CN104519499A - Method for forming security cooperation beams in amplifying and forwarding wireless relay networks - Google Patents

Abstract

The invention discloses a method for forming security cooperation beams in amplifying and forwarding wireless relay networks. The method includes steps of 1), acquiring accessible information speeds I<1> at first source nodes T<i>, accessible information speeds I<2> at second source nodes T<2> and accessible information rates at eavesdroppers E<k> in the amplifying and forwarding wireless relay networks; 2), constructing optimization problems for controlling single relay power according to security and rate maximization criteria, converting the optimization problems into semi-definite programming problems, acquiring the optimal matrixes x<opt> by the aid of iteration processes and then acquiring the optimal security and rates according to the optimal matrixes x<opt>. The matrixes x<opt> meet an equation of rank(X<opt>)=1. The method has the advantages that the maximum security and rates for forming the security cooperation beams in the amplifying and forwarding wireless relay networks can be implemented by the aid of the method, accordingly the probability that the eavesdroppers steal information of legal users can be obviously reduced, and the spectral efficiency of security communication can be improved.

Description

A kind of method of security cooperation wave beam forming in amplification forwarding wireless relay network

Technical field

The invention belongs to wireless communication field, relate to the method for security cooperation wave beam forming in a kind of amplification forwarding wireless relay network.

Background technology

The intrinsic opening of wireless channel accelerates the development of wireless communication system, but too increases the probability be ravesdropping simultaneously.Safety of physical layer to obtain at secure communications as a kind of method of raising safety newly and pays close attention to widely.Compared with traditional high rise building safety scheme, the advantage of safety of physical layer is that overhead is little, protocol stack simple and complexity is lower, is therefore suitable for distributed relay network element.Up-to-date research shows, cooperation distributed node can improve safe rate significantly.

Research at present about safety of physical layer is mainly concentrated in mimo systems, and the distributed relay that cooperates can improve safe rate significantly.In distributed relay network, the secure communication of one-way junction cooperative beam figuration is suggested.Along with the development of secure communication, in order to improve spectrum efficiency, network scenarios has been extended to bilateral relay network.And the scheme of the suboptimum about secure communication has been proposed in bilateral network, such as, the kernel cooperative beam figuration when known listener-in's channel condition information and the man made noise's scheme when unknown listener-in's channel condition information.But the optimization aim in above scheme is all and speed instead of safety and speed.Also been proposed the research of the general approach of the kernel wave beam forming in the restriction of source node through-put power based on this, Optimality Criteria is safety and speed.But more than research is only suitable for the scene of an existence listener-in.In addition, in amplification forwarding bilateral relay network, propose a kind of integration and cooperation wave beam forming of suboptimum and the scheme of man made noise, the program can obtain higher safety and speed.

In sum, in amplification forwarding bilateral relay network, the research about the linear arrangement of secure communication is necessary.

Summary of the invention

The object of the invention is to the shortcoming overcoming above-mentioned prior art, provide the method for security cooperation wave beam forming in a kind of amplification forwarding wireless relay network, the method can realize the figuration of security cooperation wave beam in amplification forwarding wireless relay network, remarkable reduction listener-in steals the informational probability of proper user, improves the spectrum efficiency of secure communication.

For achieving the above object, in amplification forwarding wireless relay network of the present invention, the method for security cooperation wave beam forming comprises the following steps:

Comprise the following steps:

1) in amplification forwarding wireless relay network, first source node T ₁and second source node T ₂by one group of relaying R _nexchange message, listener-in E _kbe passive, and attempt illegal wiretapping first source node T ₁with second source node T ₂the information at place, wherein, n=1,2 ..., N, k=1,2 ..., K, N are relaying sum, and K is the quantity of listener-in, then first source node T ₁place can reach information rate I ₁, second source node T ₂place can reach information rate I ₂and listener-in E _kplace can reach information rate be respectively

$I_1=\frac{1}{2}\log (1+\frac{P_2{w}^H{R}_{\mathrm{fg}}w}{w^H{R}_{\mathrm{ff}}w+1+f_R^T\mathrm{\&Sigma;}{f}_R^{*}})---\left(9\right)$

$I_2=\frac{1}{2}\log (1+\frac{P_1{w}^H{R}_{\mathrm{fg}}w}{w^H{R}_{\mathrm{gg}}w+1+g_R^T\mathrm{\&Sigma;}{g}_R^{*}})---\left(10\right)$

$I_{E_k}=\frac{1}{2}\log ({\mathrm{\&gamma;}}_k+\frac{w^H{V}_{k}w}{w^H{R}_{c_k{c}_k}w+1+c_{E_k}^T\mathrm{\&Sigma;}{c}_{E_k}^{*}})---\left(11\right)$

Wherein P ₁be first source node T ₁average transmit power, P ₂be second source node T ₂average transmit power, w is wave beam formed matrix, f _rbe first source node T ₁to the channel of all relayings, f _eto the first source node T ₁to the channel of listener-in, g _rbe second source node T ₂to the channel of all relayings, g _ebe second source node T ₂to the channel of listener-in, c _efor being relayed to the quasistatic fading coefficients of listener-in, for being relayed to the quasistatic fading coefficients of a kth listener-in, r _ff=diag (| f _{r, 1}| ², | f _{r, 2}| ²..., | f _{r, N}| ²), $R_{c_k{c}_k}=\mathrm{diag}({\left|c_{E_k,1}\right|}^2,{\left|c_{E_k,2}\right|}^2,...,{\left|c_{E_k,N}\right|}^2),$ a _fg＝f _Rοg _R， $R_{\mathrm{fg}}=a_{\mathrm{fg}}{a}_{\mathrm{fg}}^H,$ R _gg＝diag(|f _g，1| ²，|f _g，2| ²，...，|f _g，N| ²)， $V_k=(P_1{P}_2{\left|g_{E_k}\right|}^2+P_1)R_{c_{k}f}+(P_1{P}_2{\left|f_{E_k}\right|}^2+P_2)R_{c_{k}g}-P_1{P}_2{f}_{E_k}{g}_{E_k}^{*}{a}_{c_{k}g}{a}_{c_{k}f}^H-P_1{P}_2{f}_{E_k}^{*}{g}_{E_k}{a}_{c_{k}f}{a}_{c_{k}g}^H,$ $R_{c_{k}f}=a_{c_{f}f}{a}_{c_{k}f}^H,$ $R_{c_{k}g}=a_{c_{f}g}{a}_{c_{k}g}^H;$

2) then the optimization problem of the single relay power control of criteria construction is maximized namely according to safety and speed

$Q1:\underset{w,\mathrm{\&Sigma;}}{\max }\underset{k}{\min }\{I_1+I_2-I_{E_k}\},$

$s.t.{\left[x_R^H{x}_R\right]}_{n,n}\&le;P_{R_n},\&ForAll;n$

Wherein, x _rcarry out wave beam forming to the received signal for relaying and add the signal after man made noise, p _rfor the gross power of all relayings, then formula (9), formula (10) and formula (11) are brought in Q1,

$\begin{array}{c}Q2:\underset{w,\mathrm{\&Sigma;}}{\max }\underset{k}{\min }\frac{1+w^H(R_{\mathrm{ff}}+P_2{R}_{\mathrm{fg}})w+f_R^T\mathrm{\&Sigma;}{f}_R^{*}}{1+w^H{R}_{\mathrm{ff}}w+f_R^T\mathrm{\&Sigma;}{f}_R^{*}}\\ \&CenterDot;\frac{1+w^H(R_{\mathrm{gg}}+P_1{R}_{\mathrm{fg}})w+g_R^T{\mathrm{\&Sigma;g}}_R^{*}}{1+w^H{R}_{\mathrm{gg}}w+g_R^T{\mathrm{\&Sigma;g}}_R^{*}}\\ \&CenterDot;\frac{1+w^H{R}_{c_k{c}_k}w+c_{E_k}^T{\mathrm{\&Sigma;c}}_{E_k}^{*}}{w^H({\mathrm{\&gamma;}}_k{R}_{c_k{c}_k}+V_k)w+{\mathrm{\&gamma;}}_k(1+c_{E_k}^T{\mathrm{\&Sigma;c}}_{E_k}^{*})}\end{array}$

$s.t.{\left[x_R^H{x}_R\right]}_{n,n}\&le;P_{R_n},\&ForAll;n,$

Wherein, Q2 is a non-convex problem, Q2 is converted into semi definite programming problem, and obtains optimum matrix X by the method for iteration _opt, the matrix X of wherein said optimum _optmeet rank (X _opt)=1, then according to the matrix X of described optimum _optoptimum safety and speed, then carry out the figuration of security cooperation wave beam in amplification forwarding wireless relay network according to the safety of described optimum and speed.

2, the method for security cooperation wave beam forming in amplification forwarding wireless relay network according to claim 1, is characterized in that, if B ₁=R _ff+ P ₂r _fg, B ₂=R _gg+ P ₁r _fg, ${\mathrm{\&sigma;}}_1^2=1+f_R^T{\mathrm{\&Sigma;f}}_R^{*},$ ${\mathrm{\&sigma;}}_2^2=1+g_R^T{\mathrm{\&Sigma;g}}_R^{*},$ ${\mathrm{\&sigma;}}_{3k}^2=1+c_{E_k}^T{\mathrm{\&Sigma;c}}_{E_k}^{*},$ C ₁=R _ff, C ₂=R _ggwith then optimization problem Q2 can be expressed as

$Q3:\underset{w,\mathrm{\&Sigma;},k}{\max \min }\frac{w^H{B}_{1}w+{\mathrm{\&sigma;}}_1^2}{w^H{C}_{1}w+{\mathrm{\&sigma;}}_1^2}\&CenterDot;\frac{w^H{B}_{2}w+{\mathrm{\&sigma;}}_2^2}{w^H{C}_{2}w+{\mathrm{\&sigma;}}_2^2}\&CenterDot;\frac{w^H{B}_{3k}w+{\mathrm{\&sigma;}}_{3k}^2}{w^H{C}_{3k}w+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2};$

$s.t.{[w^H(P_1{R}_{\mathrm{ff}}+P_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)w+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},\&ForAll;n.$

Make X=ww ^h, then optimization problem Q3 can abbreviation be:

$Q4:\underset{X,\mathrm{\&Sigma;},{\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2,{\mathrm{\&alpha;}}_{3k},{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_{3k},k}{\max \min }\log \left({\mathrm{\&alpha;}}_1\right)+\log \left({\mathrm{\&alpha;}}_2\right)+\log \left({\mathrm{\&alpha;}}_{3k}\right)-\log \left({\mathrm{\&beta;}}_1\right)-\log \left({\mathrm{\&beta;}}_2\right)-\log \left({\mathrm{\&beta;}}_{3k}\right)$

$s.t.{[(P_1{R}_{\mathrm{ff}}{+P}_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)X+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},{\&ForAll;n}_{}$

${\mathrm{\&alpha;}}_1=\mathrm{tr}\left(B_{1}X\right)+{\mathrm{\&sigma;}}_1^2,{\mathrm{\&alpha;}}_2=\mathrm{tr}\left(B_{2}X\right)+{\mathrm{\&sigma;}}_2^2;$

${\mathrm{\&alpha;}}_{3k}=\mathrm{tr}\left(B_{3k}X\right)+{\mathrm{\&sigma;}}_{3k}^2,{\mathrm{\&beta;}}_1=\mathrm{tr}\left(C_{1}X\right)+{\mathrm{\&sigma;}}_1^2$

${\mathrm{\&beta;}}_2=\mathrm{tr}\left(C_{2}X\right)+{\mathrm{\&sigma;}}_2^2,{\text{\&beta;}}_{3k}=\mathrm{tr}\left(C_{3k}X\right)+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2$

X≥0，rαnk{X}＝1.

Target function due to optimization problem Q4 is the difference of two convex functions, so optimization problem Q4 is non-convex problem, carries out linear approximation to the target function of optimization problem Q4, order $\log \left({\mathrm{\&beta;}}_j\right)=\log \left({\mathrm{\&beta;}}_{j,0}\right)+\frac{1}{{\mathrm{\&beta;}}_{j,0}}({\mathrm{\&beta;}}_j-{\mathrm{\&beta;}}_{j,0}),j=\mathrm{1,2,3}k,$ β _{j, 0}be the initial value of Taylor expansion, the order 1 removed in optimization problem Q4 limits, then optimization problem Q4, can be reduced to:

$Q5:\underset{X,\mathrm{\&Sigma;},{\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2,{\mathrm{\&alpha;}}_{3k},{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_{3k},k}{\max \min }\log \left({\mathrm{\&alpha;}}_1\right)+\log \left({\mathrm{\&alpha;}}_2\right)+\log \left({\mathrm{\&alpha;}}_{3k}\right){-t}_1-t_2-t_{3k}$

$s.t.{[(P_1{R}_{\mathrm{ff}}{+P}_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)X+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},{\&ForAll;n}_{}$

${\mathrm{\&alpha;}}_1=\mathrm{tr}\left(B_{1}X\right)+{\mathrm{\&sigma;}}_1^2,{\mathrm{\&alpha;}}_2=\mathrm{tr}\left(B_{2}X\right)+{\mathrm{\&sigma;}}_2^2$

${\mathrm{\&alpha;}}_{3k}=\mathrm{tr}\left(B_{3k}X\right)+{\mathrm{\&sigma;}}_{3k}^2,{\mathrm{\&beta;}}_1=\mathrm{tr}\left(C_{1}X\right)+{\mathrm{\&sigma;}}_1^2;$

${\mathrm{\&beta;}}_2=\mathrm{tr}\left(C_{2}X\right)+{\mathrm{\&sigma;}}_2^2,{\text{\&beta;}}_{3k}=\mathrm{tr}\left(C_{3k}X\right)+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2$

$\log \left({\mathrm{\&beta;}}_{j,0}\right)+\frac{1}{{\mathrm{\&beta;}}_{j,0}}({\mathrm{\&beta;}}_j-{\mathrm{\&beta;}}_{j,0})\&le;t_j,j=\mathrm{1,2,3}k$

Work as β _{j, 0}=β _{j, opt}time, log (β _j) first order Taylor expand into real Taylor expansion, the further abbreviation of optimization problem Q5 is

$Q6:\underset{X,\mathrm{\&Sigma;},{\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2,{\mathrm{\&alpha;}}_{3k},{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_{3k},k}{\min }\mathrm{\&tau;}$

s.t.-(log(α ₁)+log(α ₂)+log(α _3k))+t ₁+t ₂+t _3k＜＝τ

${[(P_1{R}_{\mathrm{ff}}+P_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)X+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},\&ForAll;n$

${\mathrm{\&alpha;}}_1=\mathrm{tr}\left(B_{1}X\right)+{\mathrm{\&sigma;}}_1^2,{\mathrm{\&alpha;}}_2=\mathrm{tr}\left(B_{2}X\right)+{\mathrm{\&sigma;}}_2^2;$

${\mathrm{\&alpha;}}_{3k}=\mathrm{tr}\left(B_{3k}X\right)+{\mathrm{\&sigma;}}_{3k}^2,{\mathrm{\&beta;}}_1=\mathrm{tr}\left(C_{1}X\right)+{\mathrm{\&sigma;}}_1^2$

${\mathrm{\&beta;}}_2=\mathrm{tr}\left(C_{2}X\right)+{\mathrm{\&sigma;}}_2^2,{\text{\&beta;}}_{3k}=\mathrm{tr}\left(C_{3k}X\right)+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2$

$\log \left({\mathrm{\&beta;}}_{j,0}\right)+\frac{1}{{\mathrm{\&beta;}}_{j,0}}({\mathrm{\&beta;}}_j-{\mathrm{\&beta;}}_{j,0})\&le;t_j,j=\mathrm{1,2,3}k.$

Optimization problem Q6 is step 2) in semi definite programming problem.

The present invention has following beneficial effect:

In amplification forwarding wireless relay network of the present invention, the method for security cooperation wave beam forming considers the situation of multiple listener-in, the optimization problem of the single relay power control of standard construction is maximized according to safety and speed, and this optimization problem is changed into semi definite programming problem by linear approximation, optimum safety and speed is obtained again by the method for iteration, then optimum safety and speed is obtained described in basis, and then significantly reduce the informational probability that listener-in steals proper user, improve the spectrum efficiency of secure communication.

Accompanying drawing explanation

When Fig. 1 is relaying number N=20 in emulation experiment, safety and speed are with P _rchange;

Fig. 2 works as P in emulation experiment _rduring=20dBW, safety and speed are with the variation diagram of iterations.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail:

Obtain first source node T ₁place can reach information rate I ₁, second source node T ₂place can reach information rate I ₂and listener-in E _kplace can reach information rate method specifically comprise the following steps:

At amplification forwarding wireless relay network, first source node T ₁with second source node T ₂by one group of relaying R _nexchange message, n=1,2 ..., N, listener-in E _kpassive, k=1,2 ..., K, and attempt illegal wiretapping first source node T ₁place and second source node T ₂the information at place, in system, all nodes only have an antenna, and are all semiduplex;

F _rbe first source node T ₁to the channel of all relayings, f _eto the first source node T ₁to the channel of listener-in, g _rbe second source node T ₂to the channel of all relayings, g _ebe second source node T ₂to the channel of listener-in, c _efor being relayed to the quasistatic fading coefficients of listener-in, global channel state information (CSI) is known;

Transmission is divided into two time slots, at time slot 1, and first source node T ₁with second source node T ₂simultaneously to repeat transmitted information, then the signal vector received at relaying place is

$y_R=\sqrt{P_1}{f}_R{s}_1+\sqrt{P_2}{g}_R{s}_2+n_R,---\left(1\right)$

Wherein, P ₁and P ₂the average transmit power of first source node and second source node respectively, s ₁and s ₂the transmitting information of first source node and second source node respectively.If E [| s _m| ²]=1, m=1,2, n _rbe relaying place average be 0, the additive white Gaussian noise of unit covariance, therefore, in a kth information that listener-in place receives is

$y_{E_k}^{\left(1\right)}=\sqrt{P_1}{f}_{E_k}{s}_1+\sqrt{P_2}{g}_{E_k}{s}_2+n_{E_k}^{\left(1\right)},---\left(2\right)$

Wherein, listener-in E _kthe average at place is 0, the additive white Gaussian noise of unit covariance.

At time slot 2, relaying carries out wave beam forming first to the received signal and adds man made noise, then signal can be expressed as after treatment

x _R＝Wy _R+n _a， (3)

Wherein, wave beam formed matrix n _afor man made noise, and covariance matrix ∑>=0;

Then relaying resends x _r, first source node T ₁with second source node T ₂the signal that place receives can be expressed as

$y_{T_1}=\sqrt{P_2}{f}_R^T{\mathrm{Wg}}_R{s}_2+\sqrt{P_1}{f}_R^T{\mathrm{Wf}}_R{s}_1+{\stackrel{\&OverBar;}{n}}_{T_1},---\left(4\right)$

$y_{T_2}=\sqrt{P_1}{g}_R^T{\mathrm{Wf}}_R{s}_1+\sqrt{P_2}{g}_R^T{\mathrm{Wg}}_R{s}_2+{\stackrel{\&OverBar;}{n}}_{T_2}.---\left(5\right)$

In like manner, listener-in E _kthe signal that place receives is

$y_{E_k}^{\left(2\right)}=\sqrt{P_1}{c}_{E_k}^T{\mathrm{Wf}}_R{s}_1+\sqrt{P_2}{c}_{E_k}^T{\mathrm{Wg}}_R{s}_2{+\stackrel{\&OverBar;}{n}}_{E_k}^{\left(2\right)},---\left(6\right)$

Wherein, ${\stackrel{\&OverBar;}{n}}_{T_1}=f_R^{T}W+f_R^T{n}_a+n_{T_1},$ ${\stackrel{\&OverBar;}{n}}_{T_2}=g_R^{T}W+g_R^T{n}_a+n_{T_2},$ ${\stackrel{\&OverBar;}{n}}_{E_k}^{\left(2\right)}=c_{E_k}^{T}W+c_{E_k}^T{n}_a+n_{E_k}^{\left(2\right)};$ with t respectively ₁, T ₂and E _kthe average at place is 0, the additive noise of unit covariance.

Information after self-interference is eliminated desired by source node can be expressed as

$y_{T_1}=\sqrt{P_2}{w}^H{a}_{\mathrm{fg}}{s}_2+{\stackrel{\&OverBar;}{n}}_{T_1},---\left(7\right)$

$y_{T_2}=\sqrt{P_1}{w}^H{a}_{\mathrm{fg}}{s}_1+{\stackrel{\&OverBar;}{n}}_{T_2},---\left(8\right)$

Wherein, a _fg=f _rο g _r, w=[w ₁, w ₂..., w _n] ^t;

Then T ₁, T ₂and E _kreached at the information rate at place can be expressed as easily

$I_1=\frac{1}{2}\log (1+\frac{P_2{w}^H{R}_{\mathrm{fg}}w}{w^H{R}_{\mathrm{ff}}w+1+f_R^T\mathrm{\&Sigma;}{f}_R^{*}}),---\left(9\right)$

$I_2=\frac{1}{2}\log (1+\frac{P_1{w}^H{R}_{\mathrm{fg}}w}{w^H{R}_{\mathrm{gg}}w+1+g_R^T\mathrm{\&Sigma;}{g}_R^{*}}),---\left(10\right)$

$I_{E_k}=\frac{1}{2}\log ({\mathrm{\&gamma;}}_k+\frac{w^H{V}_{k}w}{w^H{R}_{c_k{c}_k}w+1+c_{E_k}^T\mathrm{\&Sigma;}{c}_{E_k}^{*}}),---\left(11\right)$

Wherein P ₁be first source node T ₁average transmit power, P ₂be second source node T ₂average transmit power, w is wave beam formed matrix, f _rbe first source node T ₁to the channel of all relayings, f _eto the first source node T ₁to the channel of listener-in, g _rbe second source node T ₂to the channel of all relayings, g _ebe second source node T ₂to the channel of listener-in, c _efor being relayed to the quasistatic fading coefficients of listener-in, for being relayed to the quasistatic fading coefficients of a kth listener-in, r _ff=diag (| f _{r, 1}| ², | f _{r, 2}| ²..., | f _{r, N}| ²), a _fg=f _rο g _r, $R_{c_k{c}_k}=\mathrm{diag}({\left|c_{E_k,1}\right|}^2,{\left|c_{E_k,2}\right|}^2,...,{\left|c_{E_k,N}\right|}^2),$ $R_{\mathrm{fg}}=a_{\mathrm{fg}}{a}_{\mathrm{fg}}^H,$ R _gg＝diag(|f _g，1| ²，|f _g，2| ²，...，|f _g，N| ²)， $V_k=(P_1{P}_2{\left|g_{E_k}\right|}^2+P_1)R_{c_{k}f}+(P_1{P}_2{\left|f_{E_k}\right|}^2+P_2)R_{c_{k}g}-P_1{P}_2{f}_{E_k}$ $R_{c_{k}f}=a_{c_{f}f}{a}_{c_{k}f}^H,$ $R_{c_{k}g}=a_{c_{f}g}{a}_{c_{k}g}^H;$

In amplification forwarding wireless relay network of the present invention, the method for security cooperation wave beam forming comprises the following steps:

1) in amplification forwarding wireless relay network, first source node T ₁and second source node T ₂by one group of relaying R _nexchange message, listener-in E _kpassive, and attempt illegal wiretapping first source node T ₁with second source node T ₂the information at place, wherein, n=1,2 ..., N, k=1,2 ..., K, N are relaying sum, and K is the quantity of listener-in, then first source node T ₁place can reach information rate I ₁, second source node T ₂place can reach information rate I ₂and listener-in E _kplace can reach information rate be respectively

$I_1=\frac{1}{2}\log (1+\frac{P_2{w}^H{R}_{\mathrm{fg}}w}{w^H{R}_{\mathrm{ff}}w+1+f_R^T\mathrm{\&Sigma;}{f}_R^{*}})---\left(9\right)$

$I_2=\frac{1}{2}\log (1+\frac{P_1{w}^H{R}_{\mathrm{fg}}w}{w^H{R}_{\mathrm{gg}}w+1+g_R^T\mathrm{\&Sigma;}{g}_R^{*}})---\left(10\right)$

$I_{E_k}=\frac{1}{2}\log ({\mathrm{\&gamma;}}_k+\frac{w^H{V}_{k}w}{w^H{R}_{c_k{c}_k}w+1+c_{E_k}^T\mathrm{\&Sigma;}{c}_{E_k}^{*}})---\left(11\right)$

Wherein P ₁be first source node T ₁average transmit power, P ₂be second source node T ₂average transmit power, w is wave beam formed matrix, f _rbe first source node T ₁to the channel of all relayings, f _eto the first source node T ₁to the channel of listener-in, g _rbe second source node T ₂to the channel of all relayings, g _ebe second source node T ₂to the channel of listener-in, c _efor being relayed to the quasistatic fading coefficients of listener-in, for being relayed to the quasistatic fading coefficients of a kth listener-in, r _ff=diag (| f _{r, 1}| ², | f _{r, 2}| ²..., | f _{r, N}| ²), a _fg=f _rο g _r, $R_{c_k{c}_k}=\mathrm{diag}({\left|c_{E_k,1}\right|}^2,{\left|c_{E_k,2}\right|}^2,...,{\left|c_{E_k,N}\right|}^2),$ $R_{\mathrm{fg}}=a_{\mathrm{fg}}{a}_{\mathrm{fg}}^H,$ R _gg＝diag(|f _g，1| ²，|f _g，2| ²，...，|f _g，N| ²)； $V_k=(P_1{P}_2{\left|g_{E_k}\right|}^2+P_1)R_{c_{k}f}+(P_1{P}_2{\left|f_{E_k}\right|}^2+P_2)R_{c_{k}g}-P_1{P}_2{f}_{E_k}$ $R_{c_{k}f}=a_{c_{f}f}{a}_{c_{k}f}^H,$ $R_{c_{k}g}=a_{c_{f}g}{a}_{c_{k}g}^H;$

2) then the optimization problem of the single relay power control of criteria construction is maximized namely according to safety and speed

$Q1:\underset{w,\mathrm{\&Sigma;}}{\max }\underset{k}{\min }\{I_1+I_2-I_{E_k}\},$

$s.t.{\left[x_R^H{x}_R\right]}_{n,n}\&le;P_{R_n},\&ForAll;n$

Wherein, x _rcarry out wave beam forming to the received signal for relaying and add the signal after man made noise, p _rfor the gross power of all relayings, then formula (9), formula (10) and formula (11) are brought in Q1,

$\begin{array}{c}Q2:\underset{w,\mathrm{\&Sigma;}}{\max }\underset{k}{\min }\frac{1+w^H(R_{\mathrm{ff}}+P_2{R}_{\mathrm{fg}})w+f_R^T\mathrm{\&Sigma;}{f}_R^{*}}{1+w^H{R}_{\mathrm{ff}}w+f_R^T\mathrm{\&Sigma;}{f}_R^{*}}\\ \&CenterDot;\frac{1+w^H(R_{\mathrm{gg}}+P_1{R}_{\mathrm{fg}})w+g_R^T{\mathrm{\&Sigma;g}}_R^{*}}{1+w^H{R}_{\mathrm{gg}}w+g_R^T{\mathrm{\&Sigma;g}}_R^{*}}\\ \&CenterDot;\frac{1+w^H{R}_{c_k{c}_k}w+c_{E_k}^T{\mathrm{\&Sigma;c}}_{E_k}^{*}}{w^H({\mathrm{\&gamma;}}_k{R}_{c_k{c}_k}+V_k)w+{\mathrm{\&gamma;}}_k(1+c_{E_k}^T{\mathrm{\&Sigma;c}}_{E_k}^{*})}\end{array},$

$s.t.{\left[x_R^H{x}_R\right]}_{n,n}\&le;P_{R_n},\&ForAll;n.$

Wherein, Q2 is a non-convex problem, Q2 is converted into semi definite programming problem, and obtains optimum matrix X by the method for iteration _opt, the matrix X of wherein said optimum _optmeet rank (X _opt)=1, then according to the matrix X of described optimum _optoptimum safety and speed, then carry out the figuration of security cooperation wave beam in amplification forwarding wireless relay network according to the safety of described optimum and speed.

Wherein, if B ₁=R _ff+ P ₂r _fg, B ₂=R _gg+ P ₁r _fg, ${\mathrm{\&sigma;}}_2^2=1+g_R^T{\mathrm{\&Sigma;g}}_R^{*},$ ${\mathrm{\&sigma;}}_{3k}^2=1+c_{E_k}^T{\mathrm{\&Sigma;c}}_{E_k}^{*},$ C ₁=R _ff, C ₂=R _ggwith $C_{3k}={\mathrm{\&gamma;}}_k{R}_{c_k{c}_k}{+V}_k,$ Then optimization problem Q2 can be expressed as

$Q3:\underset{w,\mathrm{\&Sigma;},k}{\max \min }\frac{w^H{B}_{1}w+{\mathrm{\&sigma;}}_1^2}{w^H{C}_{1}w+{\mathrm{\&sigma;}}_1^2}\frac{w^H{B}_{2}w+{\mathrm{\&sigma;}}_2^2}{w^H{C}_{2}w+{\mathrm{\&sigma;}}_2^2}\frac{w^H{B}_{3k}w+{\mathrm{\&sigma;}}_{3k}^2}{w^H{C}_{3k}w+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2};$

$s.t.{[w^H(P_1{R}_{\mathrm{ff}}+P_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)w+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},\&ForAll;n.$

Make X=ww ^h, then optimization problem Q3 can abbreviation be:

$Q4:\underset{X,\mathrm{\&Sigma;},{\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2,{\mathrm{\&alpha;}}_{3k},{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_{3k},k}{\max \min }\log \left({\mathrm{\&alpha;}}_1\right)+\log \left({\mathrm{\&alpha;}}_2\right)+\log \left({\mathrm{\&alpha;}}_{3k}\right)-\log \left({\mathrm{\&beta;}}_1\right)-\log \left({\mathrm{\&beta;}}_2\right)-\log \left({\mathrm{\&beta;}}_{3k}\right)$

$s.t.{[(P_1{R}_{\mathrm{ff}}{+P}_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)X+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},{\&ForAll;n}_{}$

${\mathrm{\&alpha;}}_1=\mathrm{tr}\left(B_{1}X\right)+{\mathrm{\&sigma;}}_1^2,{\mathrm{\&alpha;}}_2=\mathrm{tr}\left(B_{2}X\right)+{\mathrm{\&sigma;}}_2^2;$

${\mathrm{\&alpha;}}_{3k}=\mathrm{tr}\left(B_{3k}X\right)+{\mathrm{\&sigma;}}_{3k}^2,{\mathrm{\&beta;}}_1=\mathrm{tr}\left(C_{1}X\right)+{\mathrm{\&sigma;}}_1^2$

${\mathrm{\&beta;}}_2=\mathrm{tr}\left(C_{2}X\right)+{\mathrm{\&sigma;}}_2^2,{\text{\&beta;}}_{3k}=\mathrm{tr}\left(C_{3k}X\right)+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2$

X≥0，rαnk{X}＝1.

Target function due to optimization problem Q4 is the difference of two convex functions, so optimization problem Q4 is non-convex problem, carries out linear approximation to the target function of optimization problem Q4, order $\log \left({\mathrm{\&beta;}}_j\right)=\log \left({\mathrm{\&beta;}}_{j,0}\right)+\frac{1}{{\mathrm{\&beta;}}_{j,0}}({\mathrm{\&beta;}}_j-{\mathrm{\&beta;}}_{j,0}),j=\mathrm{1,2,3}k,$ β _{j, 0}be the initial value of Taylor expansion, the order 1 removed in optimization problem Q4 limits, then optimization problem Q4, can be reduced to:

$Q5:\underset{X,\mathrm{\&Sigma;},{\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2,{\mathrm{\&alpha;}}_{3k},{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_{3k},k}{\max \min }\log \left({\mathrm{\&alpha;}}_1\right)+\log \left({\mathrm{\&alpha;}}_2\right)+\log \left({\mathrm{\&alpha;}}_{3k}\right)-t_1-t_2-t_{3k}$

$s.t.{[(P_1{R}_{\mathrm{ff}}{+P}_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)X+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},{\&ForAll;n}_{}$

${\mathrm{\&alpha;}}_1=\mathrm{tr}\left(B_{1}X\right)+{\mathrm{\&sigma;}}_1^2,{\mathrm{\&alpha;}}_2=\mathrm{tr}\left(B_{2}X\right)+{\mathrm{\&sigma;}}_2^2$

${\mathrm{\&alpha;}}_{3k}=\mathrm{tr}\left(B_{3k}X\right)+{\mathrm{\&sigma;}}_{3k}^2,{\mathrm{\&beta;}}_1=\mathrm{tr}\left(C_{1}X\right)+{\mathrm{\&sigma;}}_1^2;$

${\mathrm{\&beta;}}_2=\mathrm{tr}\left(C_{2}X\right)+{\mathrm{\&sigma;}}_2^2,{\text{\&beta;}}_{3k}=\mathrm{tr}\left(C_{3k}X\right)+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2$

$\log \left({\mathrm{\&beta;}}_{j,0}\right)+\frac{1}{{\mathrm{\&beta;}}_{j,0}}({\mathrm{\&beta;}}_j-{\mathrm{\&beta;}}_{j,0})\&le;t_j,j=\mathrm{1,2,3}k$

Work as β _{j, 0}=β _{j, opt}time, log (β _j) first order Taylor expand into real Taylor expansion, the further abbreviation of optimization problem Q5 is

$Q6:\underset{X,\mathrm{\&Sigma;},{\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2,{\mathrm{\&alpha;}}_{3k},{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_{3k},k}{\min }\mathrm{\&tau;}$

s.t.-(log(α ₁)+log(α ₂)+log(α _3k))+t ₁+t ₂+t _3k＜＝τ

${[(P_1{R}_{\mathrm{ff}}+P_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)X+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},\&ForAll;n$

${\mathrm{\&alpha;}}_1=\mathrm{tr}\left(B_{1}X\right)+{\mathrm{\&sigma;}}_1^2,{\mathrm{\&alpha;}}_2=\mathrm{tr}\left(B_{2}X\right)+{\mathrm{\&sigma;}}_2^2;$

${\mathrm{\&alpha;}}_{3k}=\mathrm{tr}\left(B_{3k}X\right)+{\mathrm{\&sigma;}}_{3k}^2,{\mathrm{\&beta;}}_1=\mathrm{tr}\left(C_{1}X\right)+{\mathrm{\&sigma;}}_1^2$

${\mathrm{\&beta;}}_2=\mathrm{tr}\left(C_{2}X\right)+{\mathrm{\&sigma;}}_2^2,{\text{\&beta;}}_{3k}=\mathrm{tr}\left(C_{3k}X\right)+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2$

$\log \left({\mathrm{\&beta;}}_{j,0}\right)+\frac{1}{{\mathrm{\&beta;}}_{j,0}}({\mathrm{\&beta;}}_j-{\mathrm{\&beta;}}_{j,0})\&le;t_j,j=\mathrm{1,2,3}k.$

Optimization problem Q6 is step 2) in semi definite programming problem.

In order to prove that the optimal solution that Q6 obtains meets rank (X _opt)=1, first considers a following problem

$R1:\underset{X,\mathrm{\&Sigma;},u_1,u_2,u_{3k},t_1,t_2,t_{3k},k}{\min }{-u}_1-u_2-u_{3k}+t_1+t_2+t_{3k}$

$s.t.{[w^H(P_1{R}_{\mathrm{ff}}{+P}_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)w+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},{\&ForAll;n}_{}$

${\mathrm{\&alpha;}}_1=\mathrm{tr}\left(B_{1}X\right)+{\mathrm{\&sigma;}}_1^2,{\mathrm{\&alpha;}}_2=\mathrm{tr}\left(B_{2}X\right)+{\mathrm{\&sigma;}}_2^2,$

${\mathrm{\&alpha;}}_{3k}=\mathrm{tr}\left(B_{3k}X\right)+{\mathrm{\&sigma;}}_{3k}^2,{\mathrm{\&beta;}}_1=\mathrm{tr}\left(C_{1}X\right)+{\mathrm{\&sigma;}}_1^2,$

${\mathrm{\&beta;}}_2=\mathrm{tr}\left(C_{2}X\right)+{\mathrm{\&sigma;}}_2^2,{\text{\&beta;}}_{3k}=\mathrm{tr}\left(C_{3k}X\right)+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2,$

$\log \left({\mathrm{\&beta;}}_{j,0}\right)+\frac{1}{{\mathrm{\&beta;}}_{j,0}}({\mathrm{\&beta;}}_j-{\mathrm{\&beta;}}_{j,0})\&le;t_j,j=\mathrm{1,2,3}k.$

$\log \left({\mathrm{\&alpha;}}_{j,0}\right)+\frac{1}{{\mathrm{\&alpha;}}_{j,0}}({\mathrm{\&alpha;}}_j-{\mathrm{\&alpha;}}_{j,0})\&le;u_j,j=\mathrm{1,2,3}k.$

Construct Lagrangian and obtain KKT condition and be

$\begin{array}{c}\mathrm{\&psi;}=(\frac{1}{{\mathrm{\&beta;}}_{\mathrm{1,0}}}-\frac{1}{{\mathrm{\&alpha;}}_{\mathrm{1,0}}})R_{\mathrm{ff}}+(\frac{1}{{\mathrm{\&beta;}}_{\mathrm{2,0}}}-\frac{1}{{\mathrm{\&alpha;}}_{\mathrm{2,0}}})R_{\mathrm{gg}}\\ +(\frac{{\mathrm{\&gamma;}}_k}{{\mathrm{\&beta;}}_{3k,0}}-\frac{1}{{\mathrm{\&alpha;}}_{3k,0}})R_{c_k{c}_k}-(\frac{P_2}{{\mathrm{\&alpha;}}_{\mathrm{1,0}}}+\frac{P_1}{{\mathrm{\&alpha;}}_{\mathrm{2,0}}})R_{\mathrm{fg}}^T+\\ \frac{1}{{\mathrm{\&beta;}}_{3k,0}}{V}_k^T+d_1{P}_1{R}_{\mathrm{ff}}+d_1{P}_2{R}_{\mathrm{gg}}+d_{1}I,\end{array}$

$\begin{array}{c}\mathrm{\&Gamma;}=(\frac{1}{{\mathrm{\&beta;}}_{\mathrm{1,0}}}-\frac{1}{{\mathrm{\&alpha;}}_{\mathrm{1,0}}}){\left(f_R{f}_R^H\right)}^T+(\frac{1}{{\mathrm{\&beta;}}_{\mathrm{2,0}}}-\frac{1}{{\mathrm{\&alpha;}}_{\mathrm{2,0}}})\\ {\left(g_R{g}_R^H\right)}^T+(\frac{{\mathrm{\&gamma;}}_k}{{\mathrm{\&beta;}}_{3k,0}}-\frac{1}{{\mathrm{\&alpha;}}_{3k,0}}){\left(c_R{c}_R^H\right)}^T+d_{1}I.\end{array}$

Carry out abbreviation to ψ can obtain

$\mathrm{\&psi;}=D\left(\mathrm{\&Gamma;}\right)-(\frac{P_2}{{\mathrm{\&alpha;}}_{\mathrm{1,0}}}+\frac{P_1}{{\mathrm{\&alpha;}}_{\mathrm{2,0}}})R_{\mathrm{fg}}^T+\frac{1}{{\mathrm{\&beta;}}_{3k,0}}{V}_k^T+d_1{P}_1{R}_{\mathrm{ff}}+d_1{P}_2{R}_{\mathrm{gg}}.---\left(12\right)$

Then (12) formula is substituted into ψ X=0 can obtain

$[D\left(\mathrm{\&Gamma;}\right)+\frac{1}{{\mathrm{\&beta;}}_{3k,0}}{V}_k^T{+d}_1(P_1{R}_{\mathrm{ff}}+P_2{R}_{\mathrm{gg}})]X=\left[(\frac{P_2}{{\mathrm{\&alpha;}}_{\mathrm{1,0}}}+\frac{P_1}{{\mathrm{\&alpha;}}_{\mathrm{2,0}}})R_{\mathrm{fg}}^T\right]X.,$

Wherein, $[D\left(\mathrm{\&Gamma;}\right)+\frac{1}{{\mathrm{\&beta;}}_{3k,0}}{V}_k^T{+d}_1(P_1{R}_{\mathrm{ff}}+P_2{R}_{\mathrm{gg}})]>0,$ Therefore can obtain

$\begin{array}{c}\mathrm{rank}\left(X\right)=\mathrm{rank}\left(\right[D\left(\mathrm{\&Gamma;}\right)+\frac{1}{{\mathrm{\&beta;}}_{3k,0}}{V}_k^T+d_1(P_1{R}_{\mathrm{ff}}+P_2{R}_{\mathrm{gg}})\left]X\right)\\ =\mathrm{rank}\left(\left[(\frac{P_2}{{\mathrm{\&alpha;}}_{\mathrm{1,0}}}+\frac{P_1}{{\mathrm{\&alpha;}}_{\mathrm{2,0}}})R_{\mathrm{fg}}^T\right]X\right)\&le;\mathrm{rank}\left(R_{\mathrm{fg}}\right)=1.\end{array},$

Namely the solution X in R1 meets rank (X)=1;

Because the problem after lax so by Q ₃the X obtained _optmeet rank (X _opt)=1.

Emulation experiment

In simulations, P ₁=P ₂=20dBW, wherein, P _rbe the gross power of all relayings, in addition, all channel coefficients are all averages is in simulations 0, the gaussian random matrix of unit covariance, and the SCA method simultaneously carried in we and document carries out the performance contrasting to assess safety and speed.

Different relay power P is compared in Fig. 1 _rtime safety and speed, as can be seen from Figure 1, safety and speed increase with the increase of relaying place power, and when relay power is larger, the method in this programme is significantly better than SCA algorithm; In addition, we find in simulations, and when listener-in's number increases, the method in this programme is stablized than SCA method, and this is also corresponding with the result in document.Compared for when channel is fixed in Fig. 2, safety and speed are with the change of iterations, and as can be seen from Figure 2, the method in the present invention can converge to maximum safety and speed faster; In addition, safety and speed increase with the increase of relaying number.

Claims (2)

1. the method for security cooperation wave beam forming in amplification forwarding wireless relay network, is characterized in that, comprise the following steps:

1) in amplification forwarding wireless relay network, first source node T ₁and second source node T ₂by one group of relaying R _nexchange message, listener-in E _kbe passive, and attempt illegal wiretapping first source node T ₁with second source node T ₂the information at place, wherein, n=1,2 ..., N, k=1,2 ..., K, N are relaying sum, and K is the quantity of listener-in, then first source node T ₁place can reach information rate I ₁, second source node T ₂place can reach information rate I ₂and listener-in E _kplace can reach information rate be respectively

$I_1=\frac{1}{2}\log (1+\frac{P_2{w}^H{R}_{\mathrm{fg}}w}{w^H{R}_{\mathrm{ff}}w+1+f_R^T\mathrm{\&Sigma;}{f}_R^{*}})---\left(9\right)$

$I_2=\frac{1}{2}\log (1+\frac{P_1{w}^H{R}_{\mathrm{fg}}w}{w^H{R}_{\mathrm{gg}}w+1+g_R^T\mathrm{\&Sigma;}{g}_R^{*}})---\left(10\right)$

$I_{E_k}=\frac{1}{2}\log ({\mathrm{\&gamma;}}_k+\frac{w^H{V}_{k}w}{w^H{R}_{c_k{c}_k}w+1+c_{E_k}^T\mathrm{\&Sigma;}{c}_{E_k}^{*}})---\left(11\right)$

Wherein P ₁be first source node T ₁average transmit power, P ₂be second source node T ₂average transmit power, w is wave beam formed matrix, f _rbe first source node T ₁to the channel of all relayings, f _eto the first source node T ₁to the channel of listener-in, g _rbe second source node T ₂to the channel of all relayings, g _ebe second source node T ₂to the channel of listener-in, c _efor being relayed to the quasistatic fading coefficients of listener-in, for being relayed to the quasistatic fading coefficients of a kth listener-in, $R_{\mathrm{ff}}=\mathrm{diag}({\left|f_{R,1}\right|}^2,{\left|f_{R,2}\right|}^2,...,{\left|f_{R,N}\right|}^2),R_{c_k,c_k}=\mathrm{diag}({\left|c_{E_k,1}\right|}^2,{\left|c_{E_k,2}\right|}^2,...,{\left|c_{E_k,N}\right|}^2),$ a _fg＝f _rog _R， $R_{\mathrm{fg}}=a_{\mathrm{fg}}{a}_{\mathrm{fg}}^H,R_{\mathrm{gg}}=\mathrm{diag}({\left|f_{g,1}\right|}^2,{\left|f_{g,2}\right|}^2,...,{\left|f_{g,N}\right|}^2),a_{c_{k}f}=c_{E_k}o{f}_R,a_{c_k,g}=c_{E_k}o{g}_R,$ $V_k=(P_1{P}_2{\left|g_{E_k}\right|}^2+P_1)R_{c_{k}f}+(P_1{P}_2{\left|f_{E_k}\right|}^2+P_2)R_{c_{k}g}-P_1{P}_2{f}_{E_k}{g}_{E_k}^{*}{a}_{c_{k}g}{a}_{c_{k}f}^H-P_1{P}_2{f}_{E_k}^{*}{g}_{E_k}{a}_{c_{k}f}{a}_{c_{k}g}^H,$ $R_{c_{k}f}=a_{c_{k}f}{a}_{c_k}^H,R_{c_{k}g}=a_{c_{k}g}{a}_{c_{k}g}^H;$

2) then the optimization problem of the single relay power control of criteria construction is maximized namely according to safety and speed

$Q1:\underset{w,\mathrm{\&Sigma;}}{\max }\underset{k}{\min }\{I_1+I_2-I_{E_k}\},$

$s.t.{\left[x_R^H{x}_R\right]}_{n,n}\&le;P_{R_n},\&ForAll;n$

Wherein, x _rcarry out wave beam forming to the received signal for relaying and add the signal after man made noise, p _rfor the gross power of all relayings, then formula (9), formula (10) and formula (11) are brought in Q1,

$\begin{array}{c}Q2:\underset{w,\mathrm{\&Sigma;}}{\max }\underset{k}{\min }\frac{1+w^H(R_{\mathrm{ff}}+P_2{R}_{\mathrm{fg}})w+f_R^T\mathrm{\&Sigma;}{f}_R^{*}}{1+w^H{R}_{\mathrm{ff}}w+f_R^T\mathrm{\&Sigma;}{f}_R^{*}}\\ \&CenterDot;\frac{1+w^H(R_{\mathrm{gg}}+P_1{R}_{\mathrm{fg}})w+g_R^T\mathrm{\&Sigma;}{g}_R^{*}}{1+w^H{R}_{\mathrm{gg}}w+g_R^T\mathrm{\&Sigma;}{g}_R^{*}}\\ \&CenterDot;\frac{1+w^H{R}_{c_k,c_k}w+c_{E_k}^T\mathrm{\&Sigma;}{c}_{E_k}^{*}}{w^H({\mathrm{\&gamma;}}_k{R}_{c_k{c}_k}+V_k)w+{\mathrm{\&gamma;}}_k(1+c_{E_k}^T\mathrm{\&Sigma;}{c}_{E_k}^{*})}\end{array}$

$s.t.{\left[x_R^H{x}_R\right]}_{n,n}\&le;P_{R_n},\&ForAll;n.$

Wherein, Q2 is a non-convex problem, Q2 is converted into semi definite programming problem, and obtains optimum matrix x by the method for iteration _opt, the matrix x of wherein said optimum _optmeet rank (x _opt)=1, then according to the matrix x of described optimum _optoptimum safety and speed, then carry out the figuration of security cooperation wave beam in amplification forwarding wireless relay network according to the safety of described optimum and speed.

2. the method for security cooperation wave beam forming in amplification forwarding wireless relay network according to claim 1, is characterized in that, if B ₁=R _ff+ P ₂r _fg, B ₂=R _gg+ P ₁r _fg, ${\mathrm{\&sigma;}}_1^2=1+f_R^T\mathrm{\&Sigma;}{f}_R^{*},{\mathrm{\&sigma;}}_2^2=1+g_R^T\mathrm{\&Sigma;}{g}_R^{*},{\mathrm{\&sigma;}}_{3k}^2=1+c_{E_k}^T\mathrm{\&Sigma;}{c}_{E_k}^{*},$ C ₁=R _ff, C ₂=R _ggwith then optimization problem Q2 can be expressed as

$Q3:\underset{w,\mathrm{\&Sigma;},k}{\max \min }\frac{w^H{B}_{1}w+{\mathrm{\&sigma;}}_1^2}{w^H{C}_{1}w+{\mathrm{\&sigma;}}_2^2}\&CenterDot;\frac{w^H{B}_{2}w+{\mathrm{\&sigma;}}_2^2}{w^H{C}_{2}w+{\mathrm{\&sigma;}}_2^2}\&CenterDot;\frac{w^H{B}_{3k}w+{\mathrm{\&sigma;}}_{3k}^2}{w^H{C}_{3k}w+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2};$

$s.t.{[w^H(P_1{R}_{\mathrm{ff}}+P_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)w+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},\&ForAll;n.$

Make X=ww ^h, then optimization problem Q3 can abbreviation be:

$Q4:\underset{X,\mathrm{\&Sigma;},{\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2,{\mathrm{\&alpha;}}_{3k},{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_{3k},k}{\max \min }\log \left({\mathrm{\&alpha;}}_1\right)+\log \left({\mathrm{\&alpha;}}_2\right)+\log \left({\mathrm{\&alpha;}}_{3k}\right)-\log \left({\mathrm{\&beta;}}_1\right)-\log \left({\mathrm{\&beta;}}_2\right)-\log \left({\mathrm{\&beta;}}_{3k}\right)$

$s.t.{[(P_1{R}_{\mathrm{ff}}+P_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)X+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},\&ForAll;n$

${\mathrm{\&alpha;}}_1=\mathrm{tr}\left(B_{1}X\right)+{\mathrm{\&sigma;}}_1^2,{\mathrm{\&alpha;}}_2=\mathrm{tr}\left(B_{2}X\right)+{\mathrm{\&sigma;}}_2^2$

${\mathrm{\&alpha;}}_{3k}=\mathrm{tr}\left(B_{3k}X\right)+{\mathrm{\&sigma;}}_{3k}^2,{\mathrm{\&beta;}}_1=\mathrm{tr}\left(C_{1}X\right)+{\mathrm{\&sigma;}}_1^2$

${\mathrm{\&beta;}}_2=\mathrm{tr}\left(C_{2}X\right)+{\mathrm{\&sigma;}}_2^2,{\mathrm{\&beta;}}_{3k}=\mathrm{tr}\left(C_{3k}X\right)+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2$

x≥0，rank{X}＝1.

Target function due to optimization problem Q4 is the difference of two convex functions, so optimization problem Q4 is non-convex problem, carries out linear approximation to the target function of optimization problem Q4, order j=1,2,3k, β _{j, 0}be the initial value of Taylor expansion, the order 1 removed in optimization problem Q4 limits, then optimization problem Q4, can be reduced to:

$Q5:\underset{X,\mathrm{\&Sigma;},{\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2,{\mathrm{\&alpha;}}_{3k},{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_{3k},k}{\max \min }\log \left({\mathrm{\&alpha;}}_1\right)+\log \left({\mathrm{\&alpha;}}_2\right)+\log \left({\mathrm{\&alpha;}}_{3k}\right)-t_1-t_2-t_{3k}$

$s.t.{[(P_1{R}_{\mathrm{ff}}+P_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)X+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},\&ForAll;n$

${\mathrm{\&alpha;}}_1=\mathrm{tr}\left(B_{1}X\right)+{\mathrm{\&sigma;}}_1^2,{\mathrm{\&alpha;}}_2=\mathrm{tr}\left(B_{2}X\right)+{\mathrm{\&sigma;}}_2^2$

；

${\mathrm{\&alpha;}}_{3k}=\mathrm{tr}\left(B_{3k}X\right)+{\mathrm{\&sigma;}}_{3k}^2,{\mathrm{\&beta;}}_1=\mathrm{tr}\left(C_{1}X\right)+{\mathrm{\&sigma;}}_1^2$

${\mathrm{\&beta;}}_2=\mathrm{tr}\left(C_{2}X\right)+{\mathrm{\&sigma;}}_2^2,{\mathrm{\&beta;}}_{3k}=\mathrm{tr}\left(C_{3k}X\right)+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2$

$\log \left({\mathrm{\&beta;}}_{j,0}\right)+\frac{1}{{\mathrm{\&beta;}}_{j,0}}({\mathrm{\&beta;}}_j-{\mathrm{\&beta;}}_{j,0})\&le;t_j,j=\mathrm{1,2,3}k$

Work as β _{j, 0}=β _{j, opt}time, log (β _j) first order Taylor expand into real Taylor expansion, the further abbreviation of optimization problem Q5 is

$Q6:\underset{X,\mathrm{\&Sigma;},{\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2,{\mathrm{\&alpha;}}_{3k},{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_{3k},k}{\max \min }\mathrm{\&tau;}$

s.t.-(log(α ₁)+log(α ₂)+log(α _3k))+t ₁+t ₂+t _3k＜＝τ

${[(P_1{R}_{\mathrm{ff}}+P_2{R}_{\mathrm{gg}}+{\mathrm{\&sigma;}}^{2}I)X+\mathrm{\&Sigma;}]}_{n,n}\&le;P_{R_n},\&ForAll;n$

${\mathrm{\&alpha;}}_1=\mathrm{tr}\left(B_{1}X\right)+{\mathrm{\&sigma;}}_1^2,{\mathrm{\&alpha;}}_2=\mathrm{tr}\left(B_{2}X\right)+{\mathrm{\&sigma;}}_2^2;$

${\mathrm{\&alpha;}}_{3k}=\mathrm{tr}\left(B_{3k}X\right)+{\mathrm{\&sigma;}}_{3k}^2,{\mathrm{\&beta;}}_1=\mathrm{tr}\left(C_{1}X\right)+{\mathrm{\&sigma;}}_1^2$

${\mathrm{\&beta;}}_2=\mathrm{tr}\left(C_{2}X\right)+{\mathrm{\&sigma;}}_2^2,{\mathrm{\&beta;}}_{3k}=\mathrm{tr}\left(C_{3k}X\right)+{\mathrm{\&gamma;}}_k{\mathrm{\&sigma;}}_{3k}^2$

$\log \left({\mathrm{\&beta;}}_{j,0}\right)+\frac{1}{{\mathrm{\&beta;}}_{j,0}}({\mathrm{\&beta;}}_j-{\mathrm{\&beta;}}_{j,0})\&le;t_j,j=\mathrm{1,2,3}k.$

Optimization problem Q6 is step 2) in semi definite programming problem.