High-degree-of-freedom MIMO radar waveform design method capable of accurately controlling ISL

Abstract

The invention discloses a high-degree-of-freedom MIMO radar waveform design method capable of accurately controlling ISL, and relates to the technical field of radars, and the method comprises the steps: S1, carrying out MIMO radar constant modulus waveform design modeling, and constructing a bivariate problem under CMC and CSC constraints; s2, introducing a penalty mechanism, constructing a unified constraint space, and converting a bivariate problem into an unconstrained optimization problem; and S3, calculating the gradient of the objective function of the converted problem in the unified constraint space, and then using an adaptive conjugate gradient algorithm to optimize the two variables in parallel to solve. According to the invention, the problem can be directly solved without loosening, and the DOF of waveform design can be enhanced.

Description

Technical Field

[0001] This invention relates to the field of radar technology, and specifically to a high-degree-of-freedom MIMO radar waveform design method that can precisely control ISL. Background Technology

[0002] Designing a constant-mode waveform with good integrated sidelobe level (ISL) suppression is a key technology in MIMO radar systems. By suppressing ISL in a specific range dimension, the detection performance and anti-jamming performance of MIMO radar systems against weak targets can be significantly improved. In practical applications, applying constant-mode constraint (CMC) to the waveform is a common method to simplify hardware design. Therefore, the design of a constant-mode waveform for MIMO radar with good ISL suppression has attracted widespread attention.

[0003] Existing methods face two main challenges in achieving the desired ISL performance: the first is the limited degrees of freedom in waveform design; the second is the performance degradation due to relaxation.

[0004] The first type of challenge arises because existing methods tend to focus only on waveform design, ignoring the extension of the degrees of freedom (DOF) in the receiver filter design, resulting in limited ISL performance. The second type of challenge arises because existing methods mainly address this issue through relaxation, which inevitably introduces relaxation errors, leading to a decrease in ISL suppression performance. Summary of the Invention

[0005] This invention provides a high-degree-of-freedom MIMO radar waveform design method that can precisely control ISL, thus solving the problems of existing technologies.

[0006] In a first aspect, the present invention provides a high-degree-of-freedom MIMO radar waveform design method that can precisely control ISL, comprising the following steps:

[0007] S1. Perform constant mode waveform design and modeling for MIMO radar, and construct a bivariate problem under CMC and CSC constraints;

[0008] S2. Introduce a penalty mechanism and construct a unified constraint space to transform the bivariate problem into an unconstrained optimization problem;

[0009] S3. Calculate the gradient of the objective function of the transformed problem in the unified constraint space, and then use the adaptive conjugate gradient algorithm to optimize the two variables in parallel to solve the problem.

[0010] Further step S1 includes:

[0011] S101. Consider a MIMO radar system with M antennas. The waveform length transmitted by a single antenna is L, and the transmitted waveform matrix is ​​represented as follows: ,in, Let be the transmitted waveform of the m-th antenna; the corresponding receiving filter is . ,in yes The corresponding mismatch filter;

[0012] S102. For each and Applying constant modulus constraints (CMC) and complex sphere constraints (CSC) are expressed as follows: and ;

[0013] The signal-to-noise ratio loss (SNRL) caused by mismatched filtering is expressed as:

[0014]

[0015] because and They are all constant modulus, therefore Size by Decide;

[0016] To prevent SNRL from becoming too large, a penalty function is constructed to control the SNRL value, expressed as:

[0017]

[0018] in, In order to suppress the response of the receiving filter ,in The weighted integral sidelobe level (WISL) with a delay of 0 can be expressed as:

[0019]

[0020] in, It is weight;

[0021] Delay is The weighted integral sidelobe level (WISL) with respect to the sidelobes can be expressed as:

[0022]

[0023] in, It is a positive time delay parameter, when hour, It is always equal to 1, and always equal to 0 in all other cases. It is a shift matrix; ultimately, it can be constructed as a bivariate problem under CMC and CSC constraints:

[0024] .

[0025] Furthermore, step S2 includes:

[0026] S201. To determine whether the inequality constraints are satisfied, a precise penalty function is introduced:

[0027]

[0028] in, This indicates that the constraint has been satisfied; otherwise, it would not be satisfied. This penalty term is constructed by introducing a maximization function, expressed as:

[0029]

[0030] The penalty term is not a continuous function, therefore a penalty is introduced. Expression (represented as) To solve this problem:

[0031]

[0032] Based on this, the bivariate problem can be reformulated as:

[0033]

[0034] in, ;

[0035] S202. To simultaneously satisfy both CMC and CSC in the problem, a combined manifold space (PM) is constructed by combining the complex circular manifold (CCM) and the complex oblique manifold (COM), denoted as:

[0036]

[0037] in, Include One CCM, satisfying The CMC is represented as:

[0038]

[0039] CCM is represented as ;

[0040] Is to make A COM that satisfies CSC is represented as:

[0041]

[0042] in, ;

[0043] Based on this, the bivariate problem can be transformed into Unconstrained optimization problems on:

[0044] .

[0045] Furthermore, step S3 includes:

[0046] S301. Due to It is a nonlinear space, and the transformed unconstrained optimization problem cannot be directly solved using gradient-based algorithms. The surrounding local features are represented by constructing a tangent space as follows:

[0047]

[0048] in, and A vector in the tangent space is represented as:

[0049]

[0050]

[0051] and The projection onto the tangent space is:

[0052]

[0053]

[0054] in, ;

[0055] S302. Traditional gradient-based algorithms determine the search direction based only on the current gradient, which is prone to oscillation. To overcome this shortcoming, a conjugate gradient algorithm (ACG) with adaptive step size is derived.

[0056] In order to achieve and Parallel optimization introduces an auxiliary variable. The Euclidean gradient can be expressed as:

[0057]

[0058] in, and Represented as:

[0059]

[0060]

[0061] Since PM is an irregular nonlinear space, the Euclidean gradient needs to be projected onto the Riemann gradient in this space before gradient-based algorithms can be used to solve it. The Riemann gradient is:

[0062]

[0063] S303. In the k-th iteration, The search direction at a location can be represented as:

[0064]

[0065] in, The Polak-Ribiere coefficient is:

[0066]

[0067] yes In tangent space The projection on is:

[0068]

[0069] Based on the above derivation, the transient solution can be... Updated to:

[0070]

[0071] Will Further shrinking to manifold space Above, recorded as:

[0072]

[0073] in, It is Shrink to The operation on is denoted as:

[0074]

[0075] in, This represents division of corresponding elements in two matrices. Indicates taking The absolute value of each element in the set is the sum of the values ​​of the elements in the set. Shrink to The operation is denoted as:

[0076]

[0077] Step length The updates conform to the Armijio standard, as shown in Table 1:

[0078] Table one step length Update Algorithm

[0079]

[0080] in, , and All values ​​are greater than 1 to improve the convergence speed;

[0081] Based on the above, the proposed high-degree-of-freedom MIMO radar waveform design method that can precisely control ISL can be summarized in Table 2:

[0082] Table 2 Summary of the proposed algorithms

[0083]

[0084] The beneficial effects of this invention are as follows: This invention introduces a precise penalty mechanism and constructs a unified constraint space that can simultaneously satisfy CMC and CSC, thereby transforming the problem into a bivariate unconstrained optimization problem in this space; then, the gradient of the two variables in the unified constraint space is derived; finally, an adaptive conjugate gradient algorithm is derived to optimize the two variables in parallel, thus solving the problem.

[0085] This invention enhances the DOF of waveform design by designing appropriate waveform receiving filters. Attached Figure Description

[0086] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and constitute a part of this invention, are not intended to limit the scope of the invention. In the drawings:

[0087] Figure 1 These are WaCAN, ADMM, and the MAS diagram of this invention;

[0088] Figure 2 These are WaCAN, ADMM, and the MCS diagram of this invention;

[0089] Figure 3 This invention is in different MAS plot under the value;

[0090] Figure 4 This invention is in different MCS plot under the value;

[0091] Figure 5 yes and SNRL A graph showing the transformation. Detailed Implementation

[0092] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention.

[0093] This invention provides a high-degree-of-freedom MIMO radar waveform design method that can precisely control ISL, aiming to solve the above-mentioned technical problems in the prior art.

[0094] The technical solution of the present invention and how the technical solution of the present invention solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0095] The technical concept of this invention is as follows: For the fourth-order nonconvex optimization problem under constant modulus constraints, existing solutions mainly face two challenges: first, the limited DOF in waveform design leads to performance limitations in ISL; second, relaxation introduces approximation errors, resulting in decreased ISL performance. This invention enhances the DOF of waveform design by designing a corresponding waveform receiving filter. Furthermore, by constructing a unified constraint space adapted to the problem and projecting it as an unconstrained problem onto this space, the problem can be solved directly without relaxation. Therefore, this invention first introduces a penalty mechanism and constructs a unified constraint space that simultaneously satisfies CMC and CSC, thereby transforming the problem into an unconstrained optimization problem in this space. Then, the gradient of the objective function in the unified constraint space is derived. Finally, an adaptive conjugate gradient algorithm is used to optimize two variables in parallel to solve the problem. Specifically:

[0096] A high-degree-of-freedom MIMO radar waveform design method with precise ISL control is characterized by the following steps:

[0097] S1. Perform constant mode waveform design and modeling for MIMO radar, and construct a bivariate problem under CMC and CSC constraints;

[0098] MIMO radar constant mode waveform design and modeling:

[0099] Consider a MIMO radar system with M antennas. The waveform length transmitted by each antenna is L, and the transmitted waveform matrix is ​​represented as follows: ,in, Let be the transmitted waveform of the m-th antenna; the corresponding receiving filter is . ,in yes The corresponding mismatch filter;

[0100] To each and Applying constant modulus constraints (CMC) and energy constraints (CSC) are expressed as follows: and ;

[0101] The signal-to-noise ratio loss (SNRL) caused by mismatched filtering is expressed as:

[0102]

[0103] because and They are all constant modulus, therefore Size by Decide;

[0104] To prevent SNRL from becoming too large, a penalty function is constructed to control the SNRL value, expressed as:

[0105]

[0106] in, In order to suppress the response of the receiving filter ,in The weighted integral sidelobe level (WISL) with a delay of 0 can be expressed as:

[0107]

[0108] in, It is weight;

[0109] Delay is The weighted integral sidelobe level (WISL) with respect to the sidelobes can be expressed as:

[0110]

[0111] in, It is a positive time delay parameter, when hour, It is always equal to 1, and always equal to 0 in all other cases. It is a shift matrix; ultimately, it can be constructed as a bivariate problem under CMC and CSC constraints:

[0112]

[0113] S2. Introduce a penalty mechanism and construct a unified constraint space to transform the bivariate problem into an unconstrained optimization problem;

[0114] Penalty mechanism and construction of unified constraint space:

[0115] To determine whether the inequality constraints are satisfied, a precise penalty function is introduced:

[0116]

[0117] in, This indicates that the constraint has been satisfied; otherwise, it would not be satisfied. This penalty term is constructed by introducing a maximization function, expressed as:

[0118]

[0119] However, this penalty term is not a continuous function, therefore a... Expression (represented as) To solve this problem:

[0120]

[0121] Based on this, the bivariate problem can be reformulated as:

[0122]

[0123] in, ;

[0124] To simultaneously satisfy both CMC and CSC in the problem, a combined manifold space (PM) is constructed by combining the complex circular manifold (CCM) and the complex oblique manifold (COM), denoted as:

[0125]

[0126] in, Include One CCM, satisfying The CMC is represented as:

[0127]

[0128] CCM is represented as ;

[0129] Is to make A COM that satisfies CSC is represented as:

[0130]

[0131] in, ;

[0132] Based on this, the bivariate problem can be transformed into Unconstrained optimization problems on:

[0133]

[0134] S3. Calculate the gradient of the objective function of the transformed problem in the unified constraint space, and then use the adaptive conjugate gradient algorithm to optimize the two variables in parallel to solve the problem.

[0135] Gradient calculation in a unified constraint space:

[0136] because It is a nonlinear space, and the transformed unconstrained optimization problem cannot be directly solved using gradient-based algorithms. The surrounding local features are represented by constructing a tangent space as follows:

[0137]

[0138] in, and A vector in the tangent space is represented as:

[0139]

[0140]

[0141] and The projection onto the tangent space is:

[0142]

[0143]

[0144] in, ;

[0145] Traditional gradient-based algorithms determine the search direction based solely on the current gradient, which is prone to oscillations. To overcome this drawback, a conjugate gradient algorithm (ACG) with an adaptive step size is derived.

[0146] In order to achieve and Parallel optimization introduces an auxiliary variable. Its Euclidean gradient can be expressed as:

[0147]

[0148] in, and Represented as:

[0149]

[0150]

[0151] Since PM is an irregular nonlinear space, the Euclidean gradient needs to be projected onto the Riemann gradient in this space before gradient-based algorithms can be used to solve it. The Riemann gradient is:

[0152]

[0153] Adaptive conjugate gradient algorithm:

[0154] In the k-th iteration, The search direction at a location can be represented as:

[0155]

[0156] in, The Polak-Ribiere coefficient is:

[0157]

[0158] yes In tangent space The projection on is:

[0159]

[0160] Based on the above derivation, the transient solution can be... Updated to:

[0161]

[0162] Will Further shrinking to manifold space Above, recorded as:

[0163]

[0164] in, It is Shrink to The operation on is denoted as:

[0165]

[0166] in, This represents division of corresponding elements in two matrices. Indicates taking The absolute value of each element in the set is the sum of the values ​​of the elements in the set. Shrink to The operation is denoted as:

[0167]

[0168] Step length The update complies with the Armijio standard.

[0169] Existing solutions:

[0170] 1: ADMM method, 2: WeCAN method

[0171] In simulation experiments, the performance of this invention compared with ADMM and WeCAN in terms of runtime, maximum autocorrelation sidelobe (MAS), and maximum cross-correlation sidelobe (MCS), where MAS and MCS are denoted as:

[0172]

[0173]

[0174] Furthermore, the ability of this invention to accurately control WISL and SNRL was evaluated; to ensure fairness in the comparison, the initial input of all methods was a single-mode linear frequency modulated (LFM) signal, and the iteration stopping criterion was... ;

[0175] A. WISL suppression effect

[0176] Figure 1 and Figure 2 WaCAN, ADMM, and the MA and MCS of this invention are given, with the parameters set as follows: L = 128, M = 4, d = 20, w = 1. This invention has a deeper notch than the other two methods and is about 40 dB lower.

[0177] Table 3 provides a detailed comparison of the runtime and WISL of the three methods under different L values. The present invention consistently outperforms the other two methods in terms of runtime while maintaining good WISL suppression performance. For L=128, the present invention is at least 6 minutes faster than WeCAN and ADMM, and its WISL suppression performance is still two orders of magnitude ahead of WeCAN and ADMM. Although ADMM outperforms the proposed method in WISL suppression at L=256, it requires more than two hours to run. Table 4 further provides the SNRL of the present invention under different d conditions, showing that increasing d leads to a sharp increase in SNRL at L=64. When L=128 and L=256, the present invention can suppress SNRL to below 0.5 dB.

[0178] Table 3. Running Time and WISL under Different L Values

[0179]

[0180] Table 4 SNRL of the present invention

[0181]

[0182] B. SNRL and WISL Control

[0183] Figure 3 and Figure 4 This invention is in different MAS and MCS at values ​​(2, 0.2, and 0.02); it was observed that as... The reduction in the amount of material increases the depth of the notches in the MAS and MCS within the target range, and the present invention is able to form notches below -60 dB and -55 dB in the MAS and MCS, respectively.

[0184] To further evaluate the control performance of this invention in terms of WISL and SNRL, such as Figure 5 middle and SNRL The curve of the transformation is shown, for all From 0.1 to 1, The value is always lower than 0, which meets the inequality constraint of the target problem; in addition, the present invention will The value was controlled within 0.01, indicating that the present invention can accurately control WISL; the present invention consistently kept SNRL below 0.21 dB, indicating that it exhibits good WISL suppression performance while maintaining an acceptable SNRL level.

[0185] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0186] Furthermore, in the embodiments of the present invention, the functional modules can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated module can be implemented in hardware or in the form of hardware plus software functional modules.

[0187] Those skilled in the art will understand that embodiments of the present invention can be provided as methods or systems. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects.

[0188] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0189] The above are merely embodiments of the present invention and are not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

[0190] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the invention disclosed herein in the specification and examples. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the foregoing claims.

[0191] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A high-degree-of-freedom MIMO radar waveform design method with precise control over ISL, characterized in that: Includes the following steps: S1. Perform constant mode waveform design and modeling for MIMO radar, and construct a bivariate problem under constant mode constraint (CMC) and complex sphere constraint (CSC); S2. Introduce a penalty mechanism and construct a unified constraint space to transform the bivariate problem into an unconstrained optimization problem; S3. Calculate the gradient of the objective function of the transformed problem in the unified constraint space, and then use the adaptive conjugate gradient algorithm to optimize the two variables in parallel to solve the problem.

2. The high-degree-of-freedom MIMO radar waveform design method with precise controllable ISL according to claim 1, characterized in that: Step S1 includes: S101. Consider a MIMO radar system with M antennas. The waveform length transmitted by a single antenna is L, and the transmitted waveform matrix is ​​represented as follows: , in, , where is the transmitted waveform of the m-th antenna; The corresponding receiving filter is ,in yes The corresponding mismatch filter; S102. For each and Apply constant modulus constraint (CMC) and complex sphere constraint (CSC). They are represented as follows: and ; The signal-to-noise ratio loss (SNRL) caused by mismatched filtering is expressed as: because and They are all constant modulus, therefore Size by Decide; To prevent SNRL from becoming too large, a penalty function is constructed to control the SNRL value, expressed as: in, In order to suppress the response of the receiving filter , in The weighted integral sidelobe level (WISL) with a delay of 0 can be expressed as: in, It is weight; Delay is The weighted integral sidelobe level (WISL) with respect to the sidelobes can be expressed as: when hour, It is always equal to 1, and always equal to 0 in all other cases. It is a shift matrix; Ultimately, this can be constructed as a bivariate problem under CMC and CSC constraints: in, It is a positive time delay parameter.

3. The high-degree-of-freedom MIMO radar waveform design method with precise control of ISL according to claim 2, characterized in that: Step S2 includes: S201. To determine whether the inequality constraints are satisfied, a precise penalty function is introduced: in, This indicates that the constraint has been satisfied; otherwise, it would not be satisfied. This penalty term is constructed by introducing a maximization function, expressed as: The penalty term is not a continuous function, therefore a penalty is introduced. expression: To solve this problem: Based on this, the bivariate problem can be reformulated as: in, ; S202. To simultaneously satisfy both CMC and CSC in the problem, a complex circular manifold CCM and a complex oblique manifold COM are combined to construct a product manifold space PM, denoted as: in, Include One CCM, satisfying The CMC is represented as: CCM is represented as ; Is to make A COM that satisfies CSC is represented as: in, ; Based on this, the bivariate problem can be transformed into Unconstrained optimization problems on: 。 4. The high-degree-of-freedom MIMO radar waveform design method with precise ISL control according to claim 3, characterized in that: Step S3 includes: S301. Due to It is a nonlinear space, and the transformed unconstrained optimization problem cannot be directly solved using gradient-based algorithms. The surrounding local features are represented by constructing a tangent space as follows: in, and A vector in the tangent space is represented as: and The projection onto the tangent space is: in, ; S302. Traditional gradient-based algorithms determine the search direction based only on the current gradient, which is prone to oscillation. To overcome this shortcoming, a conjugate gradient algorithm with adaptive step size, ACG, is derived. In order to achieve and Parallel optimization introduces an auxiliary variable. The Euclidean gradient can be expressed as: in, and Represented as: Since PM is an irregular nonlinear space, the Euclidean gradient needs to be projected onto the Riemann gradient in this space before gradient-based algorithms can be used to solve it. The Riemann gradient is: S303. In the k-th iteration, The search direction at this location can be represented as: in, The Polak-Ribiere coefficient is: yes In tangent space The projection on is: Based on the above derivation, the transient solution can be... Updated to: Will Further shrinking to manifold space Above, recorded as: in, It is Shrink to The operation on is denoted as: in, This represents division of corresponding elements in two matrices. Indicates taking The absolute value of each element in the set is the sum of the values ​​of the elements in the set. Shrink to The operation is denoted as: Step length The update complies with the Armijio standard.

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