CN110109061A - A kind of frequency spectrum zero setting Design of Signal method based on template matching - Google Patents
A kind of frequency spectrum zero setting Design of Signal method based on template matching Download PDFInfo
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- CN110109061A CN110109061A CN201910274637.2A CN201910274637A CN110109061A CN 110109061 A CN110109061 A CN 110109061A CN 201910274637 A CN201910274637 A CN 201910274637A CN 110109061 A CN110109061 A CN 110109061A
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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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques
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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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/28—Details of pulse systems
- G01S7/282—Transmitters
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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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/35—Details of non-pulse systems
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- Computer Networks & Wireless Communication (AREA)
- Radar, Positioning & Navigation (AREA)
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- Radar Systems Or Details Thereof (AREA)
Abstract
The frequency spectrum zero setting Design of Signal method based on template matching that the invention discloses a kind of, belong to radar signal processing field, in particular to a kind of fast time-domain signal design method of radar coexists suitable for the multisystem frequency spectrum of the Radar cross-section redaction under narrowband interference environment or frequency spectrum resource under nervous.For template matching fitting problems, the present invention has faster decrease speed and convergence rate, more preferable with the fitting effect of template, is able to achieve better effect of optimization, furthermore the algorithm that the present invention uses possesses lower computation complexity relative to other template algorithms, improves efficiency of algorithm.
Description
Technical field
The invention belongs to radar signal processing field, in particular to a kind of fast time-domain signal design method of radar is applicable in
Multisystem frequency spectrum under the Radar cross-section redaction under narrowband interference environment or frequency spectrum resource are nervous coexists.
Background technique
Due to the fast development that the finiteness and electromagnetic space of electromagnetic spectrum resource are applied, frequency spectrum resource is more nervous,
Spectrum compatible problem more highlights.Remote sensing is detected in radar and timely wireless telecommunications in modern battlefield environment, the wireless applications such as navigation
The overlapped intertexture of frequency spectrum.Spectrum overlapping causes the mutual interference between each application, while having seriously affected radar data reduction, because
This solves the problems, such as that the spectral compatibility between radar and each application is extremely important, spectrum utilization validity of the radar system to transmitted waveform
Demand increasingly increase.We can be perceived by electromagnetic environment, obtain power spectral information, and then prevent thunder by designing waveform
Interfered with each other up to signal with civil signal and hostility interference influence.
Dynamic spectrum estimated information, the phase sequence of Computer Aided Design phase-coded waveform are obtained by electromagnetic environment perception
Column are distributed so as to adjust the power spectral density of waveform, are the effective ways for solving the problems, such as spectral compatibility.For the application that gears to actual circumstances
Scene, radar emission signal usually require to meet some constraint conditions.Specifically, for the transmitting for making full use of radar transmitter
Power, the signal of design meet energy constraint and peak-to-average force ratio (PAR) constraint.Assuming that needing the waveform designed in normalized frequency
Certain several frequency range on have very low power spectral density, pass through minimize modelled signal frequency spectrum and design template covariance
So that the close desired template of the frequency spectrum of design waveform.Document " P.Ge, G.Cui, S.M.Karbasi, L.Kong, and J.Yang,
``A template fitting approach for cognitive unimodular sequence design,”
Signal Processing, vol.128, pp.360-368, Nov.2016 " are made in the algorithm using tolerance iteration decreasing principle
The power spectrum of waveform must be designed and auto-correlation function progressive alternate approaches template, and then realize spectral compatibility and target acquisition performance
It is required that.However, this method optimizes limited capacity, constrained using the non-PAR of permanent modular constraint.
Summary of the invention
For frequency spectrum coexistence problems under narrowband interference environment, present invention assumes that the anti-narrowband of target interferes, such as other communication systems
System considers that PAR constraint and energy propose a kind of base by minimizing the frequency spectrum of modelled signal and the covariance of design template
In the frequency spectrum zero setting Design of Signal method of template matching.Realization approach of the invention is to establish template according to spectrum environment first,
And derived object function；Then constitution optimization problem finally solves the optimization problem.
The technical scheme is that a kind of frequency spectrum zero setting Design of Signal method based on template matching comprising as follows
Step:
Step 1: establishing problem model；
Consideration transmitted waveform s=[s (1), s (2) ..., s (N)]TIt is the fast time signal that N × 1 is tieed up, ()TIndicate transposition；
The passband and stopband for defining its frequency spectrum are respectively ΩpassAnd Ωstop, and meet Ωpass∪Ωstop=0,1 ..., N-1 }；s(n)
Indicate n-th of code word of phase-coded waveform, the discrete Fourier transform of signal s is y, fiFor i-th of lattice of normalized frequency
Point；Assuming that desired energy spectral density template p (i) is
Wherein: ζ indicates stopband expectation amplitude, and to enable the ESD of signal close to desired ESD template, objective function is
Wherein,Expression frequency is fiWhen Fourier transformation
Vector, w (i) >=0, i=0 ..., N-1 are the weight to i-th of frequency lattice point, and α is the matching it is expected ESD and design ESD energy
Scale factor；| | indicate modulus；
In addition, transmitting signal s meets energy constraint and peak-to-average force ratio (PAR) constraint, i.e.,
sHS=N
γ indicates the amplitude constraint to waveform, therefore the optimization problem constrained
Step 2: the problem is solved using four suboptimization algorithm of sequence iteration；
Step 2.1:
Enable α for design the ratio between ESD and desired ESD energy, then α is converted into α=sHCs；Wherein C is Hermitian matrix；Building
MeetHermitian matrix Υ (s), make
H (α, s)=sHΥ(s)s
Due toTherefore Υ (s) is positive semidefinite matrix, nothing but negative feature value；
Equivalence is converted into following optimization problem:
Step 2.2:
It will in the form of sequence iterationIt is converted into
Wherein s(t)Indicate that optimized variable obtained by the t times iteration, I indicate unit matrix；It willThen it is further converted to
Then the solution of the problem is
s(t+1)=Q (s(t))
Wherein, Q (), which is represented, solvesThe function of solution；
Step 3: accelerating algorithm；
Accelerated when each iteration using EM algorithm；
S is solved firsta=Q (s(t)), sb=Q (sa)；Then r=s is solveda-s(t), u=sb-sa- r, α=- | | r | |/| | u
| |, s(t+1)=Q (s(t)-2αr+α2U), saS is worked as in expression(t)When for initial valueThe solution of problem, sbS is worked as in expressionaWhen for initial value
The solution of problem, r indicate front and back iteration s twiceaWith s(t)Difference, u indicates the difference of iteration difference r twice in succession；Work as s(t+1)H[λI-Υ
(s(t))]s(t)< s(t)H[λI-Υ(s(t))]s(t), enable α=(α -1)/2, s(t+1)=Q (s(t)-2αr+α2U), it as α=- 1, moves back
Iteration out,Expression takes real part；When | | s(t+1)-s(t)| |≤ε reaches default the number of iterations or reaches default iteration time
When, iteration is exited, ε is preset threshold value；S at this time(t+1)The frequency spectrum zero setting signal optimized for the present invention.
Compared with the prior art, the present invention has the following advantages:
For template matching fitting problems, the present invention has faster decrease speed and convergence rate, the fitting with template
Effect is more preferable, is able to achieve better effect of optimization, and the algorithm that furthermore present invention uses possesses lower relative to other template algorithms
Computation complexity, improve efficiency of algorithm.
Detailed description of the invention
Fig. 1 is four suboptimization algorithm flow chart of sequence iteration；
Fig. 2 is that the stopband average power spectra that inventive algorithm and template matching (TFA) class algorithm optimization obtain is secondary with iteration
The comparison diagram of number variation
Fig. 3 be inventive algorithm with sequence obtained by TFA algorithm the power spectrum chart in the case where different PAR are constrained.
Specific embodiment
Specific implementation step of the invention is described as follows:
Step 1: establishing problem model；
Consideration transmitted waveform s=[s (1), s (2) ..., s (N)]TIt is the fast time signal that N × 1 is tieed up, defines its frequency spectrum
Passband and stopband are respectively ΩpassAnd Ωstop, and meet Ωpass∪Ωstop=0,1 ..., N-1 }.The direct computation of DFT of signal s
Leaf transformation (DFT) is
Wherein,(·)T、(·)HRespectively indicate transposition and
Conjugate transposition, fiFor i-th of lattice point of normalized frequency.Assuming that desired energy spectral density (ESD) template p (i) is
To enable the ESD of signal close to desired ESD template, objective function is
Wherein, w (i) >=0, i=0 ..., N-1 are the weight to i-th of frequency lattice point, and α is expectation ESD and design ESD energy
The matching scale factor of amount.| | indicate modulus.
In addition, transmitting signal s meets energy constraint and peak-to-average force ratio (PAR) constraint, i.e.,
sHS=N
Therefore the optimization problem of constraint
Step 2: the problem is solved using four suboptimization algorithm of sequence iteration；
Step 2.1:
Enable α for design the ratio between ESD and desired ESD energy:
Wherein,For Hermitian matrix.Then h (α, s) can be turned to
Wherein,Di, i=0 ..., N-1, Υ (s) they are conspicuous
The special matrix of rice.Then
Due toTherefore Υ (s) is positive semidefinite matrix, nothing but negative feature value.
Can equivalence be converted into following optimization problem:
Wherein
Step 2.2:
It will in the form of sequence iterationIt is converted into
Wherein s(t)Indicate optimized variable obtained by the t times iteration；It can then be further converted to
Then the solution of the problem is
s(t+1)=Q (s(t))
Wherein, Q (), which is represented, solves s(t+1)Function.Specifically,
Wherein, s(t+1)(n) nth elements of optimized variable s obtained by the t+1 times iteration are indicated.Arg (a) table
Show the angle of vector a.v(t)It can be expressed as
v(t)=(λ IN-Υ(s(t)))s(t)
It might as well assume v(t)(1)≥v(t)(2)≥…≥v(t)(N), v(t)In be not z for 0 element number.As z γ2≤N
When,
As z γ2When >=N,
|s(t+1)(n) |=min δ | v(t)(n)|,γ}
Wherein,δ can
It is solved by dichotomy.
Step 2.3:
Further, it enables
Accelerated when each iteration using EM algorithm, specifically, solving s firsta=Q (s(t)), sb=Q (sa)；So
After solve r=sa-s(t), u=sb-sa- r, α=- | | r | |/| | u | |, s(t+1)=Q (s(t)-2αr+α2u)；WhenEnable α=(α -1)/2, s(t+1)=Q (s(t)-2αr+α2U), as α=- 1, iteration is exited.Work as s(t +1)When meeting iterated conditional, iteration is exited.
Effect of the invention can further be illustrated by following emulation:
Simulating scenes: setting fast time waveform code length N=200, and initiation sequence selects random phase encoding sequence, normalization frequency
Spectrum stopband is [0.1,0.2] ∪ [0.7,0.8], enables stopband level ζ=- 150dB, when | | s(t+1)-s(t)||≤10-9When exit repeatedly
Generation.
Emulation content:
Emulation 1: identical frequency spectrum coexistence problems are directed to, the identical condition of convergence, the algorithm more of the invention used are set
With the optimization efficiency of TFA algorithm.The stopband that Fig. 2 describes inventive algorithm and other template matching algorithms are optimized is averaged function
Rate composes the change curve with the number of iterations, it follows that inventive algorithm embodies apparent advantage on optimization level, specifically
For, inventive algorithm can reach -147.2dB by 142 iteration stopband average power spectras in PAR=1, and 47 times repeatedly when PAR=4
Reach -149.7dB for stopband average power spectra；And 3000 iteration of TFA algorithm stopband average power spectra in PAR=1 reach-
43.41dB.Therefore by means of the algorithm, the present invention is able to achieve the energy zero setting of power spectrum special frequency channel, is conducive in complicated electromagnetism
Frequency spectrum under environment coexists.
Emulation 2: it for the robustness for analyzing the method for the present invention, is based under the above simulation parameter, the calculation more of the invention used
Power spectrum spectrum fitting performance of the method from TFA algorithm under different PAR constraint.
Fig. 3 describes power spectral density of the different sequences under different PAR constraint, it can be seen that three kinds of sequences all exist
Have power spectrum zero setting at [0.1,0.2] ∪ [0.7,0.8], wherein closest to template be PAR=4 when inventive algorithm optimize
The sequence that inventive algorithm optimizes when sequence, followed by PAR=1, the Spectrum Fitting effect of TFA are worst.
To sum up, the four suboptimization design method of sequence that the present invention is mentioned can be total for complicated electromagnetism crowd scene design frequency spectrum
Sequence is deposited, the interference of other electromagnetic systems in space is effective against, so that sequence coexists compared to no electromagnetism in designed sequence
Show better spectral compatibility.
Claims (1)
1. a kind of frequency spectrum zero setting Design of Signal method based on template matching comprising following steps:
Step 1: establishing problem model；
Consideration transmitted waveform s=[s (1), s (2) ..., s (N)]TIt is the fast time signal that N × 1 is tieed up, ()TIndicate transposition；Definition
The passband and stopband of its frequency spectrum are respectively ΩpassAnd Ωstop, and meet Ωpass∪Ωstop=0,1 ..., N-1 }；S (n) is indicated
N-th of code word of phase-coded waveform, the discrete Fourier transform of signal s are y, fiFor i-th of lattice point of normalized frequency；It is false
If desired energy spectral density template p (i) is
Wherein: ζ indicates stopband expectation amplitude, and to enable the ESD of signal close to desired ESD template, objective function is
Wherein,Expression frequency is fiWhen Fourier transformation to
Amount, w (i) >=0, i=0 ..., N-1 are the weight to i-th of frequency lattice point, and α is the matching ruler it is expected ESD and design ESD energy
Spend the factor；| | indicate modulus；
In addition, transmitting signal s meets energy constraint and peak-to-average force ratio (PAR) constraint, i.e.,
sHS=N
γ indicates the amplitude constraint to waveform, therefore the optimization problem constrained
Step 2: the problem is solved using four suboptimization algorithm of sequence iteration；
Step 2.1:
Enable α for design the ratio between ESD and desired ESD energy, then α is converted into α=sHCs；Wherein C is Hermitian matrix；Building meetsHermitian matrix Υ (s), make
H (α, s)=sHΥ(s)s
Due toTherefore Υ (s) is positive semidefinite matrix, nothing but negative feature value；
Equivalence is converted into following optimization problem:
Step 2.2:
It will in the form of sequence iterationIt is converted into
Wherein s(t)Indicate that optimized variable obtained by the t times iteration, I indicate unit matrix；It willThen it is further converted to
Then the solution of the problem is
s(t+1)=Q (s(t))
Wherein, Q (), which is represented, solvesThe function of solution；
Step 3: accelerating algorithm；
Accelerated when each iteration using EM algorithm；
S is solved firsta=Q (s(t)), sb=Q (sa)；Then r=s is solveda-s(t), u=sb-sa- r, α=- | | r | |/| | u | |, s(t+1)=Q (s(t)-2αr+α2U), saS is worked as in expression(t)When for initial valueThe solution of problem, sbS is worked as in expressionaWhen for initial valueProblem
Solution, r indicates front and back iteration s twiceaWith s(t)Difference, u indicates the difference of iteration difference r twice in succession；Work as s(t+1)H[λI-Υ(s(t))]s(t)< s(t)H[λI-Υ(s(t))]s(t), enable α=(α -1)/2, s(t+1)=Q (s(t)-2αr+α2U), it as α=- 1, exits
Iteration,Expression takes real part；When | | s(t+1)-s(t)| |≤ε or when reaching default the number of iterations or reaching default iteration time,
Iteration is exited, ε is preset threshold value；S at this time(t+1)The frequency spectrum zero setting signal optimized for the present invention.
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