CN109683141A - MIMO radar transmitted waveform design method based on Bayesian frame - Google Patents

MIMO radar transmitted waveform design method based on Bayesian frame Download PDF

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CN109683141A
CN109683141A CN201910036014.1A CN201910036014A CN109683141A CN 109683141 A CN109683141 A CN 109683141A CN 201910036014 A CN201910036014 A CN 201910036014A CN 109683141 A CN109683141 A CN 109683141A
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CN109683141B (en
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戴奉周
张博
张玥玥
张宇
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Xidian University
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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

Abstract

The MIMO radar transmitted waveform design method based on Bayesian frame that the invention discloses a kind of mainly solves the problems, such as that prior art target detection under related clutter environment is inaccurate.Its implementation is: 1) by target in related clutter environment there may be the case where be expressed as binary hypothesis test problem；2) likelihood ratio test based on Bayesian frame is established according to binary hypothesis test；3) solution is iterated to likelihood ratio test, the maximum value until solving likelihood ratio test, the corresponding transmitting signal of the maximum value, the transmitting signal waveform as designed.The present invention improves the rejection ability to clutter, reduces computation complexity, can be used for target detection and tracking under related clutter environment.

Description

MIMO radar transmitted waveform design method based on Bayesian frame
Technical field
The invention belongs to Radar Technology fields, further relate to MIMO radar transmitted waveform design method, It can be used for the target detection and tracking of related clutter environment.
Background technique
In recent years, MIMO radar is more and more paid close attention to by researcher and engineering staff.It is different from Traditional phased-array radar transmitting antenna can only emit coherent signal, and MIMO radar transmitting antenna can emit any letter Number, target detection, tracking and the recognition capability of radar can be significantly improved.As that studies MIMO radar gos deep into, The waveform of many systems is devised, but some traditional methods have certain problems, such as: orthogonal frequency linear frequency modulation Waveform has that airspace composite signal adaptive side-lobe is high；Limit of the orthogonal performance of polyphase orthogonal code waveform by code length System, and it is sensitive to Doppler frequency shift.
Paper " the Waveform synthesis for diversity-based that P Stoica and J Li are delivered at it transmit beampattern antennas design"(IEEE Trans on Signal Processing,2008,56 (6): 2693-2598 a kind of round-robin algorithm design waveform is proposed in), and transmitted waveform amplitude is made to remain the fluctuation of very little, And meet the condition of the flat power ratio of ebb, but this method needs complicated iterative process and successive ignition number.
Paper " the MIMO Radar Waveform Design in that Naghibi, T and F.Behnia are delivered at it Presence of Clutter"(IEEE Transactions on Aerospace&Electronic Systems 47.2 (2011): 770-781 a kind of minimum output Minimum Mean Squared Error estimation method is proposed in), it can be in irrelevant clutter ring Target is accurately detected in border, but this method is not suitable for related clutter environment.
Summary of the invention
It is an object of the invention in view of the defects existing in the prior art, propose a kind of multi input based on Bayesian frame Multi output radar emission waveform design method to improve under related clutter environment radar to the detectability of target, and reduces Computation complexity.
To achieve the above object, technical solution of the present invention includes the following:
(1) by target in related clutter environment there may be the case where be expressed as binary hypothesis test, it may be assumed that
Wherein, H0Indicate there was only the case where noise signal in echo-signal, H1Indicate there is echo signal and miscellaneous in echo-signal The case where wave signal, x indicate the echo-signal that radar receives, xtIndicate target echo signal, xcIndicate clutter echo-signal；
(2) likelihood ratio test based on Bayesian frame is established according to binary hypothesis test:
(2a) calculates clutter covariance matrix R；
Inverse Wishart is distributed the prior distribution as clutter covariance matrix R by (2b), is constructed based on Bayesian frame Probability density function f (R):
Wherein, ν indicates freedom degree, and L indicates exomonental number of samples, NRIndicate the number of receiving antenna, | |vTable Show that the ν power for seeking determinant operates,ν+the N of determinant is sought in expressionRThe operation of L power, etr () indicate that the mark asked is The index operation at bottom, R-1Indicate that covariance matrix R's is inverse,Indicate that gamma function, σ indicate that diagonal loading coefficient, I indicate single Bit matrix, Σ indicate concentration matrix；
(2c) establishes the likelihood ratio test based on Bayesian frame according to the probability density function in (2b):
Wherein, f (x | H1) indicate in H1The probability density function of x under assumed condition, and f (x | H0) indicate in H0Assumed condition The probability density function of lower x；
f(x|H1) formula it is as follows:
Wherein, f (x；R|H1) indicate in H1The joint probability density function of x and R under assumed condition, ∫ indicate indefinite integral Operation；
f(x|H0) formula it is as follows:
Wherein, f (x；R|H0) indicate in H0The joint probability density function of x and R under assumed condition；
Both the above probability density function is substituted into the likelihood ratio test L (x) based on Bayesian frame, L (x) is updated Are as follows:
Wherein, xtIndicate target echo signal, ()HConjugate transposition operation is sought in expression；
(3) likelihood ratio test is solved, likelihood ratio test reaches corresponding transmitting signal S when maximumt, the transmitting that as designs Signal waveform.
The present invention has the advantage that compared with prior art
First, since the waveform that the present invention designs is based on Bayesian frame, set compared to existing based on Gaussian Profile frame The waveform counted out, reduces computation complexity.
Second, the transmitting signal waveform based on Bayesian frame that the present invention designs compares existing orthogonal linear frequency-modulated wave Shape and polyphase orthogonal code waveform, improve the rejection ability to clutter, to improve the accuracy of target detection.
Detailed description of the invention
Fig. 1 is realization general flow chart of the invention；
Fig. 2 is the relational graph with cost function and the number of iterations in the present invention；
Fig. 3 be the waveform that designs of the present invention and existing random R based on Gaussian Profile waveform, determine R based on Gauss point The beam direction comparison diagram of cloth waveform；
Specific embodiment
The embodiment of the present invention and effect are described in further detail below in conjunction with attached drawing
Referring to Fig.1, to realization of the invention, steps are as follows:
Step 1, by target in related clutter environment there may be the case where be expressed as binary hypothesis test.
(1a) is by target echo signal xtWith clutter echo-signal xcIt respectively indicates as follows:
Wherein, α indicates the amplitude of target echo signal, ()TExpression asks transposition to operate, and S indicates transmitting signal,It indicates Kronecker product operation, NRIndicate the number of receiving antenna,Indicate NRUnit matrix is tieed up, vec () indicates vectorization operation, θtIndicate the angle of arrival of target echo signal, b (θt) expression angle of arrival be θtReceiving array steering vector, a (θt) indicate to reach Angle is θtEmission array steering vector；
NcIndicate the quantity for the clutter unit being distributed in target range ring, xc,kIt indicates k-th of clutter cell signal, meets Following formula:
Wherein, δc,kIndicate the amplitude of k-th of clutter cell signal, θc,kIndicate the angle of arrival of k-th of clutter cell signal, b(θc,k) expression angle of arrival be θc,kReceiving array steering vector, a (θc,k) expression angle of arrival be θc,kEmission array be oriented to arrow Amount；
(1b) establishes binary hypothesis test:
Wherein, H0Indicate there was only the case where noise signal in echo-signal, H1Indicate there is echo signal and miscellaneous in echo-signal The case where wave signal, x indicate the echo-signal that radar receives.
Step 2, the likelihood ratio test based on Bayesian frame is established according to binary hypothesis test.
(2a) calculates clutter covariance matrix R；
Wherein, desired operation is sought in E () expression；
Formula<2>are substituted into formula<5>, R is updated are as follows:
Wherein, ()HIndicate conjugate transposition operation；
Inverse Wishart is distributed the prior distribution as clutter covariance matrix R by (2b), is constructed based on Bayesian frame Probability density function f (R):
Wherein, ν indicates freedom degree, and L indicates exomonental number of samples, NRIndicate the number of receiving antenna, | |vTable Show that the ν power for seeking determinant operates,ν+the N of determinant is sought in expressionRThe operation of L power, etr () indicate that the mark asked is The index operation at bottom, R-1Indicate that covariance matrix R's is inverse,Indicate that gamma function, σ indicate that diagonal loading coefficient, I indicate single Bit matrix, Σ indicate concentration matrix；
(2c) establishes the likelihood ratio test based on Bayesian frame according to the probability density function in (2b):
Wherein, f (x | H1) indicate in H1The probability density function of x under assumed condition, and f (x | H0) indicate in H0Assumed condition The probability density function of lower x；
f(x|H1) formula it is as follows:
Wherein, f (x；R|H1) indicate in H1The joint probability density function of x and R under assumed condition, ∫ indicate indefinite integral Operation；
f(x|H0) formula it is as follows:
Wherein, f (x；R|H0) indicate in H0The joint probability density function of x and R under assumed condition；
Formula<9>and formula<10>are substituted into formula (8), L (x) is updated are as follows:
Wherein, xtIndicate target echo signal, ()HConjugate transposition operation is sought in expression.
Step 3, likelihood ratio test is solved, likelihood ratio test reaches corresponding transmitting signal S when maximumt, as design Emit signal waveform.
In the prior art solve likelihood ratio test optimization algorithm have: gradient descent method, steepest ascent, Newton method and Conjugate gradient method.
This example, which uses but is not limited to steepest ascent in the prior art, solves likelihood ratio test, and implementation step is such as Under:
Likelihood ratio test L (x) is taken denary logarithm by (3a), is indicated are as follows:
LnL (x)=ln | (x-xt)(x-xt)H+(ν-NRL)Σ|-(ν+1)-ln|xxH+(ν-NRL)Σ|-(ν+1),<12>
Wherein, | |-(v+1)Indicate to ask determinant-operation of (ν+1) power, Σ indicates concentration matrix, meets following public Formula:
Wherein, σ indicates that diagonal loading coefficient, I indicate unit matrix；
(3b) is according to lnL (x) ∝ ln | xxH+(ν-NRL)Σ|-ln|(x-xt)(x-xt)H+(ν-NRL) Σ | relationship, enable:
H (x)=ln | xxH+(ν-NRL)Σ|-ln|(x-xt)(x-xt)H+(ν-NRL) Σ |,<14>
Wherein, ∝ indicates proportional relation, ln | | the absolute value of expression pair takes the index operation with 10 bottom of for；
Formula<1>and formula<13>are substituted into formula<14>by (3c), obtain following cost function:
Wherein, St=ST, S expression transmitting signal, STIndicate the transposition of S, St *Indicate StAdjoint matrix, x indicate radar connect The echo-signal received, ν indicate freedom degree,
(3d) solves cost function h (St,St *) maximum value, the corresponding S of the maximum valuetThe transmitting signal wave as designed Shape, implementation step are as follows:
(3d1) iteration since m=1 gives transmitting signal initial valueWith iteration step length μ；
(3d2) is by the iteration point of the m-1 times iterationSubstitute into following iteration point formula:
Wherein, vec () is indicated vectorization, St (m)Indicate the iteration point of the m times iteration, ()*Indicate adjoint matrix Battle array,It indicates the corresponding cost function gradient of the iteration point of the m-1 times iteration, meets following formula:
Wherein,Expression asks local derviation to operate, h (St (m-1),(St (m-1))*) indicate St (m-1)Corresponding cost function；
Formula<16>are substituted into following formula by (3d3):
Wherein, St *(m)Indicate that the argument of the iteration point of the m times iteration, exp are indicated using natural number as the index operation at bottom, j Indicate imaginary number, arg () expression takes argument to operate；
(3d4) enables m=m+1, repeats (3d2) and (3d3), until It is correspondingFor cost The maximum value of function, wherein St (k)Indicate the iteration point of kth time iteration,When indicating k → ∞Limiting value.
Of the invention is further described effect of the invention by emulation experiment.
1. experiment condition
The hardware platform of emulation experiment of the invention is: MIMO radar, MATLAB R2017a.
Radar is set there are four transmitting antenna and four receiving antennas.Assuming that the angle of arrival of point target is 0 °, the arrival of clutter Angular region is θ ∈ (- 180 °, 180 °), and the amplitude of clutter cell signal indicates are as follows:
Wherein, k=1,2 ..., Nc, Nc=361.
2. experiment content and interpretation of result
Experiment 1: amplitude α=100 for the echo signal that sets up an office, iteration step length μ=10, number of samples L=16, freedom degree v= 4NRL=256, with the relationship of MATLAB R2017a software emulation cost function and the number of iterations of the invention, as a result such as Fig. 2, Abscissa in Fig. 2 indicates the number of iterations, and ordinate indicates cost function.
As can be seen from Figure 2: this example solves likelihood ratio test and only needs iteration 4 times, and cost function just can reach maximum value, explanation The number of iterations that the present invention solves likelihood ratio test is few, calculates simple.
Experiment 2: with MATLAB R2017a software emulate respectively the waveform designed of the invention and existing random R based on height This distribution waveform, the beam pattern based on Gaussian Profile waveform for determining R, as a result such as Fig. 3, the abscissa in Fig. 3 indicates mesh Target angle of arrival, ordinate indicate beam direction.
As can be seen from Figure 3: the clutter side lobe height for the waveform that the present invention designs is -27db, and existing random R's is divided based on Gauss Cloth waveform and the clutter side lobe height based on Gaussian Profile waveform for determining R are -23db, illustrate the transmitting signal that the present invention designs Waveform is good to the rejection ability of clutter.

Claims (5)

1. a kind of MIMO radar transmitted waveform design method based on Bayesian frame, which is characterized in that including such as Under:
(1) by target in related clutter environment there may be the case where be expressed as binary hypothesis test, it may be assumed that
Wherein, H0Indicate there was only the case where noise signal in echo-signal, H1Indicate there is echo signal and clutter letter in echo-signal Number the case where, x indicates the echo-signal that receives of radar, xtIndicate target echo signal, xcIndicate clutter echo-signal；
(2) likelihood ratio test based on Bayesian frame is established according to binary hypothesis test:
(2a) calculates clutter covariance matrix R；
Inverse Wishart is distributed the prior distribution as clutter covariance matrix R by (2b), constructs the probability based on Bayesian frame Density function f (R):
Wherein, ν indicates freedom degree, and L indicates exomonental number of samples, NRIndicate the number of receiving antenna, | |vExpression is asked The ν power of determinant operates,ν+the N of determinant is sought in expressionRThe operation of L power, etr () indicate that the mark asked is the finger at bottom Number operation, R-1Indicate that covariance matrix R's is inverse,Indicate that gamma function, σ indicate that diagonal loading coefficient, I indicate unit square Battle array, Σ indicate concentration matrix；
(2c) establishes the likelihood ratio test based on Bayesian frame according to the probability density function in (2b):
Wherein, f (x | H1) indicate in H1The probability density function of x under assumed condition, and f (x | H0) indicate in H0X under assumed condition Probability density function；
f(x|H1) formula it is as follows:
Wherein, f (x；R|H1) indicate in H1The joint probability density function of x and R under assumed condition, ∫ indicate indefinite integral behaviour Make；
f(x|H0) formula it is as follows:
Wherein, f (x；R|H0) indicate in H0The joint probability density function of x and R under assumed condition；
Both the above probability density function is substituted into the likelihood ratio test L (x) based on Bayesian frame, L (x) is updated are as follows:
Wherein, xtIndicate target echo signal, ()HConjugate transposition operation is sought in expression；
(3) likelihood ratio test is solved, likelihood ratio test reaches corresponding transmitting signal S when maximumt, the transmitting signal that as designs Waveform.
2. the method according to claim 1, wherein the target echo signal x in (1)tWith clutter echo-signal xc It respectively indicates as follows:
Wherein, α indicates the amplitude of target echo signal, ()TExpression asks transposition to operate, and S indicates transmitting signal,Indicate Crow Interior gram of product operation, NRIndicate the number of receiving antenna,Indicate NRUnit matrix is tieed up, vec () indicates vectorization operation, θtTable Show the angle of arrival of target echo signal, b (θt) expression angle of arrival be θtReceiving array steering vector, a (θt) indicate that angle of arrival is θtEmission array steering vector；
NcIndicate the quantity for the clutter unit being distributed in target range ring, xc,kIt indicates k-th of clutter cell signal, meets following public Formula:
Wherein, δc,kIndicate the amplitude of k-th of clutter cell signal, θc,kIndicate the angle of arrival of k-th of clutter cell signal, b (θc,k) expression angle of arrival be θc,kReceiving array steering vector, a (θc,k) expression angle of arrival be θc,kEmission array be oriented to arrow Amount.
3. method according to claim 1 or 2, which is characterized in that clutter covariance matrix R is calculated in (2a), by such as Lower formula calculates:
Wherein, desired operation is sought in E () expression；
By clutter echo-signal xcAbove formula is substituted into, R is updated are as follows:
Wherein, ()HIndicate conjugate transposition operation.
4. method according to claim 1 or 2, which is characterized in that (3) the solution likelihood ratio test described in, it is specific real It is now as follows:
Likelihood ratio test L (x) is taken denary logarithm by (3a), is indicated are as follows:
LnL (x)=ln | (x-xt)(x-xt)H+(ν-NRL)Σ|-(ν+1)-ln|xxH+(ν-NRL)Σ|-(ν+1),
Wherein, | |-(v+1)Indicate ask determinant-(ν+1) power operation, Σ indicate concentration matrix, meet following formula:
Wherein, σ indicates that diagonal loading coefficient, I indicate unit matrix；
(3b) is according to lnL (x) ∝ ln | xxH+(ν-NRL)Σ|-ln|(x-xt)(x-xt)H+(ν-NRL) Σ | relationship, enable:
H (x)=ln | xxH+(ν-NRL)Σ|-ln|(x-xt)(x-xt)H+(ν-NRL) Σ |,
Wherein, ∝ indicates proportional relation, ln | | the absolute value of expression pair takes the index operation with 10 bottom of for；
(3c) is by target echo signal xtH (x) formula is substituted into concentration matrix Σ, obtains following cost function:
Wherein, St=ST, S expression transmitting signal, STIndicate the transposition of S, St *Indicate StAdjoint matrix, x indicate radar receive Echo-signal, ν indicate freedom degree,
(3d) solves cost function h (St,St *) maximum value, the corresponding S of the maximum valuetThe transmitting signal waveform as designed.
5. according to the method described in claim 4, it is characterized in that solving cost function h (S in (3d)t,St *) maximum value, It is accomplished by
(4a) iteration since m=1 gives transmitting signal initial valueWith iteration step length μ；
(4b) is by the iteration point of the m-1 times iterationSubstitute into following iteration point formula:
Wherein, vec () is indicated vectorization, St (m)Indicate the iteration point of the m times iteration, ()*Indicate adjoint matrix,It indicates the corresponding cost function gradient of the iteration point of the m-1 times iteration, meets following formula:
Wherein,Expression asks local derviation to operate, h (St (m-1),(St (m-1))*) indicate St (m-1)Corresponding cost function；
(4c) is by iteration pointSubstitute into following argument formula:
Wherein, St *(m)Indicate that the argument of the iteration point of the m times iteration, exp indicate that, using natural number as the index operation at bottom, j is indicated Imaginary number, arg () expression take argument to operate；
(4d) enables m=m+1, repeats (4b) and (4c), until It is correspondingFor cost function Maximum value, wherein St (k)Indicate the iteration point of kth time iteration,When indicating k → ∞Limiting value.
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