CN108363042A - The waveform implementation method of adaptive spectrum template constraint - Google Patents
The waveform implementation method of adaptive spectrum template constraint Download PDFInfo
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- CN108363042A CN108363042A CN201711340018.6A CN201711340018A CN108363042A CN 108363042 A CN108363042 A CN 108363042A CN 201711340018 A CN201711340018 A CN 201711340018A CN 108363042 A CN108363042 A CN 108363042A
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Abstract
The invention discloses a kind of waveform implementation method of adaptive spectrum template constraint, step includes：Step 1：Build the mathematical model of waveform；Step 2：Object function is added in inequality constraints in step 1 gained functional expression in the form of penalty term, which is non-differentiable function；The non-penalty term that can be micro- is approached with continuously differentiable function again, obtains the mathematical model that gradient descent method can be used to solve；Step 3：The functional expression constructed using gradient descent method solution procedure 2；Step 4：Step 3 is repeated, until x restrains, when meeting the condition of convergence, stops iteration and exports finally obtained waveform x=x(t+1)With spectrum mask α=α(t+1), β=k(t+1)α(t+1),.The waveform that the method for the present invention obtains has diversity, therefore is also equipped with counterreconnaissance characteristic.
Description
Technical field
The invention belongs to wave control technology fields, are related to a kind of waveform implementation method of adaptive spectrum template constraint.
Background technology
Electromagnetic spectrum is as a kind of limited resources of preciousness, in communication, broadcast, television broadcasting, radionavigation and radar
Electromagnetic equipment inside is widely used, and these electromagnetic equipments usually all have bandwidth demand.Since national defence and civilian installation need
Continuous increase, the demand of bandwidth is asked constantly to expand so that natively limited radio-frequency spectrum more seems increasingly
Crowded, the main influence brought is：Many electromagnetism business are forced in a limited frequency range and coexist, hence it is evident that increase mutually dry
The possibility disturbed.Therefore, it is compatible should to reach coordination with other electromagnetic applications for radar emission waveform：1) electromagnetic wave of different business is answered
When the different frequency band of use；2) even if some business use identical frequency range, they should will also interfere with each other and be reduced to and can hold
The level born.
In order to adapt to crowded radio-frequency spectrum, the internationally famous Radar Signal Processing expert of Univ Florida USA and
IEEE Fellow Jian professors Li propose meet spectral constraints (i.e. radar emission waveform is larger in the energy of working frequency range,
The energy that frequency range is occupied in inoperative frequency range or other business is small) SHAPE Waveform Design algorithms, SHAPE algorithms introduce
Then auxiliary variable alternately updates the value of wave sequence and auxiliary variable.In order to reduce radar inoperative frequency range or other
Business occupies the signal energy of frequency range, reduces its interference to other business, Northwestern Polytechnical University professor Liang Junli proposes profit
With the LPNN methods of the thought progressive updating iteration wave sequence of neural network.Further, it is contemplated that radar energy is in inoperative frequency range
Or other business occupy the signal energy of frequency range, the equally distributed actual demand on working frequency range, professor Liang Junli also proposes
The frequency spectrum of waveform implementation method based on ADMM Frame Designs, preferably to meet the demand, the waveform of this method design is shown in
Fig. 1.
The waveform implementation method of above-mentioned spectral constraints is in given radar signal spectrum mask (i.e. in the minimum of working frequency range
The ceiling capacity of energy and inoperative frequency range) under the premise of carry out Waveform Design.However, given spectrum mask is not most to close
Suitable template, deficiency have：1) waveform for meeting spectrum mask is not present；2) exist when meeting the spectrum requirement of working frequency range,
The ceiling capacity of inoperative frequency range can design lower；3) exist when meeting the spectrum requirement of inoperative frequency range, work frequency
The higher that the minimum energy of section can design.Therefore, it is all had some limitations using above method design waveform.
Invention content
The object of the present invention is to provide a kind of waveform implementation methods of adaptive spectrum template constraint, solve the prior art
In, the ceiling capacity of the least energy and inoperative frequency range of adaptive determining working frequency range cannot be taken into account, it is difficult in spectrum mask
Spectrum mask is automatically updated under unknown situation and is led to the problem of meets the spectrum mask requirement waveform.
The technical solution adopted in the present invention is, a kind of waveform implementation method of adaptive spectrum template constraint, according to
Lower step is implemented：
Step 1, the mathematical model for building waveform,
The functional expression (1) of founding mathematical models：
It in view of object function is the ratio of two known variables α and β, is not easy to solve, introduces substitute variableThen
Above-mentioned functional expression (1) variation is functional expression (2)：
Object function is added in inequality constraints in step 1 gained functional expression (2) by step 2 in the form of penalty term, should
Penalty term is non-differentiable function；The non-penalty term that can be micro- is approached with continuously differentiable function again, obtains to use under gradient
The mathematical model that drop method solves；
Step 3, the functional expression constructed using gradient descent method solution procedure 2；
Step 4 repeats step 3, until x restrains,
When meeting the condition of convergence, stops iteration and export finally obtained waveform x=x(t+1)With spectrum mask α=
α(t+1), β=k(t+1)α(t+1),.
The invention has the advantages that in the case of not given spectrum mask, suitable template, and institute are adaptively obtained
Obtained waveform is in the ratio between the upper energy limit of inoperative frequency range and the energy lower limit of working frequency range very little so that the energy quantity set of radar
In in working frequency range, reach and do not waste radar signal energy information and the demand to other electromagnetism traffic interferences of reduction；Meanwhile this
The waveform that inventive method obtains has diversity, therefore is also equipped with counterreconnaissance characteristic.
Description of the drawings
Fig. 1 is the spectrogram for the waveform that the ADMM methods of the prior art obtain；
Fig. 2 is that the factor is approached in the method for the present invention with approximating function to penalty approximation ratio schematic diagram；
Fig. 3 is waveform in the method for the present invention in the ratio between the ceiling capacity of inoperative frequency range and the least energy of working frequency range
Iteration result figure；
Fig. 4 is the spectrogram for the waveform that the method for the present invention obtains.
Specific implementation mode
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
The waveform implementation method of the adaptive spectrum template constraint of the present invention, builds the mathematical model of waveform first；Then
The inequality constraints of model is replaced with continuously differentiable function appropriate, and is transferred in object function, new mathematical modulo is obtained
Type；It finally uses gradient descent method to solve new model and finally obtains one to obtain the detection waveform x for meeting constraints
Signal sequence x={ the x that a length is N, mould is 11,...,xNSo that signal sequence inoperative frequency range highest energy β with
The ratio between the minimum energy α of working frequency range minimums.
The waveform implementation method of the adaptive spectrum template constraint of the present invention, implements according to the following steps：
Step 1, the mathematical model for building waveform,
During actual transmission, waveform needs to meet following condition：
1) permanent mould：In order to maximize emission effciency and detectivity, it is desirable that power amplifier is operated in saturation stage, i.e.,
Emit signal constant mould；Therefore need to design single mode sequence, i.e. x meets | x (n) |=1, n=1 ..., N, wherein x=[x
(1),…,x(N)]TFor the vectorial expression-form of sequence x to be designed, T is transposition symbol；
2) interested frequency range is normalized to：According to the frequency domain theory of signal system it is found that x
Frequency-region signal be：Y=FHX=[y1,…,yN]T,
Wherein, H is conjugate transposition symbol, F=[f1,… fN], fn=[1, ej2πn,…,ej2πn(N-1)]T, n is normalized
Frequency, value are
3) mostly anti-interference using coexisting：Due to being continuously increased for national defence and civilian installation demand, many electromagnetism business are forced
Coexisted in a limited frequency range, radar emission waveform should reach with other electromagnetic applications coordinate it is compatible, i.e.,：
On using specified working frequency range P, the energy of radar signal is all higher than certain level α, i.e., Indicate the aleatory variable in set；On the frequency range S that other business use, radar
The energy of signal is reduced under certain level β, i.e.,Frequency range P and S meets
4) spectrum mask is unknown：That is α and β is unknown to be calculated, in order to improve radar signal as much as possible in working frequency range
Energy reduces interference of the radar signal to other business, it is desirable that the ratio for meeting β and α is as small as possible, i.e.,It is the smaller the better,
In summary four conditions establish the functional expression of mathematical model shown in following formula (1)：
It in view of object function is the ratio of two known variables α and β, is not easy to solve, introduces substitute variableThen
Above-mentioned functional expression (1) variation is functional expression (2)：
Object function is added in inequality constraints in step 1 gained functional expression (2) by step 2 in the form of penalty term, should
Penalty term is non-differentiable function；The non-penalty term that can be micro- is approached with continuously differentiable function again, obtains to use under gradient
The mathematical model that drop method solves, detailed process are：
2.1) object function is added in inequality constraints in the form of penalty term,
Define penalty gsWith gpRespectively：
So, functional expression (2) is equivalent to following target function type (4)：
Wherein,WithFor the corresponding penalty term of two inequality constraints in formula (2),
Obviously, it is constrained when the energy of radar signal in inoperative frequency range meets no more than k α, that is, x, α and k
When, gs=0；Otherwise, gs>0 and radar energyDegree more than given energy value k α is bigger, penalty gsIt is bigger,
Subitem g in penalty terms 2Value it is bigger；
It is constrained when the energy of radar signal on working frequency range meets not less than α, that is, x and βWhen, gp=0；It is no
Then, gp>0 and radar energyDegree less than given energy value α is bigger, penalty gpIt is bigger, the son in penalty term
Item gp 2Value it is bigger.
Therefore, when the energy of radar signal meets the inequality constraints in functional expression (2), penalty term
Be 0, otherwise penalty term be positive value and be unsatisfactory for item departure degree it is bigger, the subitem value of corresponding penalty term is bigger.
Because functional expression (3-1) and (3-2) are non-differentiable functions, also right and wrong can for the object function in functional expression (4)
Micro- function；The method of the present invention is by introducing a new, continuously differentiable function come approximating function formula (3-1) and (3-2) and letter
Corresponding penalty term in numerical expression (4), so construction one can use the optimization problem that gradient descent method solves, and then convenient pair
The problem is solved.
2.2) the continuously differentiable approximating function of penalty,
For continuously differentiable functionWith continuously differentiable functionS ∈ S, p ∈ P, then have：
Wherein, μ>0, then there are following two inferences：
Inference 1：With gsRelationship bes∈S；With gp gsRelationship be
p∈P；
It proves：It enables Then f1With f2It is considered as about change
Measure ysFunction, from functional expression (3-1) and function formula (5-1)：
1) work as ysWhen≤0,
2) when 0<ysWhen≤μ,
So, And if only if ysF when=μ1'=
f2'=0, then haveAnd if only if ysF when=01=0, and if only if ysF when=μ2=0；
3) work as μ<ysWhen,
To sum up,s∈S；Proving by the same methods
Inference 2：Work as parameter μ>0 is smaller,More approach gs(s∈S)、More approach gp(p∈P)；
It proves：It enables It is obtained according to inference 1It can
It obtains
Therefore, as μ → 0, f1→ 0, i.e.,Similarly, as μ → 0,
It is based on inference 2 as a result, the method for the present invention parameter μ is referred to as to approach the factor, in order to have more intuitively to inference 2
Solution, approaches factor value and functionTo gsThe schematic diagram of approximation ratio is shown in Fig. 2.
According to inference 1 and inference 2 as a result, approach factor mu value it is smaller when, by by the penalty g of non-differentiabilitysWith
gpReplace with continuously differentiable functionWithMode so that the approximate variation of functional expression (4) is following functional expression (7)：
Wherein, object functionIt is continuously differentiable function；
Step 3, the functional expression (7) constructed using gradient descent method solution procedure 2,
The gradient of function h (x, k, α) is：
Correlated variables value mode difference therein is as follows,
Using gradient descent method, update solves variable α, k：
In view of the permanent modular constraint about x：| x (n) |=1, n=1 ..., N, variable x(t+1)Be updated to：
Step 4 repeats step 3, until x restrains, obtains detection waveform x and adaptive spectrum template α, β,
In view of working as target function value h (x(t+1),k(t+1),α(t+1)) and h (x(t),k(t),α(t)) difference very little when, can will
h(x(t+1),k(t+1),α(t+1)) local minimum of approximatively regarding object function h (x, k, α) as, i.e., it approximatively obtains meeting mould
The waveform x=x of type function formula (1)(t+1)With spectrum mask α=α(t+1), β=k(t+1)α(t+1), therefore, the present invention is by the condition of convergence
It is determined as：
When meeting the condition of convergence, stops iteration and export finally obtained waveform x=x(t+1)With spectrum mask α=
α(t+1), β=k(t+1)α(t+1),.
Finally, the present invention obtains that a length is N, power amplifier is operated in the detection waveform x that saturation stage i.e. mould is 1
With adaptive spectrum template α, β so that waveform x is sufficiently small to reduce it to industry coexists in the highest energy β of inoperative frequency range
The interference of business, and the ratio between minimum energy α of β and working frequency range is minimum, and radar energy is concentrated on working frequency range to realize, and
And do not waste the energy of radar detection.
Embodiment
One length of the method for the present invention the Realization of Simulation is the waveform of N=162.
Corresponding parameter is：Approach factor mu=10-3, radar sampling frequency 810kHz, 200 μ s of pulse spacing are occupied
Frequency band facilities are shown in Table 1, and passband is all frequency ranges outside band occupancy in table 1.
Table 1, occupied frequency band facilities
Fig. 3 is the obtained waveform of the embodiment of the present invention in the ceiling capacity of inoperative frequency range and the least energy of working frequency range
The ratio between iteration result figure.The spectrogram of gained waveform is shown in Fig. 4.Ceiling capacity of the waveform of the method for the present invention in inoperative frequency range
It can be down to -18.80dB with the ratio between the least energy of working frequency range.
Claims (5)
1. a kind of waveform implementation method of adaptive spectrum template constraint, which is characterized in that implement according to the following steps：
Step 1, the mathematical model for building waveform, the functional expression (1) of founding mathematical models：
It in view of object function is the ratio of two known variables α and β, is not easy to solve, introduces substitute variableIt is then above-mentioned
Functional expression (1) variation is functional expression (2)：
Object function is added in inequality constraints in step 1 gained functional expression (2) by step 2 in the form of penalty term, the punishment
Item is non-differentiable function；The non-penalty term that can be micro- is approached with continuously differentiable function again, obtains that gradient descent method can be used
The mathematical model of solution；
Step 3, the functional expression constructed using gradient descent method solution procedure 2；
Step 4 repeats step 3, until x restrains,
When meeting the condition of convergence, stops iteration and export finally obtained waveform x=x(t+1)With spectrum mask α=α(t+1), β=
k(t+1)α(t+1),.
2. the waveform implementation method of adaptive spectrum template constraint according to claim 1, which is characterized in that the step
In rapid 1, waveform needs to meet following condition：
1) permanent mould：Need to design single mode sequence, i.e. x meets | x (n) |=1, n=1 ..., N, wherein x=[x (1) ..., x (N)]T
For the vectorial expression-form of sequence x to be designed, T is transposition symbol；
2) interested frequency range is normalized to：According to the frequency domain theory of signal system it is found that the frequency domain of x
Signal is：Y=FHX=[y1,…,yN]T,
Wherein, H is conjugate transposition symbol, F=[f1,… fN], fn=[1, ej2πn,…,ej2πn(N-1)]T, n is normalized frequency
Rate, value are
3) mostly anti-interference using coexisting：On using specified working frequency range P, the energy of radar signal is all higher than certain level α,
I.e. Indicate the aleatory variable in set；On the frequency range S that other business use, thunder
Energy up to signal is reduced under certain level β, i.e.,Frequency range P and S meets
4) spectrum mask is unknown：That is α and β is unknown to be calculated, it is desirable that the ratio for meeting β and α is as small as possible, i.e.,It is the smaller the better.
3. the waveform implementation method of adaptive spectrum template constraint according to claim 2, which is characterized in that the step
In rapid 2, detailed process is：
2.1) object function is added in inequality constraints in the form of penalty term,
Define penalty gsWith gpRespectively：
So, functional expression (2) is equivalent to following target function type (4)：
Wherein,WithFor the corresponding penalty term of two inequality constraints in formula (2),
It is constrained when the energy of radar signal in inoperative frequency range meets no more than k α, that is, x, α and kWhen, gs=0, it is no
Then gs>0 and radar energyDegree more than given energy value k α is bigger, penalty gsIt is bigger, the son in penalty term
Item gs 2Value it is bigger；
It is constrained when the energy of radar signal on working frequency range meets not less than α, that is, x and βWhen, gp=0, otherwise gp>0
And radar energyDegree less than given energy value α is bigger, penalty gpIt is bigger, the subitem g in penalty termp 2's
Value is bigger,
Therefore, when the energy of radar signal meets the inequality constraints in functional expression (2), penalty termIt is 0,
Otherwise penalty term be positive value and be unsatisfactory for item departure degree it is bigger, the subitem value of corresponding penalty term is bigger；
2.2) the continuously differentiable approximating function of penalty,
For continuously differentiable functionWith continuously differentiable functionS ∈ S, p ∈ P, then have：
Wherein, μ>0, then there are following two inferences：
Inference 1：With gsRelationship bes∈S；With gp gsRelationship bep∈P；
Inference 2：Work as parameter μ>0 is smaller,More approach gs(s∈S)、More approach gp(p∈P)；
It is based on inference 2 as a result, the method for the present invention parameter μ is referred to as to approach the factor,
According to inference 1 and inference 2 as a result, approach factor mu value it is smaller when, by by the penalty g of non-differentiabilitysWith gpIt replaces
It is changed to continuously differentiable functionWithMode so that the approximate variation of functional expression (4) is following functional expression (7)：
Wherein, object functionIt is continuously differentiable function.
4. the waveform implementation method of adaptive spectrum template constraint according to claim 3, which is characterized in that the step
In rapid 3, using the functional expression (7) of the construction of gradient descent method solution procedure 2, detailed process is：The gradient of function h (x, k, α) is：
Correlated variables value mode difference therein is as follows,
Using gradient descent method, update solves variable α, k：
In view of the permanent modular constraint about x：| x (n) |=1, n=1 ..., N, variable x(t+1)Be updated to：
5. the waveform implementation method of adaptive spectrum template constraint according to claim 4, which is characterized in that the step
In rapid 4, detailed process is：
In view of working as target function value h (x(t+1),k(t+1),α(t+1)) and h (x(t),k(t),α(t)) difference very little when, by h (x(t +1),k(t+1),α(t+1)) local minimum of approximatively regarding object function h (x, k, α) as, i.e., it approximatively obtains meeting model letter
The waveform x=x of numerical expression (1)(t+1)With spectrum mask α=α(t+1), β=k(t+1)α(t+1), the condition of convergence is determined as：
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| CN113283413A (en) * | 2021-07-26 | 2021-08-20 | 枫树谷(成都)科技有限责任公司 | Method, system, storage medium and device for creating pulse waveform template library |
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