RIS-assisted MIMO radar transmission beam forming method based on beam pattern matching

Abstract

The invention discloses an RIS-assisted MIMO radar transmitted beam forming method based on beam pattern matching, and the method comprises the steps: taking the minimization of a beam pattern matching error as a criterion, and carrying out the combined optimization of a transmitted waveform and an RIS reflection coefficient; applying constant modulus constraint to the transmitted waveform; applying per-unit mode constraint to the RIS reflection coefficient; constructing a non-convex optimization problem model for a target based on beam pattern matching error minimization; decomposing an optimization problem into two sub-problems of transmitted waveform optimization and RIS reflection coefficient optimization by adopting an alternating minimization framework; converting the non-convex objective function into a quadratic convex function by using a maximum and minimum method; adopting a gradient projection algorithm to quickly solve a quadratic programming problem under the constant modulus constraint and the per-unit modulus constraint; alternately optimizing a transmitted waveform and an RIS reflection coefficient; according to the method, the optimized transmitted waveform and the RIS reflection coefficient are obtained, and the optimal matching of the actual transmitted beam pattern and the ideal beam pattern is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and specifically relates to a RIS (intelligent metasurface) assisted MIMO radar transmit beamforming method based on beam pattern matching. Background Art

[0002] The transmit beam pattern can describe the spatial distribution of radar radiation power. In different radar mission scenarios, the transmit beam pattern needs to be designed in a targeted manner. For example, multiple beams can be designed to track multiple targets, wide beam coverage can be used to improve target search efficiency, and null areas can be designed to suppress clutter and interference. Therefore, the intelligent metasurface-assisted multiple-input multiple-output (MIMO) radar transmit beamforming based on the beam pattern matching criterion has important engineering application value.

[0003] By minimizing the integral sidelobe-mainlobe ratio criterion, the transmitted energy after beamforming can be more effectively concentrated in the mainlobe area, but the shape of the mainlobe cannot be adjusted. That is, the energy in the mainlobe area is controllable, but the specific shape of the mainlobe is not controllable. For the precise control of the shape of the transmit beam pattern, a finite-length filter is used for equal-ripple optimization, and the mainlobe ripple, sidelobe level, transition bandwidth, expected power level and number of transmitting antennas are adjusted through the waveform covariance matrix to improve the robustness of the target azimuth, but there are problems such as the transmit waveform is not ideal and the computational complexity is high. Summary of the invention

[0004] The purpose of the present invention is to propose a RIS-assisted MIMO radar transmit beamforming design method based on beam pattern matching.

[0005] The technical solution adopted by the present invention is a RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching, comprising:

[0006] Step 1: With the goal of minimizing the beam pattern matching error, the signal model and cost function of RIS-assisted MIMO radar transmit beamforming are established;

[0007] Step 2: A constant modulus constraint is applied to the MIMO radar transmit waveform, and a unimodular constraint is applied to the RIS reflection coefficient. A non-convex constrained optimization mathematical model is established based on the signal model and cost function of RIS-assisted MIMO radar transmit beamforming.

[0008] Step 3: Convert the cost function optimization problem of the non-convex constrained optimization mathematical model into three independent optimization sub-problems of the parameter variables, and use the maximum minimization method to convert the objective function in the non-convex constrained optimization mathematical model into a convex function;

[0009] Step 4: Based on the alternating minimization framework, iterative optimization is performed to solve the emission waveform and RIS reflection coefficient.

[0010] Compared with the prior art, the present invention has the following significant advantages: the control of the main lobe shape of the beam pattern is more accurate, and the robustness of the target detection performance of the MIMO radar is improved. In addition, the simulation results show that the RIS-assisted MIMO radar transmit beamforming design method using the beam pattern matching criterion has a lower main lobe ripple of the beam pattern and has a significant suppression effect on the peak side lobe and the null depth. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the embodiments of the present application or the existing technical solutions, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in the present application, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor.

[0012] Figure 1 This is the single main lobe beam pattern matching error convergence curve.

[0013] Figure 2 It is a single main lobe beam pattern.

[0014] Figure 3 This is the convergence curve of the dual main lobe beam pattern matching error.

[0015] Figure 4 It is a dual main lobe beam pattern.

[0016] Figure 5 It is the convergence curve of the null-steering-single main lobe beam pattern matching error.

[0017] Figure 6 It is a null-steering-single main lobe beam pattern.

[0018] Figure 7 To solve the variables using MM (maximum minimization) technique and GP (gradient projection) algorithm Algorithm flow chart.

[0019] Figure 8 To solve the variables using MM technology and GP algorithm Algorithm flow chart.

[0020] Fig. 9 Flowchart of the algorithm for solving RIS-assisted MIMO radar transmit beamforming. DETAILED DESCRIPTION

[0021] The present invention is further described below with reference to the accompanying drawings and examples, which is a method for RIS-assisted MIMO radar transmit beamforming based on beam pattern matching criterion.

[0022] A method for transmitting beamforming of MIMO radar assisted by intelligent metasurface (RIS) based on beam pattern matching. The present invention combines the advantages of methods such as alternating minimization, maximum minimization and gradient projection technology, and proposes a more accurate and efficient solution algorithm. The algorithm is suitable for solving non-convex optimization problems under the criterion of minimizing beam pattern matching error. In the algorithm, the signal model of the RIS-assisted MIMO radar transmitting beamforming problem and the objective function of minimizing the beam pattern matching error are first established, and the constant modulus constraint and unimodular constraint are respectively used for the waveform and the reflection coefficient of RIS to obtain the non-convex optimization model of the problem. Then, based on the alternating minimization method, the maximum minimization method is used to transform the subproblem into a quadratic programming problem under the constant modulus constraint / unimodular constraint, and then the gradient projection method is used for rapid solution, and the transmitting waveform and RIS reflection coefficient are jointly optimized. The present invention is suitable for solving non-convex optimization problems under the criterion of minimizing beam pattern matching error, and realizes the best matching between the actual beam pattern and the ideal beam pattern.

[0023] A method for RIS-assisted MIMO radar transmit beamforming based on beam pattern matching criterion, the specific implementation steps are as follows:

[0024] Step 1: With the goal of minimizing the beam pattern matching error, a model for minimizing the beam pattern matching error problem of RIS-assisted MIMO radar is established. Specifically:

[0025] Assume that the transmitting antenna of the MIMO radar is a one-dimensional uniform linear array with an array element spacing of The uniform linear array is The angle of the steering vector is expressed as:

[0026] (1)

[0027] in, represents the angle from the array normal, represents the array element spacing, To detect the signal wavelength, represents the number of transmitting array elements, express dimensional complex domain;

[0028] The reflection coefficient matrix for constructing RIS is V, which is a diagonal matrix. The reflection coefficient matrix is ​​a vector composed of the diagonal elements of V. It is expressed as:

[0029] (2)

[0030] In the formula, Indicates the number of antenna units on RIS, express The reflection coefficient of each RIS unit, represents the phase shift part of the RIS reflection coefficient, express dimensional complex domain;

[0031] No. The array element is The signal transmitted at each sampling moment is , Indicates the total number of samples per pulse. The antenna is The spatial transmission waveform vector at a moment can be expressed as:

[0032] (3)

[0033] In the formula, express The antenna is The spatial emission waveform at the moment, express dimensional complex domain;

[0034] The space-time transmission waveform matrix of MIMO radar is expressed as:

[0035] (4)

[0036] In the formula, express The spatial emission waveform at a moment, express The complex domain of

[0037] Under the assumption of narrowband signal and non-dispersive propagation, determine the transmission waveform X at The composite signal in the direction is:

[0038] (5)

[0039] In the formula, express dimensional identity matrix.

[0040] exist direction, determine the composite signal Power generated The expression is:

[0041] (6)

[0042] Building RIS Directional emission response vector The expression is:

[0043] (7)

[0044] In the formula, Indicates the element spacing of RIS;

[0045] The transmission signal of RIS-assisted MIMO radar contains two propagation paths: line-of-sight (LoS) path and non-line-of-sight (NLoS) path. The angle difference between the NLoS path and the LoS path in the transmission direction is ,Right now , synthetic signal On the LoS and NLoS paths, they are represented as:

[0046] (8)

[0047] (9)

[0048] In the formula, Represents the channel matrix between the MIMO radar transmit array and the RIS;

[0049] RIS-assisted MIMO radar Transmit beam in direction The expression is:

[0050] (10)

[0051] in,

[0052] ,

[0053] , express dimensional complex domain.

[0054] A cost function is constructed to quantify the difference between the transmit beam pattern and the desired beam pattern, and the cost function is expressed as:

[0055] (11)

[0056] in, is the squared error of beam pattern matching in The weight of the point, is the number of grids after the entire transmit beam illumination space is discretized, and the desired beam pattern is expressed as , express The desired beam pattern in the direction, is the direction angle of the discretized beam space, is the beam pattern normalization parameter that needs to be optimized.

[0057] Step 2: Constant modulus constraint and unimodulus constraint are respectively applied to the reflection coefficient of the waveform and RIS to obtain the non-convex optimization model for minimizing the beam pattern matching error of RIS-assisted MIMO radar, which is expressed as:

[0058] (12)

[0059] in is the total emission energy.

[0060] Step 3: Figures 7-9 As shown in the figure, based on the MM technology and using the alternating optimization algorithm, the objective function optimization problem is transformed into three independent optimization sub-problems of parameter variables, specifically:

[0061] Sub-question 1:

[0062] (13)

[0063] Sub-question 2:

[0064] (14)

[0065] in, .

[0066] Sub-question 3:

[0067] (15)

[0068] Step 4: Based on the GP algorithm, the alternating optimization method is used to iteratively solve the three parameter variables to optimize the objective function and give a specific method for the transmit beamforming design.

[0069] Step 4.1: Set initialization conditions , , , , , , , , , , Represents the current iteration number; , , Variable waveform variables , the reflection coefficient of RIS , normalized parameter The initial value of is the cut-off tolerance, is the maximum number of iterations;

[0070] Step 4.2: Derivative the objective function of subproblem 1 and set it to zero, solve the equivalent subproblem 1, and obtain alternating optimization The normalized parameters after It is expressed as:

[0071] (16)

[0072] In the formula, Representation of subproblem 2 No. The value of the alternating optimization;

[0073] Step 4.3: According to MM technology, Applied to the objective function of subproblem 2 and ignoring the constant term, subproblem 2 can be transformed into a series of constant modulus constrained quadratic programming problems, which are equivalent to:

[0074] (17)

[0075] in, , , , ;

[0076] Build , , again using the properties of the matrix trace, the above problem can be expressed as:

[0077] (18)

[0078] in, , express dimensional complex field, and They are , The vector formed, , Indicates vectorizing the matrix.

[0079] Use the GP algorithm to solve the equivalent sub-problem 2 and obtain the waveform variable No. The optimal waveform variable of the iteration operation , the specific method is:

[0080] Step 4.3.1. Set initialization conditions , , , , Indicates the current iteration number, For the transmission waveform The initial value in this iteration, is the termination tolerance, is the maximum number of iterations;

[0081] Step 4.3.2: According to the properties of the matrix trace, the objective function in subproblem 2 is optimized as follows:

[0082] (19)

[0083] in, , ;

[0084] Step 4.3.3: Calculate using GP algorithm The gradient of is:

[0085] (20)

[0086] Step 4.3.4: Use the GP algorithm to calculate The transmitted waveform The update is expressed as:

[0087] (twenty one)

[0088] in, , is the search step projection operator, Represents the vector Each element of is projected onto the unit circle. ;

[0089] Step 4.3.5: Update according to GP algorithm , determine whether the iteration termination condition is met and ; If the termination condition is met, the obtained is the optimal solution of subproblem 2 in this iteration, and Grant , if the termination condition is not met, return to step 4.4.3.

[0090] Step 4.4: Expand the objective function of subproblem 3 and ignore the constant term to simplify the objective function of subproblem 3 to:

[0091] (twenty two)

[0092] in, ;

[0093] Use the GP algorithm to solve the equivalent sub-problem 3 and obtain the RIS reflection coefficient No. The result of the iterative operation , the specific method is:

[0094] Step 4.4.1. Set initialization conditions , , , , Indicates the current iteration number, For variables The initial value of in this iteration, is the termination tolerance, is the maximum number of iterations;

[0095] Step 4.4.2: Using MM technology, according to the properties of the matrix trace, the objective function of problem 3 can be simplified to:

[0096] (twenty three)

[0097] in,

[0098] ;

[0099] Step 4.4.3: Calculate the function using the GP algorithm The gradient of is:

[0100] (twenty four)

[0101] Step 4.4.4: Use the GP algorithm to calculate The transmitted waveform The update is expressed as:

[0102] (25)

[0103] in, , is the search step length, is the projection operator;

[0104] Step 4.4.5: Pass renew After that, determine whether the iteration termination condition is met and , if the termination condition is met, What you get is the optimal solution of subproblem 3 in this iteration. If the termination condition is not met, return to step 4.4.3.

[0105] Step 4.5: Use renew After that, according to the updated objective function , determine whether the iteration termination condition is met as well as , if the termination condition is met, the obtained and are the optimal solutions of the MIMO radar transmit waveform and the RIS reflection coefficient obtained in the iteration respectively. If the termination condition is not met, return to step 4.2.

[0106] Example

[0107] The performance of the RIS-assisted MIMO radar transmit beamforming based on the beam pattern matching criterion proposed in this invention is verified through numerical experiments.

[0108] 1. Single main lobe performance analysis

[0109] 1) Simulation parameter settings

[0110] The distance between RIS and radar is 2m, and the angle between RIS and MIMO transmitting array is The path loss at the reference distance is , path loss index The element spacing of MIMO array and RIS is half wavelength, and the number of antenna elements is , Snapshots , the total antenna transmission power is set to .

[0111] The center of the main lobe is set to , the main lobe width is , that is, the main lobe area is , the side lobe area is The desired beam pattern is expressed as

[0112]

[0113] The weight of the main lobe area is set to 0.7, and the weight of the side lobe area is set to 0.3.

[0114] 2) Beam diagram drawing

[0115] In order to demonstrate the convergence performance and stability of the algorithm, the matching error convergence curve of the single main lobe beam pattern, the single main lobe beam pattern, and the evaluation index of the single main lobe beam pattern are fitted with the simulation results. It can be seen that the presence or absence of RIS and the dimension of RIS have an impact on the various indicators of the beam pattern. The horizontal axis of the beam pattern represents , the unit of the vertical axis is .

[0116] 3) Metrics

[0117] In order to facilitate analysis and comparison of performance, the beam pattern matching square error is defined as

[0118]

[0119] and represents the normalized transmit beam pattern. At the same time, the beam pattern performance is further measured by analyzing the peak sidelobe (PSL) and main lobe ripple (MRL) of the beam pattern. , the main lobe ripple is .

[0120] 4) Result analysis

[0121] Figure 1 The matching error convergence curve of the single main lobe beam pattern is shown. Regardless of whether RIS assistance is enabled or not, the algorithm proposed in this paper can reach a convergence state after multiple iterations, and the matching error gradually decreases and stabilizes at a low level. This shows that the proposed algorithm has good convergence performance and stability.

[0122] also, Figure 1 The matching error of the transmit beam pattern of the MIMO radar assisted by RIS is also shown. The results show that the matching error of the MIMO radar assisted by RIS is significantly better than that of the conventional scheme without RIS. When the dimension of RIS increases from 128 to 256, the matching error is further reduced. This shows that a higher RIS dimension improves the flexibility and optimization capability of the system and helps to accurately match the desired beam pattern.

[0123] Figure 2 The expected beam pattern and the actual transmission beam pattern in the case of a single main lobe are compared. It can be clearly seen that after the introduction of RIS, the shape of the transmission beam pattern is closer to the ideal expected beam pattern. More importantly, RIS significantly reduces the sidelobe level of the transmission beam pattern and enhances the system's ability to suppress external interference, thereby improving signal transmission quality and anti-interference performance. In addition, as the RIS dimension increases from 128 to 256, the sidelobe level is further reduced, which shows that high-dimensional RIS can more effectively optimize beam characteristics, thereby improving the overall performance of the system.

[0124] Table 1 lists Figure 2 The specific quantitative indicators of the beam pattern shown, such as Error, PSL and MRL, clearly show the difference in system performance under different configurations. It can be clearly seen from Table 1 that the matching error of the transmission beam pattern of conventional MIMO radar without RIS assistance is high, with Error of 10.91dB and 10.48dB, indicating that there is a significant deviation between the transmitted signal and the ideal signal. When 128-dimensional RIS assistance is used, the Error value is reduced to 1.11dB, and when the RIS dimension is further increased to 256, the reduction trend of SE becomes more obvious, and Error is reduced to -17.24dB. This further proves the potential and advantages of RIS technology in improving the quality of MIMO radar beam patterns.

[0125] Table 1

[0126] Error(dB) PSL(dB) MRL(dB) Literature data, no RIS 10.91 -13.27 2.51 No RIS 10.48 -13.83 2.66 <![CDATA[RIS assisted, L 2 = 128]]> 1.11 -16.30 1.29 <![CDATA[RIS assisted, L 2 = 256]]> -17.24 -21.59 0.06

[0127] 2. Dual main lobe performance analysis

[0128] 1) Simulation parameter settings

[0129] The distance between RIS and radar is 2m, and the angle between RIS and MIMO transmitting array is The path loss at the reference distance is , path loss index The element spacing of MIMO array and RIS is half wavelength, and the number of antenna elements is , Snapshots , the total antenna transmission power is set to .

[0130] The main lobe area is , the side lobe area is The desired beam pattern is expressed as

[0131]

[0132] The weight of the main lobe area is set to 0.7, and the weight of the side lobe area is set to 0.3.

[0133] 2) Beam diagram drawing

[0134] In order to demonstrate the convergence performance and stability of the algorithm, the matching error convergence curve of the single main lobe beam pattern, the single main lobe beam pattern, and the evaluation index of the single main lobe beam pattern are fitted with the simulation results. It can be seen that the presence or absence of RIS and the dimension of RIS have an impact on the various indicators of the beam pattern. The horizontal axis of the beam pattern represents , the unit of the vertical axis is .

[0135] 3) Metrics

[0136] In order to facilitate analysis and comparison of performance, the matching square error is defined as

[0137]

[0138] and represents the normalized transmit beam pattern. At the same time, the beam pattern performance is further measured by analyzing the peak sidelobe (PSL) and main lobe ripple (MRL) of the beam pattern. , the main lobe ripple is .

[0139] 4) Result analysis

[0140] Figure 3 The convergence curve of the dual mainlobe beam pattern matching error is shown. Figure 3 It can be seen that it is similar to Figure 1, both the transmit beam pattern matching error of the conventional MIMO radar and the beam pattern matching error assisted by RIS can converge after multiple iterations. This shows that the proposed algorithm also has good convergence performance and stability under the condition of double main lobes. Under the conventional state, 128-dimensional RIS-assisted and 256-dimensional RIS-assisted, the matching error gradually decreases.

[0141] Figure 4 The desired beam pattern and the transmitted beam pattern in the case of dual main lobes are shown. Figure 4 It can be seen that the RIS-assisted transmit beam pattern is closer to the expected beam pattern than the conventional MIMO radar transmit beam pattern. This improvement is mainly reflected in two aspects: first, RIS assistance significantly reduces the sidelobe level of the beam pattern; second, the main lobe of the beam pattern under RIS assistance is flatter.

[0142] Combined with the specific data given in Table 2, in the dual main lobe experiment, RIS can significantly improve the performance of the radar system when the dimensions are 128 and 256. Specifically, RIS can reduce the Error of the conventional beam pattern from 18.12dB to 12.48dB and -6.48dB. In addition, the application of RIS also significantly improves other key indicators of the beam pattern. When RIS is introduced and the dimension is increased to 256, PSL is reduced from -9.60dB to -15.64dB. At the same time, the ripple amplitude of the two main lobes is also reduced, from 2.69dB / 2.66dB to 011dB / 0.32dB. This change shows that RIS can not only optimize the overall shape of the beam pattern, but also make the signal strength in the main lobe more evenly distributed.

[0143] Table 2

[0144] Error(dB) PSL(dB) MRL(dB) Literature data, no RIS 18.3 -9.95 2.60 / 2.68 No RIS 18.12 -9.60 2.69 / 2.66 <![CDATA[RIS assisted, L 2 = 128]]> 12.48 -11.45 1.30 / 1.42 <![CDATA[RIS assisted, L 2 = 256]]> -6.48 -15.64 0.11 / 0.32

[0145] 3. Zero-sag performance analysis

[0146] 1) Simulation parameter settings

[0147] The distance between RIS and radar is 2m, and the angle between RIS and MIMO transmitting array is The path loss at the reference distance is , path loss index The element spacing of MIMO array and RIS is half wavelength, and the number of antenna elements is , Snapshots , the total antenna transmission power is set to .

[0148] The experiment considers a single main lobe desired beam pattern with a null region, and the main lobe area is The zero-sink area is , the remaining areas are set as side lobe areas, expressed as , the desired beam pattern is expressed as

[0149]

[0150] The weight of the main lobe region is set to 0.7, the weight of the side lobe region is set to 0.3, and the weight of the null region is set to 5.

[0151] 2) Beam diagram drawing

[0152] In order to demonstrate the convergence performance and stability of the algorithm, the matching error convergence curve of the single main lobe beam pattern, the single main lobe beam pattern, and the evaluation index of the single main lobe beam pattern are fitted with the simulation results. It can be seen that the presence or absence of RIS and the dimension of RIS have an impact on the various indicators of the beam pattern. The horizontal axis of the beam pattern represents , the unit of the vertical axis is .

[0153] 3) Metrics

[0154] In addition to considering the three evaluation indicators of Error, PSL and MRL, the minimum null level (MNL) is defined as .

[0155] 4) Result analysis

[0156] Figure 5 The convergence curves of the matching error of the single mainlobe beam pattern including nulling are presented. Figure 5 It can be seen that the algorithm proposed in this invention can still achieve convergence when considering null sinking. This result further verifies the conclusions obtained from the previous two simulations, that is, the introduction of RIS significantly reduces the beam pattern error containing the null sinking area. As the RIS dimension increases, the improvement effect becomes more obvious, and the Error value is further reduced.

[0157] Figure 6 The single main lobe beam patterns of conventional MIMO radar, 128-dimensional RIS-assisted and 256-dimensional RIS-assisted are shown, and all of these beam patterns have null regions. Figure 6 It can be observed that the assistance of RIS makes the sidelobe level of the beam pattern lower and the null area deeper. Combined with the specific indicators given in Table 3, it can be seen that the Error is reduced from 11.46dB in the conventional beam pattern to 12.48dB under the assistance of 128-dimensional RIS and -6.48dB under 256-dimensional RIS; PSL is reduced from -9.06dB to -13.69dB and The MRL was also improved, with the 128-dimensional RIS reducing the MRL by 0.66dB and the 256-dimensional RIS reducing the MRL by 1.5dB.

[0158] Table 3

[0159] Error(dB) PSL(dB) MRL(dB) MNL(dB) Literature data, no RIS 11.87 -12.47 2.65 -39.01 No RIS 11.46 -12.79 2.73 -39.20 <![CDATA[RIS assisted, L 2 = 128]]> 6.15 -13.69 2.07 -38.17 <![CDATA[RIS assisted, L 2 = 256]]> 2.76 -15.14 1.23 -39.61

[0160] Depend on Figure 5 , Figure 6 It can be seen that although the introduction of RIS does not significantly improve the minimum value of the null, it can be clearly seen from the waveform that the null area with the assistance of RIS is flatter. Specifically, without the assistance of RIS, the null is only low at one angle; after the assistance of RIS, the entire null area has a lower level, which means that RIS can significantly improve the overall performance of the null area.

[0161] In summary, the experimental results show that the proposed algorithm can reach a convergence state after multiple iterations. In addition, the introduction of RIS significantly reduces the matching error of the beam pattern and improves its beam matching performance. Compared with the conventional co-located MIMO radar, the RIS-assisted MIMO radar has achieved significant improvements in the main lobe ripple, peak side lobe and null depth of the beam pattern. The main lobe ripple is flatter, the peak side lobe and null depth are reduced, and the accuracy of target detection is improved.

Claims

1. A RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching, characterized in that: include: Step 1: With the goal of minimizing the beam pattern matching error, the signal model and cost function of RIS-assisted MIMO radar transmit beamforming are established; Step 2: A constant modulus constraint is applied to the MIMO radar transmit waveform, and a unimodular constraint is applied to the RIS reflection coefficient. A non-convex constrained optimization mathematical model is established based on the signal model and cost function of RIS-assisted MIMO radar transmit beamforming. Step 3: Convert the cost function optimization problem of the non-convex constrained optimization mathematical model into three independent optimization sub-problems of the parameter variables, and use the maximum minimization method to convert the objective function in the non-convex constrained optimization mathematical model into a convex function; Step 4: Based on the alternating minimization framework, iterative optimization is performed to solve the emission waveform and RIS reflection coefficient.

2. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 1, characterized in that: The specific method of establishing the signal model of RIS-assisted MIMO radar transmit beamforming is: Step 1.1: Configure the transmit steering vector of the uniform linear array MIMO radar , the launch steering vector is specifically: ； In the formula, represents the angle from the array normal, represents the array element spacing, represents the wavelength of the transmitted signal, represents the number of transmitting array elements, express dimensional complex domain; Step 1.2: Construct the reflection coefficient matrix V of RIS. The reflection coefficient matrix V is a diagonal matrix with diagonal element vectors It is expressed as: ； In the formula, Indicates the number of antenna units on RIS, express The reflection coefficient of each RIS unit, represents the phase shift part of the RIS reflection coefficient, express dimensional complex domain; Step 1.3: Construct the space-time transmission waveform matrix X. The specific expression is: ； In the formula, express The spatial emission waveform at a certain moment, express The complex domain of Step 1.4: Determine the RIS-assisted MIMO radar Transmit beam in direction : ； in, ， , is the angle between the normal of the RIS and the normal of the MIMO radar transmit array, Indicates RIS The emission response vector in the direction, represents the channel matrix between MIMO radar and RIS, express dimensional identity matrix, express dimensional complex domain.

3. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 1, characterized in that: The cost function of RIS-assisted MIMO radar transmit beamforming is established as follows: ； In the formula, is the squared error of beam pattern matching in The weight in the direction, , is the number of grids after the entire transmit beam illumination space is discretized, , represents the transmission steering vector of the MIMO radar, Indicates RIS The emission response vector in the direction, represents the channel matrix between MIMO radar and RIS, is the angle between the normal of the RIS and the normal of the MIMO radar transmit array, express The desired beam pattern in the direction, is the direction angle of the discretized beam space, is the beam pattern normalization parameter that needs to be optimized, V represents the reflection coefficient matrix of RIS, X represents the space-time transmission waveform matrix, express dimensional complex domain.

4. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 1, characterized in that: The transmit waveform is constrained to a constant modulus, and the RIS reflection coefficient is constrained to a unimodular modulus. The non-convex constrained optimization mathematical model established based on the signal model and cost function of RIS-assisted MIMO radar transmit beamforming is: ； Where V represents the reflection coefficient matrix of RIS, X represents the space-time transmission waveform matrix, is the beam pattern normalization parameter that needs to be optimized, represents the total number of samples per pulse, Indicates The reflection coefficient of each RIS unit, represents the number of transmitting array elements, Indicates the number of antenna units on RIS, express The antenna is The spatial domain emission waveform vector at the moment, Represents the total transmitted energy.

5. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 1, characterized in that: In the framework of alternating minimization, the cost function optimization problem of the non-convex constrained optimization mathematical model is transformed into solving the normalized parameter , Transmit waveform and RIS reflection coefficient 3 sub-problems, and iteratively solve the three sub-problems that are solved independently to obtain the optimal MIMO radar transmission waveform and RIS reflection coefficient. At the iteration, the corresponding sub-problems are: Sub-question 1: ； In the formula, is the squared error of beam pattern matching in The weight in the direction, , is the number of grids after the entire transmit beam illumination space is discretized, is the beam pattern normalization parameter that needs to be optimized, express The desired beam pattern in the direction, is the direction angle of the discretized beam space, , represents the transmission steering vector of the MIMO radar, Indicates RIS The emission response vector in the direction, represents the channel matrix between MIMO radar and RIS, is the angle between the normal of RIS and the normal of MIMO radar transmitting array, V represents the reflection coefficient matrix of RIS, X represents the space-time transmitting waveform matrix, express dimensional complex domain; Sub-question 2: ； in, , is the normalization parameter In the The result of the iterative solution is express The antenna is The spatial domain emission waveform vector at the moment, represents the total number of samples per pulse, represents the number of transmitting array elements, represents the total transmitted energy; Sub-question 3: ， in, Indicates the number of antenna units on RIS, Indicates The reflection coefficient of each RIS unit.

6. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 5, characterized in that: The specific method to solve sub-problem 1 is: The objective function of subproblem 1 is about the normalized parameter Taking the derivative and setting it to zero, we get the optimal solution: ； In the formula, is the normalization parameter In the The result of the iterative solution is Representation of subproblem 2 No. The value of the alternate optimization.

7. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 6, characterized in that: The specific method to solve sub-problem 2 is: According to the maximum minimization principle, subproblem 2 is transformed into a series of constant modulus constrained quadratic programming problems; in the first At the iteration, the corresponding problem is: ； In the formula, , , , ; Build , , using the properties of matrix trace, the above problem can be expressed as: ； in, , express dimensional complex field, and They are , The vector formed, , Indicates vectorizing the matrix; The gradient projection method is used to quickly solve the transformed sub-problem 2: S1: Give the initial solution under constant modulus constraints , set the initialization conditions , , , Indicates the current iteration number, For the transmission waveform The initial value in this iteration, For the termination tolerance, is the maximum number of iterations; S2: Calculation The gradient of is: ； in, , express dimensional identity matrix; S3: Using the GP algorithm, calculate the The transmitted waveform The update is expressed as: ； in, , is the search step projection operator, Represents the vector Each element of is projected onto the unit circle. ; S4: Update according to GP algorithm , determine whether the iteration termination condition is met and ; If the termination condition is met, the obtained is the optimal solution of subproblem 2 in this iteration, and Grant If the termination condition is not met, return to step S2.

8. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 5, characterized in that: The specific method to solve sub-problem 3 is: S1: Give the initial solution under constant modulus constraints , set the initialization conditions , , , , initially , Indicates the current iteration number, For variables The initial value in this iteration, For the termination tolerance, is the maximum number of iterations; S2: Optimize variables The problem is expressed as: ； in, ； In the formula, for The vector formed, Indicates the number of antenna units on RIS, express The reflection coefficient of each RIS unit, Indicates RIS The emission response vector in the direction, , for The vector formed, represents the phase shift part of the RIS reflection coefficient, express dimensional complex field, express dimensional complex field, express dimensional complex domain; calculate The gradient of is: ； S3: Using the GP algorithm, calculate the The transmitted waveform The update is expressed as: ； in, , is the search step length, is the projection operator; S4: Pass renew After that, determine whether the iteration termination condition is met and ; If the termination condition is met, What you get is the optimal solution of subproblem 3 in this iteration. If the termination condition is not met, return to S2.

9. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 5, characterized in that: The emission waveform is obtained by iterative solution and RIS reflection coefficient The specific process is: S1: Give the initial solution under constant modulus constraints , , , set the initialization condition t, , , , , ,in: Indicates the current iteration number, For the transmission waveform The initial value in this iteration, is the reflection coefficient The initial value in this iteration, is the normalization parameter The initial value in this iteration, For the termination tolerance, is the maximum number of iterations; S2: Find the optimal solution by taking the first-order derivative of the objective function and setting it equal to zero, and optimize alternately to the first At the iteration, we get The solution is ； in, is the normalization parameter In the The result of the iterative solution is Representation of subproblem 2 No. The value of the alternating optimization; S3: Using the solution of subproblem 2, calculate The transmitted waveform The update is expressed as: ； in , is the search step projection operator, Represents the vector Each element of is projected onto the unit circle. , , express dimensional complex field, , , , express dimensional identity matrix, and They are , The vector formed, , , Indicates vectorizing the matrix; S4: Using the solution to subproblem 3, calculate The transmission waveform The update is expressed as: ； in, , is the search step length, is the projection operator, , ； In the formula, Indicates the number of antenna units on RIS, express The reflection coefficient of each RIS unit, Indicates RIS The emission response vector in the direction, represents the phase shift part of the RIS reflection coefficient, express dimensional complex field, express dimensional complex domain; S5: Pass renew After that, determine whether the iteration termination condition is met and ; If the termination condition is met, then and Transmitting waveforms for MIMO radar and RIS reflection coefficient is the optimal solution. If the termination condition is not met, return to S2.

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