A Low-Complexity Receiving Beamforming Method for NSP with IRS-Assisted Direction Modulation

Abstract

The present invention provides a low-complexity receiving beamforming method for IRS-assisted direction modulation. It is assumed that the transmitter is equipped with \(N_{A}\) transmitting antennas, the IRS is equipped with \(M\) passive transmitting elements, the legitimate user and the eavesdropper are respectively equipped with \(N_{B}\) and \(N_{E}\) receiving antennas; a secure received signal model with a legitimate user and an eavesdropper is constructed; a maximization of received power and an optimization problem are established and simplified; based on the maximization of received power and criterion, the NSP method is used to alternately optimize the IRS phase shift matrix and the receiving beamforming; the computational complexity of using the NSP method is calculated; the IRS is introduced into the direction modulation system, and the received power of the legitimate user is enhanced by dynamically adjusting the phase shift of the IRS and eavesdropping by the eavesdropper is prevented, so that the transmission security of the direction modulation system can be improved and the computational complexity of the receiver can be reduced. Compared with the direction modulation scheme without IRS-assisted direction modulation and without phase shift matrix optimization, the NSP method proposed by the present invention can significantly improve the security performance of the direction modulation system.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and particularly to an NSP low-complexity receiving beamforming method for IRS-assisted direction modulation. Background Art

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

[0003] An intelligent reflecting surface (IRS) consists of a large number of controllable reflecting elements with continuous phase shifters. By intelligently regulating the reflection coefficient to change the phase shift of the incident electromagnetic wave, the transmission environment of the signal can be intelligently reconfigured to enhance the power of the desired received signal or suppress interference signals. The IRS has the characteristic of low cost and can be used to improve the spectrum and energy efficiency of wireless communication networks. Due to the rank-1 property of the channel matrix of the traditional direction modulation network, the effective transmission of two or more paths of information cannot be achieved. The null-space projection (NSP) method is a new iterative algorithm, but there is currently no research on applying NSP to the direction modulation system. Therefore, it is of great significance to study an NSP low-complexity receiving beamforming method for IRS-assisted direction modulation. Summary of the Invention

[0004] In view of this, the present invention proposes an NSP low-complexity receiving beamforming method for IRS-assisted direction modulation, which can enhance the received power of legitimate users and prevent eavesdroppers from eavesdropping on confidential information by dynamically adjusting the phase shift of the IRS, and can significantly improve the security performance of the direction modulation system.

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

[0006] An NSP low-complexity receiving beamforming method for IRS-assisted direction modulation includes the following steps:

[0007] Step S1, assume that the transmitter is equipped with N A transmitting antennas, the IRS is equipped with M passive transmitting elements, and the legitimate user and the eavesdropper are respectively equipped with N B and N E receiving antennas;

[0008] Step S2: Construct the received signal models for the legitimate user and the eavesdropper;

[0009] The step S2 further includes obtaining the baseband transmission signal, and the baseband transmission signal is:

[0010]

[0011] where s is the baseband transmission signal, x1 and x2 are privacy information, and they respectively satisfy E[‖x1‖ 2 = 1, E[‖x2‖ 2 = 1, P s is the total transmission power, β1, β2, and β3 respectively represent the power allocation factors of the privacy information and the artificial noise, and satisfy β1 + β2 + β3 = 1, and represent the beamforming vectors for sending the two paths of privacy information to the legitimate user, and respectively satisfy P AN represents the projection matrix for controlling the direction of the artificial noise, z is an artificial noise vector subject to Gaussian distribution, that is where is N A dimensional identity matrix;

[0012] The received signal model of the legitimate user in step S2 is:

[0013]

[0014] where y bi is the defined received signal of the legitimate user, represents the receive beamforming vector, represents the IRS→legitimate user channel, is the receive angle from the IRS to Bob, is the transmit angle from the IRS to Bob, is the IRS phase shift matrix, represents the phase shift of the m-th reflection element, and respectively represent the transmitter→IRS channel and the transmitter→legitimate user channel, is the receive angle from Alice to the IRS, is the transmit angle from Alice to the IRS, is the receive angle from Alice to Bob, the transmit angle from Alice to Bob, θ r and θ t respectively represent the outgoing angle and the incident angle of the channel, is the complex additive white Gaussian noise at the legitimate user, where is NB an N - dimensional identity matrix, is the noise variance of the legitimate user, g AB represents the path loss coefficient of the transmitter → legitimate user channel, g AIB = g AI g IB is the path loss coefficient of the transmitter → IRS → legitimate user channel;

[0015] The received signal model of the eavesdropper in step S2 is:

[0016]

[0017] where, y ei is the received signal of the eavesdropper, is the receive beamforming vector, and respectively represent the IRS → eavesdropper channel and the transmitter → eavesdropper channel, is the receive angle from the IRS to Eve, is the transmit angle from the IRS to Eve, is the receive angle from Alice to Eve, is the transmit angle from Alice to Eve, is the complex additive white Gaussian noise at the eavesdropper, where is N E an N - dimensional identity matrix, is the noise variance of the eavesdropper, g AIE = g AI g IE and g AE respectively represent the path loss coefficients of the transmitter → IRS → eavesdropper channel and the transmitter → eavesdropper channel;

[0018] Step S2 further includes constructing a normalized steering vector, which is expressed as:

[0019]

[0020] where Ψ θ (n)=-(n - (N + 1) / 2)dcosθ / λ, Ψ θ (n) is the phase function, θ is the angle of arrival or departure, d and λ respectively represent the antenna spacing and the wavelength, N is the number of antennas, n = 1, …, N;

[0021] Assume the artificial noise is only sent to the eavesdropper, then P AN satisfies

[0022] Define a virtual private information channel as Then P AN is expressed as

[0023]

[0024] Assume that all channels are line-of-sight channels, then 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 received signal models of legitimate users and eavesdroppers are converted to:

[0025]

[0026] Step S3: Establish a maximization of the received power and an optimization problem, and simplify it;

[0027] The specific steps of step S3 are: Let the receive beamforming vectors u b1 and u b2 satisfy the following conditions:

[0028]

[0029] The above equation indicates that the receive beamforming vector u b1 is only used to receive the private information reflected from the IRS, and u b2 only receives the private information of the direct path. Then the signal received by the legitimate user is:

[0030]

[0031] The signal received by the eavesdropper is:

[0032]

[0033] The maximization of the received power and the optimization problem are converted to:

[0034]

[0035] Step S4: Based on the maximization of the received power and the criterion, use the NSP method to alternately optimize the IRS phase shift matrix and the receive beamforming;

[0036] Step S5: Calculate the computational complexity of the NSP method.

[0037] Preferably, step S4 includes fixing the IRS phase shift matrix Θ and optimizing the receive beamforming vectors u b1 and u b2 . The specific steps are: Fix the IRS phase shift matrix Θ as a constant matrix, then the optimization problem of the maximization of the received power with respect to the receive beamforming vector u b1 is simplified to:

[0038]

[0039] According to the Rayleigh - Ritz theorem, the optimal u b1 is the eigenvector corresponding to the largest eigenvalue of the matrix Similarly, the optimal u b2 is the eigenvector corresponding to the largest eigenvalue of the matrix is the eigenvector corresponding to the largest eigenvalue of the matrix.

[0040] Preferably, the step S4 further includes fixing the receive beamforming vectors u b1 and u b2 , and optimizing the IRS phase - shift matrix Θ. The specific steps are as follows: The problem of solving the optimal θ is simplified to:

[0041]

[0042] s.t. |θ i | = 1, arg(θ i ) ∈ [0, 2π), i = 1, …, M

[0043] It can be known from the Rayleigh - Ritz theorem that the optimal θ is obtained according to the eigenvector corresponding to the largest eigenvalue of the matrix

[0044] Preferably, the computational complexity in the step S5 is:

[0045]

[0046] where L represents the maximum number of iterations.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] The present invention provides an IRS - assisted direction - modulation NSP low - complexity receive beamforming method. Introducing the IRS into the direction - modulation system can improve the transmission security of the traditional direction - modulation system and reduce the computational complexity of the receiver. Compared with the direction - modulation system without IRS assistance and without IRS phase - shift optimization, the proposed NSP method can significantly improve the security performance of the direction - modulation system. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following - described drawings are only the preferred embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.​

[0050] Figure 1 It is a flowchart of an IRS-assisted direction modulation NSP low-complexity receiving beamforming method of the present invention;

[0051] Figure 2 It is a diagram of an IRS-assisted direction modulation system;

[0052] Figure 3 It is a convergence curve graph of an IRS-assisted direction modulation NSP low-complexity receiving beamforming method of the present invention under different numbers of IRS phase shift elements;

[0053] Figure 4 It is a relationship curve graph between the secure rate and the number of IRS phase shifts of an IRS-assisted direction modulation NSP low-complexity receiving beamforming method of the present invention;

[0054] Figure 5 It is a relationship curve graph between the secure rate and the azimuth angle of the eavesdropper of an IRS-assisted direction modulation NSP low-complexity receiving beamforming method of the present invention. Detailed implementation manners

[0055] 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 described in conjunction with the accompanying drawings.

[0056] See Figure 1 , an IRS-assisted direction modulation NSP low-complexity receiving beamforming method provided by the present invention includes the following steps:

[0057] Step S1, assume that the transmitter is equipped with N A transmitting antennas, the IRS is equipped with M passive transmitting elements, the legitimate user and the eavesdropper are respectively equipped with N B and N E receiving antennas, and at the same time assume that there is no delay in the IRS reflected signal;

[0058] Step S2, construct the receiving signal models of the legitimate user and the eavesdropper;

[0059] Assume that there is a line-of-sight path, and the baseband transmitted signal is:

[0060]

[0061] where s is the baseband transmitted signal, x1 and x2 are privacy information, and respectively satisfy E[‖x1‖ 2 = 1, E = [‖x2‖ 2 = 1, P s is the total transmission power, β1, β2 and β3 respectively represent the power allocation factors of the privacy information and the artificial noise, and satisfy β1 + β2 + β3 = 1, and represent the beamforming vectors for sending two-way privacy information to legitimate users, respectively satisfying P AN represents the projection matrix for controlling the direction of artificial noise, and z is an artificial noise vector subject to Gaussian distribution, that is where is the N A dimensional identity matrix.

[0062] When there is path loss, the received signal model of the legitimate user is:

[0063]

[0064] where, y bi is the received signal of the defined legitimate user, represents the receive beamforming vector, represents the IRS→legitimate user channel, is the receiving angle from the IRS to Bob, is the transmitting angle from the IRS to Bob, is the IRS phase shift matrix, represents the phase shift of the m-th reflection element, and respectively represent the transmitter→IRS channel and the transmitter→legitimate user channel, is the receiving angle from Alice to the IRS, is the transmitting angle from Alice to the IRS, is the receiving angle from Alice to Bob, The transmitting angle from Alice to Bob, θ r and θ t respectively represent the outgoing angle and the incoming angle of the channel, is the composite additive white Gaussian noise at the legitimate user, where is the N B dimensional identity matrix, is the noise variance of the legitimate user, g AB represents the path loss coefficient of the transmitter→legitimate user channel, g AIB = g AI g IB is the path loss coefficient of the transmitter→IRS→legitimate user channel.

[0065] Similarly, the received signal model of the eavesdropper is:

[0066]

[0067] where, y ei is the received signal of the eavesdropper, is the receive beamforming vector, and represent the IRS→eavesdropper channel and the transmitter→eavesdropper channel respectively, is the receive angle from the IRS to Eve, is the transmit angle from the IRS to Eve, is the receive angle from Alice to Eve, is the transmit angle from Alice to Eve, is the composite additive white Gaussian noise at the eavesdropper, where is the N E dimensional identity matrix, is the noise variance of the eavesdropper, g AIE = g AI g IE and g AE represent the path loss coefficients of the transmitter→IRS→eavesdropper channel and the transmitter→eavesdropper channel respectively;

[0068] Step S2 further includes constructing a normalized steering vector, and the normalized steering vector is expressed as:

[0069]

[0070] where Ψ θ (n) = -(n - (N + 1) / 2)dcosθ / λ, d and λ represent the antenna spacing and wavelength respectively, N is the number of antennas, and n = 1, …, N.

[0071] where Ψ θ (n) = -(n - (N + 1) / 2)dcosθ / λ, Ψ θ (n) is the phase function, θ is the direction angle of arrival or departure, d and λ represent the antenna spacing and wavelength respectively, N is the number of antennas, and n = 1, …, N.

[0072] Define a virtual private information channel as Then P AN is expressed as

[0073]

[0074] Since all channels involved in the present invention are assumed to be line-of-sight channels, then rank(H AI ) = 1, rank(H AB ) = 1, and rank(H CM ) ≤ 2. Therefore, the projection matrix has at least N - 2 degrees of freedom, and the received signal models of the legitimate users and the eavesdropper are converted to:

[0075]

[0076] Step S3: Establish the maximum received power and optimization problem and simplify it;

[0077] The specific steps are as follows: Let the receive beamforming vectors u b1 and u b2 satisfy the following conditions:

[0078]

[0079] The above equation indicates that the receive beamforming vector u b1 is only used to receive the private information reflected from the IRS, and u b2 only receives the private information of the direct path. Then the signal received by the legitimate user is:

[0080]

[0081] The signal received by the eavesdropper is:

[0082]

[0083] The maximum received power and optimization problem is transformed into:

[0084]

[0085] Step S4: Based on the maximum received power and criterion, use the NSP method to alternately optimize the IRS phase shift matrix and the receive beamforming;

[0086] It includes fixing the IRS phase shift matrix Θ and optimizing the receive beamforming vectors u b1 and u b2 . The specific steps are as follows: Fix the IRS phase shift matrix Θ as a constant matrix. Then the optimization problem of the maximum received power with respect to the receive beamforming vector u b1 is simplified to:

[0087]

[0088] According to the Rayleigh - Ritz theorem, the optimal u b1 is the eigenvector corresponding to the largest eigenvalue of the matrix . Similarly, the optimal u b2 is the eigenvector corresponding to the largest eigenvalue of the matrix .

[0089] It also includes fixing the receive beamforming vectors u b1 and u b2 and optimizing the IRS phase shift matrix Θ. The specific steps are as follows: Simplify the problem of solving the optimal θ to:

[0090]

[0091] such that |θ i | = 1, arg(θ i ) ∈ [0, 2π), i = 1, …, M

[0092] According to the Rayleigh - Ritz theorem, the optimal θ is obtained from the eigenvector corresponding to the largest eigenvalue of the matrix and

[0093] The overall design idea of the NSP algorithm proposed by the present invention is as follows: fix the phase - shift matrix Θ, and use the Rayleigh - Ritz theorem to solve the receive beamforming vector u b1 and u b2 ; fix u b1 and u b2 , transform the target variable Θ into the vector θ, and solve θ according to the Rayleigh - Ritz theorem. If θ = exp{j∠(θ)}, then Θ = diag{θ}. The algorithm iterates alternately among u b1 、u b2 and Θ until the stopping condition is satisfied, that is, ||RPS p - RPS (p-1) || ≤ ε, where p represents the number of iterations and ε represents a predefined constant.

[0094] Preferably, the computational complexity of calculating the NSP method in step S5 is:

[0095]

[0096] where L represents the maximum number of iterations.

[0097] The present invention introduces the IRS into the direction modulation system. By dynamically adjusting the phase - shift of the IRS, it can enhance the received power of legitimate users and prevent eavesdroppers from eavesdropping on private information, which can improve the transmission security of traditional direction modulation systems and reduce the computational complexity of receivers. Compared with the non - IRS - assisted direction modulation scheme and the non - phase - shift - matrix - optimized direction modulation scheme, the IRS - assisted NSP proposed by the present invention can significantly improve the security performance of the direction modulation system.

[0098] To improve the energy efficiency and overcome the limitation that traditional direction modulation only transmits one useful information stream, the present invention introduces the IRS into the direction modulation system. Experiments show that the system can significantly improve the security performance of traditional direction modulation systems without IRS assistance. Therefore, it is of great significance to study IRS - assisted direction modulation communication systems.

[0099] The beneficial effects of the present invention are described below through some experimental data: The schematic diagram of the IRS-assisted direction modulation system is as Figure 2 shown, where Alice is the transmitter, IRS is the intelligent reflecting surface, Bob is the legitimate user, and Eve is the eavesdropper.

[0100] Figure 3 It is the convergence curve graph of the NSP algorithm when the number of IRS phase shift elements M = 40 and 100. It can be seen from the figure that as the number of iterations increases, the security rate of the proposed NSP also gradually increases and finally reaches the convergence point. In terms of computational complexity, when M = 100, the number of alternating iterations L of the proposed NSP algorithm is 3. When M tends to be large-scale, the computational complexity of the proposed NSP algorithm is much lower than that of other algorithms.

[0101] Figure 4 It is the relationship curve graph of the security rate of the proposed NSP algorithm and three benchmark methods with the number of IRS phase shifts M. It can be seen from the figure that compared with the scheme that only uses one receiving beamforming, the proposed NSP scheme of the present invention has obvious security rate performance advantages. Compared with the direction modulation schemes without IRS and with random phases of IRS, the security rate of the method proposed in the present invention gradually increases with the increase in the number of phase shifters. This shows the importance of optimizing the IRS phase shift matrix and the importance of constructing an IRS-assisted direction modulation system.

[0102] Figure 5 It is the relationship curve graph of the security rate of the system and the azimuth angle of the eavesdropper when the number of IRS phase shifts M = 80, where the value range of the azimuth angle is 0 to 180°. Since both the transmitter and the receiver are linear arrays, the security rate performance of 0 to 90° and 90 to 180° is almost symmetric. From Figure 5 it can be seen that when the direction angles of Eve and Bob are the same, that is, both are 45°, the security rate performance of the given scheme drops significantly. This is because when Eve is on the direct path from Alice to Bob, Eve can eavesdrop on the private information to the greatest extent. However, when Eve is between the paths of Alice and IRS, the performance of the proposed NSP algorithm is robust, that is, the performance will not deteriorate.

Claims

1. An IRS-assisted direction modulation NSP low-complexity receiving beamforming method, characterized in that, Including the following steps: Step S1. Assume that the transmitter is equipped with N A transmitting antennas, the IRS is equipped with M passive reflecting elements, and the legitimate user and the eavesdropper are respectively equipped with N B and N E receiving antennas; Step S2: Construct the received signal models of legitimate users and eavesdroppers; The step S2 further includes obtaining the baseband transmitted signal, and the baseband transmitted signal is: where \(s\) is the baseband transmitted signal, \(x_1\) and \(x_2\) are privacy information, and they respectively satisfy \(E[\|x_1\| 2 = 1\), \(E[\|x_2\| 2 = 1\), \(P s is the total transmit power, \(\beta_1\), \(\beta_2\) and \(\beta_3\) respectively represent the power allocation factors of privacy information and artificial noise, and satisfy \(\beta_1+\beta_2+\beta_3 = 1\), and represent the beamforming vectors for sending two-way privacy information to legitimate users, and respectively satisfy P AN represents the projection matrix for controlling the direction of artificial noise, \(z\) is an artificial noise vector subject to Gaussian distribution, that is where is the \(N A -dimensional identity matrix; The received signal model of the legitimate user in the step S2 is: where y bi is the received signal of a defined legitimate user, represents the receive beamforming vector, represents the IRS→legitimate user channel, is the receive angle from the IRS to Bob, is the transmit angle from the IRS to Bob, is the IRS phase shift matrix, represents the phase shift of the m-th reflecting element, and represent the transmitter→IRS channel and the transmitter→legitimate user channel respectively, is the receive angle from Alice to the IRS, is the transmit angle from Alice to the IRS, is the receive angle from Alice to Bob, The transmit angle from Alice to Bob, θ r and θ t represent the outgoing angle and the incoming angle of the channel respectively, is the complex additive white Gaussian noise at the legitimate user, where is the N B dimensional identity matrix, is the noise variance of the legitimate user, g AB represents the path loss coefficient of the transmitter→legitimate user channel, g AIB = g AI g IB is the path loss coefficient of the transmitter→IRS→legitimate user channel; The received signal model of the eavesdropper in the step S2 is: where y ei is the received signal of the eavesdropper, is the receive beamforming vector, and represent the IRS→eavesdropper channel and the transmitter→eavesdropper channel respectively, is the receive angle from the IRS to Eve, is the transmit angle from the IRS to Eve, is the receive angle from Alice to Eve, is the transmit angle from Alice to Eve, is the complex additive white Gaussian noise at the eavesdropper, where is the N<s E [[ID=ll22]]is the N-dimensional identity matrix, is the noise variance of the eavesdropper, g AIE = g AI g IE and g AE represent the path loss coefficients of the transmitter→IRS→eavesdropper channel and the transmitter→eavesdropper channel respectively; The step S2 further includes constructing a normalized steering vector, and the normalized steering vector is expressed as: where Ψ θ (n) = -(n - (N + 1) / 2)dcosθ / λ, Ψ θ (n) is the phase function, θ is the arrival or departure direction angle, d and λ represent the antenna spacing and wavelength respectively, N is the number of antennas, and n = 1, …, N; Assume If artificial noise is only sent to the eavesdropper, then P AN satisfies Define a virtual privacy information channel as Then P AN is expressed as Assume that all channels are line-of-sight channels, then 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 received signal models of legitimate users and eavesdroppers are converted to: Step S3: Establish the problem of maximizing the received power and optimization, and simplify it; The specific steps of step S3 are as follows: Let the received beamforming vectors u b1 and u b2 satisfy the following conditions: The above equation shows that the received beamforming vector u b1 is only used to receive the private information reflected from the IRS, and u b2 only receives the private information of the direct path. Then the signal received by the legitimate user is: The signal received by the eavesdropper is: The problem of maximizing the received power and optimization is transformed into: Step S4: Based on the criterion of maximizing the received power, use the NSP method to alternately optimize the IRS phase shift matrix and the receive beamforming; Step S5: Calculate the computational complexity of the NSP method.

2. The low-complexity receiving beamforming method for NSP with IRS-aided direction modulation according to claim 1, wherein The step S4 includes fixing the IRS phase shift matrix Θ and optimizing the receive beamforming vector u b1 and u b2 , and the specific steps are as follows: Fix the IRS phase shift matrix Θ as a constant matrix, then the optimization problem of maximizing the received power with respect to the receive beamforming vector u b1 is simplified to: According to the Rayleigh-Ritz theorem, the optimal u b1 is the eigenvector corresponding to the largest eigenvalue of the matrix Similarly, the optimal u b2 is the eigenvector corresponding to the largest eigenvalue of the matrix ​ 3. The low-complexity receiving beamforming method for NSP with IRS-assisted direction modulation according to claim 2, characterized in that, The step S4 further includes fixing the received beamforming vectors u b1 and u b2 , and optimizing the IRS phase shift matrix Θ. The specific steps are as follows: The problem of solving the optimal θ is simplified to: such that |θ i | = 1, arg(θ i ) ∈ [0, 2π), i = 1, …, M According to the Rayleigh-Ritz theorem, the optimal θ is obtained from the eigenvector corresponding to the largest eigenvalue of the matrix and 4. An IRS-assisted direction modulation NSP low-complexity receiving beamforming method according to claim 3, characterized in that The computational complexity in the step S5 is: Where L represents the maximum number of iterations.

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