CN104865558B - The combined optimization method of phase-coded signal and mismatched filter based on p norms - Google Patents
The combined optimization method of phase-coded signal and mismatched filter based on p norms Download PDFInfo
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- CN104865558B CN104865558B CN201510315814.9A CN201510315814A CN104865558B CN 104865558 B CN104865558 B CN 104865558B CN 201510315814 A CN201510315814 A CN 201510315814A CN 104865558 B CN104865558 B CN 104865558B
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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
- G01S7/2813—Means providing a modification of the radiation pattern for cancelling noise, clutter or interfering signals, e.g. side lobe suppression, side lobe blanking, null-steering arrays
Abstract
The invention belongs to Radar Technology field, the combined optimization method of a kind of phase-coded signal based on p norms and mismatched filter is disclosed.The combined optimization method comprises the following steps：Set the Baud Length of phase-coded signal and the length of mismatched filter, and maximum signal to noise ratio loss；Determine mismatched filter output result of the phase-coded signal by mismatched filter, and the phase-coded signal mismatched filter output result that passes through mismatched filter peak sidelobe；Build the Optimality Criteria of phase-coded signal and mismatched filter；Form conversion is carried out to Optimality Criteria；Solve the amplitude for obtaining the phase of phase-coded signal, the phase of mismatched filter and mismatched filter；Construct phase-coded signal and mismatched filter.The present invention can reduce the distance side lobe level of radar receiving channel.
Description
Technical field
The invention belongs to Radar Technology field, and in particular to a kind of phase-coded signal and mismatch filter based on p norms
The combined optimization method of device, the distance side lobe level for reducing radar receiving channel.
Background technology
Pulse compression technique solves the contradiction between the operating distance of radar and range resolution ratio, but pulse compression signal
Generally there is higher distance side lobe, and higher distance side lobe is unfavorable for radar and target is effectively detected, and particularly exists
Faint target detection under multiple target or strong clutter background, the main lobe of weak signal target is easily flooded by the distance side lobe of strong target echo to be made
Into false dismissal.Therefore signal waveform of the design with distance good sidelobe performance has important meaning to the detection performance for improving radar
Justice.
From at present both at home and abroad to phase-coded signal research conditions from the point of view of, two kinds suppression distance side lobes methods respectively be compile
Code is preferably and mismatch filter.The method for obtaining low distance side lobe signal in the past is that, using the special encoded signal of certain class, modern age is obtained
The major way for taking phase-coded signal is solved by optimized algorithm.By optimizing by phase-coded signal auto-correlation
The sidelobe level that the method for valve can reach is generally still higher.
Therefore the sidelobe level of system can further be reduced using the method for mismatch filter in receiving terminal.Phase code is believed
Number it is typically constant modulus signals, and the weight coefficient of mismatched filter can then break through this limitation, realize that lower distance side lobe is defeated
Go out.The problem of due to optimization means, conventional mismatch filter algorithm is generally excellent by phase-coded signal and mismatched filter difference
Change, problem is solved by way of intersecting optimization, this algorithm can be effectively reduced the distance side lobe output of system.
One existing method is by optimizing a collection of low distance side lobe phase-coded signal and being to search based on these signals
Suo Qidian, while finding the weight coefficient of phase-coded signal and mismatched filter.But, if the starting letter of phase-coded signal
Number it is the phase-coded signal with low distance side lobe level, then method may exclude the optimization knot that some may be more excellent
Really.
The content of the invention
For above-mentioned technical problem, it is an object of the invention to provide a kind of phase-coded signal based on p norms and mistake
Combined optimization method with wave filter, can reduce the distance side lobe level after phase-coded signal pulse compression.
Realizing the technical thought of the present invention is：According to the length of the Baud Length of phase-coded signal and mismatched filter with
Machine produces its initial value, under conditions of maximum signal to noise ratio loss is constraint, to minimize the peak sidelobe after mismatch filter
For Optimality Criteria, combined optimization designed phase encoded signal and mismatched filter, and using based on L-BFGS (limited
Memory Broyden-Fletcher-Goldfarb-Shanno, Quasi-Newton algorithm) Least p-norm optimized algorithm asked
Solution.
To reach above-mentioned purpose, the present invention, which is adopted the following technical scheme that, to be achieved.
The embodiment of the present invention provides a kind of combined optimization side of phase-coded signal and mismatched filter based on p norms
Method, it is characterised in that comprise the following steps：
Step 1, setting phase-coded signal s Baud Length NsWith mismatched filter h length Nh, and maximum noise
Than loss SNRloss, wherein, Nh≥NsAnd Nh+NsFor even number；
Step 2, mismatched filter output results of the phase-coded signal s by the mismatched filter h is determinedAnd the phase-coded signal s is filtered by the mismatch of the mismatched filter h
Ripple device output result ρ peak sidelobeWherein,Represent convolution, []T
Represent transposition, i ∈ [1,2 ..., Ns+Nh-1]；
Step 3, the maximum signal to noise ratio is lost into SNRlossAs constraints, to minimize the peak sidelobe
PSL is object function, and the Optimality Criteria for building the phase-coded signal s and mismatched filter h is
Wherein, energy differences γ and peak difference values δ are preset,For the phase of the phase-coded signal s, θ is described
Mismatched filter h phase, A is the amplitude of the mismatched filter h；
Step 4, form conversion is carried out to the Optimality Criteria, obtained
Wherein, vector x is the phase of the phase-coded signal s, the mismatched filter h amplitude A and the mismatch
The column vector of wave filter h phase theta compositionWherein,ρsFor by institute
State knots of the phase-coded signal s by the mismatched filter output result ρ of mismatched filter h sidelobe level Modulus of access
Really, energy weight coefficient α and peak value weight coefficient β value belong in the range of [0,1]；
Step 5, solveThe vector x is obtained, so that
To the phase of the phase-coded signal sThe phase theta of the amplitude A of the mismatched filter h and the mismatched filter h；
Step 6, according to the phase of the phase-coded signal sConstruct the phase-coded signalRoot
According to the phase theta and the amplitude A of the mismatched filter h of the mismatched filter h, the mismatched filter h=A ⊙ exp are constructed
(jθ)。
The characteristics of technical solution of the present invention and further it is improved to：
Energy differences γ described in step 3 according toIt is determined that, the peak difference values δ according toIt is determined that, wherein, SNRlossLost for maximum signal to noise ratio, NsFor the code element of the phase-coded signal s
Length.
Solved in step 5 using the optimized algorithm of the Least p-norm based on L-BFGS
Obtain the vector x.
Further, solved using the optimized algorithm of the Least p-norm based on L-BFGS
The vector x is obtained, following sub-step is specifically included
Suddenly：
(5a) defined function
(5b) sets the initial value x of the vector x0, minimum descent ε1Initial value and iterations n initial value be
1st, norm p initial value p0, multiplier μ value and the initial value f of the function f (x)0；
(5c) uses vector xn-1As initial value, by minimizing function f (xn-1) try to achieve optimum results vector xn, make fn
=f (xn)；
(5d) if | fn-fn-1|<ε1, then output vector xn, and stop circulation；Otherwise iterations n adds 1, and makes norm
pn=μ pn-1, and skip to sub-step (5c) and continue executing with；
(5e) determines the vector x.
The present invention has the following advantages that compared with prior art.Technical solution of the present invention is in certain letter than losing as constraint
Under the conditions of, to minimize the peak sidelobe after mismatch filter as criterion, combined optimization designed phase encoded signal and mismatch
Wave filter, and solved using the Least p-norm optimized algorithm based on L-BFGS, it can further reduce phase-coded signal
Peak sidelobe after mismatch filter.
Brief description of the drawings
The present invention will be further described with reference to the accompanying drawings and detailed description.
Fig. 1 is the combined optimization of the phase-coded signal provided in an embodiment of the present invention based on p norms and mismatched filter
The schematic flow sheet of method；
Fig. 2 is the schematic flow sheet of the Least p-norm optimized algorithm provided in an embodiment of the present invention based on L-BFGS；
Fig. 3 is the schematic diagram of the normalized peak sidelobe of matched filter output, and abscissa represents relative time delay,
Unit is us, and ordinate represents amplitude, and unit is dB；
Fig. 4 is to use document [Nunn C.Constrained optimization applied to pulse
compression codes and filters[C].IEEE International Radar Conference,2005:
190-194.] method mismatch filter after the normalized peak sidelobe figure that exports, abscissa represents relative time delay, unit
For us, ordinate represents amplitude, and unit is dB；
Fig. 5 is the normalized peak sidelobe figure of mismatched filter output provided in an embodiment of the present invention, abscissa
Relative time delay is represented, unit is us, and ordinate represents amplitude, and unit is dB；
Fig. 6 is the normalized peak sidelobe figure of Fig. 5 initial phase encoded signals, and abscissa represents relative time delay,
Unit is us, and ordinate represents amplitude, and unit is dB.
Embodiment
As shown in figure 1, the joint of phase-coded signal and mismatched filter provided in an embodiment of the present invention based on p norms
Optimization method, comprises the following steps：
Step 1, setting phase-coded signal s Baud Length NsWith mismatched filter h length Nh, and maximum noise
Than loss SNRloss。
Wherein, Nh≥Ns, and Nh+NsFor even number.Normal conditions require snr loss SNRloss≤1dB。
Step 2, mismatched filter output results of the phase-coded signal s by mismatched filter h is determinedAnd phase-coded signal s is exported by mismatched filter h mismatched filter
As a result ρ peak sidelobe
Wherein,Represent convolution, []TRepresent transposition, i ∈ [1,2 ..., Ns+Nh-1]。
Assuming that phase-coded signal is s, mismatched filter is h, the mismatch that phase-coded signal s passes through mismatched filter h
Wave filter output result ρ is expressed as：
Wherein,Represent convolution, []TRepresent transposition, i ∈ [1,2 ..., Ns+Nh- 1], NsRepresent phase-coded signal s's
Baud Length, NhRepresent mismatched filter h length.
The peak sidelobe for the mismatched filter output result ρ that phase-coded signal s passes through mismatched filter h is：
Wherein, | | represent Modulus of access, k ∈ [1, Ns+Nh-1]。
Step 3, maximum signal to noise ratio is lost into SNRlossAs constraints, to minimize peak sidelobe
PSL is object function, and the Optimality Criteria for building phase-coded signal s and mismatched filter h is
Wherein, energy differences γ and peak difference values δ are preset,For phase-coded signal s phase, θ is mismatch filter
Device h phase, A is mismatched filter h amplitude.
In the case where given maximum signal to noise ratio loss is constraints, using minimize the peak sidelobe after mismatch filter as
Object function, the Optimality Criteria for building phase-coded signal s and mismatched filter h is as follows：
Wherein, PSL is the peak sidelobe that mismatched filter is exported,For phase-coded signal s phase vectors, i.e.,A and θ are respectively mismatched filter h amplitude and phase, i.e. h=A ⊙ exp (j θ), and ⊙ represents dot product, exp
() represents exponential function, and j is imaginary unit, and energy differences γ and peak difference values δ set for maximum signal to noise ratio loss according to people
Fixed arithmetic number, energy differences γ and peak difference values δ can be determined according to following empirical equation respectively,
Here the energy differences γ and peak difference values δ determined is an empirical equation, in practice, according to the empirical equation
Obtained simulation result may deviate the snr loss of actual requirement, now need artificial to energy differences γ and peak value
The value of value of delta is adjusted, and the process of energy differences γ and peak difference values δ value adjustment follows following rule：Energy difference
When value γ immobilizes, peak difference values δ is bigger, and snr loss is bigger, but peak sidelobe now can be reduced；Peak difference
When value δ immobilizes, energy differences γ is bigger, and snr loss is smaller, but peak sidelobe now can be raised.Therefore,
It is determined that needing when energy differences γ and peak difference values δ to compromise to consider.
Step 4, form conversion is carried out to phase-coded signal s and mismatched filter h Optimality Criteria, obtained
Wherein, vector x is by phase-coded signal s phase, mismatched filter h amplitude A and mismatched filter h
The column vector of phase theta composition ρsFor phase-coded signal s is passed through
Cross the result of mismatched filter h mismatched filter output result ρ sidelobe level Modulus of access, energy weight coefficient α and peak value power
The value of factor beta belongs in the range of [0,1].
In order to solve conveniently, phase-coded signal s and mismatched filter h Optimality Criteria are changed, its specific bag
Include following sub-step：
(4a) passes through phase-coded signal s mismatched filter h mismatched filter output result ρ sidelobe level modulus
The result of value is designated as：
Wherein, i ∈ [1,2 ..., Ns+Nh, and i ≠ (N -1]h+Ns)/2, NsPhase-coded signal s Baud Length is represented,
NhRepresent mismatched filter h length.
(4b) conversion after Optimality Criteria be：
Wherein, vector x is by phase-coded signal s phaseMismatched filter h amplitude A and mismatched filter h's
The column vector of phase theta composition||·||∞Infinite Norm is represented, energy weight coefficient α and peak value weight coefficient β are people
For the arithmetic number of setting, for the size of compromise Sidelobe Suppression effect and snr loss, energy weight coefficient α and peak value weight coefficient
β value is selected in the range of [0,1] respectively, and then the snr loss in actual emulation result is adjusted
It is whole.
Object function peak sidelobe PSL can be written as | | ρs||∞.In fact, minimize | | ρs||∞Minimum can be passed through
Change | | ρs||pRealize, along with the increase of p numerical value, minimize a series of | | ρs||pCan approximately equivalent for minimize | | ρs||∞,
Wherein, | | | |∞Infinite Norm is represented, | | | |pRepresent p norms, p >=2.
For the Solve problems of above-mentioned Optimality Criteria, existing Minimax Algorithm can be used to optimize solution；This
Inventive embodiments are solved using a kind of minimax optimized algorithm based on Least p-norm.
Step 5, solveVector x is obtained, so as to obtain phase
Position encoded signal s phaseMismatched filter h phase theta and mismatched filter h amplitude A.
As shown in Fig. 2 to be solved using the optimized algorithm of the Least p-norm based on L-BFGS The specific sub-step of vector x is obtained, including：
(5a) defined function：
（5b）The initial value x of vector x is set0With minimum descent ε1Initial value, and iterations n initial value be 1, model
Number p initial value p0, multiplier μ=2, function initial value f0=100；
(5c) is by using document [Wang Y C, Wang X, Liu H W, et al.On the Design of
Constant Modulus Probing Signals for MIMO Radar Signal Processing[J].IEEE
Transactions on Signal Processing,2012,60(8):4432-4438.] L-BFGS algorithmic minimizing letters
Number f (x), wherein, the update times m=5 of L-BFGS algorithms, vector xn-1As the initial value of L-BFGS algorithms, optimum results are
Vector xn, make fn=f (xn)；
(5d) if | fn-fn-1|<ε1, then output vector xnAnd stop circulation；Otherwise iterations n adds 1, and makes norm pn
=μ pn-1, skip to sub-step (5c)；
The vector x that (5e) is obtained by above-mentioned sub-stepn, it is determined that vectorialSo that it is determined that phase code
Signal s phaseMismatched filter h phase theta and mismatched filter h amplitude A.
Step 6, according to phase-coded signal s phaseConstruct the phase-coded signalAccording to mistake
The amplitude A of phase theta and mismatched filter h with wave filter h, construction mismatched filter h=A ⊙ exp (j θ).
By step 5 optimize after obtained vector x so that phase-coded signal s phaseBy the 1st in column vector x to
NsIndividual element composition, mismatched filter h amplitude A is by the N in column vector xs+ 1 to Ns+NhIndividual element composition, mismatch filter
Device h phase theta is by the N in column vector xs+Nh+ 1 to Ns+Nh+NhIndividual element is constituted, then phase-coded signalMismatched filter h=A ⊙ exp (j θ), wherein ⊙ represents dot product.
The effect of the present invention can be further illustrated by following simulation result：
(1) simulated conditions
The he number N of phase-coded signal in this emulations=128, the length N of mismatched filterh=256, signal to noise ratio is damaged
Lose SNRloss≤0.25dB。
(2) emulation content
Emulation 1, using the phase-coded signal that Least p-norm algorithm optimization Baud Length is 128, phase-coded signal
Phase initial value is randomly generated, and Fig. 3 is the matched filtering result of signal.From the figure 3, it may be seen that the peak side-lobe electricity after matched filtering
Put down as -35.9332dB.
Emulation 2, utilizes the signal and document [Nunn C.Constrained optimization after the optimization of emulation 1
applied to pulse compression codes and filters[C].IEEE International Radar
Conference,2005:190-194.] in weighted iteration least square method design mismatched filter, Fig. 4 be mismatch filter after
Result.Peak sidelobe is -42.1827dB after mismatch filter as shown in Figure 4, and snr loss is -0.2448dB.
Emulation 3, simulated conditions weights α=0.2, β=0.35, for each optimization design, phase-coded signal s phase, mismatched filter h amplitude A and the initial value of phase theta all randomly generate, optimize 100 times and choose optimal results, Fig. 5
For the mismatched filter output result after phase-coded signal s and mismatched filter h combined optimizations.As shown in Figure 5, peak side-lobe
Level is -45.5728dB, and snr loss is -0.1903dB.
Fig. 6 is the normalized peak sidelobe figure of Fig. 5 initial phase encoded signals, compared with Fig. 3 result, Fig. 6
In the high 20.0641dB of peak sidelobe；Compared with the result in Fig. 4, the peak sidelobe in Fig. 5 is reduced
3.3901dB, and snr loss is smaller.Therefore, combined optimization phase-coded signal s and mismatched filter h, start-up phase are passed through
Position encoded signal need not have relatively low sidelobe level；And under conditions of snr loss is certain, can further reduce mismatch
Filtered peak sidelobe.
Above description is only example of the present invention, does not constitute any limitation of the invention.Obviously for
, all may be without departing substantially from the principle of the invention, structure after present invention and principle has been understood for one of skill in the art
In the case of, the various modifications and variations in progress form and details, but these modifications and variations based on inventive concept
Still within the claims of the present invention.
Claims (3)
1. the combined optimization method of phase-coded signal and mismatched filter based on p norms, it is characterised in that including following step
Suddenly：
Step 1, setting phase-coded signal s Baud Length NsWith mismatched filter h length Nh, and maximum signal to noise ratio damage
Lose SNRloss, wherein, Nh≥NsAnd Nh+NsFor even number；
Step 2, mismatched filter output results of the phase-coded signal s by the mismatched filter h is determinedAnd the phase-coded signal s is filtered by the mismatch of the mismatched filter h
Ripple device output result ρ peak sidelobeWherein,Represent convolution, []TTable
Show transposition, i ∈ [1,2 ..., Ns+Nh-1]；
Step 3, the maximum signal to noise ratio is lost into SNRlossAs constraints, using minimize the peak sidelobe PSL as
Object function, the Optimality Criteria for building the phase-coded signal s and mismatched filter h is
s.t. |hHh-sHs|≤γ
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Wherein, energy differences γ and peak difference values δ are preset,For the phase of the phase-coded signal s, θ is the mismatch
Wave filter h phase, A is the amplitude of the mismatched filter h；
Step 4, form conversion is carried out to the Optimality Criteria, obtained：
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Wherein, vector x is the phase of the phase-coded signal sThe amplitude A and the mismatch filter of the mismatched filter h
The column vector of device h phase theta compositionWherein,ρsFor by the phase
Results of the position encoded signal s by the mismatched filter output result ρ of mismatched filter h sidelobe level Modulus of access, energy
Amount weight coefficient α and peak value weight coefficient β value belongs in the range of [0,1]；
Step 5, solveThe vector x is obtained, so as to be combined
The phase of phase-coded signal s after optimizationMismatched filter h amplitude A and mismatched filter h phase theta；
SolveThe vector x is obtained, following sub-step is specifically included
Suddenly：
(5a) defined function
(5b) sets the initial value x of the vector x0, minimum descent ε1Initial value and iterations n value, norm p initial value
p0, multiplier μ value and the initial value f of the function f (x)0；
(5c) uses vector xn-1As initial value, by minimizing function f (xn-1) try to achieve optimum results vector xn, make fn=f
(xn)；
(5d) if | fn-fn-1|<ε1, then output vector xn, and stop circulation；Otherwise iterations n adds 1, and makes norm pn=μ
pn-1, and and skip to sub-step (5c) and continue executing with；
(5e) determines the vector x；
Step 6, according to the phase of the phase-coded signal s after combined optimizationConstruct the phase-coded signalAccording to the phase theta of the mismatched filter h and the amplitude A of the mismatched filter h, the mismatch filter is constructed
Ripple device h=A ⊙ exp (j θ).
2. phase-coded signal as claimed in claim 1 based on p norms and the combined optimization method of mismatched filter, it is special
Levy and be, energy differences γ described in step 3 according toIt is determined that, the peak difference values δ according toIt is determined that, wherein, SNRlossLost for maximum signal to noise ratio, NsFor the code element of the phase-coded signal s
Length.
3. phase-coded signal as claimed in claim 1 based on p norms and the combined optimization method of mismatched filter, it is special
Levy and be, solved in steps of 5 using the optimized algorithm of the Least p-norm based on L-BFGS Obtain the vector x.
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| CN105301572B (en) * | 2015-09-17 | 2017-11-10 | 西安电子科技大学 | Multi-peak low sidelobe phase-coded signal and mismatched filter co-design method |
| CN105116382B (en) * | 2015-09-17 | 2017-11-14 | 西安电子科技大学 | The mismatched filter design method of the low Doppler sidelobne phase-coded signal of multi-peak |
| CN108736939B (en) * | 2017-04-13 | 2021-02-09 | 华为技术有限公司 | Method and apparatus for beam training |
| CN107843877B (en) * | 2017-09-28 | 2021-10-01 | 西安电子科技大学 | Mismatching filter bank combined design method based on double-minimum p-norm algorithm |
| CN111025258B (en) * | 2019-12-04 | 2022-02-08 | 北京理工大学 | Joint mismatch filter for radar waveform diversity and design method thereof |
| CN113489573B (en) * | 2021-09-07 | 2021-11-12 | 中国人民解放军国防科技大学 | Bistatic radar communication integrated waveform design method, computer device and medium |
| CN116482621B (en) * | 2023-06-14 | 2023-08-22 | 北京理工大学 | Initial phase agile pulse train waveform design method based on distance gating performance optimization |
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