CN116953623B - Orthogonal multiphase coding frequency modulation signal generation method - Google Patents
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Abstract
The invention discloses a method for generating orthogonal multiphase coded frequency modulation signals, which comprises the following steps: constructing a time-frequency relation function of the multiphase coding frequency modulation signal based on a second-order code sequence; constructing a time domain function of the multiphase encoded frequency modulation signal based on the time-frequency relation function; based on the relevant performance parameters corresponding to the multiphase encoded frequency modulation signals, an optimization model is established, and the model is an optimization model with low cross-correlation energy; acquiring an initialization signal of the multiphase coded frequency modulation signal; and optimizing the initialization signal by utilizing a genetic algorithm based on the optimization model to obtain an orthogonal multiphase coding frequency modulation signal. The invention can obtain orthogonal multiphase coding frequency modulation signals with low cross-correlation energy and reduce the fuzzy energy of SAR images.
Description
Technical Field
The invention relates to a radar emission signal waveform design, signal processing and optimization technology, in particular to a method for generating orthogonal multiphase coding frequency modulation (PCFM) signals.
Background
Synthetic aperture radar (Synthetic Aperture Radar, SAR) is an important earth observation means, can observe all weather and earth all the time, and is widely applied. Due to antenna sidelobes and pulse emission regimes, SAR systems will inevitably suffer from distance ambiguity, which degrades radar image quality. The alternate transmission scheme in the related art suppresses the distance ambiguity by transmitting the orthogonal waveform of low cross correlation energy, which has received much attention with little additional system cost compared to other ambiguity suppression schemes. The core is how to design the same-band orthogonal signals with low cross-correlation energy.
At present, the conventional orthogonal signals, such as positive and negative frequency modulation signals, have the inhibition effect limited to point targets and have poor inhibition effect on distributed targets. This is because the positive and negative frequency modulated signals essentially break up the cross-correlation energy into the whole time domain, and their own energy does not vanish. In addition, as an improvement, researchers have proposed an orthogonal frequency division multiplexing OFDM-chirp signal that inherits the good doppler characteristics of a chirp signal, but due to the modulation factor between sub-pulses, there is a periodic grating lobe in the signal, which cannot reduce the cross-correlation energy of the signal.
Compared with the signals, the PCFM signals combine the physical realizable characteristics of the frequency modulation waveform with the parameterized structure of the phase code, so that the time-frequency relationship of the signals can be changed by optimizing the bottom code, and the cross-correlation energy is reduced, and the design freedom is great. In view of the foregoing, there is a need for effective suppression of distance ambiguity by designing and optimizing the PCFM signal to minimize cross-correlation energy.
Disclosure of Invention
In order to solve the technical problems, the invention provides a method for generating orthogonal multiphase coding frequency modulation signals, and the generated PCFM signals have lower cross-correlation energy.
In order to achieve the above object, the technical method of the present invention is as follows:
a method for generating orthogonal multiphase coded frequency modulation signals comprises the following steps:
step 1, constructing a time-frequency relation function of a multiphase coding frequency modulation signal based on a second-order code sequence;
step 2, constructing a time domain function of the multiphase coding frequency modulation signal based on the time-frequency relation function;
step 3, establishing an optimization model of low cross-correlation energy based on the performance parameters of the multiphase coded frequency modulation signals;
step 4, obtaining an initialization signal of the multiphase coded frequency modulation signal;
and step 5, optimizing the initialization signal by utilizing a genetic algorithm based on the optimization model to obtain an orthogonal multiphase coding frequency modulation signal.
Further, the step 1 includes:
constructing a second-order code function of the multiphase encoded frequency modulation signal based on the second-order code sequence;
and constructing a time-frequency relation function of the multiphase coding frequency modulation signal based on the second-order code function.
Further, the step 1 includes:
defining a time-frequency relation coordinate of the multiphase encoded frequency modulation signal as (T, f), wherein T represents corresponding time on an abscissa axis, f represents corresponding instantaneous frequency of the multiphase encoded frequency modulation signal on an ordinate axis, the pulse width of the signal is T, and the bandwidth is B;
constructing a second-order code function χ (t) of the multiphase encoded FM signal according to a second-order code sequence as follows:
wherein a is n For the nth second order sequence value, the time-varying tone frequency is represented, namely: a= [ a ] 1 ,a 2 ,...,a N ]N is the number of second-order sequences; t (T) p =t/N, expressed as pulse width per segment; g (t) is defined in the interval [0, T ] p ]A rectangular shaped filter;
according to the second-order code function, constructing a time-frequency relation function f (t) of the multiphase coding frequency modulation signal as follows:
f(t)=∫χ(t′)dt′+ω 0
where t' is the integral variable, ω 0 The initial frequency of the frequency modulated signal is encoded for a plurality of phases.
Further, the step 2 includes:
constructing a phase function of the multiphase encoded frequency modulation signal based on the time-frequency relation function;
and constructing a time domain function of the multiphase encoded frequency modulation signal based on the phase function.
Further, the step 2 includes:
according to the time-frequency relation function, constructing a phase function theta (t) of the multiphase coding frequency modulation signal as follows:
θ(t)=∫f(t)dt+θ 0
wherein θ 0 An initial phase of the multi-phase encoded FM signal;
constructing a time domain function of the multiphase coded frequency modulation signal with the amplitude A according to the phase function:
s(t)=Aexp{jθ(t)}
where j is the imaginary part of the time domain model, exp {.cndot }, is an exponential function.
Further, the step 3 includes:
determining performance parameters based on the performance of the multi-phase encoded frequency modulated signal, the performance parameters comprising peak-to-side lobe ratio PSLR and cross correlation energy CCE;
an optimization model of low cross-correlation energy of the multi-phase encoded frequency modulated signal is determined based on the performance parameters.
Further, the step 3 includes:
peak sidelobe ratio PSLR is:the unit is dB;
the cross-correlation energy CCE is as follows:
CCE(s 1 s 2 )=∫|S 1 (f)| 2 |S 2 (f)| 2 df
wherein CCE is the cross-correlation energy of the multi-phase coded frequency modulation signal, S 1 (f) Corresponding multiphase encoded FM signal s 1 (t) frequency spectrum, S 2 (f) Corresponding multi-phase coded FM signals 2 A frequency spectrum of (t), f being the instantaneous frequency of said multi-phase encoded fm signal;
the optimization model is as follows:
wherein->
Wherein,and->Represented respectively as multi-phase encoded FM signals s 1 (t) and s 2 Peak sidelobe ratio of (t), c and d being s respectively 1 (t) and s 2 A constraint value for peak sidelobe ratio of (t).
Further, the step 4 includes:
setting the second-order sequences to equal amounts, i.e. to causeAt this time, the multiphase encoded FM signal s 1 (t) is a chirp signal;
encoding a polyphase frequency modulated signal s using genetic algorithm 1 Optimizing peak sidelobe ratio of (t) to obtain initialized multiphase coded frequency modulation signal s 1 (t);
Will s 1 Time-frequency relation function f of (t) 1 (t) taking negative value to obtain another initialized multiphase coded FM signal s 2 Time-frequency relation function f of (t) 2 (t), namely: f (f) 2 (t)=-f 1 (t)。
Further, the step 5 includes:
and optimizing the acquired initialization signal by utilizing a genetic algorithm according to the time domain function and the optimization model of the multiphase coding frequency modulation signal until the genetic algorithm converges.
The beneficial effects are that:
the present invention suppresses distance ambiguity by transmitting orthogonal waveforms with low cross-correlation energy, which is of little concern with respect to other ambiguity suppression schemes, which require little additional system cost.
Drawings
FIG. 1 is a flow chart of a method for generating quadrature multi-phase encoded FM signals provided by the invention;
FIG. 2 is a schematic diagram of an exemplary PCFM signal time-frequency function generation provided by the present invention;
FIG. 3 is a flow chart of an exemplary PCFM signal time domain function generation provided by the present invention;
FIG. 4 is an exemplary PCFM signal auto-correlation output waveform provided by the present invention;
fig. 5 is a cross-correlation function comparison plot of an exemplary PCFM signal provided by the present invention.
Detailed Description
In order to make the characteristics and technical content of the embodiments of the present invention more clear, the specific technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. The drawings are only for purposes of illustration and are not intended to limit the embodiments of the invention.
Example 1
The invention provides a method for generating orthogonal multiphase coded frequency modulation signals, which is shown in figure 1 and comprises the following steps:
step 101, constructing a time-frequency relation function of the multiphase coding frequency modulation signal based on a second-order code sequence;
102, constructing a time domain function of the multiphase encoded frequency modulation signal based on the time-frequency relation function;
step 103, an optimization model is established based on performance parameters corresponding to the multiphase encoded frequency modulation signals, and the model is an optimization model with low cross-correlation energy;
104, acquiring an initialization signal of the multiphase encoded frequency modulation signal;
and 105, optimizing the initialization signal by utilizing a genetic algorithm based on the optimization model to obtain an orthogonal multiphase coding frequency modulation signal.
Specifically, step 101 includes:
step 101a, constructing a second-order code function of the multiphase encoded fm signal based on the second-order code sequence, including:
in a Cartesian coordinate system, a time-frequency relation plane of the multiphase encoded FM signal is defined as a (T, f) plane, wherein T represents a corresponding time on an abscissa axis, f represents an instantaneous frequency of the multiphase encoded FM signal on an ordinate axis, the pulse width of the signal is T, and the bandwidth is B.
Constructing a second-order code function χ (t) of the multiphase encoded FM signal according to a second-order code sequence as follows:
wherein a is n For the nth second order sequence value, the time-varying tone frequency is represented, namely: a= [ a ] 1 ,a 2 ,...,a N ]. Delta (t) is denoted as an impulse function. N is the number of second order sequences. T (T) p =t/N, expressed as pulse width per segment. g (t) is defined in the interval [0, T ] p ]The above shaping filter is herein referred to as a rectangular shaping filter.
The shaping filter g (t) may be set as:
step 101b, constructing a time-frequency relation function of the PCFM signal based on the second-order code function, including:
according to the second-order code function, constructing a time-frequency relation function f (t) of the multiphase coding frequency modulation signal as follows:
f(t)=∫χ(t′)dt′+ω 0
wherein t' is an integral variable, ω 0 The initial frequency of the frequency modulated signal is encoded for a plurality of phases. Omega can be taken here 0 =-πB。
Fig. 2 shows a schematic diagram of time-frequency function generation of a multi-phase encoded fm signal.
In the embodiment of the present invention, based on the above description, the second-order sequence a is determined n After the value of (2), the formula can be utilized to construct the time-frequency relation function of the multiphase frequency modulation signal.
102, constructing a time domain function of the multiphase encoded frequency modulation signal based on the time-frequency relation function, including:
102a, constructing a phase function of the multiphase encoded fm signal based on the time-frequency relationship function, including:
according to the time-frequency relation function, constructing a phase function model theta (t) of the multiphase coding frequency modulation signal as follows:
θ(t)=∫f(t)dt+θ 0
wherein θ 0 For multiphase encoding of the initial phase of the FM signal, at which time θ 0 Set to 0.
Step 102b, constructing a time domain model of the multiphase encoded fm signal based on the phase function model, including:
constructing a time domain model s (t) of the multiphase coded frequency modulation signal with the amplitude A according to the phase function model:
s(t)=Aexp{jθ(t)}
where j is the imaginary part of the time domain model, exp {. Cndot. } is an exponential function, and A can take a value of 1 at this time.
Fig. 3 is a flow chart showing the generation of a time domain function of a multi-phase encoded fm signal.
Step 103, based on the performance parameters corresponding to the multiphase encoded frequency modulation signal, an optimization model is established, wherein the model is an optimization model with low cross-correlation energy, and the method comprises the following steps:
step 103a, determining performance parameters based on the correlation performance of the multi-phase encoded frequency modulated signal, wherein the performance parameters comprise peak sidelobe ratio PSLR and cross correlation energy CCE, and the step comprises:
in order to obtain quadrature multi-phase encoded fm signals, it is desirable to have as low cross-correlation energy as possible, while at the same time ensuring that the peak-to-side ratio is satisfactory. Thus, here, two key performance parameters of the multi-phase encoded fm signal are chosen-peak side lobe ratio PSLR and cross correlation energy CCE.
The time domain model of the multi-phase encoded fm signal is s (t) =aexp { j θ (t) }, then the autocorrelation function of the multi-phase encoded fm signal is:
wherein, superscript * Expressed as the conjugate of the signal, τ is the integral variable.
And converting the signal amplitude into a dB form, and obtaining the peak sidelobe ratio PSLR of the multiphase coded frequency modulation signal. The peak side lobe ratio PSLR is the side lobe maximum except for the main lobe. Specifically, the peak side lobe ratio PSLR is defined as follows:
PSLR: the ratio of the highest side lobe to the peak height of the main lobe is expressed in dB;
the cross-correlation energy of the multiphase encoded frequency modulation signal is:
CCE(s 1 s 2 )=∫|S 1 (f)| 2 |S 2 (f)| 2 df
wherein CCE is the cross-correlation energy of the multi-phase coded frequency modulation signal, S 1 (f) Corresponding multiphase encoded FM signal s 1 (t) frequency spectrum, S 2 (f) Corresponding multiphase encoded FM signal s 2 The frequency spectrum of (t), f being the instantaneous frequency of said multi-phase encoded fm signal.
Step 103b, determining an optimization model of the signal based on the performance parameter, wherein the model is an optimization model with low cross-correlation energy, and the method comprises the following steps:
determining an optimization model of the signal according to the related performance parameters:
wherein->
Wherein,and->Represented respectively as multi-phase encoded FM signals s 1 (t) and s 2 Peak side lobe ratio of (t). c and d are s respectively 1 (t) and s 2 A constraint value for peak sidelobe ratio of (t). a is represented as a second order sequence>This means that the second order sequence a is optimized so that the cross-correlation energy CCE of its constitution is minimized.
Step 104, obtaining an initialization signal of the multiphase encoded fm signal, including:
setting the second-order sequences to equal amounts, i.e. to causeAt this time the multiphase encoded FM signal s 1 (t) is a chirp signal;
pair s using genetic algorithm 1 Optimizing peak sidelobe ratio of (t) to obtain initialized multiphase coded frequency modulation signal s 1 (t)。
Will s 1 Time-frequency relation function f of (t) 1 (t) taking negative value to obtain another initialized multiphase coded FM signal s 2 Time-frequency relation function f of (t) 2 (t), namely: f (f) 2 (t)=-f 1 (t)。
Step 105, optimizing the initialization signal by using a genetic algorithm based on the optimization model to obtain an orthogonal multiphase coding frequency modulation signal, which comprises the following steps:
according to the time domain model and the optimization model of the multiphase coding frequency modulation signal, the acquired initialization signal is optimized by utilizing a genetic algorithmFrom the optimization model, the constraint conditions are as follows:andthat is, the peak sidelobe level of the two signals is ensured not to exceed a constraint value in the optimization process. The objective function is CCE(s) 1 s 2 ) I.e. minimizing the side lobe levels under constraint conditions.
And calculating the fitness of each multiphase coded frequency modulation signal in the current multiphase coded frequency modulation signal set according to the objective function, selecting a parent multiphase coded frequency modulation signal from the signal set according to the fitness of each multiphase coded frequency modulation signal, performing cross processing and mutation processing on the parent multiphase coded frequency modulation signal to obtain a multiphase coded frequency modulation signal of the next iteration, and repeating the operation until the genetic algorithm converges.
The convergence of the genetic algorithm indicates that the generation of the quadrature polyphase encoded fm signal has been completed.
Example two
In the embodiment of the invention, the method for generating the orthogonal multiphase coding frequency modulation signal provided by the embodiment of the invention is described by combining the design parameters of the large time-width signal commonly used in a specific synthetic aperture radar SAR system.
The design parameters of the large time-width signal comprise a pulse width of 10 mu s, a bandwidth of 100MHz, a sampling frequency of 130MHz and a second-order code sequence number of 100. By setting the second-order sequence to be constant, the initial signal can be made to be a chirp signal, and the cross-correlation energy of the chirp signal and the polyphase coded fm signal at this time is shown in the following table:
signal signal | CCE(dB) |
Initial signal | 63.43 |
PCFM signals | 60.85 |
It can be seen that the cross-correlation energy of the quadrature multi-phase encoded fm signal designed using the present invention can be suppressed by 2.6dB compared to the chirp signal. Fig. 4 is an autocorrelation function plot of an orthogonal PCFM signal with side lobe heights of-13.6 dB and-13.3 dB, respectively. The main lobe width is close to the chirp signal, and is 0.9. Fig. 5 is a graph comparing cross-correlation functions of a chirp signal and a quadrature PCFM signal.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (7)
1. A method for generating an orthogonal polyphase coded frequency modulated signal, comprising the steps of:
step 1, constructing a time-frequency relation function of a multiphase coding frequency modulation signal based on a second-order code sequence;
step 2, constructing a time domain function of the multiphase coding frequency modulation signal based on the time-frequency relation function;
step 3, determining performance parameters based on the performance of the multiphase encoded frequency modulation signal, wherein the performance parameters comprise peak sidelobe ratio PSLR and cross correlation energy CCE;
peak sidelobe ratio PSLR is:the unit is dB;
the cross-correlation energy CCE is as follows:
CCE(s 1 s 2 )=∫|S 1 (f)| 2 |S 2 (f)| 2 df
wherein CCE is the cross-correlation energy of the multi-phase coded frequency modulation signal, S 1 (f) Corresponding multiphase encoded FM signal s 1 (t) frequency spectrum, S 2 (f) Corresponding multiphase encoded FM signal s 2 A frequency spectrum of (t), f being the instantaneous frequency of said multi-phase encoded fm signal;
based on the performance parameters, determining an optimization model of low cross-correlation energy of the multiphase encoded frequency modulated signal as:
wherein->
Wherein,and->Represented respectively as multi-phase encoded FM signals s 1 (t) and s 2 Peak sidelobe ratio of (t), c and d being s respectively 1 (t) and s 2 A constraint value of peak sidelobe ratio of (t);
step 4, obtaining an initialization signal of the multiphase coded frequency modulation signal;
and step 5, optimizing the initialization signal by utilizing a genetic algorithm based on the optimization model to obtain an orthogonal multiphase coding frequency modulation signal.
2. The method for generating an orthogonal polyphase coded fm signal according to claim 1, wherein said step 1 comprises:
constructing a second-order code function of the multiphase encoded frequency modulation signal based on the second-order code sequence;
and constructing a time-frequency relation function of the multiphase coding frequency modulation signal based on the second-order code function.
3. The method for generating an orthogonal polyphase coded fm signal according to claim 1, wherein said step 1 comprises:
defining a time-frequency relation coordinate of the multiphase encoded frequency modulation signal as (T, f), wherein T represents corresponding time on an abscissa axis, f represents corresponding instantaneous frequency of the multiphase encoded frequency modulation signal on an ordinate axis, the pulse width of the signal is T, and the bandwidth is B;
constructing a second-order code function χ (t) of the multiphase encoded FM signal according to a second-order code sequence as follows:
wherein a is n For the nth second order sequence value, the time-varying tone frequency is represented, namely: a= [ a ] 1 ,a 2 ,...,a N ]N is the number of second-order sequences; t (T) p =t/N, expressed as pulse width per segment; g (t) is defined in the interval [0, T ] p ]A rectangular shaped filter; delta (t) is expressed as an impulse function;
according to the second-order code function, constructing a time-frequency relation function f (t) of the multiphase coding frequency modulation signal as follows:
f(t)=∫χ(t′)dt′+ω 0
where t' is the integral variable, ω 0 The initial frequency of the frequency modulated signal is encoded for a plurality of phases.
4. A method for generating an orthogonal polyphase coded fm signal according to claim 3, wherein said step 2 comprises:
constructing a phase function of the multiphase encoded frequency modulation signal based on the time-frequency relation function;
and constructing a time domain function of the multiphase encoded frequency modulation signal based on the phase function.
5. A method for generating an orthogonal polyphase coded fm signal according to claim 3, wherein said step 2 comprises:
according to the time-frequency relation function, constructing a phase function theta (t) of the multiphase coding frequency modulation signal as follows:
θ(t)=∫f(t)dt+θ 0
wherein θ 0 An initial phase of the multi-phase encoded FM signal;
constructing a time domain function of the multiphase coded frequency modulation signal with the amplitude A according to the phase function:
s(t)=Aexp{jθ(t)}
where j is the imaginary part of the time domain model, exp {.cndot }, is an exponential function.
6. The method of generating an orthogonal polyphase coded fm signal according to claim 5, wherein said step 4 comprises:
setting the second-order sequences to equal amounts, i.e. to causeAt this time, the multiphase encoded FM signal s 1 (t) is a chirp signal;
encoding a polyphase frequency modulated signal s using genetic algorithm 1 Optimizing peak sidelobe ratio of (t) to obtain initialized multiphase coded frequency modulation signal s 1 (t);
Will s 1 Time-frequency relation function f of (t) 1 (t) taking negative value to obtain another initialized multiphase coded FM signal s 2 Time-frequency relation function f of (t) 2 (t), namely: f (f) 2 (t)=-f 1 (t)。
7. The method of generating an orthogonal polyphase coded fm signal according to claim 6, wherein said step 5 comprises:
and optimizing the acquired initialization signal by utilizing a genetic algorithm according to the time domain function and the optimization model of the multiphase coding frequency modulation signal until the genetic algorithm converges.
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