CN104901730A - Method for improving MIMO safety capacity based on weighting matrix - Google Patents

Abstract

The present invention discloses a method for improving MIMO safety capacity based on a weighting matrix. The method includes: (1) adding a weighting matrix Dk at a transmitting terminal to decrease the matrix dimensions of the system matrix such that a zero space is available; (2) calculating a precoding matrix Fk of each user at the transmitting terminal to obtain an equivalent channel matrix DkHkFk, wherein Hk represents the channel matrix of the kth user; (3) performing SVD decomposition of the equivalent channel matrix and water injection power distribution for each user; (4) adding a weighting matrix Wk at a receiving terminal, and calculating sum capacity of each user; and (5) calculating a weighting matrix We and wiretapping capacity at a wiretapping terminal, and calculating the difference between the sum capacity and the wiretapping capacity to obtain confidential capacity. According to the method, only one matrix is required to be added at the receiving end, so that the implementation is easy, and the safety capacity of the user system is greatly increased.

Description

Based on the MIMO safe capacity raising method of weighting matrix

Technical field

The present invention relates to wireless communication technology field, be specifically related to a kind of MIMO based on weighting matrix (Multiple-Input Multiple-Output, multi-input multi-output system) safe capacity raising method.

Background technology

For adapting to the business need of development and the MIMO technology receiving-transmitting sides that produces all adopts multiple antenna, make full use of multiple independently transmission channel to reach required data rate request.MIMO precoding technique refers to that the channel condition information obtained by utilization at transmitting terminal carries out certain linear or nonlinear transformation process to sending signal, to reach opposing channel fading, the objects such as erasure signal interference, thus a kind of technology improving systematic function.Precoding technique as one of the key technology of MIMO technology, the quality of Precoding Design and the lifting of performance closely bound up.Especially in multi-user comm, interference suffered by user derives from the interference of own user antenna interference and other users, so how to eliminate interference, by improving capacity, reduce the error rate, reduce complexity and improve the problem that systematic function has just become urgent need consideration, therefore need to select rational pre-coding scheme.

Capacity is one of important performance indexes of mimo system, and theoretical research is verified, and MIMO technology significantly can increase power system capacity when not increasing transmitting power and bandwidth, and the capacity of increase can be used for the transmission rate of increase information.For eliminating multi-user interference, classical algorithm is the ZF precoding algorithms of BD algorithm or improvement.These classic algorithm completely eliminate multi-user interference, but bring the restriction of receiving-transmitting sides number of antennas, and subscriber channel matrix does not exist kernel, cause solving pre-coding matrix.

Summary of the invention

In order to solve the antenna number restriction in multi-user system, the present invention proposes the MIMO safe capacity raising method based on weighting matrix, by increasing and capacity raising secrecy capacity.

The present invention is based on the MIMO safe capacity raising method of weighting matrix, comprise the following steps,

Step 1, increase a weighting matrix D at transmitting terminal _k, the dimension of channel matrix H is reduced to and can obtains kernel;

The pre-coding matrix F of step 2, each user of calculating transmitting terminal _k, obtain equivalent channel matrix D _kh _kf _k, wherein H _krepresent the channel matrix of a kth user;

Step 3, the equivalent channel matrix of each user carried out to SVD decomposition and water injection power is distributed;

Step 4, increase weighting matrix W at receiving terminal _k, calculate each user's and capacity;

Step 5, the weighting matrix W held according to eavesdropping _ewith eavesdropping capacity, the difference of calculating and capacity and eavesdropping capacity, is secrecy capacity.

Wherein increase weighting matrix D in step 1 _kbefore, threshold value threshold is set, the channel being less than threshold value is set to zero.

In step 3, water injection power distribution is specially, and the power on each user's kth transmitting antenna is:

$p_k={(\frac{1}{l\ln 2}-\frac{{\mathrm{\δ}}_n^2}{{\mathrm{\λ}}_k})}^{+}$

Wherein for a kth singular value of this user's equivalent channel matrix, () ⁺represent p _konly get positive, m is by power limited equation try to achieve, now the capacity of each user is

$C=\underset{k=1}{\overset{L}{\mathrm{\Σ}}}{\log }_2(1+\frac{{({\mathrm{\λ}}_k/l\ln 2-{\mathrm{\δ}}_n^2)}^{+}}{{\mathrm{\δ}}_n^2}).$

Step 4 detailed process is:

4-1, increase weighting matrix W _kafter, the capacity of each user is obtain ρ during optimal value thus _k;

4-2, according to ρ _kwith equivalent channel matrix D _kh _kf _ksVD decompose left unitary matrice calculate W _k;

4-3, by W _ksubstitute into secrecy capacity formula, calculate the secrecy capacity of user.

The present invention has following beneficial effect:

1, pass through adding weighting matrix W _kafter equivalent channel matrix carry out SVD decomposition, the W of summation capacity optimum when water-filling algorithm carries out to it _k, improve and capacity.

2, keep pre-coding matrix constant, thus eavesdropping capacity remains unchanged, therefore by increasing and capacity and then can improve secrecy capacity.

3, only need in receiving terminal many interpolations matrix W _k, be easy to realize.

Accompanying drawing explanation

Fig. 1 is the multi-user MIMO system scene graph containing eavesdropping user;

Fig. 2 is the multi-user MIMO system model schematic utilizing man made noise to disturb eavesdropping user;

Fig. 3 is the matrix arrangement schematic diagram (supposing that weighting matrix is the matrix of 3*3) that receiving terminal of the present invention needs to increase;

Fig. 4 is the correlation curve figure that the present invention and existing method obtain secrecy capacity.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

In the system model of Fig. 2, suppose that transmitting terminal has N _ttransmit antennas, receiving terminal has K validated user and 1 eavesdropping user, and the receiving terminal antenna of each user is N _rroot.The signal that a kth validated user and eavesdropping user receive is respectively:

$y_k=H_k{F}_k{x}_k+H_k\underset{j\≠k}{\mathrm{\Σ}}{F}_j{x}_j+H_k{F}_{e}z+n_k---\left(1\right)$

$y_e=H_e\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{F}_j{x}_j+H_e{F}_{e}z+n_e---\left(2\right)$

Wherein H _krepresent the channel matrix of a kth validated user, H _erepresent the channel matrix of eavesdropping user, x _krepresent the signal that a kth validated user sends, y _krepresent the signal that a kth validated user receives, y _erepresent the signal that eavesdropping user receives, F _krepresent the pre-coding matrix sending useful signal, F _erepresent the pre-coding matrix sending artificial interference signal respectively, z represents man made noise, n _kand n _eit is the noise effect that user is subject to.So, the signal after a kth validated user receiving terminal process and the signal after eavesdropping the process of user's receiving terminal are:

${\hat{y}}_k=w_k{y}_k---\left(3\right)$

${\hat{y}}_e=w_e{y}_e---\left(4\right)$

W _kand w _efor the weighing vector of receiving terminal, if n _k=n _e.Assuming that the accurate channel condition information of eavesdropping end known system, transmitting terminal does not know the channel matrix of disabled user, but the channel matrix of known all validated users.

A. the weighting matrix D of sending and receiving end antenna number restriction is eliminated _kdesign

In order to solve the situation that cannot obtain kernel when transmitting antenna number is less than reception antenna number, by arranging the threshold value threshold of each user, the value of threshold value can need the number setting of the data flow received according to user.In channel matrix H, the threshold coefficient value of a jth antenna is defined as:

${\mathrm{IR}}_j=\frac{{\left|\right|H_j\left|\right|}^2}{\underset{i\≠j}{\overset{N_R}{\mathrm{\Σ}}}{\left|\right|H_j\left|\right|}^2}---\left(5\right)$

If IR _jthe row of this antenna is then set to zero by≤threshold.

Wherein, D _koften row is all only containing one 1 for matrix, and 1 of each row all at same row, is equivalent to unit matrix and fills the matrix column conversion that n row 0 element formed.Such as, in multi-user system, if kth user's reception antenna is 6, transmitting antenna is 4, supposes that the 5th reception antenna of this user and the 6th reception antenna do not meet threshold requirement, the D that so this user is corresponding _kmatrix is:

$D_k=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\end{array}\right]---\left(7\right)$

B. the design of multi-user pre-coding

Introduce D _kafter matrix, channel matrix is equivalent to D _kh _k, now, transmitting terminal transmitting antenna number is greater than the reception antenna number for signal, can adopt BD algorithm to eliminate multi-user interference, and trying to achieve kth user's pre-coding matrix is F _k.The channel of a definition kth user is mended matrix and is:

${\tilde{H}}_k={[{\left(D_1{H}_1\right)}^H,{\left(D_2{H}_2\right)}^H,...{\left(D_{k-1}{H}_{k-1}\right)}^H,{\left(D_{k+1}{H}_{k+1}\right)}^H,...{\left(D_k{H}_k\right)}^H]}^T---\left(8\right)$

According to BD algorithm, try to achieve the pre-coding matrix F of a kth user _kfor:

$F_k={\tilde{V}}_k^{\left(0\right)}---\left(9\right)$

In order to try to achieve the pre-coding matrix F of eavesdropping user _e, F _eshould meet that is:

$\tilde{H}{F}_e={[{\left(D_1{H}_1\right)}^H,{\left(D_2{H}_2\right)}^H,...{\left(D_k{H}_k\right)}^H...{\left(D_k{H}_k\right)}^H]}^T{F}_e---\left(10\right)$

Right carry out SVD decomposition:

$\tilde{H}=\tilde{U}\tilde{D}{[{\tilde{V}}^{\left(1\right)},{\tilde{V}}^{\left(0\right)}]}^T---\left(11\right)$

The pre-coding matrix F of Human disturbance can be obtained _efor:

$F_e={\tilde{V}}^{\left(0\right)}---\left(12\right)$

For the channel matrix H of eavesdropping user _e, due to H _ef _e≠ 0, H _ef _j≠ 0, and H _jf _e=0, the pre-coding matrix F of such man made noise _ethe interference suffered by disabled user can be made maximum, and on validated user without any impact.Now this user's receiving end signal is equivalent to:

y _k＝D _kH _kF _kx _k+n _k(13)

C. the power of each antenna of water-filling algorithm distributing user is utilized

In order to make user's power system capacity maximum, when each user's gross power is determined, water-filling algorithm can be adopted to distribute power to the antenna of each user.Power on each user's kth transmitting antenna is:

$p_k={(\frac{1}{l\ln 2}-\frac{{\mathrm{\δ}}_n^2}{{\mathrm{\λ}}_k})}^{+}---\left(14\right)$

for a kth singular value of this user's equivalent channel matrix, () ⁺represent p _konly get positive, if p _kbe calculated as negative, then by p _kbe set to zero.L can by power limited equation try to achieve.Now the power system capacity of each custom system can be expressed as:

$C=\underset{k=1}{\overset{L}{\mathrm{\Σ}}}{\log }_2(1+\frac{{({\mathrm{\λ}}_k/l\ln 2-{\mathrm{\δ}}_n^2)}^{+}}{{\mathrm{\δ}}_n^2})---\left(15\right)$

D. receiving terminal matrix w _kand w _esolve

D _kbe equivalent to the weighting matrix of kth user's receiving terminal.To D _kh _kf _kcarry out SVD decomposition:

D _kH _kF _k＝U _kΛ _kV _k(16)

To the capacity that each user does when water filling distributes be:

$C_k=\underset{k=1}{\overset{L}{\mathrm{\Σ}}}{\log }_2(1+\frac{{\mathrm{\λ}}_k{p}_k}{{\mathrm{\δ}}_n^2})---\left(17\right)$

Wherein, for Λ _kcornerwise i-th element.P _kfor the power on the kth antenna that this user water-filling algorithm when not introducing weighing vector is tried to achieve.Weighting matrix D _kit is not the weighting matrix making water-filling algorithm optimum.If W _kfor the weighting matrix required, then:

$\left\{\begin{array}{c}{D}_k{H}_k{F}_j=0,k\≠j\\ D_k{H}_k{F}_k\≠0\end{array}\right.\⇒\left\{\begin{array}{c}{W}_k{D}_k{H}_k{F}_j=0,k\≠j\\ W_k{D}_k{H}_k{F}_k\≠0\end{array}\right.---\left(18\right)$

Visible W _kimpact be there is no on multi-user interference.To W _kcarry out SVD to divide and solve:

$W_k={\hat{U}}_k{\widehat{\mathrm{\Λ}}}_k{\hat{V}}_k---\left(19\right)$

Order ${\hat{V}}_k=U_k^H,$ Then

for W _ka kth singular value, also can regard as the non-negative square root of a kth characteristic value, be variable to be asked.

Therefore, weighing vector W is being added _kafter, C _kcan be expressed as further:

$C_k=\underset{k=1}{\overset{L}{\mathrm{\Σ}}}{\log }_2(1+\frac{{\mathrm{\ρ}}_k{\mathrm{\λ}}_k{p}_k}{{\mathrm{\δ}}_n^2})---\left(21\right)$

Suppose that the power each antenna being subject to noise is identical, in order to introduce W _kafter in order to noise can not be made to increase, constraints is:

$\mathrm{tr}\left(W_k{D}_k{D}_k^H{W}_k^H\right)=\mathrm{tr}\left(D_k{D}_k^H\right)---\left(22\right)$

Due to

$D_k{D}_k^H=E---\left(23\right)$

Wherein, E is unit battle array, can obtain:

$\mathrm{tr}\left(D_k{D}_k^H\right)=\mathrm{rank}\left(D_k\right)=m---\left(24\right)$

M is constant, and the value of m is the reception antenna number meeting threshold value in a kth user, therefore:

$\mathrm{tr}\left(W_k{D}_k{D}_k^H{W}_k^H\right)=\mathrm{tr}\left(W_k{W}_k^H\right)=\mathrm{tr}\left({\mathrm{UDVV}}^H{D}^H{U}^H\right)={\mathrm{\ρ}}_1+{\mathrm{\ρ}}_2+...{\mathrm{\ρ}}_m---\left(25\right)$

Constraints can be reduced to:

ρ ₁+ρ ₂+…ρ _m＝m (26)

According to C _kexpression formula obtain goal expression and be:

$f=\underset{k=1}{\overset{m}{\mathrm{\Π}}}(1+\frac{{\mathrm{\ρ}}_k{\mathrm{\λ}}_k{p}_k}{{\mathrm{\δ}}_n^2})---\left(27\right)$

P _kfor this user is not introducing weighing vector W _ktime the kth antenna of trying to achieve with water-filling algorithm on power, through type (21) obtains.Thus the ρ that can try to achieve when capacity f obtains maximum under constraints ₁, ρ ₂..., ρ _m, therefore required weighing vector W _kfor:

U _kby D _kh _kf _kcarry out SVD decomposition to try to achieve. the unitary matrice of desirable any m dimension.If eavesdropping end is interested in the signal of a jth user, so for eavesdropping end:

$W_e={\left(H_e(\underset{j\≠k}{\overset{K}{\mathrm{\Σ}}}\left(F_j{F}_j^H\right)+F_e{F}_e^H)H_e^H\right)}^{-1}{H}_e{F}_j---\left(29\right)$

When not containing other artificial noise jamming, the safe capacity that MIMO eavesdrops a kth user of system can be expressed as:

$C={\log }_2\det (I+{\stackrel{\‾}{H}}_k{Q}_k{\stackrel{\‾}{H}}_k^H)-{\log }_2\det (I+{\stackrel{\‾}{H}}_e{Q}_k{\stackrel{\‾}{H}}_e^H)---\left(30\right)$

Wherein, I representation unit matrix, two, the front and back in above formula represent the capacity of legitimate channel and illegal channel respectively.

Now, with validated user k and the equivalent channel matrix eavesdropping user respectively.Be Signal to Interference plus Noise Ratio principle for best receive mode eavesdropping user, only relevant with channel matrix H with transmission precoding, therefore the method compares with original method not comprising receiving terminal weighting matrix the capacity having identical illegal channel, and the capacity of legitimate channel is improved, therefore the method can play the effect improving secrecy capacity.

E. the design of receiving terminal weighting matrix in engineering

With every k user's weighting matrix W _kfor the matrix of 3*3 dimension is example, the signal after this user's receiving terminal A/D converts is y, and the signal after weighting matrix process is (the output signal yy in corresponding diagram 3), now:

$\left[\begin{array}{c}{\hat{y}}_1\\ {\hat{y}}_2\\ {\hat{y}}_3\end{array}\right]=\left[\begin{array}{ccc}w11& w12& w13\\ w21& w22& w23\\ w31& w32& w33\end{array}\right]\left[\begin{array}{c}{y}_1\\ y_2\\ y_3\end{array}\right]---\left(31\right)$

Fig. 3 is the structure chart of this matrix disposal of receiving terminal.

Simulated environment is: transmitting terminal has 12 transmit antennas altogether, and the number of validated user and eavesdropping user is 2 and 1 respectively, and the receiving terminal antenna of all users is 6.Assuming that three reception antennas that have of each user do not meet threshold requirement.Transmitting terminal does not know the channel state matrix eavesdropping end, but the channel state matrix of known all validated users.The known all channel condition informations of eavesdropping user, eavesdropping user side maximize SINR principle Received signal strength.Assuming that each validated user is identical with the power of man made noise.By the method proposed, obtain weighting matrix W _kfor the matrix of 3*3, as shown in Figure 3, as shown in Figure 4, can find out, secrecy capacity is improved simulation result its structure.

Technological means disclosed in the present invention program is not limited only to the technological means disclosed in above-mentioned execution mode, also comprises the technical scheme be made up of above technical characteristic combination in any.

Claims (4)

1., based on the MIMO safe capacity raising method of weighting matrix, it is characterized in that, comprise the following steps,

Step 1, increase a weighting matrix D at transmitting terminal _k, the dimension of channel matrix H is reduced to and can obtains kernel;

The pre-coding matrix F of step 2, each user of calculating transmitting terminal _k, obtain equivalent channel matrix D _kh _kf _k, wherein H _krepresent the channel matrix of a kth user;

Step 3, the equivalent channel matrix of each user carried out to SVD decomposition and water injection power is distributed;

Step 4, increase weighting matrix W at receiving terminal _k, calculate each user's and capacity;

Step 5, the weighting matrix W held according to eavesdropping _ewith eavesdropping capacity, the difference of calculating and capacity and eavesdropping capacity, is secrecy capacity.

2., according to MIMO safe capacity raising method according to claim 1, it is characterized in that, in step 1, increase weighting matrix D _kbefore, threshold value threshold is set, the channel being less than threshold value is set to zero.

3. according to MIMO safe capacity raising method according to claim 1, it is characterized in that, in step 3, water injection power distribution is specially, and the power on each user's kth transmitting antenna is:

$p_k={(\frac{1}{l\ln 2}-\frac{{\mathrm{\δ}}_n^2}{{\mathrm{\λ}}_k})}^{+}$

Wherein for a kth singular value of this user's equivalent channel matrix, () ⁺represent p _konly get positive, l is by power limited equation try to achieve, now the capacity of each user is

$C=\underset{k=1}{\overset{L}{\mathrm{\Σ}}}{\log }_2(1+\frac{{({\mathrm{\λ}}_k/l\ln 2-{\mathrm{\δ}}_n^2)}^{+}}{{\mathrm{\δ}}_n^2}).$

4., according to MIMO safe capacity raising method according to claim 1, it is characterized in that, step 4 detailed process is:

4-1, increase weighting matrix W _kafter, the capacity of each user is obtain ρ during optimal value thus _k;

4-2, according to ρ _kwith equivalent channel matrix D _kh _kf _ksVD decompose left unitary matrice calculate W _k;

4-3, by W _ksubstitute into secrecy capacity formula, calculate the secrecy capacity of user.