CN109343058A - Nonlinear Orthogonal FM signal generation method and device based on hybrid algorithm - Google Patents

Nonlinear Orthogonal FM signal generation method and device based on hybrid algorithm Download PDF

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CN109343058A
CN109343058A CN201811290686.7A CN201811290686A CN109343058A CN 109343058 A CN109343058 A CN 109343058A CN 201811290686 A CN201811290686 A CN 201811290686A CN 109343058 A CN109343058 A CN 109343058A
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nlfm signal
nlfm
signal
time
frequency
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CN109343058B (en
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金国栋
王宇
邓云凯
刘开雨
王伟
龙雅君
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Institute of Electronics of CAS
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G01S13/08—Systems for measuring distance only
    • G01S13/32—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated
    • G01S13/34—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated using transmission of continuous, frequency-modulated waves while heterodyning the received signal, or a signal derived therefrom, with a locally-generated signal related to the contemporaneously transmitted signal
    • G01S13/345—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated using transmission of continuous, frequency-modulated waves while heterodyning the received signal, or a signal derived therefrom, with a locally-generated signal related to the contemporaneously transmitted signal using triangular modulation

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Abstract

The embodiment of the invention discloses a kind of Nonlinear Orthogonal frequency modulation NLFM signal creating method and device based on hybrid algorithm, which comprises the relationship between frequency and time function of NLFM signal is determined according to piecewise linear function；The time-domain function of the NLFM signal is determined according to the relationship between frequency and time function；The correlation performance parameters of the NLFM signal are determined according to the time-domain function；The mathematical model of the NLFM signal is determined according to the correlation performance parameters；NLFM signal is initialized according to the pulse width of the NLFM signal and with width setting；According to the mathematical model, the initialization NLFM signal is iterated using augmentation Lagrange genetic simulated annealing hybrid algorithm, obtains orthogonal NLFM signal；The generating means of the embodiment of the invention also discloses a kind of orthogonal NLFM signal based on hybrid algorithm.

Description

Nonlinear Orthogonal FM signal generation method and device based on hybrid algorithm
Technical field
The present embodiments relate to fields of communication technology, relate to, but are not limited to a kind of Nonlinear Orthogonal based on hybrid algorithm The generation method and device of frequency modulation (Non-linear frequency modulation, NLFM) signal.
Background technique
Synthetic aperture radar (Synthetic Aperture Radar, SAR) can round-the-clock, it is round-the-clock, the whole world over the ground Observation, is widely used, but it is limited to two basic problems:
1, the constraint of resolution ratio and mapping bandwidth: azimuth resolution is higher, it is meant that pulse recurrence frequency (pulse Repetition frequency, PRF) it is higher, selectable mapping band is narrower, so azimuth resolution and distance are to survey Drawing bandwidth cannot improve simultaneously.
2, the constraint relationship of azimuth ambiguity and range ambiguity: PRF is higher, i.e. orientation over-sampling is big, and azimuth ambiguity is smaller, Corresponding meeting to be received by higher secondary lobe, so that range ambiguity is bigger, thus may be used so that range ambiguity offset signaling zone is closer Know, it is in shifting relationship that azimuth ambiguity and range ambiguity, which are medium using PRF,.
In the application of general satellite-borne SAR, orientation band is roomy, PRF high, in order to guarantee mapping swath width, over-sampling rate Low, general over-sampling rate is 1.2, so its range ambiguity and azimuth ambiguity exist simultaneously, is influenced serious.It is general in the related technology Inhibit range ambiguity by the way of alternate emission orthogonal signalling, but for example positive and negative FM signal of traditional orthogonal signalling, Cross-correlation energy is broken up to entire time domain, but energy does not disappear.The image of SAR is distributed object, so its energy It can accumulate, so that fuzzy energy does not have reduction.In addition, orthogonal signalling design or multiple-input and multiple-output (Multi- Input Multi-Output, MIMO) SAR system realize critical issue, need to separate waveform, thus inhibit not Crosstalk energy between same waveform.
Existing orthogonal signalling generally have following problem: 1) it is in short-term orthogonal, but energy can accumulated distally, energy It is not reduced, such as orthogonal signalling in short-term；2) orthogonal signalling do not export same frequency range；3) discrete signal is not suitable for distribution field Scape.
NLFM signal can construct relationship between frequency and time, to construct power spectrum, realize the energy distribution in entire frequency band, It is possible to mutually filtering, so that cross-correlation energy reduces.There is following advantage by the signal of NLFM Design of Signal: 1) with frequency Band；2) overall cross-correlation energy decline；3) continuous signal is used in distributed scene.
The research interest of NLFM signal is concentrated mainly on the autocorrelation performance index such as peak sidelobe ratio of signal at present (PSLR), 3dB main lobe width (MW) integrates the optimization design and its application of secondary lobe ratio (ISLR), and design class method mainly has: 1) it is based on principle in phase bit, by designing specific window function, and then acquires complete signal；2) some optimization sides are based on The power spectrum of the specific window function of method such as least square approximation；3) to overcome NLFM to Doppler frequency domain sensitive issue, pass through width It spends adding window combination first method and designs NLFM signal, however the above method is all not concerned with the orthogonal potentiality of NLFM signal.
In conclusion how under acceptable side lobe height and main lobe width the NLFM orthogonal signalling of design optimization are SAR radar inhibits range ambiguity and solves urgent problem to be solved in the design of MIMO-SAR system at present.
Summary of the invention
In view of this, the generation method of an embodiment of the present invention is intended to provide a kind of orthogonal NLFM signal based on hybrid algorithm And device, can under acceptable secondary lobe and main lobe width promotion signal orthogonal performance, inhibit cross-correlation energy.
The technical solution of the embodiment of the present invention is achieved in that
In a first aspect, providing a kind of orthogonal NLFM signal creating method and device based on hybrid algorithm, the method Include:
The relationship between frequency and time function of NLFM signal is determined according to piecewise linear function；Institute is determined according to the relationship between frequency and time function State the time-domain function of NLFM signal；
The correlation performance parameters of the NLFM signal are determined according to the time-domain function；It is true according to the correlation performance parameters The mathematical model of the fixed NLFM signal；
NLFM signal is initialized according to the pulse width of the NLFM signal and with width setting；
According to the mathematical model, using augmentation Lagrange genetic simulated annealing hybrid algorithm to the initialization NLFM Signal is iterated, and obtains orthogonal NLFM signal.
In the above scheme, the relationship between frequency and time function that the NLFM signal is determined according to piecewise linear function；According to The relationship between frequency and time function determines the time-domain function of the NLFM signal, comprising:
The relationship between frequency and time coordinate of the NLFM signal is defined as (t, f), the pulse width of the NLFM signal is corresponding for T In the time coordinate t of the relationship between frequency and time coordinate, the bandwidth of the NLFM signal is the frequency that B corresponds to the relationship between frequency and time coordinate The pulse width and the bandwidth are divided into 2n+2 sections of linear functions, time point in the relationship between frequency and time coordinate by rate coordinate f Section point is uniformly distributed, 2n+3 time slice point vector are as follows:Wherein,For known quantity；In the relationship between frequency and time coordinate Define 2n frequency control point, frequency control point vector BcAre as follows: Bc=[- B2n,…,B21,B11,…,B1n]T, corresponding 2n+3 frequency Rate waypoint then determines the relationship between frequency and time function of the NLFM signal according to piecewise linear function are as follows:
Wherein, k1iCharacterization is by frequency segmentation pointWith time slice point Each section of frequency modulation rate of the piecewise linear function of composition, k2iCharacterization is by frequency segmentation pointAnd when Between waypointEach section of frequency modulation rate of the piecewise linear function of composition, the frequency modulation rate are as follows:
Determine that amplitude is the time-domain function of the NLFM signal of A according to the relationship between frequency and time function of the NLFM signal are as follows:
In the above scheme, the correlation performance parameters that the NLFM signal is determined according to the time-domain function；According to The correlation performance parameters determine the mathematical model of the NLFM signal, comprising:
The autocorrelation performance parameter of the NLFM signal, the autocorrelation performance parameter packet are determined according to the time-domain function It includes: peak sidelobe ratio PSLR and main lobe width MW；
The first mathematical model of the NLFM signal is determined according to the autocorrelation performance parameter are as follows:
cMW(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the PSLR of the NLFM signal of variable, BcFor The frequency control point vector of the NLFM signal, cMW(Bc) characterize with the BcMW for the NLFM signal of variable is non-linear Inequality constraints.
In the above scheme, the correlation performance parameters that the NLFM signal is determined according to the time-domain function；According to The correlation performance parameters determine the mathematical model of the NLFM signal, comprising:
The cross-correlation energy of the NLFM signal, the cross-correlation energy are determined according to the time-domain function are as follows:
ECC=∫ | S1(f)|2|S2(f)|2df
ECC is the cross-correlation energy of the NLFM signal, S1(f) corresponding NLFM signal S1(t) frequency spectrum, S2(f) corresponding NLFM signal S2(t) frequency spectrum.
The second mathematical model of the NLFM signal is determined according to the cross-correlation energy are as follows:
cMW(Bc)≤0,cPSLR(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the ECC of the NLFM signal of variable, cMW (Bc) characterize with the BcFor the MW nonlinear complementary problem of the NLFM signal of variable, cPSLR(Bc) characterize with the BcFor The PSLR nonlinear complementary problem of the NLFM signal of variable.
In the above scheme, the correlation performance parameters that the NLFM signal is determined according to the time-domain function；According to The correlation performance parameters determine the mathematical model of the NLFM signal, comprising:
The autocorrelation performance parameter of the NLFM signal, the autocorrelation performance parameter packet are determined according to the time-domain function It includes: peak sidelobe ratio PSLR and main lobe width MW；
The cross-correlation energy of the NLFM signal, the cross-correlation energy are determined according to the time-domain function are as follows:
ECC=∫ | S1(f)|2|S2(f)|2df
ECC is the cross-correlation energy of the NLFM signal, S1(f) corresponding NLFM signal S1(t) frequency spectrum, S2(f) corresponding NLFM signal S2(t) frequency spectrum.
The first mathematical model of the NLFM signal is determined according to the autocorrelation performance parameter are as follows:
cMW(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the PSLR of the NLFM signal of variable, BcFor The frequency control point vector of the NLFM signal, cMW(Bc) characterize with the BcMW for the NLFM signal of variable is non-linear Inequality constraints；
The second mathematical model of the NLFM signal is determined according to the cross-correlation energy are as follows:
cMW(Bc)≤0,cPSLR(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the ECC of the NLFM signal of variable, cMW (Bc) characterize with the BcFor the MW nonlinear complementary problem of the NLFM signal of variable, cPSLR(Bc) characterize with the BcFor The PSLR nonlinear complementary problem of the NLFM signal of variable.
In the above scheme, described according to the mathematical model, it is mixed and is calculated using augmentation Lagrange genetic simulated annealing Method is iterated the initialization NLFM signal, comprising:
Setting initialization iterative parameter；
According to the mathematical model, using augmentation Lagrange genetic simulated annealing hybrid algorithm to the initialization NLFM Signal carries out first time iteration, obtains the first NLFM signal, and obtains the corresponding first iteration ginseng of the initialization iterative parameter Number；
According to the mathematical model, the first NLFM is believed using augmentation Lagrange genetic simulated annealing hybrid algorithm It number carries out continuing iteration, until the augmentation Lagrange genetic simulated annealing hybrid algorithm is restrained.
In the above scheme, described according to the mathematical model, it is mixed and is calculated using augmentation Lagrange genetic simulated annealing Method carries out first time iteration to the initialization NLFM signal, obtains the first NLFM signal, and obtains the initialization iteration ginseng Corresponding first iterative parameter of number, comprising:
According to the mathematical model, determine that the corresponding augmentation glug of the mathematical model is bright using augmentation Lagrangian Arithmetic Day formula；
According to the augmentation lagrange formula, the fitness of the target NLFM signal is determined；
The selection processing that genetic algorithm is carried out to the initialization NLFM signal, obtains target NLFM signal；
According to the fitness, augmentation Lagrange genetic simulated annealing hybrid algorithm is utilized to the target NLFM signal Solution obtains optimization aim NLFM signal；
According to the augmentation lagrange formula, corresponding first iterative parameter of the initialization iterative parameter is determined；
The cross processing and variation processing that the genetic algorithm is carried out to the optimization aim NLFM signal, obtain first NLFM signal.
Second aspect, provides a kind of generating means of orthogonal NLFM signal based on hybrid algorithm, and described device includes:
Described device includes: the first determining module, the second determining module, setting module and iteration module；Wherein,
First determining module, for determining the relationship between frequency and time function of NLFM signal according to piecewise linear function；According to The relationship between frequency and time function determines the time-domain function of the NLFM signal；
Second determining module, for determining the correlation performance parameters of the NLFM signal according to the time-domain function； The mathematical model of the NLFM signal is determined according to the correlation performance parameters；
The setting module, for the pulse width according to the NLFM signal and with width setting initializing signal；
The iteration module, for being mixed and being calculated using augmentation Lagrange genetic simulated annealing according to the mathematical model Method is iterated the initialization NLFM signal, obtains orthogonal NLFM signal.
The third aspect, provides a kind of generating means of orthogonal NLFM signal based on hybrid algorithm, and described device includes: Processor and memory for storing the computer program that can be run on a processor, wherein the processor is for transporting Row the computer program when, execute first aspect the method the step of.
The generation method and device of orthogonal NLFM signal based on hybrid algorithm provided by the embodiment of the present invention, according to point Section linear function determines the relationship between frequency and time function of NLFM signal；According to the relationship between frequency and time function determine the NLFM signal when Domain function；The correlation performance parameters of the NLFM signal are determined according to the time-domain function；It is true according to the correlation performance parameters The mathematical model of the fixed NLFM signal；NLFM signal is initialized according to the pulse width of the NLFM signal and with width setting； According to the mathematical model, the initialization NLFM signal is carried out using augmentation Lagrange genetic simulated annealing hybrid algorithm Iteration obtains orthogonal NLFM signal；In this way, the generation of the orthogonal NLFM signal based on hybrid algorithm using the embodiment of the present invention Method can design and obtain same frequency band, the orthogonal NLFM signal of big time width.
Detailed description of the invention
Fig. 1 is the flow diagram of the generation method of the orthogonal NLFM signal based on hybrid algorithm of the embodiment of the present invention One；
Fig. 2 is the flow diagram of the generation method of the orthogonal NLFM signal based on hybrid algorithm of the embodiment of the present invention Two；
Fig. 3 is that the piecewise linear function of the embodiment of the present invention indicates relationship between frequency and time schematic diagram；
Fig. 4 a is the NLFM signal spectrum comparison diagram one after optimization of the embodiment of the present invention；
Fig. 4 b is the NLFM signal spectrum comparison diagram two after optimization of the embodiment of the present invention；
Fig. 5 is the NLFM signal autocorrelation schematic diagram after optimization of the embodiment of the present invention；
Fig. 6 is the structural schematic diagram of the generating means of the orthogonal NLFM signal based on hybrid algorithm of the embodiment of the present invention；
Fig. 7 is the structural schematic diagram of the generating means of the orthogonal NLFM signal based on hybrid algorithm of the embodiment of the present invention.
Specific embodiment
With reference to the accompanying drawing and specific embodiment the present invention is described in further detail.
Fig. 1 is the flow diagram of the generation method of the orthogonal NLFM signal based on hybrid algorithm of the embodiment of the present invention, As shown in Figure 1, method includes the following steps:
Step 101: the relationship between frequency and time function of NLFM signal is determined according to piecewise linear function；According to the relationship between frequency and time letter Number determines the time-domain function of the NLFM signal；
The relationship between frequency and time function that NLFM signal is determined using piecewise linear function, according to the relationship between frequency and time function of NLFM signal Determine the time-domain function of NLFM signal.
In one embodiment, the relationship between frequency and time function that the NLFM signal is determined according to piecewise linear function；According to The relationship between frequency and time function determines the time-domain function of the NLFM signal, comprising:
The relationship between frequency and time coordinate of the NLFM signal is defined as (t, f), the pulse width of the NLFM signal is corresponding for T In the time coordinate t of the relationship between frequency and time coordinate, the bandwidth of the NLFM signal is the frequency that B corresponds to the relationship between frequency and time coordinate The pulse width and the bandwidth are divided into 2n+2 sections of linear functions, time slice point in the relationship between frequency and time coordinate by coordinate f That is abscissa waypoint is uniformly distributed, 2n+3 time slice point vector are as follows: Wherein,For known quantity；In the relationship between frequency and time coordinate Define 2n frequency control point, frequency control point vector BcAre as follows: Bc=[- B2n,…,B21,B11,…,B1n]T, corresponding 2n+3 Frequency segmentation point then determines the relationship between frequency and time function of the NLFM signal according to piecewise linear function are as follows:
Wherein, k1iCharacterization is by frequency segmentation pointWith time slice point Each section of frequency modulation rate of the piecewise linear function of composition, k2iCharacterization is by frequency segmentation pointAnd when Between waypointEach section of frequency modulation rate of the piecewise linear function of composition, the frequency modulation rate are as follows:
Determine that amplitude is the time-domain function of the NLFM signal of A according to the relationship between frequency and time function of the NLFM signal are as follows:
Step 102: the correlation performance parameters of the NLFM signal are determined according to the time-domain function；According to the correlation Energy parameter determines the mathematical model of the NLFM signal；
The correlation performance parameters that NLFM signal is determined according to time-domain function include: to determine NLFM signal according to time-domain function Autocorrelation performance parameter, the cross-correlation energy that NLFM signal is determined according to time-domain function.Correspondingly, joined according to the correlated performance Number determines that the mathematical models of the NLFM signals include: to determine the of NLFM signal according to the autocorrelation performance parameter of NLFM signal One mathematical model, the second mathematical model that NLFM signal is determined according to the cross-correlation energy of NLFM signal.
In one embodiment, the correlation performance parameters that the NLFM signal is determined according to the time-domain function；According to The correlation performance parameters determine the mathematical model of the NLFM signal, comprising:
The autocorrelation performance parameter of the NLFM signal, the autocorrelation performance parameter packet are determined according to the time-domain function It includes: peak sidelobe ratio PSLR and main lobe width MW；
The first mathematical model of the NLFM signal is determined according to the autocorrelation performance parameter are as follows:
cMW(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the PSLR of the NLFM signal of variable, BcFor The frequency control point vector of the NLFM signal, cMW(Bc) characterize with the BcMW for the NLFM signal of variable is non-linear Inequality constraints.
Determine that the autocorrelation performance parameter of NLFM signal, autocorrelation performance parameter include: peak side-lobe according to time-domain function Than PSLR and main lobe width MW, it is defined respectively as:
1) PSLR: the ratio of highest secondary lobe and main lobe peak height, unit dB,
2) size of MW:3dB main lobe width, is typically normalized to sampled point.
According to the autocorrelation performance parameter of NLFM signal: PSLR and MW determines the first mathematical model of NLFM signal are as follows:
In one embodiment, the correlation performance parameters of the NLFM signal are determined according to the time-domain function；According to described Correlation performance parameters determine the mathematical model of the NLFM signal, comprising:
The cross-correlation energy of the NLFM signal, the cross-correlation energy are determined according to the time-domain function are as follows:
ECC=∫ | S1(f)|2|S2(f)|2df
ECC is the cross-correlation energy of the NLFM signal, S1(f) corresponding NLFM signal S1(t) frequency spectrum, S2(f) corresponding NLFM signal S2(t) frequency spectrum.
The second mathematical model of the NLFM signal is determined according to the cross-correlation energy are as follows:
cMW(Bc)≤0,cPSLR(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the ECC of the NLFM signal of variable, cMW (Bc) characterize with the BcFor the MW nonlinear complementary problem of the NLFM signal of variable, cPSLR(Bc) characterize with the BcFor The PSLR nonlinear complementary problem of the NLFM signal of variable.
The cross-correlation energy of NLFM signal is determined according to time-domain function are as follows:
ECC=∫ | S1(f)|2|S2(f)|2df
According to the cross-correlation energy of NLFM signal: ECC determines the second mathematical model of NLFM signal are as follows:
In one embodiment, the correlation performance parameters of the NLFM signal are determined according to the time-domain function；According to described Correlation performance parameters determine the mathematical model of the NLFM signal, comprising:
The autocorrelation performance parameter of the NLFM signal, the autocorrelation performance parameter packet are determined according to the time-domain function It includes: peak sidelobe ratio PSLR and main lobe width MW；
The cross-correlation energy of the NLFM signal, the cross-correlation energy are determined according to the time-domain function are as follows:
ECC=∫ | S1(f)|2|S2(f)|2df
ECC is the cross-correlation energy of the NLFM signal, S1(f) corresponding NLFM signal S1(t) frequency spectrum, S2(f) corresponding NLFM signal S2(t) frequency spectrum.
The first mathematical model of the NLFM signal is determined according to the autocorrelation performance parameter are as follows:
cMW(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the PSLR of the NLFM signal of variable, BcFor The frequency control point vector of the NLFM signal, cMW(Bc) characterize with the BcMW for the NLFM signal of variable is non-linear Inequality constraints；
The second mathematical model of the NLFM signal is determined according to the cross-correlation energy are as follows:
cMW(Bc)≤0,cPSLR(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the ECC of the NLFM signal of variable, cMW (Bc) characterize with the BcFor the MW nonlinear complementary problem of the NLFM signal of variable, cPSLR(Bc) characterize with the BcFor The PSLR nonlinear complementary problem of the NLFM signal of variable.
Autocorrelation performance parameter and cross-correlation energy that NLFM signal is determined according to time-domain function, according to NLFM signal from Correlation performance parameters determine the first mathematical model of NLFM signal, determine NLFM signal according to the cross-correlation energy of NLFM signal Second mathematical model.
Step 103: initializing NLFM signal according to the pulse width of the NLFM signal and with width setting；
The relationship between frequency and time letter of NLFM signal is obtained according to the pulse width of NLFM signal and bandwidth usage piecewise linear function Number, and then determine the frequency control point of NLFM signal, obtain initialization NLFM signal.
In practical applications, two groups of signals, corresponding first mathematical model of first group of signal, second group of signal pair can be defined The second mathematical model is answered, sets first group of signal or second group of signal as initialization NLFM signal.
Step 104: according to the mathematical model, using augmentation Lagrange genetic simulated annealing hybrid algorithm to described first Beginningization NLFM signal is iterated, and obtains orthogonal NLFM signal.
According to the first mathematical model or the second mathematical model, augmentation Lagrange genetic simulated annealing hybrid algorithm is utilized Calculating is iterated to initialization NLFM signal, obtains orthogonal NLFM signal.
In one embodiment, described according to the mathematical model, it is mixed and is calculated using augmentation Lagrange genetic simulated annealing Method is iterated the initialization NLFM signal, comprising: setting initialization iterative parameter；According to the mathematical model, utilize Augmentation Lagrange genetic simulated annealing hybrid algorithm carries out first time iteration to the initialization NLFM signal, obtains first NLFM signal, and obtain corresponding first iterative parameter of the initialization iterative parameter；According to the mathematical model, augmentation is utilized Lagrangian genetic simulated annealing hybrid algorithm carries out the first NLFM signal to continue iteration, until the augmentation glug is bright Day genetic simulated annealing hybrid algorithm convergence.
Wherein, initialization iterative parameter includes: Lagrangian λ, offset s.
According to the first mathematical model or the second mathematical model, augmentation Lagrange genetic simulated annealing hybrid algorithm pair is utilized It initializes NLFM signal and carries out first time iteration, obtain the first NLFM signal the first iteration ginseng corresponding with initialization iterative parameter Number；Further according to the first mathematical model or the second mathematical model, and the first obtained NLFM signal and the first iterative parameter, utilize Augmentation Lagrange genetic simulated annealing hybrid algorithm carries out the first NLFM signal to continue iteration, until augmentation glug is bright Day genetic simulated annealing hybrid algorithm convergence, the NLFM letter that augmentation Lagrange genetic simulated annealing hybrid algorithm obtains when restraining Number be orthogonal NLFM signal.
Here, if initialization NLFM signal is the corresponding second group of signal of the second mathematical model, according to the second mathematical modulo Type carries out first time iteration to second group of signal using augmentation Lagrange genetic simulated annealing hybrid algorithm, obtains first NLFM signal the first iterative parameter corresponding with initialization iterative parameter；Further according to the second mathematical model, and obtain first NLFM signal and the first iterative parameter, using augmentation Lagrange genetic simulated annealing hybrid algorithm to the first NLFM signal It carries out continuing iteration, until augmentation Lagrange genetic simulated annealing hybrid algorithm is restrained, augmentation Lagrange genetic mimic is moved back The NLFM signal that fiery hybrid algorithm obtains when restraining is orthogonal NLFM signal, i.e., second group of orthogonal signal, according to orthogonal Second group of signal recalculates first group of signal, obtains first group of orthogonal signal.
It should be noted that utilizing augmentation Lagrange Hereditary Modules according to the first mathematical model or the second mathematical model When quasi- annealing hybrid algorithm optimizes, the optimization sequence of signal can change, i.e., can optimize first group of signal for the first time, the It is secondary to optimize second group of signal.
In one embodiment, described according to the mathematical model, it is mixed and is calculated using augmentation Lagrange genetic simulated annealing Method carries out first time iteration to the initialization NLFM signal, obtains the first NLFM signal, and obtains the initialization iteration ginseng Corresponding first iterative parameter of number, comprising: according to the mathematical model, determine the mathematical modulo using augmentation Lagrangian Arithmetic The corresponding augmentation lagrange formula of type；According to the augmentation lagrange formula, the adaptation of the target NLFM signal is determined Degree；The selection processing that genetic algorithm is carried out to the initialization NLFM signal, obtains target NLFM signal；According to the adaptation Degree, solves to obtain optimization aim NLFM to the target NLFM signal using augmentation Lagrange genetic simulated annealing hybrid algorithm Signal；According to the augmentation lagrange formula, corresponding first iterative parameter of the initialization iterative parameter is determined；To described Optimization aim NLFM signal carries out the cross processing and variation processing of the genetic algorithm, obtains the first NLFM signal.
According to the first mathematical model, determine that corresponding first augmentation of the first mathematical model is drawn using augmentation Lagrangian Arithmetic Ge Lang formula；Or according to the second mathematical model, the second mathematical model corresponding is determined using augmentation Lagrangian Arithmetic Two augmentation lagrange formulas.
Augmentation Lagrange genetic algorithm is the popularizing form of genetic algorithm, is genetic algorithm and augmented Lagrangian algorithm In conjunction with solve Complex Constraints optimize advanced algorithm.
Its mathematical description are as follows:
Wherein λiIt is a non-negative number, s for Lagrange multiplieriFor a non-negative number, whole offset is represented Guarantee that the antilog non-zero of logarithm, ρ are to discipline the factor, ceq as a warningi(x) and ci(x) equality constraint and nonlinear inequalities are respectively represented about Beam, f (x) are fitness function, and m represents the number of nonlinear restriction, and mt represents total constraint number.
First mathematical model requires to reduce secondary lobe as much as possible in the case where not broadening main lobe, that is, requires autocorrelation performance Minimum, the then corresponding first augmentation lagrange formula of the first mathematical model are as follows:
Θ(Bc, λ, s) and=f (Bc)-λslog(s-c(Bc))
Wherein, f (Bc)=PSLR (Bc) it is according to frequency control point BcThe PSLR of the NLFM signal acquired, c (Bc)=MW (Bc) it is according to frequency control point BcThe MW of the NLFM signal acquired.
Second mathematical model requires to reduce cross-correlation energy in the case where guaranteeing certain main lobe width and peak side-lobe height Amount requires cross-correlation energy minimum, then the corresponding second augmentation lagrange formula of the second mathematical model are as follows:
Θ(Bc, λ, s) and=f (Bc)-λ1s1log(s1-c1(Bc))-λ2s2log(s2-c2(Bc))
Wherein, f (Bc)=ECC (Bc) it is according to frequency control point BcThe cross-correlation energy of the signal acquired, c1(Bc)=MW (Bc) it is according to frequency control point BcThe MW of the NLFM signal acquired, c2(Bc)=PSLR (Bc) it is according to frequency control point BcIt acquires NLFM signal PSLR.
The selection processing that genetic algorithm is carried out to obtained initialization NLFM signal, selects target NLFM signal.Heredity Algorithm generally includes selection processing, cross processing and the mutation operation of chromosome.Selection contaminates according to certain rules for selection processing Colour solid, the rule can are as follows: the selected probability of individual is directly proportional to its fitness function value size, for example, selection processing can For wheel disc back-and-forth method (Roulette Wheel Selection, RWS).
The basic thought of wheel disc back-and-forth method is: the selected probability of individual is directly proportional to its fitness function value size.It is false If group size is N, individual xiFitness be f (xi), then individual xiSelect probability are as follows:
Wheel disc back-and-forth method includes the following steps:
1) an equally distributed random number r is generated in [0,1]；
If 2) r≤q1, then chromosome xiIt is selected；
If 3) qk-1<r≤qk(2≤k≤N), then chromosome xkIt is selected；Q thereiniReferred to as chromosome xi(i=1, 2 ..., N) accumulation probability, its calculation formula is:
The suitable of initialization NLFM signal is calculated using the first augmentation lagrange formula or the second augmentation lagrange formula Response, and the step of according to above-mentioned wheel disc selection algorithm, the selection target NLFM signal from initialization NLFM signal.
According to the first augmentation lagrange formula or the second augmentation lagrange formula, the adaptation of target NLFM signal is determined Spend f (Bc)；According to obtained fitness, target NLFM signal is solved to obtain optimization aim NLFM letter using simulated annealing Number.
Simulated annealing is derived from " solid annealing " principle, and the local search ability of simulated annealing is very strong, and energy It is enough that local extremum problem solution is refused with certain probability, jump out other state solutions that Local Extremum continues mining state space.
Simulated annealing the following steps are included:
1) using target NLFM signal as initial optimum point, calculating target function value；
2) initial temperature T is set0, iteration index k=0, final temperature Tf, temperature damping's factor-alpha, step factor ε is each At a temperature of iteration ends tolerance Tolerance；
3) random fluctuation is done with step factor ε to current optimum point i, generates a new explanation j ∈ D, calculating target function value Increment △ f=f (j)-f (i), if f < 0 △, receiving j is current optimal solution i=j, is otherwise entered step 4)；
4) f (i) is current optimal, but receives current poor point j, p=exp {-△ f/T with certain Probability pk, it generates Random number r, r ∈ (0,1) receives i=j if p > r；
5) reach thermal equilibrium state, i.e. inner iteration meets termination tolerance, enters step 6), otherwise turns to step 3)；
6) Current Temperatures T is reducedk+1=α Tk, k=k+1, if Tk+1<Tf, then algorithm stops, and otherwise turns to step 3).
Here, objective function f (i) can be to be obtained according to the first augmentation lagrange formula or the second augmentation lagrange formula Fitness function f (the B obtainedc)。
According to the first augmentation lagrange formula or the second augmentation lagrange formula, determine that initialization iterative parameter is corresponding The first iterative parameter, here, the first iterative parameter includes: Lagrangian λ and offset s.
In practical applications, λ and s is obtained using following formula:
Wherein, parameter μ can be according to the fitness in the first augmentation lagrange formula or the second augmentation lagrange formula Function obtains.
The infall of the genetic algorithm is carried out to the optimization aim NLFM signal solved according to simulated annealing Reason and variation processing, obtain the first NLFM signal.
In genetic algorithm, it is assumed that the total number of chromosome is K.In cross processing, be K chromosome generate K it is a with Machine number.If the corresponding random number of chromosome is lower than crossover probability rc, then show that these chromosomes are selected for cross processing. Here, 1 crosspoint crossover operation is taken, by being randomly generated, male parent exchanges gene in crosspoint and generates newly for the position in crosspoint Chromosome.
Variation processing refers to the changed operation of gene in chromosome, and the gene of variation is selected randomly.One NLFM signal can regard a chromosome as, and the gene number of each chromosome is 2n, then the total number L of gene is L=2Kn. The number M of variation determines by mutation probability, specially M=rmL chooses M progress mutation operation, mutation operator in L at random are as follows:
pk(j)=pk(i)*(1+rand)
Wherein, pkIt (i) is the chromosome before variation processing, pkIt (j) is variation treated chromosome, rand is random Value.
According to the process of above-mentioned cross processing and variation processing, optimization aim NLFM signal is handled, obtains first NLFM signal.
In embodiments of the present invention, the relationship between frequency and time function of NLFM signal is determined according to piecewise linear function；According to described Relationship between frequency and time function determines the time-domain function of the NLFM signal；The correlation of the NLFM signal is determined according to the time-domain function Performance parameter；The mathematical model of the NLFM signal is determined according to the correlation performance parameters；According to the arteries and veins of the NLFM signal It rushes width and initializes NLFM signal with width setting；According to the mathematical model, augmentation Lagrange genetic simulated annealing is utilized Hybrid algorithm is iterated the initialization NLFM signal, obtains orthogonal NLFM signal；It so, it is possible in acceptable secondary lobe With the orthogonal performance of promotion signal under main lobe width, inhibit cross-correlation energy, obtains same frequency band, the orthogonal NLFM letter of big time width Number.
The present embodiment is calculated based on mixing by generating the specific steps of orthogonal NLFM signal provided in an embodiment of the present invention The generation method of the orthogonal NLFM signal of method is illustrated.
Fig. 2 is the implementation process signal of the generation method of the orthogonal NLFM signal based on hybrid algorithm of the embodiment of the present invention Figure, as shown in Fig. 2, method includes the following steps:
Step 201: when defining the relationship between frequency and time function of NLFM signal using piecewise linear function, and then defining NLFM signal Domain function；
In Cartesian coordinates, the relationship between frequency and time coordinate of NLFM signal is defined (t, f).Assuming that the pulse width of signal Bandwidth for T, signal is B, is divided into 2n+2 sections of linear functions, as shown in Figure 3.In time frequency plane, time shaft waypoint, that is, horizontal seat Mark waypoint is uniformly distributed, 2n+3 time slice point vectorWherein For known quantity.It is closed in time-frequency It is that 2n frequency control point vector B is given in coordinate planecAre as follows: Bc=[- B2n,…,B21,B11,…,B1n]T, then corresponding 2n+3 A frequency segmentation point vector isSegmentation in given relationship between frequency and time Point can then describe the relationship between frequency and time of signal using piecewise linear function:
Wherein, k1iAnd k2iThe frequency modulation rate of every section of piecewise linear function is represented, frequency modulation rate can be by formula (2) and formula (3) It obtains.
Then the NLFM signal that amplitude is A is indicated are as follows:
F (t) is the corresponding frequency-portions of entire time shaft, by f+(t) and f-(t) two parts are constituted.
Step 202: the auto-correlation function and cross correlation energy according to signal, definition signal optimizing index；
The ideal performance of the auto-correlation function of NLFM signal are as follows: main lobe narrow as far as possible, alap PSLR and quickly under The secondary lobe of drop fluctuates envelope.However these three ideal performances cannot meet simultaneously.Under ordinary meaning, NLFM signal from Correlated performance is 3dB main lobe width and side lobe height, is respectively defined as:
1) peak sidelobe ratio (PSLR): the ratio of highest secondary lobe and main lobe peak height, unit dB
2) size of 3dB main lobe width (MW): 3dB main lobe width, is typically normalized to sampled point.
Here primary optimization aim is the orthogonal good NLFM signal of performance of building, traditional 2 signal S of definition1(t) and S2 (t) orthogonal, i.e. S1(t) and S2(t) cross-correlation is 0, is shown below:
It is according to the property of Fourier transformation
∫|S1(f)S2(f)|2Df=0 (7)
However for same band signal, according to principle of conservation of energy, this is unable to satisfy, so defined formula (8) conduct The evaluation index of orthogonal performance:
ECC=∫ | S1(f)|2|S2(f)|2df (8)
Wherein, ECC represents cross-correlation energy (energy of cross-correlation), S1(f) corresponding NLFM signal S1(t) frequency spectrum, S2(f) corresponding NLFM signal S2(t) frequency spectrum.
It is defined by formula (1) to formula (4) it is found that control point determines NLFM signal concrete form.Once frequency control point After number is determined, abscissa waypoint tsIt is uniformly distributed on a timeline, is known quantity.NLFM signal can be by containing 2n frequency The B at rate control pointsVector definition.To which the performance indicator of auto-correlation and cross-correlation can be by the B at 2n frequency control pointsVector Definition, in other words it is BsFunction.
Step 203: determining the first mathematic optimal model；
Here, what is needed is two groups of signals, pays close attention to autocorrelation signal characteristic, i.e. main lobe width for first group of signal And side lobe height, need require its under conditions of not broadening main lobe, as far as possible reduction secondary lobe, be one it is non-linear about Beam optimization problem, the problem it can be said that
Step 204: determining the second mathematic optimal model；
Cross-correlated signal characteristic, i.e. cross-correlation ENERGY E CC are paid close attention to for second group of signal, while needing to guarantee that its main lobe is wide Degree and side lobe height, be a Solution of Nonlinear Optimal Problem, the problem it can be said that
Step 205: according to the first mathematic optimal model, optimizing autocorrelation performance；According to the second mathematic optimal model, optimization The orthogonal performance of cross-correlation；
For first group of signal, its autocorrelative performance is emphasized, and the performance of its cross-correlation is emphasized for second group of signal, So according to the first of design group of signal and second group of signal, can optimize further using second group of signal as initializing signal The orthogonal performance of cross-correlation can recalculate first group of optimization signal, to obtain preferably orthogonal performance.
Step 206: according to the first mathematic optimal model or the second mathematic optimal model, utilizing augmentation Lagrange heredity Simulated annealing optimizes, and Optimal Signals can be obtained.
Augmentation Lagrange genetic algorithm is the popularizing form of genetic algorithm, is genetic algorithm and augmented Lagrangian algorithm In conjunction with solve Complex Constraints optimize advanced algorithm.
Its mathematical description are as follows:
Wherein λiIt is a non-negative number, s for Lagrange multiplieriFor a non-negative number, whole offset is represented Guarantee that the antilog non-zero of logarithm, ρ are to discipline the factor, ceq as a warningi(x) and ci(x) equality constraint and nonlinear inequalities are respectively represented about Beam, f (x) are fitness function, and m represents the number of nonlinear restriction, and mt represents total constraint number.
When designing first group of optimization signal, it is desirable that reduce secondary lobe as much as possible in the case where not broadening main lobe, this is asked Topic it can be said that
Θ(Bc, λ, s) and=f (Bc)-λslog(s-c(Bc)) (12)
Wherein, f (Bc)=PSLR (Bc) it is according to frequency control point BcThe PSLR of the NLFM signal acquired, c (Bc)=MW (Bc) it is according to frequency control point BcThe MW of the NLFM signal acquired.
When designing second group of optimization signal, it is desirable that in the case where guaranteeing certain main lobe width and peak side-lobe height, As far as possible reduce cross-correlation energy, the problem it can be said that
Θ(Bc, λ, s) and=f (Bc)-λ1s1log(s1-c1(Bc))-λ2s2log(s2-c2(Bc)) (13)
Wherein, f (Bc)=ECC (Bc) it is according to frequency control point BcThe cross-correlation energy of the NLFM signal acquired, c1(Bc) =MW (Bc) it is according to frequency control point BcThe MW of the NLFM signal acquired, c2(Bc)=PSLR (Bc) it is according to frequency control point Bc The PSLR of the NLFM signal acquired.
Specific Solve problems are divided into two parts by augmentation Lagrange genetic simulated annealing hybrid algorithm: a part is biography The genetic algorithm of system and the hybrid algorithm of simulated annealing, a part are augmentation Lagrangian Arithmetic.Augmentation Lagrange is calculated Method constantly updates λ and s for solving restricted problem, according to formula (14).
Optimization problem is modeled to the dynamic improving process of the natural selection of " survival of the fittest " by genetic algorithm.In search space In, chromosome represents the variable to be determined of specific Solve problems, genetic algorithm generally includes the selection of chromosome, intersect and Mutation operation.Variable is encoded according to Solve problems first, is moderately pressed according to target function value progress chromosome certain Rule carries out selective staining body.Secondly, selected chromosome is to according to the probability r that matescIntersect and generates offspring；Finally, according to According to certain mutation probability rmMutation operation is carried out to the gene of chromosome, new individual is generated in search variables space.? Entire iteration updates in optimization process, and the probability that the high chromosome of fitness is selected for generating offspring is big, fitness The individual of difference is replaced by more preferably offspring.
Simulated annealing is derived from " solid annealing " principle, makes to be attained by equilibrium state at each temperature, be finally reached The local search ability of ground state, simulated annealing is very strong, and can refuse local extremum problem solution with certain probability, jumps out Other state solutions in Local Extremum continuation mining state space.It can use simulated annealing to carry out each chromosome Optimization, increases the diversity of entire population, avoids genetic algorithm is premature from falling into local search.
Optimize for NLFM signal, for operatings of genetic algorithm part, during representation, each chromosome is seen At a control point vector B containing 2n frequency componentc, initializing signal is selected, it can be to control point vector BcWith each parameter of algorithm It is initialized.
The invention carries out selection male parent using wheel disc back-and-forth method (Roulette Wheel Selection, RWS) and hands over Fork process.Assuming that the total number for the chromosome chosen is K.In crossover process, K random number first is generated for this K chromosome. If the corresponding random number of chromosome is lower than crossover probability rc, then show that these chromosomes are selected for crossover operation.Here 1 crosspoint crossover operation is taken, the position in crosspoint is by being randomly generated.Male parent exchanges gene in crosspoint and generates new dyeing Body.Variation refers to the changed operation of gene in chromosome.The gene of variation is selected randomly.Because NLFM signal optimizes, The gene number of each chromosome is 2n, then the total number L of gene is L=2Kn.The number M of variation is determined have by mutation probability Body is M=rmL.M progress mutation operation, mutation operator are chosen at random in L are as follows:
pk(i)=pk(i)*(1+rand) (15)
After all genetic manipulation and selection operation have carried out n times, simulated annealing operation is carried out to all chromosome, First is that keeping the corresponding fitness of chromosome higher, second is that increasing the diversity of population.Simulated annealing is carried out to each chromosome The operation of algorithm is as follows:
Step 1: using current chromosome as initial optimum point, calculating target function value；
Step 2: setting initial temperature T0, iteration index k=0, final temperature Tf, temperature damping's factor-alpha, step factor ε, Iteration ends tolerance Tolerance at each temperature；
Step 3: random fluctuation being done with step factor to current optimum point i, generates a new explanation j ∈ D, calculates functional value and increases △ f=f (j)-f (i) is measured, if f < 0 △, receiving j is current optimal solution i=j；Otherwise 4 are entered step；
Step 4:f (i) is current optimal, but receives current poor point j, p=exp {-△ f/T with certain Probability pk, It generates random number r ∈ (0,1) and receives i=j if p > r；
Step 5: reducing Current Temperatures Tk+1=α Tk, k=k+1, if Tk+1<Tf, then algorithm stops, and otherwise turns to step 3.
In conclusion the NLFM orthogonal signalling design process based on augmentation Lagrange genetic simulated annealing hybrid algorithm can It is as follows to be summarized as algorithm:
Step 1: initialization algorithm parameter: setting initialization algorithm parameter: chromosome number n, crossover probability rc, variation is generally Rate rm, Lagrangian λ, offset s；
Step 2: being based on principle in phase bit, generate initialization NLFM signal, obtain its initial frequencies control point Bc, i.e., Initialize chromosome；
Step 3: to control point represented by each chromosome, determining corresponding NLFM signal according to (1) to (4) formula, then The fitness of chromosome is calculated according to mathematic optimal model (12) formula or (13) formula.And augmentation is utilized according to (12) formula or (13) formula Lagrangian Arithmetic calculates the λ and offset s of next suboptimization；
Step 4: according to wheel disc back-and-forth method selective staining body.Judge whether by n times heredity and selection operation, if so, Enter step 5；
Step 5: to selectively chromosome carry out simulated annealing optimizing；
Step 6: according to crossover probability rcCarry out a crosspoint crossover operation；
Step 7: according to mutation probability rmCarry out formula (15) mutation operation；
Step 8: circulation step 3 to step 7, until algorithmic statement.
The present embodiment is by specific effect of optimization to the orthogonal NLFM provided in an embodiment of the present invention based on hybrid algorithm The generation method of signal is illustrated.
The design of the present embodiment NLFM orthogonal signalling and optimization method process include the following steps:
Firstly, defining the relationship between frequency and time function of NLFM signal using piecewise linear function, and then define NLFM signal time domain Function；
Secondly, defining signal optimized mathematical model according to the performance of the auto-correlation of signal and cross-correlation function；
Then, it according to optimized mathematical model, is optimized using augmentation Lagrange genetic simulated annealing hybrid algorithm, i.e., Optimal Signals can be obtained；
Finally, the signal of optimization is if not satisfied, optimization requirement, excellent further using second group of signal as initializing signal Change the orthogonal performance of cross-correlation, first group of optimization signal can be recalculated, to obtain preferably orthogonal performance.
Such as: linear FM signal and the pulsewidth of NLFM signal are 20us, bandwidth 300MHz, and sample frequency is 400MHz, linear FM signal and NLFM signal optimum results are as shown in the table:
As can be seen that using the orthogonal NLFM signal of optimization design of the present invention compared to linear FM signal, cross-correlation Energy can inhibit 5.3dB.Fig. 4 a and Fig. 4 b are the frequency spectrum of orthogonal NLFM signal and linear FM signal, it can be seen that orthogonal NLFM signal and linear FM signal spectrum width having the same are in identical frequency band.Fig. 5 is the NLFM signal after optimization Auto-correlation function, side lobe height are respectively -23.2dB and -19.2dB, and main lobe width is 1.2 and 1.1, it can be seen that it has can The secondary lobe and main lobe width of receiving.
From the above description, it will be seen that effectively can design and optimize using method provided in an embodiment of the present invention Orthogonal NLFM signal is obtained, identical frequency band is in, there is acceptable main lobe width and side lobe height.
The generating means of the present embodiment provides a kind of orthogonal NLFM signal based on hybrid algorithm, as shown in fig. 6, orthogonal The generating means 60 of NLFM signal include: the first determining module 601, the second determining module 602, setting module 603；With iteration mould Block 604；Wherein,
First determining module 601, for determining the relationship between frequency and time function of NLFM signal according to piecewise linear function；According to institute State the time-domain function that relationship between frequency and time function determines the NLFM signal；
Second determining module 602, for determining the correlation performance parameters of the NLFM signal according to the time-domain function；Root The mathematical model of the NLFM signal is determined according to the correlation performance parameters；
Setting module 603 initializes NLFM signal for the pulse width according to the NLFM signal and with width setting；
Iteration module 604, for utilizing augmentation Lagrange genetic simulated annealing hybrid algorithm according to the mathematical model The initialization NLFM signal is iterated, orthogonal NLFM signal is obtained.
In one embodiment, the first determining module 601 is also used to: the relationship between frequency and time coordinate of the NLFM signal is defined as (t, f), the pulse width of the NLFM signal are the time coordinate t that T corresponds to the relationship between frequency and time coordinate, the NLFM signal Bandwidth be B correspond to the relationship between frequency and time coordinate frequency coordinate f, by the pulse width in the relationship between frequency and time coordinate It is divided into 2n+2 sections of linear functions with the bandwidth, time slice point, that is, abscissa waypoint is uniformly distributed, 2n+3 time slice Point vector are as follows:
Wherein,For known quantity；When described 2n frequency control point, frequency control point vector B are defined in frequency relationship coordinatecAre as follows: Bc=[- B2n,…,B21,B11,…,B1n]T, Corresponding 2n+3 frequency segmentation point, then determine the relationship between frequency and time function of the NLFM signal according to piecewise linear function are as follows:
Wherein, k1iCharacterization is by frequency segmentation pointWith time slice point Each section of frequency modulation rate of the piecewise linear function of composition, k2iCharacterization is by frequency segmentation pointAnd when Between waypointEach section of frequency modulation rate of the piecewise linear function of composition, the frequency modulation rate are as follows:
Determine that amplitude is the time-domain function of the NLFM signal of A according to the relationship between frequency and time function of the NLFM signal are as follows:
In one embodiment, the second determining module 602 is also used to: determining the NLFM signal according to the time-domain function Autocorrelation performance parameter, the autocorrelation performance parameter include: peak sidelobe ratio PSLR and main lobe width MW；
The first mathematical model of the NLFM signal is determined according to the autocorrelation performance parameter are as follows:
cMW(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the PSLR of the NLFM signal of variable, BcFor The frequency control point vector of the NLFM signal, cMW(Bc) characterize with the BcMW for the NLFM signal of variable is non-linear Inequality constraints.
In one embodiment, the second determining module 602 is also used to: determining the NLFM signal according to the time-domain function Cross-correlation energy, the cross-correlation energy are as follows:
ECC=∫ | S1(f)|2|S2(f)|2df
ECC is the cross-correlation energy of the NLFM signal, S1(f) corresponding NLFM signal S1(t) frequency spectrum, S2(f) corresponding NLFM signal S2(t) frequency spectrum.
The second mathematical model of the NLFM signal is determined according to the cross-correlation energy are as follows:
cMW(Bc)≤0,cPSLR(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the ECC of the NLFM signal of variable, cMW (Bc) characterize with the BcFor the MW nonlinear complementary problem of the NLFM signal of variable, cPSLR(Bc) characterize with the BcFor The PSLR nonlinear complementary problem of the NLFM signal of variable.
In one embodiment, the second determining module 602 is also used to: determining the NLFM signal according to the time-domain function Autocorrelation performance parameter, the autocorrelation performance parameter include: peak sidelobe ratio PSLR and main lobe width MW；According to the time domain Function determines the cross-correlation energy of the NLFM signal, the cross-correlation energy are as follows:
ECC=∫ | S1(f)|2|S2(f)|2df
ECC is the cross-correlation energy of the NLFM signal, S1(f) corresponding NLFM signal S1(t) frequency spectrum, S2(f) corresponding NLFM signal S2(t) frequency spectrum.
The first mathematical model of the NLFM signal is determined according to the autocorrelation performance parameter are as follows:
cMW(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the PSLR of the NLFM signal of variable, BcFor The frequency control point vector of the NLFM signal, cMW(Bc) characterize with the BcMW for the NLFM signal of variable is non-linear Inequality constraints；
The second mathematical model of the NLFM signal is determined according to the cross-correlation energy are as follows:
cMW(Bc)≤0,cPSLR(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the ECC of the NLFM signal of variable, cMW (Bc) characterize with the BcFor the MW nonlinear complementary problem of the NLFM signal of variable, cPSLR(Bc) characterize with the BcFor The PSLR nonlinear complementary problem of the NLFM signal of variable.
In one embodiment, iteration module 604 is also used to: setting initialization iterative parameter；According to the mathematical model, benefit First time iteration is carried out to the initialization NLFM signal with augmentation Lagrange genetic simulated annealing hybrid algorithm, obtains first NLFM signal, and obtain corresponding first iterative parameter of the initialization iterative parameter；According to the mathematical model, augmentation is utilized Lagrangian genetic simulated annealing hybrid algorithm carries out the first NLFM signal to continue iteration, until the augmentation glug is bright Day genetic simulated annealing hybrid algorithm convergence.
In one embodiment, iteration module 604 is also used to: according to the mathematical model, utilizing augmentation Lagrangian Arithmetic Determine the corresponding augmentation lagrange formula of the mathematical model；According to the augmentation lagrange formula, the target is determined The fitness of NLFM signal；The selection processing that genetic algorithm is carried out to the initialization NLFM signal, obtains target NLFM signal； According to the fitness, the target NLFM signal is solved to obtain using augmentation Lagrange genetic simulated annealing hybrid algorithm Optimization aim NLFM signal；According to the augmentation lagrange formula, determine that the initialization iterative parameter corresponding first changes For parameter；The cross processing and variation processing that the genetic algorithm is carried out to the optimization aim NLFM signal, obtain first NLFM signal.
It should be noted that the generating means of the orthogonal NLFM signal provided by the above embodiment based on hybrid algorithm are in life Be orthogonal NLFM signal when, can be according to need all only with the division progress of above-mentioned each program module for example, in practical application It wants and completes above-mentioned processing distribution by different program modules, i.e., the internal structure of device is divided into different program moulds Block, to complete all or part of processing described above.
Based on embodiment above-mentioned, the embodiment of the present invention provides a kind of orthogonal NLFM device based on hybrid algorithm, such as Fig. 7 Shown, described device includes processor 702 and the memory for storing the computer program that can be run on processor 702 701；Wherein, when the processor 702 is used to run the computer program, to realize:
The relationship between frequency and time function of NLFM signal is determined according to piecewise linear function；Institute is determined according to the relationship between frequency and time function State the time-domain function of NLFM signal；
The correlation performance parameters of the NLFM signal are determined according to the time-domain function；It is true according to the correlation performance parameters The mathematical model of the fixed NLFM signal；
NLFM signal is initialized according to the pulse width of the NLFM signal and with width setting；
According to the mathematical model, using augmentation Lagrange genetic simulated annealing hybrid algorithm to the initialization NLFM Signal is iterated, and obtains orthogonal NLFM signal.
The method that the embodiments of the present invention disclose can be applied in the processor 702, or by the processor 702 realize.The processor 702 may be a kind of IC chip, the processing capacity with signal.During realization, Each step of the above method can pass through the integrated logic circuit of the hardware in the processor 702 or the instruction of software form It completes.The above-mentioned processor 702 can be general processor, DSP or other programmable logic device, discrete gate or Person's transistor logic, discrete hardware components etc..The processor 702 may be implemented or execute in the embodiment of the present invention Disclosed each method, step and logic diagram.General processor can be microprocessor or any conventional processor etc..Knot The step of closing method disclosed in the embodiment of the present invention, can be embodied directly in hardware decoding processor and execute completion, Huo Zheyong Hardware and software module combination in decoding processor execute completion.Software module can be located in storage medium, which is situated between Matter is located at memory 701, and the processor 702 reads the information in memory 701, and the step of preceding method is completed in conjunction with its hardware Suddenly.
It is appreciated that the memory (memory 701) of the embodiment of the present invention can be volatile memory or non-volatile Property memory, may also comprise both volatile and non-volatile memories.Wherein, nonvolatile memory can be read-only storage Device (ROM, Read Only Memory), programmable read only memory (PROM, Programmable Read-Only Memory), Erasable Programmable Read Only Memory EPROM (EPROM, Erasable Programmable Read-Only Memory), Electrically erasable programmable read-only memory (EEPROM, Electrically Erasable Programmable Read-Only Memory), magnetic RAM (FRAM, ferromagnetic random access memory), flash Device (Flash Memory), magnetic surface storage, CD or CD-ROM (CD-ROM, Compact Disc Read-Only Memory)；Magnetic surface storage can be magnetic disk storage or magnetic tape storage.Volatile memory can be arbitrary access and deposit Reservoir (RAM, Random Access Memory) is used as External Cache.By exemplary but be not restricted explanation, The RAM of many forms is available, such as static random access memory (SRAM, Static Random Access Memory), same Walk static random access memory (SSRAM, Synchronous Static Random Access Memory), dynamic random Access memory (DRAM, Dynamic Random Access Memory), Synchronous Dynamic Random Access Memory (SDRAM, Synchronous Dynamic Random Access Memory), double data speed synchronous dynamic RAM It is (DDRSDRAM, Double Data Rate Synchronous Dynamic Random Access Memory), enhanced same Walk dynamic random access memory (ESDRAM, Enhanced Synchronous Dynamic Random Access Memory), synchronized links dynamic random access memory (SLDRAM, SyncLink Dynamic Random Access Memory), direct rambus random access memory (DRRAM, Direct Rambus Random Access Memory). The memory of description of the embodiment of the present invention is intended to include but is not limited to the memory of these and any other suitable type.
It need to be noted that: the description of the above terminal embodiment item, be with above method description it is similar, have same The identical beneficial effect of embodiment of the method, therefore do not repeat them here.For undisclosed technical detail in terminal embodiment of the present invention, Those skilled in the art please refers to the description of embodiment of the present invention method and understands, to save length, which is not described herein again.
In the exemplary embodiment, the embodiment of the invention also provides a kind of computer storage mediums, and as computer can Storage medium is read, the memory 701 for example including storage computer program, above-mentioned computer program can be handled by processor 702, To complete step described in preceding method.Computer readable storage medium can be FRAM, ROM, PROM, EPROM, EEPROM, The memories such as Flash Memory, magnetic surface storage, CD or CD-ROM.
The embodiment of the present invention also provides a kind of computer readable storage medium, is stored thereon with computer program, the calculating Realization when machine program is processed by the processor:
The relationship between frequency and time function of NLFM signal is determined according to piecewise linear function；Institute is determined according to the relationship between frequency and time function State the time-domain function of NLFM signal；
The correlation performance parameters of the NLFM signal are determined according to the time-domain function；It is true according to the correlation performance parameters The mathematical model of the fixed NLFM signal；
NLFM signal is initialized according to the pulse width of the NLFM signal and with width setting；
According to the mathematical model, using augmentation Lagrange genetic simulated annealing hybrid algorithm to the initialization NLFM Signal is iterated, and obtains orthogonal NLFM signal.
It need to be noted that: above computer media implements the description of item, be with above method description it is similar, With the identical beneficial effect of same embodiment of the method, therefore do not repeat them here.For undisclosed skill in terminal embodiment of the present invention Art details, those skilled in the art please refer to the description of embodiment of the present invention method and understand, to save length, here no longer It repeats.
The foregoing is only a preferred embodiment of the present invention, is not intended to limit the scope of the present invention.

Claims (9)

1. a kind of Nonlinear Orthogonal frequency modulation NLFM signal creating method based on hybrid algorithm, which is characterized in that the method packet It includes:
The relationship between frequency and time function of NLFM signal is determined according to piecewise linear function；According to relationship between frequency and time function determination The time-domain function of NLFM signal；
The correlation performance parameters of the NLFM signal are determined according to the time-domain function；Institute is determined according to the correlation performance parameters State the mathematical model of NLFM signal；
NLFM signal is initialized according to the pulse width of the NLFM signal and with width setting；
According to the mathematical model, using augmentation Lagrange genetic simulated annealing hybrid algorithm to the initialization NLFM signal It is iterated, obtains orthogonal NLFM signal.
2. the method according to claim 1, wherein described determine the NLFM signal according to piecewise linear function Relationship between frequency and time function；The time-domain function of the NLFM signal is determined according to the relationship between frequency and time function, comprising:
The relationship between frequency and time coordinate of the NLFM signal is defined as (t, f), the pulse width of the NLFM signal corresponds to institute for T The time coordinate t of relationship between frequency and time coordinate is stated, the bandwidth of the NLFM signal is the frequency seat that B corresponds to the relationship between frequency and time coordinate F is marked, the pulse width and the bandwidth are divided into 2n+2 sections of linear functions, time slice point in the relationship between frequency and time coordinate It is uniformly distributed, 2n+3 time slice point vector are as follows:Wherein,For known quantity；It is fixed in the relationship between frequency and time coordinate Adopted 2n frequency control point, frequency control point vector BcAre as follows: Bc=[- B2n,…,B21,B11,…,B1n]T, corresponding 2n+3 frequency Waypoint then determines the relationship between frequency and time function of the NLFM signal according to piecewise linear function are as follows:
Wherein, k1iCharacterization is by frequency segmentation pointWith time slice pointStructure At piecewise linear function each section of frequency modulation rate, k2iCharacterization is by frequency segmentation pointAnd the time WaypointEach section of frequency modulation rate of the piecewise linear function of composition, the frequency modulation rate are as follows:
Determine that amplitude is the time-domain function of the NLFM signal of A according to the relationship between frequency and time function of the NLFM signal are as follows:
3. the method according to claim 1, wherein described determine the NLFM signal according to the time-domain function Correlation performance parameters；The mathematical model of the NLFM signal is determined according to the correlation performance parameters, comprising:
Determine that the autocorrelation performance parameter of the NLFM signal, the autocorrelation performance parameter include: according to the time-domain function Peak sidelobe ratio PSLR and main lobe width MW；
The first mathematical model of the NLFM signal is determined according to the autocorrelation performance parameter are as follows:
cMW(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the PSLR of the NLFM signal of variable, BcIt is described The frequency control point vector of NLFM signal, cMW(Bc) characterize with the BcIt non-linear is differed for the MW of the NLFM signal of variable Formula constraint.
4. the method according to claim 1, wherein described determine the NLFM signal according to the time-domain function Correlation performance parameters；The mathematical model of the NLFM signal is determined according to the correlation performance parameters, comprising:
The cross-correlation energy of the NLFM signal, the cross-correlation energy are determined according to the time-domain function are as follows:
ECC=∫ | S1(f)|2|S2(f)|2df
ECC is the cross-correlation energy of the NLFM signal, S1(f) corresponding NLFM signal S1(t) frequency spectrum, S2(f) corresponding NLFM letter Number S2(t) frequency spectrum.
The second mathematical model of the NLFM signal is determined according to the cross-correlation energy are as follows:
cMW(Bc)≤0,cPSLR(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the ECC of the NLFM signal of variable, cMW(Bc) table Sign is with the BcFor the MW nonlinear complementary problem of the NLFM signal of variable, cPSLR(Bc) characterize with the BcFor variable The NLFM signal PSLR nonlinear complementary problem.
5. the method according to claim 1, wherein described determine the NLFM signal according to the time-domain function Correlation performance parameters；The mathematical model of the NLFM signal is determined according to the correlation performance parameters, comprising:
Determine that the autocorrelation performance parameter of the NLFM signal, the autocorrelation performance parameter include: according to the time-domain function Peak sidelobe ratio PSLR and main lobe width MW；
The cross-correlation energy of the NLFM signal, the cross-correlation energy are determined according to the time-domain function are as follows:
ECC=∫ | S1(f)|2|S2(f)|2df
ECC is the cross-correlation energy of the NLFM signal, S1(f) corresponding NLFM signal S1(t) frequency spectrum, S2(f) corresponding NLFM letter Number S2(t) frequency spectrum.
The first mathematical model of the NLFM signal is determined according to the autocorrelation performance parameter are as follows:
cMW(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the PSLR of the NLFM signal of variable, BcIt is described The frequency control point vector of NLFM signal, cMW(Bc) characterize with the BcIt non-linear is differed for the MW of the NLFM signal of variable Formula constraint；
The second mathematical model of the NLFM signal is determined according to the cross-correlation energy are as follows:
cMW(Bc)≤0,cPSLR(Bc)≤0,-B/2≤Bc≤B/2
Wherein,Characterization is sought with the BcFor the minimum value of the ECC of the NLFM signal of variable, cMW(Bc) table Sign is with the BcFor the MW nonlinear complementary problem of the NLFM signal of variable, cPSLR(Bc) characterize with the BcFor variable The NLFM signal PSLR nonlinear complementary problem.
6. bright using augmentation glug the method according to claim 1, wherein described according to the mathematical model Day genetic simulated annealing hybrid algorithm is iterated the initialization NLFM signal, comprising:
Setting initialization iterative parameter；
According to the mathematical model, using augmentation Lagrange genetic simulated annealing hybrid algorithm to the initialization NLFM signal First time iteration is carried out, obtains the first NLFM signal, and obtain corresponding first iterative parameter of the initialization iterative parameter；
According to the mathematical model, using augmentation Lagrange genetic simulated annealing hybrid algorithm to the first NLFM signal into Row continues iteration, until the augmentation Lagrange genetic simulated annealing hybrid algorithm is restrained.
7. according to the described in any item methods of claim 3 to 6, which is characterized in that it is described according to the mathematical model, utilize increasing Wide Lagrange genetic simulated annealing hybrid algorithm carries out first time iteration to the initialization NLFM signal, obtains the first NLFM Signal, and obtain corresponding first iterative parameter of the initialization iterative parameter, comprising:
According to the mathematical model, determine that the corresponding augmentation Lagrange of the mathematical model is public using augmentation Lagrangian Arithmetic Formula；
According to the augmentation lagrange formula, the fitness of the target NLFM signal is determined；
The selection processing that genetic algorithm is carried out to the initialization NLFM signal, obtains target NLFM signal；
According to the fitness, the target NLFM signal is solved using augmentation Lagrange genetic simulated annealing hybrid algorithm Obtain optimization aim NLFM signal；
According to the augmentation lagrange formula, corresponding first iterative parameter of the initialization iterative parameter is determined；
The cross processing and variation processing that the genetic algorithm is carried out to the optimization aim NLFM signal, obtain the first NLFM letter Number.
8. a kind of generating means of the Nonlinear Orthogonal frequency modulation NLFM signal based on hybrid algorithm, which is characterized in that described device It include: the first determining module, the second determining module, setting module and iteration module；Wherein,
First determining module, for determining the relationship between frequency and time function of NLFM signal according to piecewise linear function；According to described Relationship between frequency and time function determines the time-domain function of the NLFM signal；
Second determining module, for determining the correlation performance parameters of the NLFM signal according to the time-domain function；According to The correlation performance parameters determine the mathematical model of the NLFM signal；
The setting module, for the pulse width according to the NLFM signal and with width setting initializing signal；
The iteration module, for utilizing augmentation Lagrange genetic simulated annealing hybrid algorithm pair according to the mathematical model The initialization NLFM signal is iterated, and obtains orthogonal NLFM signal.
9. a kind of generating means of the Nonlinear Orthogonal frequency modulation NLFM signal based on hybrid algorithm, which is characterized in that including processing Device and memory for storing the computer program that can be run on a processor；Wherein, the processor is for running institute When stating computer program, the step of perform claim requires any one of 1 to 7 the method.
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