Optimization and Design of Beamforming for Cellular Internet-of-Things with Energy Efficiency Maximization in Short Packet Domain
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摘要: 为了满足未来蜂窝物联网(IoT)中超高可靠和超低时延的要求，该文提出一种适用于多小区多用户超高可靠极低时延网络短包域公平性能量效率最大化算法。首先，以最小用户传输速率、每个发射机最大功率等约束为限制，构建了一个关于波束成形矢量的非线性分式规划资源配置模型。随后，采用变量代换、连续凸近似等技术，将原始非凸优化问题转化为标准的凸问题，进而提出一种短包域迭代能量效率最优化方法进行求解。最后，数值仿真结果验证了所提算法在短包域具有良好的能量效率性能。Abstract: In order to meet the requirements of ultra-high reliability and ultra-low latency in future cellular Internet-of-Things (IoT), an algorithm for such networks, which ensures the fairness-aware energy efficiency maximization in short packet domain, is developed. Firstly, a nonlinear fractional programming resource allocation model, which optimize the beamforming vector, is constructed with several constraints such as minimum user transmission rate and maximum power of per transmitter. Subsequently, the original non-convex optimization problem is transformed into a standard convex problem by exploiting the variable substitution and continuous convex approximation. Furthermore, an iterative energy efficiency optimization algorithm is developed in short packet regime. Finally, the numerical simulation results verify that the proposed algorithm has good energy efficiency performance in the short packet domain.
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1 短包域能量效率最大化算法(算法1)
(1) 令$n = 0 $，设置满足功率约束的初始波束矢量${{\boldsymbol{w}}^{\left( n \right)}} $，算法的
最大迭代次数为${N_{\max }} $。(2) 通过约束${\text{C}}{{\text{3}}'} $，C4，C5，式(8)和式(13)，计算得到和
$\left\{ {x_j^{\left( n \right)},y_j^{\left( n \right)},{\boldsymbol{\upsilon}} _j^{\left( n \right)},\zeta _{j,k}^{\left( n \right)} } \right\}$。(3) 开始循环： (4) 依据${{\boldsymbol{w}}^{\left( n \right)}} $, $x_j^{\left( n \right)} $, $y_j^{\left( n \right)} $, ${\boldsymbol{\upsilon}} _j^{\left( n \right)}$和$ \zeta _{j,k}^{\left( n \right)} $，通过求解P1，输出相应
的解${t^ * } $, ${{\boldsymbol{w}}^{\text{*} } }$, $x_j^ * $, $y_j^ * $, ${\boldsymbol{\upsilon}} _j^ *$和$\zeta _{j,k}^ * $。(5) 更新${{\boldsymbol{w}}^{\left( {n + 1} \right)}} = {{\boldsymbol{w}}^ * } $, $ x_j^{\left( {n + 1} \right)} = x_j^ * $, $y_j^{\left( {n + 1} \right)} = y_j^ * $,
${\boldsymbol{\upsilon}} _j^{\left( {n + 1} \right)} = {\boldsymbol{\upsilon}} _j^ *$, $\zeta _{j,k}^{\left( {n + 1} \right)} = \zeta _{j,k}^ * $。(6) 更新P1的代价函数值：${t^{\left( {n + 1} \right)}} = {t^ * } $。 (7) 若$ \left| {{t^{\left( {n + 1} \right)}} - {t^{\left( n \right)}}} \right| < \xi $或$n > {N_{\max }} $，其中$\xi $表示预置的任意小
的数，则跳出循环并输出最终的解；否则，$n = n + 1 $,
${{\boldsymbol{w}}^{\left( n \right)}} = {{\boldsymbol{w}}^ * } $, $x_j^{\left( n \right)} = x_j^ * $, $y_j^{\left( n \right)} = y_j^ * $, ${\boldsymbol{\upsilon}} _j^{\left( n \right)} = {\boldsymbol{\upsilon}} _j^ *$,
$\zeta _{j,k}^{\left( n \right)} = \zeta _{j,k}^ * $, ${t^{\left( n \right)}} = {t^ * } $，回到第(3)步。
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