Optimization Method for IRS Phase Shift Matrix and Received Beamforming in Direction Modulation

Abstract

The present invention discloses an optimization method for the IRS phase shift matrix and the receiving beamforming in direction modulation, specifically as follows: Based on null space projection, two receiving beamforming vectors are designed to receive the transmission signals on two paths respectively, simplifying the objective optimization problem of maximizing the sum of the received powers at the legitimate users; fixing the phase shift matrix of the IRS, the two receiving beamforming vectors are optimized respectively according to the Rayleigh-Ritz theorem; fixing the receiving beamforming vectors, the IRS phase shift matrix is converted into a phase shift vector, and the optimal solution of the phase shift vector is obtained according to the Rayleigh-Ritz theorem; the receiving beamforming vectors and the IRS phase shift matrix are alternately updated until the absolute value of the difference between the received powers before and after reception is less than the set threshold. The method of the present invention solves the design problem at the receiving end in the IRS-assisted direction modulation system with relatively low complexity and better improves the security performance of the system.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and particularly to an optimization method for the IRS phase shift matrix and receiving beamforming in direction modulation. Background Art

[0002] In recent years, communication technologies have developed rapidly, and among them, wireless communication technologies have become a major research focus in communication technologies. In practical applications, wireless communication faces many challenges, such as path loss caused by the transmission path distance, small-scale effects caused by multipath fading, and strong information interference and eavesdropping behaviors between the transmitter and the receiver. Therefore, to ensure the secure transmission of private information in wireless network communication, physical layer security technologies have become one of the current research hotspots. Physical layer security technologies utilize the characteristics of the underlying wireless channel to maximize the channel difference between legitimate users and eavesdroppers, increasing the gap in channel capacity between the two, thereby improving the security of channel transmission.

[0003] Direction modulation is one of the key technologies for physical layer wireless transmission. This technology realizes the directivity of signal transmission and improves the security of private information transmission by optimizing the design of beamforming and adding artificial noise to the transmitted signal. In addition, as a revolutionary low-cost technology, the Intelligent Reflecting Surface (IRS) can use passive reflection elements to change the phase of the reflected signal, constructing a friendly multipath environment for wireless communication systems. Therefore, introducing IRS into the direction modulation system can overcome the limitation that the base station of the traditional direction modulation system can only send a single private bit stream to the user when using multiple antennas, further improving the security of the communication system.

[0004] The existing research focuses on maximizing the security rate of the system by designing the transmitting beamforming at the transmitting end and the phase shift matrix of the IRS, without considering the problem of high detection complexity at the receiving end. Summary of the Invention

[0005] The purpose of the present invention is to provide an optimization method for the IRS phase shift matrix and receiving beamforming in direction modulation. By using the null space projection to reduce the complexity of the method, and then using the alternating iteration method to design the receiving beamforming vector and the phase shift matrix of the IRS, the power sum at the receiving end is increased, thereby improving the transmission security of the system.

[0006] The technical solution for achieving the purpose of the present invention is: an optimization method for the IRS phase shift matrix and receiving beamforming in direction modulation, specifically:

[0007] Step 1: Based on null space projection, design two receive beamforming vectors to receive the transmission signals on two paths respectively, and simplify the objective optimization problem of maximizing the sum of the received powers at the legitimate users.

[0008] Step 2: Fix the phase shift matrix of the IRS, and optimize the two receive beamforming vectors respectively according to the Rayleigh-Ritz theorem.

[0009] Step 3: Fix the receive beamforming vectors, convert the IRS phase shift matrix into a phase shift vector, and obtain the optimal solution of the phase shift vector according to the Rayleigh-Ritz theorem.

[0010] Step 4: Alternately update the receive beamforming vectors and the IRS phase shift matrix until the absolute value of the difference between the received powers before and after reception is less than the set threshold.

[0011] Compared with the prior art, the significant advantages of the present invention are as follows: (1) Considering the problem of the detection complexity at the receiving end in the IRS-assisted communication system, by jointly optimizing the IRS phase shift matrix and the two-path receive beamforming vectors, the security of system transmission can be improved while reducing the detection complexity at the receiving end; (2) Using the null space projection criterion to design the two-path receive beamforming vectors, so that the useful information received by the two paths does not interfere with each other, and there are closed-form solutions for the phase shift matrix and the receive beamforming vectors in each update iteration, making the method of the present invention have a lower complexity. Description of the Drawings

[0012] Figure 1 It is a flowchart of the optimization method for the IRS phase shift matrix and receive beamforming in the direction modulation of the present invention. Detailed Embodiment

[0013] The present invention will be further clarified below in conjunction with the drawings and specific examples. It should be understood that these examples are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent forms of modification by those skilled in the art fall within the scope defined by the appended claims of this application.

[0014] In order to overcome the deficiencies existing in the prior art, the present invention provides a design method for the IRS phase shift matrix and receive beamforming based on null space projection in direction modulation.

[0015] Combined with Figure 1, in the optimization method of the IRS phase shift matrix and the receiving beamforming in the direction modulation of the present invention, the idea of null space projection is first used to simplify the target optimization problem; then the phase shift matrix is fixed, and two receiving beamforming vectors are updated according to the Rayleigh-Ritz theorem; then the receiving beamforming vectors are fixed, the diagonal phase shift matrix is converted into a phase shift vector, the phase shift vector is calculated according to the Rayleigh-Ritz theorem and reconstructed, and the phase shift matrix is updated according to the phase shift vector; finally, the receiving beamforming vectors and the IRS phase matrix are alternately updated until the termination condition is met. Specifically:

[0016] Step 1: Based on null space projection, design two receiving beamforming vectors to receive the transmission signals on two paths respectively, and simplify the target optimization problem of maximizing the sum of the received powers at the legitimate users.

[0017] Step 2: Fix the phase shift matrix of the IRS, and optimize the two receiving beamforming vectors respectively according to the Rayleigh-Ritz theorem.

[0018] Step 3: Fix the receiving beamforming vectors, convert the IRS phase shift matrix into a phase shift vector, and obtain the optimal solution of the phase shift vector according to the Rayleigh-Ritz theorem.

[0019] Step 4: Alternately update the receiving beamforming vectors and the IRS phase shift matrix until the absolute value of the difference between the received powers before and after reception is less than the set threshold.

[0020] As a specific implementation manner, the construction process of the target optimization problem of maximizing the sum of the received powers at the legitimate users is as follows:

[0021] The present invention gives an IRS-assisted secure direction modulation system model, where the base station is configured with N A antennas, the IRS consists of M low-cost passive reflection elements, and the legitimate user and the illegal user have N B and N E antennas respectively. Introducing the IRS into the direction modulation system can establish a friendly multipath environment, enabling the direction modulation system to simultaneously transmit two privacy information flows. The signal transmitted by the base station is expressed as

[0022]

[0023] where P s is the total transmission power, β 1 and β 2 are the power allocation factors of the two privacy information flows, β 3 is the power allocation factor of the artificial noise, and it satisfies β 1 +β 2 +β 3 =1. and are the transmit beamforming vectors for transmitting two-way private information, satisfying x 1 and x 2 are private information, satisfying is the artificial noise projection matrix, is the transmitted artificial noise, which follows a complex Gaussian distribution, i.e.,

[0024] In the direction modulation communication system, the wireless communication channel is a line-of-sight channel, and the normalized channel vector is

[0025]

[0026] where N is the total number of antennas at the transmitter or receiver, and the phase function Ψ θ (n) is defined as

[0027]

[0028] In this formula, θ, n, d, and λ represent the direction angles of arrival or departure, the index number of the antenna, the element spacing in the transmit antenna array, and the wavelength, respectively.

[0029] In the following, the channel matrices from the base station Alice to the legitimate user Bob, Alice to the IRS, Alice to the illegal user Eve, IRS to Bob, and IRS to Eve are denoted as and The corresponding path losses are g AB , g AI , g AE , g IB , and g IE . Among them, θ r,AB , θ t,AB are the direction angles of arrival and departure from Alice to Bob; θ r,AI , θ t,AI are the direction angles of arrival and departure from Alice to the IRS; θ r,AE , θ t,AE are the direction angles of arrival and departure from Alice to Eve; θ r,IB , θ t,IB are the direction angles of arrival and departure from the IRS to Bob; θ r,IE , θ t,IE are the direction angles of arrival and departure from the IRS to Eve;

[0030] After channel transmission and receive beamforming, the received signal at the legitimate user Bob can be expressed as

[0031]

[0032] where is the receive beamforming vector at Bob, is the phase shift matrix of the IRS, represents the phase shift generated by the m-th reflecting element of the IRS. represents the additive Gaussian white noise at Bob, g AIB = g AI g IB represents the equivalent path loss coefficient of the channel from Alice through the IRS to Bob.

[0033] Similarly, the received signal at the illegal user Eve can be expressed as

[0034]

[0035] where is Eve's receive beamforming vector, represents the additive Gaussian white noise at Eve, g AIE = g AI g IE represents the equivalent path loss coefficient of the channel from Alice through the IRS to Eve.

[0036] In this system model, P AN is designed to project the artificial noise onto the null space of the channels from Alice to Bob and from Alice to the IRS, and P AN satisfies the condition

[0037]

[0038] Then, combining H AI and into a virtual large channel H CM , that is

[0039]

[0040] The artificial noise projection matrix can be expressed as

[0041]

[0042] In this case, the expressions of the received signals at the Bob side and the Eve side can be rewritten as

[0043]

[0044]

[0045] To maximize the total received power at Bob, we jointly optimize the two receive beamforming vectors and the IRS phase shift matrix. The optimization problem can be expressed as

[0046]

[0047] where

[0048]

[0049] Since the variables in the above optimization problem are coupled with each other, it is difficult to directly find the solution to the optimization problem. For this reason, we first simplify the target optimization problem by using the idea of null space projection, and then divide the optimization problem into two sub-problems of solving the two receive beamforming vectors and solving the IRS phase shift matrix, and obtain the solution to the target optimization problem by iteratively solving these two sub-problems.

[0050] As a specific implementation manner, in step 1, based on null space projection, the receive beamforming vectors are designed to receive the transmission signals on two paths respectively, and the target optimization problem of maximizing the sum of the received powers at legitimate users is simplified, specifically as follows:

[0051] Let the two receive beamforming vectors receive the transmission signals on two paths respectively. According to the idea of null space projection, the two receive beamforming vectors satisfy the constraint conditions

[0052]

[0053] where, u b1 is designed to only receive the privacy information of the IRS reflection path, while u b2 is used to receive the privacy information transmitted on the direct path. In this case, the expression of the received signal at Bob can be re-expressed as

[0054]

[0055]

[0056] Thus, the optimization problem of maximizing the sum of the received powers at Bob is transformed into

[0057]

[0058] As a specific implementation manner, in step 2, the phase shift matrix Θ of the IRS is fixed, and the receive beamforming vectors and are optimized respectively according to the Rayleigh-Ritz theorem as follows:

[0059] When the phase shift matrix Θ of the IRS is given, the maximized received power and optimization problem with respect to the u b1 variable at Bob can be simplified to

[0060]

[0061] According to the Rayleigh - Ritz theorem, the optimal solution of u b1 is the eigenvector corresponding to the largest eigenvalue of the matrix .

[0062] Similarly, given the known Θ, the maximized received power and optimization problem with respect to the u b2 variable at Bob can be simplified to

[0063]

[0064] According to the Rayleigh - Ritz theorem, the optimal u b2 is the eigenvector corresponding to the largest eigenvalue of the matrix .

[0065] As a specific implementation, in step 3, the receive beamforming vectors u b1 and u b2 are fixed, and the phase shift matrix Θ of the IRS is optimized. By converting the diagonal matrix Θ into a phase shift vector θ, then solving this vector according to the Rayleigh - Ritz theorem, then considering the modulus constraint condition of the phase shift vector, and then reconstructing the vector, and finally converting the vector back to a diagonal matrix, specifically as follows:

[0066] When the receive beamforming vectors u b1 and u b2 are given, the maximized received power and optimization problem with respect to the phase shift matrix Θ can be expressed as

[0067]

[0068] Define all the elements on the diagonal of the phase shift matrix Θ of the IRS as the phase shift vector θ, that is

[0069]

[0070] Then the phase shift vector should satisfy the condition

[0071] |θ i | = 1, arg(θ i ) ∈ [0, 2π), i = 1, …, M (21)

[0072] Define h A1 = H AI v 1, the maximization of the received power and the optimization problem with respect to the phase shift vector θ can be expressed as

[0073]

[0074] Then, let According to the Rayleigh - Ritz theorem, the optimal solution of the phase shift vector of the IRS is the eigenvector corresponding to the largest eigenvalue of the matrix Meanwhile, to satisfy the modulus constraint condition of Equation (21), reconstruct Then the optimal IRS phase shift matrix is

[0075] S4. Calculate the absolute value of the difference between the received powers before and after the update of the receive beamforming vector and the IRS phase shift matrix until the termination condition is met.

[0076] In summary, the present invention provides a method for designing the IRS phase shift matrix and receive beamforming in direction modulation. Through the joint design of the IRS phase shift matrix and receive beamforming, the sum of the received powers at the legitimate users is maximized, thereby improving the security performance of the system. This method first uses the idea of null - space projection to design two - path receive beamforming vectors to receive signals from two paths respectively, simplifying the maximization of the sum of powers and the optimization problem to be solved. When the IRS phase shift matrix is fixed, the optimal receive beamforming vector can be obtained according to the Rayleigh - Ritz theorem; when the receive beamforming vector is fixed, the IRS phase shift matrix is converted into a phase shift vector, and this vector is obtained according to the Rayleigh - Ritz theorem. After reconstruction, the corresponding phase shift matrix can be obtained. According to the above method, the receive beamforming vector and the IRS phase shift matrix are alternately updated until the convergence condition is reached, and then the designed IRS phase shift matrix and receive beamforming vector can be obtained. This method solves the design problem at the receiving end in the IRS - assisted direction modulation system with a relatively low complexity and better improves the security performance of the system.

Claims

1. An optimization method for the IRS phase shift matrix and receiving beamforming in direction modulation, characterized in that, specifically: Step 1: Based on null space projection, design two receiving beamforming vectors to receive the transmission signals on two paths respectively, and simplify the objective optimization problem of maximizing the sum of received powers at the legitimate user; Step 2: Fix the phase shift matrix of the IRS, and optimize the two receiving beamforming vectors respectively according to the Rayleigh - Ritz theorem; Step 3: Fix the receiving beamforming vectors, convert the IRS phase shift matrix into a phase shift vector, and obtain the optimal solution of the phase shift vector according to the Rayleigh - Ritz theorem; Step 4: Alternately update the receiving beamforming vectors and the IRS phase shift matrix until the absolute value of the difference between the received powers before and after reception is less than the set threshold; The specific construction process of the objective optimization problem of maximizing the sum of received powers at the legitimate user is as follows: Establish an IRS-assisted direction modulation system, where the base station is configured with N A antennas, the IRS consists of M passive reflecting elements, and the legitimate user and the illegal user have N B and N E antennas respectively; Introduce the IRS into the direction modulation system so that the direction modulation system can simultaneously transmit two privacy information streams. The signal s transmitted by the base station is expressed as Among them, P s is the total transmission power, β 1 and β 2 are the power allocation factors of the two-way private information flows, β 3 is the power allocation factor of the artificial noise, and satisfies β 1 +β 2 +β 3 = 1; and are the transmit beamforming vectors for transmitting the two-way private information, satisfying x 1 and x 2 are private information, satisfying is the artificial noise projection matrix; is the transmitted artificial noise, which follows a complex Gaussian distribution, that is In the direction modulation system, the wireless communication channel is a line - of - sight channel, and the normalized channel vector is where N is the total number of antennas of the transmitter or receiver, and the phase function Ψ θ (n) is defined as where θ, n, d, λ represent the direction angle of arrival or departure, the index number of the antenna, the element spacing in the transmitting antenna array, and the wavelength respectively; The channel matrices from base station Alice to legitimate user Bob, from Alice to IRS, from Alice to illegal user Eve, from IRS to Bob, and from IRS to Eve are denoted as The corresponding path losses are g AB ,g AI ,g AE ,g IB and g IE ; where θ r,AB ,θ t,AB are the angle of arrival and the angle of departure from Alice to Bob, respectively; θ r,AI ,θ t,AI are the angle of arrival and the angle of departure from Alice to IRS, respectively; θ r,AE ,θ t,AE are the angle of arrival and the angle of departure from Alice to Eve, respectively; θ r,IB ,θ t,IB are the angle of arrival and the angle of departure from IRS to Bob, respectively; θ r,IE ,θ t,IE are the angle of arrival and the angle of departure from IRS to Eve, respectively; After channel transmission and receive beamforming, the received signal y at the legitimate user Bob bi is expressed as Among them, is the receive beamforming vector at Bob, is the phase shift matrix of the IRS, represents the phase shift generated by the m-th reflecting element of the IRS; represents the additive white Gaussian noise at Bob, g AIB = g AI g IB represents the equivalent path loss coefficient of the channel from Alice through the IRS to Bob; Received signal y at illegal user Eve ei Denoted as Among them, is Eve's receive beamforming vector, represents the additive white Gaussian noise at Eve, g AIE = g AI g IE represents the equivalent path loss coefficient of the channel from Alice through the IRS to Eve; P AN To project artificial noise onto the null spaces of the channels from Alice to Bob and from Alice to IRS, P AN satisfies the condition Combine H AI and to synthesize a virtual large channel H CM , that is The artificial noise projection matrix is expressed as In this case, the received signal expressions at the Bob side and the Eve side are rewritten as To maximize the total received power at Bob, jointly optimize the two receiving beamforming vectors and the IRS phase shift matrix, and the optimization problem is expressed as where In Step 1, based on null space projection, design the receiving beamforming vectors to receive the transmission signals on two paths respectively, and simplify the objective optimization problem of maximizing the sum of received powers at the legitimate user. Specifically: Let the two receiving beamforming vectors receive the transmission signals on two paths respectively. According to the idea of null space projection, the two receiving beamforming vectors satisfy the constraint conditions where u b1 is only used to receive the privacy information of the IRS reflection path, while u b2 is used to receive the privacy information of the direct path transmission; in this case, the received signal expression at the Bob side is re-expressed as Thus, the optimization problem of maximizing the sum of received powers at Bob is transformed into 2. The optimization method for the IRS phase shift matrix and receiving beamforming in direction modulation according to claim 1, characterized in that, In step 2, fix the phase shift matrix Θ of the IRS, and optimize the two receive beamforming vectors respectively according to the Rayleigh-Ritz theorem and Specifically as follows: When the phase shift matrix Θ of the IRS is given, the maximization of the received power and the optimization problem regarding the u b1 variable at Bob are simplified to According to the Rayleigh-Ritz theorem, the optimal solution of u b1 is the eigenvector corresponding to the largest eigenvalue of the matrix ; Similarly, given a known Θ, the maximization of the received power and the optimization problem with respect to the u b2 variable at Bob are reduced to According to the Rayleigh-Ritz theorem, the optimal u b2 is the eigenvector corresponding to the largest eigenvalue of the matrix .

3. The optimization method for the IRS phase shift matrix and receiving beamforming in direction modulation according to claim 2, characterized in that, In step 3, fix the receive beamforming vector u b1 and u b2 , optimize the phase shift matrix Θ of the IRS. By converting the diagonal matrix Θ into a phase shift vector θ, then solving this phase shift vector θ according to the Rayleigh-Ritz theorem. After that, considering the modulus constraint condition of the phase shift vector, reconstruct the vector, and then convert the vector back to a diagonal matrix, specifically as follows: When the given receive beamforming vectors are $\mathbf{u}$ b1 and $\mathbf{u}$ b2 , the maximization of the received power and the optimization problem with respect to the phase shift matrix $\boldsymbol{\Theta}$ are expressed as Define all the elements on the diagonal of the phase shift matrix Θ of the IRS as the phase shift vector θ, that is Then the phase shift vector should satisfy the condition |θ i | = 1, arg(θ i ) ∈ [0, 2π), i = 1, …, M (21) Define h A1 = H AI v 1 , the maximization of the received power and the optimization problem with respect to the phase shift vector θ are expressed as Then, let According to the Rayleigh-Ritz theorem, the optimal solution of the phase shift vector of the IRS is the eigenvector corresponding to the largest eigenvalue of the matrix ; meanwhile, to satisfy the modulus constraint condition of Equation (21), reconstruct Then the optimal IRS phase shift matrix is

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