Joint design method of transmit waveform set and receive filter bank for suppressing range sidelobes

Abstract

This invention discloses a joint design method for suppressing range sidelobes using a transmitted waveform set and a received filter bank. The method includes: establishing an objective function to minimize the range sidelob level of the non-periodic transmitted waveform set and the unmatched filter bank, utilizing the degrees of freedom of the radar transmitter and receiver; establishing a template-free fractional optimization model by combining the constant-mode nature of the transmitted waveform, the constant-energy characteristics of the unmatched filter sequence, and the signal-to-noise ratio loss; and iteratively solving the fractional optimization model based on the ADMM algorithm framework to obtain the optimal waveform set and unmatched filter bank sequence. This invention can effectively avoid problems such as weak target inundation and increased false alarm rate, meet stricter range sidelob requirements, and improve radar detection and parameter estimation performance.

Description

Technical Field

[0001] This invention belongs to the field of radar signal technology and relates to a joint design method for transmitting waveform sets and receiving filter banks to suppress range sidelobes. Background Technology

[0002] In MIMO radar signal processing, the correlation between the transmitted waveform and the receiving filter plays a decisive role in target detection. However, some traditional methods only design the transmitted waveform and apply matched filters as the receiving filters, which is insufficient to meet the more stringent range sidelobe requirements. Currently, the WeCAN algorithm for multi-waveform design in MIMO radar aims to minimize the integral sidelobe level, setting weighting factors across multiple range intervals to achieve local low sidelobe effects. Li Feng et al., based on the WeCAN algorithm, constructed an optimization objective function under the ISL criterion using 0 / 1 weighting factors and performed waveform optimization based on the spatial trust region algorithm. For a fixed transmitted waveform, Sun et al. designed a corresponding receiving filter to effectively suppress range sidelobes in specific intervals. Zhou et al. assumed the interference situation in the current electromagnetic environment was known and constructed an intermittent relay jamming signal, using maximizing the new interference-to-noise ratio as the criterion to jointly optimize the transmitted waveform and the unmatched filter.

[0003] In existing methods, to achieve better range sidelobe suppression, the length of the unmatched filter sequence at the receiver is often set to 2-3 times the signal length. This undoubtedly increases the computational complexity of optimization, consumes computational resources, and is not conducive to engineering implementation. Summary of the Invention

[0004] The purpose of this invention is to address the problem in the prior art that, in order to obtain better range sidelobe suppression, the length of the unmatched filter sequence at the receiving end is often set to 2-3 times the signal length, which increases the computational complexity of optimization, consumes computational resources, and is not conducive to engineering implementation. This invention provides a joint design method for the transmit waveform set and the receive filter bank for suppressing range sidelobes.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A joint design method for suppressing range sidelobes using transmit waveform sets and receive filter banks includes:

[0007] Using the degrees of freedom of the radar transmitter and receiver, an objective function is established to minimize the range sidelobe level of the aperiodic transmitted waveform set and the unmatched filter bank.

[0008] By combining the constant mode characteristics of the transmitted waveform, the constant energy characteristics of the unmatched filter sequence, and the signal-to-noise ratio loss, a template-free fractional optimization model is established.

[0009] Based on the ADMM algorithm framework, variable decoupling is achieved, and the fractional optimization model is iteratively solved to obtain the optimal waveform set and unmatched filter bank sequence.

[0010] A further improvement of the present invention is that:

[0011] Furthermore, an objective function is established to minimize the range sidelobe level for the aperiodic transmit waveform set and the unmatched filter bank, specifically:

[0012] make and Let x represent the sets of M non-periodic transmit waveforms and unmatched filters to be designed, where each sequence has a length of N, i.e., x m =[x m (1),x m (2),...,x m (N)] T ,h m =[h m (1),h m (2),...,h m (N)] T Define a selection matrix S of dimension N×N. d The elements in the g-th row and h-th column of the array are as follows:

[0013] S d (g,h)=δ(gh-d+N),d∈Ω (1)

[0014] Where δ(·) represents the Dirac function; the function value is 1 when the input variable value is 0; the function value is 0 when the input variable value is not 0; Ω represents the index of the distance displacement d, Ω=[1,2,...,2N-1];

[0015] Based on the aforementioned variable settings, establish the objective function model:

[0016]

[0017] Among them, Ω m,p Indicates based on waveform sequence x m Unmatched filter sequence h p The low sidelobe region of the combination case; α m,p,d Represents the weighting factor at the sidelobe level; the numerator term in the objective function Represents waveform x p After passing through filter h m After filtering, the output at a distance k is as follows: denominator term x represents the peak level of the main lobe of the m-th transmitted waveform and the output of the m-th unmatched filter; m,nLet n represent the nth element in the mth waveform, which needs to satisfy the constant modulus constraint, while the mth filter sequence needs to satisfy the constant energy constraint; a similarity constraint between the transmitted waveform and the corresponding unmatched filter sequence is introduced. The signal-to-noise ratio loss at the output of the unmatched filter at the receiver is controlled by the similarity factor β.

[0018] Furthermore, combining the constant-mode characteristic of the transmitted waveform, the constant-energy characteristic of the unmatched filter sequence, and the signal-to-noise ratio loss, a template-free fractional optimization model is established, specifically as follows:

[0019] Integrate multiple short-sequence variables from the aperiodic emission waveform set and the unmatched filter bank into a single long-sequence variable w:

[0020]

[0021] Define the selection matrix U m V m And the auxiliary matrix Ξ:

[0022]

[0023] Using the selection matrix to select x m and h m Represented as:

[0024]

[0025] Using formulas (4) and (5), the optimization model in formula (2) is transformed into:

[0026]

[0027] Introduce auxiliary variables:

[0028]

[0029] Equation (6) can be transformed into:

[0030]

[0031] Furthermore, based on the ADMM algorithm framework, variable decoupling is achieved, and the fractional optimization model is iteratively solved as follows:

[0032] Constructing the Lagrange augmented function:

[0033]

[0034] Where ρ represents the step size, {λ m,p,d ,κ m,p,d ,ξ} are Lagrange multipliers. This indicates retrieving the real part of the element inside the parentheses;

[0035] The iteration exit condition is set as follows:

[0036]

[0037] Where ε > 0.

[0038] Furthermore, obtaining the optimal waveform set and unmatched filter bank sequence includes:

[0039] The fractional optimization model is broken down into subproblems to be solved.

[0040] The subproblems to be solved are processed to obtain the optimal waveform set order and unmatched filter bank.

[0041] Furthermore, the fractional optimization model is broken down into subproblems to be solved, specifically:

[0042] During the (t+1)th iteration, {η(t+1),y m,p,d (t+1),z m,p,d The steps to solve for (t+1),k(t+1)} are as follows:

[0043] Decomposing formula (9) yields two sub-problems to be optimized:

[0044]

[0045]

[0046] in:

[0047]

[0048] w(t),λ m,p,d (t),κ m,p,d (t), ξ(t) represent variables w, λ m,p,d ,κ m,p,d ξ is the result obtained in the t-th optimization.

[0049] Furthermore, the subproblem to be solved is processed to obtain the optimal waveform set order and unmatched filter bank, specifically as follows:

[0050] When η is determined, we get y. m,p,d (t+1) and z m,p,d (t+1):

[0051]

[0052]

[0053] Define step function

[0054]

[0055] Substituting equations (14) to (16) into equation (11) yields...

[0056]

[0057] Formula (17) is transformed into a single-variable problem concerning η. The optimal value η(t+1) is found for this single-variable problem, and then substituted into formulas (14) and (15) to obtain y. m,p,d (t+1) and z m,p,d (t+1).

[0058] Furthermore, processing the subproblems to be solved to obtain the optimal waveform set order and unmatched filter bank also includes:

[0059] For the subproblems in formula (12), we obtain:

[0060]

[0061] The optimization problem regarding variable w is further obtained using the Lagrange augmented function in formula (9):

[0062]

[0063] in:

[0064]

[0065] The problem in formula (19) is equivalent to:

[0066]

[0067] in:

[0068]

[0069] vec(·) indicates that the matrix within the parentheses is vectorized.

[0070] Formula (21) is a fourth-order problem about w, which can be reduced to a first-order problem by minimizing the upper bound function.

[0071] For variable {λ m,p,d ,κ m,p,d The solution process for ξ is as follows:

[0072]

[0073] Where m, p = 1, ..., M, d ∈ Ω m,p .

[0074] Compared with the prior art, the present invention has the following beneficial effects:

[0075] This invention establishes an objective function for minimizing the range sidelobe level of an aperiodic transmit waveform set and an unmatched filter bank, and establishes a template-free fractional optimization model to fully utilize design degrees of freedom. Based on the ADMM algorithm framework, variable decoupling is achieved, and the Lagrange augmented function is iteratively updated to obtain the optimal waveform set and unmatched filter bank sequence. For the fourth-order polynomial optimization problem involved in the optimization process, an upper bound function minimization optimization method is used to relax it into a simple first-order problem for solution. Through multiple iterations, a waveform set sequence and unmatched filter sequence with excellent correlation characteristics are obtained. In practical applications, this invention can effectively avoid adverse situations such as weak target overload and increased false alarm rate, meet stricter range sidelobe requirements, and improve radar detection and parameter estimation performance. Attached Figure Description

[0076] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0077] Figure 1 This is a flowchart of the method for jointly designing the transmit waveform set and receive filter bank to suppress range sidelobes according to the present invention.

[0078] Figure 2 The cross-correlation sidelobe diagram of waveform 1 and unmatched filter 1;

[0079] Figure 3 The cross-correlation sidelobe plots for waveform 1 and unmatched filter 2 are shown.

[0080] Figure 4 The cross-correlation sidelobe diagram of waveform 2 and unmatched filter 1;

[0081] Figure 5 The cross-correlation sidelobe diagrams for waveform 2 and unmatched filter 2 are shown. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0083] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0084] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0085] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0086] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0087] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0088] The present invention will now be described in further detail with reference to the accompanying drawings:

[0089] See Figure 1 This invention discloses a joint design method for a transmit waveform set and a receive filter bank to suppress range sidelobes, comprising:

[0090] S101 utilizes the degrees of freedom of the radar transmitter and receiver to establish an objective function that minimizes the range sidelobe level of the aperiodic transmitted waveform set and the unmatched filter bank.

[0091] make and Let x represent the sets of M non-periodic transmit waveforms and unmatched filters to be designed, where each sequence has a length of N, i.e., x m =[x m (1),x m (2),...,x m (N)] T ,h m =[h m (1),h m (2),...,h m (N)] T Define a selection matrix S of dimension N×N. d The elements in the g-th row and h-th column of the array are as follows:

[0092] S d (g,h)=δ(gh-d+N),d∈Ω (1)

[0093] Where δ(·) represents the Dirac function; the function value is 1 when the input variable value is 0; the function value is 0 when the input variable value is not 0; Ω represents the index of the distance displacement d, Ω=[1,2,...,2N-1];

[0094] Based on the aforementioned variable settings, establish the objective function model:

[0095]

[0096] Among them, Ω m,p Indicates based on waveform sequence x m Unmatched filter sequence h p The low sidelobe region of the combination case; α m,p,d Represents the weighting factor at the sidelobe level; the numerator term in the objective function Represents waveform x p After passing through filter h m After filtering, the output at a distance k is as follows: denominator term x represents the peak level of the main lobe of the m-th transmitted waveform and the output of the m-th unmatched filter; m,n Let n represent the nth element in the mth waveform, which needs to satisfy the constant modulus constraint, while the mth filter sequence needs to satisfy the constant energy constraint; a similarity constraint between the transmitted waveform and the corresponding unmatched filter sequence is introduced. The signal-to-noise ratio loss at the output of the unmatched filter at the receiver is controlled by the similarity factor β.

[0097] S102. Combining the constant mode characteristics of the transmitted waveform, the constant energy characteristics of the unmatched filter sequence, and the signal-to-noise ratio loss, a template-free fractional optimization model is established.

[0098] Integrate multiple short-sequence variables from the aperiodic emission waveform set and the unmatched filter bank into a single long-sequence variable w:

[0099]

[0100] Define the selection matrix U m V m And the auxiliary matrix Ξ:

[0101]

[0102] Using the selection matrix to select x m and h m Represented as:

[0103]

[0104] Using formulas (4) and (5), the optimization model in formula (2) can be transformed into:

[0105]

[0106] Introduce auxiliary variables:

[0107]

[0108] Equation (6) can be transformed into:

[0109]

[0110] S103, based on the ADMM algorithm framework, achieves variable decoupling, iteratively solves the fractional optimization model, and obtains the optimal waveform set and unmatched filter bank sequence.

[0111] Constructing the Lagrange augmented function:

[0112]

[0113] Where ρ represents the step size, {λ m,p,d ,κ m,p,d ,ξ} are Lagrange multipliers. This indicates retrieving the real part of the element inside the parentheses.

[0114] The iteration exit condition is set as follows:

[0115]

[0116] Where ε > 0.

[0117] Obtain the optimal waveform set and unmatched filter bank sequence, including:

[0118] The fractional optimization model is broken down into subproblems to be solved.

[0119] The subproblems to be solved are processed to obtain the optimal waveform set order and unmatched filter bank.

[0120] The fractional optimization model is broken down into subproblems to be solved, specifically:

[0121] During the (t+1)th iteration, {η(t+1),y m,p,d (t+1),z m,p,d The steps to solve for (t+1),k(t+1)} are as follows:

[0122] Decomposing formula (9) yields two sub-problems to be optimized:

[0123]

[0124]

[0125] in:

[0126]

[0127] w(t),λ m,p,d (t),κ m,p,d (t), ξ(t) represent variables w, λ m,p,d ,κ m,p,d ξ is the result obtained in the t-th optimization.

[0128] The subproblems to be solved are processed to obtain the optimal waveform set order and unmatched filter bank, specifically as follows:

[0129] When η is determined, we get y. m,p,d (t+1) and z m,p,d (t+1):

[0130]

[0131]

[0132] Define step function

[0133]

[0134] Substituting equations (14) to (16) into equation (11) yields...

[0135]

[0136] Formula (17) is transformed into a single-variable problem concerning η. The optimal value η(t+1) is found for this single-variable problem, and then substituted into formulas (14) and (15) to obtain y. m,p,d (t+1) and z m,p,d (t+1).

[0137] The process of handling the subproblems to be solved, obtaining the optimal waveform set order and unmatched filter bank, also includes:

[0138] For the subproblems in formula (12), we obtain:

[0139]

[0140] The optimization problem regarding variable w is further obtained using the Lagrange augmented function in formula (9):

[0141]

[0142] in:

[0143]

[0144] The problem in formula (19) is equivalent to:

[0145]

[0146] in:

[0147]

[0148] vec(·) indicates that the matrix within the parentheses is vectorized.

[0149] Formula (21) is a fourth-order problem about w, which can be reduced to a first-order problem by minimizing the upper bound function.

[0150] For variable {λ m,p,d ,κ m,p,d The solution process for ξ is as follows:

[0151]

[0152] Where m, p = 1, ..., M, d ∈ Ω m,p .

[0153] The experimental setup of this invention is as follows: a set of transmitted waveforms of type 2 and length 128 and an unmatched filter bank (M=2, N=128) are designed, the low sidelobe region is set as [-43, 43], and the corresponding sequence set is obtained by iterative operation of formula (13) to formula (23). Figures 2 to 5The normalized correlation function obtained shows that, compared with existing methods, the waveform and unmatched filter proposed in this invention can achieve a distance sidelobe level of -92.13dB in the set low sidelobe region, while the corresponding algorithm is -32.7dB.

[0154] The above are merely preferred embodiments of the present invention and are not intended to limit the present 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 principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for jointly designing a transmit waveform set and a receive filter bank to suppress range sidelobes, characterized in that, The application relates to a method for optimizing a non-periodic radar waveform set and a non-matched filter set. According to the variable setting, a target function model is established: make and They represent the designs to be created. A set of sequences consisting of aperiodic transmit waveforms and unmatched filters, each sequence having a length of [length missing]. ,Right now , Define the dimension as Selection matrix The first in OK The elements of the column are as follows: （1） wherein, represents a Dirac function; when the function input variable value is 0, the function value is 1; when the function input variable value is not 0, the function value is 0; represents a distance displacement index of, ; In combination with the constant modulus characteristic of the transmission waveform, the constant energy characteristic of the non-matched filter sequence and the signal-to-noise ratio loss condition, a fractional optimization model without a template is established; specifically: （2） wherein, represents the low side lobe region according to the combination of the waveform sequence and the mismatched filter sequence ; represents the weighting factor at the side lobe level; the numerator term in the objective function represents the waveform passing through the filter ; the output after filtering at the distance displacement ; the denominator term represents the main lobe peak level of the first m transmit waveform and the first m mismatched filter output; represents the first element in the first waveform, which needs to satisfy the constant modulus constraint, and the first filter sequence needs to satisfy the constant energy constraint; the similarity constraint between the transmit waveform and the corresponding mismatched filter sequence is introduced , and the similarity factor is used to regulate the signal-to-noise ratio loss of the mismatched filter output at the receiving end; By using formula (4) and formula (5), the optimization model in formula (2) is converted into: Integrating a set of aperiodic transmit waveforms and a plurality of short sequence variables of a non-matched filter into a long sequence variable : （3） Definition of selection matrix , and auxiliary matrix : （4） By means of the selection matrix and is re-written as （5） An auxiliary variable is introduced: （6） Formula (6) is converted into: （7） Based on the ADMM algorithm framework, variable decoupling is realized, the fractional optimization model is iteratively solved, and an optimal waveform set and non-matched filter set sequence are obtained. （8）； Based on the ADMM algorithm framework, variable decoupling is realized, the fractional optimization model is iteratively solved, and an optimal waveform set and non-matched filter set sequence are obtained.

2. The method of claim 1, wherein, A Lagrange augmented function is constructed: The iteration jump-out condition is set as: （9） wherein denotes a step size, is a Lagrange multiplier, denotes taking the real part of the elements inside the brackets; The optimal waveform set and non-matched filter set sequence are obtained, and the method comprises the following steps: (10) wherein .

3. The method of claim 2, wherein, The fractional optimization model is split to obtain a sub-problem to be solved; The sub-problem to be solved is processed to obtain an optimal waveform set sequence and a non-matched filter set. The fractional optimization model is split to obtain a sub-problem to be solved, and the method comprises the following steps:

4. The method of claim 3, wherein, Formula (9) is split to obtain two sub-problems to be optimized: In the first iteration process, the solving step is: Wherein: (11) (12) The sub-problem to be solved is processed to obtain an optimal waveform set sequence and a non-matched filter set. (13) representing variables In the first the results of the second optimization.

5. The method of claim 4, wherein, A step function is defined When determined, the result is and : (14) (15) Formula (14) to formula (16) are brought into formula (11) to obtain (16) The sub-problem to be solved is processed to obtain an optimal waveform set sequence and a non-matched filter set, and the method further comprises the following steps: (17) Equation (17) is converted into a single variable problem with respect to , and the optimal value of the single variable problem is found , which is substituted into Equations (14) and (15) to find and .

6. The method of claim 5, wherein, For the sub-problem in formula (12), the following is obtained: Wherein: (18) By the Lagrangian multiplier in equation (9), we further obtain the optimization problem with respect to the variables ​ (19) The problem in formula (19) is equivalent to (20) Wherein: (21) The problem in formula (19) is equivalent to (22) represents a vectorization operation on the matrix within the parentheses; In equation (21) is a quartic problem in is reduced to a linear problem by the upper bound function minimization optimization method. On the variables The solution process is as follows: (23) wherein , .

Images