
算法3 基于接入与回传一体化小基站的用户满意度最大化全局算法 步骤1 初始化带宽分配比例 $\beta $和误差 $\varDelta = {10^{ - 5}}$； 步骤2 根据式(27)求子问题 ${\rm{P}}2.1$UE回传带宽分配方案的局部最优解 ${\mu _k}\!\!^*$； 步骤3 根据算法1求问题 ${\rm{P}}2.2$每个用户的接入带宽分配方案的局部最优 ${\eta _{1,k}}\!\!\!\!^*\ $； 步骤4 将最优解 ${\mu _k}\!\!^*$与最优解 ${\eta _{1,k}}\!\!\!\!^*\ $代入式(26)，根据算法2求问题 ${\rm{P}}2.3$回传带宽分配比例的局部最优解 ${\beta^*}$；
步骤5 将 ${\mu _k}\!\!^*$与 ${\eta _{1,k}}\!\!\!\!^*\ ,{\beta ^*}$代入到最初目标问题P2中，检查收敛条件 $\left\| {f\left( {\eta _{1,k}^{(n)}(t),\mu _k^{(n)}(t),{\beta ^{(n)}}(t)} \right) - f\left( {\eta _{1,k}^{(n - 1)}(t),\mu _k^{(n - 1)}(t),{\beta ^{(n - 1)}}(t)} \right)}\right\| \le \varDelta $是否
满足，否则令 $\beta = {\beta ^*}$，并依此执行步骤2 $ \sim $步骤5；当满足收敛条件，则获得最初问题 ${\rm P}2$的全局最优解 ${\beta ^*}$, ${\eta _{1,k}}\!\!\!\!^*\ $和 ${\mu _k}\!\!^*$。
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