CN110082731B - Continuous-phase MIMO radar optimal waveform design method - Google Patents

Continuous-phase MIMO radar optimal waveform design method Download PDF

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CN110082731B
CN110082731B CN201910351705.0A CN201910351705A CN110082731B CN 110082731 B CN110082731 B CN 110082731B CN 201910351705 A CN201910351705 A CN 201910351705A CN 110082731 B CN110082731 B CN 110082731B
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任程麟
皮维超
周建明
陈宁
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Beijing Institute of Technology BIT
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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
    • 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
    • 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
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    • G01S2013/0245—Radar with phased array antenna

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Abstract

The invention provides a continuous-phase MIMO radar optimal waveform design method, which considers the scene that clutter irrelevant to a target signal and white Gaussian noise exist at the same time, takes the output SINR of a maximized receiver as a design criterion, and applies constant modulus and similarity constraint to obtain an optimization problem with complexity of NP-Hard; then designing an upper boundary and a lower boundary of an optimization problem, and determining the upper boundary and the lower boundary by adopting a strategy of gradually iterating and fixing an objective function in order to overcome the nonlinearity of the objective function about an independent variable in the upper boundary and the lower boundary; then, selecting the subproblems meeting the requirements of the upper and lower bounds from the subproblem set, and then iteratively solving the upper and lower bounds of the subproblems until the upper and lower bounds are converged, thereby obtaining the optimal solution of the original optimization problem; compared with the suboptimal waveform obtained by the prior SQR algorithm, the optimal waveform obtained by the method has better SINR performance.

Description

Continuous-phase MIMO radar optimal waveform design method
Technical Field
The invention belongs to the field of radar signal processing, and particularly relates to a method for designing an optimal waveform of a continuous-phase MIMO (Multiple input Multiple output) radar.
Background
The proposed MIMO radar opens up a completely new research area for signal processing and radar system design. In 2004, e.fisher, new jersey institute of technology, usa, formally proposed the concept of MIMO radar at the IEEE radar conference. Since then, MIMO radar has attracted high attention and extensive research in the global academic and industrial sectors. Compared with the traditional phased array radar, the MIMO radar has potential advantages in the aspects of target detection, parameter estimation, parameter identification, resolution capability, interference suppression and the like.
Currently, signal processing research on MIMO radars in the academic world mainly focuses on waveform diversity, waveform design, target detection, parameter estimation and the like. The study of waveform design mainly considers how to design the detection waveform of the MIMO radar. At present, the academic world mostly adopts a convex optimization technology to carry out optimization design on radar waveforms. Design criteria include, but are not limited to: 1) MIMO radar beam pattern synthesis, namely, a transmitting beam pattern is given, and how to design a waveform to approximate the pattern; 2) the signal-to-interference-and-noise ratio is maximized, namely a radar waveform is designed under the condition that noise, interference and clutter exist, so that the signal-to-interference-and-noise ratio of a received echo is maximized; 3) the design of the constant envelope waveform is to design the waveform to make the envelope constant so as to adapt to the nonlinearity of the high-power radar amplifier and simultaneously complete the basic radar detection function.
The target detection probability of the radar and the SINR (Signal to Interference plus Noise Ratio) output by the receiver are important indexes of performance such as radar target detection, and have a decisive effect on improving the performance of a radar system by improving the Signal to Interference plus Noise Ratio. The optimization criterion of maximizing the output SINR is adopted, so that the design of the MIMO radar transmission waveform is also an important research direction. Convex optimization remains the mainstream of the academic world today in solving these optimization problems. Considering the Constraint conditions of Constant Modulus (CMC) and waveform Similarity (SC), the optimization problem becomes an NP (Non-Deterministic polynomic) problem that cannot be solved in Polynomial time.
The traditional semi-definite Relaxation (SDR) method only can obtain a local optimal solution due to the limitation of randomness, and the time overhead is often huge in the solving process. Thereafter, when studying the MIMO radar waveform design problem with PAPR (Peak to Average Power Ratio) and energy constraints in colored gaussian noise, researchers provided high-quality sub-optimal solutions with polynomial time computation complexity for both continuous and discrete phase cases, respectively, based on SDR and randomization techniques. Then, researchers consider that clutter interference and white gaussian noise exist at the same time, and propose a Sequence Optimization Algorithm (SOA) based on SDR for the MIMO radar continuous phase waveform design of CMC and SC, and achieve the purpose of approximating a nonlinear objective function by repeating the strategy of iterating and fixing the objective function, and finally obtain a solution with higher precision. For the optimization problem, later, another learner develops a new analysis method, namely a Sequential QCQP Refinement (SQR), that is, the original non-convex optimization problem is converted into a series of convex QCQP (symmetric deterministic mathematical programming) sub-problems, and the sub-problems are solved iteratively, so that the finally obtained optimal waveform has a better suboptimal solution than the SOA algorithm.
However, the above algorithms can only obtain a sub-optimal solution, i.e. a local optimal solution, of the optimization problem, but not a global optimal solution.
Disclosure of Invention
In view of this, the invention provides a continuous-phase MIMO radar optimal waveform design method, and compared with the SQR algorithm which can only solve suboptimal waveforms at present, the method of the invention can obtain global optimal waveforms, and the obtained waveforms have higher SINR.
The technical scheme for realizing the invention is as follows:
a continuous-phase MIMO radar optimal waveform design method comprises the following steps:
step 1: under the conditions of constant modulus constraint and similarity constraint, the expression x of the SINR of the output signal of the receiving end is usedHPhi (x) x is an objective function, and a continuous waveform optimization problem of maximizing SINR is constructed;
step 2, segmenting the feasible domain of the optimization problem to obtain a sub-optimization problem set of the optimization problem; the division rule is as follows: will NTThe feasible region of N dimension is along the arc (l) of a certain dimension spacek,uk) Averagely dividing, and keeping the circular arcs arc (l) of other dimensionsi,ui) I ≠ k is invariant, where the segmented arc satisfies:
Figure BDA0002044142090000031
step 3, utilizing theObtaining a feasible solution set of the optimization problem by the sub-optimization problem set, and enabling a feasible domain arc (l) of each sub-optimization problemk,uk) The relaxation is a segment surrounded by the arc and the corresponding chord length, and a relaxation solution set of the optimization problem is obtained; respectively obtaining an upper bound and a lower bound of the optimization problem by using the maximum values in the relaxation solution set and the feasible solution set;
step 4, the child optimization problems are segmented again to obtain child optimization problems, corresponding relaxation solutions and feasible solutions are obtained, if the relaxation solution of a child optimization problem is larger than the lower bound of the optimization problem, the child optimization problem is reserved in a new child optimization problem set, otherwise, the child optimization problem is removed, and the upper bound and the lower bound of the optimization problem are updated based on the new child optimization problem set;
and step 5, circularly executing the operation of the step 4, and when the difference value between the upper bound and the lower bound of the optimization problem converges to 0, the solution corresponding to the upper bound or the lower bound is the optimal solution of the optimization problem, namely the optimal waveform is obtained
Figure BDA0002044142090000033
Further, in step 3, the obtaining of the feasible solution set of the optimization problem by using the sub-optimization problem set specifically includes: for each sub-optimization problem, solving is carried out by fixing phi (x) in an objective function of the sub-optimization problem to phi, and the obtained solution is a feasible solution of the optimization problem, so that a feasible solution set of the optimization problem is obtained.
Further, the similarity constraint of the sub-optimization problem is expressed as:
Figure BDA0002044142090000032
wherein [ ·]*Representing the conjugate transpose, x represents the transmit signal matrix,
Figure BDA0002044142090000042
which represents the Hadamard product, is,
Figure BDA0002044142090000041
has the advantages that:
1. firstly, establishing a sub-problem set of an optimization problem by dividing feasible domains; then designing an upper boundary and a lower boundary of an optimization problem, and determining the upper boundary and the lower boundary by adopting a strategy of gradually iterating and fixing an objective function in order to overcome the nonlinearity of the objective function about an independent variable in the upper boundary and the lower boundary; and screening out the subproblems meeting the requirements of the upper and lower bounds from the subproblem set, and then iteratively solving the upper and lower bounds of the subproblems until the upper and lower bounds are converged, thereby obtaining the optimal solution of the original optimization problem. Compared with the SQR algorithm which can only solve suboptimal waveforms at present, the optimal waveform obtained by the method has higher SINR.
2. The invention utilizes the maximum values in the relaxation solution set and the feasible solution set to respectively obtain the upper bound and the lower bound of the optimization problem. The former chooses the maximum value because the left and right child optimization problems generated after each division may have a relaxed solution smaller than that of the current child problem, so the maximum upper bound is chosen to ensure that the upper bound generated by the iterative process is still the upper bound of the problem; the latter chooses the maximum value in order to obtain a tighter lower bound for each iteration, thereby speeding up the convergence of the algorithm.
3. The method divides the current child feasible region into a left child feasible region and a right child feasible region every time the division is carried out, so that the optimization problem of the left child and the right child is obtained. When calculating the relaxation solution and the feasible solution corresponding to the child optimization problem, if the relaxation solution of a certain child optimization problem is larger than the lower bound of the optimization problem, the child optimization problem is reserved in the child optimization problem set, otherwise, the child optimization problem is removed from the child optimization problem set. By eliminating sub-problems that have no value, unnecessary calculations in the iterative process can be reduced.
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FIG. 1 is a diagram of the feasible domain of the child optimization problem defined by the circular arc (l)k,uk) The relaxation is a schematic diagram of a segment surrounded by the arc and the corresponding chord length.
Fig. 2 is a comparison of receiver output SINR for optimized waveforms obtained by the BnB algorithm and the SQR algorithm.
Fig. 3 is a flow chart of the method of the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a continuous-phase MIMO radar optimal waveform design method, which considers a continuous-phase scene and aims at the MIMO radar waveform optimization problem based on the continuous phase, and firstly creates a sub-problem set of the optimization problem by dividing feasible regions; then designing an upper boundary and a lower boundary of an optimization problem, and determining the upper boundary and the lower boundary by adopting a strategy of gradually iterating and fixing an objective function in order to overcome the nonlinearity of the objective function about an independent variable in the upper boundary and the lower boundary; and screening out the subproblems meeting the requirements of the upper and lower bounds from the subproblem set, and then iteratively solving the upper and lower bounds of the subproblems until the upper and lower bounds are converged, thereby obtaining the global optimal solution of the original optimization problem. Compared with the SQR algorithm which can only solve suboptimal waveforms at present, the optimal waveform obtained by the method has higher SINR.
As shown in fig. 3, the method of the present invention comprises the following steps:
step 1: the method comprises the following steps of deducing a mathematical expression of the SINR of a receiving end output signal by taking the maximum SINR as a design criterion, taking the expression as a target function of an optimization problem, and simultaneously considering constraint conditions of constant modulus and similarity, thereby constructing a model of the optimization problem:
the receiving and transmitting arrays of the MIMO radar are uniform linear arrays, and the distance between the antennas is half of the radar wavelength. Number of transmitting antennas is NTThe number of receiving antennas is NRAnd the length of the signal radiated by each antenna is N. The transmit signal matrix can be expressed as:
Figure BDA0002044142090000051
wherein the nth column of the matrix X can be regarded as NTThe nth sampled signal from the transmit antenna, denoted as vector x (n)Where N is 1, …, N, and x is [ x ]T(1),xT(2),…,xT(N)]T。
Consider a scenario in which there is both an interferer and additive white gaussian noise that are independent of the echo signal. Without loss of generality, assuming that a matched filter w of Finite Impulse Response (FIR) is configured at the receiving end, the output signal of the receiving end can be represented as:
Figure BDA0002044142090000061
wherein alpha is0And alphamRespectively representing the power of a target echo signal and the power of an mth interference source, wherein M represents the number of the interference sources; v represents a mean of 0 and a covariance matrix of
Figure BDA0002044142090000062
The cyclic complex gaussian white noise vector of (a); (.)HRepresenting the conjugate transpose of the matrix.
Figure BDA0002044142090000063
Is a steering matrix, IN which IN is an N × N identity matrix, transmits steering vectors atAnd receiving a steering vector arRespectively as follows:
Figure BDA0002044142090000064
the SINR of the output signal can therefore be expressed as:
Figure BDA0002044142090000065
wherein the signal to noise ratio
Figure BDA0002044142090000066
E[·]Indicating a desire;
Figure BDA0002044142090000067
dry-to-noise ratio of mth interference signal
Figure BDA0002044142090000068
Then considering the constraint conditions of constant modulus and similarity, if the reference waveform is x0Then the optimization problem can be expressed as:
Figure BDA0002044142090000069
Figure BDA00020441420900000610
argx(k)∈[lk,uk]
wherein the first term constraint represents a normalized constant modulus constraint and the second term constraint represents a similarity constraint. And lk＝argx0(k)-arccos(1-ε2/2)，uk＝argx0(k)+arccos(1-ε2/2), where ε represents a similarity constraint parameter, i.e. | | x-x0||∞Less than or equal to epsilon, wherein | | | x | | non-woven phosphor∞Represents infinite norm of x, and the value range of epsilon is more than or equal to 0 and less than or equal to 2. Specifically, when ∈ is 0, the designed waveform is the reference waveform; when ε is 2, the similarity constraint will not exist, when there is only a constant modulus constraint. Through a series of mathematical operations, the optimization problem can be converted into the following unitary optimization problem:
Figure BDA0002044142090000071
Figure BDA0002044142090000072
argx(k)∈[lk,uk]
wherein the content of the first and second substances,
Figure BDA0002044142090000073
step 2: and (3) aiming at the optimization problem in the step 1, dividing the feasible domain of the optimization problem to obtain a sub-problem set of the optimization problem.
The division rule is as follows: will NTThe feasible region of N dimension is along the arc (l) of a certain dimension spacek,uk) Average division, /)kDenotes the starting point of the arc, ukRepresenting the end point of the arc while maintaining the arc (l) of the other dimensioni,ui) I ≠ k is invariant, where the segmented arc satisfies:
Figure BDA0002044142090000074
i.e. only to NTThe longest circular arc in the N-dimensional space is divided, and feasible domains in other dimensional spaces are kept unchanged.
And step 3: obtaining a feasible solution set of the optimization problem by using the sub-optimization problem set, and enabling a feasible domain arc (l) of each sub-optimization problemk,uk) The relaxation is a segment surrounded by the arc and the corresponding chord length, and a relaxation solution set of the optimization problem is obtained; and respectively obtaining an upper bound and a lower bound of the optimization problem by using the maximum values in the relaxation solution set and the feasible solution set.
Considering first the lower bound of the optimization problem, for the angular constraint of the child optimization problem, under the condition of constant modulus, the linear constraint can also be expressed in the form of the following vector:
Figure BDA0002044142090000075
wherein Re (. cndot.) represents the real part of the complex number, [. cndot. ]]*Which represents the transpose of the conjugate,
Figure BDA00020441420900000710
which represents the Hadamard product, is,
Figure BDA0002044142090000076
thus it isThe optimization sub-problem can in turn be expressed in the form:
Figure BDA0002044142090000077
Figure BDA0002044142090000078
Figure BDA0002044142090000079
solving the non-convex problem, wherein the obtained solution is a feasible solution of the optimization problem and is recorded as xl. Substituting the expression of the objective function into the expression of the objective function to obtain a lower bound of the optimization problem: h isL＝xl HΦ(xl)xlI.e. a lower bound of the sub-problem set.
For the upper bound of the optimization problem, relaxing the child optimization problem into the following convex problem:
Figure BDA0002044142090000081
Figure BDA0002044142090000082
Figure BDA0002044142090000083
as shown in FIG. 1, the feasible field of the child optimization problem at this time is defined by arc (l)k,uk) The slack is a segment surrounded by the arc and the corresponding chord length. The solution to the convex problem is called a relaxed solution to the optimization problem, denoted xu. Substituting it into the expression of the objective function, an upper bound of the problem can be obtained: h isU＝xu HΦ(xu)xuI.e. an upper bound of the sub-problem set.
Aiming at the nonlinearity of a quadratic matrix phi (x) in the child optimization problem about x, a strategy of iteratively optimizing an objective function with fixed phi is adopted in the solving process. In particular, during the ith iteration, we first compute the matrix Φ ═ Φ (x)i-1) Wherein x isi-1Representing the solution of the i-1 th iteration, and then the solution x of the current iteration is expressediThe matrix phi (x) used in the next iteration processi) And (4) calculating. Therefore, the above optimization problem for solving the upper and lower bounds of the sub-problem set can be respectively converted into:
Figure BDA0002044142090000084
Figure BDA0002044142090000085
Figure BDA0002044142090000086
Figure BDA0002044142090000087
Figure BDA0002044142090000088
Figure BDA0002044142090000089
both optimization problems can be solved directly by the built-in function fmincon of MATLAB. Through a certain number of iterative calculations, a relaxation solution set and a feasible solution set of the sub-problem set can be obtained.
And respectively obtaining an upper bound and a lower bound of the optimization problem by using the maximum values in the relaxation solution set and the feasible solution set. The former chooses the maximum value because the left and right child optimization problems generated after each division may have a relaxed solution smaller than that of the current child problem, so the maximum upper bound is chosen to ensure that the upper bound generated by the iterative process is still the upper bound of the problem; the latter chooses the maximum value in order to obtain a tighter lower bound for each iteration, thereby speeding up the convergence of the algorithm.
And 4, step 4: and segmenting the sub-optimization problems again to obtain child optimization problems, obtaining corresponding relaxation solutions and feasible solutions, if the relaxation solution of a certain child optimization problem is larger than the lower bound of the optimization problem, keeping the child optimization problem in a new sub-optimization problem set, otherwise, removing the child optimization problem, and updating the upper bound and the lower bound of the optimization problem based on the new sub-optimization problem set.
Every time the partition is carried out, the current child feasible region is partitioned into a left child feasible region and a right child feasible region, so that a left child optimization problem and a right child optimization problem are obtained, and an angle constraint parameter l in the two child optimization problems is updated at the same timekAnd uk. And calculating a relaxation solution and a feasible solution corresponding to the child optimization problem, if the relaxation solution of a certain child optimization problem is larger than the lower bound of the optimization problem, the child optimization problem is valuable, the child optimization problem is reserved to the child optimization problem set to enter next iterative calculation, and otherwise, the child optimization problem is removed from the child optimization problem set. In particular, if all child optimization problems in the iterative process satisfy the condition, there is 2 in the subset when proceeding to the ith segmentationiSub-problems. And after all the subproblems are calculated, updating the upper and lower bounds of the subproblem set, namely the upper and lower bounds of the optimization problem.
And step 5, circularly executing the operation of the step 4, and when the difference value between the upper bound and the lower bound of the optimization problem is converged to 0, obtaining the optimal solution of the optimization problem, namely obtaining the optimal waveform
Figure BDA0002044142090000091
The present invention performs numerical simulations by the following examples: number of transmitting antennas is NTNumber of receiving antennas is N ═ 4RThe number of symbols radiated by each antenna is N16. The space azimuth angle and the power of the target echo signal are respectively theta 015 ° and | α0|210 dB. Suppose the number of interference sources M is 3, and the attitude and power are θ1＝-50°,θ2＝-10°,θ340 ° and | α1|2＝|α2|2＝|α3|230 dB. The covariance of additive white Gaussian noise in space is
Figure BDA0002044142090000101
Reference waveform selection orthogonal LFM waveform
Figure BDA0002044142090000102
Corresponding transmitting waveform matrix
Figure BDA0002044142090000103
Can be calculated from the following formula:
Figure BDA0002044142090000104
fig. 2 shows the receiver output SINR of the optimized waveforms obtained by the BnB algorithm and the SQR algorithm, wherein the similarity constraint parameter epsilon varies from 0 to 2. By comparing with SQR algorithm, we also find that when ∈ 0, the optimized waveform obtained by the two algorithms is the reference waveform LFM, and the waveform optimization will not make sense. When the similarity constraint is strong, the BnB algorithm has obvious superiority, and the output SINR corresponding to the optimized waveform is obviously higher than that of the SQR algorithm. And it can be seen from the figure that the SINR difference between the two outputs is maximum when ∈ is 0.6. But with the gradual relaxation of the similarity constraint, the difference of the output SINR of the two gradually decreases; when ε is 1.4, the difference between the output SINR of the two algorithms remains almost the same. When epsilon is 2, only constant modulus constraint exists, and similarity constraint does not exist.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. A continuous-phase MIMO radar optimal waveform design method is characterized by comprising the following steps:
step 1: under the conditions of constant modulus constraint and similarity constraint, the expression x of the SINR of the output signal of the receiving end is usedHPhi (x) x is an objective function, and a continuous waveform optimization problem of maximizing SINR is constructed;
wherein Φ (x) is a quadratic matrix;
step 2, segmenting the feasible domain of the optimization problem to obtain a sub-optimization problem set of the optimization problem; the division rule is as follows: will NTThe feasible region of N dimension is along the arc (l) of a certain dimension spacek,uk) Averagely dividing, and keeping the circular arcs arc (l) of other dimensionsi,ui) I ≠ k is invariant, where the segmented arc satisfies:
Figure FDA0002747966140000011
step 3, obtaining a feasible solution set of the optimization problem by utilizing the sub-optimization problem set, and enabling a feasible region arc (l) of each sub-optimization problemk,uk) The relaxation is a segment surrounded by the arc and the corresponding chord length, and a relaxation solution set of the optimization problem is obtained; respectively obtaining an upper bound and a lower bound of the optimization problem by using the maximum values in the relaxation solution set and the feasible solution set;
step 4, the child optimization problems are segmented again to obtain child optimization problems, corresponding relaxation solutions and feasible solutions are obtained, if the relaxation solution of a child optimization problem is larger than the lower bound of the optimization problem, the child optimization problem is reserved in a new child optimization problem set, otherwise, the child optimization problem is removed, and the upper bound and the lower bound of the optimization problem are updated based on the new child optimization problem set;
and step 5, circularly executing the operation of the step 4, and when the difference value between the upper bound and the lower bound of the optimization problem converges to 0, the solution corresponding to the upper bound or the lower bound is the optimal solution of the optimization problem, namely the optimal waveform is obtained
Figure FDA0002747966140000012
2. The method according to claim 1, wherein in step 3, obtaining the feasible solution set of the optimization problem by using the sub-optimization problem set specifically comprises: for each sub-optimization problem, solving is carried out by fixing phi (x) in an objective function of the sub-optimization problem to phi, and the obtained solution is a feasible solution of the optimization problem, so that a feasible solution set of the optimization problem is obtained.
3. The method of claim 1, wherein the similarity constraint of the sub-optimization problem is expressed as:
Figure FDA0002747966140000021
wherein [ ·]*Representing the conjugate transpose, x represents the transmit signal matrix,
Figure FDA0002747966140000022
which represents the Hadamard product, is,
Figure FDA0002747966140000023
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CN109061578A (en) * 2018-07-12 2018-12-21 西安电子科技大学 Recess directional diagram waveform synthesis design method based on MIMO radar
CN109459729A (en) * 2018-11-02 2019-03-12 北京理工大学 A kind of asymmetric beam pattern method of MIMO radar based on permanent modular constraint

Family Cites Families (3)

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KR101263747B1 (en) * 2011-03-11 2013-05-13 국방과학연구소 Method for improving the performance by dynamic grouping/precoding in the MIMO radar system
US20180292510A1 (en) * 2017-04-07 2018-10-11 Texas Instruments Incorporated Calibration of a cascaded radar system
CN108802718B (en) * 2018-05-30 2021-11-26 北京理工大学 Time division MIMO radar space-time phase decoupling method based on random transmitted pulse

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109061578A (en) * 2018-07-12 2018-12-21 西安电子科技大学 Recess directional diagram waveform synthesis design method based on MIMO radar
CN109459729A (en) * 2018-11-02 2019-03-12 北京理工大学 A kind of asymmetric beam pattern method of MIMO radar based on permanent modular constraint

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
MIMO Radar Waveform Design With Constant Modulus and Similarity Constraints;Guolong Cui et al.;《IEEE TRANSACTIONS ON SIGNAL PROCESSING》;20170131;第62卷(第2期);第343-351页 *
恒模和相似性约束下机载MIMO雷达快速波形设计优化算法;童日武 等;《舰船电子对抗》;20191231;第42卷(第6期);第45-51页 *

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