Reconfigurable intelligent surface assisted movable antenna direction modulation method and system

Abstract

The application discloses a reconfigurable intelligent surface assisted movable antenna direction modulation method and system, specifically, an optimization problem model is established on the basis of an active intelligent reflecting surface assisted large-scale multiple-input multiple-output system, confidential information transmitted by a base station equipped with a movable antenna reaches a legal user and an eavesdropper through two main paths; under power constraints, maximum reflection coefficient constraints and movable antenna position constraints, the maximum safe rate of the legal user and the eavesdropper is designed; in the transmission end weight vector optimization stage, the movable antenna position constraints are converted into l2 norm by using a compression sensing method, the transmission rate that can be realized by the eavesdropper is fixed, and a singular value decomposition is used to obtain the transmission end weight vector; in the phase shift matrix optimization stage, the transmission rate that can be realized by the legal user is fixed, and a singular value decomposition is used to obtain the intelligent reflecting surface phase shift matrix. The application greatly improves the achievable safe rate.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, in particular to a reconfigurable intelligent surface assisted movable antenna direction modulation method and system. BACKGROUND

[0002] Movable antennas are antenna systems that can adjust their position based on performance requirements. They are useful in a variety of applications. The design of such antennas allows them to move in physical position through flexible structures to optimize signal reception or transmission. Movable antennas are commonly used in military communications, satellite communications, broadcasting, radio astronomy and certain types of wireless networks. They can adapt to dynamic environments, such as tracking moving satellites or adjusting to avoid signal interference. In the field of wireless communication, movable antennas can improve signal quality, enhance network coverage, and quickly deploy when necessary. In addition to the above applications, movable antennas also play a key role in emergency response and disaster recovery. After natural disasters, traditional communication infrastructure may be damaged, and movable antennas can be quickly deployed to provide temporary communication support to affected areas, assisting in the coordination of rescue operations and information transmission. This flexibility makes movable antennas particularly important in situations that require high adaptability and mobility.

[0003] In summary, the flexibility and adjustability of movable antennas make them an indispensable part of modern communication systems. They not only improve communication efficiency and signal quality, but also play a key role in situations that require rapid adaptation to environmental changes and provide stable communication links. With the development of antenna technology, new security requirements have been proposed, and the study of movable antennas is of great significance to improve the security of wireless systems. SUMMARY

[0004] The purpose of the present application is to provide an active intelligent surface assisted movable antenna direction modulation method and system, which can effectively reduce the eavesdropping rate of eavesdroppers, enhance the transmission rate of legitimate users, and improve physical layer security.

[0005] The technical solution for achieving the purpose of the present application is a reconfigurable intelligent surface assisted movable antenna direction modulation method, the specific steps of which are as follows:

[0006] Step 1, provide a direction modulation network with movable antennas;

[0007] Step 2, establish a receiving signal model for the active intelligent surface assisted movable antenna system;

[0008] Step 3, use the receiving signal model to derive the security performance index, i.e. the security rate;

[0009] Step 4, design an optimization scheme based on the security performance index;

[0010] Step 5, using the compression sensing technology, optimizing the movable antenna position and the transmitting end weight coefficient through singular value decomposition;

[0011] Step 6, using singular value decomposition to optimize the intelligent reflecting surface phase shift matrix through the transmission rate that the legitimate user can achieve.

[0012] Further, the direction modulation network of the movable antenna in step 1 is as follows:

[0013] Using active intelligent reflecting surface to assist the base station to send confidential information to the legitimate user, while sending artificial noise to effectively interfere the eavesdropper, wherein the base station is equipped with a movable antenna; the confidential information reaches the legitimate user through two paths, which are the direct path and the reflection path through the intelligent reflecting surface.

[0014] Further, the step 2 is as follows:

[0015] The receiving signal model of the active intelligent reflecting surface assisted movable antenna system is established, the base station BS sends confidential information to the legitimate user through two paths, which are the direct path and the reflection path through the intelligent reflecting surface RIS, and the signal y received by the legitimate user Bob is:

[0016]

[0017] Wherein f u , G and h u represent the channels from RIS to Bob, from BS to RIS and from BS to Bob respectively; [] T and [] H are the transpose and conjugate transpose operations respectively; w represents the transmitting end weight vector, s represents the transmitted confidential symbol, Φ represents the intelligent reflecting surface phase shift matrix, and represent the electromagnetic interference at the intelligent reflecting surface and the noise experienced by the legitimate user respectively; the signal e received by the eavesdropper Eve is:

[0018]

[0019] Wherein f e and h e represent the channels from RIS to Eve and from BS to Eve respectively, represents the noise experienced by the eavesdropper; the subscript e refers to the eavesdropper.

[0020] Further, the step 3 is as follows:

[0021] The security performance indicator, i.e., the secure rate, is derived using the received signal model; According to the Shannon formula, the transmission rate r achievable at Bob is u is expressed as:

[0022]

[0023] where t u denotes the amplitude of the received useful signal at Bob, denotes the sum of the electromagnetic interference power and the noise power experienced by Bob, q u denotes the aggregate channel from the BS to Bob;

[0024] The transmission rate achievable at Eve is expressed as:

[0025]

[0026] where t e denotes the amplitude of the received useful signal at Eve, denotes the sum of the electromagnetic interference power and the noise power experienced by Eve, q e denotes the aggregate channel from the BS to Eve;

[0027] According to the transmission rates achievable at Bob and Eve, the secrecy rate R s is expressed as:

[0028]

[0029] where, [] + denotes a value greater than or equal to zero.

[0030] Further, the design of the optimization scheme according to the security performance indicator proposed in step 4 is as follows:

[0031] Under the constraints of maximum transmission power and amplification factor, the phase shift matrix of the RIS and the weight vector at the BS are jointly optimized to achieve the position selection of the movable antenna array and the maximization of the secrecy rate, and the optimization problem can be expressed as:

[0032]

[0033] where constraint C1 denotes the symbol designed at Bob, s e denotes the rotation operation on the legitimate information s, constraint C2 denotes the synthesized symbol at Eve, constraints C3 and C5 respectively denote the threshold values of the transmission power and the RIS amplification factor, and C4 denotes the selection of the movable antenna using the l0 norm, a non-zero value indicates the weight coefficient corresponding to the movable antenna, and a zero value weight corresponds to a position without an antenna; P0, N a , θ mand η represent the transmit power threshold, the number of mobile antennas, the first adjustable amplitude of m elements on the active IRS, and the amplification coefficient threshold, respectively; represents the IRS element index set, and and represent the l2 norm and l0 norm, respectively;

[0034] An auxiliary variable ∈ is introduced, and the constraint optimization of the antenna position is approximated to obtain:

[0035] C4′:||δ·w||≤∈ (7)

[0036] where δ = 1 / (|w|+||w|| ∞ ) represents the reweighting coefficient, and | | | | ∞ is the l ∞ norm, and ∈ represents the power threshold after reweighting; the maximum secrecy rate objective function is equivalently transformed as:

[0037]

[0038] where μ is the required secrecy rate of the system, and ρ = t u +τ is the proportional factor, is the amplitude of the signal received at the eavesdropper; then, the optimization problem is equivalently written as:

[0039]

[0040] Further, in step 5, the compressive sensing technology is used to optimize the movable antenna position and the transmit end weight coefficient through singular value decomposition, specifically as follows:

[0041] Given the initial phase shift matrix, the maximum secrecy rate problem with respect to the transmit end weight vector is described as:

[0042]

[0043] where Q(1,:) = q u represents that the first row of Q is q u , Q(2,:) = q e represents that the second row of Q is q e ; and are the aggregate channels from the BS to Bob and Eve, respectively, g u and g e are the concatenated channels from the BS to the user and the eavesdropper, respectively; t = [t u , t e ] T and c = [s, s e ] T s H represent the amplitude set and the sign set, respectively;

[0044] Then, through singular value decomposition and power constraint, we obtain:

[0045]

[0046] where is the matrix obtained after singular value decomposition and is the transmit weight coefficient vector obtained after reweighting;

[0047] Then, using the root-finding formula, we obtain the value of the objective function value as:

[0048]

[0049] where

[0050]

[0051] where a0, b0 and c0 are auxiliary variables; denotes taking the real part; in the transmit weight vector optimization stage, given the intelligent reflecting surface phase shift matrix, the amplitude of the useful signal at Eve t e is obtained, and the maximum secrecy rate is ε.

[0052] Further, step 6 optimizes the intelligent reflecting surface phase shift matrix by fixing the transmission rate that the legitimate user can achieve, as follows:

[0053] In order to improve the robustness of the system, consider that even in the case of a decline in the channel quality of the direct path channel, the RIS reflected path can also be transmitted safely, and the channel reflected by the active intelligent reflecting surface is converted to:

[0054]

[0055] where diag() represents the diagonalization operation,

[0056] Then, given the transmit weight coefficient, the optimization problem about the RIS phase shift matrix is described as:

[0057]

[0058] where Z represents the set of concatenated channels; through singular value decomposition of Z, we obtain where

[0059]

[0060] Then, introduce the matrix

[0061]

[0062] Considering the transmission power as P0, there is The singular value decomposition is performed on P to obtain By using the root formula, the value of the objective function is

[0063]

[0064] wherein

[0065]

[0066] So far, the two-stage variable optimization is completed, and the final security rate is obtained by alternately optimizing the transmitting end weight vector and the RIS phase shift matrix.

[0067] The application further provides a movable antenna direction modulation system assisted by a reconfigurable intelligent surface, which is used for implementing the movable antenna direction modulation method assisted by the reconfigurable intelligent surface, and comprises a first module to a sixth module.

[0068] The first module is provided with a direction modulation network of a movable antenna.

[0069] The second module establishes a receiving signal model of an active intelligent reflecting surface assisted movable antenna system.

[0070] The third module obtains a security performance index, i.e., a security rate, by using the receiving signal model.

[0071] The fourth module designs an optimization scheme according to the security performance index.

[0072] The fifth module optimizes the movable antenna position and the transmitting end weight coefficient by using a compression sensing technology and singular value decomposition.

[0073] The sixth module optimizes the intelligent reflecting surface phase shift matrix by using singular value decomposition through the transmission rate that can be realized by a fixed legal user.

[0074] The application further provides a mobile terminal, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, and the processor implements the movable antenna direction modulation method assisted by the reconfigurable intelligent surface when executing the program.

[0075] The application further provides a computer readable storage medium, which stores a computer program, and the program is executed by a processor to implement the steps in the movable antenna direction modulation method assisted by the reconfigurable intelligent surface.

[0076] Compared with the prior art, the application has the following advantages:

[0077] (1) On the basis of active intelligent reflecting surface assisted large-scale multiple-input multiple-output system, an optimization problem model is established, and confidential information transmitted by the base station equipped with a movable antenna reaches the legitimate user and the eavesdropper through two main paths, which are the direct path and the reflection path through the intelligent reflecting surface;

[0078] (2) Under the power constraint, the maximum reflection coefficient constraint and the movable antenna position constraint, the maximum achievable security rate of the legitimate user and the eavesdropper can be realized by designing the symbol;

[0079] (3) In the transmission end weight vector optimization stage, the movable antenna position constraint is converted into l2 norm by using the compressive sensing method, the achievable transmission rate of the eavesdropper is fixed, and the transmission end weight vector is obtained by using singular value decomposition, in the intelligent reflecting surface phase shift matrix optimization stage, the achievable transmission rate of the legitimate user is fixed, and the intelligent reflecting surface phase shift matrix is obtained by using singular value decomposition;

[0080] (4) The security is effectively improved and the calculation complexity is reduced by using the movable antenna to design the direction modulation, compared with the traditional fixed position antenna, and the achievable security rate is greatly improved compared with the traditional fixed antenna array. BRIEF DESCRIPTION OF DRAWINGS

[0081] The drawings constituting a part of this application are used to provide further understanding of the application, the illustrative embodiments of the application and the description thereof are used to explain the application, and do not constitute improper limitation of the application. In the drawings:

[0082] Figure 1 A flow chart of the active intelligent surface assisted movable antenna direction modulation method of the application.

[0083] Figure 2 A movable antenna system direction modulation model diagram of the active intelligent reflecting surface assisted embodiment of the application.

[0084] Figure 3 A movable antenna system direction modulation model diagram of the active intelligent reflecting surface assisted embodiment of the application.

[0085] Figure 4 A movable antenna system direction modulation model diagram of the active intelligent reflecting surface assisted embodiment of the application.

[0086] Figure 5 A movable antenna system direction modulation model diagram of the active intelligent reflecting surface assisted embodiment of the application.

[0087] Figure 6 Figure 8 is a diagram showing the relationship between the number of intelligent reflecting surface units and the security rate of the embodiment of the present application at a transmission power of 20 dBm, a number of movable antennas of 24, and an amplification factor of 1.5. DETAILED DESCRIPTION

[0088] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0089] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in an order different from that shown herein.

[0090] In the embodiment, a movable antenna direction modulation method assisted by an active intelligent surface is provided, which includes: under the assistance of an active intelligent reflecting surface, a base station transmitter equipped with a movable antenna transmits confidential information to a legitimate user direction, while interfering eavesdroppers with artificial noise, thereby ensuring the security of the legitimate information. Mainly includes two paths, one is a reflection path from the base station to the active intelligent reflecting surface and then to the user, and the other is a direct path from the base station to the user, as shown in Figure 1 .

[0091] In combination Figure 1 , the active intelligent surface assisted movable antenna direction modulation method of the present application includes the following steps:

[0092] Step 1, establish a receiving signal model of the active intelligent reflecting surface assisted movable antenna system, as shown in Figure 2 , specifically as follows:

[0093] The base station (BS) transmits confidential information through two paths to the legitimate user, which are the direct path and the reflection path through the intelligent reflecting surface (RIS), and the signal received by the legitimate user (Bob) is:

[0094]

[0095] where f u , G and h u represent the channels from RIS to Bob, from BS to RIS and from BS to Bob, respectively; [] T and [] H are the transpose and conjugate transpose operations, respectively; w represents the transmit weight vector, s represents the transmitted confidential symbol, and Φ represents the intelligent reflecting surface phase shift matrix, and respectively, represent the electromagnetic interference at the smart reflecting surface and the noise experienced by the legitimate user; lowercase and non-bold represent a scalar, lowercase and bold represent a vector, and uppercase and bold represent a matrix, subscript u denotes a user, superscript 2 denotes a square operation; the signal e received by the eavesdropper Eve is:

[0096]

[0097] where f e and h e represent the channels from the RIS to Eve and from the BS to Eve, respectively, represents the noise experienced by the eavesdropper; subscript e denotes an eavesdropper.

[0098] Step 2, obtain the security performance index, i.e., the secure rate, using the received signal model, as follows:

[0099] According to the Shannon formula, the transmission rate achievable at Bob is represented as:

[0100]

[0101] where t u represents the amplitude of the received useful signal at Bob, represents the sum of the electromagnetic interference power and the noise power experienced by Bob, q u represents the aggregated channel from the BS to Bob;

[0102] The transmission rate achievable at Eve is represented as:

[0103]

[0104] where t e represents the amplitude of the received useful signal at Eve, represents the sum of the electromagnetic interference power and the noise power experienced by Eve, q e represents the aggregated channel from the BS to Eve;

[0105] According to the transmission rates achievable at Bob and Eve, the secrecy rate R s is represented as:

[0106]

[0107] where, [] + represents a value greater than or equal to zero.

[0108] Step 3, design an optimization scheme according to the security performance index, as follows:

[0109] The phase shift matrix of the RIS and the weight vector at the BS are jointly optimized to realize the position selection of the movable antenna array and the maximization of the secrecy rate under the constraints of the maximum transmission power and the amplification coefficient, and the optimization problem can be expressed as:

[0110]

[0111] where constraint C1 represents the symbol designed at Bob, s e represents a rotation operation on the legal information s, constraint C2 represents the symbol synthesized at Eve, constraints C3 and C5 represent the thresholds of the transmission power and the RIS amplification factor respectively, and C4 represents the selection of the movable antenna by using the l0 norm, a non-zero value indicating the weight coefficient corresponding to the movable antenna, and a zero value weight corresponding to a position without an antenna; P0, N a , θ m and η respectively represent the transmission power threshold, the number of mobile antennas, the first adjustable amplitude of the m elements on the active intelligent reflecting surface and the amplification coefficient threshold; represents the intelligent reflecting surface element index set, and |||| and ||||0 represent the l2 norm and the l0 norm respectively;

[0112] An auxiliary variable ∈ is introduced, and the antenna position optimization constraint is approximately processed to obtain:

[0113] C4′:||δ·w||≤∈ (1.7)

[0114] where δ=1 / (|w|+||w|| ∞ ) represents a reweighting coefficient, and ∣||∣ ∞ is the l ∞ norm, and ∈ represents the power threshold after reweighting; the secrecy rate maximization objective function is equivalently transformed, that is:

[0115]

[0116] where μ is the required secrecy rate of the system, ρ=t u +τ is a proportional factor, is the signal amplitude received at the eavesdropper; then, the optimization problem is equivalently written as:

[0117]

[0118] Step 4: The movable antenna position and the transmission end weight coefficient are optimized by singular value decomposition using the compressed sensing technology, which is as follows:

[0119] Given the initial phase shift matrix, the secrecy rate maximization problem about the transmission end weight vector is described as:

[0120]

[0121] where Q(1,:) = q u denotes that the first row of Q is q u , Q(2,:) = q e denotes that the second row of Q is q e ; and are the aggregate channels from the BS to Bob and Eve, respectively, g u and g e are the cascaded channels from the BS to the user and the eavesdropper, respectively; t = [t u , t e ] T and c = [s, s e ] T s H denote the amplitude set and the sign set, respectively;

[0122] Then, by singular value decomposition and power constraint, we have:

[0123]

[0124] where is the matrix obtained after singular value decomposition and is the transmit weight vector obtained after reweighting; Note that singular value decomposition is a classical matrix decomposition method, and the three matrices obtained (from left to right) are orthogonal matrix, diagonal matrix and orthogonal matrix, respectively;

[0125] Then, using the root-finding formula, we can obtain the value of the objective function value as:

[0126]

[0127] where

[0128]

[0129] where a0, b0and c0are auxiliary variables; denotes taking the real part; accordingly, in the transmit weight vector optimization phase, given the intelligent reflecting surface phase shift matrix, the amplitude t e of the useful signal at Eve can be obtained, and the maximum secrecy rate is ε.

[0130] Step 5, by fixing the transmission rate that can be achieved by the legitimate user, the intelligent reflecting surface phase shift matrix is optimized using singular value decomposition, as follows:

[0131] In order to improve the robustness of the system, consider that even in the case of a decline in the channel quality of the direct path channel, the RIS reflected path can also be safely transmitted, and the channel reflected by the active intelligent reflecting surface is converted to:

[0132]

[0133] Then, given the transmit end weight coefficient, the optimization problem about the RIS phase shift matrix is described as:

[0134]

[0135] where Z represents the set of concatenated channels; where is obtained by singular value decomposition of Z, where

[0136]

[0137] Then, the matrix

[0138]

[0139] Considering that the transmission power is P0, we have The singular value decomposition of P can obtain Using the root formula, the value of the objective function is

[0140]

[0141] where

[0142]

[0143] At this point, the two-stage variable optimization is completed, and by alternately optimizing the transmit end weight vector and the RIS phase shift matrix, the final secrecy rate can be obtained.

[0144] Figure 3 The secrecy rate under different numbers of antennas is shown. The transmission power of the BS is set to 20 dBm, and the amplification coefficient of the RIS is 1.5. The secrecy rate obtained by the movable antenna under different active ranges is given, which are 64d×64d, 81d×81d, 100d×100d, and 121d×121d, where d is the half-wavelength interval, representing the minimum distance between antennas. Expanding the movable area can improve the secrecy rate, and under the condition that the movable area is sufficient, the secrecy performance of the movable antenna is better than that of the fixed position antenna. Using the average and minimum values of 100 Monte Carlo experiments, the secrecy rate curve of the fixed position antenna under the worst position and random position is obtained. The secrecy rate obtained by this method is higher than that of the fixed position antenna under random position and worst position. In the case of fewer antennas, equipping with movable antennas can significantly improve performance.

[0145] Figure 4 The secrecy rate under different amplification coefficients of the RIS is shown, where M = 64 × 64, N a=36, P0=20dBm. The secrecy rate value presents a stable trend after the amplification coefficient is 25dBm. Under the condition of the same amplification coefficient, increasing the movable range can obtain higher secrecy rate.

[0146] Figure 5 The secrecy rate under different transmission powers is described, wherein M=64x64, N a =12, η=1.5. With the increase of the transmission power, the secrecy rate increases.

[0147] Figure 6 The secrecy rate obtained under different RIS unit quantities is shown. With the increase of the RIS unit quantity, the secrecy rate improves.

[0148] The application further provides a reconfigurable intelligent surface assisted movable antenna direction modulation system for realizing the reconfigurable intelligent surface assisted movable antenna direction modulation method.

[0149] The first module is equipped with a direction modulation network of a movable antenna.

[0150] The second module establishes a receiving signal model of an active intelligent reflecting surface assisted movable antenna system.

[0151] The third module obtains a security performance index, i.e., a security rate, by using the receiving signal model.

[0152] The fourth module designs an optimization scheme according to the security performance index.

[0153] The fifth module optimizes the movable antenna position and the transmitting end weight coefficient by using a singular value decomposition through a compressed sensing technology.

[0154] The sixth module optimizes an intelligent reflecting surface phase shift matrix by using a singular value decomposition through a fixed transmission rate of a legal user.

[0155] The application further provides a mobile terminal comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor realizes the reconfigurable intelligent surface assisted movable antenna direction modulation method when executing the program.

[0156] The application further provides a computer readable storage medium having a computer program stored thereon, wherein the program is executed by a processor to realize the steps in the reconfigurable intelligent surface assisted movable antenna direction modulation method.

[0157] The above merely provides the preferred embodiments of the present application, and the protection scope of the present application is not limited thereto, and any changes or substitutions within the technical scope disclosed by the present application should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A reconfigurable intelligent surface assisted movable antenna direction modulation method, characterized in that, The specific steps are as follows: Step 1, a direction modulation network equipped with a movable antenna; Step 2, establish a receiving signal model of the active intelligent reflecting surface assisted movable antenna system; Step 3, use the receiving signal model to derive the security performance index, i.e. the security rate; Step 4, design an optimization scheme according to the security performance index; Step 5, use the compressive sensing technology to optimize the movable antenna position and the transmitting end weight coefficient through singular value decomposition; Step 6, optimize the intelligent reflecting surface phase shift matrix through the transmission rate that can be achieved by fixing the legitimate user. The direction modulation network of the movable antenna in step 1 is as follows: The active intelligent reflecting surface assisted base station transmits confidential information to the legitimate user while sending artificial noise to effectively interfere with the eavesdropper, wherein the base station is equipped with a movable antenna; the confidential information reaches the legitimate user through two paths, namely the direct path and the reflection path through the intelligent reflecting surface; The step 2 is specifically: A receive signal model of an active intelligent reflecting surface assisted movable antenna system is established. Confidential information of a base station (BS) transmitter reaches a legitimate user through two paths, a direct path and a reflection path through an intelligent reflecting surface (RIS). The signal received by the legitimate user Bob is is: （1） where denotes the channels from RIS to Bob, from BS to RIS and from BS to Bob; and are the transpose and conjugate transpose operations, respectively; denotes the transmit-end weight vector, denotes the transmitted confidential symbol, denotes the smart reflecting surface phase shift matrix, and denote the electromagnetic interference at the smart reflecting surface and the noise experienced by the legitimate user, respectively; the signal received by the eavesdropper Eve is: （2） wherein denotes the channel from the RIS to Eve and from the BS to Eve, denotes the noise experienced by the eavesdropper; the subscript denotes the eavesdropper; The step 3 is specifically: The security performance index, i.e., the security rate, is derived using the received signal model; and the transmission rate achievable at Bob is derived using the obtained received signal and Shannon's formula is represented as: （3） wherein denotes the amplitude of the useful signal received at Bob, denotes the sum of the electromagnetic interference power and the noise power experienced by Bob, denotes the aggregate channel from the BS to Bob; The transmission rate that can be achieved at Eve is represented as: （4） wherein denotes the amplitude of the useful signal received at Eve, denotes the sum of the electromagnetic interference power and the noise power experienced by Eve, denotes the aggregate channel from the BS to Eve; Based on the achievable transmission rates at Bob and Eve, the secrecy rate is expressed as: （5） wherein represents a value greater than or equal to zero; The step 4 proposes to design an optimization scheme according to the security performance index, which is as follows: Under the condition of satisfying the maximum transmission power and the amplification coefficient constraint, the phase shift matrix of RIS and the weight vector at BS are jointly optimized to realize the position selection of the movable antenna array and the maximization of the secrecy rate, and the optimization problem can be represented as: （6） where constraint C1 represents the symbol designed at Bob, represents the legitimate information is rotated, constraint C2 represents the symbol synthesized at Eve, constraints C3 and C5 represent the threshold of the transmit power and the RIS amplification factor respectively, and C4 represents the threshold of the norm selects the movable antennas, and the non-zero value represents the weight coefficient corresponding to the movable antenna, and the zero value weight corresponds to the position without antenna; and respectively represent the threshold of the transmit power, the number of movable antennas, and the threshold of the first adjustable amplitude and the amplification factor of the element on the active intelligent reflecting surface; represents the set of intelligent reflecting surface element indices, and respectively represent norm and norm; Introducing auxiliary variables The approximation of the optimization constraint for the antenna position is given by （7） wherein denotes a reweighting coefficient, is a norm, denotes a reweighted power threshold; an equivalent transformation of the secrecy rate maximization objective function is （8） where is the secrecy rate required by the system, is the amplitude of the signal received at the eavesdropper; then, the optimization problem is equivalently written as: （9） In step 5, the compressive sensing technology is used to optimize the movable antenna position and the transmitting end weight coefficient through singular value decomposition, which is as follows: Given the initial phase shift matrix, the maximization of the secrecy rate with respect to the transmitting end weight vector is described as: （10） wherein represents The first row of , ; and are the aggregate channels from the BS to Bob and Eve, respectively, and are the cascaded channels from the BS to the user and the eavesdropper, respectively; and represent the set of amplitudes and the set of signs, respectively; Then, through singular value decomposition and power constraint, the following is obtained: （11） wherein , is the re-weighted transmit weight coefficient vector; Then, using the root formula, the value of the objective function value is obtained as: （12） Wherein （13） wherein, and are auxiliary variables; denotes taking the real part; in the weight vector optimization phase at the transmitting end, given the phase shift matrix of the intelligent reflecting surface, the amplitude of the useful signal at Eve is designed , and the maximum secrecy rate is .

2. The reconfigurable smart surface assisted movable antenna direction modulation method of claim 1, wherein, In step 6, the intelligent reflecting surface phase shift matrix is optimized through the transmission rate that can be achieved by fixing the legitimate user, which is as follows: In order to improve the robustness of the system, even in the case of the decline of the channel quality of the direct path channel, the RIS reflection path can also be safely transmitted, and the channel reflected by the active intelligent reflecting surface is converted into: （14） wherein denotes a diagonalization operation, ; Then, given the transmitting end weight coefficient, the optimization problem with respect to the RIS phase shift matrix is described as: （15） wherein wherein （16） Then, the matrix （17） Consider the transmission power is , there are ; to singular value decomposition to obtain ; using the root formula, the value of the objective function is （18） Wherein （19） At this point, the two-stage variable optimization is completed, and the final secrecy rate is obtained by alternating optimization of the transmitting end weight vector and the RIS phase shift matrix.

3. A reconfigurable intelligent surface assisted movable antenna direction modulation system, characterized in that, The system is used to realize the reconfigurable intelligent surface assisted movable antenna direction modulation method of any one of claims 1-2, and the system comprises first module to sixth module, and the functions of each module are as follows: The first module is a direction modulation network equipped with a movable antenna; The second module is to establish a receiving signal model of the active intelligent reflecting surface assisted movable antenna system; The third module uses the receiving signal model to derive the security performance index, i.e. the security rate; The fourth module designs an optimization scheme according to the security performance index; The fifth module uses the compressive sensing technology to optimize the movable antenna position and the transmitting end weight coefficient through singular value decomposition; The sixth module optimizes the intelligent reflecting surface phase shift matrix through the transmission rate that can be achieved by fixing the legitimate user.

4. A mobile terminal comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the reconfigurable smart surface assisted movable antenna direction modulation method of any one of claims 1-2 when executing the program.

5. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the steps in the reconfigurable smart surface assisted movable antenna direction modulation method of any one of claims 1-2.

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