Low-sidelobe waveform design method and system based on neural network

Abstract

The invention discloses a low-sidelobe waveform design method and system based on a neural network, and the method comprises the steps: introducing an expectation self-correlation function and an expectation cross-correlation function as penalty term objective functions based on an MIMO radar system, and constructing a low-correlation sidelobe optimization problem of an MIMO waveform set; based on a similarity constrained neural network, solving a low correlation sidelobe optimization problem to obtain a loss function value; and determining parameters of the similarity-constrained neural network according to the loss function value, performing forward propagation, and outputting a final waveform matrix as an optimized waveform. According to the embodiment of the invention, the waveform set with better related performance can be generated through the low-sidelobe waveform design method of the neural network, and the calculation efficiency of generation is improved. The method can be widely applied to the technical field of radar waveform design.

Description

Technical Field

[0001] The present application relates to the technical field of radar waveform design, and in particular to a low-sidelobe waveform design method and system based on a neural network. Background Art

[0002] Radar waveform design is a key technology for achieving high-performance detection in modern radar systems. Low-sidelobe waveform design plays a crucial role in improving radar resolution, suppressing clutter interference, and enhancing target detection capabilities. With the increasing complexity of electronic warfare environments and the development of multi-function radar systems, the demand for low-sidelobe waveforms is becoming increasingly urgent.

[0003] Related technologies: Waveform design methods based on parameter optimization include direct parameter optimization. Its principle is to use waveform phase / amplitude parameters as optimization variables, establish an objective function (such as the integrated sidelobe ratio (ISL) and the peak sidelobe ratio (PSLR), and use numerical algorithms such as gradient descent and Newton's method to solve it. Another method is convex relaxation optimization, which transforms non-convex problems into convex problems for solution, often using semi-definite programming (SDP) or second-order cone programming (SOCP). However, this technology suffers from computational complexity bottlenecks, local optimality issues, multi-objective optimization conflicts, and poor dynamic adaptability. Furthermore, in applications such as MIMO radar systems and CDMA systems, waveform sets with good correlation characteristics are increasingly required. The design of such waveform sequence sets requires simultaneous optimization of autocorrelation and cross-correlation characteristics. At this point, waveform design methods based on parameter optimization are no longer suitable for complex scenarios with multiple constraints.

[0004] In summary, the technical problems existing in the relevant technologies need to be improved. Summary of the Invention

[0005] The main purpose of the embodiments of the present application is to propose a low-sidelobe waveform design method and system based on a neural network, which can generate a waveform set with better correlation performance through the low-sidelobe waveform design method of the neural network and improve the generated computational efficiency.

[0006] To achieve the above objectives, one aspect of an embodiment of the present application provides a low sidelobe waveform design method based on a neural network, the method comprising:

[0007] Based on the MIMO radar system, the expected autocorrelation function and the expected cross-correlation function are introduced as penalty target functions to construct the low-correlation sidelobe optimization problem of the MIMO waveform set.

[0008] Solving the low-correlation sidelobe optimization problem based on a similarity-constrained neural network to obtain a loss function value;

[0009] The parameters of the similarity-constrained neural network are determined according to the loss function value, and forward propagation is performed to output the final waveform matrix as the optimized waveform.

[0010] In some embodiments, the MIMO radar system introduces an expected autocorrelation function and an expected cross-correlation function as penalty target functions to construct a low-correlation sidelobe optimization problem for a MIMO waveform set, including:

[0011] Based on the MIMO radar system, determining the number of transmitting antennas and the amount of time snapshot data transmitted by each transmitting antenna, and constructing a transmission data matrix of the MIMO radar system;

[0012] Defining correlation based on the transmission data matrix of the MIMO radar system to determine the correlation function between the transmission waveform sequences;

[0013] Based on the correlation function between the transmit waveform sequences, the peak sidelobe level is used as an optimization indicator, and a constant modulus constraint is introduced to obtain a preliminary low-correlation sidelobe optimization problem of the MIMO waveform set, wherein the peak sidelobe level includes the autocorrelation peak sidelobe and the cross-correlation peak sidelobe;

[0014] Converting the low-correlation sidelobe optimization problem of the preliminary MIMO waveform set into a phase matrix;

[0015] According to Welch theory, a reference value of the lower bound of the peak sidelobe of the correlation function is defined, and an expected autocorrelation function and an expected cross-correlation function are constructed, wherein the expected autocorrelation function is a Dirac function and the expected cross-correlation function is a constant sidelobe level;

[0016] The expected autocorrelation function and the expected cross-correlation function are introduced into the phase matrix as penalty item target functions to obtain a low-correlation sidelobe optimization problem of the MIMO waveform set.

[0017] In some embodiments, the expression of the reference value of the lower bound of the correlation function peak sidelobe is specifically as follows:

[0018]

[0019] In the above formula, PSL represents the peak sidelobe level, M represents the number of antennas, N represents the time snapshot data transmitted by each transmitting antenna, and η a represents the expected autocorrelation function sidelobe level, η c represents the desired cross-correlation function sidelobe level, It represents the number of combinations of selecting q elements from 2N+q-2 elements.

[0020] In some embodiments, the expressions of the expected autocorrelation function and the expected cross-correlation function are specifically as follows:

[0021]

[0022] E ccf (k) = η c

[0023] In the above formula, E acf (·) represents the expected autocorrelation function, E ccf (·) represents the expected cross-correlation function, η a represents the expected autocorrelation function sidelobe level, η c represents the expected sidelobe level of the cross-correlation function, and k represents the time delay variable in the correlation function.

[0024] In some embodiments, the expression of the low-correlation sidelobe optimization problem of the MIMO waveform set is specifically as follows:

[0025]

[0026] In the above formula, min X L represents the low-correlation sidelobe optimization problem, f mse (·) represents the mean square error function, λ1 represents the error coefficient of ACF, λ2 represents the error coefficient of CCF, ω1 represents the weight coefficient of APSL, ω2 represents the weight coefficient of CPSL, ACF m represents the autocorrelation function of the mth transmitting antenna, E acf represents the expected autocorrelation function, CCF m represents the cross-correlation function of the mth transmitting antenna, E ccf represents the expected cross-correlation function, APSL m Represents the autocorrelation peak sidelobe of the waveform sequence transmitted by the mth antenna, CPSL m represents the cross-correlation peak sidelobe of the waveform sequence transmitted by the mth antenna, M represents the number of antennas, and X represents the transmit data matrix of the MIMO radar system.

[0027] In some embodiments, the similarity-constrained neural network solves the low-correlation sidelobe optimization problem to obtain a loss function value, including:

[0028] Constructing a neural network based on similarity constraints, wherein the neural network includes an input layer, a hidden layer, and an output layer;

[0029] Acquire the phase matrix and perform vectorized expansion processing to obtain an expanded phase matrix column vector;

[0030] Performing a linear transformation on the expanded phase matrix column vector through the neural network to output an optimized phase vector;

[0031] Reconstructing the dimension of the optimized phase vector to obtain a preliminary waveform matrix;

[0032] The loss function is calculated and the adaptive moment is estimated for the low-correlation sidelobe optimization problem according to the preliminary waveform matrix to obtain the loss function value.

[0033] In some embodiments, performing loss function calculation and adaptive moment estimation on the low-correlation sidelobe optimization problem according to the preliminary waveform matrix to obtain the loss function value includes:

[0034] determining a time delay correlation function based on the preliminary waveform matrix;

[0035] Normalizing and modulus-calculating the delay-related function to obtain an information vector having a delay dimension;

[0036] Extracting the autocorrelation function and the cross-correlation function of the antenna based on the information vector with the time delay dimension;

[0037] Calculating the autocorrelation function and the cross-correlation function respectively by a smooth maximum approximation operator to obtain an autocorrelation peak sidelobe and a cross-correlation peak sidelobe;

[0038] Substituting the information vector with the time delay dimension, the autocorrelation peak sidelobe, and the cross-correlation peak sidelobe into the low-correlation sidelobe optimization problem to obtain a preliminary loss function value;

[0039] The preliminary loss function value is judged. If the preliminary loss function value is greater than a preset threshold, the steps of solving the low-correlation sidelobe optimization problem are repeated until the preliminary loss function value is less than the preset threshold, and the loss function value is output.

[0040] In some embodiments, a preset acceleration mechanism is introduced to accelerate the process of solving the low-correlation sidelobe optimization problem, specifically including:

[0041] The side lobes of antennas whose autocorrelation functions are smaller than the expected autocorrelation function side lobe level and the side lobes of antennas whose cross-correlation functions are smaller than the expected cross-correlation function side lobe level are eliminated to accelerate the solution of the low-correlation side lobe optimization problem.

[0042] In some embodiments, determining the parameters of the similarity-constrained neural network according to the loss function value, performing forward propagation, and outputting a final waveform matrix as an optimized waveform includes:

[0043] Determining parameters of the similarity-constrained neural network according to the loss function value, and constructing an optimal neural network, wherein the parameters include a weight matrix and a bias vector;

[0044] The phase matrix is ​​input into the optimal neural network for forward propagation, and the final waveform matrix is ​​output as the optimized waveform.

[0045] To achieve the above objectives, another aspect of the present invention provides a low sidelobe waveform design system based on a neural network, the system comprising:

[0046] The first module is used to construct the low-correlation sidelobe optimization problem of the MIMO waveform set based on the MIMO radar system by introducing the expected autocorrelation function and the expected cross-correlation function as the penalty target function;

[0047] The second module is used to solve the low-correlation sidelobe optimization problem based on a similarity-constrained neural network to obtain a loss function value;

[0048] The third module is used to determine the parameters of the similarity-constrained neural network according to the loss function value, perform forward propagation, and output the final waveform matrix as the optimized waveform.

[0049] The embodiments of the present application include at least the following beneficial effects: The present application provides a low-sidelobe waveform design method and system based on a neural network. The scheme introduces the expected autocorrelation function and the expected cross-correlation function as penalty item target functions based on the MIMO radar system, constructs a low-correlation sidelobe optimization problem of the MIMO waveform set, and introduces the similarity constraint as a penalty item into the calculation of the loss function, thereby obtaining a waveform set whose correlation function is close to the ideal correlation function. The low-correlation sidelobe optimization problem is further solved based on the neural network with similarity constraints, and the target function is reconstructed using the network layer structure of the neural network. With the help of the forward propagation and backward propagation mechanism of the neural network, the input vector matrix can be updated while updating the network parameters to achieve optimization of the waveform set. The low-sidelobe waveform design method of the neural network can be used to generate a set with good correlation performance, while achieving high computational efficiency, and solving the problem of waveform design optimization in complex scenarios with multiple constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of a low sidelobe waveform design method based on a neural network provided in an embodiment of the present application;

[0051] Figure 2 1 is a schematic structural diagram of a low sidelobe waveform design system based on a neural network provided in an embodiment of the present application;

[0052] Figure 3 Schematic diagram of a MIMO transmission waveform data block provided in an embodiment of the present application;

[0053] Figure 4Schematic diagram of a neural network waveform design based on similarity constraints provided in an embodiment of the present application;

[0054] Figure 5 Schematic diagram of the structure of a neural network based on similarity constraints provided in an embodiment of the present application;

[0055] Figure 6 Schematic diagram of the forward propagation process of a neural network provided in an embodiment of the present application;

[0056] Figure 7 Schematic diagram of the neural network backpropagation process provided by the embodiment of the present application;

[0057] Figure 8 Schematic diagram of the performance of the autocorrelation function of the waveform set generated by different methods provided in the embodiments of the present application;

[0058] Figure 9 Schematic diagram of the performance of the cross-correlation function of the waveform sets generated by different methods provided in the embodiments of the present application;

[0059] Figure 10 Schematic diagram of the impact of APSL on sequences generated by different methods provided in the examples of this application;

[0060] Figure 11 Schematic diagram of the impact of CPSL generated by different methods provided in the embodiments of the present application;

[0061] Figure 12 This is a schematic diagram of the autocorrelation function generated by the first two sequences of the waveform set provided in the embodiment of the present application;

[0062] Figure 13 This is a schematic diagram of the cross-correlation function generated by the first two sequences of the waveform set provided in an embodiment of the present application. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of the present application. They are merely examples of systems and methods consistent with some aspects of the embodiments of the present application as detailed in the appended claims.

[0064] It will be understood that the terms "first", "second", etc. used in this application may be used herein to describe various concepts, but unless otherwise specified, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of the embodiments of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the words "if" and "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0065] The terms "at least one", "plurality", "each", "any", etc. used in this application include "at least one", "two" or more, "plurality" or "each", "any" or "any one", "each" or "any one" as used herein.

[0066] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this application pertains. The terms used herein are for the purpose of describing the embodiments of this application only and are not intended to limit this application.

[0067] First, it's important to note that radar waveform design must meet the following key performance indicators: 1. Range resolution, which is closely related to signal bandwidth; 2. Velocity resolution, which depends on the signal's time width; 3. Sidelobe level, which affects weak target detection and multi-target resolution; 4. Ambiguity function characteristics, which determine the radar's range-velocity resolution performance; and 5. Orthogonality, which is particularly important for MIMO radar and multi-waveform applications. The technical development of low-sidelobe waveform design can be divided into two areas: traditional waveform design methods and phase-coded waveform design. Among traditional waveform design methods, early low-sidelobe waveform design was primarily based on linear frequency modulation (LFM) and nonlinear frequency modulation (NLFM) signals. LFM signals primarily reduce sidelobes through windowing, but this results in a widened mainlobe and loss of signal-to-noise ratio. NLFM signals primarily achieve low sidelobes by optimizing the frequency modulation pattern, such as methods based on STFT. In phase-coded waveform design, the phase-coded signal achieves low sidelobe by optimizing the phase sequence: using two-phase coding such as Barker code and m-sequence, but the sidelobe performance is limited; using multi-phase coding such as Frank code and P1 / P2 / P3 / P4 code provides better sidelobe control; using optimization algorithm design: using genetic algorithm, simulated annealing, etc. to optimize the phase sequence.

[0068] There are some deficiencies in the related technology, such as:

[0069] 1) Traditional FM waveform optimization methods use windowing functions (such as Hamming and Kaiser windows) to suppress LFM signal sidelobes, resulting in a broadening of the mainlobe (typically a 15-20% loss of 3dB width). Nonlinear FM can suppress sidelobes to the order of -30dB through STFT time-frequency distribution design, but this still results in a decrease in Doppler tolerance.

[0070] 2) Phase coding methods: Binary phase codes (such as Barker codes) are limited by sequence length (maximum length 13), and the sidelobe suppression ratio is fixed at 20log(1 / N). Polyphase codes (such as P4 codes) optimize the phase through gradient descent, with a measured sidelobe of approximately -35dB.

[0071] 3) Modern optimization algorithms. Convex optimization methods (such as semidefinite programming) use ISL (integrated sidelobe ratio) as the objective function with a computational complexity of O(N3). The cyclic algorithm (CAN) is implemented through FFT iteration. After convergence, the sidelobe can reach -40dB, but it requires 50-100 iterations.

[0072] 4) Orthogonal waveform set design, based on Golay code groups with complementary sequences, cross-correlation sidelobes <-25dB, and weighted joint optimization (WJIO) method to simultaneously optimize auto-correlation and cross-correlation. The computational time increases exponentially with the number of waveforms.

[0073] Therefore, the main technical challenges facing the current design of low-sidelobe waveform sets include: the conflict between orthogonality and sidelobe suppression: the requirement for orthogonality between waveforms and the requirement for low sidelobe for individual waveforms; optimization in a multi-objective environment: the need to simultaneously optimize both autocorrelation and cross-correlation characteristics; computational complexity: the computational burden of solving high-dimensional non-convex optimization problems; and practical system constraints: considering practical constraints such as transmitter nonlinearities and bandwidth limitations. Designing radar low-sidelobe waveform sets is a multi-objective optimization problem that requires striking a balance between sidelobe suppression, maintaining orthogonality, and system implementation constraints.

[0074] In view of this, a low-sidelobe waveform design method based on a neural network is provided in an embodiment of the present application. By introducing similarity constraints as penalty terms into the calculation of the loss function, a waveform set whose correlation function is close to the ideal correlation function is obtained. First, the low-sidelobe waveform set design problem is modeled, and then the objective function is reconstructed using the network layer structure of the neural network. With the help of the forward propagation and backward propagation mechanisms of the neural network, the input vector matrix can be updated while updating the network parameters to achieve the optimization of the waveform set. Compared with the optimization method based on waveform parameters and the traditional convex optimization method, the low-sidelobe waveform design method using a neural network has the advantages of good correlation performance of the generated waveform set and high computational efficiency.

[0075] Reference Figure 1 , Figure 1A flowchart of a low sidelobe waveform design method based on a neural network provided in an embodiment of the present invention, referring to Figure 1 , the method comprises the following steps:

[0076] S100, based on the MIMO radar system, introduces the expected autocorrelation function and the expected cross-correlation function as penalty target functions to construct the low-correlation sidelobe optimization problem of the MIMO waveform set;

[0077] It should be noted that, in some embodiments, step S100 may include steps S110 to S160:

[0078] S110. Based on the MIMO radar system, determine the number of transmitting antennas and the amount of time snapshot data transmitted by each transmitting antenna, and construct a transmission data matrix of the MIMO radar system.

[0079] In this embodiment, if Figure 3 As shown, consider a MIMO radar system with M antennas and each transmitting antenna transmitting N time snapshots of data. For the mth antenna in this MIMO radar system, it corresponds to a transmitting sequence transmitting waveform vector x m =[x m (0),x m (1),…,x m (N-1)] T (m=1,2,…,M). Then the expression of the transmission data matrix X of the entire MIMO radar system is as follows:

[0080] X N×M =[x1,x2,…,x M ]

[0081] In the above formula, X N×M Represents the transmit data matrix of the entire MIMO radar system.

[0082] S120, defining correlation according to the transmission data matrix of the MIMO radar system, and determining a correlation function between transmission waveform sequences;

[0083] In this embodiment, the transmission waveform sequence x i and the emission waveform sequence x j The expression of the correlation function between is as follows:

[0084]

[0085] In the above formula, r i,j (k) represents the time delay correlation function.

[0086] S130. Based on the correlation function between the transmitted waveform sequences, the peak sidelobe level is used as an optimization indicator, and a constant modulus constraint is introduced to obtain a preliminary low-correlation sidelobe optimization problem for the MIMO waveform set. The peak sidelobe level includes the autocorrelation peak sidelobe and the cross-correlation peak sidelobe.

[0087] In this embodiment, in order to design a waveform set with low correlation side lobes, PSL (peak sidelobe level) is used as an optimization index, and its expression is:

[0088]

[0089] In order to consider the sidelobe effects of the autocorrelation function and the cross-correlation function on the overall correlation function, the PSL is divided into two parts: the autocorrelation peak sidelobe (APSL) and the cross-correlation peak sidelobe (CPSL). The definitions of the autocorrelation PSL and the cross-correlation PSL are as follows:

[0090] APSL m =max|r m,m (k)|

[0091] CPSL m =PSL m≠j |r m,j (k)|

[0092] Among them, APSL m and CPSL m They represent the APSL and CPSL of the waveform sequence transmitted by the mth antenna respectively. Therefore, the sidelobe level of the overall correlation function corresponding to the waveform sequence transmitted by the mth antenna can be expressed as:

[0093] pL m =ω1APSL m +ω2CPSL m

[0094] Among them, ω1 is the weight coefficient of APSL, and ω2 is the weight coefficient of CPSL.

[0095] In addition, it should be noted that the constant modulus constraint on the waveform is crucial for the radar system, so the waveform must also meet the following requirements:

[0096] |x m (n)|=1,n=1,...,N

[0097] The low-correlation sidelobe optimization problem of the MIMO waveform set, that is, the preliminary low-correlation sidelobe optimization problem of the MIMO waveform set, is expressed as follows:

[0098] st|x m (n)|=1,n=1,...,N

[0099] Because APSL and CPSL contain the absolute value function |·|, and the maximum function max(·) is convex only when the inputs are convex, the objective function of the initial low-correlation sidelobe optimization problem for a set of MIMO waveforms is non-convex. Furthermore, due to the constant modulus constraint, the feasible solution space is a non-convex set, resulting in high computational complexity using traditional methods. Deep learning neural networks (NNs) are machine learning models inspired by biological neural systems and are widely used in fields such as pattern recognition, signal processing, and optimization. Therefore, a similarity-constrained neural network was constructed for radar waveform design, effectively reducing computational complexity.

[0100] S140, converting the low-correlation sidelobe optimization problem of the preliminary MIMO waveform set into a phase matrix;

[0101] In this embodiment, in order to improve the efficiency of the transmitter, a constant modulus constraint is imposed on the waveform, and thus the waveform model is selected as a phase-coded waveform, which is expressed as follows:

[0102]

[0103] Among them, φ m (n) corresponds to the data collected by the nth time snapshot on the mth antenna. Therefore, the design problem of the waveform set is transformed into the design problem of the phase matrix Φ, which is expressed as:

[0104]

[0105] In the above formula, Φ represents the phase matrix.

[0106] S150. According to Welch theory, a reference value of the lower bound of the peak sidelobe of the correlation function is defined, and an expected autocorrelation function and an expected cross-correlation function are constructed. The expected autocorrelation function is a Dirac function, and the expected cross-correlation function is a constant sidelobe level.

[0107] In this embodiment, the phase matrix Φ is used as input data for the neural network, where it is optimized until the output meets the expected waveform set. Based on the concept of similarity constraints, it is desired to obtain the corresponding waveform data based on an ideal correlation function. Considering that the ideal distance ambiguity function is the Dirac function, its expression is:

[0108]

[0109] Assuming that the time delay variable in the correlation function is k, the expressions of the ideal autocorrelation function and cross-correlation function are E acf (k) and E ccf (k), its expression is:

[0110]

[0111] Among them, η a and η c are the expected autocorrelation function sidelobe levels and the expected cross-correlation function sidelobe levels, respectively.

[0112] It's also important to note that in MIMO (Multiple Input, Multiple Output) radar systems, the lower the peak value of the waveform cross-correlation function, the better the orthogonality between the waveforms, which in turn improves the system's waveform diversity gain. Studying the lower bound of the acyclic cross-correlation function helps determine the limit of the waveform diversity gain, which is of great significance to the design and application of MIMO radar waveforms. Phase-coded waveform sets are currently the most widely studied MIMO radar waveform set, and the lower bound of their correlation function has been extensively studied.

[0113] According to Welch theory, the lower bound of the peak side lobe of the correlation function can be taken as η a and η c The reference value of is expressed as:

[0114]

[0115] Where q is a positive real number used to adjust the calculation accuracy of the lower bound.

[0116] S160 , introducing the expected autocorrelation function and the expected cross-correlation function as penalty-item target functions into the phase matrix to obtain a low-correlation sidelobe optimization problem of the MIMO waveform set.

[0117] In some specific embodiments, in order to more accurately solve the problem in the expression of the low-correlation sidelobe optimization problem of the preliminary MIMO waveform set, the expected autocorrelation function and the expected cross-correlation function are introduced into the objective function as penalty terms, so that the final optimization problem model is as follows:

[0118]

[0119] In the above formula, min X L represents the low-correlation sidelobe optimization problem, f mse (·) represents the mean square error function, λ1 represents the error coefficient of ACF, λ2 represents the error coefficient of CCF, ω1 represents the weight coefficient of APSL, ω2 represents the weight coefficient of CPSL, ACF m represents the autocorrelation function of the mth transmitting antenna, E acf represents the expected autocorrelation function, CCF m represents the cross-correlation function of the mth transmitting antenna, E ccf represents the expected cross-correlation function, APSL mRepresents the autocorrelation peak sidelobe of the waveform sequence transmitted by the mth antenna, CPSL m represents the cross-correlation peak sidelobe of the waveform sequence transmitted by the mth antenna, M represents the number of antennas, and X represents the transmit data matrix of the MIMO radar system.

[0120] S200, solving the low-correlation sidelobe optimization problem based on a similarity-constrained neural network to obtain a loss function value;

[0121] It should be noted that, in some embodiments, step S200 may include steps S210 to S250:

[0122] It should be noted that, Figure 4 as well as Figure 5 As shown in Figure 1, a neural network designed based on similarity constraints is used to solve the low-correlation sidelobe optimization problem of MIMO waveform sets. The network based on similarity constraints mainly consists of two computational processes: forward propagation and backward propagation.

[0123] S210, constructing a neural network based on similarity constraints, the neural network including an input layer, a hidden layer, and an output layer;

[0124] S220, obtaining a phase matrix and performing vectorized expansion processing to obtain an expanded phase matrix column vector;

[0125] S230, performing a linear transformation on the expanded phase matrix column vector through a neural network, and outputting an optimized phase vector;

[0126] S240, reconstructing the dimension of the optimized phase vector to obtain a preliminary waveform matrix;

[0127] In steps S210 to S240, for some specific embodiments, such as Figure 6 As shown in Figure 1, the forward propagation process consists of three parts: input layer, hidden layer, and output layer. When inputting the phase matrix, in order to match the input of the subsequent fully connected layer, the phase matrix is ​​vectorized and expanded into a column vector Φ of NM×1 in As the input layer, its expression is:

[0128] Φ in =[φ1(0),…,φ1(N-1),…,φ M (0),φ M (N-1)] T

[0129] Then Φ inThe input is sent to a hidden layer consisting of three fully connected layers. These three fully connected layers consist of 128, 256, and 256 neurons respectively. For the first fully connected layer fc1, its weight matrix W1 and bias vector b1 together form the output y1 of the first layer under the action of the activation function sigmoid, which is expressed as:

[0130] y1=fc1(φ in )=sigmoid(W1·φ in +b1)

[0131] in

[0132] The weight matrix and bias vector of the second fully connected layer are and b2∈256×1, which is expressed as:

[0133] y2=fc2(y1)=sigmoid(W2·y1+b2)

[0134] By taking the output y2 of the first two fully connected layers as the input of the third fully connected layer, we can get the optimized phase vector φ out , whose expression is:

[0135] φ out =fc3(y2)=sigmoid(W3·y2+b3)

[0136] By out The new waveform matrix X can be obtained by reconstructing the dimension and calculating using the following formula: * , specifically:

[0137]

[0138] in, ( is the floor function), r = i - Nc.

[0139] S250. Perform loss function calculation and adaptive moment estimation on the low-correlation sidelobe optimization problem based on the preliminary waveform matrix to obtain a loss function value.

[0140] First of all, it should be noted that Figure 7 As shown in the figure, the back propagation process mainly consists of two parts: loss function calculation and Adaptive Moment Estimation (Adam) algorithm. * After substituting the loss function into the calculation, if it is found that the value of the loss function is still greater than the output threshold, the Adam optimizer will be used to update the parameters of the neural network.

[0141] S251. Determine a time delay correlation function based on a preliminary waveform matrix;

[0142] In this embodiment, for X * The delay correlation function is calculated for each column of , and its expression is:

[0143]

[0144] In the above formula, r i,j (k) represents the time delay correlation function.

[0145] S252: performing normalization and modulus calculation on the delay-related function to obtain an information vector having a delay dimension;

[0146] In this embodiment, the modulus value of the normalized correlation function can then be expressed as:

[0147]

[0148] Where k∈0,1,…,N-1 and m∈0,1,…,N-1. According to the modulus expression, the normalized information vector r with delay dimension can be defined i,j , whose expression is:

[0149]

[0150] In the above formula, Represents the modulus value of the normalized information vector with delay dimension.

[0151] S253. Extracting the autocorrelation function and the cross-correlation function of the antenna based on the information vector having the time delay dimension;

[0152] S254, respectively calculating the autocorrelation function and the cross-correlation function using a smooth maximum approximation operator to obtain an autocorrelation peak side lobe and a cross-correlation peak side lobe;

[0153] S255, substituting the information vector with the time delay dimension, the autocorrelation peak sidelobe, and the cross-correlation peak sidelobe into the low-correlation sidelobe optimization problem to obtain a preliminary loss function value;

[0154] S256. Judge the preliminary loss function value. If the preliminary loss function value is greater than the preset threshold, repeat the steps of solving the low-correlation sidelobe optimization problem until the preliminary loss function value is less than the preset threshold, and output the loss function value.

[0155] In this embodiment, the autocorrelation function (ACF) of the waveform sequence corresponding to the mth antenna can be obtained by normalizing the expression of the information vector with the time delay dimension: m and cross-correlation function CCF mIn order to calculate APSL and CPSL while avoiding the problem that the max(·) function is not differentiable at the maximum point, which affects the network training process, the smooth maximum approximation operator Mellomax operator is used here to replace the calculation of the max(·) function. The expression of Mellowmax is as follows:

[0156]

[0157] Where x=[x1,x2,…,x N ] T .

[0158] So APSL m and CPSL m The expression is as follows:

[0159]

[0160] Normalize the expression of the information vector with time delay dimension, the expression of Mellowmax, APSL m and CPSL m Substituting the expression of into the low correlation sidelobe optimization problem of MIMO waveform set, we can get the network output matrix X * The calculated loss function value.

[0161] In some specific embodiments, the steps for solving the low-correlation sidelobe optimization problem based on a similarity-constrained neural network are shown in Table 1:

[0162] Table 1 Solution table for low correlation sidelobe optimization problem

[0163]

[0164]

[0165] Finally, it should be noted that after the forward propagation based on the similarity network, the optimized waveform matrix X * According to the following loss function calculation, we can determine whether to output the optimized waveform or continue to perform backward propagation. The expression of the loss function is:

[0166]

[0167] According to the expression of the normalized information vector with time delay dimension, the loss function is calculated over the entire domain, which means that in each training round, the neural network needs to evaluate all points in the sequence. Taking the autocorrelation function as an example, in the early iteration, most ACF m The side lobes in the α-axis all exceed the expected autocorrelation peak side lobe level η. a, which naturally helps to reduce the loss function value. However, as the training progresses, these high side lobes are gradually suppressed effectively, and some of them are below the threshold η a The side lobes of are still included in the calculation range of the loss function. This approach is obviously not the most efficient: because in the loss function f mse In the penalty term of (·), the value lower than η a The side lobes may even reversely increase the overall loss value. In addition, as the size of the waveform set increases significantly, if all side lobes are still supervised and calculated, the network training will encounter bottlenecks in terms of computing performance. To improve training efficiency, an acceleration mechanism is designed in the embodiment of the present invention. In each round of training, only the side lobes exceeding the threshold are focused on, and the low side lobes that meet the constraints are ignored. For a certain autocorrelation function ACF m , the corresponding loss function f mse (·) can be updated as follows:

[0168]

[0169] Among them, the set Ω a represents the autocorrelation sidelobe index that satisfies the following conditions, and its expression is:

[0170]

[0171] Weight w a is defined as follows:

[0172]

[0173] Among them, w a It is used to constrain which side lobes will be included in the calculation of the autocorrelation loss function, and Ω a It represents the ACF m Exceeded expected APSL level η a Index set. Usually, for the m (n)<η a The side lobes of the image can be removed from the calculation by assigning a weight of 0.

[0174] Similarly, for a certain cross-correlation function CCF m The corresponding cross-correlation loss function f mse (·) can be updated as follows:

[0175]

[0176] Among them, the set Ω c Denotes the cross-correlation sidelobe indices that satisfy the following conditions:

[0177]

[0178] Weight w c is defined as follows:

[0179]

[0180] Among them, w c It is used to constrain which side lobes will be included in the calculation of the cross-correlation loss function, and Ω c Indicates CCF m Exceeding expected CPSL level η c Index set. Usually, for the m (n)<η c The side lobes of the image can be removed from the calculation by assigning a weight of 0.

[0181] S300. Determine the parameters of the similarity-constrained neural network according to the loss function value, perform forward propagation, and output the final waveform matrix as the optimized waveform.

[0182] It should be noted that, in some embodiments, step S300 may include: S310, determining the parameters of the similarity-constrained neural network based on the loss function value, and constructing an optimal neural network, the parameters including a weight matrix and a bias vector; S320, inputting the phase matrix into the optimal neural network for forward propagation, and outputting the final waveform matrix as the optimized waveform.

[0183] Finally, a comparison is made between the traditional waveform optimization methods: the loop optimization algorithm (CAN), the peak sidelobe optimization loop (POCA), the neural network method based on implicit gradient descent (GD), and the neural network method based on similarity constraints proposed in this paper. Unless otherwise specified, the number of antennas M = 3 and the number of samples collected for each antenna N = 100. The expected correlation function sidelobe level η a =η c =-34dB, the evaluation index of waveform performance adopts the definition expression of autocorrelation PSL and cross-correlation PSL.

[0184] The embodiments of the present invention mainly examine the relevant performance of waveform sets generated by different optimization methods. Figure 8 as well as Figure 9 are the autocorrelation functions and cross-correlation functions of the waveform sets generated by the CAN method, the POCA method, the GD method, and the method proposed in the present invention when N = 100. The results of APSL are summarized in Table 2.

[0185] Table 2 Average optimization results of APSL (100 Monte Carlo experiments)

[0186] \ Original CAN POCA GD Ours APSL(dB) -13 -26.55 -42.7 -32.5 -33.5 Time(s) \ 0.06 1.02 35.3 5.53

[0187] Depend on Figure 8 It can be seen that all methods have low side lobes near the main lobe. As the delay increases, the side lobe level also increases, and the peak side lobes of the four methods appear around |n|=90. From the APSL of the correlation function of the sequences generated by different methods, the APSL of the CAN method is about -27dB, the APSL generated by the POCA method is about -43dB, the APSL generated by the GD method is about -32.5dB, and the APSL generated by the method proposed in the present invention is about -33.5dB. Since the CAN method and the POCA method are based on traditional optimization iterative methods, the overall side lobe fluctuations are large, especially for the POCA method, which sacrifices constant modulus performance in exchange for a reduction in the side lobe level of the correlation function. For the method proposed in the present invention, the overall fluctuation of the side lobes is small, which is due to the introduction of a penalty term of the similarity constraint during the network training process. Compared with the GD method, which also uses a neural network, its APSL and overall side lobe level are both reduced by 1-2dB. This shows that the method proposed in the present invention can generate a waveform set with lower correlation sidelobes. At the same time, since the phase coding model is used in modeling, the constant modulus constraint is naturally satisfied.

[0188] Depend on Figure 9 It can be seen that all methods have higher sidelobe levels when the cross-correlation delay |n| is low. As the cross-correlation delay increases, the cross-correlation sidelobe level decreases. Looking at the CPSL of the correlation functions of the sequences generated by different methods, the CPSL generated by the CAN method is around -17dB, the CPSL generated by the POCA method is around -16dB, the CPSL generated by the GD method is around -15dB, and the CPSL generated by the proposed method is around -30dB.

[0189] Therefore, the method proposed in the present invention can effectively generate a radar waveform set with low-correlation sidelobes, and the sidelobe level has obvious advantages compared with existing methods.

[0190] Further robustness analysis is carried out. The embodiment of the present invention discusses the robustness of the method proposed in the present invention based on the following aspects: 1. When generating sequences of different lengths, the APSL and CPSL of the sequences generated by different methods are discussed. 2. When generating sequences of different lengths, the APSL and CPSL of the sequences generated by different methods are discussed. a and the expected cross-correlation sidelobe level η c 3. The impact of the penalty term introduced by similarity constraint on the optimization results of the correlation function is discussed.

[0191] like Figure 10 as well as Figure 11 Shown is a comparison of the PSL of waveform sets generated by different methods as the sequence length changes.

[0192] According to ηa and η c To set the desired autocorrelation function sidelobe level and the desired cross-correlation function sidelobe level. Figure 10 In the a The autocorrelation functions generated by the first sequence of the waveform set are -23dB, -34dB and -43dB respectively. a = -23dB, the APSL of the output waveform is also around -23dB, but its side lobe fluctuates greatly, indicating that η a Setting does not realize the maximum potential of the optimization algorithm; when η a =-34dB, the peak side lobe of the autocorrelation function of the output waveform is about -34dB, and the side lobe fluctuation of the correlation function is small, which is closer to the Dirac function; when η a = -43dB, the APSL of the waveform output is about -20dB, which is higher than η a =-23dB and η a =-34dB, which means that the APSL threshold set at this time has deviated from the performance optimization upper limit that can be achieved by the proposed method.

[0193] Figure 11 is η c -23dB, -34dB, and -43dB are the cross-correlation functions generated by the first two sequences of the waveform set. Figure 10 The case of autocorrelation is similar, when the desired cross-correlation sidelobe η c =-23dB and η c =-43dB, the former is because the threshold is set too high, resulting in insufficient CPSL optimization, and the latter is because the threshold is set too low, resulting in an erroneous offset in the optimization result.

[0194] Depend on Figure 12 as well as Figure 13 The delay results in the above table show that for the expected correlation function threshold η a and η c The setting of has a great influence on the final optimization results of the proposed method.

[0195] Finally, the time performance analysis is carried out, as shown in Table 3.

[0196] Table 3. Data table of calculation time changes with sequence length

[0197] N CAN POCA GD Ours 100 0.06 1.02 35.3 5.53 200 0.07 5.52 63.4 5.93 300 0.08 12.7 96.5 6.63 400 0.08 20.7 127.8 6.93 500 0.12 32.5 164.0 7.23 600 0.18 49.1 203.0 8.61 700 0.19 92.9 250.1 8.87 800 0.21 285.2 280.3 9.12 900 0.23 428.5 395.1 9.45 1000 0.25 510.3 400.1 9.82

[0198] Table 3 compares the time required by different methods to generate waveform sets of varying lengths. First, the CAN method has the fastest computational speed of all methods, and its computational time remains nearly constant as N increases. For example, when N = 1000, it takes only 0.25 seconds, demonstrating extremely low computational complexity and making it suitable for computationally resource-sensitive real-time systems. However, its performance in optimizing PSL is relatively limited, making it difficult to meet the requirements of high-performance radars.

[0199] While the POCA method possesses strong optimization capabilities, its computational time increases exponentially with sequence length, from 1.02 seconds for N = 100 to 510.3 seconds for N = 1000. This method faces significant computational bottlenecks in large-scale waveform design problems, making it difficult to use for real-time optimization.

[0200] The neural network-based GD method has slightly better computational overhead than POCA, but it also faces serious convergence speed issues when N is large. For example, when N = 1000, it takes 400.1 seconds, indicating that direct loss optimization still has limited efficiency in high-dimensional spaces.

[0201] In contrast, the proposed method achieves a good balance between efficiency and performance. While maintaining the performance advantage of optimizing the correlation function's sidelobes, its computational time increases approximately linearly, from 5.53 seconds for N = 100 to only 9.82 seconds for N = 1000, significantly outperforming both the POCA and GD methods. This demonstrates the proposed method's scalability and practical deployment potential, making it suitable for modern MIMO radar systems with stringent requirements for both real-time performance and waveform quality.

[0202] In summary, the differences between the embodiments of the present invention and the prior art are:

[0203] 1) A low-correlation sidelobe waveform set design method based on neural network is proposed. With the help of the forward propagation and backward propagation mechanism of the neural network, the input vector matrix can be updated while updating the network parameters to achieve the optimization of the waveform set.

[0204] 2) The low sidelobe waveform design method using neural networks generates waveform sets with good correlation performance and high computational efficiency.

[0205] 3) The similarity constraint is introduced into the calculation of the loss function, and a set of waveforms whose correlation function is close to the ideal correlation function is obtained.

[0206] Therefore, the advantages of the embodiments of the present invention over the prior art are that, in applications such as MIMO radar systems and CDMA systems, waveform sets with good correlation characteristics are more often needed. The design of such waveform sequence sets requires simultaneous optimization of both autocorrelation and cross-correlation characteristics. In this case, waveform design methods based on parameter optimization are no longer applicable to complex scenarios with multiple constraints. Compared to the prior art, the present invention is based on neural networks, which have excellent fitting capabilities for nonlinear problems. The low-sidelobe waveform design method of neural networks can be used to generate sets with good correlation performance while achieving high computational efficiency. This can solve the problem of waveform design optimization in complex scenarios with multiple constraints.

[0207] See also Figure 2 The present application also provides a neural network-based low sidelobe waveform design system, which can implement the above-mentioned neural network-based low sidelobe waveform design method. The system includes:

[0208] The first module 201 is used to introduce an expected autocorrelation function and an expected cross-correlation function as penalty target functions based on a MIMO radar system to construct a low-correlation sidelobe optimization problem for a MIMO waveform set;

[0209] The second module 202 is used to solve the low-correlation sidelobe optimization problem based on a similarity-constrained neural network to obtain a loss function value;

[0210] The third module 203 is used to determine the parameters of the similarity-constrained neural network according to the loss function value, perform forward propagation, and output the final waveform matrix as the optimized waveform.

[0211] It can be understood that the contents of the above method embodiments are all applicable to the present system embodiments, the functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0212] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and essence of the present invention should be within the scope of the present invention.

Claims

1. A low sidelobe waveform design method based on neural network, characterized in that: The method comprises the following steps: Based on the MIMO radar system, the expected autocorrelation function and the expected cross-correlation function are introduced as penalty target functions to construct the low-correlation sidelobe optimization problem of the MIMO waveform set. Solving the low-correlation sidelobe optimization problem based on a similarity-constrained neural network to obtain a loss function value; The parameters of the similarity-constrained neural network are determined according to the loss function value, and forward propagation is performed to output the final waveform matrix as the optimized waveform.

2. The method according to claim 1, characterized in that The method is based on a MIMO radar system, introducing an expected autocorrelation function and an expected cross-correlation function as penalty target functions to construct a low-correlation sidelobe optimization problem of a MIMO waveform set, including: Based on the MIMO radar system, determining the number of transmitting antennas and the amount of time snapshot data transmitted by each transmitting antenna, and constructing a transmission data matrix of the MIMO radar system; Defining correlation based on the transmission data matrix of the MIMO radar system to determine the correlation function between the transmission waveform sequences; Based on the correlation function between the transmit waveform sequences, the peak sidelobe level is used as an optimization indicator, and a constant modulus constraint is introduced to obtain a preliminary low-correlation sidelobe optimization problem of the MIMO waveform set, wherein the peak sidelobe level includes the autocorrelation peak sidelobe and the cross-correlation peak sidelobe; Converting the low-correlation sidelobe optimization problem of the preliminary MIMO waveform set into a phase matrix; According to Welch theory, a reference value of the lower bound of the peak sidelobe of the correlation function is defined, and an expected autocorrelation function and an expected cross-correlation function are constructed, wherein the expected autocorrelation function is a Dirac function and the expected cross-correlation function is a constant sidelobe level; The expected autocorrelation function and the expected cross-correlation function are introduced into the phase matrix as penalty item target functions to obtain a low-correlation sidelobe optimization problem of the MIMO waveform set.

3. The method according to claim 2, characterized in that The expression of the reference value of the lower bound of the peak side lobe of the correlation function is specifically as follows: In the above formula, PSL represents the peak sidelobe level, M represents the number of antennas, N represents the time snapshot data transmitted by each transmitting antenna, and η a represents the expected autocorrelation function sidelobe level, η c represents the desired cross-correlation function sidelobe level, It represents the number of combinations of selecting q elements from 2N+q-2 elements.

4. The method according to claim 2, characterized in that The expressions of the expected autocorrelation function and the expected cross-correlation function are specifically as follows: E ccf (k)=η c In the above formula, E acf (·) represents the expected autocorrelation function, E ccf (·) represents the expected cross-correlation function, η a represents the expected autocorrelation function sidelobe level, η c represents the expected sidelobe level of the cross-correlation function, and k represents the time delay variable in the correlation function.

5. The method according to claim 2, characterized in that The expression of the low-correlation sidelobe optimization problem of the MIMO waveform set is specifically as follows: In the above formula, min X L represents the low-correlation sidelobe optimization problem, f mse (·) represents the mean square error function, λ1 represents the error coefficient of ACF, λ2 represents the error coefficient of CCF, ω1 represents the weight coefficient of APSL, ω2 represents the weight coefficient of CPSL, ACF m represents the autocorrelation function of the mth transmitting antenna, E acf represents the expected autocorrelation function, CCF m represents the cross-correlation function of the mth transmitting antenna, E ccf represents the expected cross-correlation function, APSL m Represents the autocorrelation peak sidelobe of the waveform sequence transmitted by the mth antenna, CPSL m represents the cross-correlation peak sidelobe of the waveform sequence transmitted by the mth antenna, M represents the number of antennas, and X represents the transmit data matrix of the MIMO radar system.

6. The method according to claim 2, characterized in that The similarity-constrained neural network solves the low-correlation sidelobe optimization problem to obtain a loss function value, including: Constructing a neural network based on similarity constraints, wherein the neural network includes an input layer, a hidden layer, and an output layer; Acquire the phase matrix and perform vectorized expansion processing to obtain an expanded phase matrix column vector; Performing a linear transformation on the expanded phase matrix column vector through the neural network to output an optimized phase vector; Reconstructing the dimension of the optimized phase vector to obtain a preliminary waveform matrix; The loss function is calculated and the adaptive moment is estimated for the low-correlation sidelobe optimization problem according to the preliminary waveform matrix to obtain the loss function value.

7. The method according to claim 6, characterized in that The step of performing loss function calculation and adaptive moment estimation on the low-correlation sidelobe optimization problem according to the preliminary waveform matrix to obtain the loss function value includes: determining a time delay correlation function based on the preliminary waveform matrix; Normalizing and modulus-calculating the delay-related function to obtain an information vector having a delay dimension; Extracting the autocorrelation function and the cross-correlation function of the antenna based on the information vector with the time delay dimension; Calculating the autocorrelation function and the cross-correlation function respectively by a smooth maximum approximation operator to obtain an autocorrelation peak sidelobe and a cross-correlation peak sidelobe; Substituting the information vector with the time delay dimension, the autocorrelation peak sidelobe, and the cross-correlation peak sidelobe into the low-correlation sidelobe optimization problem to obtain a preliminary loss function value; The preliminary loss function value is judged. If the preliminary loss function value is greater than a preset threshold, the steps of solving the low-correlation sidelobe optimization problem are repeated until the preliminary loss function value is less than the preset threshold, and the loss function value is output.

8. The method according to claim 7, characterized in that The invention also includes introducing a preset acceleration mechanism to accelerate the process of solving the low-correlation sidelobe optimization problem, specifically including: The side lobes of antennas whose autocorrelation functions are smaller than the expected autocorrelation function side lobe level and the side lobes of antennas whose cross-correlation functions are smaller than the expected cross-correlation function side lobe level are eliminated to accelerate the solution of the low-correlation side lobe optimization problem.

9. The method according to claim 2, characterized in that The process of determining the parameters of the similarity-constrained neural network according to the loss function value, performing forward propagation, and outputting a final waveform matrix as an optimized waveform includes: Determining parameters of the similarity-constrained neural network according to the loss function value, and constructing an optimal neural network, wherein the parameters include a weight matrix and a bias vector; The phase matrix is ​​input into the optimal neural network for forward propagation, and the final waveform matrix is ​​output as the optimized waveform.

10. A low sidelobe waveform design system based on neural network, characterized in that: The system comprises: The first module is used to construct the low-correlation sidelobe optimization problem of the MIMO waveform set based on the MIMO radar system by introducing the expected autocorrelation function and the expected cross-correlation function as the penalty target function; The second module is used to solve the low-correlation sidelobe optimization problem based on a similarity-constrained neural network to obtain a loss function value; The third module is used to determine the parameters of the similarity-constrained neural network according to the loss function value, perform forward propagation, and output the final waveform matrix as the optimized waveform.

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