MIMO系统探通一体化信号矩阵设计方法

杨婧 余显祥 沙明辉 崔国龙 孔令讲

杨婧, 余显祥, 沙明辉, 等. MIMO系统探通一体化信号矩阵设计方法[J]. 雷达学报, 待出版. doi: 10.12000/JR22087
引用本文: 杨婧, 余显祥, 沙明辉, 等. MIMO系统探通一体化信号矩阵设计方法[J]. 雷达学报, 待出版. doi: 10.12000/JR22087
YANG Jing, YU Xianxiang, SHA Minghui, et al. Dual function radar and communication signal matrix design method for MIMO system[J]. Journal of Radars, in press. doi: 10.12000/JR22087
Citation: YANG Jing, YU Xianxiang, SHA Minghui, et al. Dual function radar and communication signal matrix design method for MIMO system[J]. Journal of Radars, in press. doi: 10.12000/JR22087

MIMO系统探通一体化信号矩阵设计方法

doi: 10.12000/JR22087
基金项目: 国家自然科学基金(U19B2017, 62101097),长江学者奖励计划,中国博士后科学基金(2020M680147, 2021T140096)
详细信息
    作者简介:

    杨 婧,电子科技大学博士。主要研究方向为雷达波形设计与处理、最优化理论算法以及阵列信号处理等

    余显祥,电子科技大学博士后。主要研究方向为雷达波形设计与处理、最优化理论算法以及阵列信号处理等

    沙明辉,研究员。主要研究方向为雷达抗干扰和信号处理等

    崔国龙,电子科技大学教授,博士生导师。主要研究方向为最优化理论和算法、雷达目标检测理论、波形多样性以及阵列信号处理等

    孔令讲,电子科技大学教授,博士生导师。主要研究方向为新体制雷达、统计信号处理、优化理论和算法、雷达信号处理、非合作信号处理技术和自适应阵列信号处理等

    通讯作者:

    崔国龙 cuiguolong@uestc.edu.cn

  • 责任主编:梁军利 Corresponding Editor: LIANG Junli
  • 中图分类号: TN958

Dual Function Radar and Communication Signal Matrix Design Method for MIMO System

Funds: The National Natural Science Foundation of China (U19B2017, 62101097), The Chang Jiang Scholars Program, Postdoctoral Science Foundation under Grants (2020M680147, 2021T140096)
More Information
  • 摘要: 由于多输入多输出(MIMO)系统具有波形、空间分集和多路复用等优势,MIMO探通一体化(DFRC)系统通过共享软硬件资源以同时实现目标探测和保密通信功能受到了极大关注。该文针对基于预编码矩阵调制的MIMO探通一体化系统,提出了基于交替方向乘子(ADMM)的一体化信号矩阵设计方法。通过用户和窃听用户参考密码本约束下最大化方向图峰值主瓣旁瓣电平比(PMSR),保证了探测方向图性能的同时防止通信信息被窃听。针对预编码矩阵通信解调问题,提出了基于交替方向惩罚(ADPM)的排序学习优化解调方法,提升了一体化波形信息解调效率。数值仿真验证了所提设计方法实现探通一体化的有效性,与已有算法相比可实现多用户通信和更高的PMSR。

     

  • 图  1  基于预编码矩阵调制的MIMO探通一体化系统框架示意图

    Figure  1.  The framework diagram of the MIMO DFRC system based on permutation matrix modulation

    图  2  假设$\theta _1^{{\text{com}}} = - {60^\circ }$时发射方向图

    Figure  2.  The transmit beampattern with $\theta _1^{{\text{com}}} = - {60^\circ }$

    图  3  通信星座图

    Figure  3.  Communication constellation diagram

    图  4  不同算法SER随SNR变化曲线

    Figure  4.  SER versus SNR for different algorithms

    图  5  SER随角度变化曲线

    Figure  5.  SER versus angle

    图  6  ${\boldsymbol{s}}\left( {{{65}^\circ }} \right)$${\boldsymbol{s}}\left( { - {{60}^\circ }} \right)$元素分布

    Figure  6.  The element distributions of ${\boldsymbol{s}}\left( {{{65}^\circ }} \right)$ and ${\boldsymbol{s}}\left( { - {{60}^\circ }} \right)$

    图  7  算法1与算法2计算复杂度

    Figure  7.  The computational complexities of Alg. 1 and Alg. 2

    图  8  探通一体化性能

    Figure  8.  DFRC performance

    图  9  SER随SNR变化曲线

    Figure  9.  SER versus SNR

    算法1 基于ADMM的一体化信号矩阵设计方法
    Alg. 1 DFRC waveform matrix design method based on ADMM
    输入:$\left\{ {\boldsymbol{y} }_{i}^{(0)}\right\},{ {\epsilon} }^{(0)},\left\{ {\boldsymbol{z} }_{s}^{(0)}\right\},{ {\eta} }^{(0)},\left\{ {\boldsymbol{x} }_{c}^{(0)}\right\},\left\{ {\boldsymbol{v} }_{h}^{(0)}\right\},\left\{ {\boldsymbol{\mu} }_{i}^{(0)}\right\},\left\{ {\boldsymbol{\iota} }_{s}^{(0)}\right\},\left\{ {\boldsymbol{\xi} }_{c}^{(0)}\right\},\left\{ { {\boldsymbol{\lambda} } }_{h}^{(0)}\right\},{\boldsymbol{n} }^{\left(0\right)},{\boldsymbol{\zeta} }^{\left(0\right)},{\boldsymbol{\rho} },\varDelta ,{\delta }_{1}$;
    输出:MIMO一体化系统加权向量$ {{\boldsymbol{\boldsymbol{w}}}^ \star } $;
    步骤1. $ t = 0 $;
    步骤2. 通过求解以下问题更新$ {\boldsymbol{w}}^{\left(t\text{+}1\right)},\left\{{\boldsymbol{y}}_{i}^{\left(t\text{+}1\right)}\right\},{{\epsilon}}^{\left(t\text{+}1\right)},\left\{{\boldsymbol{z}}_{s}^{\left(t\text{+}1\right)}\right\},{{\eta}}^{\left(t\text{+}1\right)},\left\{{\boldsymbol{x}}_{c}^{\left(t\text{+}1\right)}\right\},\left\{{\boldsymbol{v}}_{h}^{\left(t\text{+}1\right)}\right\}, $$ {{\boldsymbol{\boldsymbol{n}}}^{\left( {t{\text{ + }}1} \right)}} $:
    ${\boldsymbol{w} }^{(t+1)}:=\mathrm{arg}\;\underset{\boldsymbol{w} }{\mathrm{min} }\;{L}_{ { {\boldsymbol \rho} } }\left({\boldsymbol{w}},\left\{ {\boldsymbol{y} }_{i}^{(t)}\right\},{ {\epsilon} }^{(t)},\left\{ {\boldsymbol{z} }_{s}^{(t)}\right\},{ {\eta} }^{(t)},\left\{ {\boldsymbol{x} }_{c}^{(t)}\right\},\left\{ {\boldsymbol{v} }_{h}^{(t)}\right\},\left\{ {\boldsymbol{\mu} }_{i}^{(t)}\right\},\left\{ {\boldsymbol{\iota} }_{s}^{(t)}\right\},\left\{ {\boldsymbol{\xi} }_{c}^{(t)}\right\},{ {\boldsymbol{\lambda} } }_{h}^{(t)},{\boldsymbol{n} }^{\left(t\right)},{\boldsymbol{\zeta} }^{\left(t\right)}\right)$ (22)
    $\begin{aligned}& \left\{ {\boldsymbol{y} }_{i}^{(t+1)},{ {\epsilon} }^{(t+1)}\right\}:=\mathrm{arg}\;\underset{ {\boldsymbol{y} }_{i},\epsilon}{\mathrm{min} }\;{L}_{ { {\boldsymbol \rho} } }\left({\boldsymbol{w} }^{(t+1)},\left\{ {\boldsymbol{y} }_{i}\right\},\epsilon,\left\{ {\boldsymbol{z} }_{s}^{(t)}\right\},{ {\eta} }^{(t)}, \left\{ {\boldsymbol{x} }_{c}^{(t)}\right\},\left\{ {\boldsymbol{v} }_{h}^{(t)}\right\},\left\{ {\boldsymbol{\mu} }_{i}^{(t)}\right\},\left\{ {\boldsymbol{\iota} }_{s}^{(t)}\right\},\left\{ {\boldsymbol{\xi} }_{c}^{(t)}\right\},{ {\boldsymbol{\lambda} } }_{h}^{(t)},{\boldsymbol{n} }^{\left(t\right)},{\boldsymbol{\zeta} }^{\left(t\right)}\right)\text{ }\\ & \quad\text{s}\text{.t}\text{. }{\Vert {\boldsymbol{y} }_{i}\Vert }^{2}\ge \epsilon,i=1,2,\cdots ,I; \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad\;\, (23)\end{aligned}$
    $\begin{array}{l}\left\{ {\boldsymbol{z} }_{s}^{(t+1)},{ {\eta} }^{(t+1)}\right\}:=\mathrm{arg}\;\underset{ {\boldsymbol{z} }_{s},\eta }{\mathrm{min} }\;{L}_{ { {\boldsymbol \rho} } }\left({\boldsymbol{w} }^{(t+1)},\left\{ {\boldsymbol{y} }_{i}^{(t+1)}\right\},{ {\epsilon} }^{(t+1)},\left\{ {\boldsymbol{z} }_{s}\right\}, \eta ,\left\{ {\boldsymbol{x} }_{c}^{(t)}\right\},\left\{ {\boldsymbol{v} }_{h}^{(t)}\right\},\left\{ {\boldsymbol{\mu} }_{i}^{(t)}\right\},\left\{ {\boldsymbol{\iota} }_{s}^{(t)}\right\},\left\{ {\boldsymbol{\xi} }_{c}^{(t)}\right\},{ {\boldsymbol{\lambda} } }_{h}^{(t)},{\boldsymbol{n} }^{\left(t\right)},{\boldsymbol{\zeta} }^{\left(t\right)}\right)\text{ }\\ \quad\text{s}\text{.t}\text{. }{\Vert {\boldsymbol{z} }_{s}\Vert }^{2}\le \eta ,s=1,2,\cdots ,S; \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\;\;\, (24)\end{array}$
    $\begin{array}{l}\left\{ {\boldsymbol{x} }_{c}^{(t+1)},{b}_{c}^{(t+1)}\right\}:=\mathrm{arg}\underset{ {\boldsymbol{x} }_{c},{b}_{c} }{\mathrm{min} }{L}_{ { {\boldsymbol \rho} } }\left({\boldsymbol{w} }^{(t+1)},\left\{ {\boldsymbol{y} }_{i}^{(t+1)}\right\},{ {\epsilon} }^{(t+1)},\left\{ {\boldsymbol{z} }_{s}^{(t+1)}\right\}, { {\eta} }^{(t+1)},\left\{ {\boldsymbol{x} }_{c}\right\},\left\{ {\boldsymbol{v} }_{h}^{(t)}\right\},\left\{ {\boldsymbol{\mu} }_{i}^{(t)}\right\},\left\{ {\boldsymbol{\iota} }_{s}^{(t)}\right\},\left\{ {\boldsymbol{\xi} }_{c}^{(t)}\right\},{ {\boldsymbol{\lambda} } }_{h}^{(t)},{\boldsymbol{n} }^{\left(t\right)},{\boldsymbol{\zeta} }^{\left(t\right)}\right)\text{ }\\ \quad\text{s}\text{.t}\text{. }{\boldsymbol{x} }_{c}={b}_{c}{\overline{{\boldsymbol{a}}} }_{1},{l}_{c}\le {b}_{c}\le {u}_{c},c=1,2,\cdots ,C; \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\, (25)\end{array}$
    $\begin{aligned}& \left\{ {\boldsymbol{v} }_{h}^{(t+1)},{r}_{h}^{(t+1)} \right\} :=\mathrm{arg}\underset{ {\boldsymbol{v} }_{h},{r}_{h} }{\mathrm{min} }\;{L}_{ { {\boldsymbol \rho} } }\left({\boldsymbol{w} }^{(t+1)},\left\{ {\boldsymbol{y} }_{i}^{(t+1)}\right\},{ {\epsilon} }^{(t+1)},\left\{ {\boldsymbol{z} }_{s}^{(t+1)} \right\}, { {\eta} }^{(t+1)},\left\{ {\boldsymbol{x} }_{c}^{(t+1)} \right\},\left\{ {\boldsymbol{v} }_{h}\right\},\left\{ {\boldsymbol{\mu} }_{i}^{(t)}\right\},\left\{ {\boldsymbol{\iota} }_{s}^{(t)}\right\},\left\{ {\boldsymbol{\xi} }_{c}^{(t)} \right\},{ {\boldsymbol{\lambda} } }_{h}^{(t)},{\boldsymbol{n} }^{\left(t\right)},{\boldsymbol{\zeta} }^{\left(t\right)}\right)\\ & \quad\text{s}\text{.t}\text{. }{\boldsymbol{v} }_{h}={r}_{h} { {\textit{1}}}_{K},h=1,2,\cdots ,E \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\;\, (26)\end{aligned}$
    $\begin{aligned}& {\boldsymbol{n} }^{\left(t\text{+}1\right)}:=\mathrm{arg}\;\underset{\boldsymbol{n} }{\mathrm{min} }\;{L}_{ { {\boldsymbol \rho} } }\left({\boldsymbol{w} }^{(t+1)},\left\{ {\boldsymbol{y} }_{i}^{(t+1)}\right\},{ {\epsilon} }^{(t+1)},\left\{ {\boldsymbol{z} }_{s}^{(t+1)}\right\}, { {\eta} }^{(t+1)},\left\{ {\boldsymbol{x} }_{c}^{(t+1)}\right\},\left\{ {\boldsymbol{v} }_{h}^{(t+1)}\right\},\left\{ {\boldsymbol{\mu} }_{i}^{(t)}\right\},\left\{ {\boldsymbol{\iota} }_{s}^{(t)}\right\},\left\{ {\boldsymbol{\xi} }_{c}^{(t)}\right\},{ {\boldsymbol{\lambda} } }_{h}^{(t)},{\boldsymbol{n} },{\boldsymbol{\zeta} }^{\left(t\right)}\right)\\& \quad\text{s}\text{.t}\text{. }{\Vert {\boldsymbol{n} }\Vert }^{2}=\varDelta \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \quad\;\, (27)\end{aligned}$
    步骤3. 通过下列公式更新$\left\{ {{\boldsymbol{\boldsymbol{\mu}}}_i^{(t + 1)}} \right\},\left\{ {{\boldsymbol{\boldsymbol{\iota}}}_s^{(t + 1)}} \right\},\left\{ {{\boldsymbol{\boldsymbol{\xi}}}_c^{(t + 1)}} \right\},\left\{ {{\boldsymbol{\lambda }}_h^{(t + 1)}} \right\},{{\boldsymbol{\boldsymbol{\zeta}}}^{\left( {t{\text{ + }}1} \right)}}$:
             $ {\boldsymbol{\boldsymbol{\mu}}}_i^{(t + 1)}: = {\boldsymbol{\boldsymbol{\mu}}}_i^{(t)} + {\boldsymbol{\boldsymbol{y}}}_i^{(t + 1)} - {{\boldsymbol{A}}^{\text{H}}}\left( {{\theta _i}} \right){{\boldsymbol{\boldsymbol{w}}}^{(t + 1)}} $ (28)
             $ {\boldsymbol{\boldsymbol{\iota}}}_s^{(t + 1)}: = {\boldsymbol{\boldsymbol{\iota}}}_s^{(t)} + {\boldsymbol{\boldsymbol{z}}}_s^{(t + 1)} - {{\boldsymbol{A}}^{\text{H}}}\left( {{\vartheta _s}} \right){{\boldsymbol{\boldsymbol{w}}}^{(t + 1)}} $ (29)
             $ {\boldsymbol{\boldsymbol{\xi}}}_c^{(t + 1)}: = {\boldsymbol{\boldsymbol{\xi}}}_c^{(t)} + {\boldsymbol{\boldsymbol{x}}}_c^{(t + 1)} - {{\boldsymbol{A}}^{\text{H}}}\left( {\theta _c^{{\text{com }}}} \right){{\boldsymbol{\boldsymbol{w}}}^{(t + 1)}} $ (30)
             $ {\boldsymbol{\lambda }}_h^{(t + 1)}: = {\boldsymbol{\lambda }}_h^{(t)} + {\boldsymbol{\boldsymbol{v}}}_h^{(t + 1)} - {{\boldsymbol{A}}^{\text{H}}}\left( {\theta _h^{{\text{eav }}}} \right){{\boldsymbol{\boldsymbol{w}}}^{(t + 1)}} $ (31)
             ${{\boldsymbol{\boldsymbol{\zeta}}}^{\left( {t{\text{ + }}1} \right)}} = {{\boldsymbol{\boldsymbol{\zeta}}}^{\left( t \right)}} + {{\boldsymbol{\boldsymbol{n}}}^{(t + 1)}} - {{\boldsymbol{\boldsymbol{w}}}^{(t + 1)}}$ (32)
    步骤4. 如果原始可行性容差$V_1^{(t + 1)} = \displaystyle\sum\limits_{i = 1}^I {{{\left\| {{\boldsymbol{\boldsymbol{y}}}_i^{(t + 1)} - {{\boldsymbol{A}}^{\text{H}}}\left( {{\theta _i}} \right){{\boldsymbol{\boldsymbol{w}}}^{(t + 1)}}} \right\|}^2}} + $$\displaystyle\sum\limits_{s = 1}^S {{{\left\| {{\boldsymbol{\boldsymbol{z}}}_s^{(t + 1)} - {{\boldsymbol{A}}^{\text{H}}}\left( {{\vartheta _s}} \right){{\boldsymbol{\boldsymbol{w}}}^{(t + 1)}}} \right\|}^2}} + $$\displaystyle\sum\limits_{c = 1}^C { { {\left\| { {\boldsymbol{\boldsymbol{x} } }_c^{(t + 1)} - { {\boldsymbol{A} }^{\text{H} } }\left( {\theta _c^{ {\text{com } } } } \right){ {\boldsymbol{\boldsymbol{w} } }^{(t + 1)} } } \right\|}^2} }$
     $+\displaystyle\sum\limits_{h = 1}^E { { {\left\| { {\boldsymbol{\boldsymbol{v} } }_h^{(t + 1)} - { {\boldsymbol{A} }^{\text{H} } }\left( {\theta _h^{ {\text{eav } } } } \right){ {\boldsymbol{\boldsymbol{w} } }^{(t + 1)} } } \right\|}^2} }$$+ {\left\| { { {\boldsymbol{\boldsymbol{n} } }^{(t + 1)} } - { {\boldsymbol{\boldsymbol{w} } }^{(t + 1)} } } \right\|^2} \le {\delta _1}$,则输出${{\boldsymbol{\boldsymbol{w}}}^ \star } = {{\boldsymbol{\boldsymbol{w}}}^{\left( {t + 1} \right)}}$;否则$t: = t + 1$,回到步骤2。
    下载: 导出CSV
    算法2 基于ADPM的排序学习优化解调方法
    Alg. 2 The permutation learning demodulation method
    based on ADPM
     输入:${{\boldsymbol{p}}^0},{\boldsymbol{u}}_1^0,{\boldsymbol{u}}_2^0,{\boldsymbol{\kappa }}_1^0,{\boldsymbol{\kappa }}_2^0,{\rho ^0},{\boldsymbol{g}},{\boldsymbol{B}},{\boldsymbol{C}},{\delta _2},{\delta _3}$;
     输出:问题(56)的最优解$ {{\boldsymbol{p}}^ \star } $;
     步骤1. $ l = 0 $;
     步骤2. 通过求解以下问题更新${{\boldsymbol{p}}^{l{\text{ + }}1}},{\boldsymbol{u}}_1^{l{\text{ + }}1},{\boldsymbol{u}}_2^{l{\text{ + }}1}$:
     $\begin{aligned} { {\boldsymbol{p} }^{l + 1} }: =& \arg \mathop {\min }\limits_{\boldsymbol{p} } {\mathcal{L}_{ {\rho ^l} } }\left( { {\boldsymbol{p} },{\boldsymbol{u} }_1^l,{\boldsymbol{u} }_2^l,{\boldsymbol{\kappa } }_1^l,{\boldsymbol{\kappa } }_2^l} \right){\text{ } } \\& {\text{s} }{\text{.t} }{\text{. } }{p_i} \in \{ 0,1\} ,i = 1,2, \cdots ,{K^2} \qquad\qquad\qquad\qquad\; (60)\end{aligned}$
      $\begin{aligned} {\boldsymbol{u} }_1^{l + 1}: =& \arg \mathop {\min }\limits_{ {\boldsymbol{u} }_1^{} } {\mathcal{L}_{ {\rho ^l} } }\left( { { {\boldsymbol{p} }^{l + 1} },{\boldsymbol{u} }_1^{},{\boldsymbol{u} }_2^l,{\boldsymbol{\kappa } }_1^l,{\boldsymbol{\kappa } }_2^l} \right){\text{ } } \\ & {\text{s} }{\text{.t} }{\text{. } }{\boldsymbol{B} }{ {\boldsymbol{u} }_1} = { { { {\textit{1} } } }_K} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad\;\, (61)\end{aligned}$
      $\begin{aligned} {\boldsymbol{u} }_2^{l + 1}: =& \arg \mathop {\min }\limits_{ { {\boldsymbol{u} }_2} } {\mathcal{L}_{ {\rho ^l} } }\left( { { {\boldsymbol{p} }^{l + 1} },{\boldsymbol{u} }_1^{l + 1},{\boldsymbol{u} }_2^{},{\boldsymbol{\kappa } }_1^l,{\boldsymbol{\kappa } }_2^l} \right){\text{ } } \\ & {\text{s} }{\text{.t} }{\text{. } }{\boldsymbol{C} }{ {\boldsymbol{u} }_2} = { { { {\textit{1} } } }_K} \qquad\qquad\quad\qquad\qquad\qquad\qquad\quad\; (62)\end{aligned}$
     步骤3. 通过下列公式更新${\boldsymbol{\kappa }}_1^{l + 1},{\boldsymbol{\kappa }}_2^{l + 1},{\rho ^{l + 1}}$:
      ${\rho }^{l+1}=\left\{\begin{aligned}& {\delta }_{2}{\rho }^{l},\text{ }\Vert {p}^{l+1}-{p}^{l}\Vert =0 \\ & {\rho }^{l},\text{ }其他\text{ } \end{aligned}\right.$ (63)
     $ {\boldsymbol{\kappa }}_1^{l + 1}: = {\boldsymbol{\kappa }}_1^l + {\rho ^{l + 1}}\left( {{\boldsymbol{u}}_1^{l + 1} - {{\boldsymbol{p}}^{l + 1}}} \right) $ (64)
     $ {\boldsymbol{\kappa }}_2^{l + 1}: = {\boldsymbol{\kappa }}_2^l + {\rho ^{l + 1}}\left( {{\boldsymbol{u}}_2^{l + 1} - {{\boldsymbol{p}}^{l + 1}}} \right) $ (65)
     4. 如果原始可行性容差
     ${V}_2^{l + 1} = {\left\| { {\boldsymbol{u} }_1^{l + 1} - { {\boldsymbol{p} }^{l + 1} } } \right\|^2} + {\left\| { {\boldsymbol{u} }_2^{l + 1} - { {\boldsymbol{p} }^{l + 1} } } \right\|^2} \le {\delta _3}$,则输出
     $ {{\boldsymbol{p}}^ \star } = {{\boldsymbol{p}}^{l + 1}} $;否则$ l: = l + 1 $,回到步骤2。
    下载: 导出CSV

    表  1  不同算法所得PMSR

    Table  1.   PMSR derived by different methods

    数值PSK-ADMMQAM-ADMMPSK-TRPIS
    $K = 4$18.769318.771517.8392
    $K = 8$18.769318.7735
    $K = 16$18.753518.8135
    下载: 导出CSV

    表  2  不同算法所需时间

    Table  2.   Computing time required by different methods

    数值PSK-ADMMQAM-ADMMPSK-TRPIS
    $K = 4$8.3548.4348.276
    $K = 8$5.5025.1828.281
    $K = 16$9.2217.3988.282
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-05-07
  • 修回日期:  2022-08-27
  • 网络出版日期:  2022-09-09

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