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一种基于有限内存拟牛顿法的混合波束成形算法

严军荣 江沛莲 李沛

严军荣, 江沛莲, 李沛. 一种基于有限内存拟牛顿法的混合波束成形算法[J]. 电子与信息学报, 2024, 46(6): 2542-2548. doi: 10.11999/JEIT230656
引用本文: 严军荣, 江沛莲, 李沛. 一种基于有限内存拟牛顿法的混合波束成形算法[J]. 电子与信息学报, 2024, 46(6): 2542-2548. doi: 10.11999/JEIT230656
YAN Junrong, JIANG Peilian, LI Pei. A Hybrid Beamforming Algorithm Based on Limited-Broyden-Fletcher-Goldfarb-Shanno[J]. Journal of Electronics & Information Technology, 2024, 46(6): 2542-2548. doi: 10.11999/JEIT230656
Citation: YAN Junrong, JIANG Peilian, LI Pei. A Hybrid Beamforming Algorithm Based on Limited-Broyden-Fletcher-Goldfarb-Shanno[J]. Journal of Electronics & Information Technology, 2024, 46(6): 2542-2548. doi: 10.11999/JEIT230656

一种基于有限内存拟牛顿法的混合波束成形算法

doi: 10.11999/JEIT230656
基金项目: 国家自然科学基金(U21A20450, 62301204)
详细信息
    作者简介:

    严军荣:男,讲师,研究方向为无线通信网络、软件定义网络、视觉目标跟踪等

    江沛莲:女,硕士生,研究方向为无线电通信系统、毫米波大规模MIMO系统中的预编码技术

    李沛:女,讲师,研究方向为多波束传输、空间资源优化、延时感知节能方案等

    通讯作者:

    严军荣 yjrcn@163.com

  • 中图分类号: TN929.5

A Hybrid Beamforming Algorithm Based on Limited-Broyden-Fletcher-Goldfarb-Shanno

Funds: The National Natural Science Foundation of China (U21A20450, 62301204)
  • 摘要: 针对现有混合波束成形算法运行时间长、频谱效率低、误码率高的问题,该文提出一种基于有限内存拟牛顿法的混合波束成形算法(LBFGS)。该算法首先通过数字预编码器的最小二乘解构建单变量目标函数;然后采用目标函数的梯度近似黑塞矩阵的逆得到搜索方向并沿搜索方向更新模拟预编码器,直到满足停止条件;最后固定模拟预编码器得到数字预编码器。MATLAB仿真结果表明,LBFGS算法较现有MO算法减少了28%的运行时间,频谱效率提高了1.05%,误码率降低了1.06%。
  • 图  1  点对点毫米波混合波束成形系统

    图  2  不同波束成形算法的内部循环总次数随信噪比变化曲线

    图  3  不同波束成形算法的运行时间随信噪比的变化曲线

    图  4  不同波束成形算法的频谱效率随信噪比的变化曲线

    图  5  不同波束成形算法的误码率随信噪比的变化曲线

    算法1 计算搜索方向
     输入:${\gamma _0}{\text{ = }}1$,${\mathrm{grad}}{{\boldsymbol{\mathcal{J}}}_{{{\boldsymbol{v}}_k}}}$,已存储的梯度向量
     $ \{ {\boldsymbol{s}}_i^{(k)},{\boldsymbol{y}}_i^{(k)}\} _{i = k - m}^{k - 1} $
     输出: 搜索方向${{\boldsymbol{\eta}} _k}$
     ${\boldsymbol{\mathcal{H}}}_k^0 = {\gamma _k}$;
     $ {\boldsymbol{d}} \leftarrow {\mathrm{grad}}{{\boldsymbol{\mathcal{J}}}_{{v_k}}} $;
     If $m \ne 0$
      for $i = k - 1,k - 2, \cdots ,k - m$do
       ${\boldsymbol{\alpha}} \leftarrow {\rho _i} < {\boldsymbol{s}}_i^{(k)},{\boldsymbol{d}} > $
       ${\boldsymbol{d}} \leftarrow {\boldsymbol{d}} - {\alpha _i}{\boldsymbol{y}}_i^{(k)}$
      end for
      ${\boldsymbol{e}} \leftarrow {\boldsymbol{\mathcal{H}}}_k^0{\boldsymbol{d}}$
      for $i = k - m,k - m + 1, \cdots ,k - 1$
       $\beta \leftarrow {\rho _i} < {\boldsymbol{y}}_i^{(k)},{\boldsymbol{e}} > $
       $ {\boldsymbol{e}} \leftarrow {\boldsymbol{e}} + {\boldsymbol{s}}_i^{(k)} < {\varepsilon _i} - \beta > $
       end for
       ${{\boldsymbol{\eta}} _k} = - {\boldsymbol{e}}$
     else
      ${{\boldsymbol{\eta}} _k} = - {\boldsymbol{\mathcal{H}}}_k^0{\boldsymbol{d}}$
     end if
    下载: 导出CSV
    算法2 基于有限内存拟牛顿法的模拟预编码器算法
     输入:最优全数字矩阵${{\boldsymbol{V}}_{\rm{opt}}}$,初始模拟波束成形矩阵${\boldsymbol{V}}_{\rm{RF}}^0$,内存
     容量$\forall M \in \mathbb{Z}$且$M > 0$。
     输出:${{\boldsymbol{V}}_{\rm{RF}}}$
     初始化:内部循环次数$k = 0$,内存占用量$m = 0$
     根据式(10)计算黎曼梯度${\mathrm{grad}}{{\boldsymbol{\mathcal{J}}}_{{{\boldsymbol{v}}_0}}}$
     while梯度的范数达到阈值${\mu _2}$
      根据算法1计算搜索方向${{\boldsymbol{\eta}} _k}$
      线搜索并回缩得到${{\boldsymbol{v}}_{k + 1}}{\text{ = }}{{{R}}_{{{\boldsymbol{v}}_k}}}({\alpha _k}{{\boldsymbol{\eta}} _k})$
      计算黎曼梯度${\mathrm{grad}}{{\boldsymbol{\mathcal{J}}}_{{{\boldsymbol{v}}_{k + 1}}}}$
      计算$ {\boldsymbol{s}}_k^{(k + 1)} $,$ {\boldsymbol{y}}_k^{(k + 1)} $,${\rho _{k + 1}} = 1/ < {\boldsymbol{s}}_k^{(k + 1)},{\boldsymbol{y}}_k^{(k + 1)} > $
      if 满足存储条件
       计算${\gamma _{k + 1}} = < {\boldsymbol{s}}_k^{(k + 1)},{\boldsymbol{y}}_k^{(k + 1)} > /||{\boldsymbol{y}}_k^{(k + 1)}|{|^2}$
       if溢出
        丢弃$ {\boldsymbol{s}}_{k - M}^{(k)} $,$ {\boldsymbol{y}}_{k - M}^{(k)} $;
       end if
       历史梯度向量传输
       存储$ {\text{\{ }}{\boldsymbol{s}}_k^{(k + 1)},{\boldsymbol{y}}_k^{(k + 1)}{\text{\} }} $
       若$m < M$,那么$m = m + 1$,否则$m = M$
      else
       ${\gamma _{k + 1}} = {\gamma _k}$;
      end if
      $k \leftarrow k + 1$
     end
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-07-03
  • 修回日期:  2023-11-13
  • 录用日期:  2023-11-14
  • 网络出版日期:  2023-11-21
  • 刊出日期:  2024-06-30

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