Symbol-level precoding-based general-inductance integrated safety waveform design method

Abstract

The invention provides a symbol-level precoding-based communication and inductance integrated safety waveform design method. The method comprises the following steps of: designing and maximizing a minimum value in signal to interference plus noise ratios (SINR) of all target echoes as a target function; the objective function is used for ensuring perceptual performance of the system; the constraint conditions for setting the target function comprise that the communication performance constraint is realized by setting a minimum communication quality of service (QoS) requirement; according to the security constraint, a received signal at a radar target is fitted with random noise, so that a symbol received by the radar target is approximate to complex Gaussian distribution; setting the energy of the transmitted waveform to be not greater than the total transmitting power by the power constraint; and solving the target function meeting the constraint condition to obtain a transmitted signal vector and a scaling factor for controlling a transmitted waveform to complete waveform design. According to the method, good cooperation of communication and sensing functions can be realized under the condition of limited spectrum resources and power, and eavesdropping of a malicious sensing target to communication information is effectively prevented while stable communication and accurate sensing are ensured.

Description

Technical Field

[0001] The present invention relates to electromagnetic wave design technology, in particular to synaesthesia integrated safety waveform design technology. Background Art

[0002] With the widespread application of fifth-generation communication technology, the demand for high-speed, stable, and low-latency communications has been greatly met. However, facing the future of massive data transmission and diverse application scenarios (such as industrial Internet of Things, intelligent transportation, virtual reality, etc.), existing communication technologies still face challenges in spectrum efficiency and energy efficiency. At the same time, radar perception technology plays an important role in military and civilian fields (such as autonomous driving and air traffic control), but traditional radar systems have problems such as spectrum interference and waste of hardware resources. ISAC technology, which integrates communication and perception functions by sharing hardware platforms and spectrum resources, can reduce equipment costs, improve resource utilization, and tap into the synergistic gains of communication and perception. However, existing ISAC systems still face challenges in waveform design, such as the difficulty in balancing communication and perception performance and security threats. A new waveform design method is urgently needed to improve the overall performance of the system.

[0003] While current ISAC systems can achieve both communication and perception, they still face deficiencies in secure waveform design. Traditional ISAC waveform design faces a fundamental contradiction: Perception requires directing beam energy toward a target. However, when these targets, such as unauthorized vehicles or drones, become potential eavesdroppers, the communication information carried in the waveform faces a serious risk of leakage.

[0004] Symbol-level precoding (SLP) dynamically adjusts the precoding matrix for each transmitted symbol to optimize system performance by leveraging channel state information (CSI) and the characteristics of the symbol itself. Unlike traditional precoding, SLP independently optimizes the precoding strategy within each symbol period.

[0005] Existing security waveform designs are mainly based on traditional precoding technology and have not yet fully utilized the technical advantages of SLP. Summary of the Invention

[0006] SLP technology can fully utilize communication information, providing a new possibility for resolving this security conflict. However, research on the application of SLP in ISAC security waveform design is still limited. This makes it difficult for the system to effectively prevent information leakage while ensuring perception performance, restricting the application and expansion of ISAC technology in security-sensitive scenarios. The technical problem to be solved by this present invention is to provide a new security waveform design scheme that combines SLP technology with the ISAC system.

[0007] The technical solution adopted by the present invention to solve the above technical problems is a method for designing a synaesthesia-integrated security waveform based on symbol-level precoding, comprising the following steps:

[0008] 1) Set the base station's transmitting and receiving antennas to form a uniform linear array (ULA); collect transmitting channel information, all communication user data, radar targets, and clutter source locations, treating radar targets as potential eavesdroppers; and set system parameters.

[0009] 2) Designing an objective function that maximizes the minimum SINR of all target echoes; the objective function is used to ensure the perceptual performance of the system;

[0010] 3) Setting the constraints of the objective function includes: communication performance constraints, security constraints, and power constraints;

[0011] The communication performance constraint sets a minimum communication service quality QoS requirement and ensures that the received signal is greater than or equal to the minimum communication service quality QoS requirement, so that the received signal is kept away from the decision boundary;

[0012] The safety constraint is achieved by fitting the received signal at the radar target with random noise so that the symbols received by the radar target are approximately distributed in a complex Gaussian manner.

[0013] The power constraint sets the energy of the transmitted waveform to be no greater than the total transmit power;

[0014] 4) Solve the objective function that satisfies the constraints, obtain the transmitted signal vector and the scaling factor used to control the transmission waveform to complete the waveform design.

[0015] Specifically, the objective function is:

[0016]

[0017] Where w is the space-time receiving filter at the base station, x is the transmitted signal vector, d is the scaling factor, is the variance of the additive white Gaussian noise at the receiving antenna, is the variance of the additive white Gaussian noise at the oth radar target, A is the steering matrix of the receiving antenna and the transmitting antenna on the base station; θ0 represents the azimuth angle of the oth radar target, and the set Θ is the set of angles of all radar targets to be detected.

[0018] Specifically, the system parameters set in step 1) include the number of transmitting antennas N of the base station s and the number of receiving antennas N r , the number of users K u , the number of clutter sources M, the communication block length L, the symbol error rate SNR threshold Γ, the k-th user angle θ kRange, the oth radar target angle θ0 Range, the mth clutter angle θ m Range, number of radar targets K t , total power P, fitting noise error threshold∈.

[0019] Specifically, the communication performance constraints are:

[0020]

[0021] in, represents the real part operation, Indicates the operation of taking the imaginary part, represents the MISO channel vector between the base station and the kth communication user, H represents the conjugate transpose, x[n] is the nth subvector in x, e is a natural constant, j is an imaginary unit, Φ is the offset between the decision boundary and the symbol phase, ∠s k [n] is the symbol point s modulated by the kth communication user k The angle between the direction of [n] and the real axis is ∠s k [n], β k is the minimum communication service quality QoS requirement, is the minimum communication service quality QoS requirement pre-set for the kth user, σ z is the standard deviation of the additive white Gaussian noise at the kth user, It means any;

[0022] Specifically, the security constraints are:

[0023]

[0024] Among them, a s is the transmission steering vector of the ULA antenna, u[n] is the nth element of the independent and identically distributed sample u of the standard complex Gaussian distribution;

[0025] Specifically, the power constraints are:

[0026] ||x|| 2 ≤P

[0027] Here, ||·|| is the L2 norm.

[0028] This invention employs a unique pseudo-noise security constraint. By making the symbols received by an eavesdropper resemble a complex Gaussian distribution, it prevents them from effectively intercepting user communications and even detecting communication activity within the ISAC waveform, achieving a similar covert communication effect. Using SLP technology in waveform design, it fully utilizes communication information, reduces the symbol error rate, and improves target detection performance.

[0029] Furthermore, a method is provided for simplifying the solution of the objective function by introducing auxiliary variables to replace the minimum operation in the objective function.

[0030] In the process of solving the objective function, the objective function is processed using the optimization-minimization MM algorithm framework;

[0031] The proximal distance PDA algorithm is used to iteratively process each constraint, and the projection mean of the current solution on each constraint set is calculated. Then, the penalty variable ζ is introduced to transform the original problem into an unconstrained subproblem, and an efficient solution is achieved in a closed-form iterative method.

[0032] The beneficial effect of the present invention is that it can achieve good coordination between communication and perception functions under limited spectrum resources and power conditions, while ensuring stable communication and accurate perception, and effectively prevent malicious perception targets from eavesdropping on communication information. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of the application scenario of the present invention;

[0034] Figure 2 Flowchart of the present invention;

[0035] Figure 3 This is a schematic diagram of the comparison of instantaneous transmission beam patterns;

[0036] Figure 4 This is a schematic diagram of the SEP curve at the user end under PSK modulation;

[0037] Figure 5 (a) shows the eavesdropping effect of radar target on communication users under the Beamform method; Figure 5 (b) Eavesdropping effect of radar target on communication users under SLP method; Figure 5 (c) in the figure is the eavesdropping effect of the radar target on the communication user under the SECSL method;

[0038] Figure 6 is the JS divergence value of the received symbol distribution of the user and the target under QPSK modulation. DETAILED DESCRIPTION

[0039] Application scenarios of the present invention are as follows Figure 1 The specific description is as follows:

[0040] Assume there is a multiple-input single-output (MISO) communication-aware integrated downlink system: Consider a network equipped with N s Transmitting antennas and N rThe base station has a base station with 10 receiving antennas, which are arranged in a uniform linear array (ULA) with a spacing of Δ and a wavelength of λ′. In the same antenna array, the signal transmission and reception functions are realized in different time segments. In the initial stage, the base station transmits an integrated waveform that combines communication and perception functions. This waveform has the dual functions of communication and perception. On the one hand, it can transmit K u On the other hand, K s The base station detects malicious targets, which are themselves potential eavesdroppers and can use the communication information carried in the integrated waveform to eavesdrop on communicating users. After completing the transmission, the base station switches to radar reception mode to receive the echo signal reflected back from the target in order to estimate relevant target parameters (such as position and velocity). These malicious targets can be considered potential eavesdroppers, potentially intercepting information sent from the base station to legitimate users. At the same time, the presence of M independent clutter sources in the environment will interfere with the target echo signal received by the base station receiver.

[0041] set up Represents the transmitted signal vector. At the communication user, the signal received by the kth user in the nth time slot is expressed as:

[0042] y k [n]=h k x[n]+z c [n]

[0043] Here, represents the MISO channel vector between the base station and the kth communication user, we assume that h k It is a slow time-varying block-type Rician fading channel. Specifically, the channel remains constant within a relatively long time block, while the channel characteristics change slowly between different time blocks. is the additive Gaussian white noise at the kth user, with a mean of 0 and a variance of

[0044] SLP is based on the principle of constructive interference. In multi-user communication scenarios, harmful multi-user interference can be transformed into beneficial constructive signals, pushing the received signal away from its decision threshold, thereby reducing the communication user's symbol error rate (SER). When the distance between the noise-removed signal received by the communication user and the decision boundary closest to the signal point is greater than or equal to the set threshold, the user's symbol detection accuracy requirement is met, thereby ensuring system reliability. Taking QPSK modulation as an example, the communication performance indicator constraint can be expressed as:

[0045]

[0046] in is the minimum communication service quality QoS requirement pre-set for the kth user, Γ represents the SNR threshold. The offset between the decision boundary and the symbol phase Φ = π / M′, where M′ is the modulation order. The symbol point s after modulation by the kth user k The angle between the direction of [n] and the real axis is ∠s k [n]. represents the real part operation, Indicates the operation of taking the imaginary part, H represents the conjugate transpose, and j is the imaginary unit.

[0047] At the nth symbol time, the baseband signal vector at the radar receiving array can be expressed as:

[0048]

[0049] Among them, θ0 represents the azimuth angle of the oth target, θ m Denotes the azimuth angle of the mth clutter. Define the set Θ as the set of all target angles to be detected, that is, Complex amplitudes α0 and α m Corresponding to the target and the mth clutter respectively, and their second-order moments satisfy and Noise vector z r [n] has a mean of zero and a covariance matrix of The complex Gaussian distribution of The noise vector represents the additive white Gaussian noise at the receiving antenna. r (θ) and a s (θ) are the receiving and transmitting steering vectors of the ULA antenna at angle θ. The specific mathematical expressions are as follows:

[0050]

[0051] Where θ is the directional variable and e is a natural constant.

[0052] Furthermore, Where L is the block length, T is the transpose. Let is the space-time receiving filter at the base station, then the output after filtering by w is:

[0053]

[0054] where A is the steering matrix of the ULA antenna, defined as Here represents the Kronecker product, I N is the N-order identity matrix.

[0055] For radar systems, the goal is to extract target signals in complex clutter and noise environments. The signal-to-interference-and-noise ratio (SINR) quantifies the degree to which this goal is achieved: when the SINR is low, the interference signal is relatively strong, and the target signal may be overwhelmed by the interference, making it difficult for the radar to accurately detect the target, potentially resulting in a high probability of false alarms and missed alarms. When the SINR is high, the target signal is more prominent in the received signal, allowing the radar system to more reliably detect and track targets, thereby improving system performance. The output SINR for a single target can be expressed as:

[0056]

[0057] in As the covariance matrix of the clutter signal, the interference effect of the clutter source on the target signal at different angles is comprehensively considered.

[0058] We propose a secure transmission waveform design strategy from a signal processing perspective. In ISAC systems, since signals combine radar sensing and communication functions, there is a risk of interception by potential eavesdroppers. To address this, we design a unique transmission waveform constraint that forces the symbols received by an eavesdropper to approximate a complex Gaussian distribution. This prevents them from effectively acquiring user communications and even detecting communication activity within the ISAC waveform. Specifically, this constraint can be expressed as:

[0059]

[0060] Among them, ∈>0, the value of which has a direct impact on the strictness of the constraint and the control accuracy of the noise similarity. is a scaling factor. Since it is closely related to the transmission waveform x[n], in the actual optimization process, it is necessary to jointly optimize x[n] at each moment n to ensure that the overall performance of the system is optimal. Its elements are independent and identically distributed samples from the standard complex Gaussian distribution, denoted as u~CN(0,I L ), where I L is the L-order identity matrix.

[0061] Assuming that the transmitter knows the channel information, the data of all communicating users, and the locations of the target and clutter sources, we formulate the following optimization problem:

[0062]

[0063] st

[0064]

[0065] ||x|| 2 ≤P

[0066] where ||·|| is the L2 norm, Indicates any.

[0067] It can be observed that the objective function of the problem is to maximize the minimum value of the SINR of multiple target echoes to ensure the perceptual performance of the system. This problem also contains three constraints: communication performance constraint, security constraint and power constraint. Among them, the communication performance constraint is achieved by setting an appropriate threshold value β k , keeping the received signal as far away from the decision boundary as possible, thereby ensuring the communication SER. The security constraint ensures the system's physical layer security (PLS) by fitting the received signal at the radar target with random noise. Finally, the power constraint limits the energy of the transmitted waveform, where P > 0 represents the total transmit power over the entire transmission block.

[0068] Once the optimization problem is determined, those skilled in the art can use existing tools to solve it. In the embodiment, the optimization is simplified and deformed before solving it.

[0069] When the transmitted waveform x is fixed, the original problem is transformed into a minimum variance distortion-free response problem with w as the variable. Its optimal solution can be expressed as a function of x: for any non-zero constant η:

[0070]

[0071] Substitute the optimal solution of w into the original problem and transform it into the following more concise form through a series of equivalent transformations:

[0072]

[0073] ||x|| 2 ≤P

[0074] When k is an even number, When k is an odd number,

[0075] To simplify the above max-min problem, we solve it using the epigraph form of the minimization problem. Specifically, we introduce an auxiliary variable γ, which replaces the minimum operation in the objective function. γ represents the lower bound of the value of the objective function on the set Θ. In this way, the original optimization problem is reformulated as:

[0076]

[0077] ||x|| 2 ≤P

[0078]

[0079] Since the last constraint is non-convex, we introduce the following notation to find its replacement function. Definition:

[0080]

[0081] At the tth iteration, x t is the x of the t-th iteration, then f(x,X) is at the point (x t ,X t ) is replaced by the upper bound function:

[0082]

[0083] Where Tr represents the trace of the matrix;

[0084]

[0085] At the tth iteration, the original problem can finally be expressed as:

[0086]

[0087] ||x t || 2 ≤P

[0088]

[0089] Describe the final expression of the objective function alone, that is, remove the iteration symbol t.

[0090] After the above derivation, the original problem can be solved with the Majorization-Minimization (MM) algorithm framework. Specifically, given the initial point x 0 Under the premise of , the above convex proxy problem is solved by iteration. For the number of iterations t = 0, 1, ..., the iterative calculation is continued until a pre-set stopping criterion is met.

[0091] In order to efficiently solve this multi-constrained convex proxy problem, we use the Proximal Distance Algorithm (PDA) to solve it. PDA calculates the projection mean of the current solution on each constraint set, and then transforms the original problem into an unconstrained subproblem by introducing a penalty term, and achieves efficient solution in a closed-form iterative manner. During the iteration process, the penalty term is used to optimize the objective while gradually approaching the feasible domain that satisfies the constraints. The core of determining the complexity of the PDA algorithm lies in whether the projection calculation of the constraints in each round of iteration can find a closed-form solution, and the process of calculating the iterative solution through the proximal operator. Based on this, we give the derivation process of the constraint projection calculation and the proximal operator solution for the current problem below. The details are as follows:

[0092] First determine the variables that need to be iteratively updated Except for the first iteration which uses the initial assignment, all subsequent iterations use the results of the previous iteration; for The nth subvector in ;

[0093] 1) Projection of constraint 1

[0094] Defining a projection

[0095] Given In order to get it The projection of , we need to solve the following problems:

[0096]

[0097] Assume Lagrangian function Where μ≥0 is the Lagrange multiplier. From this we can get the optimal solution y for the above projection * for:

[0098]

[0099] Among them, the optimal μ should satisfy There are two situations:

[0100] a) When μ=0, it indicates is the optimal solution to this problem and satisfies

[0101] b) When μ>0, in this case, we need to find The value of μ can be deduced as follows:

[0102]

[0103] In summary, the optimal solution y for the projection problem is * for:

[0104]

[0105] in

[0106] Traverse n=1,…,L, and for each n traverse k=1,…,2K u Get 2K u dimensional vector y * , and set y corresponding to n=1,…,L * The vector x1 is sequentially formed as the transmitted signal vector obtained by constraint-projection;

[0107] 2) Projection of Constraint 2

[0108] The projection problem can be written as:

[0109]

[0110] Let y = [x T [1],…,x T [L],d] T , The above problem can be transformed into:

[0111]

[0112] st‖By‖ 2 ≤L ∈

[0113] The intermediate matrix This is a quadratically constrained quadratic programming problem, and its solution is:

[0114]

[0115] in Is satisfied ‖By * ‖ 2 ≤L ∈ The optimal Lagrange multiplier of . For λ, there are two cases:

[0116] a) When λ = 0, it means Right now Already in the feasible set.

[0117] b) When λ>0, then Set BB H =UΣU H For BB H The singular value decomposition of . Then we have:

[0118]

[0119] Intermediate variables get Where the diagonal matrix Σ=Diag(σ1,…,σ i ,,σ r )≥0, ≥0 means it is a semi-positive definite matrix, r is BB H rank, For the i-th element y in , the optimal λ can be determined by bisection.

[0120] calculate:

[0121]

[0122] Then from y ★Take out the first L sub-vectors to form vector x2 as the transmitted signal vector obtained by constraint two projection, and transform y ＊ The last sub-vector in is used as the new scaling factor

[0123] 3) Projection of Constraint Three

[0124] The projection problem can be written as:

[0125]

[0126] Similarly, this is a quadratically constrained quadratic programming problem, and its solution is:

[0127]

[0128] The value of λ is divided into the following two cases:

[0129] a) When λ=0, it means ||x|| 2 ≤P, that is Already in the feasible set.

[0130] b) When λ>0, ||x|| 2 =P can be deduced but

[0131] In actual calculation,

[0132] The calculated vector x3 is used as the transmitted signal vector obtained by constrained three-projection.

[0133] 4) Projection of Constraint Four

[0134] The projection problem can be written as:

[0135]

[0136] Its Lagrangian function is expressed as:

[0137]

[0138] Where C represents the constant part on the right side of the inequality constraint in the original formula, that is, 2Tr(P e X t )-f(x t ,X t ). The update formulas for variables x and γ are:

[0139]

[0140] There are two cases for the value of λ:

[0141] a) When λ = 0, it means and Already in the feasible set.

[0142] b) When λ>0, since the updated formula brings back the original Lagrangian function and contains a quartic term related to λ, it is necessary to use Newton's method to iteratively solve the constructed Lagrangian function to obtain the optimal λ. Substituting the updated formula back into the constraints, we obtain the nonlinear equation for λ:

[0143]

[0144] Using Newton's method to solve the equation, the update formula is:

[0145]

[0146] Among them, g(λ k ) is the nonlinear equation to be solved, g′(λ k ) is the derivative of this equation, and the solution is obtained by iterative updating until convergence. After solving for λ, substituting it back into the update formula for the variables x and γ yields the solution to the projection problem.

[0147] In actual calculation, determine whether If so, then remain unchanged, otherwise, The calculated vector x4 is used as the transmitted signal vector obtained by the constrained three-projection, and the updated As a new auxiliary variable

[0148] 5) Obtaining the comprehensive result includes averaging the vectors x1, x2, x3 and x4 to update the iterative result of the transmitted signal vector Step 7 And the result from step 9

[0149] 6) Calculate the proximal operator

[0150] For comprehensive results, PDA needs to perform proximal mapping, and the formula is:

[0151]

[0152] The optimal solution γ can be easily obtained * and x * :

[0153]

[0154] In addition, the optimal solution d ＊ ,

[0155] In an iterative process, the optimal solution is output as a final iterative result, that is,

[0156] like Figure 2 As shown, the embodiment uses the MM algorithm as the outer loop and the PDA algorithm as the inner loop. The specific implementation steps of the waveform design are as follows:

[0157] Step 1: Input parameters. Number of base station transmitting antennas N t , the number of receiving antennas N r , the number of users K u , the number of clutter M = 2, the communication block length L. In terms of angle parameters, the user angle θ k =[-30°,30°], malicious target angle θ0 =[-25°,25°], clutter angle θ m =[-60°,60°], the number of malicious targets K t The power-related parameters are total power P = 100; SNR threshold Γ range is 0dB ~ 12dB. Other parameters are fitting noise error threshold ∈ = 0.1, noise power Clutter Energy The ratio of the antenna spacing to the carrier wavelength is Δ / λ′=1 / 2; the initial value of the penalty variable ζ is ζ0=2 and the maximum value is ζ max =2 30 .

[0158] Step 2: Calculate the threshold variable β in the communication performance constraint k , Γ represents a given SNR threshold.

[0159] Initialization steps of the MM algorithm:

[0160] Step 3: Initialize the number of iterations of the MM algorithm to t = 0, and randomly initialize x0 = x 0 ,γ0=γ 0 ,d0=d 0 , set the maximum number of iterations of the MM algorithm MMiter = 100 and the termination threshold of the MM algorithm ∈ 2;

[0161] The tth iteration step of the MM algorithm:

[0162] Step 4: Use x t , the non-convex constraints are linearized using the first-order Taylor expansion to obtain the expansion results, specifically:

[0163]

[0164] Among them, A, θ0, R and The explanation of is given in the previous reformulation of the optimization problem;

[0165] Initialization steps of the PDA algorithm:

[0166] Step 5: Initialize the number of iterations of the PDA algorithm i = 0, set the maximum number of iterations of the PDA algorithm K = 100, the PDA algorithm termination threshold value ∈ 1 and the penalty variable ζ = ζ0, and initialize The i-th iteration step of the PDA algorithm:

[0167] Step 6: Calculate the projection of constraint 1, specifically:

[0168] Traverse n=1,…,L, and for each n traverse k=1,…,2K u Get 2K u dimensional vector y * :

[0169] for The nth subvector in ; where, With h k The calculation of can be found in the previous projection part of 1) constraint 1;

[0170] Set y corresponding to n=1,…,L * The vector x1 is sequentially formed as the transmitted signal vector obtained by constraint-projection;

[0171] Step 7: Calculate the constrained second projection, specifically:

[0172] use and composition

[0173] calculate:

[0174] The calculation of B can be found in the previous projection part of constraint 2);

[0175] Then from y ★ Take out the first L sub-vectors to form vector x2 as the transmitted signal vector obtained by constraint two projection, and transform y ★ The last sub-vector in is used as the new scaling factor

[0176] Step 8: Calculate the constrained three projections, specifically:

[0177]

[0178] The calculated vector x3 is used as the transmitted signal vector obtained by constrained three-projection;

[0179] Step 9: Calculate the constrained four-projection, specifically:

[0180] Determine whether the expansion result obtained in step 4 is greater than or equal to Right now If so, then remain unchanged, otherwise, The calculated vector x4 is used as the transmitted signal vector obtained by constrained three-projection;

[0181] Step 10: Take the average of vectors x1, x2, x3 and x4 to get the value of the i-th iteration The result obtained in step 7 As the i-th iteration The result obtained in step 9 As the i-th iteration

[0182] Step 11: Obtain the optimal solution for the i-th iteration by calculating the proximal operator, i.e.

[0183] Step 12: Update PDA variables

[0184] Step 13: Update the penalty variable ζ new =min(ζ*2,ζ max ), and let ζ = ζ new ;

[0185] Step 14: Determine whether i+1 is equal to K. If so, end the i-th iteration of the PDA algorithm and let the output x new =x i+1 ,γ new =γ i+1 ,d new =d i+1 Then go to step 16; otherwise, update Then update i=i+1 and return to step 6;

[0186] Step 15: Determine ||x i+1 -x i || / ||x i Is ||≤∈1 true? If not, update Then update i=i+1 and return to step 6. If it is true, the i-th iteration of the PDA algorithm ends and the output x new =x i+1 ,γ new =γ i+1 ,d new =d i+1 Then proceed to step 16;

[0187] Step 16: Update MM variable x t+1 =xnew ,γ t+1 =γ new ,d t+1 =d new

[0188] Step 17: Determine whether the number of iterations t+1 is equal to MMeter. If so, set the output x t+1 ,γ t+1 ,d t+1 End the loop and go to step 19;

[0189] Step 18: Determine ||x t+1 -x t || / ||x t ||≤∈2,||γ t+1 -γ t Is ||≤∈2 true? If not, update t=t+1 and return to step 4. If true, go to step 19;

[0190] Step 19: Get the last iteration x t+1 ,γ t+1 ,d t+1 , using x t+1 As the transmitted signal vector and the scaling factor d used to control the transmission waveform t+1 The waveform design is finalized.

[0191] Simulation experiment

[0192] The present invention designs the transmit waveform x with the goal of maximizing the minimum SINR among multiple target echoes and ensuring that the user end meets the QoS requirements. In addition, we hope that the SER of the eavesdropping target is as high as possible.

[0193] The system settings are as follows: Number of base station transmitting antennas N t =15, the number of receiving antennas N r =15, number of users K u =2, the number of clutter M = 2, the communication block length L = 4. In terms of angle parameters, the user angle θ k =[-30°,30°], target angle θ t =[-25°,25°], clutter angle θ m =[-60°,60°], target number K t =2. The power-related parameters are total power P = 100; SNR threshold Γ range is 0dB ~ 12dB. Other parameters are fitting noise error threshold ∈ = 0.1, noise power Clutter Energy The ratio of the antenna spacing to the carrier wavelength is Δ / λ′ = 1 / 2. Unless otherwise specified, the target angle and user angle use the default values. We use SECSLP to refer to the algorithm designed in this paper, SLP to refer to the SLP algorithm without PLS constraints, and Beamform to refer to the traditional beamforming algorithm.

[0194] The instantaneous transmit beam pattern in the direction θ during the nth time slot is defined as follows:

[0195] P(θ;x[n])=x H [n]a(θ)a H (θ)x[n]

[0196] The SECSLP algorithm we designed is compared with the algorithms that only consider SLP and the Beamform algorithm. The angle range [-90°, 90°] is uniformly sampled with a sampling interval of 1°. By observing the instantaneous emission waveform at each angle, we can clearly understand the distribution of signal energy at different angles. The instantaneous emission pattern of the algorithm of the present invention compared with the existing SLP and Beamform algorithms is shown in the figure below. Figure 3 shown.

[0197] In this study, two target angles θ were set. t0 = -15° and θ t1 =15°, and the two communication user positions θ k0 = -30° and θ k1 =30°, and set the SNR threshold to 3dB.

[0198] In terms of radar performance, the SECSLP-based ISAC waveform design suffers from a certain loss in beam energy rate in the target direction compared to the Beamform algorithm and the standard SLP algorithm. However, from the perspective of the communication user, the SECSLP algorithm's beam energy is essentially the same as the other two algorithms, indicating no significant degradation in communication performance. Further comparison of the standard SLP and SECSLP waveforms reveals extremely similar beam pattern performance, demonstrating that the SECSLP algorithm ensures communication security without significantly negatively impacting perception capabilities. This demonstrates that the SECSLP algorithm successfully achieves an effective balance between communication security and perception performance, providing a new solution for secure waveform design in ISAC systems.

[0199] exist Figure 4Figure 2 shows the changing trends of the average user SER under the three methods. As the CI SNR threshold Γ increases, the SER decreases significantly, which is consistent with the relationship between signal quality and SNR in communication theory. Compared to the beamform algorithm, the two SLP-based algorithms optimize communication performance and reduce SER by converting MUI into a beneficial signal, pushing the received signal away from the decision threshold. However, the SECSLP algorithm with the PLS constraint achieves a higher SER than the standard SLP algorithm. This is because the PLS constraint increases coding complexity, sacrificing some communication efficiency to ensure security. This phenomenon provides guidance for subsequent optimization, such as reducing SER and improving communication efficiency while ensuring security.

[0200] exist Figure 5 In this paper, by calculating the symbol error rate of the symbols received by the eavesdropper relative to the actual information sent by the communicating user, the three methods are shown in detail. Based on the pre-designed position layout of users and eavesdroppers, two eavesdroppers will have a more significant eavesdropping effect on users who are closer to them.

[0201] Observations show that as the SNR threshold Γ increases, eavesdroppers' eavesdropping on communication users becomes increasingly severe. Because the SLP algorithm performs nonlinear processing on transmitted symbols, it possesses a certain degree of anti-eavesdropping capability compared to traditional beamforming techniques. However, at higher SNR levels, the traditional SLP algorithm's anti-eavesdropping performance remains unsatisfactory, with the eavesdropper's SER approaching 0.075. This value indicates that eavesdropping is still quite severe at this level, and communication content faces a significant risk of leakage. In sharp contrast, the SECSLP algorithm proposed in this chapter, by introducing the PLS constraint, successfully maintains the eavesdropper's SER at approximately 0.75, effectively suppressing eavesdropping on users and significantly improving communication security.

[0202] Next, we quantitatively analyze the symbol distributions received by the target and user. Specifically, we evaluate the structural similarity between the user and radar target by calculating the Jensen-Shannon (JS) divergence of the symbol distributions received by the user and radar target. To ensure the rigor and accuracy of the experiment, the symbol distribution received by the radar target is linearly scaled based on the symbol distribution received by the user before the calculation, so that the two are within the same range, allowing for a more effective comparison of their structural similarities. When calculating the JS divergence, the input complex signal is first converted into a two-dimensional point set. These point sets are then precisely aligned using Procrustes analysis. Kernel density estimation is then used to accurately estimate the probability density functions of the two point sets. Finally, the specific value of the JS divergence is calculated according to its definition.

[0203] from Figure 6It can be intuitively seen that SECSLP has a significantly higher JS divergence value compared to SLP and beamforming. A larger JS divergence value indicates a greater difference between the two distributions. This means that under the SECSLP algorithm, the symbol distribution received by the target differs significantly from the symbol distribution received by the user. This difference makes it difficult for an eavesdropper to effectively obtain the modulation method of the user's communication, thereby enhancing communication security and demonstrating the effectiveness of the SECSLP algorithm in improving communication security.

Claims

1. A synaesthesia-integrated security waveform design method based on symbol-level precoding, characterized in that: Including steps: 1) The base station's transmitting and receiving antennas are arranged in a uniform linear array (ULA). The system collects transmitting channel information, all communication user data, radar targets, and clutter source locations, treating radar targets as potential eavesdroppers. Set system parameters; 2) Design the objective function to maximize the minimum value of the signal-to-interference-and-noise ratio (SINR) of all target echoes; The objective function is used to ensure the perceived performance of the system; 3) Setting the constraints of the objective function includes: communication performance constraints, security constraints, and power constraints; The communication performance constraint sets a minimum communication service quality QoS requirement and ensures that the received signal is greater than or equal to the minimum communication service quality QoS requirement, so that the received signal is kept away from the decision boundary; The safety constraint is achieved by fitting the received signal at the radar target with random noise so that the symbols received by the radar target are approximately distributed in a complex Gaussian manner. The power constraint sets the energy of the transmitted waveform to be no greater than the total transmit power; 4) Solve the objective function that satisfies the constraints, obtain the transmitted signal vector and the scaling factor used to control the transmission waveform to complete the waveform design.

2. The method according to claim 1, wherein: The objective function is: Where w is the space-time receiving filter at the base station, x is the transmitted signal vector, d is the scaling factor, is the variance of the additive white Gaussian noise at the receiving antenna, is the variance of the additive white Gaussian noise at the oth radar target, A is the steering matrix of the receiving antenna and the transmitting antenna on the base station; θ0 represents the azimuth angle of the oth radar target, and the set Θ is the set of angles of all radar targets to be detected.

3. The method according to claim 2, wherein: The system parameters set in step 1) include the number of transmitting antennas N of the base station s and the number of receiving antennas N r , the number of users K u , the number of clutter sources M, the communication block length L, the symbol error rate SNR threshold Γ, the k-th user angle θ k Range, the oth radar target angle θ0 Range, the mth clutter angle θ m Range, number of radar targets K t , total power P, fitting noise error threshold∈.

4. The method according to claim 3, wherein: The communication performance constraints are as follows: in, represents the real part operation, Indicates the operation of taking the imaginary part, represents the MISO channel vector between the base station and the kth communication user, H represents the conjugate transpose, x[n] is the nth subvector in x, e is a natural constant, j is an imaginary unit, Φ is the offset between the decision boundary and the symbol phase, ∠s k [n] is the symbol point s modulated by the kth communication user k The angle between the direction of [n] and the real axis is ∠s k [n], β k is the minimum communication service quality QoS requirement, is the minimum communication service quality QoS requirement pre-set for the kth user, σ z is the standard deviation of the additive white Gaussian noise at the kth user, It means any; The specific security constraints are: Among them, a s is the transmission steering vector of the ULA antenna, u[n] is the nth element of the independent and identically distributed sample u of the standard complex Gaussian distribution; The power constraints are as follows: ||x|| 2 ≤P Here, ||·|| is the L2 norm.

5. The method according to claim 4, wherein: To simplify the solution of the objective function, an auxiliary variable γ is introduced to replace the minimum operation in the objective function. γ represents the lower bound of the value of the objective function on the set Θ. Then, intermediate variables X, Ψ(X), and f(x,X) are introduced. X=xx H , Among them, I NrL Indicates the order is N r L is the identity matrix, R is the covariance matrix of the clutter signal; The objective function is simplified as: Among them, when k is an even number, the intermediate quantity Intermediate amount When k is an odd number, the intermediate quantity Intermediate amount Tr represents the trace of the matrix.

6. The method according to claim 5, wherein: In the process of solving the objective function, the objective function is processed using the optimization-minimization MM algorithm framework; The proximal distance PDA algorithm is used to iteratively process each constraint, and the projection mean of the current solution on each constraint set is calculated. Then, the penalty variable ζ is introduced to transform the original problem into an unconstrained subproblem, and an efficient solution is achieved in a closed-form iterative method.

7. The method according to claim 6, wherein: The system parameters set in step 1) also include the initial value ζ0 of the penalty variable ζ and the maximum value ζ max ; Initialization steps of the MM algorithm: Initialize the number of iterations of the MM algorithm to t = 0, randomly initialize the initial value of the MM algorithm of the transmitted signal vector x0 = x 0 , the initial value of the MM algorithm scaling factor d0 = d 0 , the initial value of the auxiliary variable γ in the MM algorithm γ0=γ 0 , x 0 d 0 and γ 0 is a random value, and the maximum number of iterations of the MM algorithm MMiter and the termination threshold of the MM algorithm are set to ∈2; The tth iteration step of the MM algorithm: using x t , the non-convex constraint is linearized using the first-order Taylor expansion to obtain the expansion result: Initialization steps of the PDA algorithm: Initialize the number of iterations of the PDA algorithm i = 0, set the maximum number of iterations of the PDA algorithm K, the PDA algorithm termination threshold value ∈ 1 and the penalty variable ζ = ζ0, initialize the initial value of the PDA algorithm of the transmitted signal vector x PDA algorithm initial value of the scaling factor Initial value of the auxiliary variable γ in the PDA algorithm The i-th iteration step of the PDA algorithm: (1) Calculate the projection of constraint 1, specifically: Traverse n=1,…,L, and for each n traverse k=1,…,2K u Get 2K u dimensional vector y * : The nth subvector in ; Set y corresponding to n=1,…,L * The vector x1 is sequentially formed as the transmitted signal vector obtained by constraint-projection; (2) Calculate the constrained second projection: use and Composition vector Calculate vector y ★ : Where λ is the optimal Lagrange multiplier; Then from y ★ Take out the first L sub-vectors to form vector x2 as the transmitted signal vector obtained by constraint two projection, and transform y ＊ The last sub-vector in is used as the new scaling factor (3) Calculate the constrained three projections: The calculated vector x3 is used as the transmitted signal vector obtained by constrained three-projection; (4) Calculate the constrained four-projection: Determine whether the expansion result obtained in the tth iteration step of the MM algorithm is greater than or equal to Right now If so, then remain unchanged, otherwise, The calculated vector x4 is used as the transmitted signal vector obtained by constrained three-projection; (5) The vectors x1, x2, x3 and x4 are averaged to obtain the value obtained in the i-th iteration. The result obtained in step 7 As the i-th iteration The result obtained in step 9 As the i-th iteration (6) The optimal solution of the i-th iteration is obtained by calculating the proximal operator, that is, (7) Update PDA variables (8) Update the penalty variable ζ new =min(ζ*2,ζ max ), and let ζ = ζ new ; (9) Determine whether i+1 is equal to K. If so, end the i-th iteration of the PDA algorithm and let the output x new =x i+1 ,γ new =γ i+1 ,d new =d i+1 Then go to step (11); otherwise, update Then update i=i+1 and return to step (1); (10) Determine ||x i+1 -x i || / ||x i Is ||≤∈1 true? If not, update Then update i=i+1 and return to step (1). If it is established, the i-th iteration of the PDA algorithm is terminated and the output x is new =x i+1 ,γ new =γ i+1 ,d new =d i+1 Then proceed to step (11); (11) Update MM variable x t+1 =x new ,γ t+1 =γ new ,d t+1 =d new ; (12) Determine whether the number of iterations t+1 is equal to MMeter. If so, set the output x t+1 ,γ t+1 ,d t+1 End the loop and go to step (14); (13) Step 18: Determine || x t+1 -x t || / ||x t ||≤∈2,||γ t+1 -γ t Is ||≤∈2 true? If not, update t=t+1 and return to the tth iteration step of the MM algorithm. If true, go to step (14); (14) Output the last iteration x t+1 ,γ t+1 ,d t+1 is the solution of the objective function.

Images