CN103856299B - Signal safe transmission method of MIMO amplifying forwarding relay network - Google Patents

Abstract

The invention provides a signal safe transmission method of an MIMO amplifying forwarding relay network. According to the method, in the process of designing a precoding matrix, the GSVD-ZF-SVD joint strategy is adopted to parallelize a system, the expression mode of the safety speed of the system is simplified, and an optimization problem is solved under power constraint; in the power distribution process, the non-convexity of the original problem makes direct solutions difficult to work out, each sub-problem can have the only optimal solution due to the adoption of alternating iteration and optimization, and a point of convergence can be finally obtained through alternating iteration. In the method, joint precoding of a sending node end and a relay node is considered, channels are parallelized through the GSVD-ZF-SVD method, and therefore problem analysis is simplified. Power distribution is optimized. Calculation complexity is small.

Description

A kind of signals security transmission method of MIMO amplification forwarding junction network

Technical field

The invention belongs to radio transmission technical field, particularly to a kind of signals security of MIMO amplification forwarding junction network Transmission method.

Background technology

Safety problem is one of radio communication basic problem.The opening of wireless medium, brings more to safety Big challenge.The safety of physical layer technology of radio communication is a new wireless signal secure transmission technique.It does not rely on profit Encrypt to realize Security Data Transmission with key, but by appropriate design signal, distribution power and modulation coding mode, come Improving the safe rate of signal transmission, preventing the stolen hearer of information from eavesdropping, thus improving the safety of information transfer.In recent years, Radio physical layer has obtained safely the very big concern of academia.

Multiple-input and multiple-output（MIMO）Technology and trunking traffic technology are two safety of physical layer lifting radio communications Means.They can be by using spatial degrees of freedom so that the design of signal be more flexible, can raising radio transmission Safe rate.Both are combined the physical layer transmission safety that can lift radio communication further.But, a MIMO is relayed The safety of physical layer transmission signal of network directly carry out optimal design extremely difficult it is impossible to obtain an effective result, therefore The result of study of this respect is less at present.

J.Huang, A.L.Swindlehutst are in document " Cooperative jamming for secure communications in MIMO relay network,”IEEE Trans.Signal Processing,vol.59, Consider in no.10, pp.4871-4884, Oct.2011 and realize signals security transmission using repeat transmitted interference signal.But Consider is the trunking plan that relaying is forwarded using decoding.Decoding forwarding scheme requires via node that information is decoded, this The complexity making system increases, and the time delay of simultaneity factor increases, and in via node it must also be ensured that being correctly decoded.

Liu Yang, Song Mei, Zhang Yong et al. carry in patent of invention " the safe retransmission method of the wireless relay based on hierarchical modulation " Arrive the problem of relaying safety, but do not accounted for utilizing MIMO technology, in addition, inventor's consideration is also to enter in via node Row decoding.

Content of the invention

It is an object of the invention to provide a kind of signals security transmission method of MIMO amplification forwarding junction network, to improve The safety of communication；The present invention is that one algorithm complex of proposition is relatively low simultaneously safely to the radio physical layer under MIMO junction network The method being capable of higher rate.

To achieve these goals, the present invention adopts the following technical scheme that：

A kind of signals security transmission method of MIMO amplification forwarding junction network, described MIMO amplification forwarding junction network bag Include a sending node, a via node, an eavesdropping node and a receiving node, each node is equipped with many days Line, number of antennas is respectively N_A,N_R,N_E,N_B；

Described signals security transmission method comprises the following steps：

1）First stage, sending node carries out linear predictive coding to transmission information, and via node and eavesdropping node receive The information of sending node transmitting is respectively：y_R=H_ARFs+n_R,Wherein H_AR,H_AEIt is that sending node arrives Via node and the channel matrix of eavesdropping node, F is sending node Linear precoding matrix, and s is sending node transmitting information arrow Measure, covariance matrix isn_R,It is additive Gaussian noise vector, covariance matrix isy_R,It is to receive arrow Amount；

2）Second stage, via node, by the signal receiving, is amplified forwarding, and pre-coding matrix is W, receiving node The information receiving with eavesdropping node is to be respectively：

y_B=H_RBWH_ARFs+H_RBWn_R+n_B, $y_E^{\left(2\right)}=H_{\mathrm{RE}}{\mathrm{WH}}_{\mathrm{AR}}\mathrm{Fs}+H_{\mathrm{RE}}{\mathrm{Wn}}_R+n_E^{\left(2\right)}.$

Wherein H_RB,H_REIt is the channel matrix to receiving node and eavesdropping node for the via node, n_B,It is additive white gaussian Noise, covariance matrix isy_B,It is to receive vector；

Equivalent eavesdropping node receive information is：

$y_E=\left[\begin{array}{c}{y}_E^{\left(1\right)}\\ y_E^{\left(2\right)}\end{array}\right]=H_{E}s+n_E,$ $H_E=\left[\begin{array}{c}{H}_{\mathrm{AE}}F\\ H_{\mathrm{RE}}{\mathrm{WH}}_{\mathrm{AR}}F\end{array}\right],$ $n_E=\left[\begin{array}{c}{n}_E^{\left(1\right)}\\ H_{\mathrm{RE}}{\mathrm{Wn}}_R+n_E^{\left(2\right)}\end{array}\right]$

3）Under power constraint, maximize the speed of safe transmission, i.e. optimized power distribution, realize maximum safety speed Rate：

R_s=max(I(y_B;s)-I(y_E;s))⁺

$s.t.{\mathrm{\σ}}_s^2\mathrm{tr}\left({\mathrm{FF}}^H\right)\≤P_1$

$\mathrm{tr}({\mathrm{\σ}}_s^2{\mathrm{WH}}_{\mathrm{AR}}{\mathrm{FF}}^H{H}_{\mathrm{AR}}^H{W}^H+{\mathrm{\σ}}_n^2{\mathrm{WW}}^H)\≤P_2$

The present invention is further improved by：The step obtaining the pre-coding matrix of sending node and via node includes：

First to channel matrix H_AR,H_AECarry out generalized singular value decomposition to obtain：

H_AR=UΛ_ARΦ

H_AE=VΛ_AEΦ

Wherein Φ=R Ψ^HIt is a N_A×N_ANonsingular matrix, U, V are unitary matrice Λ_ARAnd Λ_AEFor：

${\mathrm{\Λ}}_{\mathrm{AR}}={\left(\begin{array}{cc}0& 0\\ D_{\mathrm{AR}}& 0\\ 0& I_{q\×q}\end{array}\right)}_{N_R\×M}$

${\mathrm{\Λ}}_{\mathrm{AE}}={\left(\begin{array}{cc}{D}_{\mathrm{AE}}& 0\\ 0& 0_{(N_E-s)\×q}\end{array}\right)}_{N_E\×M}$

Wherein q+s=N_A,K=N_A=M,

D_AR=diag(d_AR,1,d_AR,2,…,d_AR,s),D_AE=diag(d_AE,1,d_AE,2,…,d_AE,s), wherein d_AR,iAscending order arranges, d_AE,iDescending；Designing pre-coding matrix of making a start is：

$F=\frac{{\mathrm{\ΨR}}^{-1}}{\left|\right|R^{-1}\left|\right|}\sqrt{P_a}$

Wherein $P_a=\mathrm{diag}(\sqrt{p_{a,1}},\sqrt{p_{a,2}},\·\·\·,\sqrt{p_{a,K}});$

If the singular value decomposition of via node to validated user channel matrix is

${\mathrm{\Σ}}_{\mathrm{RB}}=\left(\begin{array}{cc}0& {\stackrel{\‾}{\mathrm{\Σ}}}_{\mathrm{RB}}\end{array}\right),$ ${\stackrel{\‾}{\mathrm{\Σ}}}_{\mathrm{RB}}=\mathrm{diag}({\mathrm{\λ}}_{\mathrm{RB},1},{\mathrm{\λ}}_{\mathrm{RB},2},\·\·\·,{\mathrm{\λ}}_{\mathrm{RB},K}),$ Design pre-coding matrix W makes Node must be eavesdropped and do not receive any information in second stage, even It is H_REThe projection of kernel Matrix is so that H_REW=0；Then utilize singular value decomposition, design relaying pre-coding matrix is

$\stackrel{\‾}{W}=\stackrel{\‾}{V}\sqrt{P_r}{U}^H$

$W=H_{\mathrm{RE}}^{\⊥}\stackrel{\‾}{V}\sqrt{P_r}{U}^H$

Wherein,This completes sending node and relaying section The design of the pre-coding matrix of point；

The present invention is further improved by：Step 3）In obtain safe rate and its power constraint is：

$\underset{p_{a,k},p_{r,k}}{\max }{R}_s=\frac{1}{2}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}[\log (1+\frac{\stackrel{\‾}{\mathrm{\ρ}}{p}_{r,k}{p}_{a,k}{\mathrm{\λ}}_{\mathrm{RB},k}^2{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2}{1+p_{r,k}{\mathrm{\λ}}_{\mathrm{RB},k}^2})-\log (1+\stackrel{\‾}{\mathrm{\ρ}}{p}_{a,k}{\stackrel{\‾}{d}}_{\mathrm{AE},k}^2)]$

$s.t.P_A={\mathrm{\σ}}_s^2\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{p}_{a,k}\≤P_1$

$P_R={\mathrm{\σ}}_n^2\underset{k=1}{\overset{K}{\mathrm{\Σ}}}(\stackrel{\‾}{\mathrm{\ρ}}{p}_{r,k}{p}_{a,k}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2+p_{r,k})\≤P_2$

Wherein P₁,P₂It is the general power of sending node and via node respectively, ${\stackrel{\‾}{D}}_{\mathrm{AR}}=\mathrm{diag}(d_{\mathrm{AR},1},d_{\mathrm{AR},2},\·\·\·,d_{\mathrm{AR},s},1,\·\·\·,1),$ ${\stackrel{\‾}{D}}_{\mathrm{AE}}=\mathrm{diag}(d_{\mathrm{AE},1},d_{\mathrm{AE},2},\·\·\·,d_{\mathrm{AE},s},0,\·\·\·,0)$ It is respectivelyK-th diagonal element.

The present invention is further improved by：Safe rate and its power constraint are adopted with the method that alternating iteration solves； Carry out substitution of variable z first_k=p_a,k, $r_k=\stackrel{\‾}{\mathrm{\ρ}}{p}_{r,k}{p}_{a,k}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2+p_{r,k},$ ${\stackrel{\‾}{P}}_1=P_1/{\mathrm{\σ}}_s^2,{\stackrel{\‾}{P}}_2=P_2/{\mathrm{\σ}}_n^2,$ To upper State optimization problem to be deformed, as given z_k, optimize r_kObtaining optimization problem is：

$\underset{r_k}{\max }\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\log \left(\frac{1+{\mathrm{\λ}}_{\mathrm{RB},k}^2{r}_k}{1+{\mathrm{\λ}}_{\mathrm{RB},k}^2{r}_k+\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2{z}_k}\right)$

$s.t.\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{r}_k\≤{\stackrel{\‾}{P}}_2,r_k\≥0,k=\mathrm{1,2},\·\·\·,K.$

It solves and is

$r_k^{*}\left(v\right)=\frac{1}{2{\mathrm{\λ}}_{\mathrm{RB},k}^2}{[\sqrt{{\left(\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2{z}_k\right)}^2+4\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2{z}_k{\mathrm{\λ}}_{\mathrm{RB},k}^{2}v}-\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2{z}_k-2]}^{+}$

Wherein [x]⁺Represent the greater taking between x and 0, variable ν needs to meet following formula

$\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{r}_k^{*}\left(v\right)={\stackrel{\‾}{P}}_2$

As fixing r_k, optimize z_k, obtaining optimization problem is

$\underset{z_k}{\max }\underset{k=1}{\overset{K}{\mathrm{\Σ}}}[\log \left(\frac{1+a_k{z}_k}{1+b_k+c_k{z}_k}\right)-\log \left(1{+c}_k{z}_k\right)]$

$s.t.\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{z}_k\≤{\stackrel{\‾}{P}}_1,z_k\≥0,k=\mathrm{1,2},\·\·\·,K.$

The present invention is further improved by：When sending node is fewer than eavesdropping node antennas or identical situation, Xie Wei：

（1）When ${\mathrm{\Σ}}_{k\∈\mathrm{\Ω}}{\stackrel{\‾}{P}}_{c,k}\≤{\stackrel{\‾}{P}}_1$ When, Xie WeiWherein set omega is all to meet d_k= a_kb_k-b_kc_k-c_k>0 k composition, ${\stackrel{\‾}{P}}_{c,k}=\frac{-{2a}_k{c}_k+\sqrt{{4a}_k^2{c}_k^2+{4a}_k^2{c}_k{d}_k}}{{2a}_k^2{c}_k}$

（2）When ${\mathrm{\Σ}}_{k\∈\mathrm{\Ω}}{\stackrel{\‾}{P}}_{c,k}>{\stackrel{\‾}{P}}_1$ When, Xie WeiWhereinIt is $\ln 2(1+a_k{z}_k)(1+b_k+a_k{z}_k)(1+c_k{z}_k)\mathrm{\μ}+a_k^2{c}_k{z}_k^2+{2a}_k{c}_k{z}_k-d_k=0$ Three Individual solution, and meet $\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{z}_k^{*}={\stackrel{\‾}{P}}_1;$

When sending node has the situation of more antennas, Xie Wei than eavesdropping node antennas：

Wherein set omega₀={k:k∈Ω,c_k=0 }, Ω₊={k:k∈Ω,c_k>0}；

By alternating iteration, end product converges at a point, that is, obtain power distribution.

Compared with the existing methods, the invention has the beneficial effects as follows：

1st, consider the joint precoding of sending node end and via node, using GSVD-ZF-SVD method, by channel simultaneously Rowization, simplifies the analysis difficulty of problem；And carried out the power distribution of optimum.Realize on the premise of safe transmission the most at a high speed Rate is transmitted.

2nd, computation complexity is relatively low：The result of alternating iteration optimization has two, and one is to obtain closed solutions, and one is to obtain The result of one similar water filling, computation complexity is low.

Brief description

Fig. 1 is the system model involved by the inventive method.

Fig. 2 is equivalent parallel channel figure in the present invention.

Fig. 3 a and Fig. 3 b is the simulation result of existing method, wherein：Fig. 3 a gives safe rate and via node power The change curve of constraint, Fig. 3 b gives safe rate and the change curve of sending node end power constraint.

Specific embodiment

The present invention is described in further detail with specific embodiment below in conjunction with the accompanying drawings.

The present invention relates to system model is as shown in figure 1, there is a sending node（Alice）, a via node （Relay）, a receiving node（Bob）And an eavesdropping node（Eve）, each node is equipped with multiple antennas, antenna Number is respectively N_A,N_R,N_E,N_B.Via node adopts the repetition policy of AF (amplification forwarding) receipt signal to be amplified turn Send out.By right（Sending node-trunk channel matrix, sending node-tapping channel matrix）Using generalized singular value decomposition （GSVD）, at sending node end, design pre-coding matrix is matching, and obtaining sending node pre-coding matrix isIn via node, via node is to the Information Pull ZF-SVD method design precoding square receiving Battle array, obtaining relaying pre-coding matrix isIt is achieved thereby that the parallelization of channel, as accompanying drawing 2 institute Show.

A, when sending node end number of antennas be not so good as eavesdropping node many when, the power distribution obtaining is：

(1) when ${\mathrm{\Σ}}_{k\∈\mathrm{\Ω}}{\stackrel{\‾}{P}}_{c,k}\≤{\stackrel{\‾}{P}}_1$ When, Xie WeiWherein set omega is all to meet d_k= a_kb_k-b_kc_k-c_k>0 k composition, ${\stackrel{\‾}{P}}_{c,k}=\frac{-{2a}_k{c}_k+\sqrt{{4a}_k^2{c}_k^2+{4a}_k^2{c}_k{d}_k}}{{2a}_k^2{c}_k}$

(2) when ${\mathrm{\Σ}}_{k\∈\mathrm{\Ω}}{\stackrel{\‾}{P}}_{c,k}>{\stackrel{\‾}{P}}_1$ When, Xie WeiWhereinIt is $\ln 2(1+a_k{z}_k)(1+b_k+a_k{z}_k)(1+c_k{z}_k)\mathrm{\μ}+a_k^2{c}_k{z}_k^2+{2a}_k{c}_k{z}_k-d_k=0$ Three solutions, and meet $\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{z}_k^{*}={\stackrel{\‾}{P}}_1.$

B and when sending node end number of antennas is more, obtaining power distribution is：

Can see, when sending node number of antennas is less, sending node end power is not The more the better, it exists One optimal value, this can reflect from Fig. 3 b.In this case, if sending node end power all uses, make First stage leakage rate increases, and the rate of information throughput of second stage is subject to the constraint of via node power so that system Safe rate reduce on the contrary.And when sending node number of antennas is more it may appear that c_k=0 situation, this when, surreptitiously Listen node to be actually information not available, thus all distribution sending node power is not in the situation of the anti-fall of speed.This Discuss a bit from Fig. 3 it can be seen that coming.No matter which kind of situation, final safe rate all can tend to be steady, and this is to send section The reason point end or via node power limited.

A kind of signals security transmission method of present invention MIMO amplification forwarding junction network, comprises the following steps：

1）First stage, sending node carries out linear predictive coding to transmission information, and via node and eavesdropping node connect respectively Receive information y of sending node transmitting_R=H_ARFs+n_R,Wherein H_AR,H_AEIt is channel matrix, F is Sending node Linear precoding matrix, s is sending node transmitting information vector, n_R,It is additive Gaussian noise vector, y_R,It is to receive vector.

2）Second stage, via node by the signal receiving, be amplified forward, pre-coding matrix be W, receiving node and The information that eavesdropping node receives is y_B=H_RBWH_ARFs+H_RBWn_R+n_B, $y_E^{\left(2\right)}=H_{\mathrm{RE}}{\mathrm{WH}}_{\mathrm{AR}}\mathrm{Fs}+H_{\mathrm{RE}}{\mathrm{Wn}}_R+n_E^{\left(2\right)}.$ This Sample can be obtained by equivalent eavesdropping node receive information

$y_E=\left[\begin{array}{c}{y}_E^{\left(1\right)}\\ y_E^{\left(2\right)}\end{array}\right]=H_{E}s+n_E,$ $H_E=\left[\begin{array}{c}{H}_{\mathrm{AE}}F\\ H_{\mathrm{RE}}{\mathrm{WH}}_{\mathrm{AR}}F\end{array}\right],$ $n_E=\left[\begin{array}{c}{n}_E^{\left(1\right)}\\ H_{\mathrm{RE}}{\mathrm{Wn}}_R+n_E^{\left(2\right)}\end{array}\right]$

3）Under power constraint, maximize the speed of safe transmission, i.e. optimized power distribution, realize maximum safety speed Rate：

R_s=max(I(y_B;s)-I(y_E;s))⁺

$s.t.{\mathrm{\σ}}_s^2\mathrm{tr}\left({\mathrm{FF}}^H\right)\≤P_1$

$\mathrm{tr}({\mathrm{\σ}}_s^2{\mathrm{WH}}_{\mathrm{AR}}{\mathrm{FF}}^H{H}_{\mathrm{AR}}^H{W}^H+{\mathrm{\σ}}_n^2{\mathrm{WW}}^H)\≤P_2$

According to above-mentioned method it is necessary first to obtain the pre-coding matrix of sending node and via node, then carry out Excellent power distribution.

Method using GSVD-ZF-SVD：

1st, first to channel matrix H_AR,H_AECarry out generalized singular value decomposition to obtain：

H_AR=UΛ_ARΦ

H_AE=VΛ_AEΦ

Wherein Φ=R Ψ^HIt is a N_A×N_ANonsingular matrix, Λ_ARAnd Λ_AEThere is following form

${\mathrm{\Λ}}_{\mathrm{AR}}={\left(\begin{array}{cc}0& 0\\ D_{\mathrm{AR}}& 0\\ 0& I_{q\×q}\end{array}\right)}_{N_R\×M}$

${\mathrm{\Λ}}_{\mathrm{AE}}={\left(\begin{array}{cc}{D}_{\mathrm{AE}}& 0\\ 0& 0_{(N_E-s)\×q}\end{array}\right)}_{N_E\×M}$

Wherein q+s=N_A,K=N_A=M,

D_AR=diag(d_AR,1,d_AR,2,…,d_AR,s),D_AE=diag(d_AE,1,d_AE,2,…,d_AE,s), wherein d_AR,iAscending order arranges, d_AE,iDescending.

Designing sending node pre-coding matrix is：

$F=\frac{{\mathrm{\ΨR}}^{-1}}{\left|\right|R^{-1}\left|\right|}\sqrt{P_a}$

Wherein $P_a=\mathrm{diag}(\sqrt{p_{a,1}},\sqrt{p_{a,2}},\·\·\·,\sqrt{p_{a,K}}).$

2nd, set via node to receiving node channel matrix singular value decomposition asDesign prelists Code matrix W makes eavesdropping node not receive any information in second stage, even It is H_REZero is empty Between projection matrix so that H_REW=0.Then utilize singular value decomposition, design relaying pre-coding matrix is

$\stackrel{\‾}{W}=\stackrel{\‾}{V}\sqrt{P_r}{U}^H$

This completes the design of the pre-coding matrix of sending node and via node.

3rd, in order to realize the power distribution of optimum, in the case of the pre-coding matrix designing above, obtain safe rate And its power constraint is

$\underset{p_{a,k},p_{r,k}}{\max }{R}_s=\frac{1}{2}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}[\log (1+\frac{\stackrel{\‾}{\mathrm{\ρ}}{p}_{r,k}{p}_{a,k}{\mathrm{\λ}}_{\mathrm{RB},k}^2{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2}{1+p_{r,k}{\mathrm{\λ}}_{\mathrm{RB},k}^2})-\log (1+\stackrel{\‾}{\mathrm{\ρ}}{p}_{a,k}{\stackrel{\‾}{d}}_{\mathrm{AE},k}^2)]$

$s.t.P_A={\mathrm{\σ}}_s^2\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{p}_{a,k}\≤P_1$

$P_R={\mathrm{\σ}}_n^2\underset{k=1}{\overset{K}{\mathrm{\Σ}}}(\stackrel{\‾}{\mathrm{\ρ}}{p}_{r,k}{p}_{a,k}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2+p_{r,k})\≤P_2$

Above direct solution, optimization problem difficulty is larger, the method being solved using alternating iteration.It is substitution of variable z_k=p_a,k, $r_k=\stackrel{\‾}{\mathrm{\ρ}}{p}_{r,k}{p}_{a,k}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2+p_{r,k},$ ${\stackrel{\‾}{P}}_1=P_1/{\mathrm{\σ}}_s^2,{\stackrel{\‾}{P}}_2=P_2/{\mathrm{\σ}}_n^2,$ Above-mentioned optimization problem is deformed, as given z_k, Optimize r_kObtaining optimization problem is：

$\underset{r_k}{\max }\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\log \left(\frac{1+{\mathrm{\λ}}_{\mathrm{RB},k}^2{r}_k}{1+{\mathrm{\λ}}_{\mathrm{RB},k}^2{r}_k+\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2{z}_k}\right)$

$s.t.\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{r}_k\≤{\stackrel{\‾}{P}}_2,r_k\≥0,k=\mathrm{1,2},\·\·\·,K.$

It solves and is

$r_k^{*}\left(v\right)=\frac{1}{2{\mathrm{\λ}}_{\mathrm{RB},k}^2}{[\sqrt{{\left(\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2{z}_k\right)}^2+4\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2{z}_k{\mathrm{\λ}}_{\mathrm{RB},k}^{2}v}-\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{\mathrm{AR},k}^2{z}_k-2]}^{+}$

Wherein [x]⁺Represent the greater taking between x and 0, variable ν needs to meet following formula

$\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{r}_k^{*}\left(v\right)={\stackrel{\‾}{P}}_2$

As fixing r_k, optimize z_k, obtaining optimization problem is

$\underset{z_k}{\max }\underset{k=1}{\overset{K}{\mathrm{\Σ}}}[\log \left(\frac{1+a_k{z}_k}{1+b_k+c_k{z}_k}\right)-\log \left(1{+c}_k{z}_k\right)]$

$s.t.\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{z}_k\≤{\stackrel{\‾}{P}}_1,z_k\≥0,k=\mathrm{1,2},\·\·\·,K.$

When sending node is fewer than eavesdropping node antennas or identical situation, Xie Wei

(1) when ${\mathrm{\Σ}}_{k\∈\mathrm{\Ω}}{\stackrel{\‾}{P}}_{c,k}\≤{\stackrel{\‾}{P}}_1$ When, Xie WeiWherein set omega is all to meet d_k= a_kb_k-b_kc_k-c_k>0 k composition, ${\stackrel{\‾}{P}}_{c,k}=\frac{-{2a}_k{c}_k+\sqrt{{4a}_k^2{c}_k^2+{4a}_k^2{c}_k{d}_k}}{{2a}_k^2{c}_k}$

(2) when ${\mathrm{\Σ}}_{k\∈\mathrm{\Ω}}{\stackrel{\‾}{P}}_{c,k}>{\stackrel{\‾}{P}}_1$ When, Xie WeiWherein It is $\ln 2(1+a_k{z}_k)(1+b_k+a_k{z}_k)(1+c_k{z}_k)\mathrm{\μ}+a_k^2{c}_k{z}_k^2+{2a}_k{c}_k{z}_k-d_k=0$ Three solution, and And meet $\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{z}_k^{*}={\stackrel{\‾}{P}}_1.$

When sending node has the situation of more antennas, Xie Wei than eavesdropping node antennas

Wherein set omega₀={k:k∈Ω,c_k=0 }, Ω₊={k:k∈Ω,c_k>0}.

By alternating iteration, end product converges at a point, obtains power distribution.

The present invention proposes a kind of signals security transmission method of MIMO amplification forwarding junction network, in design precoding square During battle array, employ the federation policies of GSVD-ZF-SVD so that system in parallel, simplify the expression-form of system safe rate, An optimization problem is solved under conditions of power constraint.When carrying out power distribution, the nonconvex property of former problem makes Direct solution is difficult to carry out, and by the way of alternating iteration optimizes, each subproblem can obtain unique optimal solution, and Final alternating iteration can obtain a convergence point, and this convergence point is a critical point certainly.When eavesdropping node antennas number Mesh is no less than sending node end, and when via node power is fixing, power of making a start has an optimal value.

Claims (2)

1. a kind of signals security transmission method of MIMO amplification forwarding junction network is it is characterised in that described MIMO amplification forwarding Junction network includes a sending node, a via node, an eavesdropping node and a receiving node, and each node is all Equipped with multiple antennas, number of antennas is respectively N_A,N_R,N_E,N_B；

Described signals security transmission method comprises the following steps：

1) first stage, sending node carries out linear predictive coding to transmission information, and via node and eavesdropping node receive transmission The information of node transmitting is respectively：Wherein H_AR,H_AEIt is sending node To the channel matrix of via node and eavesdropping node, F is sending node Linear precoding matrix, and s is sending node transmitting information Vector, covariance matrix isn_RWithIt is respectively the additive Gaussian noise at first stage via node and eavesdropping node Vector, both covariance matrixes arey_RWithIt is respectively the reception letter of first stage via node and eavesdropping node Number vector；

2) second stage, via node by the signal receiving, be amplified forward, pre-coding matrix be W, receiving node and steal The information that node receives is listened to be respectively：

$y_B=H_{RB}{\mathrm{WH}}_{AR}Fs+H_{RB}{\mathrm{Wn}}_R+n_B,y_E^{\left(2\right)}=H_{RE}{\mathrm{WH}}_{AR}Fs+H_{RE}{\mathrm{Wn}}_R+n_E^{\left(2\right)}.$

Wherein H_RB,H_REIt is the channel matrix to receiving node and eavesdropping node for the via node, n_BWithIt is respectively second stage to connect Receive the additive white Gaussian noise at node and eavesdropping node, both covariance matrixes arey_BWithIt is respectively second Stage receiving node and the receipt signal vector of eavesdropping node；

Equivalent eavesdropping node receive information is：

$y_E=\left[\begin{array}{c}{y}_E^{\left(1\right)}\\ y_E^{\left(2\right)}\end{array}\right]=H_{E}s+n_E,H_E=\left[\begin{array}{c}{H}_{AE}F\\ H_{RE}W{H}_{AR}F\end{array}\right],n_E=\left[\begin{array}{c}{n}_E^{\left(1\right)}\\ H_{RE}{\mathrm{Wn}}_R+n_E^{\left(2\right)}\end{array}\right]$

3) under power constraint, maximize the speed of safe transmission, i.e. optimized power distribution, realize maximum safe rate：

R_s=max (I (y_B；s)-I(y_E；s))⁺

$\begin{array}{cc}s.t.& {\mathrm{\σ}}_s^{2}tr\left({\mathrm{FF}}^H\right)\≤P_1\end{array}$

$tr({\mathrm{\σ}}_s^2{\mathrm{WH}}_{AR}{\mathrm{FF}}^H{H}_{AR}^H{W}^H+{\mathrm{\σ}}_n^2{\mathrm{WW}}^H)\≤P_2$

The step obtaining the pre-coding matrix of sending node and via node includes：

First to channel matrix H_AR,H_AECarry out generalized singular value decomposition to obtain：

H_AR=U Λ_ARΦ

H_AE=V Λ_AEΦ

Wherein Φ=R Ψ^HIt is a N_A×N_ANonsingular matrix, U, V are unitary matrice, Λ_ARAnd Λ_AEFor：

${\mathrm{\Λ}}_{AR}={\left(\begin{array}{cc}0& 0\\ D_{AR}& 0\\ 0& I_{q\×q}\end{array}\right)}_{N_R\×M}$

${\mathrm{\Λ}}_{AE}={\left(\begin{array}{cc}{D}_{AE}& 0\\ 0& 0_{(N_E-s)\×q}\end{array}\right)}_{N_E\×M}$

Wherein q+s=N_A, K=N_A=M,

D_AR=diag (d_AR,1, d_AR,2..., d_AR,s),D_AE=diag (d_AE,1, d_AE,2..., d_AE,s), wherein d_AR,iAscending order arranges, d_AE,iDescending；Designing pre-coding matrix of making a start is：

$F=\frac{{\mathrm{\ΨR}}^{-1}}{\left|\right|R^{-1}\left|\right|}\sqrt{P_a}$

WhereinR^-1Inverse matrix for R；

If the singular value decomposition of via node to validated user channel matrix is Design pre-coding matrix W makes eavesdropping section Point does not receive any information in second stage, even It is H_REThe projection matrix of kernel so that H_REW=0；Then utilize singular value decomposition, design relaying pre-coding matrix is

$\stackrel{\‾}{W}=\stackrel{\‾}{V}\sqrt{P_r}{U}^H$

$W=H_{RE}^{\⊥}\stackrel{\‾}{V}\sqrt{P_r}{U}^H$

Wherein,This completes the pre- of sending node and via node The design of encoder matrix；

Using generalized singular value decomposition and singular value decomposition, channel is converted into the parallel eavesdropping in K road subchannel, P_a,kRepresent and send The transmission power of the parallel subchannel in node Chuk road, P_r,kRepresent the transmission power of the parallel subchannel in via node Chuk road；

Step 3) in obtain safe rate and its power constraint is：

$\begin{array}{cc}\underset{p_{a,k},p_{r,k}}{\max }& R_s=\frac{1}{2}\underset{k=1}{\overset{K}{\Σ}}\[\log \left(1+\frac{\stackrel{\‾}{\mathrm{\ρ}}{p}_{r,k}{p}_{a,k}{\mathrm{\λ}}_{RB,k}^2{\stackrel{\‾}{d}}_{AR,k}^2}{1+p_{r,k}{\mathrm{\λ}}_{RB,k}^2}\right)-\log (1+\stackrel{\‾}{\mathrm{\ρ}}{p}_{a,k}{\stackrel{\‾}{d}}_{AE,k}^2)\]\end{array}$

$\begin{array}{cc}s.t.& P_A={\mathrm{\σ}}_s^2\underset{k=1}{\overset{K}{\Σ}}{p}_{a,k}\≤P_1\end{array}$

$P_R={\mathrm{\σ}}_n^2\underset{k=1}{\overset{K}{\Σ}}(\stackrel{\‾}{\mathrm{\ρ}}{p}_{r,k}{p}_{a,k}{\stackrel{\‾}{d}}_{AR,k}^2+p_{r,k})\≤P_2$

Wherein P₁,P₂It is the general power of sending node and via node respectively, It is respectivelyK-th diagonal element；

Safe rate and its power constraint are adopted with the method that alternating iteration solves；Carry out substitution of variable first

To above-mentioned optimization problem Deformed, as given z_k, optimize r_kObtaining optimization problem is：

$\begin{array}{cc}\underset{r_k}{max}& \underset{k=1}{\overset{K}{\Σ}}log\left(\frac{1+{\mathrm{\λ}}_{RB,k}^2{r}_k}{1+{\mathrm{\λ}}_{RB,k}^2{r}_k+\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{AR,k}^2{z}_k}\right)\end{array}$

$\begin{array}{cccc}s.t.& \underset{k=1}{\overset{K}{\Σ}}{r}_k\≤{\stackrel{\‾}{P}}_2,& r_k\≥0,& k=1,2,\mathrm{...},K\end{array}$

It solves and is

$r_k^{*}\left(v\right)=\frac{1}{2{\mathrm{\λ}}_{RB,k}^2}{\[\sqrt{{\left(\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{AR,k}^2{z}_k\right)}^2+4\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{AR,k}^2{z}_k{\mathrm{\λ}}_{RB,k}^{2}v}-\stackrel{\‾}{\mathrm{\ρ}}{\stackrel{\‾}{d}}_{AR,k}^2{z}_k-2\]}^{+}$

Wherein [x]⁺Represent the greater taking between x and 0, variable ν needs to meet following formula

$\underset{k=1}{\overset{K}{\Σ}}{r}_k^{*}\left(v\right)={\stackrel{\‾}{P}}_2$

As fixing r_k, optimize z_k, obtaining optimization problem is

$\begin{array}{cc}\underset{z_k}{max}& \underset{k=1}{\overset{K}{\Σ}}\[log\left(\frac{1+a_k{z}_k}{1+b_k+c_k{z}_k}\right)-log(1+c_k{z}_k)\]\end{array}$

$\begin{array}{cccc}s.t.& \underset{k=1}{\overset{K}{\Σ}}{z}_k\≤{\stackrel{\‾}{P}}_1,& z_k\≥0,& k=1,2,\mathrm{...},K\end{array}.$

2. the signals security transmission method of a kind of MIMO amplification forwarding junction network according to claim 1, its feature exists In,

When sending node is fewer than eavesdropping node antennas or identical situation, Xie Wei：

(1) whenWhen, Xie WeiWherein set omega is all satisfactions

d_k=a_kb_k-b_kc_k-c_k>0 k composition,

(2) whenWhen, Xie WeiWhereinIt isThree

Individual solution, and meet

When sending node has the situation of more antennas, Xie Wei than eavesdropping node antennas：

Wherein set omega₀={ k:k∈Ω,c_k=0 }, Ω₊={ k:k∈Ω,c_k>0}；

By alternating iteration, end product converges at a point, that is, obtain power distribution.