MIMO radar emission sequence set design optimization method

Abstract

The embodiment of the invention relates to the technical field of radars, and discloses an MIMO radar emission sequence set design optimization method, which comprises the following steps: constructing a signal model designed based on an AF emission sequence set for an MIMO radar system, selecting ISL of minimizing local AAF and CAF as an optimization criterion, selecting an energy constraint and a dynamic range constraint as constraint conditions, and selecting an energy constraint and a dynamic range constraint as constraint conditions; establishing a four-order non-convex constraint optimization problem; decomposing the fourth-order non-convex constraint optimization problem into a plurality of sub-problems which can be iteratively solved by utilizing an MBI algorithm; sequentially solving the sub-problems by means of CVX to obtain a preliminary solution; and continuously adjusting a search direction and a step length by using a BLS algorithm, and carrying out iterative optimization on the approximate solution until an Armijo condition is met, thereby obtaining a global optimal solution meeting a design requirement, and further designing a radar emission sequence set with good related characteristics, thereby improving the target detection capability, the anti-interference capability and the resolution of the MIMO radar system.

Description

Technical Field

[0001] The embodiments of the present application relate to the field of radar technology, and in particular to a method for designing and optimizing a MIMO radar transmit sequence set. Background Art

[0002] MIMO (Multiple In Multiple Out) radar is a highly advanced radar technology that, by using multiple transmit and receive antennas, can significantly improve the radar system's performance in target detection, resolution, and anti-interference. However, the performance of MIMO radar depends heavily on the design of the transmit waveform set. If the waveform sets are poorly correlated, mutual interference between signals will occur, thereby reducing system performance. Therefore, designing orthogonal waveform sets with good correlation is a key issue in MIMO radar research. By studying different waveform design methods, the theoretical system of MIMO radar waveform design can be enriched and improved. At the same time, with the widespread application of MIMO radar in military and civilian fields, optimizing waveform design can improve its performance in scenarios such as target detection, environmental monitoring, and autonomous driving.

[0003] In radar signal processing, the ambiguity function (AF) is defined as a two-dimensional function that describes the resolution of a radar signal in both the range and Doppler frequency dimensions. AF is a key tool for measuring radar waveform performance. On the one hand, AF accurately reveals the resolution characteristics of a radar system in both the range and Doppler dimensions, which is crucial for accurately detecting the range and velocity of a target. On the other hand, AF can also be used to evaluate a waveform's anti-interference performance in complex electromagnetic environments, providing a quantitative basis for selecting and designing radar waveforms with robust anti-interference capabilities.

[0004] Currently, many studies are using AF shaping methods to improve the target detection performance of radar systems. In AF shaping methods, the transmit sequence typically uses a phase-coded sequence. Based on the phase-coding characteristics of the transmit sequence, AF design can generally be divided into fast-time AF design and slow-time AF design. A fast-time transmit waveform is composed of a series of sub-pulses, while a slow-time transmit waveform is composed of a series of pulses with a constant pulse repetition interval. One research team studied the design of a constant modulus sequence with good correlation based on AF, using the minimization of the weighted integral sidelobe level (WISL) of autocorrelation and cross-correlation as a metric. Using the fast ISQO algorithm, the non-convex quartic optimization problem is decomposed into a quadratic problem at each iteration, which can be converted into a linear optimization problem with a closed-form solution. Another research team has proposed optimizing radar system performance by minimizing the average value of the transmit waveform AF in certain specific units in the slow-time dimension. However, the problem model constructed by the above concept encounters the fourth-order polynomial optimization problem. Due to its high nonlinearity and complex constraints, traditional optimization algorithms are difficult to solve directly and effectively, which brings great challenges to the optimized waveform design. Summary of the Invention

[0005] In view of this, an embodiment of the present application proposes a MIMO radar transmit sequence set design optimization method, which aims to draw on the ideas of the MBI algorithm, decompose the fourth-order polynomial optimization problem into multiple interrelated and iteratively solvable sub-problems, obtain preliminary solutions to the sub-problems with the help of the convex optimization tool CVX, and finally use the BLS algorithm to continuously update the step size and optimize the preliminary solution until the global optimal solution is obtained, thereby designing a radar transmit sequence set with good correlation characteristics, thereby enhancing the performance of the MIMO radar system in target detection, anti-interference, and resolution improvement.

[0006] To achieve the above objectives, an embodiment of the present application proposes a MIMO radar transmit sequence set design optimization method, which is applicable to a MIMO radar system. The method includes: constructing a signal model based on an AF transmit sequence set design for a MIMO radar system, selecting the ISL that minimizes the local AAF and CAF as the optimization criterion, selecting energy constraints and dynamic range constraints as constraints, and establishing a fourth-order non-convex constrained optimization problem based on the signal model, the optimization criterion, and the constraints; using the MBI algorithm to decompose the fourth-order non-convex constrained optimization problem into multiple iteratively solvable sub-problems, and replacing the non-convex objective function and non-convex constraints in the fourth-order non-convex constrained optimization problem with corresponding convex functions; sequentially solving each sub-problem with the help of the convex optimization tool CVX to obtain a preliminary solution; using the BLS algorithm to continuously adjust the search direction and step size, and iteratively optimize the approximate solution until the Armijo condition is met, thereby obtaining a global optimal solution that meets the design requirements.

[0007] To achieve the above objectives, an embodiment of the present application further proposes a MIMO radar transmit sequence set design optimization system, which is applicable to MIMO radar systems. The system includes: an optimization problem establishment module, a convex function replacement module, a preliminary solution module, and an iterative optimization module; the optimization problem establishment module is used to construct a signal model based on the AF transmit sequence set design for the MIMO radar system, select the ISL that minimizes the local AAF and CAF as the optimization criterion, select the energy constraint and the dynamic range constraint as the constraint conditions, and establish a fourth-order non-convex constrained optimization problem based on the signal model, the optimization criterion, and the constraint conditions; the convex function replacement module is used to use the MBI algorithm to decompose the fourth-order non-convex constrained optimization problem into multiple iteratively solvable sub-problems, and the non-convex objective function and non-convex constraints in the fourth-order non-convex constrained optimization problem are replaced by corresponding convex functions; the preliminary solution module is used to sequentially solve each sub-problem with the help of the convex optimization tool CVX to obtain a preliminary solution; the iterative optimization module is used to use the BLS algorithm to continuously adjust the search direction and step size, iteratively optimize the approximate solution until the Armijo condition is met, thereby obtaining a global optimal solution that meets the design requirements.

[0008] To achieve the above objectives, an embodiment of the present application further proposes an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform a MIMO radar transmit sequence set design optimization method as described above.

[0009] To achieve the above objectives, an embodiment of the present application further proposes a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement the MIMO radar transmit sequence set design optimization method as described above.

[0010] This application proposes a MIMO radar transmit sequence set design optimization method for MIMO radar systems. This method constructs a signal model based on the AF transmit sequence set design. By determining optimization criteria and constraints, it establishes a fourth-order non-convex constrained optimization problem with the goal of minimizing the inter-segmented linear (ISL) under energy and dynamic range constraints. For this fourth-order non-convex constrained optimization problem, an innovative MBI-BLS waveform optimization method is designed. The core of this method is to first use the MBI algorithm to decompose the complex problem into multiple iterative subproblems. The convex optimization tool CVX is then used to obtain preliminary solutions to the subproblems. Finally, the BLS algorithm is used to continuously update the step size and optimize the preliminary solutions to obtain the global optimal solution. Through a reasonable update strategy for the outer MBI algorithm and effective step size adjustment for the inner BLS algorithm, the MBI-BLS waveform optimization method exhibits good overall convergence and can reliably solve the relevant optimization problem. The optimized sequence achieves an ISL value of approximately -30 dB, meeting the low ISL requirement. Given the same low energy loss and a wide range of sequence amplitudes, longer sequences yield lower ISL values. In summary, based on this method, a radar transmission sequence set with good correlation characteristics can be designed, which effectively enhances the performance of the MIMO radar system in target detection, anti-interference, and resolution improvement.

[0011] In some optional embodiments, for a MIMO radar system, a signal model designed based on an AF transmission sequence set is constructed, including:

[0012] Consider a MIMO radar system with a distributed or centralized structure, equipped with M transmitting antennas, and the transmission sequences corresponding to each transmitting antenna together constitute the set x m represents the phase-encoded signal vector of length N, x m =[x m (1),x m (2),…,x m (N)] T ;

[0013] In this system framework, its fast time AF is defined as:

[0014]

[0015] Where m represents the mth transmitting antenna, m′ represents the m′th transmitting antenna, p represents the Doppler shift index set, p∈{-N / 2,…,N / 2}, k represents the delay parameter, k∈{-N+1,-N+2,…,N-1}, if m=m′, then r m,m′ (p,k) represents AAF, if m≠m′, then r m,m′ (p,k) represents CAF;

[0016] In order to simplify the representation, r m,m′ (p,k) is expressed in matrix form as:

[0017]

[0018] Among them, Diag(·) represents the diagonal matrix, a p is the Doppler frequency shift vector, U k is the delay matrix.

[0019] In some optional embodiments, the selected optimization criterion is expressed as follows:

[0020]

[0021] Among them, Ω sa and Ω sc denote the local sidelobe regions of the AAF and CAF of interest, respectively, and ISL denotes the optimization criterion selected to minimize the ISL of the local AAF and CAF;

[0022] For AAF, Ω sa ={(m,p,k)|m=1,…,M; p=-P,…,P; k=-K,…,K}, |Ω a |=M(2P+1)(2K+1), for CAF, Ω sc ={(m,m′,p,k)|m=1,…,M-1; m′=m+1,…,M; p=-P,…,P; k=-K,…,K};

[0023] In order to facilitate understanding and processing, the expression of the optimization criterion is split into the following expressions:

[0024]

[0025] Energy constraints ensure that the MIMO radar system has sufficient energy when detecting targets while avoiding excessive radiation to non-target areas, thereby improving the accuracy and efficiency of target detection. The energy constraint is expressed as the total energy of the waveform must be less than or equal to a predetermined value. The expression of the energy constraint is shown as:

[0026]

[0027] m=1,…,M;

[0028] Where δ is the energy coefficient, 0.5≤δ≤1;

[0029] The dynamic range constraint limits the waveform amplitude range, aiming to allow the nonlinear amplifier of the MIMO radar system to operate at maximum efficiency and avoid nonlinear distortion of the output waveform. The dynamic range constraint is expressed as:

[0030] δ(1-ε) 2 ≤|x m (n)| 2 ≤δ(1+ε) 2 ;

[0031] n=1,…,N;

[0032] Among them, ε represents the fluctuation degree of the waveform amplitude, ε∈[0,1].

[0033] In some optional embodiments, the established fourth-order non-convex constrained optimization problem is expressed as follows:

[0034]

[0035] In some optional embodiments, the MBI algorithm is used to decompose the fourth-order non-convex constrained optimization problem into multiple iteratively solvable sub-problems, including:

[0036] Using the MBI algorithm, in a fixed vector Medium Under the premise of other variables besides , solve the fourth-order non-convex constrained optimization problem; Represents the result of the i+1th iteration of the MBI algorithm;

[0037] The objective function of the fourth-order non-convex constrained optimization problem It is a fourth-order polynomial and a non-convex function. We use a convex quadratic function to approximate it and transform the non-convex function into a convex function. f(x m ), f(x m ) is expressed as follows:

[0038]

[0039] in, represents the i-th iteration result of the MBI algorithm, R represents the real part, express right The first-order gradient of represents the approximation factor, for exist The positive semidefinite approximation of the Hessian matrix at ;

[0040] The constraint C2 of the fourth-order non-convex constrained optimization problem is a non-convex constraint function, which is approximated by the first-order Taylor expansion. Perform a first-order Taylor expansion at , and use the obtained linear approximate function to replace the constraint C2, thereby converting it into a convex function. The approximate convex constraint is expressed by the formula:

[0041]

[0042] n=1,…,N;

[0043] At this point, the fourth-order non-convex constrained optimization problem is decomposed into multiple sub-problems that can be solved iteratively, that is, the replaced convex problem is obtained. The replaced convex problem is expressed by the formula:

[0044]

[0045] In some optional embodiments, each subproblem is sequentially solved using the convex optimization tool CVX to obtain a preliminary solution, including:

[0046] Based on the mathematical model of each sub-problem, program according to the grammatical rules of CVX to clarify the objective function, constraints, and domain of variables;

[0047] Call the solver in the CVX toolbox to solve each sub-problem sequentially. After the solution is completed, the preliminary solution is obtained.

[0048] In some optional embodiments, the BLS algorithm is used to continuously adjust the search direction and step size to iteratively optimize the approximate solution until the Armijo condition is satisfied, thereby obtaining a global optimal solution that meets the design requirements, including:

[0049] Select As the search direction, 1 is selected as the initial step size;

[0050] In each iteration, it is determined whether the Armijo condition is met. The expression of the Armijo condition is:

[0051]

[0052] Among them, α is a small positive number, which is used to control the conservativeness of the step size;

[0053] When the Armijo condition is not met, the step size is reduced proportionally, that is, Where ξ is a number between 0 and 1, j is the current iteration number of the BLS algorithm;

[0054] When the Armijo conditions are met, the global optimal solution that meets the design requirements is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the related technologies, the following is a brief introduction to the drawings required for use in the embodiments of the present application or the description of the related technologies. Obviously, the following drawings are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. The drawings described here are only used to explain the present application and are not used to limit the present application.

[0056] Figure 1 This is a flowchart of a MIMO radar transmit sequence set design optimization method provided in one embodiment of the present application;

[0057] Figure 2 1 is a schematic diagram of the transformation of the objective function value with the number of iterations t under the MBI-BLS algorithm provided in one embodiment of the present application;

[0058] Figure 3 is a schematic diagram of normalized AF provided in one embodiment of the present application;

[0059] Figure 4 is a normalized zero-Doppler profile of AF provided in one embodiment of the present application;

[0060] Figure 5 It is a normalized AF zero-delay profile provided in one embodiment of the present application;

[0061] Figure 6 1 is a schematic diagram of the relationship between ISLs and energy coefficient δ under the MBI-BLS algorithm provided in one embodiment of the present application;

[0062] Figure 7 1 is a schematic diagram showing the relationship between ISLs and amplitude range ε ​​under the MBI-BLS algorithm, provided in one embodiment of the present application;

[0063] Figure 8 This is a schematic diagram of the relationship between ISLs and Doppler frequency range P under the MBI-BLS algorithm, provided in one embodiment of the present application;

[0064] Figure 9 1 is a schematic diagram of the relationship between ISLs and the time delay range K under the MBI-BLS algorithm provided in one embodiment of the present application;

[0065] Figure 10 is a structural diagram of a MIMO radar transmit sequence set design and optimization system provided in another embodiment of the present application;

[0066] Figure 11 It is a structural diagram of an electronic device provided in another embodiment of the present application. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, each embodiment of the present application will be described in detail below with reference to the accompanying drawings. Those skilled in the art will appreciate that in each embodiment of the present application, many technical details are provided to enable the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solutions claimed in the present application can be implemented. The division of the following embodiments is for convenience of description and should not constitute any limitation on the specific implementation of the present application. The various embodiments can be combined with each other and referenced to each other under the premise of no contradiction.

[0068] One embodiment of this application proposes a MIMO radar transmit sequence set design optimization method, applicable to MIMO radar systems and servers. The following describes the implementation details of the MIMO radar transmit sequence set design optimization method proposed in this embodiment. The following details are provided for ease of understanding and are not required for implementing this solution.

[0069] The specific process of the MIMO radar transmit sequence set design optimization method proposed in this embodiment can be as follows: Figure 1 As shown, including:

[0070] Step 11: For the MIMO radar system, a signal model based on the AF transmission sequence set design is constructed, the ISL that minimizes the local AAF and CAF is selected as the optimization criterion, the energy constraint and the dynamic range constraint are selected as the constraints, and a fourth-order non-convex constrained optimization problem is established based on the signal model, optimization criterion and constraints.

[0071] In the specific implementation, a signal model based on the AF transmit sequence set design for the MIMO radar system must first be constructed. Next, an optimization criterion and energy constraints must be determined. For various reasons, this embodiment selects minimizing the ISL of the local AAF and CAF as the optimization criterion, and energy and dynamic range constraints as the constraints. Once the signal model, optimization criterion, and constraints are in place, a fourth-order nonconvex constrained optimization problem can be established based on these three factors.

[0072] In one example, when building a signal model, it is necessary to consider a MIMO radar system, which can be a distributed structure or a centralized structure. The MIMO radar system is equipped with M transmitting antennas, and the transmission sequences corresponding to each transmitting antenna together constitute the set x m represents the phase-encoded signal vector of length N, x m =[x m (1),x m (2),…,x m (N)] T , M and N are both integers greater than 2.

[0073] In this system framework, the fast time AF of the MIMO radar system is defined as:

[0074]

[0075] Where m represents the mth transmitting antenna, m′ represents the m′th transmitting antenna, p represents the Doppler shift index set, p∈{-N / 2,…,N / 2}, k represents the delay parameter, k∈{-N+1,-N+2,…,N-1}, if m=m′, then r m,m′ (p,k) represents AAF, if m≠m′, then r m,m′ (p,k) represents CAF.

[0076] In order to simplify the representation, r m,m′ (p,k) is expressed in matrix form as:

[0077]

[0078] a p =[exp(-j2πp / N),exp(-j2π2p / N),…,exp(-j2πNp / N)] T ;

[0079]

[0080] Among them, Diag(·) represents the diagonal matrix, a p is the Doppler frequency shift vector, U k is the delay matrix.

[0081] The waveform design problem for MIMO radar systems is typically a non-convex, high-dimensional, multi-constrained optimization problem that involves waveform optimization criteria and constraints. The optimization criteria are directly or indirectly related to radar performance metrics such as target detection, parameter estimation, and anti-interference.

[0082] The ISL criterion is primarily used to control the waveform ambiguity function, reduce mutual interference between multiple targets, and improve multi-target detection performance. The smaller the ISL, the smaller the sidelobe energy returned by strong targets (clutter), and the greater the probability of detecting weak targets. Furthermore, due to the volume-invariant nature of AF, it is impossible to reduce the overall sidelobe level. Therefore, this embodiment selects ISL, which minimizes the local AAF and CAF, as the optimization criterion. Its expression is:

[0083]

[0084] Among them, Ω sa and Ω sc denote the local sidelobe regions of the AAF and CAF of interest, respectively, and ISL denotes the optimization criterion selected to minimize the ISL of the local AAF and CAF.

[0085] For AAF, Ω sa ={(m,p,k)|m=1,…,M; p=-P,…,P; k=-K,…,K}, |Ω a |=M(2P+1)(2K+1), for CAF, Ω sc ={(m,m′,p,k)|m=1,…,M-1; m′=m+1,…,M; p=-P,…,P; k=-K,…,K}.

[0086] In order to facilitate subsequent understanding and processing, we need to split the expression of the optimization criterion. The expression after splitting is:

[0087]

[0088] The selection of constraint conditions also affects the performance of the final waveform, the difficulty of the optimization process, and the optimization execution efficiency. According to actual needs, the constraint conditions selected in this embodiment include energy constraint and dynamic range constraint.

[0089] Energy constraints can ensure that the MIMO radar system has sufficient energy when detecting targets while avoiding excessive radiation to non-target areas, thereby improving the accuracy and efficiency of target detection. The energy constraint is expressed as the total energy of the waveform must be less than or equal to a predetermined value. The expression of the energy constraint is shown as:

[0090]

[0091] m=1,…,M;

[0092] Where δ is the energy coefficient, 0.5≤δ≤1.

[0093] The dynamic range constraint limits the waveform amplitude range. It aims to allow the nonlinear amplifier of the MIMO radar system to operate at maximum efficiency (saturation or near saturation) and avoid nonlinear distortion of the output waveform. The dynamic range constraint is expressed as:

[0094] δ(1-ε) 2 ≤|x m (n)| 2 ≤δ(1+ε) 2 ;

[0095] n=1,…,N;

[0096] Among them, ε represents the fluctuation degree of the waveform amplitude, ε∈[0,1].

[0097] At this point, the signal model, optimization criteria, and constraints are all ready. Next, in the context of fast-time waveform design, we can consider minimizing the ISL of local AAF and CAF under energy and dynamic range constraints, design a set of transmit sequences under a matched filter system, and formulate the optimization problem as follows:

[0098]

[0099] Step 12: Use the MBI algorithm to decompose the fourth-order non-convex constrained optimization problem into multiple sub-problems that can be solved iteratively. The non-convex objective function and non-convex constraints in the fourth-order non-convex constrained optimization problem are replaced by corresponding convex functions.

[0100] In the specific implementation, after establishing the fourth-order non-convex constrained optimization problem, the MBI-BLS waveform optimization method was innovatively designed for this fourth-order non-convex constrained optimization problem. First, the MBI algorithm is used to decompose the fourth-order non-convex constrained optimization problem into multiple sub-problems that can be solved iteratively, and the non-convex objective function and non-convex constraints in the fourth-order non-convex constrained optimization problem are replaced by corresponding convex functions.

[0101] Using the MBI algorithm, in a fixed vector Medium Under the premise of other variables besides , solve the fourth-order non-convex constrained optimization problem; Indicates the result of the i+1th iteration of the MBI algorithm.

[0102] The objective function of the fourth-order non-convex constrained optimization problem is a fourth-order polynomial and a non-convex function. In optimization theory, the difficulty of solving non-convex problems is significantly higher than that of convex optimization problems. In view of this, in order to reduce the complexity of the solution, a convex quadratic function is used to approximate it, and the non-convex function is converted into a convex function. f(x m ), f(xm ) is expressed as follows:

[0103]

[0104] in, represents the i-th iteration result of the MBI algorithm, R represents the real part, express right The first-order gradient of represents the approximation factor, for exist The positive semidefinite approximation of the Hessian matrix at .

[0105] In addition, the constraint C2 of the fourth-order non-convex constrained optimization problem is a non-convex constraint function, which will lead to higher complexity and uncertainty in the optimization solution process. According to mathematical analysis theory, the Taylor expansion of a function can approximate the function in the form of a power series in the neighborhood of a certain point. Therefore, for the constraint C2, the first-order Taylor expansion is used to approximate it. This is because the first-order Taylor expansion can more accurately reflect the changing trend of the original function in a local range, and the form is relatively simple, which is convenient for subsequent calculation and analysis. By Perform a first-order Taylor expansion at , and use the obtained linear approximate function to replace the constraint C2, thereby converting it into a convex function. The approximate convex constraint is expressed by the formula:

[0106]

[0107] n=1,…,N。

[0108] At this point, the fourth-order non-convex constrained optimization problem is decomposed into multiple sub-problems that can be solved iteratively, that is, the replaced convex problem is obtained. The replaced convex problem is expressed by the formula:

[0109]

[0110] h psd 、-|x m (n)| 2 The derivation process of the convex approximation is as follows.

[0111] First, let Its first-order gradient is:

[0112]

[0113] f(x m ) is:

[0114]

[0115]

[0116] make express Eigenvalue decomposition of , where Γ=Diag{d1,…,d N}yes is a diagonal matrix composed of the eigenvalues ​​of .

[0117] because is a Hermitian matrix, so The positive semidefinite approximation under the Frobenius norm is H psd =UΓ + U H , Γ + =Diag{max(d1,0),…,max(d N ,0)}, by The positive eigenvalues ​​of and zero.

[0118] Next, let

[0119] Its first-order gradient is:

[0120]

[0121] Therefore, f1(x m )exist The convex approximation function at is:

[0122]

[0123] Step 13: Use the convex optimization tool CVX to sequentially solve each sub-problem and obtain a preliminary solution.

[0124] In the specific implementation, after completing the transformation of the optimization problem, the convex optimization tool CVX can be used to sequentially solve each sub-problem to obtain a preliminary solution.

[0125] In one example, the CVX toolbox is a powerful tool specifically designed for solving convex optimization problems. Based on the MATLAB platform, CVX provides a concise and efficient modeling language that can describe and solve complex convex optimization problems in an intuitive way. After completing the transformation of the optimization problem, according to the mathematical model of each sub-problem, programming is performed according to the grammatical rules of CVX, clarifying the objective function, constraints, and domain of variables, and then calling the solver in the CVX toolbox to solve each sub-problem sequentially. After the solution is completed, a preliminary solution is obtained.

[0126] In step 14, the search direction and step size are continuously adjusted using the BLS algorithm to iteratively optimize the approximate solution until the Armijo condition is met, thereby obtaining the global optimal solution that meets the design requirements.

[0127] In the specific implementation, the preliminary solution is only an approximate solution. In order to obtain a better solution or the optimal solution, it is necessary to use the BLS algorithm to continuously adjust the search direction and step size, and iteratively optimize the approximate solution until the Armijo condition is met, thereby obtaining the global optimal solution that meets the design requirements.

[0128] The BLS algorithm is a line search algorithm widely used in optimization problems. Its core function is to determine the appropriate step size in a given search direction. The algorithm uses the Armijo criterion as a basis for determining the appropriate step size. During the iteration process, if the current step size does not produce a sufficient decrease in the objective function value, the step size is gradually reduced according to specific rules until the conditions set by the Armijo criterion are met. Due to the BLS algorithm's efficiency and accuracy in determining step sizes, it is often used in conjunction with other optimization algorithms to enhance optimization results.

[0129] The execution process of the BLS algorithm is as follows.

[0130] First, determine the search direction. In the iterative optimization process, the first task is to carefully determine a search direction. This is because the appropriate search direction can build the fastest descent path for the objective function in the local area, thereby achieving the optimization goal. Based on the specific actual situation, we choose as a search direction.

[0131] Second, determine the initial step size. After determining the search direction, set an initial step size. The size of the initial step size has a significant impact on the algorithm's convergence speed and performance. If the initial step size is too large, the algorithm may skip the optimal solution during the search. If the initial step size is too small, the algorithm converges too slowly and increases computational cost. A typical initial step size is 1.

[0132] Third, the Armijo condition. In each iteration, it is necessary to determine whether the Armijo condition is met. The expression of the Armijo condition is:

[0133]

[0134] α is a small positive number that controls the degree of conservatism in the step size, typically set to 0.1 or 0.2. This parameter α is crucial, balancing the algorithm's ability to explore new areas with its ability to leverage existing information. If α is too small, the step size update will be too aggressive, potentially making the algorithm unstable during the search process. If α is too large, the step size update will be too conservative, impacting the algorithm's convergence speed.

[0135] Fourth, step size reduction. When the Armijo condition is not met, a step size reduction operation needs to be performed to reduce the step size proportionally, that is, Here, ξ is a number between 0 and 1, typically 0.5, and j is the current iteration of the BLS algorithm. By gradually adjusting the step size in this way, the algorithm can more effectively approach the optimal solution while satisfying the Armijo condition.

[0136] Fifth, repeat the steps. Continuously repeat the above steps until the Armijo condition is met. During this process, the algorithm continuously adjusts the search direction and step size, gradually approaching the optimal solution of the objective function, and ultimately obtaining the global optimal solution that meets the design requirements.

[0137] In the MBI-BLS algorithm framework, the iterative update strategy of the outer MBI algorithm plays a key role in its convergence. During each iteration, the MBI algorithm updates only the variable block that minimizes the objective function value, while the remaining variable blocks retain their values ​​from the previous iteration. This update strategy effectively ensures a monotonically decreasing objective function value during the iterations, thereby ensuring the algorithm's convergence. Within the inner loop, the BLS algorithm is used to optimize the approximate solution. The BLS algorithm gradually approaches a more optimal solution by continuously adjusting the step size along the path between the selected approximate solution and the original solution. During each iteration, the BLS algorithm dynamically adjusts the step size based on the changes in the objective function value according to established backtracking rules, ensuring that each update step satisfies the convergence criteria. This optimization strategy, based on dynamic step size adjustment, theoretically ensures that the BLS algorithm converges. In summary, the MBI-BLS algorithm exhibits excellent overall convergence and can reliably solve relevant optimization problems.

[0138] This embodiment proposes a MIMO radar transmit sequence set design optimization method for MIMO radar systems. This method constructs a signal model based on the AF transmit sequence set design. By determining optimization criteria and constraints, it establishes a fourth-order non-convex constrained optimization problem with the goal of minimizing ISL under energy and dynamic range constraints. For this fourth-order non-convex constrained optimization problem, an innovative MBI-BLS waveform optimization method is designed. The core of this method is to first use the MBI algorithm to decompose the complex problem into multiple iterative subproblems. Then, using the convex optimization tool CVX, preliminary solutions to the subproblems are obtained. Finally, the BLS algorithm is used to continuously update the step size and optimize the preliminary solutions to obtain the global optimal solution. Through a reasonable update strategy for the outer MBI algorithm and effective step size adjustment for the inner BLS algorithm, the MBI-BLS waveform optimization method exhibits good overall convergence and can reliably solve the relevant optimization problem. The optimized sequence achieves an ISL value of approximately -30 dB, meeting the low ISL requirement. Given the same low energy loss and a wide range of sequence amplitudes, longer sequences yield lower ISL values. In summary, based on this method, a radar transmission sequence set with good correlation characteristics can be designed, which effectively enhances the performance of the MIMO radar system in target detection, anti-interference, and resolution improvement.

[0139] The steps of the various methods above are divided for clarity of description only. They can be combined into a single step, or some steps can be broken down into multiple steps. As long as they share the same logical relationships, they are all within the scope of protection of this application. Adding minor modifications or introducing minor design changes to the algorithm or process, but not changing the core design of the algorithm or process, also falls within the scope of protection of this application.

[0140] In one embodiment, to verify the superiority of the proposed method, we conducted relevant simulation experiments. The following describes the simulation process and results. We will conduct an in-depth analysis of the AF-based transmit sequence set design method from multiple dimensions, such as convergence speed, to verify the effectiveness and feasibility of the proposed method.

[0141] The initial transmission sequences used in the experiment are all random complex sequences with a modulus of 1. The number of transmitting antennas M = 3, and the range Doppler unit interval is {-2,…,2} p ×{-10,…,10} k The maximum number of iterations of the outer MBI algorithm is t max , the maximum number of iterations of the inner BLS algorithm is i max .

[0142] Figure 2 The relationship between the objective function value and the number of iterations under different sequence lengths N is given. Figure 2 As can be seen, the objective function values ​​of all curves gradually decrease with increasing iterations, indicating continuous optimization of the algorithm. The curve with N = 16 decreases the fastest, reaching a low objective function value after 10 iterations. The curve with N = 32 decreases the fastest, slightly slower than N = 16, and converges after around 20 iterations. The curve with N = 64 decreases even more slowly, reaching a low objective function value after 35 iterations. The curve with N = 128 decreases the slowest, and still fails to converge after 50 iterations. Overall, smaller N values ​​lead to faster convergence to a better solution.

[0143] Figure 3 The normalized AF three-dimensional graph of the MBI-BLS algorithm when N=64 is given. The top corresponds to the autocorrelation parameters {x1,x1}, {x2,x2}, {x3,x4}, and the bottom corresponds to the cross-correlation parameters {x1,x2}, {x1,x3}, {x2,x3}. Figure 2 It can be observed that the autocorrelation AF has a peak at the main lobe position {p=0, k=0} and there is a depression in the surrounding optimization area {p=2, k=10}. All AF values ​​of the cross-correlation AF should be as low as possible, and there should be no main lobe. The current performance is in line with expectations.

[0144] Figure 4 and Figure 5 The zero Doppler and zero delay profiles corresponding to normalized AF are shown respectively. Figure 4 It can be clearly observed from the locally enlarged area that the optimized autocorrelation AF value is stable at around -30dB, while the cross-correlation AF value is significantly reduced to below -50dB. This result fully verifies the effectiveness of the waveform optimization algorithm in suppressing cross-correlation interference. Figure 7 The simulation results show more detailed features. First, the main lobe level of the subgraph pair {x1, x1} does not reach the ideal 0dB standard. This is because we allow reasonable main lobe energy loss during the modeling process. This phenomenon fully complies with the preset model constraints. Secondly, it is particularly noteworthy that the optimized AF value can reach a minimum of -300dB. This excellent indicator strongly proves that the MBI-BLS algorithm has good optimization performance. In addition, through comparative analysis, it can be found that the curve fluctuations of the optimized area (partially enlarged part) in the bottom three figures are significantly greater than those in the top figure. This difference intuitively reflects the fluctuation characteristics of the cross-correlation AF value during the iterative process of the algorithm, indicating that there is a certain degree of difference in the optimization results produced by each iteration, which provides an important reference basis for subsequent algorithm improvements.

[0145] Figure 6 The trend of the integrated sidelobe level ISLs under different sequence lengths N as the parameter δ changes is depicted. Figure 6 As can be observed, for all values ​​of N, as δ increases from 0.5 to 1, the ISL value initially remains essentially stable, then begins to rise significantly when δ approaches 0.8. This indicates that the system performance is relatively stable when δ is low, ≤ 0.8. Within the low δ range, the system with a sequence length of 128 significantly outperforms other smaller values ​​of N.

[0146] Figure 7 This is the relationship between the ISLs value and the waveform amplitude range ε ​​under different sequence lengths N. Figure 7 As can be observed, when N = 16, the ISL decreases linearly with increasing ε, from approximately 13.5 dB to approximately 12 dB. When N = 32, the ISL also decreases linearly with increasing ε, from approximately 11 dB to approximately 9.7 dB. When N = 64, the ISL remains at approximately 8 dB, barely changing with ε. When N = 128, the ISL decreases linearly with increasing ε, from approximately 5.5 dB to approximately 4 dB. This indicates that the sequence length N has a significant impact on the performance metric ISL, and this impact varies with ε. Specifically, smaller N values ​​(such as N = 16 and N = 32) exhibit a larger decrease in ISL with changes in ε, while larger N values ​​(such as N = 64 and N = 128) show little change or almost no change.

[0147] Figure 8 and Figure 9 The graphs of ISLs changing with Doppler frequency range P and delay range K under MBI-BLS algorithm are shown respectively. Figure 8 We observe that when sequence length N = 16, as P increases from 2 to 3, the ISL value drops sharply from approximately 10 dB to around 2 dB, then remains constant. When N = 32, the ISL value remains at approximately 9.5 dB, unchanged with changes in P. For N = 64, the ISL value remains at approximately 6.7 dB, unchanged with changes in P. Similarly, when N = 128, the ISL value remains at approximately 4.4 dB, unchanged with changes in P. Overall, the ISL value decreases with increasing N, and when N is greater than or equal to 32, the ISL value no longer varies with changes in P. This indicates that under these conditions, the ISL value reaches a stable state.

[0148] from Figure 9 As can be seen, when N = 16, the ISL value initially remains essentially constant, remaining at approximately 10 dB. It then drops to approximately 8 dB at K = 15, and then remains constant at around 8 dB. When N = 32, N = 64, and N = 128, the ISL remains approximately 6.7 dB, 4.3 dB, and 1.4 dB, respectively, unchanged with K. This indicates that the longer the sequence, the less pronounced the effect of K on ISL.

[0149] Another embodiment of the present application provides a MIMO radar transmit sequence set design and optimization system, which is applicable to a MIMO radar system. The following is a detailed description of the MIMO radar transmit sequence set design and optimization system proposed in this embodiment. The following content is only for the convenience of understanding the implementation details and is not required for the implementation of this embodiment. Figure 10 1 is a schematic diagram of the structure of a MIMO radar transmit sequence set design optimization system proposed in this embodiment, comprising: an optimization problem establishment module 21, a convex function replacement module 22, a preliminary solution module 23 and an iterative optimization module 24.

[0150] The optimization problem establishment module 21 is used to construct a signal model based on the AF transmission sequence set design for the MIMO radar system, select the ISL that minimizes the local AAF and CAF as the optimization criterion, select the energy constraint and the dynamic range constraint as the constraint conditions, and establish a fourth-order non-convex constrained optimization problem based on the signal model, optimization criterion and constraint conditions.

[0151] The convex function replacement module 22 is used to decompose the fourth-order non-convex constrained optimization problem into multiple sub-problems that can be solved iteratively using the MBI algorithm, and the non-convex objective function and non-convex constraints in the fourth-order non-convex constrained optimization problem are replaced by corresponding convex functions.

[0152] The preliminary solution module 23 is used to sequentially solve each sub-problem with the help of the convex optimization tool CVX to obtain a preliminary solution.

[0153] The iterative optimization module 24 is used to continuously adjust the search direction and step size using the BLS algorithm to iteratively optimize the approximate solution until the Armijo condition is met, thereby obtaining a global optimal solution that meets the design requirements.

[0154] It is not difficult to find that this embodiment is a system embodiment corresponding to the above-mentioned method embodiment. This embodiment can be implemented in conjunction with the above-mentioned method embodiment. The relevant technical details and technical effects mentioned in the above-mentioned method embodiment are still valid in this embodiment. To reduce repetition, they are not repeated here. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above-mentioned method embodiment.

[0155] It is worth mentioning that all modules and modules involved in this embodiment are logical modules. In actual applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. In addition, in order to highlight the innovation of this application, this embodiment does not introduce units that are not closely related to solving the technical problems proposed by this application. However, this does not mean that other units do not exist in this embodiment.

[0156] Another embodiment of the present application provides an electronic device, the structure of which is as follows: Figure 11 As shown, it includes: at least one processor 31; and a memory 32 communicatively connected to the at least one processor 31; wherein the memory 32 stores instructions that can be executed by the at least one processor 31, and the instructions are executed by the at least one processor 31 to enable the at least one processor 31 to perform a MIMO radar transmit sequence set design optimization method as described in the above method embodiments.

[0157] The memory and processor are connected using a bus, which includes any number of interconnected buses and bridges. The bus connects various circuits of one or more processors and memories. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits. These are all well known in the art and therefore will not be described further in this article. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. Data processed by the processor is transmitted on a wireless medium via an antenna. Furthermore, the antenna also receives data and transmits it to the processor.

[0158] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory can be used to store data used by the processor when performing operations.

[0159] Another embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it can implement a MIMO radar transmit sequence set design optimization method as described in the above method embodiments.

[0160] That is, those skilled in the art will understand that all or part of the steps in the above method embodiments can be implemented by instructing related hardware through a program, which is stored in a storage medium and includes a number of instructions for causing a device (such as a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the method described in each embodiment of the present application. Storage media include: U disk, mobile hard disk, read-only memory, random access memory, magnetic disk or optical disk, etc., various media that can store program code.

[0161] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application. In actual applications, various modifications may be made to the embodiments in form and detail without departing from the spirit and scope of the present application. Those skilled in the art will appreciate that improvements and modifications may be made without departing from the principles of the present application, and such improvements and modifications are also considered to be within the scope of protection of the present application.

Claims

1. A MIMO radar transmit sequence set design optimization method, applicable to a MIMO radar system, characterized in that: The method comprises: For MIMO radar systems, a signal model based on the AF transmission sequence set design is constructed. The ISL that minimizes the local AAF and CAF is selected as the optimization criterion. Energy constraints and dynamic range constraints are selected as constraints. Based on the signal model, optimization criterion and constraints, a fourth-order non-convex constrained optimization problem is established. The MBI algorithm is used to decompose the fourth-order non-convex constrained optimization problem into multiple sub-problems that can be solved iteratively. The non-convex objective function and non-convex constraints in the fourth-order non-convex constrained optimization problem are replaced by corresponding convex functions. The convex optimization tool CVX is used to sequentially solve each subproblem and obtain a preliminary solution; The BLS algorithm is used to continuously adjust the search direction and step size, and the approximate solution is iteratively optimized until the Armijo condition is met, thereby obtaining the global optimal solution that meets the design requirements.

2. The MIMO radar transmit sequence set design optimization method according to claim 1, characterized in that: For MIMO radar systems, a signal model based on the AF transmit sequence set design is constructed, including: Consider a MIMO radar system with a distributed or centralized structure, equipped with M transmitting antennas, and the transmission sequences corresponding to each transmitting antenna together constitute the set x m represents the phase-encoded signal vector of length N, x m =[x m (1),x m (2),…,x m (N)] T ; In this system framework, its fast time AF is defined as: Among them, m represents the mth transmitting antenna, m ′ Indicates the mth ′ transmitting antennas, p represents the Doppler frequency shift index set, p∈{-N / 2,…,N / 2}, k represents the delay parameter, k∈{-N+1,-N+2,…,N-1}, if m=m′, then r m,m′ (p,k) represents AAF, if m≠m′, then r m,m′ (p,k) represents CAF; In order to simplify the representation, r m,m′ (p,k) is expressed in matrix form as: Among them, Diag(·) represents the diagonal matrix, a p is the Doppler frequency shift vector, U k is the delay matrix.

3. The MIMO radar transmit sequence set design optimization method according to claim 2, characterized in that: The expression of the selected optimization criterion is shown as: Among them, Ω sa and Ω sc denote the local sidelobe regions of the AAF and CAF of interest, respectively, and ISL denotes the optimization criterion selected to minimize the ISL of the local AAF and CAF; For AAF, Ω sa ={(m,p,k)|n=1,…,M; p=-P,…,P; k=-K,…,K}, |Ω a |=M(2P+1)(2K+1), for CAF, Ω sc ={(m,m′,p,k)|m=1,…,M-1; m′=m+1,…,M; p=-P,…,P; k=-K,…,K}; In order to facilitate understanding and processing, the expression of the optimization criterion is split into the following expressions: Energy constraints ensure that the MIMO radar system has sufficient energy when detecting targets while avoiding excessive radiation to non-target areas, thereby improving the accuracy and efficiency of target detection. The energy constraint is expressed as the total energy of the waveform must be less than or equal to a predetermined value. The expression of the energy constraint is shown as: Where δ is the energy coefficient, 0.5≤δ≤1; The dynamic range constraint limits the waveform amplitude range, aiming to allow the nonlinear amplifier of the MIMO radar system to operate at maximum efficiency and avoid nonlinear distortion of the output waveform. The dynamic range constraint is expressed as: d(1-e) 2 ≤|x m (n)| 2 ≤δ(1+ε) 2 ; n=1,…,N; Among them, ε represents the fluctuation degree of the waveform amplitude, ε∈[0,1].

4. The MIMO radar transmit sequence set design optimization method according to claim 3, characterized in that: The established fourth-order non-convex constrained optimization problem is expressed as follows:

5. The MIMO radar transmit sequence set design optimization method according to claim 4, characterized in that: The MBI algorithm is used to decompose the fourth-order non-convex constrained optimization problem into multiple sub-problems that can be solved iteratively, including: Using the MBI algorithm, in a fixed vector Medium Under the premise of other variables besides , solve the fourth-order non-convex constrained optimization problem; Represents the result of the i+1th iteration of the MBI algorithm; The objective function of the fourth-order non-convex constrained optimization problem It is a fourth-order polynomial and a non-convex function. We use a convex quadratic function to approximate it and transform the non-convex function into a convex function. is f(x m ), f(x m ) is expressed as follows: in, represents the i-th iteration result of the MBI algorithm, R represents the real part, express right The first-order gradient of represents the approximation factor, for exist The positive semidefinite approximation of the Hessian matrix at ; The constraint C2 of the fourth-order non-convex constrained optimization problem is a non-convex constraint function, which is approximated by the first-order Taylor expansion. Perform a first-order Taylor expansion at , and use the obtained linear approximate function to replace the constraint C2, thereby converting it into a convex function. The approximate convex constraint is expressed by the formula: At this point, the fourth-order non-convex constrained optimization problem is decomposed into multiple sub-problems that can be solved iteratively, that is, the replaced convex problem is obtained. The replaced convex problem is expressed by the formula:

6. The MIMO radar transmit sequence set design optimization method according to claim 5, characterized in that: The convex optimization tool CVX is used to sequentially solve each subproblem and obtain preliminary solutions, including: Based on the mathematical model of each sub-problem, program according to the grammatical rules of CVX to clarify the objective function, constraints, and domain of variables; Call the solver in the CVX toolbox to solve each sub-problem sequentially. After the solution is completed, the preliminary solution is obtained.

7. The MIMO radar transmit sequence set design optimization method according to claim 6, characterized in that: The BLS algorithm is used to continuously adjust the search direction and step size, and iteratively optimize the approximate solution until the Armijo condition is met, thereby obtaining the global optimal solution that meets the design requirements, including: Select As the search direction, 1 is selected as the initial step size; In each iteration, it is determined whether the Armijo condition is met. The expression of the Armijo condition is: Among them, α is a small positive number, which is used to control the conservativeness of the step size; When the Armijo condition is not met, the step size is reduced proportionally, that is, Where ξ is a number between 0 and 1, j is the current iteration number of the BLS algorithm; When the Armijo conditions are met, the global optimal solution that meets the design requirements is obtained.

8. A MIMO radar transmit sequence set design and optimization system, applicable to a MIMO radar system, characterized in that: The system comprises: The optimization problem establishment module is used to construct a signal model based on the AF transmission sequence set design for MIMO radar systems. The optimization criterion is to minimize the ISL of the local AAF and CAF. Energy constraints and dynamic range constraints are selected as constraints. Based on the signal model, optimization criterion and constraints, a fourth-order non-convex constrained optimization problem is established. Convex function replacement module, used to decompose the fourth-order non-convex constrained optimization problem into multiple iteratively solvable sub-problems using the MBI algorithm. The non-convex objective function and non-convex constraints in the fourth-order non-convex constrained optimization problem are replaced by corresponding convex functions; The preliminary solution module is used to sequentially solve each sub-problem with the help of the convex optimization tool CVX to obtain a preliminary solution; The iterative optimization module is used to continuously adjust the search direction and step size using the BLS algorithm, and iteratively optimize the approximate solution until the Armijo condition is met, thereby obtaining the global optimal solution that meets the design requirements.

9. An electronic device, characterized in that: include: at least one processor; as well as, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform a MIMO radar transmit sequence set design optimization method according to any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for designing and optimizing a MIMO radar transmit sequence set according to any one of claims 1 to 8 is implemented.

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