Intelligent reflector-assisted MIMO radar beamforming method for gathering main lobe transmitting power

Abstract

The invention discloses an intelligent reflecting surface (IRS)-assisted multiple-input-multiple-output (MIMO) radar transmitting beam forming method for gathering main lobe transmitting power, and aims to improve the power concentration degree of an MIMO radar main lobe area by minimizing the integral side lobe and main lobe ratio of a transmitting beam pattern so as to improve the transmitting beam forming performance of the MIMO radar main lobe area. Comprising the following steps: establishing an actual constraint optimization model of an MIMO transmitted waveform and an IRS reflection coefficient by taking a power ratio of a side lobe region to a main lobe region as a measure; converting a fraction objective function in the actual constraint optimization model into an integer objective function form by utilizing the Bukbach transform; constructing a sub-problem under an alternating minimization framework; and adopting a second-order Riemannian-Newton method to quickly solve an MIMO transmitted waveform and an IRS reflection coefficient respectively.

Description

Technical Field

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

[0002] As an advanced radar technology, MIMO radar uses multiple transmitting and receiving antennas to simultaneously send and receive signals, significantly improving the radar's detection performance. However, in some application scenarios, such as drone-mounted and vehicle-mounted MIMO radars, due to cost and volume constraints, the size and degrees of freedom of the MIMO array are limited, resulting in its beamforming performance being affected. Specifically, the sidelobe level of the transmit beam pattern is high, which easily introduces interference signals, affecting the accuracy and reliability of target detection. In addition, traditional MIMO radar systems usually require a large number of transmit channels to provide sufficient spatial degrees of freedom when transmitting beamforming, which further increases the complexity and cost of the system.

[0003] In order to solve the problem of constant modulus constraint, there are many effective algorithms and techniques in the prior art. For example, semidefinite relaxation technique and randomization are applied to the constant modulus waveform design of MIMO radar, and a continuous optimization algorithm based on relaxation method is proposed. Two refined continuous quadratic constraint quadratic programming algorithms are proposed to solve the waveform design problem that considers constant modulus constraint and similarity constraint at the same time. 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 focusing main lobe transmission power.

[0005] The technical solution adopted by the present invention is a smart reflector-assisted MIMO radar beamforming method for gathering main lobe transmission power, comprising the following steps:

[0006] 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;

[0007] 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;

[0008] 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;

[0009] 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.

[0010] Compared with the prior art, the present invention has the following significant advantages: the present invention takes minimizing ISMR as the criterion, jointly optimizes the MIMO radar transmission waveform and the IRS reflection coefficient, solves using the Riemann manifold optimization algorithm, and effectively reduces the power in the sidelobe area and increases the power concentration in the mainlobe area, which significantly improves the beamforming performance of the MIMO radar. The present invention has a wide range of practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the embodiments of the present invention or the existing technical solutions, the embodiments or the drawings of the existing technical contents are briefly introduced below.

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

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

[0014] Figure 3 This is the convergence curve of the objective function (ISMR) in dual main lobe mode.

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

[0016] Figure 5 This is a graph showing the objective function (ISMR) changing with the IRS dimension.

[0017] Figure 6 The flowchart of the algorithm proposed in the present invention.

[0018] Figure 7 Flowchart for optimizing MIMO radar transmit waveform variables using the Riemann-Newton method.

[0019] Figure 8 Flowchart for optimizing the IRS reflection coefficient matrix using the Riemann-Newton method.

[0020] Fig. 9 The overall implementation flow chart of the IRS-assisted MIMO radar beamforming method for focusing the mainlobe transmit power. DETAILED DESCRIPTION

[0021] The present invention is further described below in conjunction with the accompanying drawings and embodiments, namely, an IRS-assisted MIMO radar beamforming method for focusing mainlobe transmit power. Under the condition that the transmit waveform satisfies the constant modulus constraint and the IRS reflection coefficient amplitude satisfies the unimodular constraint, a practical constrained optimization model of the MIMO transmit waveform and the IRS reflection coefficient based on the integral sidelobe to mainlobe ratio (ISMR) minimization criterion is established; under the framework of alternating optimization, the transmit waveform and the IRS reflection coefficient are quickly solved by the second-order Riemann manifold optimization algorithm. The method establishes a practical constrained optimization model of the MIMO transmit waveform and the IRS reflection coefficient with the ISMR of the transmit beam diagram as the objective function, and the practical constrained optimization problem is a non-convex constrained quadratic function minimization problem; the fractional objective function in the optimization model is converted into an integral objective function by Dinkelbach transformation; under the framework of alternating optimization, the non-convex constrained quadratic function minimization problem is decomposed into two non-convex constant modulus constrained sub-problems, and then the Riemann-Newton method is used to solve each sub-problem. The specific implementation steps of the present invention are as follows:

[0022] Step 1: Establish a practical constrained optimization model of the MIMO transmission waveform and IRS reflection coefficient measured by the power ratio of the sidelobe area to the mainlobe area, specifically:

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

[0024] (1)

[0025] in, represents the angle from the array normal, is the detection signal wavelength.

[0026] Definition The transmitted signal of an array element at the nth sampling time is , where N is the total number of samples per pulse. For a line-of-sight path, the composite signal exist The direction can be expressed as

[0027] (2)

[0028] In the formula, Represented as a space-time emission waveform matrix, express The antenna is The spatial domain emission waveform vector at the moment, , Indicates vectorizing the matrix. represents the conjugate transpose operation, express dimensional identity matrix, represents the transpose operation, represents the Kronecker product.

[0029] Assuming that the distance between the MIMO radar and the IRS is significantly smaller than the distance between the MIMO radar or the IRS and the target, define is the target deviation direction measured by IRS, is the angle between the normal of the IRS and the normal of the MIMO radar transmit array. Then we have .

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

[0031] (3)

[0032] in, is the array element spacing of the IRS element, is the number of IRS units.

[0033] The reflection coefficient of IRS can be expressed by the diagonal matrix describe, ,in Represents an operator that transforms a vector into a diagonal matrix.

[0034] For non-line-of-sight paths, the composite signal exist The direction can be expressed as

[0035] (4)

[0036] In the formula, Represents the channel matrix from the MIMO transmit array to the IRS.

[0037] IRS assisted MIMO radar Transmit beam in direction It can be expressed as:

[0038] (5)

[0039] in for

[0040] (6)

[0041] and , , Indicates conjugation.

[0042] The integrated sidelobe to mainlobe ratio (ISMR) of the transmit beam is defined as:

[0043] (7)

[0044] in, is the main lobe area, is the side lobe area, , , and the matrix Defined as

[0045] (8)

[0046] in, represents the angle area, , , .

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

[0048] (9)

[0049] in, is the total emission energy, is the number of antennas, is the number of IRS units.

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

[0051] (10)

[0052] The actual constrained optimization problem of MIMO transmit waveform and IRS reflection coefficient is a non-convex constrained quadratic function minimization problem. The objective function For variables and They are all non-convex and difficult to solve directly.

[0053] Step 2: Use Dinkelbach transform to transform the fractional objective function of the actual constrained optimization model of MIMO transmit waveform and IRS reflection coefficient into an integer objective function.

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

[0055] (11)

[0056] The original problem can be transformed into:

[0057] (12)

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

[0059] Sub-problem 1: In the variable and Optimize the transmission waveform under fixed conditions , which is equivalent to:

[0060] (13)

[0061] in, is a positive number to ensure It is positive. express dimensional identity matrix, Indicated in The initial value for the iteration.

[0062] Sub-problem 2: Variables and Optimizing IRS reflection coefficient under fixed conditions , which is equivalent to:

[0063] (14)

[0064] in, , , , , , , represents the real part, It means to construct the diagonal elements of the matrix into column vectors.

[0065] To simplify the representation, define the matrix ,in is a guarantee matrix A positive constant, then the simplified result is:

[0066]

[0067] Step 4: Use the second-order Riemann-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 , , , maximum number of iterations and termination tolerance , set the current number of iterations ,initialization , ,

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

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

[0071] Step 4.2.2: Calculate The Riemann-Newton direction at ), the specific formula is:

[0072] (15)

[0073] And Riemann-Newton direction The plural form of is:

[0074] (16)

[0075] in, , , express The real part of express The imaginary part of is the diagonal loading factor, For function At the point The Riemann gradient at represents the imaginary part, is a complex variable In real-valued functions Euclidean gradient on .

[0076] Real Riemann Hessian Matrix is defined as:

[0077] (17)

[0078] in, , is a complex matrix The real form of is: , , express dimensional identity matrix, , is a complex matrix The real form of is: .

[0079] Step 4.2.3: Use the Riemann-Newton method to calculate In iteration The update is expressed as:

[0080] (18)

[0081] in, Representation variables In the The result in the iterations, For the Iteration search point, Indicates that Projecting the point on A common operation is to Projection onto the unit circle:

[0082] (19)

[0083] Step 4.2.4: Update according to the Riemann-Newton method , determine whether the conditions for iteration termination are met, that is: or If not satisfied, then , then return 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: Enter the maximum number of iterations and termination tolerance , set the current number of iterations ,initialization ;

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

[0087] (20)

[0088] And Riemann-Newton direction The plural form of is:

[0089] (twenty one)

[0090] in, , , express The real part of express The imaginary part of is the diagonal loading factor, Representation function At the point The Riemann gradient at is a complex variable Euclidean gradient on a real-valued function.

[0091] Real Riemann Hessian Matrix is defined as:

[0092] (twenty two)

[0093] in, , , is a complex matrix The real form of is: , , is a complex matrix The real form of is: .

[0094] Step 4.3.3: Use the Riemann-Newton method to calculate In iteration The update is expressed as:

[0095] (twenty three)

[0096] in, Indicates that Projecting the point on The contraction operation on . Projection onto the unit circle:

[0097] (twenty four)

[0098] Step 4.3.4: Update according to the Riemann-Newton method , determine whether the conditions for iteration termination are met, that is: or If not satisfied, then , then return to step 4.3.2, if satisfied, then output the IRS reflection coefficient ;

[0099] Step 4.4: In In the iteration The updates performed are expressed as:

[0100] (25)

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

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

[0103] 1) Input , , , , ;

[0104] 2) Initialization settings , , , ;

[0105] 3) In the framework of alternating optimization, the Riemann-Newton method is used to obtain , ;

[0106] 4) By definition, update ;

[0107] 5) If and ,but , return to 3), otherwise stop the iteration;

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

[0109] renew The specific process is as follows Figure 7 As shown, specifically:

[0110] 1) Input , , ;

[0111] 2) Initialization settings , ;

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

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

[0114] 5) Output MIMO radar transmission waveform .

[0115] renew The specific process is as follows Figure 8 As shown, specifically:

[0116] 1) Input , , ;

[0117] 2) Initialization settings , ;

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

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

[0120] 5) Output IRS reflection coefficient .

[0121] The invention is an IRS-assisted MIMO radar beamforming problem for focusing main lobe transmission power. Under the condition that the transmission waveform satisfies the constant modulus constraint, the ISMR of the transmission beam diagram is minimized as the design criterion, the MIMO radar transmission waveform and the IRS reflection coefficient are jointly optimized, and under the framework of alternating optimization, the complex non-convex constrained time-sharing quadratic programming problem is decomposed into several sub-problems, which are solved by using the Riemann manifold optimization algorithm.

[0122] The present invention introduces IRS in MIMO radar. IRS is a new type of reconfigurable surface antenna that can dynamically adjust the phase and amplitude of the reflected signal to optimize the signal transmission quality. By introducing IRS in 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. Based on the integrated sidelobe to mainlobe ratio (ISMR) minimization criterion, the present invention studies IRS-assisted MIMO radar transmit beamforming, wherein the transmit waveform satisfies the constant modulus constraint and the IRS reflection coefficient satisfies the unimodulus constraint. IRS can construct an additional non-line-of-sight path, and by adjusting the phase and amplitude of the reflected signal, more energy can be concentrated in the mainlobe area, while reducing the power in the sidelobe area, thereby improving the detection capability and anti-interference capability of the radar system.

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

[0124] Example

[0125] The present invention is further illustrated by Matlab simulation, which is an IRS-assisted MIMO radar beamforming method for focusing main lobe transmission power.

[0126] 1) Simulation parameter design

[0127] In this simulation, single main lobe beam mode and dual main lobe beam mode are considered respectively and the influence of IRS dimension on algorithm performance is tested. Assuming that the MIMO transmitter is placed at the origin, the distance between IRS and MIMO transmitter is , the angle between IRS and MIMO transmit array is The path loss model related to distance is: ,in The reference distance The path loss when is the path loss exponent. Channel The Rayleigh fading model is followed. The array element spacing of the MIMO array and IRS is half a wavelength, and the number of antenna array elements is , Snapshots , the total antenna transmission power is set to .

[0128] In single main lobe beam mode, The sampling interval is Uniform sampling, the main lobe area is , the side lobe area is In dual main lobe beam mode, the main lobe area is ,set up , then the side lobe area is When testing the effect of IRS dimension on algorithm performance, the IRS dimension was gradually increased from 64 to 256, with a sampling interval of 32.

[0129] 2) Beam diagram drawing

[0130] In order to intuitively demonstrate the effect of beamforming, the conventional MIMO radar without IRS assistance is compared with the IRS dimension The transmit beam patterns of the MIMO radar system are compared to analyze the impact of the introduction of IRS on the transmit beam pattern design of the MIMO radar system.

[0131] 3) Metrics

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

[0133] 4) Result analysis

[0134] The present invention has carried out 2 example simulations in total:

[0135] pass Figure 1 , Figure 2 It can be seen that in the single main lobe beam mode, with or without IRS assistance, as the number of iterations increases, the objective function has a clear downward trend and eventually stabilizes. The IRS-assisted MIMO radar system can reduce the sidelobe power while keeping the main lobe power of the transmitted waveform basically unchanged, thereby achieving a significant reduction in ISMR. Specifically, the ISMR values ​​in conventional MIMO radar, 64-unit, 128-unit, and 256-unit IRS-assisted MIMO radars are -8.8dB, -10.39dB, -11.32dB, and -17.29dB, respectively. It can be seen that with the increase in the number of IRS units, the ISMR of the transmit beam decreases significantly.

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

[0137] pass Figure 5 It can be seen that the introduction of IRS effectively reduces the ISMR value, improves the design performance of the MIMO radar system transmit beam pattern, and increases with the IRS dimension. As the ISMR increases, the ISMR gradually decreases. The reduction of ISMR in the single main lobe mode is significantly greater than that in the dual main lobe mode, which indicates that the single main lobe mode can benefit more from the application of IRS under the condition of the same number of IRS units.

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 The 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 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, 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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