Secure transmission method of MMSE beamforming in DAM system with multiple IRS assistance

Abstract

This invention discloses a secure transmission method for MMSE beamforming in a DAM system with multiple IRS assistance. The method includes constructing a broadband communication system assisted by multiple intelligent reflector IRSs, establishing a channel impulse response model, and obtaining the received signal expression. Based on the model, the asymptotic orthogonality of the channel is derived. The transmitted signal is modulated using time-delay aligned modulation (DAM). Based on the asymptotic orthogonality conclusion, and combining the maximum ratio transmit beamforming and DAM modulation results, the secure transmission rate is calculated. The optimal power allocation value for each path is determined. The path-based MMSE beamforming vector and phase shift matrix are optimized one by one to maximize the secure transmission rate between legitimate users and eavesdroppers. The design method employed in this invention eliminates ISI in multipath channels to the greatest extent possible, achieving the maximum secure transmission rate between legitimate users and eavesdroppers, providing a secure and efficient transmission solution for multi-IRS-assisted DAM systems.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a secure transmission method for MMSE beamforming in a DAM system with multiple IRS assistance. Background Technology

[0002] Orthogonal frequency division multiplexing (OFDM), after decades of development, has become the mainstream modulation scheme due to its excellent spectral efficiency (SE), strong resistance to multipath effects, and low computational complexity. However, with the continuous evolution of communication technologies, problems such as peak-to-average power ratio (PAPR) and severe inter-carrier interference (ICI) in OFDM are making it difficult to meet the stringent requirements of future communications.

[0003] Therefore, delay-alignment modulation (DAM) has emerged as a revolutionary physical layer modulation technique. DAM enables precise time-domain design of transmitted signals, allowing signals propagating along different paths to be aligned and coherently superimposed at the receiver. This not only changes the traditional "counter-multipath" approach, but also adopts a "multipath-utilizing" strategy. Furthermore, it further improves signal strength (SE) by eliminating the need for cyclic prefix (CP) insertion, while simultaneously enhancing the signal-to-noise ratio (SNR) in high-speed environments and simplifying receiver operation through transmitter preprocessing.

[0004] Meanwhile, intelligent reflecting surface (IRS), as a planar structure composed of a large number of low-cost passive reflecting units, each of which can independently adjust the phase and amplitude of the incident electromagnetic wave, has been co-designed with many wireless communication systems to improve system throughput, signal power, signal-to-interference-plus-noise ratio (SINR), SE, energy efficiency (EE), quality of service (QoS), data transmission rate, and secret rate (SR).

[0005] However, due to the frequent occurrence of eavesdropping on transmitted information in the current communication environment, physical layer security (PLS) has become a core requirement for ensuring communication privacy. Existing research on DAM systems largely focuses on beamforming resource optimization to improve transmission rate and SNR, while research on PLS is extremely scarce. Furthermore, IRS-assisted secure transmission technologies mainly revolve around traditional multicarrier (MC) systems such as OFDM, and no research has yet been conducted on PLS in IRS-DAM systems. In addition, inter-symbol interference (ISI) caused by multipath channels remains a key issue affecting transmission quality. Traditional solutions either rely on complex channel equalization techniques or sacrifice transmission efficiency, making it difficult to achieve a balance between security and efficiency.

[0006] Therefore, research on PLS in RIS-DAM systems, and optimizing the system using beamforming to solve for the maximum secure transmission rate, is of great significance. However, if zero-forcing (ZF) beamforming is used for secure transmission, it requires assuming that the ISI term in the received signal is zero and using it as one of the constraints of the optimization problem. This is obviously inconsistent with the actual wireless communication channel conditions, and the resulting maximum secure transmission rate has no practical reference value. Therefore, it is essential to use minimum mean-square error (MMSE) beamforming to study the secure transmission problem of RIS-DAM systems. Summary of the Invention

[0007] The purpose of this invention is to provide a secure transmission method for MMSE beamforming in DAM systems with multiple IRS assistance. This method can effectively eliminate ISI caused by multipath channels and maximize the transmission rate between the legitimate user (hereinafter referred to as Bob) and the eavesdropper (Eve). Ultimately, it provides a transmission solution that combines security and efficiency for broadband communication systems with multiple IRS assistance.

[0008] To achieve the above objectives, this invention provides a secure transmission method for MMSE beamforming in a DAM system with multiple IRS assistance, comprising the following steps: S1. Construct a broadband communication system assisted by multiple intelligent reflectors (IRS), establish a channel impulse response model, and thus obtain the expression of the received signal; S2. Based on the channel impulse response model, the conclusion of channel asymptotic orthogonality is derived; S3. Modulate the transmitted signal using delay-aligned modulation (DAM) technology; S4. Based on the channel asymptotic orthogonality conclusion in S2, and combining the maximum ratio transmission (MRT) beamforming with the DAM-modulated transmitted signal in S3, calculate Bob's relationship with the [missing information - likely a specific signal or characteristic]. k One eavesdropper (Eve) k The system aims to ensure secure transmission rates between paths and determine the optimal power allocation for each path. S5. Using an alternating optimization AO method, optimize the MMSE beamforming vector and phase shift matrix one by one to maximize Bob and Eve. k Secure transmission rate between C s .

[0009] Preferably, S1 is as follows: S11, Multi-IRS assisted broadband communication systems include: N t A base station (BS) with one antenna. L One IRSs, single antenna Bob, K Each single-antenna Eves; any IRS contains M A passive reflective unit; the system is achieved through... L Each IRS assists the BS in secure communication with the single-antenna Bob. S12. Establish a channel impulse response model; S13. Obtain the expression for the received signal.

[0010] Preferably, S12 is as follows: (1) Channel impulse response of BS-Bob It can be represented as: ; in, ; and They are BS-Bob and the Each intelligent reflective surface The channel vector; and These are the complex coefficients of BS-Bob and the departure angle AoD, respectively; It is a unit impulse response; and These are channels BS-Bob and Discrete time delay; yes The phase shift matrix; yes The channel matrix, where and These are the receiver array response vector and the transmitter array response vector, respectively. , and They are Middle path The complex gain, angle of arrival AoA and AoD, j It is the imaginary unit; (2) BS-Eve k Channel impulse response It can be represented as: ; in, and They are BS-Eve k and the The first intelligent reflective surface - k An eavesdropper The channel vector; It is BS-Eve k The complex coefficients; and They are BS-Eve k and Discrete time delay.

[0011] Preferably, in S13, (1) the received signal at Bob The expression is: ; in, It is the Kronecker product; It is the transmitted signal vector; yes Additive white Gaussian noise (AWGN) in the context of noise. (2) No. k Eve the eavesdropper k Received signal at the location The expression is: ; in, yes AWGN in the middle.

[0012] Preferably, in S2, when the number of base station antennas At this time, the transmit array response vector They tend to be orthogonal, that is: Therefore: ; ; ; ;in, yes The channel matrix.

[0013] Preferably, S3 is as follows: S31. Introduce Delay-Aligned Modulation (DAM) to obtain the transmitted signal modulated by DAM. for: ; in, for L +1 path count; It is a signal carrier symbol that is independently and identically distributed (iid), and its normalized power satisfies: ; It is a path The transmitted beamforming vector; For symbolic sequence Time delay; S32. Determine the base station's transmit power as follows: ; in, P yes The upper limit of power; S33. Substitute the DAM-modulated transmitted signal from S31 into the received signal expression from S13 to obtain Bob and Eve's results. k The received signal after DAM modulation.

[0014] Preferably, S4 is as follows: S41, Regarding the path Transmit beamforming vector By performing MRT beamforming, we can obtain: ; in, and The first Power allocation factor and AoD of multipath; S42, respectively, for Bob and Eve k The received signal modulated by DAM is then scaled and simplified. S43. Based on the asymptotic orthogonality conclusion between the transmit array response vectors in S2 and their asymptotic orthogonality with the channel matrix, the scaled and simplified Bob and Eve in S42 are... k The received signal modulated by DAM is optimized to eliminate ISI; S44. Convert the original time-dispersive channel into an ISI-free AWGN channel, while simultaneously achieving this without requiring complex channel equalization or MC transmission. L Multipath gain is achieved by transmitting one more multipath signal component. S45. Based on the AWGN channel without ISI in S44, calculate Bob and Eve. k The secure transmission rate between paths is determined; based on the Cauchy-Schwarz inequality, the optimal power allocation value for each path is determined.

[0015] Preferably, S5 is as follows: S51. Determine the actual transmission scenario between Bob and Eve. k Secure transmission rate C s ; S52, Build to maximize secure transmission rate C s The optimization problem with the objective in mind; S53. Using the MMSE beamforming optimization algorithm based on AO, solve the IRS. l The optimal phase shift matrix Path-based MMSE optimal beamforming vector With maximum secure transmission rate .

[0016] The preferred optimization problem in S52 is as follows: ; in, It is a path The transmitted beamforming vector; yes The phase shift vector; t k It corresponds to Eve k An auxiliary variable; and They are respectively by L +1 and The vector formed, and has ; ; ; , They are respectively by L +1 and The vector formed; It is the set of all discrete time delay differences; It is the maximum value obtained by the difference between two discrete time delays; It is the difference between two discrete time delays; ; ; and It is two 1× N t ; It is a vector; It is by K A set consisting of 10 elements; C 1 represents the secure transmission rate. C s Inequality constraints; C 2 indicates that the sum of the beamforming vectors has an upper limit; C 3 is The constraints on the phase shift vector of each reflection unit.

[0017] Preferably, S53 is as follows: First, based on the Schul complement theorem, the coupling constraints of the secure transmission rate in logarithmic form are equivalently transformed into uncoupled constraints in matrix equation form. Secondly, an alternating optimization method for path-based optimization is adopted to optimize each path-based path one by one. MMSE beamforming vector as well as phase shift vector Specifically: (1) Fixed phase shift vector Optimize path-based MMSE beamforming vector The non-convex problem is transformed into a standard convex optimization problem by re-expressing the absolute value squared terms in the constraints using binomial inequalities, and then solved using convex optimization (CVX) tools. (2) Fixed path-based MMSE beamforming vector ,optimization phase shift vector The semi-definite relaxation (SDR) technique is used to eliminate non-affine terms in the constraints, while ignoring the rank-1 constraints in the original optimization problem, thus transforming the non-convex problem into a standard semi-definite program (SDP) problem, which is then solved using the CVX tool. (3) Repeat steps (1)-(2) until the number of iterations reaches the maximum number of iterations or the safe transmission rate value obtained from two adjacent iterations is less than the set tolerance, then output. The optimal phase shift matrix Path-based MMSE optimal beamforming vector With maximum secure transmission rate ; Therefore, this invention employs the aforementioned secure transmission method for MMSE beamforming in a DAM system with multiple IRS assistance, and uses the AO method to optimize path-based beamforming one by one. MMSE beamforming vector as well as phase shift vector This allows for the attainment of the maximum secure transmission rate. Theoretical analysis and numerical results show that, compared with the ZF beamforming scheme, the MMSE beamforming scheme not only better reflects the actual wireless channel conditions, but also achieves a good maximum secure transmission rate while suppressing ISI in the received signal to the greatest extent.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a system model diagram of the present invention; Figure 2 This is a graph showing how the system's secure transmission rate changes as the number of base station antennas increases; Figure 3 This is a graph showing how the system's secure transmission rate changes as the number of IRS units increases; Figure 4 This is a graph showing how the system's secure transmission rate changes as the signal-to-noise ratio at the receiving end increases; Figure 5 It is a graph showing how the system's secure transmission rate changes as the total system transmit power increases; Figure 6 This is a graph showing how the interference power at the eavesdropper's location changes as the total system transmit power increases. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Example The present invention provides a secure transmission method for MMSE beamforming in a DAM system with multiple IRS assistance, comprising the following steps: S1. Construct a broadband communication system with multiple IRS assistance, establish a channel impulse response model, and thus obtain the expression for the received signal.

[0022] S11, such as Figure 1 As shown, a multi-IRS-assisted broadband communication system includes: N t BS of one antenna L Each IRS contains 1 IRSs, and each IRS contains 12 IRSs. M One passive reflector element, one single antenna Bob. K Each single-antenna Eves; the broadband communication system via L Each IRS assists the BS in secure communication with the single-antenna Bob.

[0023] Each IRS contains M One passive reflective unit; The expression for the diagonal phase shift matrix is: ;in, yes The phase shift matrix; yes The Middle m Phase shift of each reflecting unit, ; ; j It is the imaginary unit.

[0024] S12. Establish a channel impulse response model.

[0025] (1) Channel impulse response of BS-Bob As shown below: ; in, ; and They are BS-Bob and The channel vector; and These are the complex coefficients of BS-Bob and the departure angle AoD, respectively; δ [ n [This is] the unit impulse response; n It is a time index; and These are channels BS-Bob and Discrete time delay; yes The channel matrix, , and They are Middle path Complex gain, AoA, and AoD, and These are the receiver array response vector and the transmitter array response vector, respectively.

[0026] (2) BS-Eve k Channel impulse response It can be represented as: ; in, and They are BS-Eve k and The channel vector; It is BS-Eve k The complex coefficients; and They are BS-Eve k and Discrete time delay.

[0027] S13. Obtain the expression for the received signal.

[0028] Assume the transmitted signal is The received signal at Bob's location The expression is: ; in, It is the Kronecker product; yes AWGN in the middle.

[0029] Eve k Received signal at the location The expression is: ; in, yes Additive white Gaussian noise (AWGN) in the context of noise.

[0030] S2. Based on the channel impulse response model, the asymptotic orthogonality conclusion is derived.

[0031] when At this time, the transmit array response vector They tend to be orthogonal, that is: Therefore: ; ; ; ;in, yes The channel matrix.

[0032] S3. Modulate the transmitted signal using Delay Alignment Modulation (DAM) technology.

[0033] S31. Introduce Delay-Aligned Modulation (DAM) and transmit the signal. This can be further expressed as: ; in, for L +1 path count; It is an independent and identically distributed (iid) signal carrier symbol whose normalized power satisfies: ; It is a path l ’ The transmitted beamforming vector; It is a symbol sequence The time delay.

[0034] S32. Determine the base station's transmit power as follows: ; in, P yes The maximum power that can be achieved.

[0035] S33. Substitute the DAM-modulated transmitted signal from S31 into the received signal expression from S13 to obtain the DAM-modulated signals for Bob and Eve. k The received signal at the location is shown below: (1) The received signal at Bob's location It can be represented as: ; in, express In this situation, yes The maximum discrete time delay of the channel; It is the transmit beamforming vector for path 0; express Excluded Path All other multipaths; ,in, ; yes The phase shift vector satisfies .

[0036] (2) Eve k Received signal at the location It can be represented as: ; in,( b )express The situation; ,in, .

[0037] According to the above formula, when the receiver signal is in When locked, Bob and Eve k The received signals at all locations contain severe ISI terms, while... In the MIMO architecture, the ISI term can be effectively eliminated through the asymptotic orthogonality conclusion.

[0038] S4. Based on the channel asymptotic orthogonality conclusion of S2, and combined with the transmitted signal after MRT beamforming and DAM modulation of S3, calculate the safe transmission rate; and determine the optimal power allocation value for each path.

[0039] S41, to By performing MRT beamforming, we can obtain: ; in, and The first l ’ Power distribution factor and AoD of multipath.

[0040] Therefore: ; ; ; in, and BS-Bob and BS-Eve respectively k The conjugate of the complex coefficients; It is the power allocation coefficient for path 0.

[0041] S42, respectively, for Bob and Eve k The received signal is scaled and simplified.

[0042] First, the MRT beamforming Substitute the values ​​of Bob and Eve after DAM modulation into the values ​​respectively. k The expression for the received signal at the location, and the received signal according to... Scaling yields Bob and Eve after satisfying the asymptotic orthogonality condition. k The expressions for the received signals at each location are as follows: ; ; Secondly, multiply the above expressions by... Get Bob and Eve kThe received signal expression at the location and , respectively represented as: ; .

[0043] S43. Based on the asymptotic orthogonality conclusion between the transmit array response vectors in S2 and its asymptotic orthogonality conclusion with the channel matrix, the scaled and simplified Bob and Eve in S42 are... k The received signal after DAM modulation is optimized to eliminate ISI.

[0044] By leveraging the asymptotic orthogonality of the array response vector and the channel matrix, the MRT beamforming... Substitute Bob and Eve after DAM modulation k By scaling the received signal expression at the specified location, it can be seen that the ISI term in the received signal has been successfully eliminated.

[0045] S44. Convert the original time-dispersive channel into an ISI-free AWGN channel, while simultaneously achieving this without requiring complex channel equalization or MC transmission. L Multipath gain is obtained by transmitting one multipath signal component.

[0046] S45. Based on the AWGN channel without ISI in S44, calculate Bob and Eve. k To ensure secure transmission rates, the optimal power allocation value for each path is determined based on the Cauchy-Schwarz inequality.

[0047] (1) Bob and Eve k The secure transmission rate between them is: ; in, , and Bob and Eve k The expressions for SINR at each location are as follows: ; ; in, , , Represent , , The m One element; It is the AWGN power in the signal.

[0048] (b) are constraints based on the asymptotic orthogonality of the array response vectors, and the optimal power allocation values ​​for each path are obtained through the Cauchy-Schwarz inequality.

[0049] The 0th path and the 1st path corresponding to Bob's location path( ) optimal power allocation value and They can be represented as follows: ; in, and These are the 0th and 1st paths corresponding to Bob, respectively. Complex coefficients of the radius.

[0050] Eve k The corresponding 0th path and the 1st path Optimal power allocation value of the path and They can be represented as follows: ; in, yes The channel vector.

[0051] Because the asymptotic orthogonality conclusion used in S4 to eliminate ISI is... This condition is only valid under certain circumstances, but it is not always met in actual communication. Therefore, MMSE is usually used to optimize the beamforming vector and phase shift matrix to obtain the maximum secure transmission rate. .

[0052] S5. Employ an alternating optimization AO method to optimize path-based optimizations one by one. l ’ MMSE beamforming vector and phase shift matrix Maximize Bob and Eve k Between C s .

[0053] S51. Determine the actual transmission scenario between Bob and Eve. k Secure transmission rate between C s .

[0054] Bob and Eve k The received signals after DAM modulation are re-represented as follows: ; ; in, and They are respectively by L +1 and The vector formed, and has , , ; , They are respectively from L +1 and The vector formed; and we have It is a set consisting of all discrete time delay differences; The maximum possible value of the difference between two discrete time delays; The difference between two discrete time delays; ; ; and It is two 1× N t ; It is a vector; It is by K A set consisting of 100 elements.

[0055] Based on the above definition, secure transmission rate C s It can be represented as: ; in, It corresponds to Eve k An auxiliary variable.

[0056] S52, Build to maximize secure transmission rate C s The optimization problem is aimed at the objective.

[0057] The PLS optimization problem of MMSE-DAM (Minimum Mean Square Error-Delay Alignment Modulation) can be described as follows: ; in, It is a path The transmitted beamforming vector; It is IRS l The phase shift vector; C 1 represents the secure transmission rate. C s Inequality constraints; C2 indicates that the sum of the beamforming vectors has an upper limit; C 3 is The constraints on the phase shift vector of each reflection unit.

[0058] It is not difficult to see that the above All three constraints in the problem have non-convexity issues and need to be optimized for convexity one by one.

[0059] S53. Using the MMSE beamforming optimization algorithm based on AO, solve the IRS. l The optimal phase shift matrix Path-based MMSE optimal beamforming vector With maximum secure transmission rate .

[0060] First of all, for C 1. According to Shure's Complement theorem, after removing the logarithmic form, it can be transformed into the following matrix form: .

[0061] Secondly, the MMSE beamforming optimization algorithm based on AO optimizes path-based beamforming one by one. MMSE beamforming vector and the phase shift vector of IRSl .

[0062] (1) Fixed phase shift vector Optimize path-based MMSE beamforming vector .

[0063] For a given IRS phase shift vector At this time This can be further expressed as: ; in, The absolute value square term in the equation can be expressed by the binomial inequality as follows: ; ;in, ; ; and They are and The first in l ’ Dimensional elements; , , , These represent the values ​​of the corresponding vectors at that location. This indicates taking the real part.

[0064] then, It can be rewritten as: ; in, A 1. B 1. C 1. D 1 is The result of expanding the matrix vector at the corresponding position using the binomial inequality is as follows: ; ; ; ; in, ; ; and They are respectively and The first in Dimensional elements; , , , These represent the values ​​of the corresponding vectors at that location.

[0065] Similarly, The absolute value square term in the equation can also be reformulated using the binomial inequality as: ; in, It means except The rest L The sum of beamforming vectors for each path; , These represent the values ​​of the corresponding vectors at that location.

[0066] thus, It can be converted into: ; At this point, It is a standard convex optimization problem that can be solved using the CVX tool.

[0067] (2) Fixed path-based MMSE beamforming vector ,optimization phase shift vector .

[0068] For a given path-based MMSE beamforming vector At this time This can be further expressed as: .

[0069] In order to eliminate Non-affine terms in ,right and Perform the following transformations respectively: ; ; in, and They are, except for the path Apart from that, the rest L The sum of the products of the two vectors corresponding to each path; SDR technology was used in this area; and There are two respectively N t A vector of size ×1; and There are two respectively M A matrix of order +1.

[0070] at the same time, It can be represented in the following form: ; in, And satisfy ; ; and They are, except for the path Apart from that, the rest L The sum of the products of the two vectors corresponding to each path; and There are two respectively M A matrix of order +1.

[0071] If we ignore the constraint that has a rank of 1 ,but It can be transformed into: .

[0072] At this point, A standard SDP can be solved using the CVX tool.

[0073] The MMSE beamforming optimization algorithm based on AO is shown below: 1. Input: Optimization variables Auxiliary variables and Initial iteration count Maximum number of iterations I Tolerance ε .

[0074] 2. Given ,get .

[0075] 3. Initialization , ,calculate .

[0076] 4. Loop: When or At that time, execute: 5. Given ,according to get .

[0077] 6. Given ,according to get .

[0078] 7. Based on ,calculate .

[0079] 8. .

[0080] 9. End the loop.

[0081] 10. Return .

[0082] 11. Output: , .

[0083] To verify the characteristics of MMSE beamforming and the performance gain of the DAM system brought by the multi-IRS auxiliary scheme, different parameters were changed, such as the number of BS antennas. N t Number of IRSs reflective units L Signal-to-noise ratio (SNR) and total transmit power P t The maximum secure transmission rate of the system under different conditions was compared and analyzed. Based on experimental data, curves of the secure transmission rate as a function of parameters and curves of interference power at the eavesdropper's location were generated, such as... Figure 2-6 As shown, the secure transmission capability and anti-interference capability under different parameter conditions are intuitively presented.

[0084] Therefore, this invention employs the aforementioned secure transmission method for MMSE beamforming in a DAM system with multiple IRS assistance, by optimizing the path-based... MMSE beamforming vector and phase shift vector Optimization was performed to obtain the maximum secure transmission rate of the system under MMSE beamforming. Theoretical analysis and numerical results show that, compared with the ZF-based beamforming scheme, the MMSE-based beamforming scheme adopted in this invention not only better reflects the actual wireless channel conditions, but also achieves a good maximum secure transmission rate while suppressing ISI in the received signal to the greatest extent. This provides a transmission solution that combines security and efficiency for multi-IRS-assisted broadband communication systems.

[0085] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A secure transmission method for MMSE beamforming in a DAM system with multiple IRS assistance, characterized in that, Includes the following steps: S1. Construct a broadband communication system assisted by multiple intelligent reflectors (IRS), establish a channel impulse response model, and thus obtain the expression of the received signal; S11, a broadband communication system assisted by multiple intelligent reflectors (IRS) includes: N t Base station BS with one antenna L Multiple intelligent reflective surface IRSs, each IRS containing M One passive reflector element, one single-antenna legitimate user Bob, K A single-antenna eavesdropper, Eves; the broadband communication system via... L Multiple intelligent reflective surface (IRSs) assist the base station (BS) in secure communication with Bob, a legitimate user with a single antenna. S12. Establish a channel impulse response model; S12 specifically refers to: (1) Channel impulse response of base station - legitimate user BS-Bob It can be represented as: ； in, ; and They are BS-Bob and the Intelligent reflective surface - legitimate user IRS l -Bob's channel vector; and These are the complex coefficients of BS-Bob and the departure angle AoD, respectively; It is a unit impulse response; n It is a time index; and These are the channels BS-Bob and IRS. l - Bob's discrete time delay; yes The phase shift matrix; It is a base station - the Each intelligent reflective surface The channel matrix, where, and These are the receiver array response vector and the transmitter array response vector, respectively. , and They are The Middle Complex gain of the path, angle of arrival AoA and AoD, j It is the imaginary unit; (2) Base station - the k A wiretap by BS-Eve k Channel impulse response It can be represented as: ； in, and They are BS-Eve k and the The first intelligent reflective surface - k An eavesdropper The channel vector; It is BS-Eve k The complex coefficients; and They are BS-Eve k and Discrete time delay; S13. Obtain the expression for the received signal; S13 specifically refers to: (1) Received signal at legitimate user Bob's location It can be represented as: ； in, It is the Kronecker product; It is the transmitted signal vector; yes Additive white Gaussian noise (AWGN) in the middle; (2) No. k Eve the eavesdropper k Received signal at the location It can be represented as: ； in, yes Additive white Gaussian noise (AWGN) in the middle; S2. Based on the channel impulse response model, the conclusion of channel asymptotic orthogonality is derived; S3. Modulate the transmitted signal using delay-aligned modulation (DAM) technology; S4. Based on the channel asymptotic orthogonality conclusion of S2, and combining the maximum transmit ratio MRT beamforming with the DAM modulated transmit signal of S3, calculate the relationship between legitimate user Bob and the first... k Eve the eavesdropper k Determine the secure transmission rate between paths and the optimal power allocation value for each path. S5. Using an alternating AO optimization method, the path-based MMSE beamforming vector and phase shift matrix are optimized one by one to maximize the relationship between legitimate user Bob and the first... k Eve the eavesdropper k Secure transmission rate between C s ; S51. Determine the legitimate user Bob and the first in the actual transmission scenario. k Eve the eavesdropper k Secure transmission rate between C s The secure transmission rate Cs is represented as: ； in, It corresponds to Eve k An auxiliary variable; S52, Build to maximize secure transmission rate C s The optimization problem with the objective in mind; The optimization problem in S52 is as follows: ； in, It is a path The transmitted beamforming vector; yes The phase shift vector; t k For Eve k An auxiliary variable; and They are respectively by L +1 and The vector formed, and has ; ; ; , They are respectively from L +1 and The vector formed; and we have It is the set of all discrete time delay differences; The maximum value obtained by the difference between two discrete time delays; The difference between two discrete time delays; ; ; and It is two 1× N t ; It is a vector; It is by K A set consisting of 10 elements; C 1 represents the secure transmission rate. C s Inequality constraints; C 2 indicates that the sum of the beamforming vectors has an upper limit; C 3 is Constraints on the phase shift vector of each reflecting unit; S53. Using the MMSE beamforming optimization algorithm based on AO, solve the IRS. l The optimal phase shift matrix Path-based MMSE optimal beamforming vector With maximum secure transmission rate ; S53 specifically refers to: First, based on the Schul complement theorem, the coupling constraints of the secure transmission rate in logarithmic form are equivalently transformed into uncoupled constraints in matrix equation form. Secondly, the MMSE beamforming optimization algorithm based on AO optimizes path-based beamforming one by one. MMSE beamforming vector as well as phase shift vector Specifically: (1) Fixed phase shift vector Optimize path-based MMSE beamforming vector The non-convex problem is transformed into a standard convex optimization problem by re-expressing the absolute value squared terms in the constraints using binomial inequalities, and then solved using the convex optimization CVX tool. (2) Fixed path-based MMSE beamforming vector ,optimization phase shift vector The semidefinite relaxation SDR technique is used to eliminate non-affine terms in the constraints, while ignoring the rank-1 constraints in the original optimization problem, thus transforming the non-convex problem into a standard semidefinite programming problem, which is then solved using the CVX tool. (3) Repeat steps (1)-(2) until the number of iterations reaches the maximum number of iterations or the safe transmission rate value obtained from two adjacent iterations is less than the set tolerance, then output. The optimal phase shift matrix Path-based MMSE optimal beamforming vector With maximum secure transmission rate .

2. The secure transmission method for MMSE beamforming in a DAM system with multiple IRS assistance according to claim 1, characterized in that, In S2, when the number of base station antennas At this time, the transmit array response vector They tend to be orthogonal, that is: Therefore: ; ; ; ; in, yes The channel matrix.

3. The secure transmission method for MMSE beamforming in a DAM system with multiple IRS assistance according to claim 2, characterized in that, S3 specifically refers to: S31. Introduce Delay-Aligned Modulation (DAM) to obtain the transmitted signal modulated by DAM. for: ； in, for L +1 path count; These are independently and identically distributed signal carrier symbols, and their normalized power satisfies: ; It is a path The transmitted beamforming vector; For symbolic sequence Time delay; S32. Determine the base station's transmit power as follows: ； in, P yes The upper limit of power; S33. Substitute the DAM-modulated transmitted signal from S31 into the received signal expression from S13 to obtain the legitimate user Bob and the... k Eve the eavesdropper k The received signal after DAM modulation.

4. The secure transmission method for MMSE beamforming in a DAM system with multiple IRS assistance according to claim 3, characterized in that, S4 specifically refers to: S41, Regarding the path Transmit beamforming vector By performing beamforming on the maximum transmit ratio MRT, we can obtain: ； in, and The first Power allocation factor and AoD for each path; S42, respectively, for the legitimate user Bob and the... k Eve the eavesdropper k The received signal modulated by DAM is then scaled and simplified. S43. Based on the asymptotic orthogonality conclusion between the transmit array response vectors in S2 and their asymptotic orthogonality with the channel matrix, the scaled and simplified Bob and Eve in S42 are... k The received signal after DAM modulation is optimized to eliminate inter-symbol interference (ISI) in the received signal; S44. Convert the original time-dispersive channel into an ISI-free AWGN channel, while simultaneously achieving this without requiring complex channel equalization or multi-carrier MC transmission. L Multipath gain is achieved by transmitting one more multipath signal component. S45. Based on the AWGN channel without ISI in S44, calculate the relationship between legitimate user Bob and the... k Eve the eavesdropper k The safe transmission rate between them; and the optimal power allocation value for each path is determined based on the Cauchy-Schwarz inequality.

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