1. A method for generating a multi-degree-of-freedom frequency modulated signal, the method comprising:

constructing a time domain function of the multi-degree-of-freedom frequency modulation signal based on the piecewise nonlinear function;

according to the time domain function of the multi-degree-of-freedom frequency modulation signal, determining an impulse response width IRW and a peak side lobe ratio PSLR in the autocorrelation function performance of the multi-degree-of-freedom frequency modulation signal, and establishing a signal optimization model based on the IRW and the PSLR;

determining an algorithm model of an augmented Lagrange genetic algorithm based on the signal optimization model;

determining an initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the selected window function and a stationary phase principle POSP;

and continuously iterating the initialized frequency modulation control points of the multi-degree-of-freedom frequency modulation signals by utilizing the time domain function of the multi-degree-of-freedom frequency modulation signals and the algorithm model of the augmented Lagrange genetic algorithm until the augmented Lagrange genetic algorithm is converged.

2. The method of claim 1, wherein before constructing the time-domain function of the multi-degree-of-freedom frequency modulated signal based on the piecewise non-linear function, the method further comprises:

determining a time-frequency function of the multi-degree-of-freedom frequency modulation signal of the piecewise non-linear function based on the instantaneous frequency modulation function of the multi-degree-of-freedom frequency modulation signal of the piecewise linear function;

the method for constructing the time domain function of the multi-degree-of-freedom frequency modulation signal based on the piecewise nonlinear function comprises the following steps:

determining a phase function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function according to the time-frequency function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function;

and determining the time domain function of the multi-degree-of-freedom frequency modulation signal according to the phase function and the amplitude corresponding to the multi-degree-of-freedom frequency modulation signal.

3. The method of claim 2, wherein prior to determining the time-frequency function of the piecewise non-linear function multi-degree of freedom frequency modulated signal based on the instantaneous frequency modulation function of the piecewise linear function multi-degree of freedom frequency modulated signal, the method further comprises:

determining a time segmentation point and a frequency modulation control point in a frequency modulation relation plane;

determining an instantaneous frequency modulation function of the multi-degree-of-freedom frequency modulation signal of the piecewise linear function based on the time segmentation point and the frequency modulation control point;

the determining the time-frequency function of the multi-degree-of-freedom frequency modulation signal based on the piecewise linear function comprises the following steps:

and integrating the instantaneous frequency modulation function of the multi-degree-of-freedom frequency modulation signal of the piecewise linear function to determine the time-frequency function of the multi-degree-of-freedom frequency modulation signal of the piecewise non-linear function.

4. The method of claim 2, wherein determining the phase function of the multi-degree-of-freedom chirp signal of the piecewise non-linear function from the time-frequency function of the multi-degree-of-freedom chirp signal of the piecewise non-linear function comprises:

and integrating the time-frequency function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function to determine the phase function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function.

5. The method of claim 1, wherein the building a signal optimization model based on the IRW and the PSLR comprises:

the signal optimization model is as follows:

min PSLR(r),such that IRW(r)-β≤0,

wherein minPSLR (r), suchthataRW (r) -beta is less than or equal to 0 for representing that the side lobe is reduced under the condition of satisfying the condition of not widening the main lobe, and PSLR (r) is controlled according to the frequency modulationPSLR of the obtained multi-degree-of-freedom frequency modulation signal; IRW (r) is based on frequency modulation control pointObtaining IRW of the multi-degree-of-freedom frequency modulation signal; beta is a main lobe width control factor; r is_1i1And r_1i2Is the ordinate of a section of linear function formed in the frequency modulation relation plane; r is_2i1And r_2i2Is the ordinate of a section of linear function formed in the frequency modulation relation plane; Δ T is the time interval at which the pulse width T is divided equally into 2n +2 segments; and B is a preset bandwidth.

6. The method according to claim 1, wherein determining an algorithm model of an augmented lagrangian genetic algorithm based on the signal optimization model comprises:

determining an objective function Ψ (r, λ, s) by using an augmented Lagrange algorithm based on the signal optimization model: Ψ (r, λ, s) ═ pslr (r) - λ log (s- (irw (r) - β));

wherein r is a frequency modulation control point, λ is a Lagrange operator, s is an offset, λ and s are both non-negative numbers, and β is a constant;

determining a parameter function lambda using an augmented Lagrange algorithm_k+1：

s_k+1＝μλ_k+1；

Wherein mu is a value for ensuring that s- (IRW (r) -beta) is greater than 0, and k is a non-negative number;

and the target function and the parameter function form an algorithm model of the augmented Lagrange genetic algorithm.

7. The method of claim 1, wherein determining an initial tuning frequency control point for the multi-degree-of-freedom tuning signal based on the selected window function and a stationary phase principle (POSP) comprises:

calculating a group delay function of the multi-degree-of-freedom frequency modulation signal according to the window function and a stationary phase principle POSP;

determining an initial time-frequency function corresponding to the multi-degree-of-freedom frequency modulation signal according to the group delay function;

determining an initial frequency modulation function of the multi-degree-of-freedom frequency modulation signal according to the initial time frequency function corresponding to the multi-degree-of-freedom frequency modulation signal;

and determining an initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the initial frequency modulation function of the multi-degree-of-freedom frequency modulation signal.

8. The method of claim 1, wherein the continuously iterating the initialized frequency modulation control point for the multi-degree of freedom frequency modulated signal using the time domain function for the multi-degree of freedom frequency modulated signal and the algorithm model for the augmented lagrangian genetic algorithm until the augmented lagrangian genetic algorithm converges comprises:

determining the fitness of a first multi-degree-of-freedom frequency modulation signal and the iterative parameter of the first multi-degree-of-freedom frequency modulation signal by utilizing the time domain function of the multi-degree-of-freedom frequency modulation signal and the algorithm model of the augmented Lagrange genetic algorithm, and performing cross processing and variation processing on each first multi-degree-of-freedom frequency modulation signal based on the fitness of the first multi-degree-of-freedom frequency modulation signal and the iterative parameter of the first multi-degree-of-freedom frequency modulation signal to obtain a second multi-degree-of-freedom frequency modulation signal; in the first iteration, the first multi-degree-of-freedom frequency modulation signal is an initial multi-degree-of-freedom frequency modulation signal;

and judging whether the fitness of the second multi-degree-of-freedom frequency modulation signal meets a preset value or not according to the augmented Lagrange genetic algorithm, if not, continuing to perform the cross processing and the variation processing on the second multi-degree-of-freedom frequency modulation signal until the fitness of the multi-degree-of-freedom frequency modulation signal subjected to the cross processing and the variation processing meets the preset value.

9. A device for generating a multi-degree-of-freedom frequency modulated signal, the device comprising: the device comprises a function establishing unit, a determining unit, a model establishing unit, an initial unit and an iteration unit;

the function establishing unit is used for establishing a time domain function of the multi-degree-of-freedom frequency modulation signal based on the piecewise nonlinear function;

the determining unit is used for determining an impulse response width IRW and a peak side lobe ratio PSLR in the autocorrelation function performance of the multi-degree-of-freedom frequency modulation signal according to the time domain function of the multi-degree-of-freedom frequency modulation signal, and establishing a signal optimization model based on the IRW and the PSLR;

the model establishing unit is used for determining an algorithm model of the augmented Lagrange genetic algorithm based on the signal optimization model;

the initial unit is used for determining an initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the selected window function and the stationary phase principle POSP;

the iteration unit is used for continuously iterating the initialized frequency modulation control point of the multi-degree-of-freedom frequency modulation signal by using the time domain function of the multi-degree-of-freedom frequency modulation signal and the algorithm model of the augmented Lagrange genetic algorithm until the augmented Lagrange genetic algorithm is converged.

10. A storage medium having stored thereon computer-executable instructions that, when executed by a processor, implement the method of generating a multiple degree of freedom frequency modulated signal according to any one of claims 1 to 8.

Background

With the development of high-resolution Radar satellites, a large number of Synthetic Aperture Radars (SAR) are used in the field of remote sensing, such as TerraSAR-X, Sentinel-1 and COSMO-SkyMed. Conventional SAR systems use Linear Frequency Modulation (LFM) signals as transmit waveforms that produce high side lobe levels that can interfere with and even cover scatterers near the target. In order to suppress high side lobes generated by the target, the LFM signal is usually subjected to windowing. However, the windowing operation may cause the filtering process to no longer exactly match the Signal, thereby reducing the Signal-to-Noise Ratio (SNR) of the radar system. In order to overcome the problem of SNR loss caused by sidelobe suppression, the multi-degree-of-freedom frequency modulation signal can simultaneously keep the signal-to-noise ratio of the radar and achieve the effect of suppressing the sidelobe through windowing processing, thereby gaining the favor of a great number of radar emission signal processing workers.

However, in the prior art, in the process of using the multi-degree-of-freedom frequency modulation signal, the broadening of the main lobe is inevitably caused while the level of the side lobe is reduced, and the broadening of the main lobe can cause the resolution of the multi-degree-of-freedom frequency modulation signal to be reduced, thereby reducing the imaging quality of the SAR image.

The multi-degree-of-freedom frequency modulation signal has larger design freedom due to the nonlinear time-frequency relationship, so that how to design and optimize the multi-degree-of-freedom frequency modulation signal can reduce side lobes to the maximum extent and keep a narrower main lobe is a problem which needs to be solved at present.

Disclosure of Invention

The embodiment of the application provides a method and a device for generating a multi-degree-of-freedom frequency modulation signal and a storage medium, wherein the generated multi-degree-of-freedom frequency modulation signal can reduce side lobes to the maximum extent and widen a main lobe to the minimum extent.

The technical scheme of the application is realized as follows:

in a first aspect, an embodiment of the present application provides a method for generating a multi-degree-of-freedom frequency modulation signal, where the method includes:

constructing a time domain function of the multi-degree-of-freedom frequency modulation signal based on the piecewise nonlinear function;

according to the time domain function of the multi-degree-of-freedom frequency modulation signal, determining an Impulse Response Width (IRW) and a Peak Side Lobe Ratio (PSLR) in the autocorrelation function performance of the multi-degree-of-freedom frequency modulation signal, and establishing a signal optimization model based on the IRW and the PSLR;

determining an algorithm model of an augmented Lagrange genetic algorithm based on the signal optimization model;

determining an initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the selected window function and a Stationary Phase Principle (POSP);

and continuously iterating the initialized frequency modulation control points of the multi-degree-of-freedom frequency modulation signals by utilizing the time domain function of the multi-degree-of-freedom frequency modulation signals and the algorithm model of the augmented Lagrange genetic algorithm until the augmented Lagrange genetic algorithm is converged.

In a second aspect, an embodiment of the present application provides an apparatus for generating a multiple degree of freedom frequency modulation signal, where the apparatus includes: the device comprises a function establishing unit, a determining unit, a model establishing unit, an initializing unit and an iteration unit;

the function establishing unit is used for establishing a time domain function of the multi-degree-of-freedom frequency modulation signal based on the piecewise nonlinear function;

the determining unit is used for determining IRW and PSLR in the autocorrelation function performance of the multi-degree-of-freedom frequency modulation signal according to the time domain function of the multi-degree-of-freedom frequency modulation signal, and establishing a signal optimization model based on the IRW and the PSLR;

the model establishing unit is used for determining an algorithm model of the augmented Lagrange genetic algorithm based on the signal optimization model;

the initialization unit is used for determining an initialization frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the selected window function and the POSP;

the iteration unit is used for continuously iterating the initialized frequency modulation control point of the multi-degree-of-freedom frequency modulation signal by using the time domain function of the multi-degree-of-freedom frequency modulation signal and the algorithm model of the augmented Lagrange genetic algorithm until the augmented Lagrange genetic algorithm is converged.

In a third aspect, an embodiment of the present application provides a storage medium, where the storage medium stores computer-executable instructions, and when the computer-executable instructions are executed by a processor, the method for generating a multi-degree-of-freedom frequency modulation signal is implemented.

The embodiment of the application provides a time domain function of a multi-degree-of-freedom frequency modulation signal based on a piecewise linear function, wherein the piecewise linear function is established; according to the time domain function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function, determining IRW and PSLR in the autocorrelation function performance of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function, and establishing a signal optimization model based on the IRW and the PSLR; determining an algorithm model of an augmented Lagrange genetic algorithm based on the constraint condition and the objective function of the signal optimization model; determining an initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the selected window function and the POSP; optimizing the initialized frequency modulation control point of the multi-degree-of-freedom frequency modulation signal by utilizing the time domain function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function and the algorithm model of the augmented Lagrange genetic algorithm until the augmented Lagrange genetic algorithm is converged; the obtained multi-degree-of-freedom frequency modulation signal can reduce side lobes to the maximum extent and simultaneously widen a main lobe to the minimum extent.

Drawings

Fig. 1 is a flowchart of a method for generating a multi-degree-of-freedom frequency modulation signal according to an embodiment of the present disclosure;

FIG. 2 is a frequency modulation function of a multi-degree-of-freedom frequency modulation signal according to an embodiment of the present disclosure;

fig. 3 is a time-frequency function of a piecewise nonlinear multi-degree-of-freedom frequency modulation signal according to an embodiment of the present application;

fig. 4 is a time-frequency function of a multi-degree-of-freedom frequency modulation signal according to an embodiment of the present disclosure;

fig. 5 is a time-domain waveform of a multi-degree-of-freedom frequency modulation signal according to an embodiment of the present disclosure;

fig. 6 is an autocorrelation output waveform of a multi-degree-of-freedom fm signal according to an embodiment of the present disclosure;

fig. 7 is an alternative structural schematic diagram of a device for generating a multi-degree-of-freedom frequency modulation signal according to an embodiment of the present disclosure;

fig. 8 is an alternative structural schematic diagram of a device for generating a multi-degree-of-freedom frequency modulation signal according to an embodiment of the present disclosure.

Detailed Description

In the embodiment of the application, a time domain function of the multi-degree-of-freedom frequency modulation signal is constructed based on a piecewise nonlinear function; according to the time domain function of the multi-degree-of-freedom frequency modulation signal, determining IRW and PSLR in the autocorrelation function performance of the multi-degree-of-freedom frequency modulation signal, and establishing a signal optimization model based on the IRW and the PSLR; determining an algorithm model of an augmented Lagrange genetic algorithm based on the signal optimization model; determining an initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the selected window function and the POSP; and optimizing the initialized frequency modulation control point of the multi-degree-of-freedom frequency modulation signal by utilizing the time domain function of the multi-degree-of-freedom frequency modulation signal and the algorithm model of the augmented Lagrange genetic algorithm until the augmented Lagrange genetic algorithm is converged.

The following describes the embodiments in further detail with reference to the accompanying drawings.

The embodiment of the application provides a method for generating a multi-degree-of-freedom frequency modulation signal, as shown in fig. 1, the method includes steps S101 to S105:

s101, constructing a time domain function of the multi-degree-of-freedom frequency modulation signal based on the piecewise nonlinear function.

In some embodiments, before S101 above, the method further comprises:

and determining the time-frequency function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function based on the instantaneous frequency modulation function of the multi-degree-of-freedom frequency modulation signal of the piecewise linear function.

Here, the time-frequency function is an instantaneous frequency function, the independent variable is t, and the variable is f.

In some embodiments, the S101 includes: determining a phase function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function according to the time-frequency function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function; and determining the time domain function of the multi-degree-of-freedom frequency modulation signal according to the phase function and the amplitude corresponding to the multi-degree-of-freedom frequency modulation signal.

In practical application, the amplitude a corresponding to the multi-degree-of-freedom frequency modulation signal is generally normalized, that is, a is 1.

In some embodiments, before determining the time-frequency function of the multi-degree-of-freedom chirp signal based on the piecewise linear function, the method further comprises: determining a time segmentation point t and a frequency modulation control point r in a frequency modulation relation plane; and determining the instantaneous frequency modulation function of the multi-degree-of-freedom frequency modulation signal of the piecewise linear function based on the time segmentation point t and the frequency modulation control point r.

Here, a frequency modulation relationship (t, r) plane is defined in a cartesian coordinate system, where t is an abscissa for representing the time of the multi-degree-of-freedom frequency modulation signal of the piecewise linear function, and r is an ordinate for representing the instantaneous frequency modulation of the multi-degree-of-freedom frequency modulation signal of the piecewise linear function.

In the frequency modulation relation plane, the pulse width of the multi-degree-of-freedom frequency modulation signal is preset to be T, and if the signal with the pulse width of T is uniformly divided into 2n +2 sections, 2n +3 uniformly distributed time section points are totally arranged on the abscissaThe time segment points are evenly distributed on the abscissa,wherein, T_1iIs the abscissa, T, of a linear function formed in the plane of the frequency-modulated relationship_2iIs the abscissa of another linear function formed in the frequency modulation relation plane; the ordinate corresponds to the abscissa and has 4n +4 frequency modulation rate control points r ═ r_2n2,r_2n1,...,r₂₀₂,r₂₀₁,r₁₀₁,r₁₀₂,...,r_1n1,r_1n2]Wherein n is a positive integer.

After the time segmentation point t and the frequency modulation control point r are determined, as shown in fig. 2, every two frequency modulation control points r form a group to form a 2n +2 discontinuous piecewise linear function, wherein an instantaneous frequency modulation function r (t) corresponding to the multi-degree-of-freedom frequency modulation signal of the piecewise linear function is a formula (1):

in some embodiments, the determining the time-frequency function of the multi-degree-of-freedom chirp signal of the piecewise non-linear function based on the instantaneous chirp function of the multi-degree-of-freedom chirp signal of the piecewise linear function includes:

and integrating the instantaneous frequency modulation function of the multi-degree-of-freedom frequency modulation signal of the piecewise linear function to determine the time-frequency function of the multi-degree-of-freedom frequency modulation signal of the piecewise non-linear function.

Here, the instantaneous frequency modulation function is used to indicate a rate of change of an instantaneous frequency at a certain time. The time-frequency function is an instantaneous frequency function, the independent variable is t, and the variable is f.

As shown in fig. 3, the time-frequency function of the multi-degree-of-freedom frequency modulation signal is the determined piecewise nonlinear function.

The time-frequency function f (t) of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function is a formula (2):

wherein the coefficients are of formula (3) to formula (5):

wherein, in the formula (3), r₁₀₂、r₁₀₁、r_1i2、r_1i1、r_1n2、r_1n1、r₂₀₂、r₂₀₁、r_2i2、r_2i1、r_2n2And r_2n1Respectively, the ordinate, T, of a linear function formed in the frequency-modulation-relationship plane₁₁、T_1(i+1)、T_1i、T_1n、T₂₁、T_2(i+1)、T_2i、And T_2nRespectively, the abscissa of a linear function formed in the frequency-modulation relationship plane.

In some embodiments, the determining the phase function of the multi-degree-of-freedom frequency modulation signal of the piecewise non-linear function according to the time-frequency function of the multi-degree-of-freedom frequency modulation signal of the piecewise non-linear function includes:

integrating the time-frequency function of the piecewise nonlinear multi-degree-of-freedom frequency modulation signal to determine a phase function theta (t) of the piecewise nonlinear multi-degree-of-freedom frequency modulation signal, wherein the theta (t) can be represented by a formula (6):

θ (t) ═ 2 pi · (t) dt formula (6).

S102, determining impulse response widths IRW and PSLR in the autocorrelation function performance of the multi-degree-of-freedom frequency modulation signal according to the time domain function of the multi-degree-of-freedom frequency modulation signal, and establishing a signal optimization model based on the IRW and the PSLR.

Here, the impulse response width IRW is a 3dB main lobe width of the impulse response.

The time domain function of the multi-degree-of-freedom frequency modulation signal is the time domain function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function.

According to the time domain function of the multi-degree-of-freedom frequency modulation signal, determining the autocorrelation function of the multi-degree-of-freedom frequency modulation signal as follows: and converting the amplitude of the multi-degree-of-freedom frequency modulation signal into a dB form, and calculating the IRW and the PSLR of the multi-degree-of-freedom frequency modulation signal.

Wherein the time domain function s (t) is formula (7):

(t) Aexp { -j θ (t) } formula (7);

the autocorrelation function r (t) is formula (8):

wherein, in the formula (8), τ is a parameter;

IRW is the corresponding width at 3dB of the main lobe, PSLR is the maximum of the side lobes except the main lobe, and IRW and PSLR are defined as follows:

IRW: the 3dB main lobe width is generally normalized to a sampling point;

PSLR: the ratio of the highest sidelobe to the height of the peak value of the main lobe is dB;

in some embodiments, building a signal optimization model based on the IRW and PSLR includes:

the signal optimization model is as follows:

min PSLR(r),such that IRW(r)-β≤0,

wherein min PSLR (r), sub th IRW (r) -beta is not more than 0 and is used for representing that the side lobe is reduced under the condition of satisfying the condition of not widening the main lobe, and PSLR (r) is controlled according to the frequency modulationPSLR of the obtained multi-degree-of-freedom frequency modulation signal; IRW (r) is based on frequency modulation control pointObtaining IRW of the multi-degree-of-freedom frequency modulation signal; β is a main lobe width control factor used to ensure that the main lobe width does not exceed this value during the optimization process; r is_1i1And r_1i2Is the ordinate of a section of linear function formed in the frequency modulation relation plane; r is_2i1And r_2i2Is the ordinate of a section of linear function formed in the frequency modulation relation plane;a time interval in which the pulse width T is divided into 2n +2 sections on average; b is a preset bandwidth; if it isAndthe frequency of the multi-degree-of-freedom frequency modulation signal can be controlled to be withinWithin the range of (1).

In the embodiment of the application, the side lobe can be reduced as much as possible under the condition of not widening the main lobe by the signal optimization model established based on the IRW and the PSLR.

S103, determining an algorithm model of the augmented Lagrange genetic algorithm based on the signal optimization model.

Here, the determining an algorithm model of an augmented lagrangian genetic algorithm based on the signal optimization model includes:

determining an objective function Ψ (r, λ, s) by using an augmented Lagrange algorithm based on the signal optimization model, wherein the objective function Ψ (r, λ, s) is represented by formula (9):

Ψ (r, λ, s) ═ pslr (r) - λ log (s- (irw (r) - β)): formula (9);

wherein r is a frequency modulation control point, λ is a Lagrange operator, s is an offset, λ and s are both non-negative numbers, the constraint condition is IRW (r) - β, and β is a constant.

Determining a parameter function using an augmented Lagrange algorithm, wherein the parameter function λ_k+1Is formula (10):

wherein mu is a value which ensures that s- (IRW (r) -beta) is greater than 0; k is a non-negative number.

And the target function and the parameter function form an algorithm model of the augmented Lagrange genetic algorithm.

Calculating the fitness of each multi-degree-of-freedom frequency modulation signal in the current multi-degree-of-freedom frequency modulation signal set according to the objective function; selecting a parent multi-degree-of-freedom frequency modulation signal from the multi-degree-of-freedom frequency modulation signal set according to the fitness value of each multi-degree-of-freedom frequency modulation signal; and performing cross processing and mutation processing on the parent multi-degree-of-freedom frequency modulation signal to obtain the next iteration parent multi-degree-of-freedom frequency modulation signal.

And calculating the Lagrangian operator and the offset of the next iteration corresponding to the current Lagrangian operator and the offset according to the parameter function.

The augmented lagrangian algorithm divides the specific solving problem into two parts: one part is the traditional genetic algorithm and the other part is the augmented Lagrange algorithm. In a traditional genetic algorithm, the fitness function is pslr (r) and the constraint is irw (r) - β. In the embodiment of the present application, because lagrangian λ is introduced, a constraint condition, i.e., irw (r) - β, can be converted into a penalty term to be added to an objective function, i.e., pslr (r) - λ log (s- (irw (r) - β)), so that a constraint problem can be converted into an unconstrained problem.

The augmented Lagrangian algorithm is used for solving the constraint problem, and lambda and s can be continuously updated according to the parameter function.

Genetic algorithms are dynamic optimization processes that simulate natural selection for "survival of the fittest". Firstly, calculating the fitness in an initial multi-degree-of-freedom frequency modulation signal set based on an augmented Lagrange genetic algorithm model, selecting a parent from the fitness in each multi-degree-of-freedom frequency modulation signal set, and performing cross processing and variation processing on the parent so as to obtain a multi-degree-of-freedom frequency modulation signal of the next iteration; and calculating the Lagrange operator and the offset of the next iteration corresponding to the current Lagrange operator and the offset according to the parameter function, selecting the frequency modulation signal with good fitness, namely better multiple degrees of freedom as a parent class, improving the diversity of offspring through cross processing and mutation processing, and evaluating the quality of the fitness again. In the whole iterative updating optimization process, individuals with high fitness are reserved, and individuals with poor fitness are eliminated, so that the optimal multi-degree-of-freedom frequency modulation signal can be obtained through multiple cycles.

And S104, determining an initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the selected window function and the POSP.

In some embodiments, the S104 includes: calculating a group delay function of the multi-degree-of-freedom frequency modulation signal according to the window function and a stationary phase principle POSP; determining an initial time-frequency function corresponding to the multi-degree-of-freedom frequency modulation signal according to the group delay function; determining an initial frequency modulation function of the multi-degree-of-freedom frequency modulation signal according to the initial time frequency function corresponding to the multi-degree-of-freedom frequency modulation signal; and determining an initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the initial frequency modulation function of the multi-degree-of-freedom frequency modulation signal.

Here, a group delay function corresponding to the multi-degree-of-freedom frequency modulation signal is calculated according to the selected window function and the POSP, wherein the group delay function T (f) is expressed by formula (11):

wherein, C is a constant,and P (f) is a power spectral density function, T is the pulse width corresponding to the multi-degree-of-freedom frequency modulation signal, and B is the bandwidth of the multi-degree-of-freedom frequency modulation signal.

In one example, the selected window function may beA taylor window p (f) of-35 sll.

In the embodiment of the present application, the stationary phase principle POSP indicates that, after a window function, for example, a taylor window, is preset, a power spectrum of the multi-degree-of-freedom fm signal is designed to be close to the preset window function, so that the multi-degree-of-freedom fm signal with low side lobes can be generated. Therefore, the performance characteristics of the generated multi-degree-of-freedom frequency modulation signal can be well predicted through the performance characteristics of the window function, and therefore the corresponding window function can be selected according to different requirements. Wherein the window function is selected asA taylor window p (f) of-35 is defined as a desired power spectrum, and means that the power spectrum of the frequency-modulated signal with multiple degrees of freedom is desired to be designed to be close to the taylor window.

The group delay function and the initial time-frequency function are a pair of inverse functions, and after the group delay function is determined, the function can be determined according to f (T) ═ T^-1(f) And determining an initial time-frequency function.

In one example, T may be determined according to f (T) ═ T^-1(f) And determining an initial time-frequency function with a curve shape approximate to an S shape.

In the embodiment of the application, derivation can be performed on the initial time-frequency function corresponding to the multi-degree-of-freedom frequency modulation signal, so that the initial frequency modulation function of the multi-degree-of-freedom frequency modulation signal is determined.

In one example, the initial tuning frequency function with the shape of a curve approximating an "U" shape may be obtained by deriving an initial time-frequency function with the shape of a curve approximating an "S" shape.

In the established frequency modulation relation plane, because 2n +3 time segmentation points t exist on the abscissa and 4n +4 frequency modulation control points r exist on the ordinate, when the initial frequency modulation function of the multi-degree-of-freedom frequency modulation signal is obtained, the point is in the process of adjusting the frequencyIs in correspondence with r_2n2At T ═ T_2nIs in correspondence with r_2n1And r_2(n-1)2…, corresponding to r at t-0₂₀₁And r₁₀₁，t＝T₁₁Is in correspondence with r₁₀₂And r₁₁₁…, at T ═ T_1nIs in correspondence with r_1(n-1)2And r_1n1In aIs in correspondence with r_1n2. In the subsequent optimization process, T is T_2nAt a corresponding r_2n1And r_2(n-1)2Will gradually separate, …, at T ═ T_1nIs in correspondence with r_1(n-1)2And r_1n1There is also a gradual separation, where gradual separation represents the frequency control point becoming better performing during optimization. And obtaining an initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the initial frequency modulation function of the multi-degree-of-freedom frequency modulation signal.

In the embodiment of the application, in order to ensure that the frequency in the time-frequency function of the multi-degree-of-freedom frequency modulation signal is withinThe frequency modulation control point r of the internal and multi-degree-of-freedom frequency modulation signals should satisfyAndif the constraint is not satisfied, the frequency modulation rate control point r needs to be multiplied by a coefficient k that satisfies equation (12):

and S105, continuously iterating the initialized frequency modulation control point of the multi-degree-of-freedom frequency modulation signal by using the multi-degree-of-freedom frequency modulation signal time domain function and the algorithm model of the augmented Lagrange genetic algorithm until the augmented Lagrange genetic algorithm is converged.

Here, after the initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal is determined in S104, the initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal is iterated through the time domain function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function determined in S101 and through the algorithm model of the augmented lagrangian genetic algorithm determined in S103 until the augmented lagrangian genetic algorithm converges.

In some embodiments, the S105 includes: determining the fitness of a first multi-degree-of-freedom frequency modulation signal and the iterative parameter of the first multi-degree-of-freedom frequency modulation signal by utilizing the time domain function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function and the algorithm model of the augmented Lagrange genetic algorithm, and performing cross processing and variation processing on each first multi-degree-of-freedom frequency modulation signal based on the fitness of the first multi-degree-of-freedom frequency modulation signal and the iterative parameter of the first multi-degree-of-freedom frequency modulation signal to obtain a second multi-degree-of-freedom frequency modulation signal; in the first iteration, the first multi-degree-of-freedom frequency modulation signal is an initial multi-degree-of-freedom frequency modulation signal; and judging whether the fitness of the second multi-degree-of-freedom frequency modulation signal meets a preset value or not according to the augmented Lagrange genetic algorithm, if not, continuing to perform the cross processing and the variation processing on the second multi-degree-of-freedom frequency modulation signal until the fitness of the multi-degree-of-freedom frequency modulation signal subjected to the cross processing and the variation processing meets the preset value.

It should be noted that, in the embodiment of the present application, the preset value is not limited, and the preset value may be 1 × 10^-6Other values are also possible.

Here, before the multi-degree-of-freedom frequency modulation signal is iterated, iteration parameters including lagrangian λ and offset s may be determined according to a parameter function. The initialized iteration parameters may be referred to as initial iteration parameters for a first iteration in the iterative process.

During the first iteration, the time domain function of the multi-degree-of-freedom frequency modulation signals of the piecewise nonlinear function and the algorithm model of the augmented Lagrange genetic algorithm are utilized to calculate the adaptability of the multi-degree-of-freedom frequency modulation signals, a plurality of father multi-degree-of-freedom frequency modulation signals are selected from the initial multi-degree-of-freedom frequency modulation signals according to the adaptability of the multi-degree-of-freedom frequency modulation signals, the selected plurality of father multi-degree-of-freedom frequency modulation signals are subjected to cross processing and variation processing to obtain the multi-degree-of-freedom frequency modulation signals of the second iteration, and the second iteration parameters corresponding to the initial iteration parameters are calculated through the parameter function.

During the second iteration, the fitness of the multi-degree-of-freedom frequency modulation signals of each second iteration is calculated by using the objective function and the second iteration parameters, a plurality of father multi-degree-of-freedom frequency modulation signals are selected from the multi-degree-of-freedom frequency modulation signals of each second iteration according to the fitness of the multi-degree-of-freedom frequency modulation signals of each second iteration, the selected plurality of father multi-degree-of-freedom frequency modulation signals are subjected to cross processing and variation processing to obtain the multi-degree-of-freedom frequency modulation signals of the third iteration, and the third iteration parameters corresponding to the second iteration parameters are calculated through the parameter functions. And analogizing in sequence until the fitness of the multi-degree-of-freedom frequency modulation signal subjected to cross processing and variation processing meets a preset value.

In the embodiment of the application, according to the algorithm model of the augmented Lagrange genetic algorithm, the multi-degree-of-freedom frequency modulation signal of the second iteration and the second iteration parameter are iterated to obtain a multi-degree-of-freedom frequency modulation signal of the third iteration and a third iteration parameter; and continuously iterating the iterated multi-degree-of-freedom frequency modulation signal and the iterated parameters based on the algorithm model of the augmented Lagrange genetic algorithm until the algorithm model of the augmented Lagrange genetic algorithm is converged, wherein the convergence of the augmented Lagrange genetic algorithm shows that the design and optimization of the multi-degree-of-freedom frequency modulation signal are completed.

The following describes a method for generating a multi-degree-of-freedom frequency modulation signal in combination with a specific example, for example, a large time-width signal design parameter commonly used in a synthetic aperture radar SAR system.

The large time width signal design parameters include:

pulse width of 10us, bandwidth of 100MHz, sampling frequency of 130MHz, time-frequency signal divided into 130 segments (i.e. n-64), main lobe width control factor β -1.18, and initial multi-degree-of-freedom frequency modulation signal based on stationary phase principleA taylor window function of-35 is generated for the power spectrum.

Based on the design parameters, the results before and after optimization of the multi-degree-of-freedom frequency modulation signal are shown in table 1:

TABLE 1

Signal	PSLR(dB)	IRW
			Initial signal	-34.9	1.19
Optimized signal	-40.6	1.17

As can be seen from table 1, the method for generating a multi-degree-of-freedom fm signal according to the embodiment of the present application can reduce the side lobe level by 5.7dB without widening the main lobe. In addition, because the taylor window is a window function with better performance, the PSLR and IRW indexes of the initial multi-degree-of-freedom frequency modulation signal are good, the sidelobe level can be continuously reduced by 5.7dB under the condition of not widening the main lobe by generating the multi-degree-of-freedom frequency modulation signal provided by the embodiment of the application, and the effectiveness of the method for generating the multi-degree-of-freedom frequency modulation signal provided by the embodiment of the application is fully verified.

As shown in fig. 4, the time-frequency function diagram is generated by the method for generating a multi-degree-of-freedom frequency modulation signal according to the embodiment of the present application, where an abscissa is time: pulse width 10us, ordinate frequency: the bandwidth is 100MHz, all normalized in the figure. It can be seen from fig. 4 that the optimized signal also has a substantially S-shaped instantaneous frequency function, but there is a slight jitter, however, it is this jitter that brings about an improvement in the signal performance.

As shown in fig. 5, the time domain waveform diagram of the optimized multi-degree-of-freedom frequency modulation signal is shown, wherein the abscissa is time, the ordinate is amplitude, the amplitude is 1, and the pulse width is 10 us; the solid line represents the real information in the time domain waveform of the signal, and the dashed line represents the imaginary information in the time domain waveform.

As shown in fig. 6, in order to output a waveform diagram for the optimized multi-degree-of-freedom fm signal autocorrelation, it can be seen from the diagram that the multi-degree-of-freedom fm signal obtained by the embodiment of the present application has a system signal-to-noise ratio retention capability of 1.2dB, compared with the same time-width LFM signal that generates equivalent sidelobe level by windowing, and has a great practical engineering significance.

As shown in fig. 7, an embodiment of the present application provides an apparatus 700 for generating a multi-degree-of-freedom frequency modulation signal, where the apparatus includes: a function establishing unit 701, a determining unit 702, a model establishing unit 703, an initializing unit 704 and an iteration unit 705;

the function establishing unit 701 is configured to establish a time domain function of the multi-degree-of-freedom frequency modulation signal based on the piecewise nonlinear function;

the determining unit 702 is configured to determine an impulse response width IRW and a peak side lobe ratio PSLR in an autocorrelation function performance of the multi-degree-of-freedom frequency modulated signal according to a time domain function of the multi-degree-of-freedom frequency modulated signal, and establish a signal optimization model based on the IRW and the PSLR;

the model establishing unit 703 is configured to determine an algorithm model of an augmented lagrangian genetic algorithm based on the signal optimization model;

the initialization unit 704 is configured to determine an initialization frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the selected window function and the stationary phase principle POSP;

the iteration unit 705 is configured to continuously iterate the initialized frequency modulation control point of the multi-degree-of-freedom frequency modulation signal by using the time domain function of the multi-degree-of-freedom frequency modulation signal and the algorithm model of the augmented lagrangian genetic algorithm until the augmented lagrangian genetic algorithm converges.

In some embodiments, the function establishing unit 701 is further configured to determine a time-frequency function of the multi-degree-of-freedom frequency modulation signal based on an instantaneous frequency modulation function of the multi-degree-of-freedom frequency modulation signal of the piecewise linear function;

the function establishing unit 701 is further configured to determine a phase function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function according to a time-frequency function of the multi-degree-of-freedom frequency modulation signal of the piecewise nonlinear function;

the function establishing unit 701 is further configured to determine a time domain function of the multi-degree-of-freedom frequency modulation signal according to the phase function and the amplitude corresponding to the multi-degree-of-freedom frequency modulation signal.

In some embodiments, the function establishing unit 701 is further configured to determine a time segmentation point t and a frequency modulation control point r in a frequency modulation relation plane;

the function establishing unit 701 is further configured to determine an instantaneous frequency modulation function of the multi-degree-of-freedom frequency modulation signal of the piecewise linear function based on the time segmentation point and the frequency modulation control point;

the function establishing unit 701 is further configured to integrate the instantaneous frequency modulation function of the multi-degree-of-freedom frequency modulation signal of the piecewise linear function, and determine a time-frequency function of the multi-degree-of-freedom frequency modulation signal of the piecewise non-linear function.

In some embodiments, the function establishing unit 701 is further configured to integrate the time-frequency function of the multi-degree-of-freedom frequency modulation signal of the piecewise non-linear function, and determine a phase function of the multi-degree-of-freedom frequency modulation signal of the piecewise non-linear function.

In some embodiments, the determining unit 702 is further configured to determine a signal optimization model, where the signal optimization model is:

min PSLR(r),such that IRW(r)-β≤0,

wherein min PSLR (r), sub that IRW (r) -beta is less than or equal to 0 and is used for representing that the side lobe is reduced under the condition of not widening the main lobe, and PSLR (r) is PSLR of the multi-degree-of-freedom frequency modulation signal obtained according to the r vector of the frequency modulation control point; IRW (r) is the IRW of the multi-degree-of-freedom frequency modulation signal obtained according to the r vector of the frequency modulation control point; beta is a main lobe width control factor; r is_1i1And r_1i2Is the ordinate of a section of linear function formed in the frequency modulation relation plane; r is_2i1And r_2i2Is the ordinate of a section of linear function formed in the frequency modulation relation plane; Δ T is the time interval at which the pulse width T is divided equally into 2n +2 segments; and B is a preset bandwidth.

In some embodiments, the model establishing unit 703 is further configured to determine an objective function by using an augmented lagrange algorithm based on the signal optimization model;

Ψ(r,λ,s)＝PSLR(r)-λlog(s-(IRW(r)-β))；

wherein, λ is Lagrange operator, s is offset, λ and s are both non-negative numbers, and β is parameter;

the model establishing unit 703 is further configured to determine a parameter function by using an augmented lagrange algorithm;

s_k+1＝μλ_k+1；

wherein mu is a value for ensuring that s- (IRW (r) -beta) is greater than 0, and k is a non-negative number;

and the target function and the parameter function form an algorithm model of the augmented Lagrange genetic algorithm.

The initial unit 704 is further configured to calculate a group delay function of the multi-degree-of-freedom frequency modulation signal according to the window function and a stationary phase principle POSP; determining an initial time-frequency function corresponding to the multi-degree-of-freedom frequency modulation signal according to the group delay function; determining an initial frequency modulation function of the multi-degree-of-freedom frequency modulation signal according to the initial time frequency function corresponding to the multi-degree-of-freedom frequency modulation signal; and determining an initial frequency modulation control point of the multi-degree-of-freedom frequency modulation signal according to the initial frequency modulation function of the multi-degree-of-freedom frequency modulation signal.

In some embodiments, the iteration unit 705 is further configured to determine a fitness of the first multi-degree-of-freedom frequency modulation signal and an iteration parameter of the first multi-degree-of-freedom frequency modulation signal by using a time domain function of the multi-degree-of-freedom frequency modulation signal and an algorithm model of the augmented lagrange genetic algorithm, and perform cross processing and variation processing on each of the first multi-degree-of-freedom frequency modulation signals based on the fitness of the first multi-degree-of-freedom frequency modulation signal and the iteration parameter of the first multi-degree-of-freedom frequency modulation signal to obtain a second multi-degree-of-freedom frequency modulation signal; in the first iteration, the first multi-degree-of-freedom frequency modulation signal is an initial multi-degree-of-freedom frequency modulation signal;

the iteration unit 705 is further configured to determine whether the fitness of the second multi-degree-of-freedom frequency modulation signal meets a preset value according to the augmented lagrangian genetic algorithm, and if not, continue to perform the cross processing and the mutation processing on the second multi-degree-of-freedom frequency modulation signal until the fitness of the multi-degree-of-freedom frequency modulation signal subjected to the cross processing and the mutation processing meets the preset value.

It should be noted that the above description of the embodiment of the apparatus, similar to the above description of the embodiment of the method, has similar beneficial effects as the embodiment of the method. For technical details not disclosed in the embodiments of the apparatus of the present application, reference is made to the description of the embodiments of the method of the present application for understanding.

It should be noted that, in the embodiment of the present application, if the instant messaging method is implemented in the form of a software functional module and is sold or used as a standalone product, the instant messaging method may also be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the embodiments of the present application may be essentially or partially implemented in the form of a software product, which is stored in a storage medium and includes several instructions to enable an instant messaging device (which may be a terminal, a server, etc.) to execute all or part of the methods described in the embodiments of the present application. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read Only Memory (ROM), a magnetic disk, or an optical disk. Thus, embodiments of the present application are not limited to any specific combination of hardware and software.

An embodiment of the present application provides a device for generating a multi-degree-of-freedom frequency modulated signal, fig. 8 is a schematic structural diagram of the device for generating a multi-degree-of-freedom frequency modulated signal according to the embodiment of the present application, and as shown in fig. 8, the device 800 includes: a processor 801, at least one communication bus 802, a user interface 803, at least one external communication interface 804 and memory 805. Wherein the communication bus 802 is configured to enable connective communication between these components. The user interface 803 may include a display screen, and the external communication interface 804 may include a standard wired interface and a wireless interface, among others. The processor 801 is configured to execute a program for generating a multi-degree-of-freedom chirp signal stored in the memory, so as to implement the steps of the method for generating a multi-degree-of-freedom chirp signal provided in the foregoing embodiments.

Accordingly, the present application further provides a storage medium (i.e., a computer storage medium) having computer-executable instructions stored thereon, where the computer-executable instructions, when executed by a processor, implement the steps of the method for generating a multi-degree-of-freedom frequency modulation signal provided in the foregoing embodiments.

The above description of the embodiments of the apparatus for generating a multi-degree-of-freedom frequency modulation signal and the computer storage medium is similar to the description of the above method embodiments, and has similar advantageous effects to the method embodiments. For technical details not disclosed in the embodiments of the apparatus for generating a multi-degree-of-freedom frequency modulated signal and the computer storage medium of the present application, please refer to the description of the embodiments of the method of the present application for understanding.

It should be appreciated that reference throughout this specification to "one embodiment" or "an embodiment" means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present application. Thus, the appearances of the phrases "in one embodiment" or "in an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. It should be understood that, in the various embodiments of the present application, the sequence numbers of the above-mentioned processes do not mean the execution sequence, and the execution sequence of each process should be determined by its function and inherent logic, and should not constitute any limitation to the implementation process of the embodiments of the present application. The above-mentioned serial numbers of the embodiments of the present application are merely for description and do not represent the merits of the embodiments.

It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.

In the several embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described apparatus embodiments are merely illustrative. In addition, the coupling, direct coupling or communication connection between the components shown or discussed may be through some interfaces, and the indirect coupling or communication connection between the devices or units may be electrical, mechanical or other forms.

The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units; can be located in one place or distributed on a plurality of network units; some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.

In addition, all functional units in the embodiments of the present application may be integrated into one processing unit, or each unit may be separately regarded as one unit, or two or more units may be integrated into one unit; the integrated unit can be realized in a form of hardware, or in a form of hardware plus a software functional unit.

Those of ordinary skill in the art will understand that: all or part of the steps for realizing the method embodiments can be completed by hardware related to program instructions, the program can be stored in a computer readable storage medium, and the program executes the steps comprising the method embodiments when executed; and the aforementioned storage medium includes: various media that can store program codes, such as a removable Memory device, a Read Only Memory (ROM), a magnetic disk, or an optical disk.

Alternatively, the integrated units described above in the present application may be stored in a computer-readable storage medium if they are implemented in the form of software functional modules and sold or used as independent products. Based on such understanding, the technical solutions of the embodiments of the present application may be essentially implemented or portions thereof contributing to the prior art may be embodied in the form of a software product stored in a storage medium, and including several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the methods described in the embodiments of the present application. And the aforementioned storage medium includes: a removable storage device, a ROM, a magnetic or optical disk, or other various media that can store program code.

The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present application, and shall be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.