Waveform design method and apparatus for space-frequency transmission pattern of broadband MIMO radar

Abstract

This application relates to a waveform design method and apparatus for the space-frequency transmission pattern of a broadband MIMO radar. The method proposes a waveform design framework for accurately shaping the transmission pattern of a broadband MIMO radar, enabling the radar to adapt to various operating scenarios. Specifically, it involves: establishing a signal model; deriving the synthetic energy of a single discrete space-frequency point based on DFT transform; establishing dynamic modulus constraints; establishing a maxima-minima multi-objective optimization model; smoothing and approximating the objective function; and using KKT conditions for effective solution. This method achieves precise control of the spatial and frequency domain radiation directions under diverse operating scenarios by minimizing the maximum fitting error between the synthesized transmission beam pattern and the desired pattern; and introduces dynamic modulus constraints to regulate the amplitude fluctuations of the time-domain waveforms of each antenna element to meet different hardware and operating environment requirements.

Description

Technical Field

[0001] This invention belongs to the field of radar waveform design technology, and relates to a waveform design method and apparatus for a broadband MIMO radar space-frequency transmission pattern. Background Technology

[0002] In existing work on wideband multiple-input multiple-output (MIMO) radar transmit pattern optimization, some works use the least squares criterion to minimize the average error between the energy focused by the transmitted waveform in the spatial-frequency domain and the ideal energy distribution template. This type of problem can be reduced to a fourth-order non-convex optimization under modulus constraints, with two solution strategies: a two-step method that first optimizes the waveform covariance matrix and then approximates the waveform satisfying the modulus constraint; and a one-step method that directly solves the optimized waveform. Other works use a min-max optimization framework to improve control accuracy by minimizing the maximum local error. This type of problem is highly non-convex and non-smooth, making direct solutions difficult. Therefore, some works use the ADMM method for solution: for example, replacing the max structure with boundary variables, proposing a variable substitution ADMM method to solve for both the original and boundary variables; or using the Lawson algorithm to transform the original min-max problem into an iterative weighted square minimization problem, also solved within the ADMM framework. Still other works use the lp norm to smooth the max function, then gradually simplify the problem based on the MM framework to find the optimal solution.

[0003] In current modulus constraints, the constant modulus constraint limits the waveform to a constant modulus, the peak-to-average power ratio (PAPR) constraint restricts the peak value of the waveform, and the ratio constraint restricts the ratio of the maximum to the minimum value of the waveform. The looser the waveform constraints, the greater the optimization freedom offered. However, existing techniques have the following drawbacks:

[0004] (1) A two-step design was carried out. First, the ideal power spectrum was derived by SDP technology, and then the ideal power spectrum was matched by an optimization algorithm. The two-step operation reduced the computational efficiency of the problem.

[0005] Existing technologies, when building models, consider minimizing the average matching error, focusing only on the magnitude of the average error and ignoring the peak error at key spatial frequency points, resulting in insufficient energy control precision.

[0006] (2) The ADMM algorithm has the following defects: First, the algorithm involves a high degree of variable dimension and the calculation process is relatively cumbersome and complex. Second, the performance of the ADMM algorithm depends to a large extent on the selection of parameters. When the parameters are not well selected, the algorithm will not perform well. Third, the ADMM algorithm lacks a universal convergence criterion for non-convex optimization problems.

[0007] (3) The p-norm optimization method also has its drawbacks: the accuracy of the p-norm approximation is significantly affected by the choice of p value and the distribution of extreme values. When there are extremely large error points, the optimization deviation may be amplified, which is not conducive to solving the original problem.

[0008] (4) Existing modulus constraints have limitations: Current work is insufficient in accurately controlling the range of modulus variation of each antenna waveform. While constant modulus constraints can maximize the working efficiency of nonlinear amplifiers, they severely limit the degree of freedom in waveform optimization. Peak-to-average power ratio (PAPR) constraints relax constant modulus constraints to constraints on the maximum modulus, improving the degree of freedom in optimization while ensuring that the waveform does not produce distortion after amplification. However, this has a significant impact on the working efficiency of the waveform amplifier. In order to balance the degree of freedom in optimization and working efficiency, ratio constraints control the waveform modulus within a specific ratio range. However, constraining only the ratio of the maximum and minimum modulus cannot accurately control the instantaneous modulus, which also causes certain limitations. Summary of the Invention

[0009] To address the problems existing in the above-mentioned traditional methods, this invention proposes a waveform design method and apparatus for broadband MIMO radar space-frequency transmission patterns.

[0010] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0011] On the one hand, a waveform design method for the space-frequency transmission pattern of a broadband MIMO radar is provided, including the following steps:

[0012] Establish a signal model and determine the expression for the synthesized transmit power of the broadband MIMO platform in the far field.

[0013] The composite transmit power expression is transformed using DFT to determine the composite energy at each spatial frequency point.

[0014] Dynamic mode constraints are established based on the total antenna power and baseband signal transmitted by each antenna within a single pulse.

[0015] Based on the synthesized energy at each spatial frequency point, the desired beam pattern, the dynamic mode constraint, and the scaling factor, a mode-constrained optimization objective function for maxima-minima multi-objective optimization is constructed; the scaling factor is used to eliminate the dimensional difference between the designed beam direction and the desired beam pattern.

[0016] Based on the objective function constrained by the modulus, the scaling factor is solved by the bisection method. Then, LES is used to smooth and replace the maximum value function. Finally, the MM algorithm is used to transform the multi-objective optimization problem into multiple constrained linear subproblems.

[0017] The constrained linear subproblem is solved using KKT conditions and search rules to obtain the final waveform optimization optimal solution; and the quadratic iteration algorithm is used to accelerate the algorithm.

[0018] On the other hand, a waveform design device for a broadband MIMO radar space-frequency transmission pattern is also provided, comprising:

[0019] The signal model building module is used to build a signal model and determine the expression for the synthetic transmit power of the broadband MIMO platform in the far field.

[0020] The module for determining the composite energy at each spatial frequency point is used to perform a DFT transform on the composite transmit power expression to determine the composite energy at each spatial frequency point.

[0021] The dynamic mode constraint construction module is used to establish dynamic mode constraints based on the total antenna power and baseband signal transmitted by each antenna within a single pulse.

[0022] The module for constructing the mode-constrained optimization objective function is used to construct a maxima-minima multi-objective optimization objective function based on the synthetic energy at each spatial frequency point, the desired beam pattern, the dynamic mode constraint, and the scaling factor. The scaling factor is used to eliminate the dimensional difference between the designed beam direction and the expected beam pattern.

[0023] The multi-objective optimization problem transformation module is used to solve the scaling factor using the bisection method based on the objective function constrained by the modulus. Then, LES is used to smooth and replace the maximum value function. Finally, the MM algorithm is used to transform the multi-objective optimization problem into multiple constrained linear subproblems.

[0024] The waveform optimization optimal solution module is used to solve constrained linear subproblems using KKT conditions and search rules to obtain the final waveform optimization optimal solution; and the quadratic iteration algorithm is used to accelerate the algorithm.

[0025] One of the above technical solutions has the following advantages and beneficial effects:

[0026] The aforementioned waveform design method and apparatus for the space-frequency transmission pattern of a broadband MIMO radar proposes a waveform design framework for accurately shaping the transmission pattern of a broadband MIMO radar, enabling the broadband MIMO radar to adapt to various operating scenarios. Specifically, it involves: establishing a signal model; deriving the synthetic energy of a single discrete space-frequency point based on DFT transform; establishing dynamic modulus constraints; establishing a maxima-minima multi-objective optimization model; smoothing and approximating the objective function; and using KKT conditions for effective solution. This method achieves precise control of the spatial and frequency domain radiation directions under diverse operating scenarios by minimizing the maximum fitting error between the synthetic transmission beam pattern and the desired pattern; and introduces dynamic modulus constraints to regulate the amplitude fluctuations of the time-domain waveforms of each antenna element to cope with different hardware and operating environment requirements. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of this application or the conventional technology, the drawings used in the description of the embodiments or the conventional technology will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a flowchart illustrating the waveform design method for the air-frequency transmission pattern of a broadband MIMO radar in one embodiment.

[0029] Figure 2 In one embodiment, the average error and maximum error of the method compared to the prior art vary with the number of iterations. Figure 2 Figure (a) shows the curve of the average error as a function of the number of iterations. Figure 2 (b) is a graph showing the maximum error as a function of the number of iterations.

[0030] Figure 3 This document presents an example of a conventional method and an optimized space-frequency transmission pattern based on the present method; wherein... Figure 3 (a) shows the optimized space-frequency transmission pattern using the existing method. Figure 3 (b) represents the method in this context. Time-optimized space-frequency transmission pattern; Figure 3 (c) represents the method in this context. Time-optimized space-frequency transmission pattern; Figure 3 (d) represents the method in this context. Time-optimized space-frequency transmission pattern; Figure 3 (e) represents the method in this context. Time-optimized space-frequency transmission pattern;

[0031] Figure 4 This is a spatial transmission pattern for each frequency point in an embodiment, showing the existing method and the optimized method of this invention; wherein... Figure 4 (a) shows the spatial transmission pattern for each frequency point after optimization using existing technology. Figure 4 (b) represents the method in this context. The time-optimized spatial transmission pattern for each frequency point; Figure 4 (c) represents the method in this context. The time-optimized spatial transmission pattern for each frequency point; Figure 4 (d) represents the method in this context. The time-optimized spatial transmission pattern for each frequency point; Figure 4 (e) represents the method in this context. The time-optimized spatial transmission pattern for each frequency point;

[0032] Figure 5 This is a schematic diagram of the waveform sampling point magnitude values ​​under different modulus constraints in one embodiment;

[0033] Figure 6 In one embodiment, under a single-beam radar detection mission, this method optimizes the power spectral density, autocorrelation function, and optimized transmit beam pattern of the synthesized waveform in the radar direction. Figure 6 Image (a) is a schematic diagram of the power spectral density. Figure 6 (b) is a schematic diagram of the autocorrelation function. Figure 6 (c) shows the optimized transmit beam pattern;

[0034] Figure 7 The figures provided are the power spectral density map of the synthesized waveform optimized using this method in the detection direction and the optimized space-frequency transmission pattern in a multi-beam radar detection mission, as shown in one embodiment. Figure 7 (a) shows the power spectral density of the synthesized waveform optimized using this method in the detection direction; Figure 7 (b) shows the space-frequency transmission pattern optimized using this method;

[0035] Figure 8 Here are the spatial transmission pattern and space-frequency transmission pattern for each frequency point optimized using this method under a spectrum congestion environment in one embodiment. Figure 8 (a) shows the spatial transmission pattern of each frequency point after optimization using this method. Figure 8 (b) shows the space-frequency transmission pattern optimized using this method. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0037] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0038] It should be noted that, in this document, the reference to "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The presentation of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art will understand that the embodiments described herein can be combined with other embodiments. The term "and / or" as used herein refers to any combination of one or more of the associated listed items, and all possible combinations, including such combinations.

[0039] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0040] In one embodiment, such as Figure 1 As shown, a waveform design method for the space-frequency transmission pattern of a broadband MIMO radar is provided, which may include the following processing steps 100 to 106:

[0041] Step 100: Establish a signal model and determine the expression for the synthesized transmit power of the broadband MIMO platform in the far field.

[0042] Specifically, as a preferred option, the broadband MIMO array platform has One transmitting antenna, with an element spacing of half a wavelength. A uniform linear array distribution is achieved. The waveform transmitted by each antenna is , .in For carrier frequency, It is a baseband signal with a bandwidth of .

[0043] This step establishes the expression for the synthetic transmit power in the far field, and the broadband signal steering vector preserves the effect of propagation delay in broadband operating mode.

[0044] Step 101: Apply DFT transform to the composite transmit power expression to determine the composite energy at each spatial frequency point.

[0045] Specifically, the synthesized energy of grid points and frequency points is derived based on DFT transform. Digital signal processing techniques are used to discretize the signal, and the synthesized energy of a single spatial frequency point is derived using DFT transform.

[0046] Step 102: Establish dynamic mode constraints based on the total antenna power and baseband signal transmitted by each antenna in a single pulse.

[0047] Specifically, considering the different requirements for modulus constraints in different application scenarios, dynamic modulus constraints are established to accurately control the modulus range of each antenna.

[0048] This innovative approach introduces dynamic modulus constraints to regulate the amplitude fluctuations of the time-domain waveforms of each antenna element, achieving multi-dimensional and precise control over the total energy and instantaneous energy extrema of a single antenna. It can also incorporate constant modulus constraints and peak-to-average power ratio (PAPR) constraints in special cases to address diverse hardware and operating environment requirements. Furthermore,

[0049] Step 103: Based on the synthesized energy at each spatial frequency point, the desired beam pattern, the dynamic mode constraint, and the scaling factor, construct the mode constraint optimization objective function for maxima-minima multi-objective optimization; the scaling factor is used to eliminate the dimensional difference between the designed beam direction and the desired beam pattern.

[0050] Specifically, to ensure the worst-case fitting performance in both the spatial and frequency domains, a minimax-maximum multi-objective optimization model is established by introducing a scaling factor. This reduces the workload caused by dimension conversion. The mode-constrained optimization objective function achieves precise control of the spatial and frequency domain radiation directions under diverse working scenarios by minimizing the maximum fitting error between the synthesized transmitted beam pattern and the desired pattern.

[0051] To overcome the fitting error caused by the LS model, a mathematical model is established based on the minimum-maximum design criterion, driven by the need for precise allocation of space-frequency energy.

[0052] Step 104: Based on the objective function constrained by the modulus, the scaling factor is solved using the bisection method. Then, LES is used to smooth and replace the maximum value function. Finally, the MM algorithm is used to transform the multi-objective optimization problem into multiple constrained linear subproblems.

[0053] Specifically, the objective function of the modulus-constrained optimization is smoothed and approximated. First, the scaling factor is solved using the bisection method. Then, the LSE (Low Sequence of Employment) algorithm is used to smooth and replace the maximum value function. Finally, the MM (Multiple-Match) algorithm is used to transform the original objective function into a linear objective function.

[0054] To overcome the impact of ADMM algorithm and p-norm fitting, other efficient and convergent algorithms are used to solve the model, reducing the computational complexity of the problem and improving the real-time transmission capability of waveforms.

[0055] For the established modulus-constrained optimization objective function, which is a non-convex and non-smooth model, an optimization algorithm was developed to alternately optimize the scale factor and waveform: the waveform optimization method first approximates the non-smooth maximum function with a logarithmic-exponential substitution function to smooth the objective, then uses the MM algorithm to transform the problem into a series of constrained linear subproblems, and finally solves the problem efficiently through KKT conditions.

[0056] Step 105: Solve the constrained linear subproblem using KKT conditions and search rules to obtain the final waveform optimization optimal solution; and accelerate the algorithm using the quadratic iteration algorithm.

[0057] Specifically, to overcome the computational efficiency impact of the two-step method, the model is solved directly in one step, avoiding waveform approximation errors and compromising optimization performance.

[0058] The curves showing the changes in the average and maximum errors of this method compared to existing technologies with the number of iterations are as follows: Figure 2 As shown, Figure 2 Figure (a) shows the curve of the average error as a function of the number of iterations. Figure 2 (b) is a graph showing the maximum error as a function of the number of iterations.

[0059] The aforementioned waveform design method for the space-frequency transmission pattern of a broadband MIMO radar proposes a waveform design framework for accurately shaping the transmission pattern of a broadband MIMO radar, enabling the broadband MIMO radar to adapt to various operating scenarios. Specifically, the method involves: establishing a signal model; deriving the synthetic energy of a single discrete space-frequency point based on DFT transform; establishing dynamic modulus constraints; establishing a maxima-minima multi-objective optimization model; smoothing and approximating the objective function; and using KKT conditions for effective solution. This method achieves precise control of the spatial and frequency domain radiation directions under diverse operating scenarios by minimizing the maximum fitting error between the synthetic transmission beam pattern and the desired pattern; and introduces dynamic modulus constraints to regulate the amplitude fluctuations of the time-domain waveforms of each antenna element to cope with different hardware and operating environment requirements.

[0060] In one embodiment, in step 100, let the first The waveform transmitted by each antenna is The broadband MIMO platform at the far field angle frequency The expression for the combined transmit power is:

[0061] (1)

[0062] in, From the platform's perspective in the far field, , Baseband signal Fourier transform, , This represents the total number of transmit antennas in the broadband MIMO array platform. This refers to the transmit antenna number in the broadband MIMO array platform. For carrier frequency, For the transmission frequency, For bandwidth, This is the space-frequency transmit steering vector for the broadband MIMO array platform. c For the speed of light, The element spacing is half a wavelength.

[0063] In one embodiment, step 101 includes: defining the airspace Divided into Discrete grid points The synthesized transmit power expression is processed using DFT transform to obtain the synthesized energy at each spatial frequency point:

[0064] (2)

[0065] in, For grid points Synthetic energy on , For the discrete Fourier transform of the baseband signal, This represents the total number of transmit antennas in the broadband MIMO array platform. Indicates the signal frequency. N The number of sampling points for the signal. For discrete space frequency steering vectors, For discrete sampling time, For waveform emission matrix, The zero-padded waveform emission vector, This represents the discrete form of the baseband signal, where... The number of sampling points. For pulse delay, To vectorize the waveform emission matrix, For the transformed first Fourier transform matrix of each frequency point It is an L-order identity matrix. Indicates the first Fourier transform vectors of each frequency point.

[0066] Specifically, if digital signal processing technology is used to sample the signal, the discrete sampling time... The baseband waveform can be re-represented in discrete form. ,in Indicates the number of sampling points. This is the oversampling time of the baseband signal. The discrete Fourier transform of the baseband signal is given by the following equation.

[0067] This indicates the number of sampling points for the signal. The Fourier transform form of the baseband signal is then:

[0068] (3)

[0069] in Indicates the signal frequency. , The restriction to zero at the end is to make the signal spectrum smoother and to obtain more details of the frequency domain characteristics; Indicates the first Fourier transform vectors of each frequency point.

[0070] airspace Divided into Discrete grid points Therefore, at grid points The energy on it is shown in formula (2).

[0071] In one embodiment, step 102 includes: precisely controlling the transmission energy of each antenna within a predetermined range based on the total antenna power and baseband signal transmitted by each antenna within a single pulse, and establishing dynamic mode constraints as follows:

[0072] (4)

[0073] in, For dynamic module constraints, For the first The total antenna power transmitted by the antenna within a single pulse. N The number of sampling points for the signal. The number of sampling points. This represents the total number of transmit antennas in the broadband MIMO array platform. For the first The root antenna is at the n Discrete form of the baseband signal at each sampling point The upper bound of the dynamic range, The lower bound of the dynamic range, when When, it transforms into a constant modulus constraint; when When this occurs, it is transformed into a peak mode constraint.

[0074] Specifically, modulus constraints are crucial for ensuring the amplification performance of the system's nonlinear power amplifier. The goal is to precisely control the transmit energy of each antenna within a predetermined range to adapt to diverse application scenarios. Assume the... The total antenna power transmitted by the antenna within a single pulse is , Then the dynamic modulus (DM) constraint can be shown in formula (4).

[0075] In one embodiment, the scaling factor is used to eliminate the dimensionality difference between the designed beam direction and the expected beam pattern; step 103 includes: constructing a mode constraint optimization objective function for maxima-minima multi-objective optimization based on the synthesized energy at each spatial frequency point, the desired beam pattern, the dynamic mode constraint, and the scaling factor:

[0076] (5)

[0077] in, , For the desired beam pattern matrix, For grid points The desired beam pattern is shown above. It's a scaling factor, a scaling factor. Used to eliminate dimensional differences between the designed beam pattern and the desired beam pattern. It is a weight vector used to adjust the importance of energy control at different angle-frequency beam pattern points. The weights corresponding to the grid. The guiding vector corresponding to the space frequency grid. It is a continuous form of the baseband signal. , This is the discrete form of the baseband signal. The number of sampling points. N The number of sampling points for the signal. This represents the total number of transmit antennas in the broadband MIMO array platform. Indicates the first Fourier transform vectors at each frequency point For dynamic module constraints, The lower bound of the dynamic range, The upper bound of the dynamic range, For the first The total power of the antenna transmitted by the antenna within a single pulse.

[0078] Specifically, in order to achieve the beam pattern required by the broadband MIMO radar platform, the waveform needs to be optimized to match the desired beam pattern as closely as possible. Based on the minimax optimization criterion, a mode-constrained optimization objective function as shown in Equation (5) is constructed.

[0079] In one embodiment, the first l The constrained linear subproblems are:

[0080] (6)

[0081] in, The lower bound of the dynamic range, The upper bound of the dynamic range, For the first The total antenna power transmitted by the antenna within a single pulse. The zero-padded waveform emission vector, This is the discrete form of the baseband signal. The number of sampling points. N The number of sampling points for the signal. This represents the total number of transmit antennas in the broadband MIMO array platform. For the first The vector corresponding to the root antenna.

[0082] Specifically, the scaling factor problem is a convex optimization problem, which can be solved efficiently using the bisection method. Since the objective function of the waveform design subproblem is highly non-convex, this embodiment uses a logarithmic exponential smoothing function to smooth and approximate it:

[0083] (7)

[0084] Then, the MM framework is used to simplify it step by step:

[0085] (8)

[0086] Simplify again:

[0087] (9)

[0088] Simplify again:

[0089] (10)

[0090] Where Re represents the real part.

[0091] In one embodiment, step 105 includes: for the first l The constrained linear subproblem is transformed to obtain the transformed optimization problem:

[0092] (11)

[0093] in, To obtain the magnitude of the emitted vector of the waveform after zero-padding, To obtain the first The magnitude of the vector corresponding to the root antenna. This is the upper bound of the waveform magnitude.

[0094] Let the Lagrange function of the optimization problem after transformation be:

[0095] (12)

[0096] in, Let Lagrangian function be the function of the optimization problem after transformation. For Lagrange multipliers, Let be a Lagrange vector. It is a vector consisting entirely of 1s.

[0097] The KKT conditions satisfied by the primal and dual optimal solutions of the Lagrange function include:

[0098] Condition 1: (13)

[0099] Condition 2: (14)

[0100] Condition 3: (15)

[0101] Condition 4: (16)

[0102] in, For vectors The corresponding nth value, For the optimal Lagrange vector The corresponding nth value, For the optimal Lagrange vector The corresponding nth value, Lagrange multipliers The optimal value, To be optimal The corresponding nth value, For the first The lower bound of the magnitude corresponding to the root antenna. For the first The upper bound of the magnitude corresponding to the root antenna. To be optimal .

[0103] Based on conditions 2 and 3, determine the original optimal solution. and The relation is:

[0104] (17)

[0105] in, Lagrange multipliers The optimal value;

[0106] Based on condition 4 and the original optimal solution and The relationship determines the optimal solution for the search and solution. ;

[0107] Based on the original optimal solution The final optimal solution for waveform optimization is obtained; finally, the quadratic iteration method is used to accelerate the algorithm.

[0108] In one embodiment, based on condition 4 and the original optimal solution... and The relationship is used to determine the optimal search solution. and Including: settings for ascending sequence, For the first i Interval Define a set , , From condition 4, we can obtain information about... The relational equation is:

[0109] (18)

[0110] if When the energy constraint is satisfied, the constraint conditions are as follows: At that time, When constraints are in At that time, i Increase by 1 and continue the solution process.

[0111] if ,but No real roots i Increase by 1 and continue the solution process.

[0112] if ,but The solution is:

[0113] (19)

[0114] like ,but i Increase by 1 and continue the solution process.

[0115] Otherwise, if At that time, , ,and It cannot be uniquely determined if ,but:

[0116] (20)

[0117] like Then the optimal solution ,according to Seeking .

[0118] Specifically, the waveform design subproblem can be decomposed into L subproblems. The l-th subproblem is shown in equation (6). It is solved using KKT conditions and a search rule:

[0119] for For example, its best angle is ,make , , , The above optimization problem can be transformed into:

[0120] (twenty one)

[0121] Solve the above equation using the KKT conditions. The Lagrangian function for the optimization problem is:

[0122] (twenty two)

[0123] make and The original optimal solution and the dual optimal solution are respectively, and should satisfy the following KKT conditions as shown in formula (16) of formula (13); from formula (14) and formula (15), it can be seen that, and If either of them must be 0, then there are three possible scenarios:

[0124] 1) , ,at this time , ;

[0125] 2) , ,at this time , ;

[0126] 3) , ,at this time, ;

[0127] In summary:

[0128] (twenty three)

[0129] Below, we will solve the optimal search problem based on formula (16). and .

[0130] make ,in for Let the ascending sequence be... .

[0131] Beginning: For the first i Interval Define a set , , From formula (16), we can see that:

[0132] (twenty four)

[0133] right The solutions are classified and discussed:

[0134] (1) If , This indicates the number of elements in a set. Due to energy constraints, only this case exists: , ,at this time If the constraints are , Let's go back to the beginning.

[0135] (2) If No real roots Let's go back to the beginning.

[0136] (3) If ,but The solution is:

[0137] (25)

[0138] like ,but Return to the beginning;

[0139] Otherwise, if ,at this time, And at this time It cannot be uniquely determined, and At this point, we define:

[0140] (26)

[0141] like At this point, the optimal solution According to Seeking Get After that, we can obtain .but .

[0142] Finally, the quadratic iteration method is used to accelerate the algorithm.

[0143] In some implementations, numerical experiments demonstrate that the designed algorithm outperforms existing methods in frequency-space energy allocation and the synthesis of waveforms with desired spectral characteristics. The framework exhibits significant flexibility, allowing for rapid adaptation to diverse operational needs such as synthesizing specific power spectral density waveforms and addressing spectral congestion by adjusting parameters.

[0144] from Figure 3 and Figure 4 The optimized space-frequency transmission pattern of this method compared to existing technologies, along with the angular transmission beam patterns at different frequencies for each frequency point, demonstrates that the model and algorithm employed in this invention consistently outperform the original models and algorithms in terms of maximum matching error. The proposed method exhibits superior space-frequency energy allocation and can meet diverse application requirements by adjusting the p-value.

[0145] Figure 3 Images (a) to (e) show the optimized space-frequency transmission pattern using the existing method, and the pattern optimized by this method, respectively. , , , Time-optimized space-frequency transmission pattern. Figure 4 Images (a) to (e) show the spatial transmission patterns for each frequency point optimized using existing technologies, and the methods described in this paper. , , , The optimized spatial transmission pattern for each frequency point. Figure 4 As can be seen, the magnitude values ​​of all sampling points strictly remain within a specific range, which proves the effectiveness of the KKT condition derivation. It also confirms that the model proposed in this application can achieve multi-dimensional and precise control over the total energy and instantaneous energy extrema of each antenna, which is very useful for meeting diverse hardware and operational requirements.

[0146] Figure 5 To optimize the power spectral density, autocorrelation function, and optimized transmit beam pattern of the synthesized waveform in the detection direction for single-beam radar detection missions, this method provides the following: Figure 6 In the middle (a), the power spectral density is... Figure 6 In the middle (b), the autocorrelation function is... Figure 6 (c) shows the optimized transmit beam pattern; from Figure 6 As can be seen, this invention achieves energy focusing within the detection area, and the synthesized radar waveform exhibits a relatively flat power spectrum and good autocorrelation characteristics. This fully demonstrates the advantages of this invention in accurately synthesizing power spectra.

[0147] Figure 7The power spectral density map of the synthesized waveform optimized using this method in the detection direction and the optimized space-frequency transmission pattern are shown in this image for multi-beam radar detection missions. Figure 7 (a) shows the power spectral density of the synthesized waveform optimized using this method in the detection direction; Figure 7 (b) shows the optimized space-frequency transmission pattern using this method; from Figure 7 As can be seen, this invention can achieve multi-beam space-frequency energy focusing, and can detect multiple radar targets simultaneously;

[0148] Figure 8 The spatial transmission pattern and space-frequency transmission pattern for each frequency point are optimized using this method under spectrum congestion conditions. Figure 8 (a) shows the spatial transmission pattern of each frequency point after optimization using this method. Figure 8 Image (b) shows the optimized space-frequency transmission pattern using this method. It can be seen that this invention achieves energy focusing at different angles across different frequency bands. It can also be seen that this invention can be applied to spectrum congestion environments, creating a spectrum dip at a specific angle to protect our equipment.

[0149] It should be understood that, although the above Figure 1 The steps are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise explicitly stated in this document, there is no strict order in which these steps are executed; they can be performed in other orders. Furthermore, the above... Figure 1 At least some of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0150] In one embodiment, a waveform design apparatus for a broadband MIMO radar space-frequency transmission pattern is also provided, comprising:

[0151] The signal model building module is used to build a signal model and determine the expression for the synthetic transmit power of the broadband MIMO platform in the far field.

[0152] The module for determining the composite energy at each spatial frequency point is used to perform a DFT transform on the composite transmit power expression to determine the composite energy at each spatial frequency point.

[0153] The dynamic mode constraint construction module is used to establish dynamic mode constraints based on the total antenna power and baseband signal transmitted by each antenna within a single pulse.

[0154] The module for constructing the mode-constrained optimization objective function is used to construct a maxima-minima multi-objective optimization objective function based on the synthetic energy at each spatial frequency point, the desired beam pattern, the dynamic mode constraint, and the scaling factor. The scaling factor is used to eliminate the dimensional difference between the designed beam direction and the expected beam pattern.

[0155] The multi-objective optimization problem transformation module is used to solve the scaling factor using the bisection method based on the objective function constrained by the modulus. Then, LES is used to smooth and replace the maximum value function. Finally, the MM algorithm is used to transform the multi-objective optimization problem into multiple constrained linear subproblems.

[0156] The waveform optimization optimal solution module is used to solve constrained linear subproblems using KKT conditions and search rules to obtain the final waveform optimization optimal solution; and the quadratic iteration algorithm is used to accelerate the algorithm.

[0157] In one embodiment, the broadband MIMO platform in the signal model building module has a far-field angle. frequency The expression for the synthesized transmit power is shown in formula (1).

[0158] In one embodiment, the spatial frequency point synthesis energy determination module is further used to determine the spatial domain. Divided into Discrete grid points The expression for the synthesized transmit power is processed by DFT transformation to obtain the synthesized energy at each spatial frequency point. The expression for the synthesized energy at each spatial frequency point is shown in formula (2).

[0159] In one embodiment, the dynamic mode constraint construction module is also used to precisely control the transmission energy of each antenna within a predetermined range based on the total antenna power and baseband signal transmitted by each antenna in a single pulse, and to establish dynamic mode constraints as shown in formula (4).

[0160] In one embodiment, the scaling factor is used to eliminate the dimensional difference between the designed beam direction and the expected beam pattern; the mode constraint optimization objective function construction module is also used to construct the mode constraint optimization objective function of the maxima-minima multi-objective optimization as shown in Equation (5) based on the synthetic energy of each spatial frequency point, the expected beam pattern, the dynamic mode constraint and the scaling factor.

[0161] In one embodiment, the first module in the modulus-constrained optimization objective function construction module... l The constrained linear subproblem is shown in Equation (6).

[0162] In one embodiment, the multi-objective optimization problem transformation module is further used to transform the third objective problem into a multi-objective optimization problem. lThe constrained linear subproblem is transformed to obtain the transformed optimization problem as shown in formula (11).

[0163] The Lagrangian function of the optimization problem after transformation is set as shown in formula (12).

[0164] The KKT conditions satisfied by the original optimal solution and dual optimal solution of the Lagrange function include four conditions, as shown in formulas (13) to (16).

[0165] Based on conditions 2 and 3, the original optimal solution is determined as shown in formula (17). and The relational expression.

[0166] Based on condition 4 and the original optimal solution and The relationship is used to determine the optimal search solution. and .

[0167] according to The final optimal solution for waveform optimization is obtained; finally, the quadratic iteration method is used to accelerate the algorithm.

[0168] In one embodiment, the multi-objective optimization problem transformation module is also used to set for ascending sequence, For the first i Interval Define a set , , From condition 4, we can obtain the following equation (18) regarding... The relational equation.

[0169] if When the energy constraint is satisfied, the constraint conditions are as follows: , At that time, When constraints are in At that time, i Increase by 1 and continue the solution process.

[0170] if ,but No real roots i Increase by 1 and continue the solution process.

[0171] if ,but The solution is shown in formula (19).

[0172] like ,but iIncrease by 1 and continue the solution process.

[0173] Otherwise, if At that time, , ,and It cannot be uniquely determined if ,but As shown in formula (20).

[0174] like Then the optimal solution ,according to Seeking .

[0175] It is understood that for a detailed explanation of the waveform design device for the broadband MIMO radar space-frequency transmission pattern, please refer to the corresponding explanations of the various embodiments of the waveform design method for the broadband MIMO radar space-frequency transmission pattern above, and will not be repeated here. Each module in the above-described waveform design device for the broadband MIMO radar space-frequency transmission pattern can be implemented entirely or partially through software, hardware, or a combination thereof. Each module can be embedded in hardware or independently of a device with data processing capabilities, or stored in software in the memory of the aforementioned device, so that the processor can call and execute the operations corresponding to each module. The aforementioned device can be, but is not limited to, various types of data processing computer devices already existing in the art.

[0176] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0177] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of protection of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and all such modifications and improvements fall within the scope of protection of this application.

Claims

1. A waveform design method for the space-frequency transmission pattern of a broadband MIMO radar, characterized in that, Including the following steps: Establish a signal model and determine the expression for the synthesized transmit power of the broadband MIMO platform in the far field; The synthesized transmit power expression is subjected to DFT transformation to determine the synthesized energy at each spatial frequency point; Based on the total antenna power and baseband signal transmitted by each antenna within a single pulse, dynamic mode constraints are established. Specifically, this includes: precisely controlling the transmission energy of each antenna within a predetermined range based on the total antenna power and baseband signal transmitted by each antenna within a single pulse, and establishing the dynamic mode constraints as follows: in, For dynamic module constraints, For the first The total antenna power transmitted by the antenna within a single pulse. N The number of sampling points for the signal. The number of sampling points. This represents the total number of transmit antennas in the broadband MIMO array platform. For the first The root antenna is at the n Discrete form of the baseband signal at each sampling point The upper bound of the dynamic range, The lower bound of the dynamic range, when When, it transforms into a constant modulus constraint; when When this occurs, it is transformed into a peak mode constraint; Based on the synthesized energy at each spatial frequency point, the desired beam pattern, the dynamic mode constraint, and the scaling factor, a mode constraint optimization objective function for maxima-minima multi-objective optimization is constructed; the scaling factor is used to eliminate the dimensional difference between the designed beam direction and the desired beam pattern. Based on the objective function constrained by the modulus, the scaling factor is solved by the bisection method. Then, LES is used to smooth and replace the maximum value function. Finally, the MM algorithm is used to transform the multi-objective optimization problem into multiple constrained linear subproblems. The constrained linear subproblem is solved using KKT conditions and search rules to obtain the final waveform optimization optimal solution; and the quadratic iteration algorithm is used to accelerate the algorithm.

2. The waveform design method for the space-frequency transmission pattern of a broadband MIMO radar according to claim 1, characterized in that, The far-field angle of the broadband MIMO platform frequency The expression for the combined transmit power is: in, From the platform's perspective in the far field, , Baseband signal Fourier transform, , This represents the total number of transmit antennas in the broadband MIMO array platform. This refers to the transmit antenna number in the broadband MIMO array platform. For carrier frequency, For the transmission frequency, For bandwidth, This is the space-frequency transmit steering vector for the broadband MIMO array platform. c For the speed of light, The element spacing is half a wavelength.

3. The waveform design method for the space-frequency transmission pattern of a broadband MIMO radar according to claim 1, characterized in that, The composite transmit power expression is subjected to a DFT transform to determine the composite energy at each spatial frequency point, including: airspace Divided into Discrete grid points The synthesized transmit power expression is processed using a DFT transform to obtain the synthesized energy at each spatial frequency point: in, For grid points Synthetic energy on , For the discrete Fourier transform of the baseband signal, This represents the total number of transmit antennas in the broadband MIMO array platform. Indicates the signal frequency. N The number of sampling points for the signal. For discrete space frequency steering vectors, For discrete sampling time, For waveform emission matrix, The zero-padded waveform emission vector, This represents the discrete form of the baseband signal, where... The number of sampling points. For pulse delay, To vectorize the waveform emission matrix, For the transformed th Fourier transform matrix of each frequency point It is an L-order identity matrix. Indicates the first Fourier transform vectors of each frequency point.

4. The waveform design method for the space-frequency transmission pattern of a broadband MIMO radar according to claim 1, characterized in that, The scaling factor is used to eliminate the dimensionality difference between the designed beam direction and the expected beam pattern; based on the synthesized energy at each spatial frequency point, the desired beam pattern, the dynamic mode constraint, and the scaling factor, the mode constraint optimization objective function for maxima-minima multi-objective optimization is constructed as follows: in, , For the desired beam pattern matrix, For grid points The desired beam pattern is shown above. It is a scaling factor. It is a weight vector used to adjust the importance of energy control at different angle-frequency beam pattern points. The weights corresponding to the grid. The guiding vector corresponding to the space frequency grid. It is a continuous form of the baseband signal. , This is the discrete form of the baseband signal. The number of sampling points. N The number of sampling points for the signal. This represents the total number of transmit antennas in the broadband MIMO array platform. Indicates the first Fourier transform vectors at each frequency point For dynamic module constraints, The upper bound of the dynamic range, The lower bound of the dynamic range, For the first The total power of the antenna transmitted by the antenna within a single pulse.

5. The waveform design method for the space-frequency transmission pattern of a broadband MIMO radar according to claim 1, characterized in that, No. l The constrained linear subproblems are: in, The lower bound of the dynamic range, The upper bound of the dynamic range, For the first The total antenna power transmitted by the antenna within a single pulse. The zero-padded waveform emission vector, This is the discrete form of the baseband signal. The number of sampling points. N The number of sampling points for the signal. This represents the total number of transmit antennas in the broadband MIMO array platform. For the first The vector corresponding to the root antenna.

6. The waveform design method for the space-frequency transmission pattern of a broadband MIMO radar according to claim 5, characterized in that, The constrained linear subproblem is solved using KKT conditions and search rules to obtain the final waveform optimization optimal solution; The algorithm is accelerated using a quadratic iteration algorithm, including: For the l The constrained linear subproblem is transformed to obtain the transformed optimization problem: in, To obtain the magnitude of the emitted vector of the zero-padded waveform, To obtain the first The magnitude of the vector corresponding to the root antenna. This is the upper bound of the waveform magnitude; Let the Lagrange function of the optimization problem after transformation be: in, Let Lagrangian function be the function of the optimization problem after transformation. For Lagrange multipliers, Let be a Lagrange vector. It is a vector consisting entirely of 1s; The KKT conditions satisfied by the primal and dual optimal solutions of the Lagrange function include: Condition 1: ; Condition 2: ; Condition 3: ; Condition 4: , ; in, For vectors The corresponding nth value, For the optimal Lagrange vector The corresponding nth value, For the optimal Lagrange vector The corresponding nth value, Lagrange multipliers The optimal value, To be optimal The corresponding nth value, For the first The lower bound of the magnitude corresponding to the root antenna. For the first The upper bound of the magnitude corresponding to the root antenna. To be optimal ; Based on conditions 2 and 3, determine the original optimal solution. and The relation is: in, Lagrange multipliers The optimal value; Based on condition 4 and the original optimal solution and The relationship determines the optimal solution for the search and solution. ; Based on the original optimal solution The final optimal solution for waveform optimization is obtained; finally, the quadratic iteration method is used to accelerate the algorithm.

7. The waveform design method for the space-frequency transmission pattern of a broadband MIMO radar according to claim 6, characterized in that, Based on condition 4 and the original optimal solution and The relationship determines the optimal solution for the search and solution. ,include: set up for ascending sequence, ; For the i Interval Define a set , , From condition 4, we obtain information about... The relational equation is: if When the energy constraint is satisfied, the constraint conditions are as follows: , At that time, When constraints are in At that time, i Increase by 1 and continue the solution process; where, This indicates the number of elements in a set; if ,but No real roots i Increase by 1 and continue solving; if ,but The solution is: like ,but i Increase by 1 and continue solving; Otherwise, if At that time, , ,and It cannot be uniquely determined if ,but: like Then the optimal solution ,according to Seeking .

8. A waveform design device for a broadband MIMO radar space-frequency transmission pattern, characterized in that, include: The signal model building module is used to build the signal model and determine the expression for the synthetic transmit power of the broadband MIMO platform in the far field. The composite energy determination module for each space frequency point is used to perform a DFT transform on the composite transmit power expression to determine the composite energy for each space frequency point. The dynamic mode constraint construction module is used to establish dynamic mode constraints based on the total antenna power and baseband signal transmitted by each antenna within a single pulse. Specifically, it includes: precisely controlling the transmission energy of each antenna within a predetermined range based on the total antenna power and baseband signal transmitted by each antenna within a single pulse, thus establishing the dynamic mode constraints as follows: in, For dynamic module constraints, For the first The total antenna power transmitted by the antenna within a single pulse. N The number of sampling points for the signal. The number of sampling points. This represents the total number of transmit antennas in the broadband MIMO array platform. For the first The root antenna is at the n Discrete form of the baseband signal at each sampling point The upper bound of the dynamic range, The lower bound of the dynamic range, when When, it transforms into a constant modulus constraint; when When this occurs, it is transformed into a peak mode constraint; The module for constructing the mode-constrained optimization objective function is used to construct a maxima-minima multi-objective optimization objective function based on the synthesized energy at each spatial frequency point, the desired beam pattern, the dynamic mode constraint, and the scaling factor; the scaling factor is used to eliminate the dimensional difference between the designed beam direction and the expected beam pattern. The multi-objective optimization problem transformation module is used to solve the scaling factor using the bisection method according to the modulus-constrained optimization objective function, then use LES to smooth and replace the maximum value function, and finally use the MM algorithm to transform the multi-objective optimization problem into multiple constrained linear subproblems. The waveform optimization optimal solution module is used to solve constrained linear subproblems using KKT conditions and search rules to obtain the final waveform optimization optimal solution; and the quadratic iteration algorithm is used to accelerate the algorithm.

9. The waveform design device for the space-frequency transmission pattern of a broadband MIMO radar according to claim 8, characterized in that, The angle of the broadband MIMO platform in the far field in the signal model construction module frequency The expression for the combined transmit power is: in, From the platform's perspective in the far field, , Baseband signal Fourier transform, , This represents the total number of transmit antennas in the broadband MIMO array platform. This refers to the transmit antenna number in the broadband MIMO array platform. For carrier frequency, For the transmission frequency, For bandwidth, This is the space-frequency transmit steering vector for the broadband MIMO array platform. c For the speed of light, The element spacing is half a wavelength.

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