CN109343058B

CN109343058B - orthogonal nonlinear frequency modulation signal generation method and device based on hybrid algorithm

Info

Publication number: CN109343058B
Application number: CN201811290686.7A
Authority: CN
Inventors: 金国栋; 王宇; 邓云凯; 刘开雨; 王伟; 龙雅君
Original assignee: Institute of Electronics of CAS
Current assignee: Institute of Electronics of CAS
Priority date: 2018-10-31
Filing date: 2018-10-31
Publication date: 2019-12-10
Anticipated expiration: 2038-10-31
Also published as: CN109343058A

Abstract

the embodiment of the invention discloses a method and a device for generating orthogonal nonlinear frequency modulation (NLFM) signals based on a hybrid algorithm, wherein the method comprises the following steps: determining a time-frequency relation function of the NLFM signal according to the piecewise linear function; determining a time domain function of the NLFM signal according to the time-frequency relation function; determining the relevant performance parameters of the NLFM signals according to the time domain function; determining a mathematical model of the NLFM signal according to the relevant performance parameters; initializing the NLFM signal according to the pulse width and bandwidth setting of the NLFM signal; according to the mathematical model, utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm to iterate the initialized NLFM signal to obtain an orthogonal NLFM signal; the embodiment of the invention also discloses a device for generating the orthogonal NLFM signal based on the hybrid algorithm.

Description

orthogonal nonlinear frequency modulation signal generation method and device based on hybrid algorithm

Technical Field

The embodiment of the invention relates to the technical field of communication, in particular to a method and a device for generating a Non-linear frequency modulation (NLFM) signal based on a hybrid algorithm.

background

Synthetic Aperture Radar (SAR) is capable of all-day, all-weather, global earth-to-earth observation and has a wide range of applications, but it is limited by two basic problems:

1. constraints on resolution and mapping bandwidth: the higher the azimuth resolution, meaning the higher the Pulse Repetition Frequency (PRF), the narrower the swath that can be selected, so the azimuth resolution and the range-wise swath width cannot be increased simultaneously.

2. Constraint relation of orientation ambiguity and distance ambiguity: the higher the PRF, i.e. the greater the azimuth oversampling, the smaller the azimuth blur, the closer the range blur to the signal region, and thus received by the higher side lobe, and thus the greater the range blur, and thus it can be seen that the relationship between the azimuth blur and the range blur is reduced by taking the PRF as a medium.

in general satellite-borne SAR application, azimuth bandwidth is large, PRF is high, in order to guarantee mapping bandwidth width, oversampling rate is low, generally oversampling rate is 1.2, so distance ambiguity and azimuth ambiguity exist at the same time, and influence is serious. In the related art, the distance ambiguity is generally suppressed by alternately transmitting orthogonal signals, but the cross-correlation energy of the conventional orthogonal signals, such as positive and negative frequency modulation signals, is scattered to the whole time domain, but the energy does not disappear. The image of the SAR is a distributed target, so the energy of the SAR is accumulated, and the fuzzy energy is not reduced. In addition, the orthogonal signal design is also a key problem for implementing a multiple-Input multiple-Output (MIMO) SAR system, which needs to separate waveforms to suppress crosstalk energy between different waveforms.

The existing quadrature signals generally have the following problems: 1) short-time orthogonal, but energy is accumulated at the far end, and energy is not reduced, such as short-time orthogonal signals; 2) the orthogonal signals do not output the same frequency band; 3) discrete signal, not applicable to distributed scenarios.

The NLFM signals can construct time-frequency relation, so that a power spectrum is constructed, energy distribution in the whole frequency band is realized, mutual filtering is possible, and cross-correlation energy is reduced. The signal designed from NLFM signals has the following advantages: 1) the same frequency band; 2) overall cross-correlation energy degradation; 3) continuous signal, used in distributed scenarios.

Currently, NLFM signal research interest mainly focuses on the optimization design and application of autocorrelation performance indicators such as Peak Side Lobe Ratio (PSLR), 3dB main lobe width (MW), and Integral Side Lobe Ratio (ISLR), and the design method mainly includes: 1) based on a stationary phase principle, a complete signal is obtained by designing a specific window function; 2) power spectra based on some optimization method such as least squares approximating a particular window function; 3) to overcome the problem of sensitivity of NLFM to doppler frequency domain, the first method is combined with amplitude windowing to design NLFM signal, however none of the above methods concerns the orthogonality potential of NLFM signal.

In summary, how to design an optimized NLFM orthogonal signal under an acceptable side lobe height and main lobe width is a problem to be solved in current SAR radar distance ambiguity suppression and MIMO-SAR system design.

Disclosure of Invention

In view of this, embodiments of the present invention desirably provide a method and an apparatus for generating an orthogonal NLFM signal based on a hybrid algorithm, which can improve the orthogonality of the signal and suppress cross-correlation energy under acceptable side lobe and main lobe widths.

The technical scheme of the embodiment of the invention is realized as follows:

In a first aspect, a method and an apparatus for generating an orthogonal NLFM signal based on a hybrid algorithm are provided, where the method includes:

Determining a time-frequency relation function of the NLFM signal according to the piecewise linear function; determining a time domain function of the NLFM signal according to the time-frequency relation function;

Determining the relevant performance parameters of the NLFM signals according to the time domain function; determining a mathematical model of the NLFM signal according to the relevant performance parameters;

Initializing the NLFM signal according to the pulse width and bandwidth setting of the NLFM signal;

and according to the mathematical model, utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm to iterate the initialized NLFM signal to obtain an orthogonal NLFM signal.

in the above scheme, the time-frequency relationship function of the NLFM signal is determined according to a piecewise linear function; determining a time domain function of the NLFM signal according to the time-frequency relation function, wherein the time domain function comprises the following steps:

Defining the time-frequency relation coordinate of the NLFM signal as (T, f), wherein the pulse width of the NLFM signal is T corresponding to the time coordinate T of the time-frequency relation coordinate, the bandwidth of the NLFM signal is B corresponding to the frequency coordinate f of the time-frequency relation coordinate, the pulse width and the bandwidth are divided into 2n +2 sections of linear functions in the time-frequency relation coordinate, time segmentation points are uniformly distributed, and 2n +3 time segmentation point vectors are as follows:Wherein the content of the first and second substances,Is a known amount; defining 2n frequency control points in the time-frequency relation coordinate, and defining a frequency control point vector B_cComprises the following steps: b is_c＝[-B_2n,…,B₂₁,B₁₁,…,B_1n]^TAnd corresponding to 2n +3 frequency segmentation points, determining the time-frequency relation function of the NLFM signal according to the piecewise linear function as follows:

Wherein k is_1iCharacterizing segmentation points by frequencyAnd time segmentation pointfrequency modulation, k, of each segment of the constructed piecewise linear function_2iCharacterizing segmentation points by frequencyand time segmentation pointThe frequency modulation rate of each section of the formed piecewise linear function is as follows:

Determining the time domain function of the NLFM signal with the amplitude of A according to the time-frequency relation function of the NLFM signal as follows:

in the above scheme, the determining, according to the time domain function, a relevant performance parameter of the NLFM signal; determining a mathematical model of the NLFM signal from the correlation performance parameters, comprising:

Determining autocorrelation performance parameters of the NLFM signal according to the time domain function, wherein the autocorrelation performance parameters comprise: peak side lobe ratio PSLR and main lobe width MW;

Determining a first mathematical model of the NLFM signal according to the autocorrelation performance parameter as follows:

c_MW(B_c)≤0,-B/2≤B_c≤B/2

Wherein the content of the first and second substances,the characterization is solved by said B_cMinimum value of PSLR of the NLFM signal being a variable, B_cIs a frequency control point vector, c, of the NLFM signal_MW(B_c) Characterized by the fact that B_cA MW nonlinear inequality constraint of the NLFM signal that is a variable.

Determining cross-correlation energy of the NLFM signal according to the time domain function, wherein the cross-correlation energy is as follows:

ECC＝∫|S₁(f)|²|S₂(f)|²df

ECC is the cross-correlation energy, S, of the NLFM signal₁(f) Corresponding to NLFM signal S₁(t) spectrum of S₂(f) corresponding to NLFM signal S₂(t) spectrum.

determining a second mathematical model of the NLFM signal from the cross-correlation energy as:

c_MW(B_c)≤0,c_PSLR(B_c)≤0,-B/2≤B_c≤B/2

Wherein the content of the first and second substances,the characterization is solved by said B_cMinimum value of ECC of the NLFM signal as variable, c_MW(B_c) Characterized by the fact that B_cA MW non-linear inequality constraint of the NLFM signal as a variable, c_PSLR(B_c) Characterized by the fact that B_ca PSLR nonlinear inequality constraint of the NLFM signal being a variable.

ECC＝∫|S₁(f)|²|S₂(f)|²df

c_MW(B_c)≤0,-B/2≤B_c≤B/2

Wherein the content of the first and second substances,The characterization is solved by said B_cMinimum value of PSLR of the NLFM signal being a variable, B_cis a frequency control point vector, c, of the NLFM signal_MW(B_c) Characterized by the fact that B_cA MW nonlinear inequality constraint of the NLFM signal being a variable;

c_MW(B_c)≤0,c_PSLR(B_c)≤0,-B/2≤B_c≤B/2

In the foregoing solution, the iterating the initialized NLFM signal by using the augmented lagrangian genetic simulation annealing mixture algorithm according to the mathematical model includes:

Setting initialization iteration parameters;

According to the mathematical model, carrying out first iteration on the initialized NLFM signal by utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm to obtain a first NLFM signal and obtain a first iteration parameter corresponding to the initialized iteration parameter;

And continuously iterating the first NLFM signal by utilizing an augmented Lagrange genetic simulated annealing hybrid algorithm according to the mathematical model until the augmented Lagrange genetic simulated annealing hybrid algorithm converges.

In the foregoing scheme, the performing, according to the mathematical model, a first iteration on the initialized NLFM signal by using an augmented lagrangian genetic simulation annealing hybrid algorithm to obtain a first NLFM signal, and obtaining a first iteration parameter corresponding to the initialized iteration parameter includes:

determining an augmented Lagrange formula corresponding to the mathematical model by utilizing an augmented Lagrange algorithm according to the mathematical model;

Determining the fitness of the target NLFM signal according to the augmented Lagrange formula;

Carrying out selection processing of a genetic algorithm on the initialized NLFM signal to obtain a target NLFM signal;

According to the fitness, solving the target NLFM signal by using an augmented Lagrange genetic simulation annealing mixed algorithm to obtain an optimized target NLFM signal;

Determining a first iteration parameter corresponding to the initialization iteration parameter according to the augmented Lagrange formula;

and performing cross processing and mutation processing of the genetic algorithm on the optimization target NLFM signal to obtain a first NLFM signal.

in a second aspect, an apparatus for generating an orthogonal NLFM signal based on a hybrid algorithm is provided, the apparatus comprising:

The device comprises: the device comprises a first determining module, a second determining module, a setting module and an iteration module; wherein the content of the first and second substances,

The first determining module is used for determining a time-frequency relation function of the NLFM signal according to the piecewise linear function; determining a time domain function of the NLFM signal according to the time-frequency relation function;

The second determining module is configured to determine a relevant performance parameter of the NLFM signal according to the time domain function; determining a mathematical model of the NLFM signal according to the relevant performance parameters;

The setting module is used for setting an initialization signal according to the pulse width and the bandwidth of the NLFM signal;

And the iteration module is used for iterating the initialization NLFM signal by utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm according to the mathematical model to obtain an orthogonal NLFM signal.

in a third aspect, an apparatus for generating an orthogonal NLFM signal based on a hybrid algorithm is provided, the apparatus including: a processor and a memory for storing a computer program operable on the processor, wherein the processor is operable to perform the steps of the method of the first aspect when executing the computer program.

according to the orthogonal NLFM signal generation method and device based on the hybrid algorithm, provided by the embodiment of the invention, a time-frequency relation function of the NLFM signal is determined according to a piecewise linear function; determining a time domain function of the NLFM signal according to the time-frequency relation function; determining the relevant performance parameters of the NLFM signals according to the time domain function; determining a mathematical model of the NLFM signal according to the relevant performance parameters; initializing the NLFM signal according to the pulse width and bandwidth setting of the NLFM signal; according to the mathematical model, utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm to iterate the initialized NLFM signal to obtain an orthogonal NLFM signal; therefore, by adopting the orthogonal NLFM signal generation method based on the hybrid algorithm, the orthogonal NLFM signal with the same frequency band and large time width can be designed and obtained.

drawings

Fig. 1 is a first flowchart illustrating a method for generating an orthogonal NLFM signal based on a hybrid algorithm according to an embodiment of the present invention;

fig. 2 is a schematic flow chart of a method for generating an orthogonal NLFM signal based on a hybrid algorithm according to an embodiment of the present invention;

FIG. 3 is a diagram illustrating a time-frequency relationship represented by a piecewise linear function according to an embodiment of the present invention;

FIG. 4a is a first comparison graph of the frequency spectrum of an optimized NLFM signal according to the present invention;

FIG. 4b is a graph showing a comparison of the frequency spectrum of an optimized NLFM signal according to the present invention;

FIG. 5 is a schematic diagram of an optimized NLFM signal autocorrelation according to an embodiment of the present invention;

Fig. 6 is a schematic structural diagram of an apparatus for generating an orthogonal NLFM signal based on a hybrid algorithm according to an embodiment of the present invention;

Fig. 7 is a schematic structural diagram of an apparatus for generating an orthogonal NLFM signal based on a hybrid algorithm according to an embodiment of the present invention.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.

Fig. 1 is a schematic flow chart of a method for generating an orthogonal NLFM signal based on a hybrid algorithm according to an embodiment of the present invention, as shown in fig. 1, the method includes the following steps:

step 101: determining a time-frequency relation function of the NLFM signal according to the piecewise linear function; determining a time domain function of the NLFM signal according to the time-frequency relation function;

And determining a time-frequency relation function of the NLFM signal by utilizing the piecewise linear function, and determining a time-domain function of the NLFM signal according to the time-frequency relation function of the NLFM signal.

In an embodiment, the time-frequency relation function of the NLFM signal is determined according to a piecewise linear function; determining a time domain function of the NLFM signal according to the time-frequency relation function, wherein the time domain function comprises the following steps:

Defining the time-frequency relation coordinate of the NLFM signal as (T, f), wherein the pulse width of the NLFM signal is T corresponding to the time coordinate T of the time-frequency relation coordinate, the bandwidth of the NLFM signal is B corresponding to the frequency coordinate f of the time-frequency relation coordinate, dividing the pulse width and the bandwidth into 2n +2 sections of linear functions in the time-frequency relation coordinate, the time segmentation points are uniformly distributed, namely, the abscissa segmentation points, and 2n +3 time segmentation point vectors are as follows:Wherein the content of the first and second substances,is a known amount; defining 2n frequency control points in the time-frequency relation coordinate, and defining a frequency control point vector B_cComprises the following steps: b is_c＝[-B_2n,…,B₂₁,B₁₁,…,B_1n]^Tand corresponding 2n +3 frequency segmentation points, determining the time-frequency relation function of the NLFM signal according to the piecewise linear function as follows:

step 102: determining the relevant performance parameters of the NLFM signals according to the time domain function; determining a mathematical model of the NLFM signal according to the relevant performance parameters;

Determining the relevant performance parameters of the NLFM signal according to the time domain function includes: and determining autocorrelation energy parameters of the NLFM signals according to the time domain function, and determining cross-correlation energy of the NLFM signals according to the time domain function. Accordingly, determining a mathematical model of the NLFM signal from the correlation performance parameter includes: and determining a first mathematical model of the NLFM signal according to the autocorrelation energy parameters of the NLFM signal, and determining a second mathematical model of the NLFM signal according to the cross-correlation energy of the NLFM signal.

in one embodiment, the determining the relevant performance parameter of the NLFM signal according to the time domain function; determining a mathematical model of the NLFM signal from the correlation performance parameters, comprising:

c_MW(B_c)≤0,-B/2≤B_c≤B/2

Determining autocorrelation performance parameters of the NLFM signal according to the time domain function, wherein the autocorrelation performance parameters comprise: the peak side lobe ratio PSLR and the main lobe width MW are defined as follows:

1) PSLR: the ratio of the peak height of the highest side lobe to the peak height of the main lobe is dB,

2) MW: the magnitude of the 3dB main lobe width is typically normalized to the sample point.

according to the autocorrelation performance parameter of the NLFM signal: the first mathematical model for PSLR and MW determination of NLFM signals is:

In one embodiment, determining a relevant performance parameter of the NLFM signal according to the time domain function; determining a mathematical model of the NLFM signal from the correlation performance parameters, comprising:

ECC＝∫|S₁(f)|²|S₂(f)|²df

c_MW(B_c)≤0,c_PSLR(B_c)≤0,-B/2≤B_c≤B/2

determining the cross-correlation energy of the NLFM signal according to the time domain function as follows:

ECC＝∫|S₁(f)|²|S₂(f)|²df

From the cross-correlation energy of the NLFM signal: the second mathematical model for the ECC to determine the NLFM signal is:

ECC＝∫|S₁(f)|²|S₂(f)|²df

c_MW(B_c)≤0,-B/2≤B_c≤B/2

c_MW(B_c)≤0,c_PSLR(B_c)≤0,-B/2≤B_c≤B/2

Determining autocorrelation energy parameters and cross-correlation energy of the NLFM signal according to the time domain function, determining a first mathematical model of the NLFM signal according to the autocorrelation energy parameters of the NLFM signal, and determining a second mathematical model of the NLFM signal according to the cross-correlation energy of the NLFM signal.

step 103, initializing the NLFM signal according to the pulse width and the bandwidth setting of the NLFM signal;

And obtaining a time-frequency relation function of the NLFM signal by utilizing a piecewise linear function according to the pulse width and the bandwidth of the NLFM signal, further determining a frequency control point of the NLFM signal, and obtaining an initialized NLFM signal.

In practical applications, two sets of signals may be defined, the first set of signals corresponding to the first mathematical model and the second set of signals corresponding to the second mathematical model, and the first set of signals or the second set of signals may be set as the initialization NLFM signal.

step 104: and according to the mathematical model, utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm to iterate the initialized NLFM signal to obtain an orthogonal NLFM signal.

and according to the first mathematical model or the second mathematical model, performing iterative computation on the initialized NLFM signal by using an augmented Lagrange genetic simulation annealing hybrid algorithm to obtain an orthogonal NLFM signal.

In an embodiment, the iterating the initialized NLFM signal using an augmented lagrange genetic simulated annealing hybrid algorithm according to the mathematical model includes: setting initialization iteration parameters; according to the mathematical model, carrying out first iteration on the initialized NLFM signal by utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm to obtain a first NLFM signal and obtain a first iteration parameter corresponding to the initialized iteration parameter; and continuously iterating the first NLFM signal by utilizing an augmented Lagrange genetic simulated annealing hybrid algorithm according to the mathematical model until the augmented Lagrange genetic simulated annealing hybrid algorithm converges.

Wherein initializing the iteration parameters comprises: lagrange operator λ, offset s.

Performing first iteration on the initialized NLFM signal by utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm according to the first mathematical model or the second mathematical model to obtain a first NLFM signal and a first iteration parameter corresponding to the initialized iteration parameter; and continuously iterating the first NLFM signal by using an augmented Lagrange genetic simulation annealing mixed algorithm according to the first mathematical model or the second mathematical model, the obtained first NLFM signal and the obtained first iteration parameter until the augmented Lagrange genetic simulation annealing mixed algorithm is converged, wherein the NLFM signal obtained when the augmented Lagrange genetic simulation annealing mixed algorithm is converged is the orthogonal NLFM signal.

if the initialized NLFM signal is a second group of signals corresponding to the second mathematical model, performing first iteration on the second group of signals by using an augmented Lagrange genetic simulation annealing hybrid algorithm according to the second mathematical model to obtain a first NLFM signal and a first iteration parameter corresponding to the initialized iteration parameter; and continuously iterating the first NLFM signal by using an augmented Lagrange genetic simulation annealing mixed algorithm according to the second mathematical model, the obtained first NLFM signal and the obtained first iteration parameter until the augmented Lagrange genetic simulation annealing mixed algorithm is converged, wherein the NLFM signal obtained when the augmented Lagrange genetic simulation annealing mixed algorithm is converged is an orthogonal NLFM signal, namely an orthogonal second group of signals, and recalculating the first group of signals according to the orthogonal second group of signals to obtain the orthogonal first group of signals.

it should be noted that, when the optimization is performed by using the augmented lagrange genetic simulation annealing hybrid algorithm according to the first mathematical model or the second mathematical model, the optimization sequence of the signals may be changed, that is, the first group of signals may be optimized for the first time, and the second group of signals may be optimized for the second time.

In an embodiment, the performing, according to the mathematical model, a first iteration on the initialized NLFM signal by using an augmented lagrangian genetic simulation annealing hybrid algorithm to obtain a first NLFM signal, and obtaining a first iteration parameter corresponding to the initialized iteration parameter includes: determining an augmented Lagrange formula corresponding to the mathematical model by utilizing an augmented Lagrange algorithm according to the mathematical model; determining the fitness of the target NLFM signal according to the augmented Lagrange formula; carrying out selection processing of a genetic algorithm on the initialized NLFM signal to obtain a target NLFM signal; according to the fitness, solving the target NLFM signal by using an augmented Lagrange genetic simulation annealing mixed algorithm to obtain an optimized target NLFM signal; determining a first iteration parameter corresponding to the initialization iteration parameter according to the augmented Lagrange formula; and performing cross processing and mutation processing of the genetic algorithm on the optimization target NLFM signal to obtain a first NLFM signal.

Determining a first augmented Lagrange formula corresponding to the first mathematical model by utilizing an augmented Lagrange algorithm according to the first mathematical model; or determining a second augmented Lagrange formula corresponding to the second mathematical model by using an augmented Lagrange algorithm according to the second mathematical model.

The augmented Lagrange genetic algorithm is a popularization form of the genetic algorithm, and is an advanced algorithm which is combined with the genetic algorithm and the generalized Lagrange algorithm and solves complex constraint optimization.

The mathematical description is as follows:

wherein λ_iFor lagrange multipliers to be a non-negative number, s_iIs a non-negative number representing the overall offset to ensure that the logarithm has a non-zero true number, and p is a penalty factor, ceq_i(x) And c_i(x) Respectively representing equality constraint and nonlinear inequality constraint, f (x) is a fitness function, m represents the number of nonlinear constraints, and mt represents the total constraint number.

the first mathematical model requires that the side lobe is reduced as much as possible without widening the main lobe, that is, the autocorrelation performance is minimum, and then a first augmented lagrange formula corresponding to the first mathematical model is as follows:

Θ(B_c,λ,s)＝f(B_c)-λslog(s-c(B_c))

wherein, f (B)_c)＝PSLR(B_c) To control point B according to frequency_cPSLR, c (B) of the NLFM signal thus obtained_c)＝MW(B_c) To control point B according to frequency_cMW of NLFM signal found.

The second mathematical model requires that the cross-correlation energy is reduced under the condition of ensuring a certain main lobe width and peak side lobe height, that is, the cross-correlation energy is required to be minimum, and a second augmented lagrangian formula corresponding to the second mathematical model is as follows:

Θ(B_c,λ,s)＝f(B_c)-λ₁s₁log(s₁-c₁(B_c))-λ₂s₂log(s₂-c₂(B_c))

wherein, f (B)_c)＝ECC(B_c) To control point B according to frequency_ccross-correlation energy of the signals obtained, c₁(B_c)＝MW(B_c) To control point B according to frequency_cMW, c of the NLFM signal found₂(B_c)＝PSLR(B_c) To control point B according to frequency_cPSLR of the NLFM signal is obtained.

and carrying out selection processing of a genetic algorithm on the obtained initialized NLFM signal, and selecting a target NLFM signal. Genetic algorithms typically include selection processing, crossover processing, and mutation operations of chromosomes. The selection process selects chromosomes according to a rule that may be: the probability of the individual being selected is proportional to the magnitude of the fitness function value, for example, the Selection process may be Roulette Wheel Selection (RWS).

The basic idea of the wheel selection method is as follows: the probability of an individual being selected is proportional to the magnitude of its fitness function value. Assuming a population size N, an individual x_iHas a fitness of f (x)_i) Then the individual x_iThe selection probability of (2) is:

The wheel disc selection method comprises the following steps:

1) Generating a uniformly distributed random number r in [0, 1 ];

2) If r is less than or equal to q₁Then chromosome x_iSelecting the selected plants;

3) if q is_k-1<r≤q_k(2. ltoreq. k. ltoreq.N), then chromosome x_kSelecting the selected plants; wherein q is_ireferred to as chromosome x_i(i ═ 1, 2, …, N) and is calculated as:

and calculating the fitness of the initialized NLFM signal by utilizing a first augmented Lagrange formula or a second augmented Lagrange formula, and selecting a target NLFM signal from the initialized NLFM signal according to the step of the wheel disc selection algorithm.

Determining the fitness f (B) of the target NLFM signal according to the first augmented Lagrange formula or the second augmented Lagrange formula_c) (ii) a And solving the target NLFM signal by using a simulated annealing algorithm according to the obtained fitness to obtain an optimized target NLFM signal.

The simulated annealing algorithm is based on the solid annealing principle, has strong local searching capability, can reject the local extreme problem solution with a certain probability, and jumps out of the local extreme point to continue exploiting other state solutions of the state space.

The simulated annealing algorithm comprises the following steps:

1) calculating an objective function value by taking the target NLFM signal as an initial optimal point;

2) setting the initial temperature T₀iteration index k is 0, termination temperature T_fTemperature attenuation factor alpha, step factor epsilon, iteration termination Tolerance Tolerance at each temperature;

3) Randomly changing the current optimal point i by using a step factor epsilon to generate a new solution j epsilon D, calculating the increment of an objective function value delta f ═ f (j) -f (i), if the delta f is less than 0, accepting j as the current optimal solution i ═ j, and otherwise, entering a step 4);

4) f (i) is currently optimal, but accepts the currently poor point j with a certain probability p, p ═ exp { -. DELTA.f/T_kGet the random number r, r belongs to (0,1), if p>r, then accept i ═ j;

5) reaching a thermal equilibrium state, i.e. the inner iteration meets the termination tolerance, entering step 6), otherwise turning to step 3);

6) Lowering the current temperature T_k+1＝αT_kK is k +1, if T_k+1<T_fthe algorithm stops, otherwise go to step 3).

Here, the objective function f (i) may be a fitness function f (B) obtained according to the first augmented lagrangian formula or the second augmented lagrangian formula_c)。

determining a first iteration parameter corresponding to the initialization iteration parameter according to the first augmented Lagrange formula or the second augmented Lagrange formula, wherein the first iteration parameter comprises: lagrange operator λ and offset s.

In practical applications, λ and s are obtained using the following equations:

the parameter mu can be obtained according to a fitness function in the first augmented Lagrange formula or the second augmented Lagrange formula.

And performing cross processing and mutation processing of the genetic algorithm on the optimized target NLFM signal obtained by solving according to the simulated annealing algorithm to obtain a first NLFM signal.

In genetic algorithms, the total number of chromosomes is assumed to be K. In the crossover process, K random numbers are generated for K chromosomes. If the corresponding random number of the chromosome is lower than the cross probability r_cThis indicates that these chromosomes are selected for crossover processing. Here, 1 crossover operation was taken, the position of the crossover was randomly generated, and the father exchanged the gene at the crossover to generate a new chromosome.

Mutation processing is an operation in which a gene in a chromosome is changed, and the mutated gene is randomly selected. An NLFM signal can be regarded as a chromosome, and the number of genes per chromosome is 2n, so that the total number L of genes is 2 Kn. The number M of the variations is determined by the variation probability, specifically, M ═ r_mAnd L, randomly selecting M from the L to perform mutation operation, wherein the mutation operation is as follows:

p_k(j)＝p_k(i)*(1+rand)

Wherein p is_k(i) for chromosomes before mutation treatment, p_k(j) Rand is a random value for the mutated chromosome.

And processing the optimized target NLFM signal according to the processes of the cross processing and the mutation processing to obtain a first NLFM signal.

In the embodiment of the invention, a time-frequency relation function of the NLFM signal is determined according to the piecewise linear function; determining a time domain function of the NLFM signal according to the time-frequency relation function; determining the relevant performance parameters of the NLFM signals according to the time domain function; determining a mathematical model of the NLFM signal according to the relevant performance parameters; initializing the NLFM signal according to the pulse width and bandwidth setting of the NLFM signal; according to the mathematical model, utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm to iterate the initialized NLFM signal to obtain an orthogonal NLFM signal; therefore, the orthogonal performance of the signal can be improved under the condition of acceptable side lobe and main lobe width, the cross-correlation energy is suppressed, and the orthogonal NLFM signal with the same frequency band and large time width is obtained.

The present embodiment explains the method for generating an orthogonal NLFM signal based on a hybrid algorithm according to the present invention by using specific steps for generating the orthogonal NLFM signal.

Fig. 2 is a schematic flow chart illustrating an implementation process of a method for generating an orthogonal NLFM signal based on a hybrid algorithm according to an embodiment of the present invention, as shown in fig. 2, the method includes the following steps:

step 201: defining a time-frequency relation function of the NLFM signal by utilizing a piecewise linear function, and further defining an NLFM signal time-domain function;

And (t, f) defining the time-frequency relation coordinates of the NLFM signals in a Cartesian coordinate system. Assuming that the pulse width of the signal is T and the bandwidth of the signal is B, it is divided into 2n +2 segments of linear function, as shown in fig. 3. In the time-frequency plane, the time axis segment points, namely the abscissa segment points, are uniformly distributed, and 2n +3 time segment point vectorswherein In known amounts. Giving 2n frequency control point vectors B in a time-frequency relation coordinate plane_cComprises the following steps: b is_c＝[-B_2n,…,B₂₁,B₁₁,…,B_1n]^Tthen the corresponding 2n +3 frequency segmentation point vectors areGiven a piecewise point within the time-frequency relationship, the time-frequency relationship of the signal can be described by a piecewise linear function:

Wherein k is_1iand k_2ithe tuning frequency of each segment of the piecewise linear function is represented by formula (2) and formula (3)。

Then for an NLFM signal of amplitude a, the expression is:

f (t) is the frequency part corresponding to the whole time axis, and f₊(t) and f_-(t) two parts.

Step 202: defining a signal optimization index according to an autocorrelation function and cross-correlation performance of a signal;

The ideal performance of the autocorrelation function for NLFM signals is: a main lobe as narrow as possible, a PSLR as low as possible and a rapidly decreasing side lobe fluctuation envelope. However, these three desirable properties are not simultaneously satisfied. In general terms, the autocorrelation of an NLFM signal can be 3dB main lobe width and side lobe height, which are defined as:

1) peak Side Lobe Ratio (PSLR): the ratio of the peak height of the highest side lobe to the peak height of the main lobe is dB

2)3dB main lobe width (MW): the magnitude of the 3dB main lobe width is typically normalized to the sample point.

The primary optimization goal here is to construct an NLFM signal with good orthogonality, conventionally defining 2 signals S₁(t) and S₂(t) orthogonal, i.e. S₁(t) and S₂(t) has a cross-correlation of 0, as shown by:

According to the property of Fourier transform as

∫|S₁(f)S₂(f)|²df＝0 (7)

however, for the same-frequency band signal, this cannot be satisfied according to the energy conservation theorem, so equation (8) is defined as an evaluation index of the quadrature performance:

ECC＝∫|S₁(f)|²|S₂(f)|²df (8)

Where ECC represents the cross-correlation energy (S)₁(f) corresponding to NLFM signal S₁(t) spectrum of S₂(f) corresponding to NLFM signal S₂(t) spectrum.

As can be seen from the definitions of equations (1) to (4), the control point determines the specific format of the NLFM signal. Once the number of frequency control points is determined, the abscissa segment points t_sAre uniformly distributed on the time axis and are known quantities. NLFM signal can be controlled by B containing 2n frequency control points_sAnd (5) vector definition. So that the performance indexes of the auto-correlation and the cross-correlation can be controlled by B of 2n frequency control points_sVector definition, in other words it is B_sAs a function of (c).

step 203: determining a first mathematical optimization model;

Here, two sets of signals are needed, and regarding the first set of signals, the autocorrelation signal characteristics, namely, the main lobe width and the side lobe height, need to be reduced as much as possible under the condition that the main lobe is not widened, which is a nonlinear constraint optimization problem and can be described as follows:

step 204: determining a second mathematical optimization model;

Concerning the cross-correlation signal characteristic, namely cross-correlation energy ECC, for the second group of signals, it is necessary to guarantee the main lobe width and the side lobe height, which is a nonlinear constraint optimization problem, and the problem can be described as follows:

Step 205: optimizing autocorrelation performance according to a first mathematical optimization model; optimizing cross-correlation orthogonal performance according to a second mathematical optimization model;

for the first group of signals, the performance of the autocorrelation is emphasized, and for the second group of signals, the performance of the cross-correlation is emphasized, so that according to the designed first group of signals and second group of signals, the second group of signals can be further used as initialization signals to optimize the cross-correlation orthogonal performance, and the first group of optimized signals can be recalculated to obtain better orthogonal performance.

Step 206: and optimizing by using an augmented Lagrange genetic simulation annealing hybrid algorithm according to the first mathematical optimization model or the second mathematical optimization model to obtain an optimal signal.

The mathematical description is as follows:

in designing the first set of optimized signals, it is desirable to reduce the side lobes as much as possible without widening the main lobe, and the problem can be described as:

Θ(B_c,λ,s)＝f(B_c)-λslog(s-c(B_c)) (12)

in designing the second set of optimized signals, it is required to reduce the cross-correlation energy as much as possible while ensuring a certain main lobe width and peak side lobe height, and this problem can be described as:

Θ(B_c,λ,s)＝f(B_c)-λ₁s₁log(s₁-c₁(B_c))-λ₂s₂log(s₂-c₂(B_c)) (13)

Wherein, f (B)_c)＝ECC(B_c) To control point B according to frequency_cCross-correlation energy of the NLFM signal, c₁(B_c)＝MW(B_c) To control point B according to frequency_cMW, c of the NLFM signal found₂(B_c)＝PSLR(B_c) To control point B according to frequency_cPSLR of the NLFM signal is obtained.

the augmented Lagrange genetic simulated annealing hybrid algorithm divides the specific solving problem into two parts: one part is a mixed algorithm of a traditional genetic algorithm and a simulated annealing algorithm, and the other part is an augmented Lagrange algorithm. The augmented Lagrangian algorithm is used to solve the constraint problem, and λ and s are continually updated according to equation (14).

Genetic algorithms model the optimization problem as a dynamic optimization process of natural selection of "survival of the fittest". In the search space, the chromosomes represent the variables to be determined for a particular solution problem, and genetic algorithms typically include selection, intersection and mutation operations of the chromosomes. Firstly, the variables are coded according to the solved problem, and the chromosomes are selected according to a certain rule by the chromosome moderation according to the objective function value. Secondly, the selected chromosome pair is based on the mating probability r_cPerforming cross generation to generate offspring; finally, according to a certain mutation probability r_mMutation operations are performed on genes of chromosomes to generate new individuals in the search variable space. Updating throughout the iterationIn the optimization process, the probability that the chromosome individual with high fitness is selected to generate the offspring is high, and the individual with poor fitness is replaced by the offspring with better fitness.

The simulated annealing algorithm is based on the solid annealing principle, so that the equilibrium state can be reached at each temperature, the ground state is finally reached, the local searching capability of the simulated annealing algorithm is very strong, the solution of the local extreme value problem can be rejected with a certain probability, and the solution of other states of the state space can be continuously exploited by jumping out of the local extreme value point. Each chromosome can be optimized by using a simulated annealing algorithm, the diversity of the whole population is increased, and the early trapping of a genetic algorithm into local search is avoided.

Aiming at NLFM signal optimization, regarding a genetic algorithm operation part, in a problem coding process, each chromosome is regarded as a control point vector B containing 2n frequency components_cSelecting an initialization signal, possibly for a control point vector B_cAnd initializing each parameter of the algorithm.

The invention adopts a Roulette Wheel Selection (RWS) method to select parents to carry out a crossing process. Assume that the total number of chromosomes selected is K. During the crossover process, K random numbers are generated for the K chromosomes first. If the corresponding random number of the chromosome is lower than the cross probability r_cThis indicates that these chromosomes are selected for crossover operations. Here, 1 crossover operation is taken, and the position of the crossover point is randomly generated. Paternal exchanges genes at crossover points to generate new chromosomes. Mutation is an operation in which a gene in a chromosome is changed. The mutated genes were randomly selected. When the number of genes per chromosome is 2n due to NLFM signal optimization, the total number L of genes is 2 Kn. The number M of the variations is determined by the variation probability, specifically, M ═ r_mand L. Randomly selecting M in L to carry out mutation operation, wherein the mutation operation is as follows:

p_k(i)＝p_k(i)*(1+rand) (15)

After all genetic operations and selection operations are carried out for N times, simulated annealing operations are carried out on all chromosomes, so that the fitness corresponding to the chromosomes is higher, and the diversity of the population is increased. The simulated annealing algorithm for each chromosome operates as follows:

Step 1: taking the current chromosome as an initial optimal point, and calculating an objective function value;

Step 2: setting the initial temperature T₀Iteration index k is 0, termination temperature T_fTemperature attenuation factor alpha, step factor epsilon, iteration termination Tolerance Tolerance at each temperature;

And step 3: randomly changing a current optimal point i by using a step factor to generate a new solution j epsilon D, calculating a function value increment delta f ═ f (j) -f (i), and if delta f is less than 0, receiving j as the current optimal solution i ═ j; otherwise, entering step 4;

And 4, step 4: f (i) is currently optimal, but accepts the currently poor point j with a certain probability p, p ═ exp { -. DELTA.f/T_k}, generating a random number r epsilon (0,1) if p>r, then accept i ═ j;

And 5: lowering the current temperature T_k+1＝αT_kK is k +1, if T_k+1<T_fThe algorithm stops, otherwise it goes to step 3.

In summary, the NLFM orthogonal signal design process based on the augmented lagrange genetic simulation annealing hybrid algorithm can be summarized as follows:

Step 1: initializing algorithm parameters: setting initialization algorithm parameters: number of chromosomes n, crossover probability r_cProbability of variation r_mlagrange operator λ, offset s;

Step 2: based on the principle of stationary phase, generating an initialization NLFM signal to obtain an initialization frequency control point B thereof_ci.e. initializing chromosomes;

And step 3: and (3) determining a corresponding NLFM signal according to the formulas (1) to (4) for the control point represented by each chromosome, and then calculating the fitness of the chromosome according to the formula (12) or the formula (13) of a mathematical optimization model. Calculating the next optimized lambda and the offset s by using an augmented Lagrange algorithm according to the formula (12) or the formula (13);

and 4, step 4: chromosomes were selected according to the roulette selection method. Judging whether N times of genetic and selection operations are performed, if so, entering a step 5;

And 5: optimizing all selected chromosomes by a simulated annealing algorithm;

Step 6: according to the cross probability r_cperforming a cross point crossing operation;

and 7: according to the variation probability r_mPerforming a mutation operation of formula (15);

and 8: and (5) circulating the steps 3 to 7 until the algorithm is converged.

The embodiment describes a method for generating an orthogonal NLFM signal based on a hybrid algorithm according to a specific optimization effect.

the flow of the method for designing and optimizing the NLFM orthogonal signal comprises the following steps:

Firstly, defining a time-frequency relation function of an NLFM signal by utilizing a piecewise linear function, and further defining an NLFM signal time-domain function;

secondly, defining a signal optimization mathematical model according to the performances of the autocorrelation and cross-correlation functions of the signals;

Then, according to the optimized mathematical model, optimizing by utilizing an augmented Lagrange genetic simulated annealing hybrid algorithm to obtain an optimal signal;

And finally, if the optimized signals do not meet the optimization requirements, further taking the second group of signals as initialization signals to optimize cross-correlation orthogonal performance, and recalculating the first group of optimized signals to obtain better orthogonal performance.

such as: the pulse width of the linear frequency modulation signal and the NLFM signal is 20us, the bandwidth is 300MHz, the sampling frequency is 400MHz, and the optimization results of the linear frequency modulation signal and the NLFM signal are shown in the following table:

it can be seen that the cross-correlation energy of the orthogonal NLFM signal optimally designed by the present invention can be suppressed by 5.3dB compared with the chirp signal. Fig. 4a and 4b show the frequency spectrums of the quadrature NLFM signal and the chirp signal, and it can be seen that the quadrature NLFM signal and the chirp signal have the same frequency spectrum width and are in the same frequency band. Fig. 5 is the autocorrelation function of the optimized NLFM signal, with sidelobe heights of-23.2 dB and-19.2 dB, and main lobe widths of 1.2 and 1.1, respectively, which can be seen to have acceptable sidelobe and main lobe widths.

As can be seen from the above description, the method provided by the embodiment of the present invention can effectively design and optimize the orthogonal NLFM signal, which is in the same frequency band and has acceptable main lobe width and side lobe height.

in the present embodiment, there is provided an apparatus for generating an orthogonal NLFM signal based on a hybrid algorithm, as shown in fig. 6, the apparatus 60 for generating an orthogonal NLFM signal includes: a first determining module 601, a second determining module 602, and a setting module 603; and an iteration module 604; wherein the content of the first and second substances,

A first determining module 601, configured to determine a time-frequency relationship function of the NLFM signal according to a piecewise linear function; determining a time domain function of the NLFM signal according to the time-frequency relation function;

A second determining module 602, configured to determine a relevant performance parameter of the NLFM signal according to the time domain function; determining a mathematical model of the NLFM signal according to the relevant performance parameters;

a setting module 603, configured to set an initialization NLFM signal according to a pulse width and a bandwidth of the NLFM signal;

And the iteration module 604 is configured to iterate the initialized NLFM signal by using an augmented lagrangian genetic simulation annealing hybrid algorithm according to the mathematical model to obtain an orthogonal NLFM signal.

in an embodiment, the first determining module 601 is further configured to: defining the time-frequency relation coordinate of the NLFM signal as (T, f), wherein the pulse width of the NLFM signal is T corresponding to the time coordinate T of the time-frequency relation coordinate, the bandwidth of the NLFM signal is B corresponding to the frequency coordinate f of the time-frequency relation coordinate, dividing the pulse width and the bandwidth into 2n +2 sections of linear functions in the time-frequency relation coordinate, the time segmentation points are uniformly distributed, namely, the abscissa segmentation points, and 2n +3 time segmentation point vectors are as follows:

Wherein the content of the first and second substances,Is a known amount; defining 2n frequency control points in the time-frequency relation coordinate, and defining a frequency control point vector B_cComprises the following steps: b is_c＝[-B_2n,…,B₂₁,B₁₁,…,B_1n]^TAnd corresponding 2n +3 frequency segmentation points, determining the time-frequency relation function of the NLFM signal according to the piecewise linear function as follows:

in an embodiment, the second determining module 602 is further configured to: determining autocorrelation performance parameters of the NLFM signal according to the time domain function, wherein the autocorrelation performance parameters comprise: peak side lobe ratio PSLR and main lobe width MW;

c_MW(B_c)≤0,-B/2≤B_c≤B/2

In an embodiment, the second determining module 602 is further configured to: determining cross-correlation energy of the NLFM signal according to the time domain function, wherein the cross-correlation energy is as follows:

ECC＝∫|S₁(f)|²|S₂(f)|²df

c_MW(B_c)≤0,c_PSLR(B_c)≤0,-B/2≤B_c≤B/2

In an embodiment, the second determining module 602 is further configured to: determining autocorrelation performance parameters of the NLFM signal according to the time domain function, wherein the autocorrelation performance parameters comprise: peak side lobe ratio PSLR and main lobe width MW; determining cross-correlation energy of the NLFM signal according to the time domain function, wherein the cross-correlation energy is as follows:

ECC＝∫|S₁(f)|²|S₂(f)|²df

c_MW(B_c)≤0,-B/2≤B_c≤B/2

c_MW(B_c)≤0,c_PSLR(B_c)≤0,-B/2≤B_c≤B/2

in an embodiment, the iteration module 604 is further configured to: setting initialization iteration parameters; according to the mathematical model, carrying out first iteration on the initialized NLFM signal by utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm to obtain a first NLFM signal and obtain a first iteration parameter corresponding to the initialized iteration parameter; and continuously iterating the first NLFM signal by utilizing an augmented Lagrange genetic simulated annealing hybrid algorithm according to the mathematical model until the augmented Lagrange genetic simulated annealing hybrid algorithm converges.

in an embodiment, the iteration module 604 is further configured to: determining an augmented Lagrange formula corresponding to the mathematical model by utilizing an augmented Lagrange algorithm according to the mathematical model; determining the fitness of the target NLFM signal according to the augmented Lagrange formula; carrying out selection processing of a genetic algorithm on the initialized NLFM signal to obtain a target NLFM signal; according to the fitness, solving the target NLFM signal by using an augmented Lagrange genetic simulation annealing mixed algorithm to obtain an optimized target NLFM signal; determining a first iteration parameter corresponding to the initialization iteration parameter according to the augmented Lagrange formula; and performing cross processing and mutation processing of the genetic algorithm on the optimization target NLFM signal to obtain a first NLFM signal.

it should be noted that, when the apparatus for generating an orthogonal NLFM signal based on a hybrid algorithm provided in the above embodiments generates an orthogonal NLFM signal, the division of the above program modules is merely exemplified, and in practical applications, the above processing may be distributed to different program modules according to needs, that is, the internal structure of the apparatus may be divided into different program modules to complete all or part of the above-described processing.

Based on the foregoing embodiments, the present invention provides a hybrid algorithm based orthogonal NLFM apparatus, as shown in fig. 7, which includes a processor 702 and a memory 701 for storing a computer program capable of running on the processor 702; wherein the processor 702 is configured to implement, when running the computer program, the following:

the method disclosed in the above embodiments of the present invention may be applied to the processor 702, or implemented by the processor 702. The processor 702 may be an integrated circuit chip having signal processing capabilities. In implementation, the steps of the above method may be implemented by integrated logic circuits of hardware or instructions in the form of software in the processor 702. The processor 702 described above may be a general purpose processor, a DSP, or other programmable logic device, discrete gate or transistor logic device, discrete hardware components, or the like. The processor 702 may implement or perform the methods, steps, and logic blocks disclosed in embodiments of the present invention. A general purpose processor may be a microprocessor or any conventional processor or the like. The steps of the method disclosed by the embodiment of the invention can be directly implemented by a hardware decoding processor, or can be implemented by combining hardware and software modules in the decoding processor. The software modules may be located in a storage medium located in the memory 701, and the processor 702 reads the information in the memory 701 to complete the steps of the foregoing method in combination with the hardware thereof.

it will be appreciated that the memory of embodiments of the invention, memory 701, may be either volatile memory or nonvolatile memory, and may include both volatile and nonvolatile memory. The nonvolatile Memory may be a Read Only Memory (ROM), a Programmable Read Only Memory (PROM), an Erasable Programmable Read Only Memory (EPROM), an Electrically Erasable Programmable Read Only Memory (EEPROM), a magnetic random access Memory (FRAM), a Flash Memory (Flash Memory), a magnetic surface Memory, an optical Disc, or a Compact Disc Read Only Memory (CD-ROM); the magnetic surface storage may be disk storage or tape storage. Volatile Memory can be Random Access Memory (RAM), which acts as external cache Memory. By way of illustration and not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Synchronous Static Random Access Memory (SSRAM), Dynamic Random Access Memory (DRAM), Synchronous Dynamic Random Access Memory (SDRAM), Double Data Rate Synchronous Dynamic Random Access Memory (DDRSDRAM, Double Data Synchronous Random Access Memory), Enhanced Synchronous Dynamic Random Access Memory (ESDRAM, Enhanced Synchronous Dynamic Random Access Memory), Synchronous link Dynamic Random Access Memory (SLDRAM, Synchronous Dynamic Random Access Memory), Direct Memory bus (DRmb Access Memory, Random Access Memory). The described memory for embodiments of the present invention is intended to comprise, without being limited to, these and any other suitable types of memory.

here, it should be noted that: the description of the terminal embodiment is similar to the description of the method, and has the same beneficial effects as the method embodiment, and therefore, the description is omitted. For technical details that are not disclosed in the terminal embodiment of the present invention, those skilled in the art should refer to the description of the method embodiment of the present invention to understand that, for brevity, detailed description is omitted here.

in an exemplary embodiment, the embodiment of the present invention further provides a computer storage medium, that is, a computer readable storage medium, for example, a memory 701 storing a computer program, which can be processed by the processor 702 to implement the steps of the foregoing method. The computer readable storage medium may be Memory such as FRAM, ROM, PROM, EPROM, EEPROM, Flash Memory, magnetic surface Memory, optical disk, or CD-ROM.

an embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, where the computer program, when processed by a processor, implements:

here, it should be noted that: the above description of the computer medium embodiment is similar to the above description of the method, and has the same beneficial effects as the method embodiment, and therefore, the description thereof is omitted. For technical details that are not disclosed in the terminal embodiment of the present invention, those skilled in the art should refer to the description of the method embodiment of the present invention to understand that, for brevity, detailed description is omitted here.

The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention.

Claims

1. A quadrature nonlinear frequency modulation (NLFM) signal generation method based on a hybrid algorithm is characterized by comprising the following steps:

According to the mathematical model, utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm to iterate the initialized NLFM signal to obtain an orthogonal NLFM signal;

Determining a time-frequency relation function of the NLFM signal according to the piecewise linear function; determining a time domain function of the NLFM signal according to the time-frequency relation function, wherein the time domain function comprises the following steps:

Defining the time-frequency relation coordinate of the NLFM signal as (T, f), wherein the pulse width of the NLFM signal is T corresponding to the time coordinate T of the time-frequency relation coordinate, the bandwidth of the NLFM signal is B corresponding to the frequency coordinate f of the time-frequency relation coordinate, the pulse width and the bandwidth are divided into 2n +2 sections of linear functions in the time-frequency relation coordinate, time segmentation points are uniformly distributed, and 2n +3 time segmentation point vectors are as follows:wherein the content of the first and second substances,Is a known amount; defining 2n frequency control points in the time-frequency relation coordinate, and defining a frequency control point vector B_ccomprises the following steps: b is_c＝[-B_2n,...,B₂₁,B₁₁,...,B_1n]^TAnd corresponding to 2n +3 frequency segmentation points, determining the time-frequency relation function of the NLFM signal according to the piecewise linear function as follows:

2. the method of claim 1, wherein the determining the relevant performance parameters of the NLFM signal according to the time domain function; determining a mathematical model of the NLFM signal from the correlation performance parameters, comprising:

such that

c_MW(B_c)≤0,-B/2≤B_c≤B/2

3. The method of claim 1, wherein the determining the relevant performance parameters of the NLFM signal according to the time domain function; determining a mathematical model of the NLFM signal from the correlation performance parameters, comprising:

ECC＝∫|S₁(f)|²|S₂(f)|²df

ECC is the cross-correlation energy, S, of the NLFM signal₁(f) Corresponding to NLFM signal S₁(t) spectrum of S₂(f) Corresponding to NLFM signal S₂(t) frequency spectrum；

such that

c_MW(B_c)≤0,c_PSLR(B_c)≤0,-B/2≤B_c≤B/2

4. The method of claim 1, wherein the determining the relevant performance parameters of the NLFM signal according to the time domain function; determining a mathematical model of the NLFM signal from the correlation performance parameters, comprising:

ECC＝∫|S₁(f)|²|S₂(f)|²df

ECC is the cross-correlation energy, S, of the NLFM signal₁(f) Corresponding to NLFM signal S₁(t) spectrum of S₂(f) Corresponding to NLFM signal S₂(t) spectrum of frequencies;

such that

c_MW(B_c)≤0,-B/2≤B_c≤B/2

such that

c_MW(B_c)≤0,c_PSLR(B_c)≤0,-B/2≤B_c≤B/2

5. The method of claim 1, wherein said iterating said initializing NLFM signal according to said mathematical model using an augmented lagrangian genetic simulated annealing hybrid algorithm comprises:

Setting initialization iteration parameters;

6. the method according to any one of claims 2 to 5, wherein the performing a first iteration on the initialized NLFM signal according to the mathematical model by using an augmented Lagrangian genetic simulation annealing hybrid algorithm to obtain a first NLFM signal and obtain a first iteration parameter corresponding to the initialized iteration parameter comprises:

7. An apparatus for generating an orthogonal non-chirp (NLFM) signal based on a hybrid algorithm, the apparatus comprising: the device comprises a first determining module, a second determining module, a setting module and an iteration module; wherein the content of the first and second substances,

The iteration module is used for iterating the initialization NLFM signal by utilizing an augmented Lagrange genetic simulation annealing hybrid algorithm according to the mathematical model to obtain an orthogonal NLFM signal;

the first determining module is further configured to define a time-frequency relationship coordinate of the NLFM signal as (T, f), the pulse width of the NLFM signal is T, which corresponds to the time-frequency relationship coordinate T, the bandwidth of the NLFM signal is B, which corresponds to the frequency coordinate f of the time-frequency relationship coordinate, the pulse width and the bandwidth are divided into 2n +2 linear functions in the time-frequency relationship coordinate, the time segment points are uniformly distributed, and 2n +3 time segment point vectors are:Wherein the content of the first and second substances,is a known amount; defining 2n frequency control points in the time-frequency relation coordinate, and defining a frequency control point vector B_cComprises the following steps: b is_c＝[-B_2n,...,B₂₁,B₁₁,...,B_1n]^TAnd corresponding to 2n +3 frequency segmentation points, determining the time-frequency relation function of the NLFM signal according to the piecewise linear function as follows:

8. an apparatus for generating orthogonal non-chirp (NLFM) signals based on a hybrid algorithm, comprising a processor and a memory for storing a computer program capable of running on the processor; wherein the processor is adapted to perform the steps of the method of any one of claims 1 to 6 when running the computer program.