CN107976655B - Radar cross-section redaction Waveform generation method based on Stackelberg game - Google Patents
Radar cross-section redaction Waveform generation method based on Stackelberg game Download PDFInfo
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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
- G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
Abstract
The invention discloses a kind of Radar cross-section redaction Waveform generation method based on Stackelberg game, anti-interference Waveform generation method failure when anti-interference Waveform generation method of the existing technology can only be applicable in and count multiple-input and multiple-output MIMO radar and radar signal prior to interference signal transmitting is mainly solved the problems, such as.Specific steps of the invention are as follows: 1, determine parameter；2, objective function is constructed；3, anti-interference waveform when radar is leader leader is obtained；4, anti-interference waveform when radar is follower follower is obtained；5, emit radar signal.The present invention expands application range of the anti-interference Waveform generation method in different type radar, and deficiency of the interference signal prior to radar signal can only be directed to by overcoming in existing Anti-Jamming Technique.
Description
Technical field
The invention belongs to Radar Technology fields, further relate to one of Anti-jamming Technology for Radar field and are based on this tower
The Radar cross-section redaction Waveform generation method of Ke Er Burger game.The present invention is using Stackelberg game as frame, in radar
Different anti-interference waveforms is generated when leader leader and follower follower respectively, makes radar in radar signal prior to dry
Reach jamproof purpose in the case of signal transmitting and interference signal are disturbed prior to two kinds of radar signal.
Background technique
In electronic warfare, radar needs to take measures to avoid or reduce the interference being subject to as far as possible, guarantees the inspection of one's own side
Survey, tracking and other performance；Meanwhile jammer is also required to take measures to interfere radar, reduces enemy radar performance to reach
Purpose.Traditional antijamming measure is single, using fixed antijamming measure generally in radar system, but with electronics
The development of war, novel intelligent interference opportunities realize optimal interference according to the corresponding jamming exposure area of policy selection of radar
Can, cause traditional anti-interference mode performance to substantially reduce.Novel jammer makes the relationship between radar system and interference
It is more complicated --- interference opportunities make a policy according to the strategy of radar, while radar can also be taken according to the strategy of jammer
Corresponding strategy.Game theory is a kind of mathematical theory and method of the research with struggle or competition property phenomenon, it is possible to be used
Game theory is frame to portray the relationship between radar and interference.
On the other hand, the selection of radar emission waveform can directly or largely influence the performance parameter of radar system,
These parameters include target echo signal-to-noise ratio, distance resolution, velocity resolution, maximum unam, most very much not fuzzy speed
Degree etc., thus radar emission waveform design is vital for the performance of radar.When radar faces interference and threatens, from
Anti-interference in transmitted waveform is also a kind of very effective mode.
Paper " The MIMO radar and jammer gamers " ([J] that Xiufeng Song et al. is delivered at it
" IEEE TRANSACTIONS ON SIGNAL PROCESSING ", 2,012 60 (2): 687-699) in propose one kind and be based on
The radar signal and interference signal design method of game theory.The basic step of this method is: how defeated being primarily based on statistics multi input
Relationship between radar and interference is established as two people's zero-sum game models by MIMO radar out；Then target pulse response is established
With the mutual information expression formula of radar echo signal；It finally derives rich in unilateral game, Stackelberg game and symmetric information
The strategy of lower radar and interference is played chess, to obtain the statistics anti-interference waveform of multiple-input and multiple-output MIMO radar.Existing for this method
Shortcoming is that this method needs specified radar type for statistics when generating anti-interference waveform using Stackelberg game
Multiple-input and multiple-output MIMO radar, so if this method is used for other kinds of radar, such as phased-array radar, mechanical scanning
Radar etc., this method will fail.
Patented technology " a kind of anti-interference side of active radar and passive radar collaboration based on Waveform Design that University of Electronic Science and Technology possesses
It discloses in method " (application number: 201410468299.3 Authorization Notice No.: CN 104267379B) a kind of based on Waveform Design
Active radar and passive radar cooperates with anti-interference method.The step of this method, is: firstly, being utilized using active radar and passive radar cooperative work mode
The echo information of passive radar detecting real-time, detects interference and is identified, and estimates the relevant parameter of interference；Then, main
The interference information that dynamic radar utilizes passive radar to provide, designs optimal transmitted waveform；Finally echo information is handled.It should
It is disadvantageous in that existing for method, this method needs passive radar first to receive interference signal, and then Active Radar generates anti-dry
Waveform is disturbed, is to be directed to the case where interference signal is prior to radar signal in this way.If radar signal is believed prior to interference
Number transmitting, passive radar can not receive interference signal, and Active Radar can not generate anti-interference waveform, then this method will be lost
Effect.
Summary of the invention
The purpose of the present invention is in view of the above shortcomings of the prior art, propose a kind of thunder based on Stackelberg game
Up to anti-interference Waveform generation method.
Realizing the concrete thought of the object of the invention is, under Stackelberg game framework, target pulse is responded and is believed
For mutual information number between radar return signal as objective function, obtaining radar respectively using optimization algorithm is leader
Radar cross-section redaction waveform in the case of leader and two kinds of follower follower, and pre-existed and interference signal in radar signal
Emit corresponding anti-interference waveform in the case of pre-existing two kinds respectively.
To achieve the goals above, specific steps of the invention include the following:
(1) parameter is determined:
(1a) gives radar bandwidth and radar observation time according to actual radar system characteristic, determines the noise function of radar
Rate spectrum density and radar emission signal gross energy；
(1b) determines the spectrum variance of target pulse response signal according to the characteristic of radar target to be detected；
The system performance for the jammer that (1c) is carried according to target, determines interference signal general power；
(2) building objective function is as follows:
Wherein, I indicates that t moment target pulse response signal g (t) and the reception of p moment radar emit signal x (q) at the q moment
Reception signal y (p) mutual information,To the observation time of target to be detected when expression radar emission signal, ∫ df indicates integral
Operation, W indicate radar bandwidth, and ln indicates to take log operations the bottom of by of natural number, | X (m) |2Indicate the radar hair of m-th of frequency
Signal amplitude square spectrum is penetrated, | X (m) |2=| FT [x (q)] |2, | |2Indicate modulus square operation, FT [] expression takes Fourier
Map function, G (i) indicate the spectrum value of the target pulse response signal of i-th of frequency, G (i)=FT [g (t)], μG(i) it indicates
The desired value of the target pulse response signal spectrum value G (i) of i-th of frequency, μG(i)=E [G (i)], E indicate desired operation,Indicate the spectrum variance yields of the target pulse response signal of i-th of frequency,Snn
(j) the noise power spectral density value of j-th of frequency, P are indicatedj(k) the interfering signal power spectral density value of k-th of frequency is indicated,
The value of f, i, j, k are equal to each other；
(3) anti-interference waveform when radar is leader leader is obtained:
Using optimization algorithm, solving makes the maximum radar emission signal width of objective function when radar is leader leader
Degree square spectrum, by the radar emission signal amplitude square spectrum as radar for leader leader when anti-interference waveform；
(4) anti-interference waveform when radar is follower follower is obtained:
Using optimization algorithm, solving makes the maximum radar emission signal of objective function when radar is follower follower
Amplitude square spectrum, by the radar emission signal amplitude square spectrum as radar for follower follower when anti-interference waveform；
(5) emit radar signal:
The anti-interference wave of (5a) when radar signal emits prior to interference signal, when transmitting radar is leader leader
Shape detects target；
The anti-interference wave of (5b) when interference signal is prior to radar signal, when transmitting radar is follower follower
Shape detects target.
Compared with the prior art, the present invention has the following advantages:
First, the present invention pertains only to radar bandwidth, radar in the parameter of determination during Radar cross-section redaction Waveform Design
Observation time, the noise power spectral density of radar and radar emission signal gross energy, are not related to specific radar type parameter, gram
It has taken anti-interference Waveform generation method in the prior art and has been only applicable to statistics multiple-input and multiple-output MIMO radar, and be not suitable for
The deficiency of phased-array radar, mechanical scanning radar, so that the present invention is suitable for the radars classes such as phased-array radar, mechanical scanning radar
Type expands application range of the anti-interference Waveform generation method in different type radar.
Second, since the present invention is during Radar cross-section redaction Waveform Design, obtaining radar respectively is leader leader
It is first prior to interference signal transmitting and interference signal in radar signal with the anti-interference waveform in the case of two kinds of follower follower
Emit corresponding anti-interference waveform respectively in the case of two kinds of radar signal, overcoming can only needle in existing Anti-Jamming Technique
Deficiency to interference signal prior to radar signal, so that the present invention is not only adapted to radar signal and sends out prior to interference signal
The generation of anti-interference waveform when penetrating, and the generation of while being adapted to interference signal prior to radar signal anti-interference waveform.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is that present invention solution makes the maximum radar emission signal amplitude of objective function when radar is leader leader
Square spectrum step flow chart；
Fig. 3 is that present invention solution makes the maximum radar emission signal width of objective function when radar is follower follower
The flow chart of degree square spectrum step；
Fig. 4 is that radar of the present invention target pulse response signal to be detected composes variance analogous diagram；
Fig. 5 the is radar present invention obtains when being leader leader Radar cross-section redaction wave simulation figure；
Fig. 6 the is radar present invention obtains when being follower follower Radar cross-section redaction wave simulation figure.
Specific embodiment
The present invention is described further with reference to the accompanying drawing.
Referring to attached drawing 1, specific steps of the invention are described as follows.
Step 1, parameter is determined.
Radar bandwidth and radar observation time are given according to actual radar system characteristic, determines the noise power spectrum of radar
Density and radar emission signal gross energy.
The radar emission signal gross energy generates according to the following formula:
Wherein, E indicates that radar emission signal gross energy, ∫ dm indicate integration operation, and W indicates radar bandwidth, | |2Expression takes
Mould square operation, FT [] expression take Fourier transform operation, and x (q) indicates the transmitting signal at radar q moment.
According to the characteristic of radar target to be detected, the spectrum variance of target pulse response signal is determined.
According to the system performance for the jammer that target carries, interference signal general power is determined.
The interference signal general power P is generated according to the following formula:
Wherein, P indicates interference signal general power, and ∫ dk indicates integration operation, Pj(k) interference signal of k-th of frequency is indicated
Power spectral density value.
Step 2, building objective function is as follows:
Wherein, I indicates that t moment target pulse response signal g (t) and the reception of p moment radar emit signal x (q) at the q moment
Reception signal y (p) mutual information,To the observation time of target to be detected when expression radar emission signal, ∫ df indicates integral
Operation, W indicate radar bandwidth, and ln indicates to take log operations the bottom of by of natural number, | X (m) |2Indicate the radar hair of m-th of frequency
Signal amplitude square spectrum is penetrated, | X (m) |2=| FT [x (q)] |2, | |2Indicate modulus square operation, FT [] expression takes Fourier
Map function, G (i) indicate the spectrum value of the target pulse response signal of i-th of frequency, G (i)=FT [g (t)], μG(i) it indicates
The desired value of the target pulse response signal spectrum value G (i) of i-th of frequency, μG(i)=E [G (i)], E indicate desired operation,Indicate the spectrum variance yields of the target pulse response signal of i-th of frequency,Snn
(j) the noise power spectral density value of j-th of frequency, P are indicatedj(k) the interfering signal power spectral density value of k-th of frequency is indicated,
The value of f, i, j, k are equal to each other.
Step 3, anti-interference waveform when radar is leader leader is obtained.
Using optimization algorithm, solving makes the maximum radar emission signal width of objective function when radar is leader leader
Degree square spectrum, by the radar emission signal amplitude square spectrum as radar for leader leader when anti-interference waveform.
Referring to attached drawing 2, to optimization algorithm is used, solving makes the maximum thunder of objective function when radar is leader leader
Specific steps up to transmitting signal amplitude square spectrum are described as follows.
The first step sets loop termination number as 1000, and cost function value is initially 0；
The radar emission signal amplitude square spectrum under the constraint of radar emission signal gross energy is randomly generated in second step；
Radar emission signal amplitude square spectrum is substituted into objective function by third step, under interference signal total power constraint,
Search makes the smallest interfering signal power spectrum density of target function value, obtains target function value when previous cycle；
4th step, judges whether the target function value of current cycle time is greater than or equal to current cost functional value, if so,
The 5th step is then executed, otherwise, executes second step；
5th step updates current cost functional value with the target function value of current cycle time；
6th step, by current cycle time plus 1；
7th step, judges whether current cycle time is equal to loop termination number, if so, executing the 8th step, otherwise, executes
Second step；
8th step, by the radar emission signal amplitude square spectrum of current cycle time, as Stackelberg game
Radar cross-section redaction waveform when middle radar is leader leader.
Step 4, anti-interference waveform when radar is follower follower is obtained.
Using optimization algorithm, solving makes the maximum radar emission signal of objective function when radar is follower follower
Amplitude square spectrum, by the radar emission signal amplitude square spectrum as radar for follower follower when anti-interference waveform.
Referring to attached drawing 3, solving to optimization algorithm makes the maximum thunder of objective function when radar is follower follower
Specific steps up to transmitting signal amplitude square spectrum are described as follows.
The first step determines that loop termination number is 1000, and cost function value is initially
The interfering signal power spectrum density under interference signal total power constraint is randomly generated in second step；
Interfering signal power spectrum density is substituted into objective function by third step, and search makes the maximum radar hair of target function value
Signal amplitude square spectrum is penetrated, target function value when previous cycle is obtained；
4th step, judges whether the target function value of current cycle time is less than current cost functional value, if so, executing
Otherwise 5th step executes second step；
5th step updates current cost functional value with the target function value of current cycle time；
6th step, by current cycle time plus 1；
7th step, judges whether current cycle time is equal to loop termination number, if so, executing the 8th step, otherwise, executes
Second step；
8th step, by the radar emission signal amplitude square spectrum of current cycle time, as Stackelberg game
Radar cross-section redaction waveform when middle radar is follower follower.
Step 5, emit radar signal.
When radar signal emits prior to interference signal, emit anti-interference waveform when radar is leader leader, it is right
Target is detected.
When interference signal is prior to radar signal, emit anti-interference waveform when radar is follower follower,
Target is detected.
Effect of the invention can be described further by following emulation experiment.
1, simulated conditions:
The operating system that emulation experiment of the invention uses is Intel (R) Core (TM) i5-6500 CPU@3.20GHz,
64 Windows operating systems, simulation software use MATLAB (R 2016a).
2, emulation experiment content:
The parameter setting of emulation experiment of the invention is as follows, bandwidth 10MHz, radar observation time 10ms, radar emission function
Rate 1000W, jammer power 100W, the target pulse response signal of b-th of frequency composes variance in bandwidth range
Fig. 4 is that radar of the present invention target pulse response signal to be detected composes variance analogous diagram, and abscissa indicates frequency, unit
For GHz, ordinate indicates radar emission signal amplitude square spectrum, unit J-s, each point indicates to give horizontal seat on curve
Mark frequency corresponds to the target pulse response signal spectrum variance yields of ordinate.
Fig. 5 the is radar present invention obtains when being leader leader Radar cross-section redaction wave simulation figure.Fig. 5 abscissa
Indicate frequency, unit GHz, ordinate indicates radar emission signal amplitude square spectrum, unit J-s, on curve each
Point indicates that given abscissa frequency corresponds to the radar emission signal amplitude square spectrum of ordinate.Comparison diagram 4 and Fig. 5 are it is found that thunder
Shape up to anti-interference waveform is identical with the shape of target pulse response signal spectrum variance, that is, in target pulse response signal
It composes in the bigger frequency of variance, the value of Radar cross-section redaction waveform is also bigger, so when radar signal emits prior to interference signal,
The anti-interference waveform that the radar emission present invention obtains can achieve jamproof purpose.
Fig. 6 the is radar present invention obtains when being follower follower Radar cross-section redaction wave simulation figure.The horizontal seat of Fig. 6
Marking indicates frequency, unit GHz, ordinate expression radar emission signal amplitude square spectrum, unit J-s, each on curve
A point indicates that given abscissa frequency corresponds to the radar emission signal amplitude square spectrum of ordinate.Comparison diagram 6 and Fig. 4 it is found that
Radar cross-section redaction waveform only has value near the target pulse response signal spectrum maximum frequency of variance, is all in remaining frequency range
Zero, so the anti-interference waveform that the radar emission present invention obtains can achieve anti-when interference signal is prior to radar signal
The purpose of interference.
In conclusion the present invention does not need to be suitable for for specific radar type during obtaining anti-interference waveform
The radar of the types such as phased-array radar, mechanical scanning radar, to expand anti-interference Waveform generation method in different type thunder
Application range in reaching；The present invention can obtain radar signal and send out prior to interference signal using Stackelberg game as frame
It penetrates with interference signal prior to the anti-interference waveform in the case of two kinds of radar signal, can overcome in existing Anti-Jamming Technique only
Deficiency of the interference signal prior to radar signal can be directed to.
Claims (3)
1. a kind of Radar cross-section redaction Waveform generation method based on Stackelberg game, which is characterized in that radar signal is first
When interference signal transmitting, radar is the leader leader in Stackelberg game；Interference signal is prior to radar signal
When transmitting, radar is the follower follower in Stackelberg game, and specific steps include the following:
(1) parameter is determined:
(1a) gives radar bandwidth and radar observation time according to actual radar system characteristic, determines the noise power spectrum of radar
Density and radar emission signal gross energy；
(1b) determines the spectrum variance of target pulse response signal according to the characteristic of radar target to be detected；
The system performance for the jammer that (1c) is carried according to target, determines interference signal general power；
(2) building objective function is as follows:
Wherein, I (g (t), y (p)；X (q)) indicate that t moment target pulse response signal g (t) and p moment radar were received at the q moment
Emit the mutual information of the reception signal y (p) of signal x (q),When expression radar emission signal to the observation of target to be detected
Between, ∫ df indicates integration operation, and W indicates radar bandwidth, and ln indicates to take log operations the bottom of by of natural number, | X (m) |2Indicate m
The radar emission signal amplitude square spectrum of a frequency, | X (m) |2=| FT [x (q)] |2, | |2Indicate modulus square operation, FT
[] indicates to take Fourier transform operation, and G (i) indicates the spectrum value of the target pulse response signal of i-th of frequency, G (i)=FT
[g (t)], μG(i) desired value of the target pulse response signal spectrum value G (i) of i-th of frequency, μ are indicatedG(i)=E [G (i)], E
Indicate desired operation,Indicate the spectrum variance yields of the target pulse response signal of i-th of frequency,Snn(j) the noise power spectral density value of j-th of frequency, P are indicatedj(k) it indicates k-th
The interfering signal power spectral density value of frequency, the value of f, i, j, k are equal to each other；
(3) anti-interference waveform when radar is leader leader is obtained:
Using optimization algorithm, solve makes the maximum radar emission signal amplitude of objective function flat when radar is leader leader
Fang Pu, by the radar emission signal amplitude square spectrum as radar for leader leader when anti-interference waveform；
Solved using optimization algorithm makes the maximum radar emission signal amplitude of objective function flat when radar is leader leader
Specific step is as follows for side's spectrum:
The first step sets loop termination number as 1000, and cost function value is initially 0；
The radar emission signal amplitude square spectrum under the constraint of radar emission signal gross energy is randomly generated in second step；
Radar emission signal amplitude square spectrum is substituted into objective function by third step, under interference signal total power constraint, search
Make the smallest interfering signal power spectrum density of target function value, obtains target function value when previous cycle；
4th step, judges whether the target function value of current cycle time is greater than or equal to current cost functional value, if so, holding
Otherwise the 5th step of row executes second step；
5th step updates current cost functional value with the target function value of current cycle time；
6th step, by current cycle time plus 1；
7th step, judges whether current cycle time is equal to loop termination number, if so, executing the 8th step, otherwise, executes second
Step；
8th step, by the radar emission signal amplitude square spectrum of current cycle time, as thunder in Stackelberg game
Radar cross-section redaction waveform when up to for leader leader；
(4) anti-interference waveform when radar is follower follower is obtained:
Using optimization algorithm, solving makes the maximum radar emission signal amplitude of objective function when radar is follower follower
Square spectrum, by the radar emission signal amplitude square spectrum as radar for follower follower when anti-interference waveform；
Being solved using optimization algorithm makes the maximum radar emission signal amplitude of objective function when radar is follower follower
Square spectrum specific step is as follows:
The first step determines that loop termination number is 1000, and cost function value is initially
The interfering signal power spectrum density under interference signal total power constraint is randomly generated in second step；
Interfering signal power spectrum density is substituted into objective function by third step, and search makes the maximum radar emission letter of target function value
Number amplitude square spectrum, obtains target function value when previous cycle；
4th step, judges whether the target function value of current cycle time is less than current cost functional value, if so, executing the 5th
Otherwise step executes second step；
5th step updates current cost functional value with the target function value of current cycle time；
6th step, by current cycle time plus 1；
7th step, judges whether current cycle time is equal to loop termination number, if so, executing the 8th step, otherwise, executes second
Step；
8th step, by the radar emission signal amplitude square spectrum of current cycle time, as thunder in Stackelberg game
Radar cross-section redaction waveform when up to for follower follower；
(5) emit radar signal:
(5a) emits anti-interference waveform when radar is leader leader when radar signal emits prior to interference signal, right
Target is detected；
(5b) emits anti-interference waveform when radar is follower follower when interference signal is prior to radar signal,
Target is detected.
2. the Radar cross-section redaction Waveform generation method according to claim 1 based on Stackelberg game, feature
It is, radar emission signal gross energy described in step (1) generates according to the following formula:
Wherein, E indicates that radar emission signal gross energy, ∫ dm indicate integration operation, and W indicates radar bandwidth, | |2Indicate modulus square
Operation, FT [] expression take Fourier transform operation, and x (q) indicates the transmitting signal at radar q moment.
3. the Radar cross-section redaction Waveform generation method according to claim 1 based on Stackelberg game, feature
It is, interference signal general power P described in step (1) is generated according to the following formula:
Wherein, P indicates interference signal general power, and ∫ dk indicates integration operation, Pj(k) interfering signal power of k-th of frequency is indicated
Spectral density value.
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| CN111614432B (en) * | 2020-05-26 | 2021-06-08 | 电子科技大学 | Method for generating interference waveform with set threshold value and penalty term |
| CN111812599B (en) * | 2020-06-23 | 2023-11-07 | 南京航空航天大学 | Networking radar optimal waveform design method based on low interception performance under game condition |
| CN111983581B (en) * | 2020-08-26 | 2023-08-08 | 中国人民解放军军事科学院国防科技创新研究院 | Cognitive radar system, method and device for generating waveforms of cognitive radar system, and readable storage medium |
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