An intelligent reflecting surface assisted MIMO radar beamforming method for aggregating main lobe transmission power

Abstract

The present invention discloses an intelligent reflecting surface (IRS)-aided multi-input multi-output (MIMO) radar transmit beamforming method for aggregating the main lobe transmit power, aiming to improve the power concentration degree in the main lobe region of the MIMO radar by minimizing the integrated sidelobe-to-main lobe ratio of the transmit beam pattern, thereby enhancing its transmit beamforming performance. The method includes: establishing an actual constraint optimization model of the MIMO transmit waveform and the IRS reflection coefficient with the power ratio between the sidelobe region and the main lobe region as a metric; using the Dinkelbach transformation to transform the fractional objective function in the actual constraint optimization model into an integral objective function form; constructing sub-problems under the alternating minimization framework; and respectively quickly solving the MIMO transmit waveform and the IRS reflection coefficient by using the second-order Riemannian Newton method.

Description

Technical Field

[0001] The present invention belongs to the technical fields of array signal processing and radar signal processing, and specifically relates to an intelligent reflecting surface (IRS)-assisted multiple-input multiple-output (MIMO) radar beamforming method for concentrating the main lobe transmission power. Background Art

[0002] As an advanced radar technology, MIMO radar transmits and receives signals simultaneously through multiple transmit and receive antennas, significantly improving the detection performance of the radar. However, in some application scenarios, such as unmanned aerial vehicle (UAV)-borne and vehicle-mounted MIMO radars, due to cost and volume limitations, the size and degrees of freedom of the MIMO array are limited, resulting in affected beamforming performance. Specifically, the sidelobe level of the transmit beam pattern is relatively high, which is likely to introduce interference signals and affect the accuracy and reliability of target detection. In addition, when traditional MIMO radar systems perform transmit beamforming, a large number of transmit channels are usually required to provide sufficient spatial degrees of freedom, which further increases the complexity and cost of the system.

[0003] To solve the problem of constant modulus constraint, there are various effective algorithms and techniques in the prior art. For example, semi-definite relaxation technology and randomization are applied to the MIMO radar constant modulus waveform design, and a continuous optimization algorithm based on the relaxation method is proposed. Two refined continuous quadratic constraint quadratic programming algorithms are proposed to solve the waveform design problem considering both constant modulus constraint and similarity constraint. However, the convergence of these algorithms is difficult to guarantee. Summary of the Invention

[0004] The purpose of the present invention is to propose an IRS-assisted MIMO radar beamforming method for concentrating the main lobe transmission power.

[0005] The technical solution adopted by the present invention is an IRS-assisted MIMO radar beamforming method for concentrating the main lobe transmission power, including the following steps:

[0006] Step 1: Establish an actual constraint optimization model of the MIMO transmit waveform and the IRS reflection coefficient measured by the power ratio between the sidelobe region and the main lobe region. The actual constraint optimization problem of the MIMO transmit waveform and the IRS reflection coefficient is a non-convex constraint quadratic function minimization problem;

[0007] Step 2: Use the Dinkelbach transformation to transform the fractional objective function in the actual constraint optimization model of the MIMO transmit waveform and the IRS reflection coefficient into an integral objective function form;

[0008] Step 3: Under the framework of alternating minimization, decompose the non-convex constraint quadratic function minimization problem into two non-convex constant modulus constraint sub-problems;

[0009] Step 4: Use the second-order Riemannian Newton method to solve two non-convex constant modulus constraint sub-problems respectively, and obtain the optimal MIMO transmission waveform and IRS reflection coefficient.

[0010] Compared with the prior art, the significant advantages of the present invention are as follows: The present invention takes minimizing the ISMR as the criterion, jointly optimizes the MIMO radar transmission waveform and the IRS reflection coefficient, and uses the Riemannian manifold optimization algorithm to solve. Through simulation experiments, it is verified that the power in the sidelobe region is effectively reduced, the power concentration in the main lobe region is improved, and the beamforming performance of the MIMO radar is significantly enhanced. The present invention has wide practical value. Brief Description of the Drawings

[0011] In order to more clearly illustrate the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings of the embodiments or the prior art content.

[0012] Figure 1 It is a convergence curve graph of the objective function (ISMR) in the single main lobe mode.

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

[0014] Figure 3 It is a convergence curve graph of the objective function (ISMR) in the double main lobe mode.

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

[0016] Figure 5 It is a curve graph of the objective function (ISMR) varying with the IRS dimension.

[0017] Figure 6 It is a flow chart of the algorithm proposed by the present invention.

[0018] Figure 7 It is a flow chart of optimizing the MIMO radar transmission waveform variable using the Riemannian Newton method.

[0019] Figure 8 It is a flow chart of optimizing the IRS reflection coefficient matrix using the Riemannian Newton method.

[0020] Figure 9 It is a general implementation flow chart of the IRS-assisted MIMO radar beamforming method for aggregating the main lobe transmission power. Detailed Embodiments

[0021] The present invention will be further described below in conjunction with the accompanying drawings and embodiments, namely an IRS-assisted MIMO radar beamforming method for aggregating main lobe transmission power. Under the conditions that the transmitted waveform satisfies the constant modulus constraint and the magnitude of the IRS reflection coefficient satisfies the unimodular constraint, an actual constraint optimization model of the MIMO transmitted waveform and the IRS reflection coefficient is established based on the minimum integral sidelobe to main lobe ratio (ISMR) criterion; under the framework of alternating optimization, the transmitted waveform and the IRS reflection coefficient are quickly solved by the second-order Riemannian manifold optimization algorithm. This method establishes an actual constraint optimization model of the MIMO transmitted waveform and the IRS reflection coefficient with the ISMR of the transmitted beam pattern as the objective function. This actual constraint optimization problem is a non-convex constrained quadratic function minimization problem; the fractional objective function in the optimization model is transformed into an integral objective function through the Dinkelbach transformation; under the framework of alternating optimization, the non-convex constrained quadratic function minimization problem is decomposed into two non-convex constant modulus constraint sub-problems, and then the Riemannian Newton method is used to solve each sub-problem. The specific implementation steps of the present invention are as follows:

[0022] Step 1: Establish an actual constraint optimization model of the MIMO transmitted waveform and the IRS reflection coefficient measured by the power ratio between the sidelobe region and the main lobe region, specifically as follows:

[0023] Assume that the transmitting antenna of the MIMO radar is a one-dimensional uniform linear array with the number of array elements being , the inter-element distance is d, and the steering vector of this uniform linear array is:

[0024] (1)

[0025] where represents the angle deviating from the array normal, is the wavelength of the detection signal.

[0026] Define the transmitted signal of the th array element at the nth sampling time as , where N represents the total number of samples per pulse. For the line-of-sight path, the synthesized signal in the direction can be expressed as

[0027] (2)

[0028] In the formula, represents the spatio-temporal transmitted waveform matrix, represents spatial domain transmitted waveform vectors of antennas at the th moment, represents vectorizing the matrix, represents the conjugate transpose operation, represents the identity matrix of dimension denotes the transpose operation, denotes the Kronecker product.

[0029] Assume that the distance between the MIMO radar and the IRS is significantly smaller than the distance from the MIMO radar or the IRS to the target. Define as the direction deviation of the target measured by the IRS, is the angle between the normal of the IRS and the normal of the MIMO radar transmitting array. Then we have .

[0030] The transmission response vector of the IRS in the direction can be described as:

[0031] (3)

[0032] where is the element spacing of the IRS elements, is the number of elements of the IRS.

[0033] The reflection coefficient of the IRS can be described by the diagonal matrix , where denotes the operator that transforms a vector into a diagonal matrix.

[0034] For the non-line-of-sight path, the composite signal in the direction can be expressed as

[0035] (4)

[0036] In the formula, denotes the channel matrix from the MIMO transmitting array to the IRS.

[0037] The transmission beam of the IRS-assisted MIMO radar in the direction can be expressed as:

[0038] (5)

[0039] where is

[0040] (6)

[0041] and , , denotes taking the conjugate.

[0042] Define the integrated sidelobe to mainlobe ratio (ISMR) of the transmission beam as:

[0043] (7)

[0044] Among them, is the main lobe region, is the side lobe region, , , and the matrix is defined as

[0045] (8)

[0046] Among them, represents the angular region, , , .

[0047] In the IRS-assisted MIMO radar beamforming problem model, the IRS is subject to the unimodular constraint. To ensure the transmission efficiency of the transmitter, the transmitted waveform satisfies the constant modulus constraint, that is:

[0048] (9)

[0049] Among them, is the total transmission energy, is the number of antennas, is the number of elements of the IRS.

[0050] Therefore, the actual constraint optimization model of the MIMO transmitted waveform and the IRS reflection coefficient can be described as:

[0051] (10)

[0052] The actual constraint optimization problem of the MIMO transmitted waveform and the IRS reflection coefficient is a non-convex constrained quadratic function minimization problem, and the objective function is non-convex with respect to the variables and and is difficult to solve directly.

[0053] Step 2: Use the Dinkelbach transformation to transform the fractional objective function of the actual constraint optimization model of the MIMO transmitted waveform and the IRS reflection coefficient into an integral objective function.

[0054] The fractional objective function in problem (10) is difficult to handle, so an auxiliary variable is introduced, and the fractional objective function is transformed into an integral form through the Dinkelbach transformation. Specifically, is defined as:

[0055] (11)

[0056] The original problem can be transformed into:

[0057] (12)

[0058] Step 3: In the framework of alternating minimization, decompose the non-convex constrained quadratic function minimization problem (12) into two non-convex constant modulus constrained sub-problems:

[0059] Sub-problem 1: Optimize the transmit waveform and with fixed, which is equivalent to:

[0060] (13)

[0061] where is a positive constant to ensure that is positive definite, denotes the -dimensional identity matrix, and represents the initial value in the

[0062] Sub-problem 2: Optimize the IRS reflection coefficient and with fixed, which is equivalent to:

[0063] (14)

[0064] where , , , , , , denotes taking the real part, and denotes constructing the diagonal elements of the matrix into a column vector.

[0065] For simplified representation, define the matrix where is a positive constant to ensure that the matrix is positive definite, then the simplified result is:

[0066]

[0067] Step 4: Use the second-order Riemannian Newton method to solve the MIMO transmit waveform and IRS reflection coefficient sub-problems. The specific method is as follows:

[0068] Step 4.1: Input , , , the maximum number of iterations and the termination tolerance , set the current number of iterations , initialize , ,

[0069] Step 4.2: Solve problem (13) using the Riemannian Newton method.

[0070] Step 4.2.1: Input the maximum number of iterations and the termination tolerance , set the current number of iterations , initialize ;

[0071] Step 4.2.2: Calculate the Riemannian Newton direction at ( ), and the specific formula is:

[0072] (15)

[0073] and the complex form of the Riemannian Newton direction is:

[0074] (16)

[0075] where , , represents the real part of represents the imaginary part of is the diagonal loading factor, is the function at the point the Riemannian gradient, represents taking the imaginary part, is the complex variable on the real-valued function the Euclidean gradient.

[0076] The real Riemannian Hessian matrix is defined as:

[0077] (17)

[0078] where , is the real form of the complex matrix : , , represents the - dimensional identity matrix, , is a complex matrix in its real form: .

[0079] Step 4.2.3: Use the Riemann-Newton method to calculate the update in the th iteration, which is expressed as:

[0080] (18)(18)

[0081] where represents the result of the variable in the th iteration, is the search point in the th iteration, represents projecting the point on onto . A common operation is to project onto the unit circle:

[0082] (19)

[0083] Step 4.2.4: Update according to the Riemann-Newton method and determine whether the iteration termination condition is satisfied, i.e.: or . If not satisfied, then , and then go back to Step 4.2.2. If satisfied, output the MIMO radar transmit waveform ;

[0084] Step 4.3: Use the Riemann-Newton method to solve problem (14).

[0085] Step 4.3.1: Input the maximum number of iterations and the termination tolerance , set the current iteration number , and initialize ;

[0086] Step 4.3.2: Calculate the Riemann-Newton direction ( ) at . The specific formula is:

[0087] (20)

[0088] and the complex form of the Riemann-Newton direction is:

[0089] (21)

[0090] where , , denotes the real part of , and denotes the imaginary part of . is the diagonal loading factor, denotes the Riemannian gradient of the function at the point , and is the Euclidean gradient of the complex variable on the real-valued function.

[0091] The real Riemannian Hessian matrix is defined as:

[0092] (22)

[0093] where , , is the real form of the complex matrix : , , is the real form of the complex matrix : .

[0094] Step 4.3.3: The update of in the -th iteration using the Riemannian Newton method is expressed as:

[0095] (23)

[0096] where denotes the contraction operation that projects the point on onto . Similarly, project onto the unit circle:

[0097] (24)

[0098] Step 4.3.4: Update according to the Riemannian Newton method and determine whether the iteration termination condition is satisfied, i.e., or . If not satisfied, then , and then go back to Step 4.3.2. If satisfied, output the IRS reflection coefficient ;

[0099] Step 4.4: The update of in the -th iteration is expressed as:

[0100] (25)

[0101] Step 4.5: Update according to the above algorithm , and determine whether the iteration termination condition is satisfied, that is: or , where and are the termination tolerance and the maximum number of iterations respectively. If not satisfied, then , and then go back to Step 4.2 to update again. If satisfied, output the MIMO radar transmission waveform and the IRS reflection coefficient .

[0102] In summary, the algorithm flow of this optimization problem is as shown in Figure 6 and specifically:

[0103] 1) Input , , , , ;

[0104] 2) Initialize and set , , , ;

[0105] 3) Under the framework of alternating optimization, use the Riemannian Newton method to obtain , respectively;

[0106] 4) Update according to the definition;

[0107] 5) If and , then , go back to 3), otherwise stop the iteration;

[0108] 6) Output the MIMO radar transmission waveform and the IRS reflection coefficient .

[0109] The specific process of updating is as shown in Figure 7 and specifically:

[0110] 1) Input , , ;

[0111] 2) Initialize and set , ;

[0112] 3) Update according to the Riemann-Newton method ;

[0113] 4) If and , then , return to 3), otherwise stop the iteration;

[0114] 5) Output the MIMO radar transmission waveform .

[0115] The specific process of updating is as follows Figure 8 : Specifically:

[0116] 1) Input , , ;

[0117] 2) Initialize the settings , ;

[0118] 3) Update according to the Riemann-Newton method;

[0119] 4) If and , then , return to 3), otherwise stop the iteration;

[0120] 5) Output the IRS reflection coefficient .

[0121] The present invention is an IRS-assisted MIMO radar beamforming problem that aggregates the main lobe transmission power. Under the condition that the transmission waveform satisfies the constant modulus constraint, with the minimization of the ISMR of the transmission beam pattern as the design criterion, jointly optimize the MIMO radar transmission waveform and the IRS reflection coefficient. In the framework of alternating optimization, decompose the complex non-convex constrained time-sharing quadratic programming problem into several sub-problems, and use the Riemannian manifold optimization algorithm to solve it.

[0122] The present invention introduces an IRS into a MIMO radar. The IRS is a new type of reconfigurable surface antenna that can dynamically adjust the phase and amplitude of the reflected signal, thereby optimizing the signal transmission quality. By introducing the IRS into the MIMO radar system, a large number of additional degrees of freedom can be introduced without increasing the scale of the MIMO array, significantly improving the beamforming performance. The present invention studies the transmit beamforming of an IRS-assisted MIMO radar based on the minimum integral sidelobe-to-mainlobe ratio (ISMR) criterion, where the transmit waveform satisfies the constant modulus constraint and the IRS reflection coefficient satisfies the unimodular constraint. The IRS can construct an additional non-line-of-sight path. By adjusting the phase and amplitude of the reflected signal, more energy can be concentrated in the main lobe region while reducing the power in the sidelobe region, thereby improving the detection ability and anti-interference ability of the radar system.

[0123] The simulation results show that the transmit beamforming method of the IRS-assisted MIMO radar proposed by the present invention can reduce the power in the sidelobe region while keeping the main lobe power basically unchanged, achieving the purpose of reducing the ISMR and effectively improving the beamforming performance of the MIMO radar system.

[0124] Embodiment

[0125] Through Matlab simulation, the present invention, an IRS-assisted MIMO radar beamforming method for concentrating the transmit power of the main lobe, is further illustrated.

[0126] 1) Simulation parameter design

[0127] In this simulation, the single main lobe beam pattern and the dual main lobe beam pattern are respectively considered, and the influence of the IRS dimension on the algorithm performance is tested. It is assumed that the MIMO transmitter is placed at the origin, and the distance between the IRS and the MIMO transmitter , and the included angle between the IRS and the MIMO transmit array is . The path loss model related to the distance is: , where is the reference distance when the path loss, is the path loss exponent. The channel follows the Rayleigh fading model. The element spacing of the MIMO array and the IRS is both half-wavelength, the number of antenna elements , the number of snapshots , and the total transmit power of the antenna is set to .

[0128] In the single main lobe beam pattern, with as the sampling interval, uniform sampling is performed in , the main lobe region is , and the sidelobe region is . In the dual main lobe beam pattern, the main lobe region is , set , then the sidelobe region is . When testing the influence of the IRS dimension on the algorithm performance, the IRS dimension is gradually increased from 64 to 256, and the sampling interval is 32.

[0129] 2) Beam pattern plotting

[0130] To intuitively show the effect of beamforming, the transmitting beam patterns of a conventional MIMO radar without IRS assistance and the IRS dimension are compared to analyze the influence of the introduction of IRS on the design of the transmitting beam pattern of the MIMO radar system.

[0131] 3) Measurement metrics

[0132] In the present invention, in addition to the transmitting beam pattern, the ISMR of the transmitting beam is also used as a measurement metric, and the specific definition is shown in formula (7). The smaller the ISMR, the better the performance of the MIMO radar transmitting beam pattern.

[0133] 4) Result analysis

[0134] A total of 2 instance simulations are carried out in the present invention:

[0135] Through Figure 1 , Figure 2 It can be seen that in the single main lobe beam mode, whether there is IRS assistance or not, as the number of iterations increases, the objective function has an obvious downward trend and finally tends to be stable. The IRS-assisted MIMO radar system can reduce the sidelobe power while keeping the main lobe power of the transmitting waveform basically unchanged, thereby significantly reducing the ISMR. Specifically, the ISMR values in a conventional MIMO radar, a 64-element, a 128-element, and a 256-element IRS-assisted MIMO radar are -8.8 dB, -10.39 dB, -11.32 dB, and -17.29 dB respectively. It can be seen that as the number of IRS elements increases, the ISMR of the transmitting beam decreases significantly.

[0136] Through Figure 3 , Figure 4It can be seen that in the dual main-lobe beam pattern, the variation result of the objective function with the number of iterations is similar to that in the single main-lobe beam pattern, that is, the algorithm can converge as the number of iterations increases. Introducing the IRS into the MIMO radar system effectively reduces the sidelobe level of the dual main-lobe desired beam pattern, thereby reducing the value of the ISMR. In the conventional MIMO radar, the 64-element, 128-element, and 256-element IRS-assisted MIMO radars, the values of the ISMR are -7.85 dB, -8.24 dB, -8.84 dB, and -9.45 dB, respectively. Compared with the single main-lobe beam pattern, the sidelobe reduction amplitude and the ISMR reduction amplitude in the dual main-lobe case are smaller.

[0137] Through Figure 5 It can be seen that whether it is the single main-lobe beam pattern or the dual main-lobe beam pattern, the introduction of the IRS effectively reduces the value of the ISMR, improves the design performance of the transmitting beam pattern of the MIMO radar system, and as the dimension of the IRS increases, the ISMR gradually decreases. Among them, the reduction amplitude of the ISMR in the single main-lobe pattern is significantly greater than that in the dual main-lobe pattern, which indicates that under the condition of the same number of IRS elements, the single main-lobe pattern can benefit more from the application of the IRS.

Claims

1. A smart reflector-assisted MIMO radar beamforming method for focusing main lobe transmission power, characterized in that: The following steps are involved: Step 1: Establishing a practical constrained optimization model of a MIMO transmission waveform and an IRS reflection coefficient measured by the power ratio of the sidelobe region to the mainlobe region, wherein the practical constrained optimization problem of the MIMO transmission waveform and the IRS reflection coefficient is a non-convex constrained quadratic function minimization problem; Step 2: Use Dinkelbach transform to transform the fractional objective function in the actual constrained optimization model of MIMO transmit waveform and IRS reflection coefficient into an integer objective function form; Step 3: Under the framework of alternating minimization, the non-convex constrained quadratic function minimization problem is decomposed into two non-convex constant modulus constrained sub-problems; Step 4: Use the second-order Riemann-Newton method to solve the two non-convex constant modulus constraint sub-problems respectively to obtain the optimal MIMO transmit waveform and IRS reflection coefficient.

2. The method for intelligent reflector-assisted MIMO radar beamforming for focusing main lobe transmission power according to claim 1, characterized in that: The actual constrained optimization model of the MIMO transmit waveform and IRS reflection coefficient is established as follows: ， In the formula, When it is empty, it emits a waveform vector. represents the space-time emission waveform matrix, Indicates vectorizing the matrix. express The antenna is The spatial domain emission waveform vector at the moment, Indicates The array element is The transmitted signal at each sampling moment, is the total emission energy, represents the total number of samples per pulse, is the number of antennas, is the number of IRS units, For the The reflection coefficient corresponding to each IRS unit is represents the conjugate transpose operation, represents an operator that transforms a vector into a diagonal matrix, is the main lobe area, is the side lobe area, , , express dimensional identity matrix, represents the Kronecker product, and the matrix Defined as ， in, represents the angle from the array normal, , is the IRS reflection coefficient matrix, represents the angle area, , , , is the channel matrix between the MIMO radar transmit array and the IRS, represents the steering vector of the MIMO radar, Indicates that the IRS The emission response vector in the direction, is the angle between the normal to the IRS and the normal to the MIMO radar transmit array.

3. The method for intelligent reflector-assisted MIMO radar beamforming for focusing main lobe transmission power according to claim 2, characterized in that: The specific method of converting the fractional objective function of the actual constraint optimization model of MIMO transmission waveform and IRS reflection coefficient into an integer objective function by using Dinkelbach transform is: Introducing auxiliary variables The objective function of the actual constraint optimization model of the MIMO transmission waveform and the IRS reflection coefficient is converted into an integer objective function in the form of a fraction: ， in, .

4. The method for intelligent reflector-assisted MIMO radar beamforming for focusing main lobe transmission power according to claim 3, characterized in that: Based on the alternating minimization framework, the non-convex constrained quadratic function minimization problem is transformed into two non-convex constant modulus constrained sub-problems, and the MIMO transmission waveform is solved iteratively. and IRS reflection coefficient , in At the iteration, the corresponding sub-problems are: Sub-problem 1: In the variable and Optimizing MIMO transmit waveform under fixed conditions , which is equivalent to: ， in, is a positive number to ensure It is positive. express dimensional identity matrix, Indicated in The initial value of the iteration operation, is the number of antennas; Sub-problem 2: Variables and Optimizing IRS reflection coefficient under fixed conditions , which is equivalent to: ， in, , , , , , , represents the space-time emission waveform matrix, , , represents the angle area, is the channel matrix between the MIMO radar transmit array and the IRS, represents the steering vector of the MIMO radar, Indicates that the IRS The emission response vector in the direction, represents the angle from the array normal, is the angle between the normal of the IRS and the normal of the MIMO radar transmit array, is the number of IRS units, represents the real part, It means to construct the matrix diagonal elements into column vectors. represents the Hadamard product, represents the conjugate transpose operation, Represents the transpose operation; To simplify the representation, define the matrix ,in is a guarantee matrix A positive constant, then the simplified result is: 。 5. The method for intelligent reflector-assisted MIMO radar beamforming for focusing main lobe transmission power according to claim 4, characterized in that: The specific method to solve sub-problem 1 is: S1: Enter the maximum number of iterations and termination tolerance , set the current number of iterations ,initialization ; S2: Calculate the Riemann-Newton direction of subproblem 1 , the specific process is as follows: Constant modulus constraint Defined as a complex circular manifold , at point The tangent space at , the Euclidean gradient Projection to tangent space The Riemann gradient can be obtained as: ， in, represents conjugation, Indicates the length A vector of all 1s, Indicates the length The all-zero vector, express arrive The orthogonal projection of is a complex variable In real-valued functions Euclidean gradient on ; The real Riemann-Hessian matrix is ​​defined as: ， in, , , , , , It means to construct the column vector into a diagonal matrix. represents the real part, It means taking the imaginary part; Then solve Newton's equation in real form , the solution in the Riemann-Newton direction is: ， in, , , is the diagonal loading factor; Riemann-Newton Direction The plural form of is: ， in, express The real part of express The imaginary part of S3: According to the complex Riemann-Newton direction Get the first In the iteration The updated output is, the specific formula is: ， in, Indicates that Projecting the point on A common operation is to Projection onto the unit circle: ， in, For the The iteration search point is expressed as: ， S4: Update according to the second-order Riemann-Newton method , if the termination condition is met, the iteration terminates. Output the MIMO radar transmission waveform as the optimal solution in the iteration of subproblem 1 ; If the iteration termination condition is not met, return to step S2, where the termination condition is or .

6. The method for intelligent reflector-assisted MIMO radar beamforming for focusing main lobe transmission power according to claim 4, characterized in that: The specific method to solve sub-problem 2 is: S1: Enter the maximum number of iterations and termination tolerance , set the current number of iterations ,initialization ; S2: Calculate the Riemann-Newton direction of subproblem 2 , the specific process is as follows: Unimodular Constraint Defined as a complex circular manifold , which is at point The tangent space at , the Euclidean gradient Project to The Riemann gradient can be obtained as: ， in, represents conjugation, Indicates the length is A vector of all 1s, Indicates the length is The all-zero vector, express arrive The orthogonal projection of is a complex variable In real-valued functions Euclidean gradient on ; The real Riemann-Hessian matrix is ​​defined as: ， in, express dimensional identity matrix, , , , , , Indicates that the column vector is constructed into a diagonal matrix; Then solve Newton's equation in real form , the solution in the Riemann-Newton direction is: ， in, , , is the diagonal loading factor; Riemann-Newton Direction The plural form of is: ， in, express The real part of express The imaginary part of S3: According to the complex Riemann-Newton direction Get the first Iteration pair The updated output of is: ， in, Indicates that Projecting the point on The contraction operation on Projection onto the unit circle: ， in, For the The iteration search point is expressed as: ， S4: Update according to the second-order Riemann-Newton method , if the termination condition is met, the iteration terminates. The optimal solution of subproblem 2 in this iteration is output as the IRS reflection coefficient ; If the iteration termination condition is not met, return to step S2, where the termination condition is or .

7. The method for intelligent reflector-assisted MIMO radar beamforming for focusing main lobe transmission power according to claim 4, characterized in that: The emission waveform is obtained by iterative solution and IRS reflection coefficient The specific process is: S1: Enter the maximum number of iterations and termination tolerance , set the current number of iterations , randomly initialized under the constant modulus constraint , , and get the initialized auxiliary variables ; S2: According to the Riemann-Newton method, the emission waveform Iterative update, the update rule is , determine whether the iteration termination condition is met or , if satisfied, then is the optimal solution in the iteration, that is , obtain the The optimal emission waveform of the round iteration ; Then the IRS reflection coefficient Optimization update of S3: According to the Riemann-Newton method Iterative update, the update rule is , determine whether the iteration termination condition is met or , if satisfied, then the current As the solution of the Riemann-Newton method, , obtain the The optimal IRS reflection coefficient of the round iteration , and finally for the auxiliary variable Make updates; S4: According to the iterative formula Update auxiliary variables ; S5: Determine whether the iteration termination condition is met or , if satisfied, the current MIMO radar transmits the waveform and IRS reflection coefficient As the optimal result, if the iteration termination condition is not met, return to step S2.

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