CN106230476A - Information secure transmission method based on non-associating man made noise in insincere relay system - Google Patents

Abstract

The invention discloses information secure transmission method based on non-associating man made noise in a kind of insincere relay system, this insincere relay system includes: one sends node A, a via node B, a receiving node C and an interfering nodes D.The implementation method of this strategy process is as follows: first, continue in the first phase node B to signal by interfering nodes send man made noise disturb so that via node B produce error floor；On this basis, the signal in two stages is processed by receiving node C with different criterions, reduces the interference that first stage accepted signal receives, effectively reduces the bit error rate of receiving node C.Simulation result shows, the three kinds of strategies proposed: squeeze theorem, minimum mean-squared error algorithm, Maximum Likelihood Detection, the bit error rate of receiving node C all can be made significantly lower than insincere via node B, ensured safety and minimum mean-squared error algorithm and Maximum Likelihood Detection similar nature, be better than squeeze theorem.

Description

Information secure transmission method based on non-associating man made noise in insincere relay system

Technical field:

The invention belongs to wireless communication technology field, be specifically related in insincere relay system based on non-associating man made noise Information secure transmission method.

Background technology:

In order to meet people, communication service ever increasing need in advance, Next-Generation Wireless Communication Systems are needed offer more High transfer rate and more reliable transmission performance.On the other hand, future wireless system network will be that a support is multiple wireless The heterogeneous communications network of communication system, utilizes the method setting up base station will significantly carry to the coverage rate improving cordless communication network The cost of high radio communication.Multiaerial system, owing to can be obviously improved transmission performance and the spectrum efficiency of system, has been subjected to Extensive concern.But, the volume of mobile terminal and Power Limitation constrain the application of multiaerial system significantly.Collaboration communication is Becoming the study hotspot of moving communicating field in recent years, it improves the crucial skill of spectrum efficiency by becoming future mobile communication system One of art.The core concept of cooperation communication system is to utilize to cooperate between the multiple nodes in wireless network, it is achieved transmission Path is shared,.Thus improve the handling capacity of wireless network.So effectively can reduce while improving system spectral efficiency Increase the great amount of cost that base station is brought.But the forward node in relay system is not necessarily all safe and reliable, it is also possible to Obtain the content of transmission information while forwarding information, become the listener-in in wireless network.Therefore, insincere relay system Safe transmission problem is by academia and the common concern of industrial quarters.

Supplementing as to the one of conventional encryption technique, safety of physical layer technology becomes a kind of new research direction.Sending out The mode adding man made noise in the number of delivering letters is to realize the effective ways of secret communication under a kind of tapping channel that declines.Insincere In relay system, man made noise becomes the technological means of a kind of important transmission that ensures safety.Non-associating noise refers to send signal There is no co-design with man made noise, man made noise and transmission signal can not be divided in the signal that receiving node is received From.

Summary of the invention:

The invention aims to set up the error floor of insincere via node, it is provided that a kind of insincere relaying system Safe transmission method based on non-associating noise in system.Send man made noise by interfering nodes and utilize the signal of receiving node Spatial Dimension is higher than the characteristic of forward node, and this transmission method can make insincere forward node produce error floor and error code Rate is persistently higher than receiving node, thus ensures the safety of collaboration communication.

For reaching above-mentioned purpose, the present invention adopts the following technical scheme that and is achieved:

Information secure transmission method based on non-associating man made noise, this insincere relay system in insincere relay system Sending node A, a via node B, a receiving node C and an interfering nodes D including one, all nodes all configure list Slave antenna, and work in semiduplex mode, the method comprises the following steps:

1) first stage, sending node A and interfering nodes D send useful signal and man made noise the most respectively, manually Noise is white Gaussian noise, and via node B, receiving node C receive from sending node A, the signal of interfering nodes D, this The signal that will forward likely is cracked by Shi Zuowei fly-by-night via node B；

2) second stage, the signal that first stage is received by via node B, use the mode of amplification forwarding to be transmitted to Two signals that first stage and second stage are received by receiving node C, receiving node C carry out cascading judgement, obtain Sending node A transmitted information；Wherein, three kinds of signal detecting modes of this stage receiving node C employing: squeeze theorem, minimum Mean square error detection or Maximum Likelihood Detection.

The present invention is further improved by, step 1) in, the man made noise that interfering nodes D launches can disturb forwarding simultaneously Node B, receiving node C are for the reception of signal, and namely node B, the C reception signal in the first stage meets following formula:

$y_{1B}=\sqrt{P}{h}_{AB}x+\sqrt{P}{h}_{DB}{n}_D+n_{1B}---\left(1\right)$

$y_{1C}=\sqrt{P}{h}_{AC}x+\sqrt{P}{h}_{DC}{n}_D+n_{1C}=\sqrt{P}{h}_{AC}x+n^{\′}---\left(2\right)$

In formula: x represents the signal that sending node A sends, y_1B、y_1CRepresent the letter that via node B, C receive in the first stage Number, n_DRepresent that interfering nodes D sends the white complex gaussian noise with unit energy, x, n_DIt is respectively provided with unit energy and n_D～CN (0, 1), CN (μ, σ₀ ²) expression average is μ, variance is σ₀ ²The multiple Gauss distribution of Cyclic Symmetry, n_1B、n_1CRepresent the additivity at node B, C White complex gaussian noise and n_1B～CN (0, σ²)、n_1C～CN (0, σ²), n '～CN (0, P | h_DC|²+σ²), h_ijRepresent node i and node Channel coefficients between j, P represents the transmitting power of sending node and interfering nodes.

The present invention is further improved by, and sends node A, via node B, receiving node C and interfering nodes D and all configures Single slave antenna, and the man made noise that interfering nodes D launches is not present on the kernel of channel coefficient matrix.

The present invention is further improved by, step 2) in, second stage, oneself is received by via node B in the first stage To signal use amplification forwarding mode be transmitted to receiving node C, as follows:

y_2C=β h_BCy_1B+n_2C (3)

Wherein, y_1BRepresent the signal that via node B receives, h in the first stage_BCRepresent via node B and receiving node Channel coefficients between C, β is the power normalization factor,|·|²Represent that the mould of plural number is put down Side, n_2CRepresent the additive white Gaussian noise at node C, n_2C～CN (0, σ²), for convenience, Then(3) formula is carried out abbreviation obtain:

$y_{2C}=\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}x+\frac{{\mathrm{Ph}}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_D+n^{\′\′}---\left(4\right)$

Wherein,

The signal y that node C was received two stages_1CAnd y_2CAs two samples of the x sending signal, join Close judgement, constitute equation group

$\left\{\begin{array}{c}{y}_{1C}=\sqrt{P}{h}_{AC}x+\sqrt{P}{h}_{DC}{n}_D+n_{1C}\\ y_{2C}=\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}x+\frac{{\mathrm{Ph}}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_D+n^{\′\′}\end{array}\right.---\left(5\right)$

Write as vector form to have:

$\left[\begin{array}{c}{y}_{1C}\\ y_{2C}\end{array}\right]=\sqrt{P}\left[\begin{array}{cc}{h}_{AC}& h_{DC}\\ \frac{\sqrt{P}{h}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}& \frac{\sqrt{P}{h}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}\end{array}\right]\left[\begin{array}{c}x\\ n_D\end{array}\right]+\left[\begin{array}{c}{n}_{1C}\\ n^{\′\′}\end{array}\right]---\left(6\right)$

Have further:

$y=\sqrt{P}Rb+n---\left(7\right)$

Wherein, y represents reception signal phasor,Representing and launch power coefficient, R represents the channel of this relay communications system Coefficient matrix, b represents transmission signal phasor, and n represents additive white Gaussian noise vector.

The present invention is further improved by, step 2) in, when receiving node C uses squeeze theorem, the docking collection of letters number Then the inverse matrix of the channel coefficient matrix of vector premultiplication relay communications system makes decisions, and obtains observation vectorThat is:

${\hat{b}}_{ZF}=sgn\left(L_{ZF}y\right)---\left(8\right)$

Wherein, L_ZF=R^-1, sgn () is sign function, formula (7) is substituted into formula (8) and obtains,

${\hat{y}}_{ZF}=L_{ZF}y=R^{-1}(\sqrt{P}Rb+n)=\sqrt{P}b+R^{-1}n=\sqrt{P}b+\hat{n}---\left(9\right)$

ConsiderFirst element i.e.Agree as follows: to matrix or vector X, X_ijRepresenting matrix or vector X I-th row jth column element, each matrix in wushu (9), the concrete element of vector substitute into, and obtain:

${\hat{y}}_{{\mathrm{ZF}}_{11}}=\sqrt{P}x+\frac{{\mathrm{\ρ}}_{22}{n}_{1C}-{\mathrm{\ρ}}_{12}{n}^{\′\′}}{{\mathrm{\ρ}}_{11}{\mathrm{\ρ}}_{22}-{\mathrm{\ρ}}_{12}{\mathrm{\ρ}}_{21}}=\sqrt{P}x+\tilde{n}---\left(10\right)$

Wherein,Convenient in order to represent, agreement

In view of in formula (10), n_1C" it is separate with n, obtains in formula (10)Statistical property as follows:

$\tilde{n}~CN(0,\frac{{\mathrm{\ρ}}_{22}{n}_{1C}-{\mathrm{\ρ}}_{12}{n}^{\′\′}}{{({\mathrm{\ρ}}_{11}{\mathrm{\ρ}}_{22}-{\mathrm{\ρ}}_{12}{\mathrm{\ρ}}_{21})}^2})$

Substitute into further and have,

Thus obtain the Signal to Interference plus Noise Ratio of receiving node C, as follows

${\mathrm{SINR}}_C^{ZF}=\frac{P}{\mathrm{var}\left\{\tilde{n}\right\}}=\frac{{\mathrm{\γ}}_{BC}{(\sqrt{{\mathrm{\γ}}_{AC}{\mathrm{\γ}}_{DB}}-\sqrt{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{AB}})}^2}{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}+{\mathrm{\γ}}_{DC}({\mathrm{\γ}}_{BC}+{\mathrm{\γ}}_{AB}+{\mathrm{\γ}}_{DB}+1)}=\frac{{\mathrm{\γ}}_{BC}{(\sqrt{{\mathrm{\γ}}_{AC}{\mathrm{\γ}}_{DB}}-\sqrt{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{AB}})}^2}{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}+{\mathrm{\γ}}_{DC}m\widehat{\mathrm{\β}}}---\left(11\right)$

Wherein, var{ } represent variable variance.

The present invention is further improved by, step 2) in, when receiving node C uses minimum mean-squared error algorithm, return Gu formula (7), one best matrix L of signal phasor premultiplication is received in docking_MMSEThen make decisions, obtain observation vectorThat is:

${\hat{b}}_{MMSE}=\mathrm{sgn}\left(L_{MMSE}y\right)---\left(12\right)$

This best matrix L_MMSEMake the judgement vector finally given and the mean square error sending signal phasor b minimum, i.e. Meet Represent mathematic expectaion, projection theorem obtain:

Above formula is write as:

ConsiderWith Wherein I ' is determined by below equation:So by formula (13) The equivalent form of value obtains,

$\sqrt{P}{R}^H-L({\mathrm{PRR}}^H+{\mathrm{\σ}}^2{I}^{\′})=0---\left(14\right)$

The solution of the equation is exactly L_MMSE, it may be assumed that

$L_{MMSE}=\sqrt{P}{(PR+{\mathrm{\σ}}^2{I}^{\′}{\left(R^H\right)}^{-1})}^{-1}---\left(15\right)$

By above formula, in convolution (7), the definition of R, has

${\hat{y}}_{MMSE}=L_{MMSE}y=\sqrt{P}{(P\frac{\mathrm{\σ}}{\sqrt{P}}{R}^{\′}+{\mathrm{\σ}}^2{I}^{\′}\frac{\sqrt{P}}{\mathrm{\σ}}{\left(R^{\′T}\right)}^{-1})}^{-1}y={(R^{\′}+I^{\′}{\left(R^{\′T}\right)}^{-1})}^{-1}\frac{y}{\mathrm{\σ}}\stackrel{\mathrm{\Δ}}{=}{L}^{\′}{y}^{\′}---\left(16\right)$

Wherein, L '_MMSE=(R '+I ' (R '^T)^-1)^-1,

Signal to Interference plus Noise Ratio at receiving node C isVar{ } represent The variance of variable, wherein,In conjunction withWith Statistical property as follows:

${\hat{b}}_{{\mathrm{MMSE}}_{11}}~CN(L_{{\mathrm{MMSE}}_{11}}^{\′}\sqrt{{\mathrm{\γ}}_{AC}}+L_{{\mathrm{MMSE}}_{12}}^{\′}\frac{\sqrt{{\mathrm{\γ}}_{AB}{\mathrm{\γ}}_{BC}}}{\sqrt{\widehat{\mathrm{\β}}}},{\left(L_{{\mathrm{MMSE}}_{11}}^{\′}\sqrt{{\mathrm{\γ}}_{DC}}+L_{{\mathrm{MMSE}}_{12}}^{\′}\frac{\sqrt{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}}{\sqrt{\widehat{\mathrm{\β}}}}\right)}^2+{L_{{\mathrm{MMSE}}_{11}}^{\′}}^2{L_{{\mathrm{MMSE}}_{12}}^{\′}}^{2}m)---\left(17\right).$

The present invention is further improved by, step 2) in, when receiving node C uses maximum-likelihood decoding, rewrite formula (5), as follows:

$\begin{array}{c}{y}_{1C}=\sqrt{P}{h}_{AC}x+\sqrt{P}{h}_{DC}{n}_D+n_{1C}=\sqrt{P}{h}_{AC}x+n^{\′}\\ y_{2C}=\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}x+\frac{{\mathrm{Ph}}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_D+\frac{\sqrt{P}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_{1B}+n_{2C}=\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}x+n^{\′\′\′}\end{array}---\left(18\right)$

Wherein, n '～CN (0, P | h_DC|²+σ²),

Write as vector form to have,

$\left[\begin{array}{c}{y}_{1C}\\ y_{2C}\end{array}\right]=\left[\begin{array}{c}\sqrt{P}{h}_{AC}\\ \frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}\end{array}\right]x+\left[\begin{array}{c}{n}^{\′}\\ n^{\′\′\′}\end{array}\right]\⇔y=Hx+n^{\′}---\left(19\right).$

The present invention is further improved by, and receiving node C docking is received signal phasor and carried out noise whitening, then to mutually Two independent signals carry out maximum-ratio combing, then make decisions, obtain observation vector

First the characteristic of noise is analyzed,Wherein, N meets

$N=\left[\begin{array}{cc}{\mathrm{\γ}}_{DC}+1& \sqrt{\frac{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}{\widehat{\mathrm{\β}}}}\\ \sqrt{\frac{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}{\widehat{\mathrm{\β}}}}& \frac{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}{\widehat{\mathrm{\β}}}+m\end{array}\right]---\left(20\right)$

Wherein,

Noise whitening is used to need N is carried out decomposition at the tenth of the twelve Earthly Branches, i.e.M is the albefaction needed Noise matrix, meets

$M=\frac{1}{\mathrm{\σ}}\sqrt{{\mathrm{\Λ}}^{-1}}{u}^T---\left(21\right)$

Y premultiplication M is had,

$\tilde{y}=\left[\begin{array}{c}{\tilde{y}}_{1C}\\ {\tilde{y}}_{2C}\end{array}\right]=My=MHx+{\mathrm{Mn}}^{\′}=\tilde{H}x+\widetilde{n^{\′}}---\left(22\right)$

Checking,

Then, rightTwo signals carry out maximum-ratio combing (MRC) and make decisions again, the judgement vector so obtained must It is so satisfied's；

${\mathrm{SINR}}_C^{ML}={{\tilde{H}}_{11}}^2+{{\tilde{H}}_{21}}^2---\left(23\right)$

Wherein,Can be obtained, i.e. by formula (22) Representing matrixThe i-th row jth column element.

Information secure transmission method based on non-associating man made noise, tool in insincere relay system proposed by the invention Have the following advantages:

First, send man made noise by interfering nodes and utilize the signal space dimension of receiving node higher than forward node Characteristic, this transmission method can make insincere forward node produce error floor and the bit error rate persistently higher than receiving node, Thus ensure the safety of collaboration communication.

Secondly, the method, without interfering nodes and the coordination of transmitting node, reduces each internodal coordination in system Problem.Introduced unique overhead receives the linear operation of signal from receiving node C to twice, it means that institute The strategy proposed has the lowest implementation complexity.And according to description above, safe transmission is not by transmission square The kernel of battle array, this communication system being well suited for being applied to single antenna.

Accompanying drawing illustrates:

Fig. 1 is system model schematic diagram；

Fig. 2 is that under three kinds of methods, the bit error rate of receiving node C and via node B is bent with the change of system average signal-to-noise ratio Line；

Fig. 3 is to travel through the secrecy capacity change curve with system average signal-to-noise ratio under three kinds of methods；

When Fig. 4 is different threshold value under three kinds of methods, secrecy capacity outage probability is with the change curve of system average signal-to-noise ratio；

Fig. 5 be under three kinds of methods secrecy capacity outage probability with the change curve of secrecy capacity threshold value.

Detailed description of the invention:

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

As it is shown in figure 1, information secure transmission method based on non-associating man made noise in the insincere relay system of the present invention, This insincere relay system includes: one sends node A, a via node B, a receiving node C and an interfering nodes D.Send the demand having one-way communication between node A and receiving node C, but owing to they are apart from each other or are hidden by barrier Gear, therefore cannot directly set up unidirectional transmission link, needs the assistance via via node B, and via node B uses amplification forwarding Agreement.But owing to the safety of via node B is unknown, it is likely to result in the leakage of information, institute while forwarding information The safety of guarantee information is carried out to need interfering nodes D to send man made noise.But the man made noise of interfering nodes D also can affect Reception signal to receiving node C.The present invention provides information secure transmission method to be contemplated to solve the problems referred to above.Assume all Node all configures single slave antenna, and works in semiduplex mode.Without loss of generality, the transmitting power making each node is P.Will be every Additive noise at individual receiver is expressed as zero-mean, variance is σ²Multiple Gaussian random variable.

In carried strategy, first stage, sending node A and interfering nodes D send the most respectively useful signal and Man made noise, man made noise is white Gaussian noise, via node B, receiving node C all receive from node A, D containing people The useful signal of work noise, now the signal that will forward is cracked by the via node B as insincere relaying.Second The individual stage, the signal that first stage is received by via node B, use the mode of amplification forwarding (AF) to be transmitted to receiving node C. Two signals that first stage and second stage are received by receiving node C carry out cascading judgement, obtain information.Node C Reception signal all first pass around a series of linear operation after make decisions again, this stage receiving node C uses the inspection of three kinds of signals Survey mode: squeeze theorem (ZF), minimum mean-squared error algorithm (MMSE), Maximum Likelihood Detection (ML).

First stage, via node B is had:

$y_{1B}=\sqrt{P}{h}_{AB}x+\sqrt{P}{h}_{DB}{n}_D+n_{1B}---\left(1\right)$

Wherein, x represents the signal that sending node A sends, y_1BRepresent the letter that relay forwarding node B receives in the first stage Number, n_DRepresent that interfering nodes D sends the white complex gaussian noise with unit energy, x, n_DIt is respectively provided with unit energy, i.e.And n_D～CN (0,1), symbol ()^*Represent conjugate transpose, n_1BRepresent the additivity at via node B White Gaussian noise, n_1BBe the zero-mean variance of Cyclic Symmetry be σ²White complex gaussian noise, i.e. n_1B～CN (0, σ²), CN (μ, σ₀ ²) Expression average is μ, variance is σ₀ ²The multiple Gauss distribution of Cyclic Symmetry.h_ABRepresent the letter between sending node A and via node B Road coefficient, h_DBRepresent the channel coefficients between interfering nodes D and via node B.P represents the transmitting of sending node and interfering nodes Power, it is assumed that they have the same power.It is similar to, receiving node C is had:

$y_{1C}=\sqrt{P}{h}_{AC}x+\sqrt{P}{h}_{DC}{n}_D+n_{1C}=\sqrt{P}{h}_{AC}x+n^{\′}---\left(2\right)$

Wherein, y_1CRepresent the signal that via node B receives, n in the first stage_1CRepresent the additive Gaussian at receiving node C White noise, n_1C～CN (0, σ²), n '～CN (0, P | h_DC|²+σ²), n '～CN (0, P | h_DC|²+σ²)。h_ACRepresent sending node A and Channel coefficients between receiving node C, h_DCRepresent the channel coefficients between interfering nodes D and receiving node C.

Second stage, oneself is used the mode of amplification forwarding to be transmitted at the signal that the first stage receives by via node B Receiving node C,

y_2C=β h_BCy_1B+n_2C (3)

Wherein, y_1BRepresent the signal that node B receives, h in the first stage_BCRepresent via node B and receiving node C it Between channel coefficients, β is the power normalization factor,|·|²Represent the mould square of plural number, n_2CRepresent the additive white Gaussian noise at node C, n_2C～CN (0, σ²).For convenience,Then(1) formula is substituted into (3) formula, carries out abbreviation and obtain:

$\begin{array}{c}{y}_{2C}={\mathrm{\βy}}_{1B}{h}_{BC}+n_{2C}=\frac{1}{\sqrt{\widetilde{\mathrm{\β}}}}\sqrt{P}{h}_{BC}(\sqrt{P}{h}_{AB}x+\sqrt{P}{h}_{DB}{n}_D+n_{1B})+n_{2C}\\ =\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}x+\frac{{\mathrm{Ph}}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_D+n^{\′\′}\end{array}---\left(4\right)$

Wherein,

The signal y that node C was received two stages_1CAnd y_2CAs two samples of the x sending signal, join Close judgement.By (2) formula and (4) formula simultaneous, constitute equation group

$\left\{\begin{array}{c}{y}_{1C}=\sqrt{P}{h}_{AC}x+\sqrt{P}{h}_{DC}{n}_D+n_{1C}\\ y_{2C}=\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}x+\frac{{\mathrm{Ph}}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_D+n^{\′\′}\end{array}\right.---\left(5\right)$

As it was previously stated,Write as vector form to have,

$\left[\begin{array}{c}{y}_{1C}\\ y_{2C}\end{array}\right]=\sqrt{P}\left[\begin{array}{cc}{h}_{AC}& h_{DC}\\ \frac{\sqrt{P}{h}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}& \frac{\sqrt{P}{h}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}\end{array}\right]\left[\begin{array}{c}x\\ n_D\end{array}\right]+\left[\begin{array}{c}{n}_{1C}\\ n^{\′\′}\end{array}\right]---\left(6\right)$

Have further,

$y=\sqrt{P}Rb+n---\left(7\right)$

Y represents reception signal phasor,Representing and launch power coefficient, R represents the channel coefficients square of this relay communications system Battle array, b represents transmission signal phasor, and n represents additive white Gaussian noise vector.

When receiving node C uses squeeze theorem, the channel coefficients square of signal phasor premultiplication relay communications system is received in docking Then the inverse matrix of battle array makes decisions, and obtains observation vectorThat is:

${\hat{b}}_{ZF}=\mathrm{sgn}\left(L_{ZF}y\right)---\left(8\right)$

Wherein, L_ZF=R^-1, sgn () is sign function.Formula (7) is substituted into formula (8) obtain,

${\hat{y}}_{ZF}=L_{ZF}y=R^{-1}(\sqrt{P}Rb+n)=\sqrt{P}b+R^{-1}n=\sqrt{P}b+\hat{n}---\left(9\right)$

ConsiderFirst element i.e.Agree as follows: to matrix or vector X, X_ijRepresenting matrix or vector X I-th row jth column element, each matrix in wushu (9), the concrete element of vector substitute into, and just obtain,

${\hat{y}}_{{\mathrm{ZF}}_{11}}=\sqrt{P}x+\frac{{\mathrm{\ρ}}_{22}{n}_{1C}-{\mathrm{\ρ}}_{12}{n}^{\′\′}}{{\mathrm{\ρ}}_{11}{\mathrm{\ρ}}_{22}-{\mathrm{\ρ}}_{12}{\mathrm{\ρ}}_{21}}=\sqrt{P}x+\tilde{n}---\left(10\right)$

Wherein, n_1C～CN (0, σ²),Convenient in order to represent, agreement

In view of in formula (10), n_1C" it is separate with n, can obtain in formula (10)Statistical property as follows:Substitute into further and have,

Thus can obtain the Signal to Interference plus Noise Ratio (SINR) of receiving node C,

${\mathrm{SINR}}_C^{ZF}=\frac{P}{\mathrm{var}\left\{\tilde{n}\right\}}=\frac{{\mathrm{\γ}}_{BC}{(\sqrt{{\mathrm{\γ}}_{AC}{\mathrm{\γ}}_{DB}}-\sqrt{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{AB}})}^2}{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}+{\mathrm{\γ}}_{DC}({\mathrm{\γ}}_{BC}+{\mathrm{\γ}}_{AB}+{\mathrm{\γ}}_{DB}+1)}=\frac{{\mathrm{\γ}}_{BC}{(\sqrt{{\mathrm{\γ}}_{AC}{\mathrm{\γ}}_{DB}}-\sqrt{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{AB}})}^2}{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}+{\mathrm{\γ}}_{DC}m\widehat{\mathrm{\β}}}---\left(11\right)$

Wherein, var{ } represent variable variance.

When receiving node C uses minimum mean-squared error algorithm (MMSE), looking back formula (7), signal phasor premultiplication is received in docking One best matrix L_MMSEThen make decisions, obtain observation vectorThat is:

${\hat{b}}_{MMSE}=\mathrm{sgn}\left(L_{MMSE}y\right)---\left(12\right)$

This best matrix L_MMSEMake the judgement vector finally given and the mean square error sending signal phasor b minimum, i.e. MeetObtained by projection theorem:

Above formula can also be write:

ConsiderWith Wherein I ' is determined by below equation:So by formula (13) The equivalent form of value can obtain,

$\sqrt{P}{R}^H-L({\mathrm{PRR}}^H+{\mathrm{\σ}}^2{I}^{\′})=0---\left(14\right)$

The solution of the equation is exactly L_MMSE, it may be assumed that

$L=\sqrt{P}{(PR+{\mathrm{\σ}}^2{I}^{\′}{\left(R^H\right)}^{-1})}^{-1}---\left(15\right)$

By above formula, orderIn convolution (6), the definition of R, has

${\hat{y}}_{MMSE}=L_{MMSE}y=\sqrt{P}{(P\frac{\mathrm{\σ}}{\sqrt{P}}{R}^{\′}+{\mathrm{\σ}}^2{I}^{\′}\frac{\sqrt{P}}{\mathrm{\σ}}{\left(R^{\′T}\right)}^{-1})}^{-1}y={(R^{\′}+I^{\′}{\left(R^{\′T}\right)}^{-1})}^{-1}\frac{y}{\mathrm{\σ}}\stackrel{\mathrm{\Δ}}{=}{L}^{\′}{y}^{\′}---\left(16\right)$

Wherein, L '_MMSE=(R '+I ' (R '^T)^-1)^-1,Signal to Interference plus Noise Ratio at receiving node C isVar{ } represent variable variance, wherein,In conjunction withWith Statistical property as follows:

${\hat{b}}_{{\mathrm{MMSE}}_{11}}~CN(L_{{\mathrm{MMSE}}_{11}}^{\′}\sqrt{{\mathrm{\γ}}_{AC}}+L_{{\mathrm{MMSE}}_{12}}^{\′}\frac{\sqrt{{\mathrm{\γ}}_{AB}{\mathrm{\γ}}_{BC}}}{\sqrt{\widehat{\mathrm{\β}}}},{\left(L_{{\mathrm{MMSE}}_{11}}^{\′}\sqrt{{\mathrm{\γ}}_{DC}}+L_{{\mathrm{MMSE}}_{12}}^{\′}\frac{\sqrt{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}}{\sqrt{\widehat{\mathrm{\β}}}}\right)}^2+{L_{{\mathrm{MMSE}}_{11}}^{\′}}^2{L_{{\mathrm{MMSE}}_{12}}^{\′}}^{2}m)---\left(17\right)$

Now,Expression the most complicated, limited space thus omit.

When node C uses maximum-likelihood decoding, rewrite formula (5),

$\begin{array}{c}{y}_{1C}=\sqrt{P}{h}_{AC}x+\sqrt{P}{h}_{DC}{n}_D+n_{1C}=\sqrt{P}{h}_{AC}x+n^{\′}\\ y_{2C}=\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}x+\frac{{\mathrm{Ph}}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_D+\frac{\sqrt{P}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_{1B}+n_{2C}=\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}x+n^{\′\′\′}\end{array}---\left(18\right)$

Wherein, n '～CN (0, P | h_DC|²+σ²),Write as Vector form has:

$\left[\begin{array}{c}{y}_{1C}\\ y_{2C}\end{array}\right]=\left[\begin{array}{c}\sqrt{P}{h}_{AC}\\ \frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}\end{array}\right]x+\left[\begin{array}{c}{n}^{\′}\\ n^{\′\′\′}\end{array}\right]\⇔y=Hx+n^{\′}---\left(19\right)$

Receiving node C docking is received signal phasor y and is carried out noise whitening, then two separate signals is carried out maximum Than merging, then make decisions, obtain observation vector

Firstly the need of the characteristic of analysis noise,Wherein, N meets

$N=\left[\begin{array}{cc}{\mathrm{\γ}}_{DC}+1& \sqrt{\frac{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}{\widehat{\mathrm{\β}}}}\\ \sqrt{\frac{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}{\widehat{\mathrm{\β}}}}& \frac{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}{\widehat{\mathrm{\β}}}+m\end{array}\right]---\left(20\right)$

Wherein,Noise whitening is used to need N is carried out the tenth of the twelve Earthly Branches Decompose, i.e.M is the white noise matrix needed, and it meets

$M=\frac{1}{\mathrm{\σ}}\sqrt{{\mathrm{\Λ}}^{-1}}{u}^T---\left(21\right)$

Y premultiplication M is had,

$\tilde{y}=\left[\begin{array}{c}{\tilde{y}}_{1C}\\ {\tilde{y}}_{2C}\end{array}\right]=My=MHx+{\mathrm{Mn}}^{\′}=\tilde{H}x+\widetilde{n^{\′}}---\left(22\right)$

Can verify,

Then, rightTwo signals carry out maximum-ratio combing (MRC) and make decisions again, the judgement vector so obtained must It is so satisfied's.The Signal to Interference plus Noise Ratio of node C is

${\mathrm{SINR}}_C^{ML}={{\tilde{H}}_{11}}^2+{{\tilde{H}}_{21}}^2---\left(23\right)$

Wherein,Can be obtained, i.e. by formula (22) Representing matrixThe i-th row jth column element.

Said method is summarized as follows, the Signal to Interference plus Noise Ratio at node B:

${\mathrm{SINR}}_B=\frac{{\mathrm{\γ}}_{AB}}{{\mathrm{\γ}}_{DB}+1}---\left(24\right)$

1) when using ZF (ZF) detection, Signal to Interference plus Noise Ratio:

${\mathrm{SINR}}_C^{ZF}=\frac{{\mathrm{\γ}}_{BC}({\mathrm{\γ}}_{AC}{\mathrm{\γ}}_{DB}+{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{AB}-2\sqrt{{\mathrm{\γ}}_{AB}}\sqrt{{\mathrm{\γ}}_{AC}}\sqrt{{\mathrm{\γ}}_{DB}}\sqrt{{\mathrm{\γ}}_{DC}})}{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}+{\mathrm{\γ}}_{DC}({\mathrm{\γ}}_{BC}+{\mathrm{\γ}}_{AB}+{\mathrm{\γ}}_{DB}+1)}---\left(25\right)$

2) when using least mean-square error (MMSE) detection, Signal to Interference plus Noise Ratio:

Wherein,Meet formula (17).

3) when using maximum likelihood (ML) detection, Signal to Interference plus Noise Ratio:

${\mathrm{SINR}}_C^{ML}={{\tilde{H}}_{11}}^2+{{\tilde{H}}_{21}}^2---\left(27\right)$

Wherein,

When modulation system uses QPSK, then bit error rate is

$P_b=Q\left(\sqrt{SINR}\right)---\left(28\right)$

Wherein, SINR is Signal to Interference plus Noise Ratio.

In order to verify the performance of information secure transmission method proposed by the invention, the present invention has carried out following computer Emulation:

In simulations, it is assumed that all internodal channel coefficients are obeyed with the Rayleigh fading of average, this average be referred to as be System average signal-to-noise ratio.Without loss of generality, it is assumed that send node A, transmit power P=1 of interfering nodes D.Unless stated otherwise, exist In simulations below, each node all uses QPSK as modulation system.In order to compare the security performance of this method, in simulations than In the case of different independent variables, under three kinds of methods, the secrecy of receiving node C and the bit error rate of via node B, traversal is held Amount, the outage probability of secrecy capacity.

Fig. 2 gives the bit error rate of receiving node C and via node B under distinct methods and changes feelings with system average signal-to-noise ratio The simulation result of condition.Figure it is seen that there is obvious error floor in via node B, say, that the mistake of via node B Bit rate will not decline with the rising of average signal-to-noise ratio.This be by via node B be interfered node D man made noise interference Cause.In contrast, three kinds of safe transmission strategies proposed by the invention are due to can be by the interfered signal of first stage The interfered signal forwarded via via node B with second stage is adjudicated in combination, owing to receiving node C has more multidimensional Sample of signal can eliminate interference and reduce bit error rate with imitating, and therefore the bit error rate of receiving node C is by the rising along with SNR Decline rapidly.The slope approximation of three kinds of detection modes bit error rate relative signal-to-noise ratio when high s/n ratio as we can see from the figure For-0.05.

Fig. 3 depicts and travels through the secrecy capacity change curve with system average signal-to-noise ratio under three kinds of methods.As is expected As, traveling through secrecy capacity under three kinds of methods increases with system average signal-to-noise ratio and increases.Along with system average signal-to-noise ratio Increasing, the difference between the traversal secrecy capacity of three kinds of detection modes diminishes.Different from squeeze theorem, minimum mean-squared error algorithm and The performance of maximum likelihood strategy is close, and has optimal performance.

When Fig. 4 depicts different threshold value under three kinds of methods, secrecy capacity outage probability is bent with the change of system average signal-to-noise ratio Line.In figure, the threshold value 1 of secrecy capacity is 0nats/s/Hz, and threshold value 2 is 0.5nats/s/Hz.Because threshold value 1 is less than threshold value 2, institute It is less than threshold value 2 with the secrecy capacity outage probability of same system average signal-to-noise ratio lower threshold value 1 correspondence.For a certain secrecy capacity Threshold value, declines along with system average signal-to-noise ratio increases outage probability, and the secrecy capacity outage probability of squeeze theorem is higher than additionally Two kinds of detection modes.

Fig. 5 depicts under three kinds of methods secrecy capacity outage probability with the change curve of secrecy capacity threshold value.Two suite lines The system average signal-to-noise ratio that (solid line suite line and dotted line suite line) is corresponding is respectively 20dB and 40dB.The guarantor that each bar curve is corresponding Close capacity outage probability all increases along with the increase of secrecy capacity threshold value, and the secrecy that under same threshold value, solid line suite line is corresponding Capacity outage probability is more than dotted line group, this is because the system average signal-to-noise ratio of solid line group is relatively low.

Claims (8)

1. Information secure transmission method based on non-associating man made noise in the most insincere relay system, it is characterised in that this can not Letter relay system includes that one sends node A, a via node B, a receiving node C and an interfering nodes D, all joints Point all configures single slave antenna, and works in semiduplex mode, and the method comprises the following steps:

   1) first stage, sending node A and interfering nodes D send useful signal and man made noise, man made noise the most respectively For white Gaussian noise, via node B, receiving node C receive from sending node A, the signal of interfering nodes D, now make Likely the signal that will forward is cracked for fly-by-night via node B；

   2) second stage, the signal that first stage is received by via node B, use the mode of amplification forwarding to be transmitted to receive Two signals that first stage and second stage are received by node C, receiving node C carry out cascading judgement, obtain and send Node A transmitted information；Wherein, three kinds of signal detecting modes of this stage receiving node C employing: squeeze theorem, lowest mean square Error-detecting or Maximum Likelihood Detection.
2. Safe information transmission side based on non-associating man made noise in insincere relay system the most according to claim 1 Method, it is characterised in that step 1) in, the man made noise that interfering nodes D launches can disturb forward node B, receiving node C pair simultaneously In the reception of signal, namely node B, the C reception signal in the first stage meets following formula:

   $y_{1B}=\sqrt{P}{h}_{AB}x+\sqrt{P}{h}_{DB}{n}_D+n_{1B}---\left(1\right)$

   $y_{1C}=\sqrt{P}{h}_{AC}x+\sqrt{P}{h}_{DC}{n}_D+n_{1C}=\sqrt{P}{h}_{AC}x+n^{\′}---\left(2\right)$

   In formula: x represents the signal that sending node A sends, y_1B、y_1CRepresent the signal that via node B, C receive, n in the first stage_D Represent that interfering nodes D sends the white complex gaussian noise with unit energy, x, n_DIt is respectively provided with unit energy and n_D～CN (0,1), CN (μ,σ₀ ²) expression average is μ, variance is σ₀ ²The multiple Gauss distribution of Cyclic Symmetry, n_1B、n_1CRepresent the multiple height of the additivity at node B, C This white noise and n_1B～CN (0, σ²)、n_1C～CN (0, σ²), n '～CN (0, P | h_DC|²+σ²), h_ijRepresent node i and node j it Between channel coefficients, P represents the transmitting power of sending node and interfering nodes.
3. Safe information transmission side based on non-associating man made noise in insincere relay system the most according to claim 2 Method, it is characterised in that send node A, via node B, receiving node C and interfering nodes D and all configure single slave antenna, and interference joint The man made noise that some D launches is not present on the kernel of channel coefficient matrix.
4. Safe information transmission side based on non-associating man made noise in insincere relay system the most according to claim 2 Method, it is characterised in that step 2) in, second stage, oneself is used to amplify at the signal that the first stage receives and turns by via node B The mode sent out is transmitted to receiving node C, as follows:

   y_2C=β h_BCy_1B+n_2C (3)

   Wherein, y_1BRepresent the signal that via node B receives, h in the first stage_BCRepresent between via node B and receiving node C Channel coefficients, β is the power normalization factor,|·|²Represent the mould square of plural number, n_2C Represent the additive white Gaussian noise at node C, n_2C～CN (0, σ²), for convenience,Then(3) formula is carried out abbreviation obtain:

   $y_{2C}=\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}x+\frac{{\mathrm{Ph}}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_D+n^{\′\′}---\left(4\right)$

   Wherein,

   The signal y that node C was received two stages_1CAnd y_2CAs two samples of the x sending signal, carry out combining sentencing Certainly, equation group is constituted

   $\left\{\begin{array}{c}{y}_{1C}=\sqrt{P}{h}_{AC}x+\sqrt{P}{h}_{DC}{n}_D+n_{1C}\\ y_{2C}=\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}x+\frac{{\mathrm{Ph}}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_D+n^{\′\′}\end{array}\right.---\left(5\right)$

   Write as vector form to have:

   $\left[\begin{array}{c}{y}_{1C}\\ y_{2C}\end{array}\right]=\sqrt{P}\left[\begin{array}{cc}{h}_{AC}& h_{DC}\\ \frac{\sqrt{P}{h}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}& \frac{\sqrt{P}{h}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}\end{array}\right]\left[\begin{array}{c}x\\ n_D\end{array}\right]+\left[\begin{array}{c}{n}_{1C}\\ n^{\′\′}\end{array}\right]---\left(6\right)$

   Have further:

   $y=\sqrt{P}Rb+n---\left(7\right)$

   Wherein, y represents reception signal phasor,Representing and launch power coefficient, R represents the channel coefficients of this relay communications system Matrix, b represents transmission signal phasor, and n represents additive white Gaussian noise vector.
5. Safe information transmission side based on non-associating man made noise in insincere relay system the most according to claim 4 Method, it is characterised in that step 2) in, when receiving node C uses squeeze theorem, signal phasor premultiplication trunking traffic system is received in docking Then the inverse matrix of the channel coefficient matrix of system makes decisions, and obtains observation vectorThat is:

   ${\hat{b}}_{ZF}=sgn\left(L_{ZF}y\right)---\left(8\right)$

   Wherein, L_ZF=R^-1, sgn () is sign function, formula (7) is substituted into formula (8) and obtains,

   ${\hat{y}}_{ZF}=L_{ZF}y=R^{-1}(\sqrt{P}Rb+n)=\sqrt{P}b+R^{-1}n=\sqrt{P}b+\hat{n}---\left(9\right)$

   ConsiderFirst element i.e.Agree as follows: to matrix or vector X, X_ijRepresenting matrix or i-th row of vector X Jth column element, each matrix in wushu (9), the concrete element of vector substitute into, and obtain:

   ${\hat{y}}_{{\mathrm{ZF}}_{11}}=\sqrt{P}x+\frac{{\mathrm{\ρ}}_{22}{n}_{1C}-{\mathrm{\ρ}}_{12}{n}^{\′\′}}{{\mathrm{\ρ}}_{11}{\mathrm{\ρ}}_{22}-{\mathrm{\ρ}}_{12}{\mathrm{\ρ}}_{21}}=\sqrt{P}x+\tilde{n}---\left(10\right)$

   Wherein,Convenient in order to represent, agreement

   In view of in formula (10), n_1C" it is separate with n, obtains in formula (10)Statistical property as follows:

   $\tilde{n}~CN(0,\frac{{\mathrm{\ρ}}_{22}{n}_{1C}-{\mathrm{\ρ}}_{12}{n}^{\′\′}}{{({\mathrm{\ρ}}_{11}{\mathrm{\ρ}}_{22}-{\mathrm{\ρ}}_{12}{\mathrm{\ρ}}_{21})}^2})$

   Substitute into further and have,

   Thus obtain the Signal to Interference plus Noise Ratio of receiving node C, as follows

   ${\mathrm{SINR}}_C^{ZF}=\frac{P}{\mathrm{var}\left\{\tilde{n}\right\}}=\frac{{\mathrm{\γ}}_{BC}{(\sqrt{{\mathrm{\γ}}_{AC}{\mathrm{\γ}}_{DB}}-\sqrt{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{AB}})}^2}{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}+{\mathrm{\γ}}_{DC}({\mathrm{\γ}}_{BC}+{\mathrm{\γ}}_{AB}+{\mathrm{\γ}}_{DB}+1)}=\frac{{\mathrm{\γ}}_{BC}{(\sqrt{{\mathrm{\γ}}_{AC}{\mathrm{\γ}}_{DB}}-\sqrt{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{AB}})}^2}{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}+{\mathrm{\γ}}_{DC}m\widehat{\mathrm{\β}}}---\left(11\right)$

   Wherein, var{ } represent variable variance.
6. Safe information transmission side based on non-associating man made noise in insincere relay system the most according to claim 5 Method, it is characterised in that step 2) in, when receiving node C uses minimum mean-squared error algorithm, look back formula (7), the docking collection of letters number One best matrix L of vector premultiplication_MMSEThen make decisions, obtain observation vectorThat is:

   ${\hat{b}}_{MMSE}=\mathrm{sgn}\left(L_{MMSE}y\right)---\left(12\right)$

   This best matrix L_MMSEMake the judgement vector finally given and the mean square error sending signal phasor b minimum, the most satisfied Represent mathematic expectaion, projection theorem obtain:

   Above formula is write as:

   ConsiderWithWherein I ' is determined by below equation:So by the equivalence of formula (13) Form obtains,

   $\sqrt{P}{R}^H-L({\mathrm{PRR}}^H+{\mathrm{\σ}}^2{I}^{\′})=0---\left(14\right)$

   The solution of the equation is exactly L_MMSE, it may be assumed that

   $L_{MMSE}=\sqrt{P}{(PR+{\mathrm{\σ}}^2{I}^{\′}{\left(R^H\right)}^{-1})}^{-1}---\left(15\right)$

   By above formula, in convolution (7), the definition of R, has

   ${\hat{y}}_{MMSE}=L_{MMSE}y=\sqrt{P}{(P\frac{\mathrm{\σ}}{\sqrt{P}}{R}^{\′}+{\mathrm{\σ}}^2{I}^{\′}\frac{\sqrt{P}}{\mathrm{\σ}}{\left(R^{\′T}\right)}^{-1})}^{-1}y={(R^{\′}+I^{\′}{\left(R^{\′T}\right)}^{-1})}^{-1}\frac{y}{\mathrm{\σ}}\stackrel{\mathrm{\Δ}}{=}{L}^{\′}{y}^{\′}---\left(16\right)$

   Wherein, L '_MMSE=(R '+I ' (R '^T)^-1)^-1,

   Signal to Interference plus Noise Ratio at receiving node C isVar{ } represent change The variance of amount, wherein,In conjunction withWith Statistical property as follows:

   ${\hat{b}}_{{\mathrm{MMSE}}_{11}}~CN\left(L_{{\mathrm{MMSE}}_{11}}^{\′}\sqrt{{\mathrm{\γ}}_{AC}}+L_{{\mathrm{MMSE}}_{12}}^{\′}\frac{\sqrt{{\mathrm{\γ}}_{AB}{\mathrm{\γ}}_{BC}}}{\sqrt{\widehat{\mathrm{\β}}}},{\left(L_{{\mathrm{MMSE}}_{11}}^{\′}\sqrt{{\mathrm{\γ}}_{DC}}+L_{{\mathrm{MMSE}}_{12}}^{\′}\frac{\sqrt{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}}{\sqrt{\widehat{\mathrm{\β}}}}\right)}^2+{L_{{\mathrm{MMSE}}_{11}}^{\′}}^2+{L_{{\mathrm{MMSE}}_{12}}^{\′}}^{2}m\right)---\left(17\right).$
7. Safe information transmission side based on non-associating man made noise in insincere relay system the most according to claim 5 Method, it is characterised in that step 2) in, when receiving node C uses maximum-likelihood decoding, rewrite formula (5), as follows:

   $\begin{array}{c}{y}_{1C}=\sqrt{P}{h}_{AC}x+\sqrt{P}{h}_{DC}{n}_D+n_{1C}=\sqrt{P}{h}_{AC}x+n^{\′}\\ y_{2C}=\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}+\frac{{\mathrm{Ph}}_{DB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_D+\frac{\sqrt{P}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}{n}_{1B}+n_{2C}=\frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}x+n^{\′\′\′}\end{array}---\left(18\right)$

   Wherein, n '～CN (0, P | h_DC|²+σ²),

   Write as vector form to have,

   $\left[\begin{array}{c}{y}_{1C}\\ y_{2C}\end{array}\right]=\left[\begin{array}{c}\sqrt{P}{h}_{AC}\\ \frac{{\mathrm{Ph}}_{AB}{h}_{BC}}{\sqrt{\widetilde{\mathrm{\β}}}}\end{array}\right]x+\left[\begin{array}{c}{n}^{\′}\\ n^{\′\′\′}\end{array}\right]\⇔y=Hx+n^{\′}---\left(19\right).$
8. Safe information transmission side based on non-associating man made noise in insincere relay system the most according to claim 5 Method, it is characterised in that receiving node C docking is received signal phasor and carried out noise whitening, then enters two separate signals Row maximum-ratio combing, then makes decisions, and obtains observation vector

   First the characteristic of noise is analyzed,Wherein, N meets

   $N=\left[\begin{array}{cc}{\mathrm{\γ}}_{DC}+& \sqrt{\frac{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}{\widehat{\mathrm{\β}}}}\\ \sqrt{\frac{{\mathrm{\γ}}_{DC}{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}{\widehat{\mathrm{\β}}}}& \frac{{\mathrm{\γ}}_{DB}{\mathrm{\γ}}_{BC}}{\widehat{\mathrm{\β}}}+m\end{array}\right]---\left(20\right)$

   Wherein,

   Noise whitening is used to need N is carried out decomposition at the tenth of the twelve Earthly Branches, i.e.M is the white noise square needed Battle array, meets

   $M=\frac{1}{\mathrm{\σ}}\sqrt{{\mathrm{\Λ}}^{-1}}{u}^T---\left(21\right)$

   Y premultiplication M is had,

   $\tilde{y}=\left[\begin{array}{c}{\tilde{y}}_{1C}\\ {\tilde{y}}_{2C}\end{array}\right]=My=MHx+{\mathrm{Mn}}^{\′}=\tilde{H}x+\widetilde{n^{\′}}---\left(22\right)$

   Checking,

   Then, rightTwo signals carry out maximum-ratio combing (MRC) and make decisions again, the judgement vector so obtained is necessarily Meet's；

   ${\mathrm{SINR}}_C^{ML}={{\tilde{H}}_{11}}^2{+}^2{{\tilde{H}}_{21}}^2---\left(23\right)$

   Wherein,Can be obtained, i.e. by formula (22) Representing matrixThe i-th row jth column element.