A low-complexity GAO receive beamforming method with IRS-assisted directional modulation

Abstract

The present invention provides a GAO low-complexity receiving beamforming method with IRS auxiliary directional modulation. Assuming that the transmitter is equipped with N A The IRS is equipped with M passive transmitting elements, and the legitimate user and eavesdropper are equipped with N B and N E The invention discloses a method for realizing a secure reception signal receiving system using a plurality of receiving antennas; constructing a secure reception signal model in the presence of legitimate users and eavesdroppers; establishing and simplifying the maximum reception power and optimization problem; adopting the GAO method to alternately optimize the IRS phase shift matrix and the receiving beamforming based on the maximum reception power and criterion; calculating the computational complexity of the GAO method; introducing the IRS into the directional modulation system, and enhancing the receiving power of the legitimate users by dynamically adjusting the phase shift of the IRS and preventing eavesdroppers from eavesdropping, thereby improving the transmission security of the directional modulation system and reducing the computational complexity of the receiver. Compared with the directional modulation scheme without IRS-assisted directional modulation and without phase shift matrix optimization, the GAO method proposed in the present invention can significantly improve the security performance of the directional modulation system.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a GAO low-complexity receive beamforming method with IRS-assisted directional modulation. Background Art

[0002] Directional modulation (DM), as an advanced physical layer security transmission technology, is considered a promising signal transmission method in wireless communications. However, due to the broadcast nature of wireless channels, the confidential message (CM) transmitted by DM systems may be intercepted by unintended receivers. Therefore, achieving secure information transmission has become a hot research topic in the field of wireless communications.

[0003] An intelligence reflecting surface (IRS) consists of a large number of controllable reflective elements with continuous phase shifters. By intelligently manipulating the reflection coefficient to change the phase shift of the incident electromagnetic wave, it intelligently reconfigures the signal transmission environment, enhancing the power of the desired received signal or suppressing interfering signals. IRSs are low-cost and can be used to improve the spectrum and energy efficiency of wireless communication networks. Due to the rank-1 nature of the channel matrix in traditional directional modulation networks, effective transmission of two or more channels of information is impossible. While generalized alternating optimization (GAO) is a novel iterative algorithm, its application to directional modulation systems has not yet been studied. Therefore, developing a low-complexity GAO receive beamforming method using IRS-assisted directional modulation is of great significance. Summary of the Invention

[0004] In view of this, the present invention proposes a GAO low-complexity receive beamforming method with IRS-assisted directional modulation, which enhances the receiving power of legitimate users by dynamically adjusting the phase shift of IRS and prevents eavesdroppers from eavesdropping on private information, thereby significantly improving the security performance of the directional modulation system.

[0005] The technical solution of the present invention is achieved as follows:

[0006] A GAO low-complexity receive beamforming method with IRS-assisted directional modulation includes the following steps:

[0007] Step S1: Assume the transmitter is equipped with Root transmitting antenna, IRS equipped Passive transmitting elements, the legitimate user and the eavesdropper are equipped with and Root receiving antenna;

[0008] Step S2: construct the receiving signal model of the legitimate user and the eavesdropper;

[0009] Step S3: Establishing the maximum received power and optimization problem and simplifying it;

[0010] Step S4: Based on the maximum received power and criterion, the GAO method is used to alternately optimize the IRS phase shift matrix and receive beamforming;

[0011] Step S5: Calculate the computational complexity of the GAO method.

[0012] Preferably, the step S2 further includes obtaining a baseband transmission signal, where the baseband transmission signal is:

[0013]

[0014] in and For privacy information, respectively , is the total transmit power, , and Denote the power allocation factors of private information and artificial noise respectively, and satisfy , Represents the beamforming vectors that send two paths of private information to the legitimate user, satisfying , , represents the projection matrix that controls the direction of artificial noise, is an artificial noise vector that obeys Gaussian distribution, that is ,in for dimensional identity matrix.

[0015] Preferably, the received signal model of the legitimate user in step S2 is:

[0016]

[0017] in represents the receive beamforming vector, Indicates IRS→legal user channel, is the IRS phase shift matrix, represents the phase shift of the mth reflective element, ,and They represent transmitter→IRS channel and transmitter→legal user channel respectively. and represent the exit angle and incident angle of the channel respectively, is the composite additive white Gaussian noise at the legitimate user, where for -dimensional identity matrix, is the noise variance of legitimate users, represents the path loss coefficient of the transmitter→legitimate user channel, is the path loss coefficient of the transmitter→IRS→legal user channel.

[0018] Preferably, the receiving signal model of the eavesdropper in step S2 is:

[0019]

[0020] in ,and denote the IRS→eavesdropper channel and the transmitter→eavesdropper channel respectively, is the composite additive white Gaussian noise at the eavesdropper, where for -dimensional identity matrix, is the noise variance of the eavesdropper, and They represent the path loss coefficients of transmitter→IRS→eavesdropper channel and transmitter→eavesdropper channel respectively.

[0021] Preferably, the step S2 further comprises constructing a normalized steering vector, wherein the normalized steering vector is expressed as:

[0022]

[0023] in , and They represent antenna spacing and wavelength respectively, N is the number of antennas, n=1,…,N.

[0024] Preferably, assuming , the artificial noise is only sent to the eavesdropper, then satisfy ;

[0025] Define a virtual private information channel as ,but Expressed as

[0026] ;

[0027] Assuming that all channels are line-of-sight channels, , ,and , the projection matrix has at least degrees of freedom, the receiving signal model of the legitimate user and the eavesdropper is converted to:

[0028]

[0029] .

[0030] Preferably, the specific steps of step S3 are: using the channel matrix Perform singular value decomposition to obtain the beamforming vector and ,Right now ,in is the receive beamforming vector, for The singular values ​​of , ,in and They are The eigenvector corresponding to the maximum eigenvalue in , the optimization problem of maximizing the sum of received power can be written as:

[0031]

[0032] in .

[0033] Preferably, step S4 includes fixing the IRS phase shift matrix , optimize the receive beamforming vector and The specific steps are: define a virtual receiving channel as , the channel matrix Perform singular value decomposition and get , let the receive beamforming vector ,in Depend on The eigenvectors corresponding to the first two largest eigenvalues ​​in are obtained, and Fixed to a constant matrix, the received power is maximized and the receive beamforming The optimization problem is simplified to:

[0034]

[0035] According to the Rayleigh-Rize theorem, the optimal According to the matrix The eigenvector corresponding to the maximum eigenvalue is obtained. Similarly, the optimal By matrix The eigenvector corresponding to the maximum eigenvalue is obtained.

[0036] Preferably, the step S4 further comprises fixing the receive beamforming vector and , optimize the IRS phase shift matrix , the specific steps are: set the receive beamforming vector and Fixed to a constant vector, defining the IRS phase shift matrix The IRS phase shift vector of all elements on the diagonal is:

[0037]

[0038] make express No. elements, IRS phase shift vector satisfy:

[0039]

[0040] definition

[0041]

[0042] (a) is established based on , , , , then about The maximum received power and optimization problem are simplified to:

[0043]

[0044] The above objective function can be rewritten as The objective function of maximizing the received power and the simplified expression of the optimization problem is rewritten as:

[0045]

[0046] In order to obtain the optimal IRS phase shift vector, about Find the partial derivative and set it equal to 0, that is

[0047]

[0048] You can get:

[0049] .

[0050] Preferably, the computational complexity in step S5 is:

[0051]

[0052] Where L represents the maximum number of iterations.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] The present invention provides a GAO low-complexity receive beamforming method with IRS-assisted directional modulation. By introducing the IRS into the directional modulation system, the transmission security of the traditional directional modulation system can be improved and the computational complexity of the receiver can be reduced. Compared with the directional modulation system without IRS assistance and without IRS phase shift optimization, the proposed GAO method can significantly improve the security performance of the directional modulation system. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only preferred embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0056] Figure 1 This is a flow chart of a GAO low-complexity receive beamforming method with IRS-assisted directional modulation according to the present invention;

[0057] Figure 2 This is a diagram of the directional modulation system assisted by IRS;

[0058] Figure 3 This is a convergence curve diagram of a GAO low-complexity receive beamforming method with IRS-assisted directional modulation according to the present invention under different numbers of IRS phase shift elements;

[0059] Figure 4 A curve diagram showing the relationship between the safety rate and the IRS phase shift number of a GAO low-complexity receive beamforming method with IRS-assisted directional modulation according to the present invention;

[0060] Figure 5 The figure is a curve diagram showing the relationship between the security rate and the azimuth angle of the eavesdropper of the IRS-assisted directional modulation GAO low-complexity receiving beamforming method of the present invention. DETAILED DESCRIPTION

[0061] In order to make the technical content of the present invention easier to understand, a specific implementation case is provided below, and the present invention is further explained in conjunction with the accompanying drawings.

[0062] See also Figure 1 The present invention provides a GAO low-complexity receive beamforming method with IRS-assisted directional modulation, comprising the following steps:

[0063] Step S1: Assume the transmitter is equipped with Root transmitting antenna, IRS equipped Passive transmitting elements, the legitimate user and the eavesdropper are equipped with and Root receiving antenna, and assuming that the IRS reflected signal has no delay;

[0064] Step S2: construct the receiving signal model of the legitimate user and the eavesdropper;

[0065] Assuming there is a line-of-sight path, the baseband transmitted signal is:

[0066]

[0067] in and For privacy information, respectively , is the total transmit power, , and Denote the power allocation factors of private information and artificial noise respectively, and satisfy , Represents the beamforming vectors that send two paths of private information to the legitimate user, satisfying , , represents the projection matrix that controls the direction of artificial noise, is an artificial noise vector that obeys Gaussian distribution, that is ,in for dimensional identity matrix.

[0068] When there is path loss, the received signal model of the legitimate user is:

[0069]

[0070] in represents the receive beamforming vector, Indicates IRS→legal user channel, is the IRS phase shift matrix, represents the phase shift of the mth reflective element, ,and They represent transmitter→IRS channel and transmitter→legal user channel respectively. and Represent the exit angle and incident angle of the channel respectively. The specific diagrams of each angle are as follows Figure 2 As shown, is the composite additive white Gaussian noise at the legitimate user, where for -dimensional identity matrix, is the noise variance of legitimate users, represents the path loss coefficient of the transmitter→legitimate user channel, is the path loss coefficient of the transmitter→IRS→legal user channel.

[0071] Similarly, the eavesdropper's receiving signal model is:

[0072]

[0073] in ,and denote the IRS→eavesdropper channel and the transmitter→eavesdropper channel respectively, is the composite additive white Gaussian noise at the eavesdropper, where for -dimensional identity matrix, is the noise variance of the eavesdropper, and They represent the path loss coefficients of transmitter→IRS→eavesdropper channel and transmitter→eavesdropper channel respectively.

[0074] Step S2 also includes constructing a normalized steering vector, which is expressed as:

[0075]

[0076] in , and They represent antenna spacing and wavelength respectively, N is the number of antennas, n=1,…,N.

[0077] assumed , artificial noise is only sent to the eavesdropper to interfere with the eavesdropper's eavesdropping, then satisfy ;

[0078] Define a virtual private information channel as ,but Expressed as

[0079] ;

[0080] Since all channels involved in the present invention are assumed to be line-of-sight channels, , ,and , so the projection matrix has at least degrees of freedom, the receiving signal model of the legitimate user and the eavesdropper is converted to:

[0081]

[0082] .

[0083] Step S3: Establishing the maximum received power and optimization problem and simplifying it;

[0084] By channel matrix Perform singular value decomposition to obtain the beamforming vector and ,Right now ,in is the receive beamforming vector, for The singular values ​​of , ,in and They are The eigenvector corresponding to the maximum eigenvalue in , the optimization problem of maximizing the sum of received power can be written as:

[0085]

[0086] in ;

[0087] Step S4: Based on the maximum received power and criterion, the GAO method is used to alternately optimize the IRS phase shift matrix and receive beamforming;

[0088] Includes fixed IRS phase shift matrix , optimize the receive beamforming vector and ;

[0089] The specific steps are: define a virtual receiving channel as , the channel matrix Perform singular value decomposition and get , let the receive beamforming vector ,in Depend on The eigenvectors corresponding to the first two largest eigenvalues ​​in are obtained, and Fixed to a constant matrix, the received power is maximized and the receive beamforming The optimization problem is simplified to:

[0090]

[0091] According to the Rayleigh-Rize theorem, the optimal According to the matrix The eigenvector corresponding to the maximum eigenvalue is obtained. Similarly, the optimal By matrix The eigenvector corresponding to the maximum eigenvalue is obtained.

[0092] Also includes fixed receive beamforming vectors and , optimize the IRS phase shift matrix ;

[0093] The specific steps are: Set the receive beamforming vector and Fixed to a constant vector, defining the IRS phase shift matrix The IRS phase shift vector of all elements on the diagonal is:

[0094]

[0095] make express No. elements, IRS phase shift vector satisfy:

[0096]

[0097] definition

[0098]

[0099] (a) is established based on , , , , then about The maximum received power and optimization problem are simplified to:

[0100]

[0101] The above objective function can be rewritten as The objective function of maximizing the received power and the simplified expression of the optimization problem is rewritten as:

[0102]

[0103] In order to obtain the optimal IRS phase shift vector, about Find the partial derivative and set it equal to 0, that is

[0104]

[0105] You can get:

[0106] .

[0107] The overall design concept of the GAO algorithm of the present invention is: fixed phase shift matrix , optimize the receive beamforming vector and ;fixed and , according to the above formula , but The algorithm is 、 and Alternate iterations are performed until the stopping condition is met, that is, ,in represents the number of iterations, Represents a predefined constant.

[0108] Step S5: Calculate the computational complexity using the GAO method:

[0109]

[0110] Where L represents the maximum number of iterations.

[0111] The present invention introduces an IRS into a directional modulation system. By dynamically adjusting the phase shift of the IRS, the received power of legitimate users is enhanced, and eavesdroppers are prevented from eavesdropping on private information. This can improve the transmission security of traditional directional modulation systems and reduce the computational complexity of the receiver. Compared with directional modulation schemes without IRS assistance and directional modulation schemes without phase shift matrix optimization, the IRS-assisted GAO proposed in the present invention can significantly improve the security performance of the directional modulation system.

[0112] To improve energy efficiency and overcome the limitation of traditional directional modulation, which only transmits one channel of useful information, this paper introduces an IRS into the directional modulation system. Experiments have shown that this system can significantly improve the security performance of traditional directional modulation systems without IRS assistance. Therefore, research on IRS-assisted directional modulation communication systems is of great significance.

[0113] The following is a description of the beneficial effects of the present invention through some experimental data: IRS auxiliary direction modulation system schematic diagram as shown Figure 2 As shown in the figure, Alice is the transmitter, IRS is the intelligent reflecting surface, Bob is the legal user, and Eve is the eavesdropper.

[0114] Figure 3 The following graphs show the convergence of the GAO algorithm when the number of IRS phase shift elements, M, is 40 and 100. As can be seen from the graph, the safety rate of the proposed GAO algorithm gradually increases with the number of iterations, eventually reaching a convergence point. Regarding computational complexity, when M = 100, the number of alternating iterations, L, of the proposed GAO algorithm is 5.

[0115] Figure 4The following graph shows the relationship between the safety rate and the number of IRS phase shifts, M, for the proposed GAO algorithm and three benchmark methods. The graph shows that the proposed GAO scheme has a significant safety rate performance advantage over schemes using only a single receive beamformer. Compared to directional modulation schemes without an IRS or with random IRS phases, the safety rate of the proposed method increases with the number of phase shifters. This demonstrates the importance of optimizing the IRS phase shift matrix and building an IRS-assisted directional modulation system.

[0116] Figure 5 The following is a graph showing the relationship between the security rate of the system and the azimuth angle of the eavesdropper when the IRS phase shift number M = 80, where the azimuth angle ranges from 0 to 180 degrees. Since both the transmitter and receiver are linear arrays, the security rate performance of 0 to 90 degrees and 90 to 180 degrees is almost symmetrical. Figure 5 As can be seen, when Eve and Bob have the same direction angle (45°), the security rate performance of the proposed schemes drops significantly. This is because Eve can eavesdrop on private information to the greatest extent when she is on the direct path from Alice to Bob. However, when the angles from Alice to Eve and from Alice to Bob are the same, the proposed GAO algorithm still achieves the optimal security rate performance.

Claims

1. A GAO low-complexity receive beamforming method with IRS-assisted directional modulation, characterized in that: The following steps are involved: Step S1: Assume that the transmitter is equipped with N A The IRS is equipped with M passive transmitting elements, and the legitimate user and eavesdropper are equipped with N B and N E Root receiving antenna; Step S2: construct the receiving signal model of the legitimate user and the eavesdropper; Step S3: Establishing the maximum received power and optimization problem and simplifying it; Step S4: Based on the maximum received power and criterion, the GAO method is used to alternately optimize the IRS phase shift matrix and receive beamforming; Step S5: Calculate the complexity using the GAO method; The step S2 further includes obtaining a baseband transmission signal, wherein the baseband transmission signal is: Among them, x1 and x2 are private information, respectively satisfying P s is the total transmission power, β1, β2 and β3 represent the power allocation factors of privacy information and artificial noise respectively, and satisfy β1+β2+β3=1, and Represents the beamforming vectors that send two paths of private information to the legitimate user, satisfying P AN represents the projection matrix that controls the direction of the artificial noise, and z is the artificial noise vector that obeys the Gaussian distribution, that is, Among them I NA N A -dimensional identity matrix; The received signal model of the legitimate user in step S2 is: in represents the receive beamforming vector, Indicates IRS→legal user channel, is the IRS phase shift matrix, represents the phase shift of the mth reflective element, and They represent the transmitter→IRS channel and the transmitter→legal user channel, θ r and θ t represent the exit angle and incident angle of the channel respectively, is the composite additive white Gaussian noise at the legitimate user, where N B dimensional identity matrix, is the noise variance of the legitimate user, g AB represents the path loss coefficient of the transmitter→legal user channel, g AIB =g AI g IB is the path loss coefficient of the transmitter→IRS→legal user channel; The receiving signal model of the eavesdropper in step S2 is: in and denote the IRS→eavesdropper channel and the transmitter→eavesdropper channel respectively, is the composite additive white Gaussian noise at the eavesdropper, where N E dimensional identity matrix, is the noise variance of the eavesdropper, g AIE =g AI g IE and g AE They represent the path loss coefficients of transmitter→IRS→eavesdropper channel and transmitter→eavesdropper channel respectively; assumed Artificial noise is only sent to the eavesdropper, then P AN satisfy Define a virtual private information channel as Then P AN Expressed as Assuming that all channels are line-of-sight channels, rank(H AI )=1,rank(H AB )=1, and rank(H CM )≤2, the projection matrix has at least N-2 degrees of freedom, and the receiving signal model of the legitimate user and the eavesdropper is converted to: The specific steps of step S3 are: CM Perform singular value decomposition to obtain beamforming vectors v1 and v2, that is, in is the receive beamforming vector, H CM The singular values ​​of in and are the eigenvectors corresponding to the largest eigenvalues ​​in Σ, then the optimization problem of maximizing the sum of received power can be written as: in The step S4 includes fixing the IRS phase shift matrix Θ and optimizing the receive beamforming vector u b1 and u b2 The specific steps are: define a virtual receiving channel as The channel matrix H BR Perform singular value decomposition and get Let the receive beamforming vector in Obtained from the eigenvectors corresponding to the first two largest eigenvalues ​​in Σ, fixing Θ to a constant matrix, the received power and the receive beamforming u are maximized. b1 The optimization problem is simplified to: According to the Rayleigh-Rize theorem, the optimal u b1 According to the matrix The eigenvector corresponding to the maximum eigenvalue is obtained. Similarly, the optimal u b2 By matrix The eigenvector corresponding to the maximum eigenvalue is obtained; The step S4 further includes fixing the receive beamforming vector u b1 and u b2 , optimize the IRS phase shift matrix Θ, the specific steps are: receive beamforming vector u b1 and u b2 is fixed as a constant vector, and the IRS phase shift vectors of all elements on the diagonal of the IRS phase shift matrix Θ are defined as: make represents the i-th element of θ, and the IRS phase shift vector θ satisfies: |θ i |=1,arg(θ i )∈[0,2π),i=1,…,M definition h A1 =H AI v1, h A2 =H AI v2, Where (a) is established according to diag{a}b=diag{b}a, Then the optimization problem of maximizing the received power and θ is simplified to: st|θ i |=1,arg(θ i )∈[0,2π),i=1,…,M The objective function can be rewritten as maximizing the received power of θ and the objective function in the simplified expression of the optimization problem can be rewritten as: To obtain the optimal IRS phase shift vector, the partial derivative of f(θ) with respect to θ is taken and set equal to 0, that is, You can get:

2. The IRS-assisted directional modulation GAO low-complexity receive beamforming method according to claim 1, characterized in that: The step S2 further includes constructing a normalized steering vector, which is expressed as: where Ψ θ (n) = -(n-(N+1) / 2)dcosθ / λ, where d and λ represent the antenna spacing and wavelength respectively, and N is the number of antennas, n = 1,…,N.

3. The IRS-assisted directional modulation GAO low-complexity receive beamforming method according to claim 1, characterized in that: The computational complexity in step S5 is: Where L represents the maximum number of iterations.

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