Citation: | Bo ZHANG, Kaizhi HUANG. Robust Secure Transmission Scheme Based on Artificial Noise-aided for Heterogeneous Networks with Simultaneous Wireless Information and Power Transfer[J]. Journal of Electronics & Information Technology, 2019, 41(1): 1-8. doi: 10.11999/JEIT180269 |
When the Channel State Information (CSI) is not accurate in heterogeneous networks with simultaneous wireless information and power transfer, to guarantee the security and reliability of information and energy transfer simultaneously, a robust secure transmission scheme based on Artificial Noise (AN)-aided is proposed. Through jointly designing the downlink information beamforming and AN matrix of macrocell base station and femtocell base stations, the potential eavesdroppers will be jammed, and the energy harvesting performance of system can be improved. To obtain the optimal designs, the problem of maximizing the energy harvesting performance of system is modeled under the base station power limit and the outage probability limits of information transfer, energy transfer and confidential information eavesdropped. This modeled problem is non-convex. To address the problem, it is transformed into an equivalent form, which can be processed easily. Then, the Bernstein-type inequality is utilized to deal with the outage probability limits, and it is transformed into a convex problem. Simulation results validate the security and the robustness of the proposed scheme.
在异构网络中,通过在宏基站(Macrocell Base Station, MBS)覆盖范围内重叠部署小基站可以提升网络容量及频谱利用率,但同时也带来了各层网络间的互相干扰问题[1]。就传统通信而言,这些干扰百无一用。但随着无线携能通信技术的发展,有学者提出可将此类干扰作为无线携能通信的一种特殊能量来源[2,3]。与传统网络相比,这种异构携能通信网络具有更加开放的网络架构和多样化的节点类型,导致窃听者(Eavesdropper, Eve)更易接入到网络中,对信息进行窃听。作为对传统加密算法的补充,物理层安全技术[4,5]利用无线信道的物理层特性探索解决通信安全问题,近年来越来越受到业界的广泛关注。
文献[6—8]基于完整信道状态信息(Channel State Information, CSI)对携能通信网络中的物理层安全进行了研究。但在实际网络中,受时延误差等因素的影响,发送端很难获取接收端的完整CSI。针对CSI不完整情形,业界一般用确定误差和随机误差两类模型来描述CSI误差,并相应发展出基于最坏情况性能优化安全设计和基于概率约束的统计性安全设计方法。考虑Eves的CSI存在确定性误差,为最大化系统安全速率,文献[9]对MBS和微基站(Femtocell Base Stations, FBSs)的信息波束、能量波束及人工噪声的联合设计问题进行了研究,结合半定松弛技术(SemiDenite Relaxation, SDR)和递归估计近似(Successive Convex Approximation, SCA)获取原始问题的解。考虑合法用户的CSI也存在确定误差时,文献[10]对异构携能通信网络中信息波束及人工噪声的联合设计问题做了进一步探讨。需要指出的是,上述基于最坏情况性能优化的安全方法均假设CSI误差是范数有界的,但这可能不符合实际,且过于保守,因为最坏CSI误差情形发生的概率可能很低。
相反地,考虑随机CSI误差,并基于概率约束的设计思想,只保证那些发生概率充分大的CSI误差时的安全性能更加贴近实际网络。基于此,文献[11—13]对单层MISO携能通信网络中的鲁棒安全传输方案进行了探讨。将能量接收用户(Energy Receivers, ERs)视为潜在的Eves,在信息接收用户(Information Receivers, IRs)和ERs的CSI存在随机误差时,文献[11]基于能量接收和安全中断概率约束对发送功率最小化的问题进行了研究,并提出一种低复杂度的基于迭代的2阶锥求解算法。从另一角度,文献[12]基于IRs, ERs的信息接收及能量接收中断概率约束,对最小化发送功率目标下的信息波束和人工噪声的联合设计问题进行了探讨。为最大化系统能量接收性能,文献[13]对IRs, ERs的中断概率约束下的下行信息波束设计问题进行了探究,并利用Bernstein-type不等式将中断约束条件转化为线性矩阵不等式进行求解。与文献[11—13]不同,考虑MIMO携能通信网络中存在随机误差时,为最大化系统能量接收性能,文献[14]研究了目标接收端的预编码矩阵和功率分离系数的联合设计问题。综上分析可知,现有相关研究仅考虑了单层携能通信网络或包含少数通信节点场景,其无法直接适用于异构携能网络节点数目众多、层间干扰复杂的场景。而且,上述文献并未考虑多个Eves之间相互勾结的情形,此时系统安全性将受到更大威胁。
针对上述问题,本文提出一种基于人工噪声辅助的鲁棒安全传输方案。通过在MBS和FBS下行信号中同时注入人工噪声,而后联合优化设计MBS, FBS的信息波束和人工噪声协方差矩阵。在CSI随机误差下及基站发送功率约束,IRs, ERs的信息传输、能量接收中断约束和Eves的信息窃听中断约束,以最大化系统能量接收性能为目标,对该问题进行建模。建模后问题是非凸的。为求解该问题,首先通过将原始问题等效转化为一种易于处理的形式;而后,进一步利用Bernstein-type不等式对其中的中断约束进行处理,将其转化为一个凸的优化问题,并结合2次等式引理获取秩为1的信息波束成形解。仿真结果验证了该方案的安全性和鲁棒性。
如图1所示,MBS位于宏小区的中心位置,MBS覆盖范围内分布着
假设
$\begin{align}{{y}_m} =& {h}_m^{\rm{H}}{{w}_m}{{s}_m} + {h}_m^{\rm{H}}\left(\sum\limits_{p \ne m}^M {{{w}_p}{{s}_p} + {{z}_0}} \right) \\& + \sum\limits_{n = 1}^N {{h}_{n,m}^{\rm{H}}\left(\sum\limits_{k = 1}^K {{{w}_{nk}}{{s}_{nk}} + {{z}_n}} \right) + {n_m}} ,\\& \quad\quad\quad m \in [1,M]\end{align}$
|
(1) |
$\begin{align}{{y}_{nk}} =& {h}_{n,nk}^{\rm{H}}{{w}_{nk}}{{s}_{nk}} + {h}_{n,nk}^{\rm{H}}\left(\sum\limits_{t \ne k}^K {{{w}_{nt}}{{s}_{nt}} + {{z}_n}} \right) \\&+ \sum\limits_{a \ne n}^N {h}_{a,nk}^{\rm{H}}\left(\sum\limits_{t = 1}^K {{{w}_{at}}{{s}_{at}} + {{z}_a}} \right) \\&+ {h}_{nk}^{\rm{H}}\left(\sum\limits_{m = 1}^M {{{w}_m}{{s}_m} + {{z}_0}} \right) + {n_{nk}}\end{align}$
|
(2) |
$\begin{align}{{y}_{\rm Eb}} =& {h}_{\rm Eb}^{\rm{H}}{{w}_1}{{s}_1} + {h}_{\rm Eb}^{\rm{H}}\left(\sum\limits_{m = 2}^M {{{w}_m}{{s}_m}} + {{z}_0}\right) \\& + \sum\limits_{n = 1}^N {h}_{n,{\rm Eb}}^{\rm{H}}\left(\sum\limits_{k = 1}^K {{{w}_{nk}}{{s}_{nk}} + {{z}_n}}\right) + {n_{\rm Eb}} ,\\& b \in [1,B]\end{align}$
|
(3) |
其中,式(2)中
$\begin{align}{\rm{SIN}}{{\rm{R}}_m} =& {{{{\left| {{h}_m^{\rm{H}}{{w}_m}} \right|}^2}}}\Biggr/\Biggr(\sum\limits_{p \ne m}^M {{{\left| {{h}_m^{\rm{H}}{{w}_p}} \right|}^2}} + {{\left| {{h}_m^{\rm{H}}{{z}_0}} \right|}^2} \\& +\! \sum\limits_{n = 1}^N {\sum\limits_{k = 1}^K {{{\left| {{h}_{n,m}^{\rm{H}}{{w}_{nk}}} \right|}^2} \!+\! \sum\limits_{n = 1}^N {{{\left| {{h}_{n,m}^{\rm{H}}{{z}_n}} \right|}^2}} \!+\! {\sigma ^2}}} \Biggr)\end{align}$
|
(4)
${\rm{SIN}}{{\rm{R}}_{nk}} = \frac{{{{\left| {{h}_{n,nk}^{\rm{H}}{{w}_{nk}}} \right|}^2}}}{{{A_{nk}}}}$
|
(5) |
其中,
考虑Eves相互勾结的情形,此时可将其看作一个多天线Eve
$\begin{align}{\rm{SIN}}{{\rm{R}}_{\rm EB}} =& {{\sum\limits_{b = 1}^B {{{\left| {{h}_{\rm Eb}^{\rm{H}}{{w}_1}} \right|}^2}} }}\biggr/\Biggr(\xi \Biggr(\sum\limits_{b = 1}^B \Biggr(\sum\limits_{m = 2}^M {{{\left| {{h}_{\rm Eb}^{\rm{H}}{{w}_m}} \right|}^2}} \\&+\! \sum\limits_{n = 1}^N {\sum\limits_{k = 1}^K {{{\left| {{h}_{n,{\rm Eb}}^{\rm{H}}{{w}_{nk}}} \right|}^2}}}\Biggr)\Biggr) \!+\! \sum\limits_{b = 1}^B \Biggr({{\left| {{h}_{\rm Eb}^{\rm{H}}{{z}_0}} \right|}^2}\\&+ \sum\limits_{n = 1}^N {{{\left| {{h}_{n,{\rm Eb}}^{\rm{H}}{{z}_n}} \right|}^2}} \Biggr) + {\sigma ^2}\Biggr)\end{align}$
|
(6) |
其中,
$\begin{align}{{\rm{E}}_{\rm harvest}}(b) =& \kappa \Biggr(\sum\limits_{m = 1}^M {{{\left| {{h}_{\rm Eb}^{\rm{H}}{{w}_m}} \right|}^2}} + \sum\limits_{n = 1}^N \sum\limits_{k = 1}^K {{\left| {{h}_{n,{\rm Eb}}^{\rm{H}}{{w}_{nk}}} \right|}^2} \\&+ \sum\limits_{n = 1}^N {{{\left| {{h}_{n,{\rm Eb}}^{\rm{H}}{{z}_n}} \right|}^2}\Biggr)} \end{align}$
|
(7) |
其中,
本文考虑CSI存在随机误差的情形,则式(1)—式(3)中的信道矢量可表示为[11—14]
${h} = \hat{ h} + {e},\;{e} = {{Q}^{1/2}}{r},\;{r} \sim CN(0,{I})$
|
(8) |
其中,
$\mathop {\max }\limits_{\{ {{{W}}_m}\} ,{{{Z}}_0}\atop\{ {{{W}}_{nk}}\} ,\{ {{{Z}}_n}\} } \mathop {\min }\limits_{b \in [1,B]} ({{\rm{E}}_{\rm harvest}}(b))$
|
(9a) |
$\!\begin{align}&{\rm s.t.}\\ & \Pr \{ {\rm{SIN}}{{\rm{R}}_m} \le {\gamma _m}\} \le {\rho _{\rm{m}}},m \in [1,M]\end{align}$
|
(9b) |
$\Pr \{ {\rm{SIN}}{{\rm{R}}_{nk}} \le {\gamma _{nk}}\} \le {\rho _{nk}},n \in [1,N],k \in [1,K]\hspace{5t}$
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(9c) |
$ \Pr \{ {\rm{SIN}}{{\rm{R}}_{\rm EB}} \ge {\gamma _{\rm EB}}\} \le {\rho _{\rm EB}}$
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(9d) |
$\sum\limits_{m = 1}^M {{\rm{Trace(}}{{W}_m}{\rm{)}}} {\rm{ + Trace}}({{Z}_0}) \le {{{P}}_M}$
|
(9e) |
$\sum\limits_{k = 1}^K {{\rm{Trace(}}{{W}_{nk}}{\rm{)}}} {\rm{ + Trace(}}{{Z}_n}) \le {{{P}}_F},n \in [1,N]$
|
(9f) |
${\rm{rank}}({{W}_m}) = {\rm{rank}}({{W}_{nk}}) = 1$
|
(9g) |
其中,
本节将分两部分处理式(9)问题:首先对式(9)问题进行等效变换,获取其一种等价形式;而后利用Bernstein-type不等式对其中的中断概率约束条件进行处理。
引入辅助变量
$\mathop {\max }\limits_{\{ {{{W}}_m}\} ,{{{Z}}_0}\atop\{ {{{W}}_{nk}}\} ,\{ {{{Z}}_n}\} ,t} t\hspace{160}$
|
(10a) |
${\rm s.t.}{\;\;式\left( 9{\rm{b}\right)}{- 式\left( 9{\rm{g}} \right)\hspace{130}$
|
(10b) |
$\Pr \{ {{\rm{E}}_{\rm harvest}}(b) \le t\} \le {q_{\rm Eb}},\;b \in [1,B]$
|
(10c) |
其中,
$\begin{align}{{A}_{Mm}} =& {\rm diag}\Biggr(\Biggr({{W}_m} - {\gamma _m}\sum\limits_{p \ne m}^M {\left({{W}_p} + {{Z}_0}\right)}\Biggr), \\&- {\gamma _m}\left(\left({{W}_{1k}} + {{Z}_1}\right), ·\!·\!·,\left({{W}_{Nk}} + {{Z}_N}\right)\right)\Biggr)\end{align}$
|
(11) |
其中,
$\begin{align}& \Pr \{ {r}_{Mm}^{\rm{H}}{{B}_{Mm}}{{r}_{Mm}} + 2{\mathop{\rm Re}\nolimits} \{ {r}_{Mm}^{\rm{H}}{{c}_{Mm}}\} \le {d_{Mm}}\} \le {\rho _m}, \\& \quad\quad m \in [1,M]\end{align}$
|
(12) |
其中,
$\begin{align}& \Pr \{ {r}_{Fuk}^{\rm{H}}{{B}_{Fnk}}{{r}_{Fnk}} + 2{\mathop{\rm Re}\nolimits} \{ {r}_{Fuk}^{\rm{H}}{{c}_{Fnk}}\} \le {d_{Fnk}}\} \le {\rho _{nk}},\\&\quad\quad n \in [1,N],k \in [1,K]\end{align}$
|
(13) |
$\!\!\!\!\begin{align}&\Pr \{ {r}_{\rm EEB}^{\rm{H}}{{B}_{\rm EEB}}{{r}_{\rm EEB}} + {\mathop{\rm Re}\nolimits} \{ {r}_{\rm EEB}^{\rm{H}}{{c}_{\rm EB}}\} \ge {d_{\rm EEB}}\} \\& \quad\quad\le {\rho _{\rm EB}}\end{align}$
|
(14) |
$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!!\!\!\!!\!\!\!!\!\!\!!\!\!\! \begin{align}&\Pr \{ {r}_{\rm CEb}^{\rm{H}}{{B}_{\rm CEb}}{{r}_{\rm CEb}} + 2{\mathop{\rm Re}\nolimits} \{ {r}_{\rm CEb}^{\rm{H}}{{c}_{\rm CEb}}\} \\& \quad\quad \le {d_{\rm CEb}}\} \le {q_{\rm Eb}}, b \in [1,B]\end{align}$
|
(15) |
其中,式(13)中
$\left. \begin{aligned}& {{A}_{Fnk}} = \!{\rm diag}\!\left(\!\!{{W}_{nk}} - {\gamma _{nk}}\left(\!\sum\limits_{t = 1,t \ne k}^K {{{W}_{nt}} + {{Z}_n}} \right)\!\!\right)\!\!,\\& \quad\quad\quad \left( - {\gamma _{nk}}\left(\sum\limits_{m = 1}^M {{{W}_m}} + {{Z}_0}\right)\!\right)\!\!, \\& \quad\quad\quad - {\gamma _{nk}}\left( ·\!·\!· ,\left({{W}_{(n + 1)t}} + {{Z}_{n + 1}}\right), ·\!·\!· \right)\\& {{Q}_{Fnk}} = {\rm diag}\left({{Q}_{n,nk}^{1/2}},{{Q}_{nk}^{1/2}} ·\!·· ,{{Q}_{n - 1,nk}^{1/2}},\right. \\& \quad\quad\quad \left. {{Q}_{n + 1,nk}^{1/2}}, ·\!·\!· \right)\\ & {{\hat{ h}}_{Fnk}}{\rm{ = }}\!\left[\! {{\left({{\hat{ h}}_{n,nk}}\right)}^{\rm{H}}}\!\!\!,\!{{\left(\!{{\hat{ h}}_{nk}}\!\right)}^{\rm{H}}}\!\!\!, ·\!·\!· ,{{\left(\!{{\hat{ h}}_{n - 1,nk}}\!\right)}^{\rm{H}}}\!\!\!,\right. \\ & \quad\quad\quad \left.{{({{\hat{ h}}_{n + 1,nk}})}^{\rm{H}}}\!\!, ·\!·\!· \right]^{\rm{H}}\end{aligned} \!\! \right\}\quad\quad$
|
(16) |
式(14)中,
$\!\!\! \left. \begin{array}{l}{{Q}_{\rm EEB}} = {\rm diag}(\underbrace {{Q}_{E1}^{1/2}, ·\!·\!· ,{{Q}_{\rm EB}^{1/2}}}_{{共}B{项}},\underbrace {{{Q}_{1,E1}^{1/2}}, ·\!·\!· ,{{Q}_{N,E1}^{1/2}}}_{{共}N{项}},\underbrace {{{Q}_{1,E2}^{1/2}}, ·\!·\!· ,{{Q}_{N,E2}^{1/2}}}_{{共}N{项}},\underbrace { ·\!·\!· ,{{Q}_{N,{\rm EB}}^{1/2}}}_{\left( {B - 2} \right){个}N{项}})\\{{A}_{\rm EEB}} \!=\! {\rm diag}\left(\overbrace {\underbrace {\left({{W}_1} - {\gamma _{\rm EB}}\left(\xi \cdot \sum\limits_{m = 2}^M {{{W}_m}} + {{Z}_0}\right)\right)}_{{表示为}{{a}}}, ·\!·\!· ,}^{{共}B{个}{{a}}}\overbrace {\underbrace { - {\gamma _{\rm EB}}(\xi {{W}_{1k}} + {{Z}_1}), ·\!·\!· , - {\gamma _{\rm EB}}(\xi {{W}_{Nk}} + {{Z}_N})}_{{表示为}{{b}}}, ·\!·\!· }^{{共}B{个}{{b}}}\right)\\{{\hat{ h}}_{\rm EEB}} = {\left[\underbrace {{{\left({{\hat{ h}}_{{\rm{E1}}}}\right)}^{\rm{H}}}, ·\!·\!· ,{{\left({{\hat{ h}}_{{\rm{EB}}}}\right)}^{\rm{H}}}}_{{共}B{项}},\underbrace {{{\left({{\hat{ h}}_{{\rm{1,E1}}}}\right)}^{\rm{H}}}, ·\!·\!· ,{{\left({{\hat{ h}}_{{{N,{\rm E1}}}}}\right)}^{\rm{H}}}}_{{共}N{项}},\underbrace {{{\left({{\hat{ h}}_{{\rm{1,E2}}}}\right)}^{\rm{H}}}, ·\!·\!· ,{{\left({{\hat{ h}}_{{{N,{\rm E2}}}}}\right)}^{\rm{H}}}}_{{共}N{项}},\underbrace { ·\!·\!· ,{{\left({{\hat{ h}}_{{{{N},{\rm EB}}}}}\right)}^{\rm{H}}}}_{\left( {B{\rm{ - }}2} \right){个}N{项}}\right]^{\rm{H}}}\end{array} \!\!\!\right\}$
|
(17)
式(15)中,
$\left. \begin{aligned}&{{Q}_{\rm CEb}} = {\rm diag}\left({{Q}_{\rm Eb}^{1/2}},{{Q}_{1,{\rm Eb}}^{1/2}}, ·\!·\!· ,{{Q}_{N,{\rm Eb}}^{1/2}}\right)\\&{{A}_{{\rm{CEb}}}} = {\rm diag}\Biggr(\sum\limits_{m = 1}^M {{{W}_m}} ,({{W}_{1k}} + {{Z}_1}) ·\!· · \\& \quad\quad\quad ({{W}_{Nk}} + {{Z}_N})\Biggr)\\&{{\hat{ h}}_{{\rm{CEb}}}} = {\left[{\left({{\hat{ h}}_{{\rm{Eb}}}}\right)^{\rm{H}}},{\left({{\hat{ h}}_{1,{\rm{Eb}}}}\right)^{\rm{H}}}, ·\!·\!· ,{\left({{\hat{ h}}_{N,{\rm{Eb}}}}\right)^{\rm{H}}}\right]^{\rm{H}}}\end{aligned} \right\}$
|
(18) |
其中,
借助于Bernstein-type不等式[14],分别对式(12)—式(15)进行处理,可将其转化为
$ \!\!\left. \begin{array}{l}{\rm{Trace(}}{{B}_{Mm}}{\rm{)}} - {u_{Mm}}\sqrt {2{\lambda _{Mm}}} - {\lambda _{Mm}}{v_{Mm}} \!\ge\! {d_{Mm}}\\\left\| \begin{array}{l}{\rm vec}({{B}_{Mm}})\\\sqrt 2 {{c}_{Mm}}\end{array} \right\| \le {u_{Mm}}\\{v_{Mm}}{{I}_{{N_M} + N{N_F}}} + {{B}_{Mm}} \ge 0\end{array} \!\!\!\!\right\}\quad\quad\quad $
|
(19) |
$\!\! \left. \begin{array}{l}{\rm{Trace(}}{{B}_{Fnk}}{\rm{)}} - {u_{Fnk}}\sqrt {2{\lambda _{Fnk}}} - {\lambda _{Fnk}}{v_{Fnk}} \ge {d_{Fnk}}\\\left\| \begin{array}{l}{\rm vec}({{B}_{Fnk}})\\\sqrt 2 {{c}_{Fnk}}\end{array} \right\| \le {u_{Fnk}}\\{v_{Fnk}}{{I}_{{N_M} + N{N_F}}} + {{B}_{Fnk}} \ge 0\end{array} \!\!\!\!\right\}\quad\quad\quad\quad $
|
(20) |
$\!\!\! \left. \begin{array}{l}{\rm{Trace(}}{{B}_{\rm EEB}}{\rm{) + }}{u_{\rm EEB}}\sqrt {2{\lambda _{\rm EEB}}} \!+\! {\lambda _{\rm EEB}}{v_{\rm EEB}}\! \le\! {d_{\rm EEB}}\\ \left\| \begin{array}{l}{\rm{vec(}}{{B}_{\rm EEB}}{\rm{)}}\\\sqrt 2 {{c}_{\rm EEB}}\end{array} \right\| \le {u_{\rm EEB}}\\ {v_{\rm EEB}}{{I}_{B({N_M} + N{N_F})}} - {{B}_{\rm EEB}} \ge 0\end{array} \!\!\!\!\right\}\quad\quad\quad\quad\quad $
|
(21) |
$\!\! \left. \begin{array}{l}{\rm{Trace(}}{{B}_{{\rm{CEb}}}}{\rm{)}} \!- {u_{{{\rm{CEb}}}}}\sqrt {2{\lambda _{{\rm{CEb}}}}} \!- {\lambda _{{\rm{CEb}}}}{v_{{\rm{CEb}}}} \!\ge\! {d_{{\rm{CEb}}}}\\\left\| \begin{array}{l}{\rm vec}({{B}_{{\rm{CEb}}}})\\\sqrt 2 {{c}_{{\rm{CEb}}}}\end{array} \right\| \le {u_{{\rm{CEb}}}}\\{v_{{\rm{CEb}}}}{{I}_{N{N_F}}} + {{B}_{{\rm{CEb}}}} \ge 0\end{array} \!\!\!\!\! \right\}\quad\quad\quad\quad $
|
(22) |
其中,
${{W}_m} = {{w}_m}{w}_m^{\rm{H}},\;{{W}_{nk}} = {{w}_{nk}}{w}_{nk}^{\rm{H}}$
|
(23) |
可借助2次等式引理[15]对其进行处理,则此时式(9)问题可转化为
$\mathop {\max }\limits_{\{ {{{W}}_m}\} ,\{ {{{w}}_m}\} ,{{{Z}}_0}\atop\{ {{{W}}_{nk}}\} ,\{ {{{w}}_{nk}}\} ,\{ {{{Z}}_n}\} ,t} t$
|
(24a) |
$ \begin{align}{\rm s.t.}&\;\;{{式}}\left( {19} \right){,}\ {{式}}\left( {20} \right){,}\ {{式}}\left( {21} \right){,}\ {{式}}\left( {22} \right){,}\\& \;\;{{式}}\left( {9{\rm{e}}} \right){,}\ {{式}}\left( {9{\rm{f}}} \right)\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\end{align}$
|
(24b) |
$\!\!\!\left. \begin{array}{l}\left\| {\left[ {\begin{array}{*{20}{c}}{{{A}_{BS1m}}}&{{{W}_m}}&{{{w}_m}}\\{{W}_m^{\rm{H}}}&{{{A}_{BS2m}}}&{{{w}_m}}\\{{w}_m^{\rm{H}}}&{{w}_m^{\rm{H}}}&1\end{array}} \right]} \right\| \ge 0\\{\rm{Trace}}\left(\mathop {{{w}_m}}\limits^ \simeq {\rm{(}}j{\rm{)}}\mathop {{{w}_m}}\limits^ \simeq {{\rm{(}}j{\rm{)}}^{\rm{H}}}\right) \\\quad\quad+ 2{\rm Re}\left\{ {\rm Trace}\left({{w}_m} - \mathop {{{w}_m}}\limits^ \simeq {\rm{(}}j)\right){\rm{}}\mathop {{{w}_m}}\limits^ \simeq {{\rm{(}}j{\rm{)}}^{\rm{H}}} \right\} \\\quad\quad\ge {\rm{Trace(}}{{A}_{{\rm BS}1m}}{\rm{)}}\end{array} \!\!\right\}\quad\quad $
|
(24c) |
$\!\!\!\left. \begin{array}{l}\left\| {\left[ {\begin{array}{*{20}{c}}{{{A}_{{\rm BS}1nk}}}&{{{W}_{nk}}}&{{{w}_{nk}}}\\{{W}_{nk}^{\rm H}}&{{{A}_{{\rm BS}2nk}}}&{{{w}_{nk}}}\\{{w}_{nk}^{\rm{H}}}&{{w}_{nk}^{\rm{H}}}&1\end{array}} \right]} \right\| \ge 0\\{\rm{Trace}}\left(\mathop {{{w}_{nk}}}\limits^ \simeq {\rm{(}}j{\rm{)}}\mathop {{{w}_{nk}}}\limits^ \simeq {{\rm{(}}j{\rm{)}}^{\rm{H}}}\right) \\\quad\quad + 2{\rm Re}\left\{ {\rm Trace}\left({{w}_{nk}} - \mathop {{{w}_{nk}}}\limits^ \simeq {\rm{(}}j)\right)\mathop {{{w}_{nk}}}\limits^ \simeq {{\rm{(}}j{\rm{)}}^{\rm{H}}}\right\} \\\quad\quad \ge {\rm{Trace}}({{A}_{{\rm BS}1nk}})\end{array} \!\!\!\!\right\}\quad\quad\quad $
|
(24d) |
式(24)问题是一个凸的优化问题。其中,
本小节总结该方案的整体算法,具体过程如表1所示。
初始化:设置
|
循环: |
步骤 1 将
|
步骤 2 更新:
|
步骤 3 令
|
终止:直至收敛或达到最大迭代次数
|
输出:最优的
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将本文方案与以下方案进行仿真对比:(1)对比方案1:基于完整CSI的设计方案,即将获取的估计CSI视为准确CSI。(2)对比方案2:利用S-引理对联合设计问题进行处理。(3)对比方案3:与对比方案2不同,该方案分别将人工噪声限定在合法信道零空间,基于S-引理对联合优化设计问题进行求解[16]。考虑简化的大尺度路径损耗与小尺度衰落模型,小尺度衰落为瑞利衰落[9]。系统参数设置为:
从图2可以看出,随着
从图4可以看出,对比方案1不受
如图5所示,对比方案1始终具有最优的可行解性能。在3种鲁棒设计方案中,本文方案显示出了最好的性能。一方面是因为采用Bernstein-type不等式方案更加贴近实际的概率要求,而采用S-引理方案则过于保守;另一方面,采用未限定人工噪声结构方案能够有效地对
考虑异构携能通信网络中CSI存在随机误差的场景,为避免多个相互勾结的ERs对MU的下行信息进行窃听,本文提出一种基于人工噪声辅助的鲁棒安全传输方案。通过联合设计MBS, FBS的下行信息波束和人工噪声协方差矩阵,最大化系统能量接收性能。在发送功率约束,IRs的信息接收中断概率约束,Eves的信息窃听中断约束及能量接收中断概率约束下,该能量接收性能最大化问题是非凸的。为求解该问题,首先通过等效变换获取原始问题的等价形式;而后利用Bernstein-type不等式处理其中的中断概率约束,将其转化为可以直接进行求解的线性矩阵不等式。仿真结果验证了该方案的安全性和鲁棒性。
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初始化:设置
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循环: |
步骤 1 将
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步骤 2 更新:
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步骤 3 令
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终止:直至收敛或达到最大迭代次数
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输出:最优的
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