RIS-Assisted MIMO Radar Transmit Beamforming Method Based on Beam Pattern Matching

Abstract

The present invention discloses a RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching, including: jointly optimizing the transmit waveform and the RIS reflection coefficient with the criterion of minimizing the beam pattern matching error; imposing a constant modulus constraint on the transmit waveform; imposing a unimodular constraint on the RIS reflection coefficient; constructing a non-convex optimization problem model with the goal of minimizing the beam pattern matching error; adopting an alternating minimization framework to decompose the optimization problem into two sub-problems of transmit waveform optimization and RIS reflection coefficient optimization; using the max-minimization method to transform the non-convex objective function into a quadratic convex function; adopting a gradient projection algorithm to quickly solve the quadratic programming problem under the constant modulus constraint and the unimodular constraint; alternately optimizing the transmit waveform and the RIS reflection coefficient; the present invention obtains the optimized transmit waveform and the RIS reflection coefficient, realizing the best matching between the actual transmit beam pattern and the ideal beam pattern.

Description

Technical Field

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

[0002] The transmit beam pattern can describe the spatial distribution of the radar radiation power. In different radar mission scenarios, it is necessary to design the shape of the transmit beam pattern specifically. For example, multiple beams can be designed to track multiple targets, a wide - beam coverage method can be adopted to improve the target search efficiency, and a null region can be designed to suppress clutter and interference. Therefore, the RIS - assisted multiple - input multiple - output (MIMO) radar transmit beamforming based on the beam pattern matching criterion has important engineering application value.

[0003] After beamforming by minimizing the integral sidelobe - to - mainlobe ratio criterion, the transmit energy can be more effectively concentrated in the mainlobe region, but the shape of the mainlobe cannot be adjusted. That is, the energy in the mainlobe region is controllable, but the specific shape of the mainlobe is uncontrollable. For the precise control of the transmit beam pattern shape, an equal - ripple optimization is carried out using a finite - length filter, and the mainlobe ripple, sidelobe level, transition bandwidth, desired power level, and the number of transmit 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 not being ideal enough and the high computational complexity. 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, including:

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

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

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

[0009] Step 4: Based on the alternating minimization framework, iteratively optimize and solve the transmit waveform and the RIS reflection coefficient.

[0010] Compared with the prior art, the present invention has the following remarkable advantages: the control of the main lobe shape of the beam pattern is more accurate, improving the robustness of the MIMO radar target detection performance. 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 in the beam pattern and a significant suppression effect on the peak sidelobe and null depth. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments recorded in the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0012] Figure 1 It is a convergence curve graph of the single main lobe beam pattern matching error.

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

[0014] Figure 3 It is a convergence curve graph of the double main lobe beam pattern matching error.

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

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

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

[0018] Figure 7 It is an algorithm flowchart for solving the variable using the MM (maximin) technique and the GP (gradient projection) algorithm.

[0019] Figure 8 It is an algorithm flowchart for solving the variable using the MM technique and the GP algorithm.

[0020] Figure 9 It is an algorithm flowchart for solving the RIS-assisted MIMO radar transmit beamforming. DETAILED DESCRIPTION OF THE EMBODIMENTS

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

[0022] An intelligent reflecting surface (RIS)-aided MIMO radar transmit beamforming method based on beam pattern matching. The present invention integrates the advantages of methods such as alternating minimization, max-minimization, and gradient projection techniques, and proposes a more accurate and efficient solution algorithm. This algorithm is applicable to solving non-convex optimization problems under the criterion of minimizing the beam pattern matching error. In this algorithm, first, a signal model of the RIS-aided MIMO radar transmit beamforming problem and an objective function for minimizing the beam pattern matching error are established. Constant modulus constraints and unimodular constraints are respectively imposed on the waveform and the reflection coefficients of the RIS, obtaining a non-convex optimization model for this problem. Then, based on the alternating minimization method, the max-minimization method is used to transform the sub-problem into a quadratic programming problem under constant modulus constraints / unimodular constraints, and then the gradient projection method is used for fast solution, jointly optimizing the transmit waveform and the RIS reflection coefficients. The present invention is applicable to solving non-convex optimization problems under the criterion of minimizing the beam pattern matching error, achieving the best match between the actual beam pattern and the ideal beam pattern.

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

[0024] Step 1: Taking the minimization of the beam pattern matching error as the goal, establish a model for the problem of minimizing the beam pattern matching error of the RIS-aided MIMO radar, specifically:

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

[0026] (1)

[0027] where represents the angle deviating from the array normal, represents the element spacing, is the detection signal wavelength, represents the number of transmit array elements, represents the complex domain of dimension ;

[0028] Construct the reflection coefficient matrix of the RIS as V, V is a diagonal matrix, and the vector composed of the diagonal elements of the reflection coefficient matrix V is expressed as:

[0029] (2)

[0030] In the formula, represents the number of antenna elements on the RIS, represents the reflection coefficients of RIS elements, represents the phase shift part in the RIS reflection coefficient, denotes a complex domain of

[0031] the th array element transmits a signal at the th sampling time as , represents the total number of samples per pulse. The spatial domain transmission waveform vector of the th antenna at the

[0032] (3)

[0033] where denotes the spatial domain transmission waveform of the th antenna at the denotes a complex domain of

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

[0035] (4)

[0036] where denotes the spatial domain transmission waveform at the th time, denotes

[0037] Under the assumptions of narrowband signals and non-dispersive propagation, the composite signal of the transmitted waveform X in the direction is determined as follows:

[0038] (5)

[0039] where denotes an identity matrix of

[0040] In the direction, the power generated by the composite signal is expressed as:

[0041] (6)

[0042] Construct the transmission response vector of the RIS in the direction as follows:

[0043] (7)

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

[0045] The transmitted signal of the RIS-assisted MIMO radar includes two propagation paths: the line-of-sight (LoS) path and the non-line-of-sight (NLoS) path. The angular difference of the NLoS path compared to the LoS path in the transmission direction is , that is , and the composite signal is expressed as follows on the LoS and NLoS paths respectively:

[0046] (8)

[0047] (9)

[0048] In the formula, represents the channel matrix from the MIMO radar transmitting array to the RIS;

[0049] The transmitted beam of the RIS-assisted MIMO radar in the direction has the following expression:

[0050] (10)

[0051] where

[0052] ,

[0053] , represents a complex domain of dimension

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

[0055] (11)

[0056] where is the weight of the squared error of beam pattern matching at the point, is the number of grids after discretization of the entire transmitted beam illumination space, and the desired beam pattern is expressed as , represents the desired beam pattern in the direction, is the direction angle of the beam space after discretization, and

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

[0058] (12)

[0059] where is the total transmission energy.

[0060] Step 3: As Figures 7 - 9 shown, based on the MM technique, use the alternating optimization algorithm to transform the objective function optimization problem into three independent optimization sub-problems for the respective parameter variables, specifically:

[0061] Sub-problem 1:

[0062] (13)

[0063] Sub-problem 2:

[0064] (14)

[0065] where .

[0066] Sub-problem 3:

[0067] (15)

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

[0069] Step 4.1: Set the initialization conditions , , , , , , , , , , represents the current iteration number; , , are the initial values of the variable waveform variable , the reflection coefficient of the RIS, and the normalization parameter , is the cut-off tolerance, is the maximum number of iterations;

[0070] Step 4.2: Take the derivative of the objective function of sub-problem 1 and set it to zero to solve the equivalent sub-problem 1 and obtain the normalized parameters after alternating optimization which is expressed as:

[0071] (16)

[0072] wherein, represents sub-problem 2 the value after the

[0073] th alternating optimization; Step 4.3: According to the MM technique, apply

[0074] (17)

[0075] wherein, , , , ;

[0076] Construct , , and by using the property of the matrix trace again, the above problem can be expressed as:

[0077] (18)

[0078] wherein, , represents the complex field of dimension and are respectively , the vectors composed of , denotes vectorizing the matrix.

[0079] Use the GP algorithm to solve the equivalent sub-problem 2 and obtain the waveform variable the optimal waveform variable of the th iterative operation, and the specific method is:

[0080] Step 4.3.1: Set the initialization conditions , , , , represents the current iteration number, is the initial value of the transmitted waveform 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 sub - problem 2 is optimized to:

[0082] (19)

[0083] where, , ;

[0084] Step 4.3.3, Use the GP algorithm to calculate the gradient of as:

[0085] (20)

[0086] Step 4.3.4, Use the GP algorithm to calculate the update of the transmit waveform in the th iteration, which is expressed as:

[0087] (21)

[0088] where, , is the search step projection operator, means projecting each element of the vector onto the unit circle respectively, ;

[0089] Step 4.3.5, Update according to the GP algorithm, and judge whether the iteration termination condition and are satisfied; if the termination condition is satisfied, the obtained is the optimal solution of sub - problem 2 in this iteration, and assign to , if the termination condition is not satisfied, return to Step 4.4.3.

[0090] Step 4.4, Expand the objective function of sub - problem 3 and ignore the constant term to simplify the objective function of sub - problem 3 to:

[0091] (22)

[0092] where, ;

[0093] Use the GP algorithm to solve the equivalent sub - problem 3 to obtain the RIS reflection coefficient in the th iteration operation result , and the specific method is:

[0094] Step 4.4.1: Set the initialization conditions , , , , represents the current iteration number, is the initial value of variable in this iteration, is the termination tolerance, is the maximum number of iterations;

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

[0096] (23)

[0097] where,

[0098] ;

[0099] Step 4.4.3: Use the GP algorithm to calculate the gradient of the function as:

[0100] (24)

[0101] Step 4.4.4: Use the GP algorithm to calculate the update of the transmit waveform at the th iteration, which is expressed as:

[0102] (25)

[0103] where, , is the search step size, is the projection operator;

[0104] Step 4.4.5: After updating through , judge whether the iteration termination conditions and are satisfied. If the termination conditions are satisfied, the obtained through is the optimal solution of sub-problem 3 in this iteration. If the termination conditions are not satisfied, return to Step 4.4.3.

[0105] Step 4.5: After updating using , judge whether the iteration termination conditions are satisfied according to the updated objective function and , if the termination condition is satisfied, the obtained and are the optimal solutions of the MIMO radar transmission waveform and the RIS reflection coefficient obtained during the iteration respectively. If the termination condition is not satisfied, return to step 4.2.

[0106] Embodiment

[0107] Verify the performance of the RIS-assisted MIMO radar transmission beamforming proposed in the present invention through numerical experiments.

[0108] 1. Single main lobe performance analysis

[0109] 1) Simulation parameter settings

[0110] The distance between the RIS and the radar is 2 m, and the included angle with the MIMO transmission array is . The path loss of the reference distance is , and the path loss exponent . The element spacing of both the MIMO array and the RIS is half-wavelength, and the number of antenna elements , the number of snapshots , and the total antenna transmission power is set to .

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

[0112]

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

[0114] 2) Beam pattern drawing

[0115] To show the convergence performance and stability of the algorithm, the matching error convergence curve, the single main lobe beam pattern, and the evaluation index of the single main lobe beam pattern are fitted with the simulation results. The influence of the presence or absence of the RIS and the dimension of the RIS on each index of the beam pattern can be seen. The abscissa of the beam pattern represents , and the unit of the ordinate is .

[0116] 3) Measurement index

[0117] To facilitate the analysis and comparison of performance, the beam pattern matching mean square error is defined as

[0118]

[0119] and It represents the normalized transmit beam pattern. Meanwhile, the beam pattern performance is further measured by analyzing two metrics, namely the peak sidelobe (PSL) and the main lobe ripple (MRL) of the beam pattern. The peak sidelobe is , and the main lobe ripple is .

[0120] 4) Result analysis

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

[0122] In addition, Figure 1 also shows the matching error of the transmit beam pattern of the RIS-assisted MIMO radar. The results show that the RIS-assisted MIMO radar is significantly superior to the conventional scheme without RIS in terms of matching error. When the dimension of the RIS increases from 128 to 256, the matching error further decreases. This shows that a higher RIS dimension improves the flexibility and optimization ability of the system, which helps to accurately match the desired beam pattern.

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

[0124] Table 1 lists Figure 2 the specific quantization metrics of the beam pattern shown, such as Error, PSL, and MRL. These data clearly show the differences in system performance under different configurations. It can be clearly seen from Table 1 that for the conventional MIMO radar without RIS assistance, the matching error of the transmit beam pattern is relatively high, with Error being 10.91 dB and 10.48 dB, which indicates a significant deviation between the transmitted signal and the ideal signal. When assisted by a 128-dimensional RIS, the Error value decreases to 1.11 dB, and when the RIS dimension is further increased to 256, the decreasing trend of SE becomes more obvious, and Error decreases to -17.24 dB. This further proves the potential and advantages of RIS technology in improving the beam pattern quality of MIMO radars.

[0125] Table 1

[0126] Error (dB) PSL (dB) MRL (dB) Literature data, without RIS 10.91 -13.27 2.51 Without RIS 10.48 -13.83 2.66 <![CDATA[RIS assisted, L2 = 128]]> 1.11 -16.30 1.29 <![CDATA[RIS assisted, L2 = 256]]> -17.24 -21.59 0.06

[0127] 2. Dual main lobe performance analysis

[0128] 1) Simulation parameter settings

[0129] The distance between the RIS and the radar is 2 m, and the angle with the MIMO transmitting array is . The path loss at the reference distance is , and the path loss exponent . The element spacing of both the MIMO array and the RIS is half-wavelength, and the number of antenna elements , the number of snapshots , and the total antenna transmit power is set to .

[0130] The main lobe region is , and the sidelobe region is . The desired beam pattern is expressed as

[0131]

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

[0133] 2) Beam pattern plotting

[0134] To demonstrate the convergence performance and stability of the algorithm, the matching error convergence curve, the single main lobe beam pattern, and the evaluation index of the single main lobe beam pattern are fitted with the simulation results. The influence of the presence or absence of the RIS and the dimension of the RIS on each index of the beam pattern can be seen. The abscissa of the beam pattern represents , and the unit of the ordinate is .

[0135] 3) Measurement metrics

[0136] To facilitate the analysis and comparison of performance, the matching squared error is defined as

[0137]

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

[0139] 4) Result analysis

[0140] Figure 3 Shows the convergence curve of the matching error of the dual main lobe beam pattern. As can be seen from Figure 3 , similar to Figure 1, whether it is the transmit beam pattern matching error of the conventional MIMO radar or the beam pattern matching error assisted by RIS, can converge after multiple iterations. This indicates that the proposed algorithm also has good convergence performance and stability under the double main lobe condition. Under the conventional state, 128-dimensional RIS assistance, and 256-dimensional RIS assistance, the matching error gradually decreases.

[0141] Figure 4 Shows the desired beam pattern and transmit beam pattern in the case of double main lobes. From Figure 4 It can be seen that the transmit beam pattern assisted by RIS is closer to the desired beam pattern in the image than the transmit beam pattern of the conventional MIMO radar. 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 assisted by RIS is flatter.

[0142] Combined with the specific data given in Table 2, in the double 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 18.12 dB to 12.48 dB and -6.48 dB. In addition, the application of RIS has also significantly improved other key indicators of the beam pattern. When RIS is introduced and the dimension is increased to 256, the PSL is reduced from -9.60 dB to -15.64 dB. At the same time, the ripple amplitudes of the two main lobes also decrease, from 2.69 dB / 2.66 dB to 011 dB / 0.32 dB. This change shows that RIS can not only optimize the overall shape of the beam pattern but also make the signal intensity in the main lobe more evenly distributed.

[0143] Table 2

[0144] Error (dB) PSL (dB) MRL (dB) Literature data, without RIS 18.3 -9.95 2.60 / 2.68 Without RIS 18.12 -9.60 2.69 / 2.66 <![CDATA[RIS assisted, L2 = 128]]> 12.48 -11.45 1.30 / 1.42 <![CDATA[RIS assisted, L2 = 256]]> -6.48 -15.64 0.11 / 0.32

[0145] 3. Null performance analysis

[0146] 1) Simulation parameter settings

[0147] The distance between RIS and the radar is 2 m, and the angle with the MIMO transmit array is . The path loss of the reference distance is , and the path loss exponent . The element spacing of the MIMO array and RIS is both half-wavelength, the number of antenna elements , the number of snapshots , and the total antenna transmit power is set to .

[0148] The experiment considers a single main lobe desired beam pattern with a null region. The main lobe region is , and the null region is , the remaining regions are all set as sidelobe regions, denoted as , and the desired beam pattern is denoted as

[0149]

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

[0151] 2) Beam pattern plotting

[0152] To demonstrate the convergence performance and stability of the algorithm, the convergence curve of the matching error 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 the influence of the presence or absence of RIS and the dimension of RIS on each index of the beam pattern. The abscissa of the beam pattern represents , and the unit of the ordinate is .

[0153] 3) Measurement indexes

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

[0155] 4) Result analysis

[0156] Figure 5 Presents the convergence curve of the matching error of the single main lobe beam pattern with nulls. It can be seen from Figure 5 that the algorithm proposed in the present invention can still achieve convergence considering the nulls. This result further verifies the conclusions obtained from the previous two simulations, that is, introducing RIS significantly reduces the beam pattern error in the region containing nulls. As the dimension of RIS increases, the improvement effect becomes more obvious and the Error value further decreases.

[0157] Figure 6 Shows the single main lobe beam patterns of the conventional MIMO radar, 128-dimensional RIS-assisted, and 256-dimensional RIS-assisted, and these beam patterns all have null regions. It can be observed from Figure 6 that the assistance of RIS makes the sidelobe level of the beam pattern lower and the null region deeper. Combining with the specific indexes given in Table 3, it can be known that Error is reduced from 11.46 dB of the conventional beam pattern to 12.48 dB under 128-dimensional RIS assistance and -6.48 dB under 256-dimensional RIS; PSL is reduced from -9.06 dB to -13.69 dB at and -15.14 dB at

[0158] Table 3

[0159] Error (dB) PSL (dB) MRL (dB) MNL (dB) Literature data, without RIS 11.87 -12.47 2.65 -39.01 Without RIS 11.46 -12.79 2.73 -39.20 <![CDATA[RIS assisted, L2 = 128]]> 6.15 -13.69 2.07 -38.17 <![CDATA[RIS assisted, L2 = 256]]> 2.76 -15.14 1.23 -39.61

[0160] From Figure 5 and 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 region is flatter under RIS assistance. Specifically, without RIS assistance, the null value is only low at one angle; after RIS assistance, the entire null region has a low level, which means that RIS can significantly improve the overall performance of the null region.

[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 been significantly improved in terms of the main lobe ripple, peak sidelobe, and null depth of the beam pattern. The main lobe ripple is flatter, the peak sidelobe and null depth are both 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 Including: Step 1: With the goal of minimizing the beam pattern matching error, establish the signal model and cost function for RIS-assisted MIMO radar transmit beamforming. Step 2: Apply the constant modulus constraint to the MIMO radar transmit waveform and the unimodular constraint to the RIS reflection coefficients, and establish a non-convex constrained optimization mathematical model based on the signal model and cost function for RIS-assisted MIMO radar transmit beamforming. Step 3: Transform the cost function optimization problem of the non-convex constrained optimization mathematical model into three independent optimization sub-problems for each of the three parameter variables, and use the min-max method to transform the objective function in the non-convex constrained optimization mathematical model into a convex function. Specifically, in the framework of alternating minimization, transform the cost function optimization problem of the non-convex constrained optimization mathematical model into solving the normalization parameter , transmit waveform , and the RIS reflection coefficient for three sub-problems, and iteratively solve the three sub-problems solved independently to obtain the optimal MIMO radar transmit waveform and RIS reflection coefficient. At the th iteration, the corresponding sub-problems are respectively: Sub-problem 1: ； In the formula, is the weight of the squared error of beam pattern matching in the direction, , is the number of grids after discretization of the entire transmitting beam illumination space, is the beam pattern normalization parameter to be optimized, represents the desired beam pattern in the direction, , represents the transmitting steering vector of the MIMO radar, represents the transmitting response vector of the RIS in the direction, represents the channel matrix between the MIMO radar and the RIS, is the angle between the normal of the RIS and the normal of the MIMO radar transmitting array, V represents the reflection coefficient matrix of the RIS, X represents the spatio-temporal transmitting waveform matrix, represents dimensional complex domain; Sub-problem 2: ； Among them, , is a normalization parameter is the result of the -th iterative solution, represents spatial domain transmission waveform vectors of antennas at the -th moment, represents the total number of samples per pulse, represents the total transmission energy; Sub-problem 3: ， Among them, represents the number of antenna elements on the RIS, represents the th reflection coefficient of the RIS unit; Step 4: Based on the alternating minimization framework, iteratively optimize and solve the transmit waveform and RIS reflection coefficients.

2. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 1, characterized in that The specific method for establishing the signal model for RIS-assisted MIMO radar transmit beamforming is as follows: Step 1.1, configure the transmit steering vector of the MIMO radar with a uniform linear array , and the transmit steering vector is specifically as follows: ； In the formula, represents the angle deviating from the normal of the array, represents the element spacing, represents the wavelength of the transmitted signal, represents the number of transmitting elements, represents the complex domain of dimension Step 1.

2. Construct the reflection coefficient matrix V of the RIS. The reflection coefficient matrix V is a diagonal matrix, and the diagonal element vector is expressed as: ； In the formula, represents the number of antenna elements on the RIS, represents the reflection coefficient of RIS units, represents the phase shift part of the RIS reflection coefficient, represents a -dimensional complex domain; Step 1.3: Construct the space-time transmit waveform matrix X, and the specific expression is: ； In the formula, represents the airspace emission waveform at a certain moment, represents the complex domain of; Step 1.4, determine the transmit beam of the RIS-assisted MIMO radar in the direction: ； Where, ， , is the angle between the normal of the RIS and the normal of the MIMO radar transmitting array, denotes the transmission response vector of the RIS towards direction, denotes the channel matrix from the MIMO radar to the RIS, denotes the identity matrix of dimension denotes the complex number field of dimension 3. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 1, characterized in that, The specific cost function for RIS-assisted MIMO radar transmit beamforming established is: ； In the formula, is the weight of the squared error of beam pattern matching in the direction, , is the number of grids after discretization of the entire transmitting beam illumination space, , represents the transmitting steering vector of the MIMO radar, represents the transmitting response vector of the RIS in the direction, represents the channel matrix between the MIMO radar and the RIS, is the angle between the normal of the RIS and the normal of the MIMO radar transmitting array, represents the desired beam pattern in the direction, is the beam pattern normalization parameter to be optimized, V represents the reflection coefficient matrix of the RIS, X represents the spatio-temporal transmitting waveform matrix, represents the complex domain of dimension.

4. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 3, wherein Applying the constant modulus constraint to the transmit waveform and the unimodular constraint to the RIS reflection coefficients, the non-convex constrained optimization mathematical model established based on the signal model and cost function for RIS-assisted MIMO radar transmit beamforming is: ； where \(V\) represents the reflection coefficient matrix of the RIS, and \(X\) represents the space-time transmit waveform matrix, is the beam pattern normalization parameter to be optimized, represents the total number of samples per pulse, represents the reflection coefficient of the \(i\)-th RIS element, represents the number of transmit array elements, represents the number of antenna elements on the RIS, represents the spatial domain transmit waveform vector of the \(m\) antennas at the \(n\)-th time instant, represents the total transmit energy.

5. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 1, wherein The specific method for solving sub-problem 1 is: The objective function of sub-problem 1 with respect to the normalization parameter is differentiated and set to zero to obtain the optimal solution as: ； In the formula, is the normalization parameter at the result of the th iteration solution, represents sub-problem 2 at the th alternating optimization value.

6. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 5, wherein The specific method for solving sub-problem 2 is: According to the max-min principle, sub-problem 2 is transformed into a series of constant modulus constrained quadratic programming problems; at the th iteration, the corresponding problem is: ； In the formula, , , , ; Construct , , using the properties of the matrix trace, the above problem can be expressed as: ； Among them, , denotes a complex number field of dimensions, and , are respectively vectors formed by , indicating the vectorization of the matrix; Use the gradient projection method to quickly solve the transformed sub-problem 2: S1: Give the initial solution under the constant modulus constraint , set the initial conditions , , , represents the current iteration number, is the transmitted waveform the initial value in this iteration, is the termination tolerance, is the maximum number of iterations; S2: Calculate The gradient of, and the specific formula is: ； Among them, , denotes the identity matrix of dimension S3: Using the GP algorithm, calculate the update of the transmitted waveform in the th iteration is expressed as: ； Among them, , is the search step projection operator, means projecting each element of the vector onto the unit circle respectively, ; S4: Update according to the GP algorithm , and determine whether the iteration termination condition is satisfied and ; if the termination condition is satisfied, the obtained is the optimal solution of sub-problem 2 in this iteration, and assign to ; if the termination condition is not satisfied, return to step S2.

7. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 6, wherein The specific method for solving sub-problem 3 is: S1: Give the initial solution under the constant modulus constraint , set the initial conditions , , , , initially , represents the current iteration number, is the variable 's initial value in this iteration, is the termination tolerance, is the maximum number of iterations; S2: Represent the problem of the optimization variable as: ； Where, ； In the formula, is the vector formed by, indicating the number of antenna elements on the RIS, represents the reflection coefficient of RIS towards the transmit response vector in the direction, where is the vector formed by, indicating the phase shift part of the RIS reflection coefficient, represents a dimensional complex domain, represents a dimensional complex domain; Calculate The gradient of is given by the specific formula: ； S3: Using the GP algorithm, calculate the update of the reflection coefficient in the th iteration, which is expressed as: ； Among them, , is the search step size, is the projection operator; S4: By updating , determine whether the iteration termination condition is satisfied and ; if the termination condition is satisfied, through the obtained is the optimal solution of sub-problem 3 in this iteration. If the termination condition is not satisfied, return to S2.

8. The RIS-assisted MIMO radar transmit beamforming method based on beam pattern matching according to claim 6, characterized in that Obtain the transmitted waveform through iterative solution and the reflection coefficient of the RIS The specific process is as follows: S1: Give the initial solution under the constant modulus constraint , , , set the initialization condition t, , , , , , where: represents the current iteration number, is the transmitted 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, is the termination tolerance, is the maximum number of iterations; S2: Find the optimal solution by taking the first derivative of the objective function and setting it equal to zero. When alternately optimizing to the th iteration, obtain The solution of is ； Among them, is a normalization parameter at the result of the th iteration solution, indicating the value of the th alternating optimization of sub-problem 2; S3: Using the solution method of sub-problem 2, calculate the update of the transmitted waveform in the th iteration, which is expressed as: ​ ； Among them , is the search step projection operator, means projecting each element of the vector onto the unit circle respectively, , , means dimensional complex field, , , , means dimensional identity matrix, and are respectively , constitute the vector, , , means vectorizing the matrix; S4: Using the solution to subproblem 3, calculate The reflection coefficient The update is expressed as: ； Among them, , is the search step size, is the projection operator, , ； In the formula, represents the number of antenna elements on the RIS, represents the reflection coefficient of represents the transmission response vector of the RIS in the direction, represents the phase shift part in the RIS reflection coefficient, represents the complex domain of dimension represents the complex domain of dimension S5: By updating , determine whether the iteration termination condition is satisfied and ; if the termination condition is satisfied, then and are the MIMO radar transmission waveforms and the RIS reflection coefficients are the optimal solutions; if the termination condition is not satisfied, return to S2.

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