CN110082731A - A kind of MIMO radar optimum waveform design method of continuous phase - Google Patents
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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
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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
- G01S7/285—Receivers
- G01S7/295—Means for transforming co-ordinates or for evaluating data, e.g. using computers
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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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S2013/0236—Special technical features
- G01S2013/0245—Radar with phased array antenna
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Abstract
The present invention provides a kind of MIMO radar optimum waveform design methods of continuous phase, consider the clutter and white Gaussian noise simultaneous scene unrelated with echo signal, to maximize receiver output SINR as design criteria, and apply permanent mould and similarity constraint, the optimization problem that a complexity is NP-Hard is obtained, this method passes through the subproblem collection of segmentation feasible zone creation optimization problem first；Then the bound of design optimization problem, and in order to overcome objective function in bound to determine bound using the strategy of progressive alternate and fixed objective function about the non-linear of independent variable；It is concentrated again from subproblem and filters out the subproblem for meeting bound requirement, and then iteratively solve the bound of subproblem, until bound convergence, to obtain the optimal solution of former optimization problem；With existing SQR algorithm suboptimum waveform comparison obtained, there is more preferably SINR performance by this method optimum waveform obtained.
Description
Technical field
The invention belongs to radar signal processing fields, and in particular to a kind of MIMO of continuous phase (Multiple input
Multiple output, multiple-input and multiple-output) radar optimum waveform design method.
Background technique
The it is proposed of MIMO radar opens a completely new research field of signal processing and radar system design.2004
Year, the E.Fishler of the New Jersey Institute of Technology formally proposes the concept of MIMO radar in IEEE radar meeting.Hereafter,
MIMO radar just causes the highest attention and research extensively of Global Academy and industry.With traditional phased-array radar phase
Than, MIMO radar target detection, parameter Estimation, parameter identification, resolution capability and in terms of have potential advantage.
Currently, educational circles is concentrated mainly on waveform diversity, Waveform Design, target detection to the signal processing research of MIMO radar
With several aspects such as parameter Estimation.Wherein this research of Waveform Design mainly considers how the detection waveform of design MIMO radar.
Educational circles mostly uses convex optimisation technique to optimize radar waveform at present.Design criteria includes but is not limited to: 1) MIMO thunder
It is comprehensive up to beam patterns, that is, a launching beam pattern is given, waveform how is designed and approaches the pattern；2) Signal to Interference plus Noise Ratio is maximum
Change, i.e., design a kind of radar waveform there are noise, interference and clutter, so that receiving the Signal to Interference plus Noise Ratio of echo most
Greatly；3) permanent envelope waveform design, i.e. design waveform makes its envelope constant, to adapt to the non-linear of radar high power amplifier,
Basic radar detection function is also completed simultaneously.
SINR (the Signal to Interference plus of target detection probability and the receiver output of radar
Noise Ratio, Signal to Interference plus Noise Ratio) be the performances such as Radar Targets'Detection important indicator, to improve Signal to Interference plus Noise Ratio to radar system
The raising of performance has conclusive effect.To maximize output SINR as Optimality Criteria, thus to MIMO radar transmitted waveform
Being designed also becomes an important research direction.When solving these optimization problems, convex optimization is still current academia
Mainstream.In view of permanent mould (Constant Modulus Constraint, CMC) and wave-form similarity (Similarity
Constraint, SC) constraint condition, the optimization problem become a NP (Non- that can not be solved in polynomial time
Deterministic Polynomial) problem.
Traditional positive semidefinite relaxation (Semidefinite Relaxation, SDR) method due to the limitation of randomness, is led
Cause can only acquire locally optimal solution, and often time overhead is huge for solution procedure.Hereafter, researcher is studying colored Gauss
The MIMO radar of band PAPR (Peak to Average Power Ratio, papr) and energy constraint in noise
When Waveform Design problem, it is just based on SDR and randomized technique, respectively continuous and two kinds of situations of discrete phase are provided with more
The high quality suboptimal solution of item formula time computation complexity.Then, researcher is it is contemplated that noise jamming and white Gaussian noise are same
When it is existing under the conditions of, for the MIMO radar continuous phase Waveform Design of CMC and SC, propose the sequence optimisation based on SDR
Algorithm (Sequential Optimization Algorithm, SOA), by iteration and the strategy of fixed objective function,
To achieve the purpose that approximate non-linear objective function, the solution with degree of precision is finally obtained.For the optimization problem, this
Thering is scholar to develop a kind of new analysis method again afterwards --- sequential QCQP refines method (Successive QCQP
Refinement, SQR), i.e., by former non-convex optimization problem, be converted to a series of convex QCQP (Quadratically
Constrained Quadratic Programing) subproblem, and these subproblems are iteratively solved, the optimal wave finally obtained
Shape ratio SOA algorithm has more preferably suboptimal solution.
However, above-mentioned algorithm can only all obtain the suboptimal solution namely locally optimal solution of optimization problem, it is not global optimum
Solution.
Summary of the invention
In view of this, the present invention provides a kind of MIMO radar optimum waveform design methods of continuous phase, compared to mesh
Before can only solve the SQR algorithm of suboptimum waveform, the method for the present invention can obtain global optimum's waveform, and waveform obtained has
There is higher SINR.
Realize that technical scheme is as follows:
A kind of MIMO radar optimum waveform design method of continuous phase, comprising the following steps:
Step 1: under conditions of permanent modular constraint and similarity constrain, with the expression formula x of receiving end output signal SINRHΦ
(x) x is objective function, and construction maximizes the continuous wave optimization problem of SINR；
Step 2 is split the optimization problem feasible zone, to obtain the sub- optimization problem collection of the optimization problem；
Divide rule are as follows: by NTCircular arc arc (l of the feasible zone of N-dimensional in certain one-dimensional spacek,uk) averagely segmentation, keep other dimensions
Circular arc arc (li,ui), i ≠ k is constant, wherein divided circular arc meets:
Step 3 obtains the set of feasible solution of the optimization problem using the sub- optimization problem collection, by every sub- optimization problem
Feasible zone circular arc arc (lk,uk) relaxation is the circular arc and its discount vibram outlet that corresponding chord length is surrounded, and then obtains described optimize and ask
The relaxation disaggregation of topic；The upper bound of the optimization problem is respectively obtained under using the maximum value in relaxation disaggregation and set of feasible solution
Boundary；
Sub- optimization problem is divided again and obtains child's optimization problem by step 4, and obtains corresponding relaxation solution and feasible
Solution retains child's optimization problem to newly if the relaxation solution of a certain child's optimization problem is greater than the lower bound of the optimization problem
Sub- optimization problem concentrate, otherwise reject child's optimization problem, the optimization problem updated based on new sub- optimization problem collection
Bound；
Step 5, circulation execute the operation of step 4, should when the upper bound of the optimization problem and the difference of lower bound converge to 0
The upper bound or the corresponding solution of lower bound are the optimal solution of the optimization problem, i.e. acquisition optimum waveform
Further, in step 3, the set of feasible solution for obtaining the optimization problem using the sub- optimization problem collection is specific
Are as follows: for every sub- optimization problem, solved by being fixed as Φ to the Φ (x) in sub- optimization problem objective function, institute
The solution obtained is a feasible solution of the optimization problem, and then obtains the set of feasible solution of the optimization problem.
Further, the similarity constraint representation of the sub- optimization problem are as follows:
Wherein, []*Indicating conjugate transposition, x indicates transmitting signal matrix,Indicate Hadamard product,
The utility model has the advantages that
1, the present invention creates the subproblem collection of optimization problem by segmentation feasible zone first；Then design optimization problem is upper
Lower bound, and objective function is about the non-linear of independent variable in bound in order to overcome, using progressive alternate and fixed objective function
Strategy determine bound；It is concentrated again from subproblem and filters out the subproblem for meeting bound requirement, and then iteratively solved son and ask
The bound of topic, until bound convergence, to obtain the optimal solution of former optimization problem.It is secondary compared to that can only solve at present
The SQR algorithm of excellent waveform has higher SINR using the method for the present invention optimum waveform obtained.
2, the present invention using relaxation disaggregation and set of feasible solution in maximum value respectively obtain the optimization problem the upper bound and
Lower bound.It is because of the child's optimization problem of left and right two generated after segmentation every time that the former, which selects maximum value, and relaxation solution may be small
In the relaxation solution of current subproblem, therefore selecting the maximum upper bound is to guarantee that it is described that the upper bound of iterative process generation remains as
The upper bound of problem；And it is that a tighter lower bound can be obtained for each iteration that the latter, which selects maximum value, to accelerate algorithm
Convergence rate.
3, the present invention is every is once divided, and current sub- feasible zone is just divided into the two child's feasible zones in left and right, thus
Obtain the two child's optimization problems in left and right.When calculating relaxation solution corresponding to child's optimization problem and feasible solution, if a certain child
The relaxation solution of sub- optimization problem is greater than the lower bound of the optimization problem, then retains child's optimization problem to sub- optimization problem collection
In, child's optimization problem is concentrated from subproblem otherwise and is rejected.By rejecting nugatory subproblem, iteration can be reduced
Unnecessary calculating in the process.
Detailed description of the invention
Fig. 1 is the feasible zone of child's optimization problem by circular arc arc (lk,uk) relax and enclosed by the circular arc and its corresponding chord length
At the schematic diagram of discount vibram outlet.
Fig. 2 is the comparison result of the receiver output SINR of optimization waveform obtained by BnB algorithm and SQR algorithm.
Fig. 3 is the method for the present invention flow chart.
Specific embodiment
The present invention will now be described in detail with reference to the accompanying drawings and examples.
The present invention provides a kind of MIMO radar optimum waveform design method of continuous phase, this method considers continuous phase
Scene, for the MIMO radar waveform optimization problem based on continuous phase, this method pass through first segmentation feasible zone creation it is excellent
The subproblem of change problem collects；Then the bound of design optimization problem, and in order to overcome in bound objective function about from becoming
That measures is non-linear, determines bound using the strategy of progressive alternate and fixed objective function；It is concentrated again from subproblem and filters out symbol
The subproblem of lower bound requirement is closed, and then iteratively solves the bound of subproblem, until bound convergence, to obtain original
The globally optimal solution of optimization problem.Compared to the SQR algorithm that can only solve suboptimum waveform at present, obtained using the method for the present invention
Optimum waveform have higher SINR.
As shown in figure 3, specific step is as follows for the method for the present invention:
Step 1: to maximize SINR as design criteria, the mathematic(al) representation of receiving end output signal SINR is derived, with this
Objective function of the expression formula as optimization problem, while considering the constraint condition of permanent mould and similarity, and then construct the optimization and ask
The model of topic:
If the transmitting-receiving array of MIMO radar is all uniform linear array, and the distance between antenna is the one of radar wavelength
Half.Number of transmission antennas is NT, receiving antenna quantity is NR, the signal length of every aerial radiation is N.Then emit signal matrix
It can indicate are as follows:
Wherein, the n-th column of matrix X are considered as NTN-th of sampled signal of root transmitting antenna, is denoted as vector x (n),
Middle n=1 ..., N, and enable x=[xT(1),xT(2),…,xT(N)]T。
Consideration exists simultaneously the scene of the interference source and additive white Gaussian noise unrelated with echo-signal.Without loss of generality,
Assuming that then being received in the matched filter w of receiving end configuration finite impulse response (FIR) (Finite Impulse Response, FIR)
The output signal at end may be expressed as:
Wherein, α0And αmThe power of target echo signal and m-th of interference source is respectively represented, M indicates the quantity of interference source；v
Indicate that mean value is 0, covariance matrix isCirculation white complex gaussian noise vector；(·)HThe conjugate transposition of representing matrix.To be oriented to matrix, wherein IN is the unit matrix of N × N, emits steering vector atIt is led with reception
To vector arIt is respectively as follows:
Therefore the SINR of output signal may be expressed as:
Wherein, signal-to-noise ratioE [] indicates expectation；The dry ratio of making an uproar of m-th of interference signal
Permanent mould and similarity constraint condition are considered further that, if note reference waveform is x0, then the optimization problem can indicate are as follows:
argx(k)∈[lk,uk]
Wherein, the normalized permanent modular constraint of first item constraint representation, the constraint of Section 2 constraint representation similarity.And lk=
argx0(k)-arccos(1-ε2/ 2), uk=argx0(k)+arccos(1-ε2/ 2), wherein ε indicates similarity constrained parameters, i.e., |
|x-x0||∞≤ ε, wherein | | x | |∞Indicate the Infinite Norm of x, and the value range of ε is 0≤ε≤2.Particularly, as ε=0,
Designed waveform is reference waveform；As ε=2, similarity constraint will be not present, at this time only permanent modular constraint.Pass through a system
The mathematical operation of column, above-mentioned optimization problem can be converted to following unitary optimization problem again:
argx(k)∈[lk,uk]
Wherein,
Step 2: for the optimization problem in step 1, its feasible zone being split, to obtain the son of the optimization problem
Problem set.
Divide rule are as follows: by NTCircular arc arc (l of the feasible zone of N-dimensional in certain one-dimensional spacek,uk) averagely segmentation, lkTable
Show the starting point of circular arc, ukIt indicates the terminating point of circular arc, while keeping the circular arc arc (l of other dimensionsi,ui), i ≠ k is constant,
In divided circular arc meet:I.e. only to NTLongest circular arc is divided in N-dimensional space
It cuts, the feasible zone in other dimension spaces remains unchanged.
Step 3: the set of feasible solution of the optimization problem is obtained using the sub- optimization problem collection, by every sub- optimization problem
Feasible zone circular arc arc (lk,uk) relaxation is the circular arc and its discount vibram outlet that corresponding chord length is surrounded, and then obtains described optimize and ask
The relaxation disaggregation of topic；The upper bound of the optimization problem is respectively obtained under using the maximum value in relaxation disaggregation and set of feasible solution
Boundary.
The lower bound for considering the optimization problem first, for the angle restriction of child's optimization problem, under conditions of permanent mould,
The linear restriction is also denoted as following vector form:
Wherein, Re () expression takes real, []*Indicate conjugate transposition,Indicate Hadamard product,Therefore the optimization subproblem can be expressed as again as
Lower form:
The non-convex problem is solved, obtained solution is a feasible solution of the optimization problem, is denoted as xl.It is substituted into
A lower bound of the optimization problem: h can be obtained in the expression formula of objective functionL=xl HΦ(xl)xlNamely subproblem collection
A lower bound.
For the upper bound of the optimization problem, child's optimization problem is relaxed as following convex problem:
As shown in Figure 1, the feasible zone of child's optimization problem is by circular arc arc (l at this timek,uk) loose for the circular arc and its right
Answer the discount vibram outlet that chord length is surrounded.The solution of the convex problem is known as to a relaxation solution of the optimization problem, is denoted as xu.It is substituted into
A upper bound of described problem: h can be obtained in the expression formula of objective functionU=xu HΦ(xu)xuNamely the one of subproblem collection
A upper bound.
For quadratic form matrix Φ (x) in above-mentioned child's optimization problem about the non-linear of x, we are taken in solution procedure
Iteration optimization has the strategy of the objective function of fixed Φ.Particularly, during i-th iteration, our calculating matrix first
Φ=Φ (xi-1), wherein xi-1Indicate the solution of (i-1)-th iteration, then by the solution x of current iterationiFor square in next iterative process
Battle array Φ=Φ (xi) calculating.Therefore the optimization problem of above-mentioned solution subproblem collection bound can be respectively converted into:
Above-mentioned two optimization problem can be by the built-in function fmincon direct solution of MATLAB.Pass through certain number
Iterative calculation can acquire the relaxation disaggregation and set of feasible solution of subproblem collection.
The upper bound and the lower bound of the optimization problem are respectively obtained using the maximum value in relaxation disaggregation and set of feasible solution.The former
Selection maximum value is because of the child's optimization problem of left and right two generated after segmentation every time, and relaxation solution is likely less than current son and asks
The relaxation solution of topic, therefore selecting the maximum upper bound is in order to which the upper bound for guaranteeing that iterative process generates remains as the upper of described problem
Boundary；And it is that a tighter lower bound can be obtained for each iteration that the latter, which selects maximum value, to accelerate the convergence speed of algorithm
Degree.
Step 4: sub- optimization problem is divided again and obtains child's optimization problem, and obtain it is corresponding relaxation solution and it is feasible
Solution retains child's optimization problem to newly if the relaxation solution of a certain child's optimization problem is greater than the lower bound of the optimization problem
Sub- optimization problem concentrate, otherwise reject child's optimization problem, the optimization problem updated based on new sub- optimization problem collection
Bound.
It is every once to be divided, current sub- feasible zone is just divided into the two child's feasible zones in left and right, to be controlled
Two child's optimization problems, while updating the angle restriction parameter l in two child's problemskAnd uk.Calculate child's optimization problem institute
Corresponding relaxation solution and feasible solution, if the relaxation solution of a certain child's optimization problem is greater than the lower bound of the optimization problem, then should
Child's optimization problem be exactly it is valuable, then retain child's optimization problem and concentrated to sub- optimization problem and enter next iteration meter
It calculates, child's optimization problem is concentrated from subproblem otherwise and is rejected.Particularly, if all child's optimization problems in iterative process
All meet condition, then when proceeding to i-th segmentation, subproblem, which is concentrated, just 2iA subproblem.After all subproblems have been calculated,
The bound of subproblem collection namely the bound of the optimization problem are updated again.
Step 5, circulation execute the operation of step 4, should when the upper bound of the optimization problem and the difference of lower bound converge to 0
Solution corresponding to the upper bound or lower bound is the optimal solution of the optimization problem, i.e. acquisition optimum waveform
The present invention carries out numerical simulation: number of transmission antennas N by following embodimentT=4, receiving antenna quantity is NR
=8, the symbol quantity of every aerial radiation is N=16.The attitude and watt level of target echo signal are respectively θ0
=15 ° and | α0|2=10dB.Assuming that interference source quantity M=3, and its attitude and watt level are respectively θ1=-50 °,
θ2=-10 °, θ3=40 ° and | α1|2=| α2|2=| α3|2=30dB.The covariance of additive white Gaussian noise in space isReference waveform selects orthogonal LFM waveformIts corresponding transmitted waveform matrixIt can
It is calculated by following formula:
Fig. 2 illustrates the receiver output SINR of optimization waveform obtained by BnB algorithm and SQR algorithm, and wherein similarity constrains
Parameter ε variation range is from 0 to 2.By compared with SQR algorithm, it has been found that as ε=0, two kinds of algorithms are optimized
Waveform is reference waveform LFM, and waveform optimization will be nonsensical at this time.When similarity constraint is stronger, the superiority of BnB algorithm
More obvious, the corresponding output SINR of optimization waveform is apparently higher than SQR algorithm.And it can be seen from the figure that as ε=0.6
The two output SINR gap reaches maximum.But with gradually loosening for similarity constraint, the gap of the two output SINR gradually contracts
It is small；As ε=1.4, the gap of the output SINR of two kinds of algorithms is kept approximately constant.As ε=2, there was only permanent modular constraint at this time,
Similarity constraint has not existed.
In conclusion the above is merely preferred embodiments of the present invention, being not intended to limit the scope of the present invention.
All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in of the invention
Within protection scope.
Claims (3)
1. a kind of MIMO radar optimum waveform design method of continuous phase, which comprises the following steps:
Step 1: under conditions of permanent modular constraint and similarity constrain, with the expression formula x of receiving end output signal SINRHΦ(x)x
For objective function, construction maximizes the continuous wave optimization problem of SINR；
Step 2 is split the optimization problem feasible zone, to obtain the sub- optimization problem collection of the optimization problem；Segmentation
Rule are as follows: by NTCircular arc arc (l of the feasible zone of N-dimensional in certain one-dimensional spacek,uk) averagely segmentation, keep the circle of other dimensions
Arc arc (li,ui), i ≠ k is constant, wherein divided circular arc meets:
Step 3 obtains the set of feasible solution of the optimization problem using the sub- optimization problem collection, by every sub- optimization problem can
Row domain circular arc arc (lk,uk) relaxation is the circular arc and its discount vibram outlet that is surrounded of correspondence chord length, and then obtains the optimization problem
Relaxation disaggregation；The upper bound and the lower bound of the optimization problem are respectively obtained using the maximum value in relaxation disaggregation and set of feasible solution；
Sub- optimization problem is divided again and obtains child's optimization problem by step 4, and obtains corresponding relaxation solution and feasible solution, if
The relaxation solution of a certain child's optimization problem is greater than the lower bound of the optimization problem, then it is excellent to new son to retain child's optimization problem
Change in problem set, otherwise reject child's optimization problem, the upper and lower of the optimization problem is updated based on new sub- optimization problem collection
Boundary；
Step 5, circulation execute the operation of step 4, when the upper bound of the optimization problem and the difference of lower bound converge to 0, the upper bound
Or the corresponding solution of lower bound is the optimal solution of the optimization problem, i.e. acquisition optimum waveform
2. a kind of MIMO radar optimum waveform design method of continuous phase as described in claim 1, which is characterized in that step
In 3, the set of feasible solution of the optimization problem is obtained using the sub- optimization problem collection specifically: for every sub- optimization problem,
It is solved by being fixed as Φ to the Φ (x) in sub- optimization problem objective function, resulting solution is the optimization problem
A feasible solution, and then obtain the set of feasible solution of the optimization problem.
3. a kind of MIMO radar optimum waveform design method of continuous phase as described in claim 1, which is characterized in that described
The similarity constraint representation of sub- optimization problem are as follows:
Wherein, []*Indicating conjugate transposition, x indicates transmitting signal matrix,Indicate Hadamard product,
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| CN112713982B (en) * | 2020-12-23 | 2023-05-23 | 香港中文大学（深圳） | Feasible region determining method and device, electronic equipment and readable storage medium |
| CN113050078A (en) * | 2021-03-18 | 2021-06-29 | 电子科技大学长三角研究院(衢州) | MIMO radar waveform generation method based on convex relaxation |
| CN113050078B (en) * | 2021-03-18 | 2022-06-28 | 电子科技大学长三角研究院(衢州) | MIMO radar waveform generation method based on convex relaxation |
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