CN108008364A - Improve the transmitted waveform of MIMO-STAP detection performances and receive power combined optimization method - Google Patents

Improve the transmitted waveform of MIMO-STAP detection performances and receive power combined optimization method Download PDF

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CN108008364A
CN108008364A CN201711170833.2A CN201711170833A CN108008364A CN 108008364 A CN108008364 A CN 108008364A CN 201711170833 A CN201711170833 A CN 201711170833A CN 108008364 A CN108008364 A CN 108008364A
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msub
msup
circletimes
clutter
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CN108008364B (en
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王洪雁
乔惠娇
张海坤
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Dalian 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
    • G01S7/40—Means for monitoring or calibrating
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques

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  • Computer Networks & Wireless Communication (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The present invention is directed under complex environment and is based on multiple-input and multiple-output（MIMO）The processing of radar space-time adaptive（STAP）The problem of detection performance is poor, proposes a kind of transmitted waveform and receives power combined optimization method to improve MIMO STAP detection performances.On the basis of MIMO STAP models are established, Signal to Interference plus Noise Ratio is exported based on maximizing（SINR）Criterion, the present invention builds transmitted waveform in the case where transmitted waveform constant modulus property, clutter reduction and reduction secondary lobe etc. constrain and receives power combined optimization problem exports SINR and then improvement MIMO STAP detection performances to maximize.To solve gained complex nonlinear problem, the present invention proposes a kind of iterative algorithm with iterative solution transmitted waveform and receives weights.Each step can all be converted into Semidefinite Programming in carried algorithm（SDP）, thus Efficient Solution can be obtained.Numerical simulation shows that compared with only considering clutter recognition, Sidelobe Suppression algorithm and uncorrelated waveform, the detection performance of MIMO STAP can be significantly improved by carrying algorithm.

Description

Improve the transmitted waveform of MIMO-STAP detection performances and receive power combined optimization method
Technical field
The invention belongs to radar signal processing field, and in particular to one kind improves MIMO-STAP detections under complex environment The transmitted waveform of performance and reception power combined optimization method.
Background technology
In recent years, with the flourishing hair of multiple-input and multiple-output (multi-input multiple-output, MIMO) communication Exhibition, and radar is breaks through demand of itself limitation to new theory, new technology, MIMO radar concept is come into being.With that can only send out The phased-array radar for penetrating relevant waveform is compared, and MIMO radar can utilize multiple transmitter units transmitting almost random waveform.According to day The difference of linear distance, MIMO radar can be divided into distributed MIMO radar and centralized MIMO radar.Distributed MIMO radar is adjacent There is larger spacing between array element, target can be detected from different perspectives, so as to improve target detection using space diversity Energy.And spacing is nearer between centralized MIMO radar adjacent reception array element, target can only be observed from some equal angular, More degree of freedom in systems thus can be obtained, and then make angular resolution of the MIMO radar with higher, parameter identification ability, parameter Estimated accuracy, and preferably clutter and interferer suppression performance.
In MIMO radar research field, one of always very active direction of waveform optimization.MIMO radar waveform optimizes Problem can usually be summarized as the following two kinds type：Only consider transmitting terminal waveform optimization, and combined optimization transmitted waveform and reception Power.B.Friedlander maximizes output Signal to Interference plus Noise Ratio (signal-to- by designing transmitted waveform first Interference-plus-noise-ratio, SINR) and then improvement MIMO radar detection performance.However, it is calculated based on gradient Method solves gained optimization problem, it is impossible to ensures that SINR does not subtract in each iteration, and then cannot ensure to restrain.For this problem, C.Y.Chen proposes a kind of iterative algorithm for receiving power and transmitted waveform combined optimization, and each step in iteration can be ensured by carrying algorithm Do not subtract, and then can ensure that iteration convergence.
It is numerous based on space-time adaptive processing (space-time adaptive in order to improve MIMO radar detection performance Processing, STAP) the MIMO radar detection algorithm of technology is suggested in succession.STAP technologies have clutter reduction at the same time and do The characteristic disturbed, can not only realize and be effectively matched with complicated external environment, but also can be to a certain extent caused by compensation system error Influence, thus radar system performance can be significantly improved.Based on this, G.Wang etc. have extensively studied MIMO-STAP clutters order and hair The relation of ejected wave shape, and provide the criterion of definite clutter order.In addition, H.Wang etc. by designing transmitted waveform to improve MIMO- STAP detection performances.However, the studies above person only considers to improve MIMO-STAP detection performances by optimizing transmitting terminal.
The content of the invention
The present invention proposes a kind of transmitted waveform and receives power combined optimization method, to solve under complex environment based on how defeated Enter the problem of multi output (MIMO) radar space-time adaptive processing (STAP) detection performance is poor.
The present invention is that technical solution is to provide a kind of improvement MIMO-STAP detection performances used by solving its technical problem Transmitted waveform and receive power combined optimization method, it is characterised in that this method comprises the following steps：
The first step：Establish MIMO-STAP detection models
It is even linear array to receive and dispatch array, and it is respectively N and M to receive array element and transmitting element number of array, and transmitting-receiving spacing is respectively dRAnd dT, and equal parallel distribution；Radar platform is along transmitting-receiving array direction unaccelerated flight, and the pulse spacing is T；
Target, clutter and noise are modeled respectively based on above-mentioned scene：
Echo signal model：
If transmitting signal matrix is S=[s1, s2... sm]T, wherein sm∈Ck×1Represent the waveform sample of m-th of transmitter unit This, K is sample number, then the target received signal under l-th of pulse is represented by：
Wherein, fD=2 (vsin θt+vt) T/ λ are target Doppler frequency, v and vtThe radar station and target phase are represented respectively For the speed of MIMO radar；αtAnd θtComplex amplitude and the position of echo signal are represented respectively； For intended recipient steering vector,For objective emission steering vector, fs=dRsinθt/ λ is mesh Mark spatial frequency, γ=dT/dR, λ is carrier wavelength；
Based on vector quantization formulaAnd if x, y are vector, then Obtaining the output of echo signal vector quantization is：
Wherein yl=vec (Yl),Represent Kronecker products, INIt is expressed as N × N unit matrixs；
Coherent pulse process cycle if (coherent pulse interval, CPI) umber of pulse is L, then in a CPI Middle MIMO radar receives echo signalIt can be obtained by formula (2)：
WhereinFor target Doppler steering vector；
Property is accumulated based on KroneckerFormula (3) can be further rewritten as：
Wherein,For target empty time-frequency steering vector；
Based on formula (4), can obtain wave filter output is：
γ=αtwHXut(θt) (5)
In formula,For filter factor；
From formula (5), target signal output power is represented by：
Noise signal model：
Consideration system receives noise signal modeling, and clutter can be modeled as NCThe superposition of a clutter block, then L CPI pulse bar Clutter is represented by under part：
Wherein, αcAnd θcComplex amplitude and the position of noise signal are represented respectively；For clutter it is empty when Frequency steering vector,Steering vector is received for clutter,Launch steering vector, f for clutterS, c=dRsinθc/ λ is clutter spatial frequency；For clutter Doppler's steering vector, fD, c=2vTsin θc/ λ is clutter Doppler frequency；Postpone matrix for clutter；
Receiving terminal is filtered clutter processing and can obtain：
In formula,For filter factor；
From formula (8), positioned at θcClutter output power be represented by：
System noise model：
Noise modeling is white Gaussian noise, then the noise under L CPI impulsive condition is represented by：
Z=[vecT(Z1), vecT(Z2) ..., vecT(ZL)]T (10)
Wherein,L=l ..., L, ZlRow be assumed to be average be 0, covariance matrix beIndependent same point of I Cloth justifies symmetric complex vector,For noise power；
Second step：Export the derivation of SINR mathematical expressions
Based on target, clutter and noise model, MIMO-STAP outputs SINR can represent as follows：
Wherein
3rd step：Combined optimization problem under the conditions of the permanent modular constraint of structure, secondary lobe and clutter recognition
The expression formula of permanent modular constraint is：
Wherein,Represent the phase of transmitted waveform s (i)；
Under the conditions of permanent modular constraint, secondary lobe and clutter recognition, output SINR is maximized to improve MIMO-STAP detection probabilities Transmitted waveform and receive weights combined optimization problem can represent as follows：
Wherein, ΘcRepresent clutter scope, ΘsFor secondary lobe scope, μ and σ are respectively side lobe levels and noise level threshold value；
4th step：Optimization algorithm is carried to optimization problem
Alternative optimization is carried out to S and w using iterative algorithm, with solving complexity non-linear joint optimization problem (13), i.e.,：It is first S is first fixed to solve w；Secondly, w is fixed to solve S；
(1) w is solved
Fixed S is considered first to solve w, then only considers that the optimization problem for receiving power design can represent as follows：
It is based onFormula (14) is rewritten as follows SDP problems：
Wherein,
(2) S is solved
Fixed w is considered to solve S, and under the conditions of trying to achieve reception power based on formula (15), Waveform Design problem is represented by：
It is based onAndFormula (16) is rewritten as：
Wherein, vecH(X)=vecT((XH)T), W=wwH,
Vector quantization property is accumulated based on Kronecker：Kqp For permutation matrix,It can obtain：
Wherein,
Based on formula (18), formula (17) can be expressed as again：
It is following SDP problems by formula (19) relaxation, i.e.,：
Wherein, Λ=vec (IN)vecH(IN), Ξ=vec (ST)vecH(ST)；
Formula (20) can only obtain the waveform correlation matrix with permanent modular constraint, Sidelobe Suppression and clutter recognition, therefore, to ask Transmitted waveform S is solved, one group of independent same distribution Gaussian vectors ξ can be generatedk, whereinK=1 ..., Q is randomization Number, covariance matrix Represent Hadamard products,
Optimal transmitted waveform STVectorized form, i.e.,：
Wherein,
(3) iterate to calculate
Repeat step (1) and (2), stopping criterion for iteration is arranged to | | SINRi+1_SINRi||≤10-2,
Wherein i represents iterations.
The present invention has initially set up MIMO-STAP system models, and based on output SINR criterions are maximized, in transmitted waveform Transmitted waveform is built under the constraints such as constant modulus property, clutter reduction and reduction secondary lobe and receives power combined optimization problem to maximize Output SINR is so as to improve MIMO-STAP detection performances；In addition, to solve gained complex nonlinear problem, the present invention proposes one Kind transmitted waveform and the iterative algorithm for receiving weights joint alternative optimization, SDP problems can be all converted into by putting forward each step in algorithm, Efficient Solution thus can be obtained, and ensure that convergence.With only considering clutter recognition, Sidelobe Suppression algorithm and non-phase Close waveform to compare, the detection performance of MIMO radar can be significantly improved by carrying algorithm.
Brief description of the drawings
Fig. 1 is the flow chart that the present invention realizes；
Fig. 2 is SNR=-10dB, and optimal transmitting pattern obtained by algorithm is carried under the conditions of CNR=30dB；
Fig. 3 be SNR ∈ [- 20dB, 10dB], CNR ∈ [10dB, 40dB] under the conditions of propose algorithm Sidelobe Suppression and transmitting The uncorrelated obtained output SINR of waveform with SNR or CNR change curve；
Fig. 4 is to carry algorithm, only consider clutter recognition under the conditions of SNR ∈ [- 20dB, 10dB], SNR ∈ [- 20dB, 10dB] And the uncorrelated obtained output SINR of waveform of transmitting is with the change curve of SNR or CNR；
Fig. 5 changes song by carrying the output SINR that algorithm obtains under the conditions of SNR=-20dB, CNR=30dB with iterations Line chart.
Embodiment
Below in conjunction with attached drawing and specific embodiment, the present invention is further illustrated.
The flow chart realized as shown in Figure 1 for the present invention.Comprise the following steps：
The first step：Establish MIMO-STAP detection models
It is even linear array to receive and dispatch array, and it is respectively N and M to receive array element and transmitting element number of array, and transmitting-receiving spacing is respectively dRAnd dT, and equal parallel distribution；Radar platform is along transmitting-receiving array direction unaccelerated flight, and the pulse spacing is T；
Under this scene, the present invention is first respectively modeled target, clutter and noise：
Echo signal model：
Note transmitting signal matrix is S=[s1, s2... sm]T, wherein sm∈Ck×1Represent the waveform sample of m-th of transmitter unit This, K is sample number, then the target received signal under l-th of pulse is represented by：
Wherein, fD=2 (vsin θt+vt) T/ λ are target Doppler frequency, v and vtThe radar station and target phase are represented respectively For the speed of MIMO radar；αtAnd θtComplex amplitude and the position of echo signal are represented respectively； For intended recipient steering vector,For objective emission steering vector, fs=dR sinθt/ λ is Object space frequency, γ=dT/dR, λ is carrier wavelength.
Based on vector quantization formulaAnd if x, y are vector, then Obtaining the output of echo signal vector quantization is：
Wherein yl=vec (Yl),Represent Kronecker products, INIt is expressed as N × N unit matrixs；
Coherent pulse process cycle if (coherent pulse interval, CPI) umber of pulse is L, then in a CPI Middle MIMO radar receives echo signalIt can be obtained by formula (2)：
WhereinFor target Doppler steering vector.
According to matrix Padé approximants propertyFormula (3) can be rewritten as：
Wherein,For target empty time-frequency steering vector.
The docking collection of letters number is needed to be filtered processing in receiving terminal to obtain target detection sufficient statistic.Then it is based on formula (4), can obtain wave filter output is：
γ=αtwHXut(θt) (5)
In formula,For filter factor.
From formula (5), target signal output power is represented by：
Noise signal model：
Clutter can be modeled as NCThe superposition of a clutter block, then clutter is represented by under L CPI impulsive condition：
Wherein, αcAnd θcComplex amplitude and the position of noise signal are represented respectively.For clutter it is empty when Frequency steering vector,Steering vector is received for clutter,Launch steering vector, f for clutterS, c=dRsinθc/ λ is clutter spatial frequency；For clutter Doppler's steering vector, fD, c=2vTsin θc/ λ is clutter Doppler frequency；Postpone matrix for clutter.
Similarly, receiving terminal is filtered clutter processing and can obtain：
In formula,For filter factor；
From formula (8), positioned at θcClutter output power be represented by：
System noise model：
Wherein noise can be modeled as white Gaussian noise, then the noise under L CPI impulsive condition is represented by：
Z=[vecT(Z1), vecT(Z2) ..., vecT(ZL)]T (10)
Wherein,L=1 ..., L, ZlRow be assumed to be average be 0, covariance matrix beIndependent same point of I Cloth justifies symmetric complex vector,For noise power.
Second step：Export the derivation of SINR mathematical expressions
It is equivalent to maximize output SINR it can be proved that maximizing detection probability under the conditions of Gaussian noise.Then based on above-mentioned Target, clutter and noise model, MIMO-STAP outputs SINR can represent as follows：
Wherein
3rd step：Combined optimization problem under the conditions of the permanent modular constraint of structure, secondary lobe and clutter recognition
In practice, radar radio frequency amplifier is usually operated at hypersaturated state and causes transmitted waveform that constant modulus property is presented engineering So as to avoid nonlinear effect.Permanent modular constraint is：The each element moduluses of waveform S are constrained to constant, can usually be compiled by phase Code realization, i.e.,：
Wherein,Represent the phase of transmitted waveform s (i).
It should be noted that in practical application, to improve system detectio performance, not only to consider to reduce clutter power, also It need to consider Sidelobe Suppression problem.If secondary lobe is higher, Weak target nearby can be covered, so as to cause detection probability to decline.Therefore, originally Invention needs to be limited to secondary lobe and clutter in given threshold value by transmit-receive combination design.
In conclusion under the conditions of permanent modular constraint, secondary lobe and clutter recognition, output SINR is maximized to improve MIMO- The transmitted waveform of STAP detection probabilities and reception weights combined optimization problem can represent as follows：
Wherein, ΘcRepresent clutter scope, ΘsFor secondary lobe scope, μ and σ are respectively side lobe levels and noise level threshold value.
Since transmitted waveform S is permanent modular constraint, thus above-mentioned combined optimization problem is np problem.This problem is difficult to be utilized all Such as, the traditional optimization such as convex optimization solves, and such as according to the method based on gradient, then convergence cannot be guaranteed.
4th step：Optimization algorithm is carried to optimization problem
For solving complexity non-linear joint optimization problem (13), it is alternately excellent that the present invention will use iterative algorithm to carry out S and w Change, i.e., fix S first to solve w；Secondly, w is fixed to solve S.
(1) w is solved
Consider that fixed S solves w first, then only consider that the optimization problem for receiving power design can represent as follows：
ByUnderstand, problem (14) is rewritable such as Lower SDP problems：
Wherein,
(2) S is solved
Fixed w is considered to solve the Waveform Design problem of S.Under the conditions of trying to achieve reception power based on formula (15), Waveform Design is asked Topic is represented by：
According toAndUnderstand, formula (16) is rewritable to be：
Wherein,W=wwH,
Vector quantization property is accumulated by Kronecker：KqpFor Permutation matrix,It can obtain：
Wherein,
Based on formula (18), formula (17) can be expressed as again：
ByAndUnderstand, formula (19) can relax as following SDP Problem, i.e.,：
Wherein, Λ=vec (IN)vecH(IN), Ξ=vec (ST)vecH(ST).SDP problems (15), (20) can be by convex excellent Change kit for example, CVX, realizes Efficient Solution.
It is worth noting that, formula (20) can only obtain it is related to the waveform of clutter recognition with permanent modular constraint, Sidelobe Suppression Matrix.Therefore, to solve transmitted waveform S, one group of independent same distribution Gaussian vectors ξ can be generatedk, whereinK= 1 ..., Q is to be randomized number, covariance matrix Represent Hadamard products,
By above-mentioned analysis, optimal transmitted waveform S can be obtainedTVectorized form, i.e.,：
Wherein,
(3) iterate to calculate
SINR changes are little, and stopping criterion for iteration is arranged to until system exports for repeat step (1), (2) | | SINRi+1- SINRi||≤10-2, wherein i expression iterationses.
The effect of the present invention can be further illustrated by following emulation：
Simulated conditions：
Experiment simulation parameter setting is as follows：Transmitting-receiving uses uniform linear array, and it is respectively M=that transmitting, which receives element number of array, 4 and N=4, umber of pulse L=3, Signal coding length K=16, radar platform speed v=200m/s, podium level h=9km are more General Le frequency fD=0.0649, distance 12.728km interested, target velocity vt=100m/s.To compare, different condition is lower to be carried Algorithm validity, emulation experiment use two kinds of different configuration of MIMO radars：MIMO radar (0.5,0.5), i.e. γ=1, MIMO Radar (1.5,0.5), i.e. γ=3, the numerical value in bracket represent transmitting array element and receive the spacing between array element respectively.Target is believed Number position is set to θt=0 °, signal-to-noise ratioIts value range is [- 20dB, 10dB]；Clutter region for [- 60 °, 60 °], number of samples NC=1000, miscellaneous noise ratioIts value range is [10dB, 40dB]；Secondary lobe area interested Domain is [- 60 °, -10 °] ∪ [- 10 °, 60 °].Orthogonal linear fm waveform S is used for experiment simulation0As with reference to waveform, i.e.,：
Wherein, k=1 ..., M, n=1 ..., K.
Emulation content：
Emulation 1：Optimal transmitting pattern obtained by algorithm is carried under the conditions of SNR=-10dB.CNR=30dB.Can from Fig. 2 Go out, carry algorithm in target θtIt placed a peak at=0 °, show that optimization waveform can be by transmission power collection obtained by carried algorithm In in target location, so as to improve target detection probability.In addition, it can be seen that there is graing lobe appearance in Fig. 2 (b), this is because Caused by MIMO radar (1.5,0.5) the transmitting sparse arrangement of array element.
Emulation 2：Algorithm Sidelobe Suppression and hair are carried under the conditions of SNR ∈ [- 20dB, 10dB], CNR ∈ [10dB, 40dB] Penetrate change curves of the uncorrelated obtained output SINR of waveform with SNR or CNR.From figure 3, it can be seen that three kinds of methods obtain Output SINR increase with the increase of SNR, reduced with the increase of CNR.It is to be noted, however, that no matter SNR Or why CNR is worth, only considers that the SINR of side lobe suppression method output is above uncorrelated waveform, show only to consider Sidelobe Suppression side Method can improve system detectio probability, and the SINR of carried algorithm output further demonstrates that institute apparently higher than Sidelobe Suppression algorithm System detectio performance can be significantly improved by carrying algorithm.In addition, from Fig. 3 (a) and 3 (b), 3 (c) and 3 (d), radar (1.5, 0.5) SINR of output is slightly larger than radar (0.5,0.5), this virtual aperture for being attributable to radar (1.5,0.5) formation is more than thunder Up to (0.5,0.5), therefore it can obtain the diversity gain of bigger.
Emulation 3：Algorithm is carried under the conditions of SNR ∈ [- 20dB, 10dB], CNR ∈ [10dB, 40dB], only considers clutter recognition And the uncorrelated obtained output SINR of waveform of transmitting is with the change curve of SNR or CNR.As shown in Figure 4, three kinds of methods Obtained output SINR increases with the increase of SNR, is reduced with the increase of CNR, and relative to clutter recognition and not Waveform correlation, no matter why SNR or CNR is worth, and carries the output SINR that algorithm obtains and is superior to clutter recognition and uncorrelated waveform. Fig. 4 shows that compared with only considering clutter recognition and uncorrelated waveform, the detection of system can be significantly improved by carrying algorithm Energy.In addition, from Fig. 4 (a) and 4 (b), 4 (c) and 4 (d), similar conclusion can be obtained, i.e.,：The output SINR of radar (1.5,0.5) Slightly larger than radar (0.5,0.5).
Emulation 4：The output SINR that algorithm obtains is carried under the conditions of SNR=-20dB, CNR=30dB with iterations to change Curve map；As can be seen from Figure 5, as iterations increases, the output SINR fluctuations that algorithm obtains is proposed and are tapered into, and no matter Which kind of radar configuration, all only needs 6 steps or so iteration to tend to stablize, shows that carried algorithm has preferable convergence.Need to note Meaning, by Fig. 5 (a) and 5 (b) also can obtain and Fig. 3, and 4 similar to conclusion：The output SINR that radar (1.5,0.5) obtains is slightly higher In radar (0.5,0.5).
In conclusion the present invention have studied the transmitted wave that MIMO-STAP radar system detection probabilities are improved under complex environment Shape and reception weights combined optimization problem.MIMO-STAP system models have been initially set up, and it is accurate based on output SINR is maximized Then, in transmitted waveform constant modulus property, clutter reduction and reduce and build transmitted waveform under the constraint such as secondary lobe and to receive power joint excellent Change problem improves MIMO-STAP detection performances to maximize output SINR.Then, asked to solve gained complex nonlinear Topic, the present invention propose a kind of transmitted waveform and receive the iterative algorithm of weights joint alternative optimization, puies forward in algorithm each step all SDP problems can be converted into, thus Efficient Solution can be obtained, and ensure that convergence.Numerical simulation shows, with only considering Clutter recognition, Sidelobe Suppression algorithm and uncorrelated waveform are compared, and the detection performance of MIMO radar can be significantly improved by carrying algorithm. Thus, the present invention carry algorithm can be provided for the waveform optimization Study on Problems of radar signal processing field in engineer application it is solid Theory with realize foundation.

Claims (1)

1. improve the transmitted waveform of MIMO-STAP detection performances and receive power combined optimization method, it is characterised in that this method bag Include following steps：
The first step：Establish MIMO-STAP detection models
It is even linear array to receive and dispatch array, and it is respectively N and M to receive array element and transmitting element number of array, and transmitting-receiving spacing is respectively dRWith dT, and equal parallel distribution；Radar platform is along transmitting-receiving array direction unaccelerated flight, and the pulse spacing is T；Based on above-mentioned scene Target, clutter and noise are modeled respectively：
Echo signal model：
If transmitting signal matrix is S=[s1, s2... sm]T, wherein sm∈CK×1Represent the waveform sample of m-th of transmitter unit, K For sample number, then the target received signal under l-th of pulse is represented by：
<mrow> <msub> <mi>Y</mi> <mi>l</mi> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mi>t</mi> </msub> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <msub> <mi>&amp;pi;f</mi> <mi>D</mi> </msub> <mi>l</mi> </mrow> </msup> <msup> <mi>ab</mi> <mi>T</mi> </msup> <mi>S</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Wherein, fD=2 (v sin θst+vt) T/ λ are target Doppler frequency, v and vtRepresent respectively the radar station and target relative to The speed of MIMO radar；αtAnd θtComplex amplitude and the position of echo signal are represented respectively；For mesh Tag splice receives steering vector,For objective emission steering vector, fs=dRsinθt/ λ is target empty Between frequency, γ=dT/dR, λ is carrier wavelength；
Based on vector quantization formulaAnd if x, y are vector, thenObtain Echo signal vector quantization exports：
<mrow> <msub> <mi>y</mi> <mi>l</mi> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mi>t</mi> </msub> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <msub> <mi>&amp;pi;f</mi> <mi>D</mi> </msub> <mi>l</mi> </mrow> </msup> <mrow> <mo>(</mo> <msup> <mi>S</mi> <mi>T</mi> </msup> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>b</mi> <mo>&amp;CircleTimes;</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Wherein yl=vec (Yl),Represent Kronecker products, INIt is expressed as N × N unit matrixs；
If coherent pulse process cycle (CPI) umber of pulse is L, then MIMO radar reception echo signal is in a CPIIt can be obtained by formula (2)：
<mrow> <msub> <mi>&amp;chi;</mi> <mi>t</mi> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mi>t</mi> </msub> <mi>d</mi> <mo>&amp;CircleTimes;</mo> <mrow> <mo>(</mo> <msup> <mi>S</mi> <mi>T</mi> </msup> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>b</mi> <mo>&amp;CircleTimes;</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
WhereinFor target Doppler steering vector；
Property is accumulated based on KroneckerFormula (3) can be further rewritten as：
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;chi;</mi> <mi>t</mi> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>L</mi> </msub> <mo>&amp;CircleTimes;</mo> <msup> <mi>S</mi> <mi>T</mi> </msup> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>c</mi> <mo>&amp;CircleTimes;</mo> <mi>b</mi> <mo>&amp;CircleTimes;</mo> <mi>a</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mn>0</mn> </msub> <msub> <mi>Xu</mi> <mi>t</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Wherein,For target empty time-frequency steering vector；
Based on formula (4), can obtain wave filter output is：
Υ=αtwHXut(θt) (5)
In formula,For filter factor；
From formula (5), target signal output power is represented by：
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>t</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <msub> <mi>&amp;alpha;</mi> <mi>t</mi> </msub> <msup> <mi>w</mi> <mi>H</mi> </msup> <msub> <mi>Xu</mi> <mi>t</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msubsup> <mi>&amp;alpha;</mi> <mi>t</mi> <mn>2</mn> </msubsup> <msubsup> <mi>u</mi> <mi>t</mi> <mi>H</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>X</mi> <mi>H</mi> </msup> <msup> <mi>ww</mi> <mi>H</mi> </msup> <msub> <mi>Xu</mi> <mi>t</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
Noise signal model：
Consideration system receives noise signal modeling, and clutter can be modeled as NCThe superposition of a clutter block, then it is miscellaneous under L CPI impulsive condition Ripple is represented by：
Wherein, αcAnd θcComplex amplitude and the position of noise signal are represented respectively；It is oriented to for clutter sky time-frequency Vector,Steering vector is received for clutter,To be miscellaneous Ripple launches steering vector, fS, c=dRsinθc/ λ is clutter spatial frequency；It is how general for clutter Strangle steering vector, fD, c=2vT sin θsc/ λ is clutter Doppler frequency；Postpone matrix for clutter；
Receiving terminal is filtered clutter processing and can obtain：
In formula,For filter factor；
From formula (8), positioned at θcClutter output power be represented by：
System noise model：
Noise modeling is white Gaussian noise, then the noise under L CPI impulsive condition is represented by：
Z=[vecT(Z1), vecT(Z2) ..., vecT(ZL)]T (10)
Wherein,ZlRow be assumed to be average be 0, covariance matrix beIndependent same distribution circle pair Claim multiple Gauss vector,For noise power；
Second step：Export the derivation of SINR mathematical expressions
Based on target, clutter and noise model, MIMO-STAP outputs SINR is represented by：
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>S</mi> <mi>I</mi> <mi>N</mi> <mi>R</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>w</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msup> <mi>w</mi> <mi>H</mi> </msup> <msub> <mi>&amp;chi;</mi> <mi>t</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <mrow> <msup> <mi>w</mi> <mi>H</mi> </msup> <mi>E</mi> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;chi;</mi> <mi>c</mi> </msub> <msubsup> <mi>&amp;chi;</mi> <mi>c</mi> <mi>H</mi> </msubsup> <mo>+</mo> <msup> <mi>zz</mi> <mi>H</mi> </msup> <mo>&amp;rsqb;</mo> <mi>w</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>&amp;alpha;</mi> <mi>t</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>|</mo> <msup> <mi>w</mi> <mi>H</mi> </msup> <msub> <mi>Xu</mi> <mi>t</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <mrow> <msup> <mi>w</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>R</mi> <mi>z</mi> </msub> <mo>)</mo> </mrow> <mi>w</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
Wherein,
3rd step：Combined optimization problem under the conditions of the permanent modular constraint of structure, secondary lobe and clutter recognition
The expression formula of permanent modular constraint is：
Wherein,Represent the phase of transmitted waveform s (i)；
Under the conditions of permanent modular constraint, secondary lobe and clutter recognition, output SINR is maximized to improve the hair of MIMO-STAP detection probabilities Ejected wave shape and reception weights combined optimization problem are represented by：
Wherein, ΘcRepresent clutter scope, ΘsFor secondary lobe scope, μ and σ are respectively side lobe levels and noise level threshold value；
4th step：Optimization algorithm is carried to optimization problem
Alternative optimization is carried out to S and w using iterative algorithm, with solving complexity non-linear joint optimization problem (13), i.e.,：It is solid first S is determined to solve w；Secondly, w is fixed to solve S；
(1) w is solved
Fixed S is considered first to solve w, then only considers that the optimization problem for receiving power design can represent as follows：
It is based onFormula (14) is rewritten as following SDP Problem：
Wherein,
(2) S is solved
Fixed w is considered to solve S, and under the conditions of trying to achieve reception power based on formula (15), Waveform Design problem is represented by：
It is based onAnd
Formula (16) is rewritten as：
Wherein, vecH(X)=vecT((XH)T), W=wwH,
Vector quantization property is accumulated based on Kronecker：KqpTo put Change matrix,It can obtain：
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>L</mi> </msub> <mo>&amp;CircleTimes;</mo> <msup> <mi>S</mi> <mi>T</mi> </msup> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>L</mi> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>K</mi> <mrow> <mi>M</mi> <mi>N</mi> <mo>&amp;times;</mo> <mi>L</mi> </mrow> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mrow> <mi>K</mi> <mi>N</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mo>(</mo> <msub> <mi>I</mi> <mi>L</mi> </msub> <mo>)</mo> <mo>&amp;CircleTimes;</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mo>(</mo> <mrow> <msup> <mi>S</mi> <mi>T</mi> </msup> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>L</mi> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>K</mi> <mrow> <mi>M</mi> <mi>N</mi> <mo>&amp;times;</mo> <mi>L</mi> </mrow> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mrow> <mi>K</mi> <mi>N</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mo>(</mo> <msub> <mi>I</mi> <mi>L</mi> </msub> <mo>)</mo> <mo>&amp;CircleTimes;</mo> <mo>&amp;lsqb;</mo> <mo>(</mo> <msub> <mi>I</mi> <mi>M</mi> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>K</mi> <mrow> <mi>N</mi> <mo>&amp;times;</mo> <mi>K</mi> </mrow> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>(</mo> <mrow> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <msup> <mi>S</mi> <mi>T</mi> </msup> <mo>)</mo> </mrow> <mo>&amp;CircleTimes;</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>&amp;rsqb;</mo> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>L</mi> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>K</mi> <mrow> <mi>M</mi> <mi>N</mi> <mo>&amp;times;</mo> <mi>L</mi> </mrow> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mrow> <mi>K</mi> <mi>N</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mo>(</mo> <msub> <mi>I</mi> <mi>L</mi> </msub> <mo>)</mo> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mi>M</mi> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>K</mi> <mrow> <mi>N</mi> <mo>&amp;times;</mo> <mi>K</mi> </mrow> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>(</mo> <mrow> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <msup> <mi>S</mi> <mi>T</mi> </msup> <mo>)</mo> </mrow> <mo>&amp;CircleTimes;</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mo>(</mo> <msup> <mi>S</mi> <mi>T</mi> </msup> <mo>)</mo> <mo>&amp;CircleTimes;</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mo>(</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>
Wherein,
Based on formula (18), formula (17) can be expressed as again：
It is following SDP problems by formula (19) relaxation, i.e.,：
Wherein, Λ=vec (IN)vecH(IN), Ξ=vec (ST)vecH(ST)；
Formula (20) can only obtain the waveform correlation matrix with permanent modular constraint, Sidelobe Suppression and clutter recognition, therefore, be sent out to solve Ejected wave shape S, can generate one group of independent same distribution Gaussian vectors ξk, whereinK=1 ..., Q is randomization time Number, covariance matrix⊙ represents Hadamard products,
Optimal transmitted waveform STVectorized form, i.e.,：
<mrow> <mi>v</mi> <mi>e</mi> <mi>c</mi> <msup> <mrow> <mo>(</mo> <msup> <mi>S</mi> <mi>T</mi> </msup> <mo>)</mo> </mrow> <mi>&amp;Delta;</mi> </msup> <mo>=</mo> <mi>arg</mi> <munder> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <msub> <mi>s</mi> <mi>k</mi> </msub> </munder> <msubsup> <mi>&amp;alpha;</mi> <mi>t</mi> <mn>2</mn> </msubsup> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>s</mi> <mi>k</mi> </msub> <mo>&amp;CircleTimes;</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>H</mi> </msup> <msup> <mi>g</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <msubsup> <mi>U</mi> <mi>t</mi> <mi>T</mi> </msubsup> <mo>&amp;CircleTimes;</mo> <mi>W</mi> <mo>)</mo> </mrow> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>s</mi> <mi>k</mi> </msub> <mo>&amp;CircleTimes;</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mo>(</mo> <msub> <mi>I</mi> <mi>N</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mrow>
Wherein,
(3) iterate to calculate
Repeat step (1) and (2), stopping criterion for iteration is arranged to | | SINRi+1-SINRi||≤10-2,
Wherein i represents iterations.
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