CN113050078B - MIMO radar waveform generation method based on convex relaxation - Google Patents

MIMO radar waveform generation method based on convex relaxation Download PDF

Info

Publication number
CN113050078B
CN113050078B CN202110293103.1A CN202110293103A CN113050078B CN 113050078 B CN113050078 B CN 113050078B CN 202110293103 A CN202110293103 A CN 202110293103A CN 113050078 B CN113050078 B CN 113050078B
Authority
CN
China
Prior art keywords
waveform
radar
interference
optimization
constraint
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202110293103.1A
Other languages
Chinese (zh)
Other versions
CN113050078A (en
Inventor
王鹏飞
张伟见
胡进峰
魏志勇
邹欣颖
李玉枝
董重
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Yangtze River Delta Research Institute of UESTC Huzhou
Original Assignee
Yangtze River Delta Research Institute of UESTC Huzhou
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Yangtze River Delta Research Institute of UESTC Huzhou filed Critical Yangtze River Delta Research Institute of UESTC Huzhou
Priority to CN202110293103.1A priority Critical patent/CN113050078B/en
Publication of CN113050078A publication Critical patent/CN113050078A/en
Application granted granted Critical
Publication of CN113050078B publication Critical patent/CN113050078B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • General Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses a MIMO radar waveform generation method based on convex relaxation, relates to the technical field of radar, and solves the problem that constant modulus constraint of MIMO radar limits SINR performance. The method comprises the steps of optimizing the emission waveform of the co-located MIMO radar and the emission end, adding penalty factors separately to an interference item and a noise item in an optimized objective function, wherein the penalty factors are used for deepening notches on a directional diagram, simultaneously carrying out maximum optimization processing on the total energy of the waveform at the snapshot position of each radar, and further carrying out relaxation processing on the constant modulus constraint of the waveform. The invention can obtain deeper notches on a directional diagram, remarkably improves the MFL performance of the radar, and can obtain higher signal-to-interference-and-noise ratio under the condition of lower SNR.

Description

MIMO radar waveform generation method based on convex relaxation
Technical Field
The invention relates to the technical field of radar, in particular to a MIMO radar waveform generation method based on convex relaxation.
Background
MIMO (Multiple-Input Multiple-Output) radar has attracted much attention in recent years due to its superiority in target detection and parameter estimation performance. The MIMO radar with the densely distributed antennas transmits different waveforms on each antenna, so that more flexibility is provided for the design of a transmitting directional diagram, and the signal-to-interference-and-noise ratio is effectively improved. Therefore, waveform design is an extremely important topic for MIMO radar, and attracts wide attention.
Recently, waveform design based on maximized SINR (signal to interference and noise ratio) has become a research hotspot, and the methods thereof mainly include two types:
the first type is jointly optimizing the transmit-side waveform and the receive-side filter weight vector. SDP (semi-deterministic planning) -stochastic optimization methods as proposed in G.Cui, H.Li, and M.Rangaswamy, MIMO radio wave Design with Design module and precision Constraints, "IEEE Trans.Signal Process", vol.62, No.2, pp.343-353, Jan.2014., and S.O.Aldayl, V.Monga and M.Rangaswamy, Successive QCQP Reference for MIMO radio wave Design derived active Constraints, "IEEE trade.Signal Process", vol.64, SQno. 14, 3760-3774, J.Y. write Design methods.
The second type of waveform design method is to optimize only the transmit waveform. Typical of these are the IA-CPC (iterative phase algorithm) method mentioned in the publications G.Cui, X.Yu, G.Foglia, Y.Huang, and J.Li, and the Quadrative optimization With spatial constraint for orthogonal sequence synthesis, the IEEE trade.Signal Process, vol.65, No.18, pp.4756-4769, Sep.2017, and the IA-CPC (iterative phase algorithm) method mentioned in the publications X.Yu, G.Cui, L.Kong, J.Li and G.Gui, structured Waveform designed derived from modified MIMO radio resource optimization, IEEE dimensional index, plant analysis, and the CD-19 (variant algorithm) method mentioned in the publications G.Cui, X.Yu, G.electronic, G.G.Gui, consistent geographical Design derived from modified MIMO radio resource optimization, and D.20155, C.S. 55, C.K.K.K.K.K.K.K.K., and the CD.K.K., the published by the published, K.K., the published, the trade, K.K.K.K.K.K., the published by the inventor, K., K.K.K., the published, K., the published by the published, K., the published by the published, the published, No. K., the published, the. The waveform design methods studied in this invention belong to the second category.
In practical scenarios, since the radar transmitting end always operates in saturation in order to avoid waveform distortion, the constant modulus constraint is a constraint that must be added in the waveform design. Due to the limitations of the constant modulus constraints, the SINR optimization problem is always NP-hard and therefore difficult to solve. The existing research usually adopts a phase-only waveform design method and carries out overall optimization on all the waveforms of the snapshots. There are two limitations to this situation. First, since the radar inevitably receives environmental disturbance in actual operation, the phase-only waveform design is not well satisfied in practice. Secondly, the overall design of the waveforms of all snapshots may cause a large difference between the waveform performances of different snapshots, which may affect the MFL (matched filtering loss) performance of the radar.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the invention provides a MIMO radar waveform generation method based on convex relaxation, which solves the problem that the SINR performance is limited by constant modulus constraint of the MIMO radar so as to maximize the signal-to-noise ratio.
The invention is realized by the following technical scheme:
a MIMO radar waveform generation method based on convex relaxation is characterized in that emission waveforms of co-located MIMO radars and emission ends are optimized, penalty factors are added to interference terms and noise terms in optimized objective functions independently, the penalty factors are used for deepening notches on a directional diagram, meanwhile, the maximum optimization processing is carried out on the total energy of waveforms at the snapshot positions of each radar, and the relaxation processing is carried out on the constant modulus constraint of the waveforms.
Further, to achieve the above object, the detailed steps are as follows:
co-located MIMO radars have NtRoot transmitting antenna and NRThe root receives the antenna. Order to
Figure GDA0003656361950000021
n＝1,2,…,NTAnd M is 1,2, …, and M represents the transmission waveform of the mth snapshot of the nth antenna. Thus, for some far-field target, the data matrix at the receiving end can be represented as
xm＝α0A(θ0)sm+dm+vm (1)
Wherein:
1)α0is the scattering coefficient, theta0Is the azimuth angle.
2)
Figure GDA0003656361950000022
at(theta) is the direction vector of the transmitting end, arAnd (theta) is a direction vector of the receiving end. a ist(theta) and ar(θ) is expressed as:
Figure GDA0003656361950000023
Figure GDA0003656361950000024
3)
Figure GDA0003656361950000025
m is 1,2, …, M, which represents the superposition vector of K signal independent point interference signals. Further, let the k-th interference source be in the direction of θkScattering coefficient of alphakK is 1,2, …, K. Thus, d (m) can be expressed as follows:
Figure GDA0003656361950000026
4)
Figure GDA0003656361950000027
m is 1,2, …, M, and represents a white gaussian noise vector with a mean of 0 and a variance of 0
Figure GDA0003656361950000028
Namely satisfy
Figure GDA0003656361950000029
The working principle of the invention is as follows:
to calculate the SINR, first the received signal energy, interference energy and noise energy should be calculated separately. For received signal energy, the target energy can be calculated from the signal model (1) as follows:
Figure GDA0003656361950000031
wherein
Figure GDA0003656361950000032
A waveform covariance matrix is shown, noting that the received steering vector has no effect on SINR. Further, there is the following transition:
Figure GDA0003656361950000033
Wherein s ═ vec(s).
Since the interference clutter is uncorrelated, the received interference energy can be calculated as follows:
Figure GDA0003656361950000034
based on the same expression method as in (6), (7) can be expressed as
Figure GDA0003656361950000035
The noise energy is
Figure GDA0003656361950000036
Order to
Figure GDA0003656361950000037
Therefore, the SINR may be expressed as follows:
Figure GDA0003656361950000038
in order to prevent distortion of the transmit waveform when the power amplifier is operating in saturation, while reducing the conversion pressure of the digital-to-analog converter, the constant modulus constraint is a condition that must be added. Conventionally, the present invention controls each modulus value of the waveform s to be 1.
In summary, the waveform optimization problem that maximizes the signal-to-dry ratio can be modeled as follows:
Figure GDA0003656361950000041
due to the constant modulus constraints, (10) becomes an NP-hard problem. In the invention, a new model is constructed to optimize the SINR. To solve the optimization problem in (10), it should be maximized | | | sHX||2While minimizing sHY||2+σ2。
First consider | | sHX||2。
Figure GDA0003656361950000042
Essentially a vector, each element of which represents the total energy at the mth snapshot in the target direction. To maximize | | sHX||2A simple method is to maximize sHEach element in X.
In practice, the amount of the liquid to be used,
Figure GDA0003656361950000043
there is a theoretical upper bound:
P0＝NT 2 (11)
for each smIn order to achieve P as much as possible0Then, an optimization problem can be modeled as:
Figure GDA0003656361950000044
Wherein ε represents
Figure GDA0003656361950000045
And P0A match error therebetween. Note that both constraints in (12) are non-convex, and therefore need to be enteredThe lines are more simplified.
For the first constraint, a slack variable is introduced
Figure GDA0003656361950000046
It can then be rewritten as:
Figure GDA0003656361950000047
wherein
Figure GDA0003656361950000048
(13) The equality of the first constraint in (1) and (12) may be represented by:
Figure GDA0003656361950000049
based on a given
Figure GDA00036563619500000410
(14) For smIs a relaxed constraint.
For the second constraint, relax it to
Figure GDA00036563619500000411
Wherein v isiIs a number NTThe vector of dimensions, the ith component of which is 1 and the remaining components are all 0
Figure GDA0003656361950000051
For convenience, define
Figure GDA0003656361950000052
In summary, an optimization problem can be given as follows:
Figure GDA0003656361950000053
due to new variables
Figure GDA0003656361950000054
(16) It is still a non-convex problem. However, when
Figure GDA0003656361950000055
At a given time, (16) relative to variable smEpsilon becomes a convex problem and can be solved directly by Matlab's CVX kit. In addition, the number of the main components is more,
Figure GDA0003656361950000056
can be set by
Figure GDA0003656361950000057
Thus obtaining the product. Thus, with an alternate optimization method, s can be updated by continually iteratingmε and
Figure GDA0003656361950000058
Figure GDA0003656361950000059
is a randomly generated vector
Figure GDA00036563619500000510
All components of which are [0,2 π]And (4) the following steps.
The optimization algorithm for solving the problem (16) at the same time is as follows:
input at(θ0),P0,
Figure GDA00036563619500000511
{v}.
Output smOf (2) an optimal solution s m,opt。
1: initialization
Figure GDA00036563619500000512
ε0＝∞,k＝0.
K is k +1, solves problem (16) and yields
Figure GDA00036563619500000513
And epsilonk+1.
3:
Figure GDA00036563619500000514
4. If it is not
Figure GDA00036563619500000515
(wherein
Figure GDA00036563619500000516
Is a parameter controlling convergence and is generally taken as 10-3) Output sm,opt＝sk+1(ii) a Otherwise, returning to the step 2 until convergence.
Next, in order to minimize interference energy and noise energy, the pair
Figure GDA00036563619500000517
A penalty factor w is added. Wherein
Figure GDA00036563619500000518
The final optimization problem can then be expressed as:
Figure GDA00036563619500000519
(18) it is still a convex optimization problem and therefore can be solved by the CVX toolbox as well. With an optimized algorithm flow similar to the solution problem (16), the algorithm flow for the solution problem (18) can also be given as follows:
input at(θ0),P0,
Figure GDA0003656361950000061
σ2,
Figure GDA0003656361950000062
{v}.
Output smOf (2) an optimal solution sm,opt。
1 initialization
Figure GDA0003656361950000063
ε0＝∞,k＝0.
K is k +1, solves problem (16) and yields
Figure GDA0003656361950000064
And
Figure GDA0003656361950000065
3:
Figure GDA0003656361950000066
4. if it is not
Figure GDA0003656361950000067
(wherein
Figure GDA0003656361950000068
Is a parameter controlling convergence and is generally taken as 10-3) Output sm,opt＝sk+1(ii) a Otherwise, go back to step 2 until convergence.
Note that (18) is only for smRather than s. But for different
Figure GDA0003656361950000069
By giving an optimization algorithm different s can be obtainedm,opt. Thus, by repeating the algorithm solving the problem (18) M times, the final optimized s can be obtained.
In the invention, prior information related to a target direction angle and a signal interference direction angle exists, and the prior information can be obtained from the previous radar beam scanning by the existing target detection method. In the invention, by adding penalty factors to the interference and noise items in the optimized objective function independently, deeper notches can be obtained on the directional diagram. Meanwhile, the waveforms of the snapshots of the radar are optimized respectively, so that the MFL performance of the radar is improved remarkably.
The invention has the following advantages and beneficial effects:
according to the method, by independently adding penalty factors to interference and noise items in the optimized objective function, deeper notches can be obtained on the directional diagram. Meanwhile, waveforms of all snapshots of the radar are optimized respectively, so that the MFL performance of the radar is improved remarkably. In addition, the invention can obtain higher signal-to-interference-and-noise ratio under the condition of lower SNR (signal-to-noise ratio).
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
fig. 1 is a graph comparing the performance of the emission patterns in the examples.
Fig. 2 is a graph comparing signal to interference and noise ratio performance in the examples.
Detailed Description
Hereinafter, the term "comprising" or "may include" used in various embodiments of the present invention indicates the presence of the invented function, operation or element, and does not limit the addition of one or more functions, operations or elements. Furthermore, as used in various embodiments of the present invention, the terms "comprises," "comprising," "includes," "including," "has," "having" and their derivatives are intended to mean that the specified features, numbers, steps, operations, elements, components, or combinations of the foregoing, are only meant to indicate that a particular feature, number, step, operation, element, component, or combination of the foregoing, and should not be construed as first excluding the existence of, or adding to the possibility of, one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing.
In various embodiments of the invention, the expression "or" at least one of a or/and B "includes any or all combinations of the words listed simultaneously. For example, the expression "a or B" or "at least one of a or/and B" may include a, may include B, or may include both a and B.
Expressions (such as "first", "second", and the like) used in various embodiments of the present invention may modify various constituent elements in various embodiments, but may not limit the respective constituent elements. For example, the above description does not limit the order and/or importance of the elements described. The foregoing description is for the purpose of distinguishing one element from another. For example, the first user device and the second user device indicate different user devices, although both are user devices. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of various embodiments of the present invention.
It should be noted that: if it is described that one constituent element is "connected" to another constituent element, the first constituent element may be directly connected to the second constituent element, and a third constituent element may be "connected" between the first constituent element and the second constituent element. In contrast, when one constituent element is "directly connected" to another constituent element, it is understood that there is no third constituent element between the first constituent element and the second constituent element.
The terminology used in the various embodiments of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the various embodiments of the invention. As used herein, the singular forms are intended to include the plural forms as well, unless the context clearly indicates otherwise. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which various embodiments of the present invention belong. The terms (such as those defined in commonly used dictionaries) should be interpreted as having a meaning that is consistent with their contextual meaning in the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein in various embodiments of the present invention.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Example 1:
a MIMO radar waveform generation method based on convex relaxation comprises the following steps:
Step 1: several parameters are required to construct the algorithm: direction a of the target directiont(θ0) Desired gain P of target direction0Random vector
Figure GDA0003656361950000071
Set of vectors v.
Step 2: initialization
Figure GDA0003656361950000072
ε0＝∞,k＝0.
And step 3: let k be k +1, solve problem (16) with matlab's CVX toolkit and get
Figure GDA0003656361950000073
And εk+1Question (16)
Figure GDA0003656361950000081
Is s.t.
Figure GDA0003656361950000082
Figure GDA0003656361950000083
And 4, step 4: order to
Figure GDA0003656361950000084
And 5: if it is not
Figure GDA0003656361950000085
(wherein
Figure GDA0003656361950000086
Is a parameter controlling convergence and is generally taken as 10-3) Optimal solution s of output waveformm,opt＝sk+1(ii) a Otherwise, go back to step 2 until convergence.
Example 2 on the basis of example 1:
a transmitting antenna NTThe fast beat number is M-16, which is 12 uniform linear arrays. Target direction is theta 015 deg. and its energy is E [ | | | α0||2]20, noise energy is σ20 dB. There are a total of three interferers, referred to for convenience as interference 1, interference 2 and interference 3, respectively. The directions of the three disturbances are respectively theta1＝-30°,θ2＝-20°,θ3The energy of three disturbances is E [ | | α, respectively, 40 °. three disturbances are each present1||2]＝30dB,E[||α2||2]＝28dB and E[||α3||2]25db noise energy of
Figure GDA0003656361950000087
The simulation scenarios are the same as the implementation scenario in document 1.
First, it is tested whether the pattern of the waveform is constant when w takes different values. For convenience, define
γ＝max(s)-min(s) (20)
Where max(s) and min(s) represent the maximum minus minimum modulo the waveform component, respectively. The smaller the value, the more remarkable the constant modulus characteristic of the waveform. Next, this embodiment provides three interference scenarios, where the first scenario is that only interference 1 exists, the second scenario is that only interference 1 and interference 2 exist simultaneously, and the third scenario is that interference 1, interference 2, and interference 3 all exist simultaneously. Table 1 shows the magnitude of γ in three scenarios for the resulting optimal waveform when w takes different values. It can be seen that γ is close to 0 for all three scenarios, and therefore the modulus of the waveform remains constant.
Table 1: value of gamma in three scenes
Figure GDA0003656361950000088
Through tests, when w is larger than or equal to 0.5, the influence of the value change on the algorithm is small, so that in the subsequent comparative experiments, w is 1. Fig. 1 shows the comparison result of the direction diagram performance of the algorithm proposed by the present invention and the prior art scheme 1 (document 1). The proposed algorithm can achieve a deeper notch in the interference direction and is about 80dB deeper than the notch of prior art scheme 1.
Fig. 2 shows the case where the SINR of the output varies with the SNR of the input. It can be seen that the SINR obtained by the proposed algorithm is significantly higher in the case of low SNR than in the case of the prior art scheme 1. Therefore, the waveform obtained by the invention has better SINR performance compared with the waveform obtained by the prior scheme 1.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (3)

1. A MIMO radar waveform generation method based on convex relaxation is characterized in that emission waveforms of co-located MIMO radars and emission ends are optimized, penalty factors are added to interference terms and noise terms in optimized objective functions independently, the penalty factors are used for deepening notches on a directional diagram, meanwhile, the maximum optimization processing is carried out on the total energy of waveforms at the snapshot positions of each radar, and the relaxation processing is carried out on the constant modulus constraint of the waveforms;
the information comprising the co-located MIMO radar is as follows:
the co-located MIMO radar has NTRoot transmitting antenna and NRRoot receiving antenna, smThe transmit waveform representing the mth snapshot of the nth antenna,
Figure FDA0003642085820000011
n＝1,2,…,NTm is equal to 1,2, …, M is a snapshot number, each modulus of the waveform s is controlled to be 1, and the data matrix of the receiving end is:
xm＝α0A(θ0)sm+d(m)+v(m) (1)
wherein:
1)α0is the scattering coefficient, theta0Is the azimuth;
2)
Figure FDA0003642085820000012
at(theta) is the direction vector of the transmitting end, ar(theta) is the direction vector of the receiving end, at(theta) and ar(θ) is expressed as:
Figure FDA0003642085820000013
Figure FDA0003642085820000014
3)
Figure FDA0003642085820000015
representing the superposition vector of the point interference signals with independent K signals, and making the direction of the K interference source be thetakScattering coefficient of alphakK is 1,2, …, K, d (m) is represented by:
Figure FDA0003642085820000016
4)
Figure FDA0003642085820000017
representing a Gaussian white noise vector with a mean of 0 and a variance of
Figure FDA0003642085820000018
Satisfy the requirements of
Figure FDA0003642085820000019
The waveform optimization problem that maximizes the signal-to-dry ratio is modeled as follows:
Figure FDA00036420858200000110
s.t.|s(i)|＝1,i＝1,2,…,MNT
wherein s ═ vec(s) and the noise energy is
Figure FDA00036420858200000111
Figure FDA0003642085820000021
The received interference energy is
Figure FDA0003642085820000022
The target energy is:
Figure FDA0003642085820000023
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003642085820000024
representing a waveform covariance matrix, target energy conversion
Figure FDA0003642085820000025
SINR is expressed as
Figure FDA0003642085820000026
Using maximised sHX||2While minimizing | | sHY||2+σ2To optimize the waveform optimization problem that maximizes the signal-to-noise-and-drying ratio, equation (10);
including minimizing sHY||2+σ2The optimization steps are as follows: minimizing interference energy and noise energy, pair
Figure FDA0003642085820000027
Adding a penalty coefficient w; wherein
Figure FDA0003642085820000028
The final optimization problem is then expressed as:
Figure FDA0003642085820000031
equation (12) remains a convex optimization problem, solved using the CVX toolset, where viIs a number NTThe vector of dimensions, the ith component of which is 1, the remaining components are all 0.
2. The method of claim 1, comprising maximizing sHX||2The optimization steps are as follows:
maximization of sHEach of the elements of X, wherein,
Figure FDA0003642085820000032
upper bound of theory of (1): p0＝NT 2(13) Based on the upper bound of theory, the modeling optimization model is as follows:
Figure FDA0003642085820000033
wherein ε represents
Figure FDA0003642085820000034
And P0The matching error between the two non-convex constraint problems in equation (14) is simplified, and for the first constraint, a relaxation variable is introduced
Figure FDA0003642085820000035
Then it is rewritten as:
Figure FDA0003642085820000036
wherein
Figure FDA0003642085820000037
The equality of the first constraint in equations (15) and (14) is represented by the following equation for
Figure FDA0003642085820000038
Comprises the following steps:
Figure FDA0003642085820000039
thus based on a given
Figure FDA00036420858200000310
Equation (16) for smIs a relaxed constraint;
equation (16) given
Figure FDA00036420858200000311
Relative to the variable s under the conditions of (1)mEpsilon becomes a convex problem and is solved directly by Matlab's CVX toolbox.
3. The method of claim 2, comprising generating the MIMO radar waveform based on convex relaxation
Figure FDA00036420858200000312
Is given an optimum value of
Figure FDA00036420858200000313
Obtaining, by means of an alternating optimization method, s by continuously iteratively updatingmε and
Figure FDA00036420858200000314
Figure FDA00036420858200000316
is a randomly generated vector
Figure FDA00036420858200000315
All components of which are [0,2 π]And (4) the following steps.
CN202110293103.1A 2021-03-18 2021-03-18 MIMO radar waveform generation method based on convex relaxation Active CN113050078B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110293103.1A CN113050078B (en) 2021-03-18 2021-03-18 MIMO radar waveform generation method based on convex relaxation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110293103.1A CN113050078B (en) 2021-03-18 2021-03-18 MIMO radar waveform generation method based on convex relaxation

Publications (2)

Publication Number Publication Date
CN113050078A CN113050078A (en) 2021-06-29
CN113050078B true CN113050078B (en) 2022-06-28

Family

ID=76513371

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110293103.1A Active CN113050078B (en) 2021-03-18 2021-03-18 MIMO radar waveform generation method based on convex relaxation

Country Status (1)

Country Link
CN (1) CN113050078B (en)

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104898113A (en) * 2015-06-19 2015-09-09 哈尔滨工业大学 Multiple-input-multiple-output radar waveform design method
CN105467365A (en) * 2015-12-08 2016-04-06 中国人民解放军信息工程大学 A low-sidelobe emission directional diagram design method improving DOA estimated performance of a MIMO radar
CN107024681A (en) * 2017-05-05 2017-08-08 大连大学 MIMO radar transmit-receive combination optimization method under the conditions of not known based on clutter knowledge
CN110082731A (en) * 2019-04-28 2019-08-02 北京理工大学 A kind of MIMO radar optimum waveform design method of continuous phase

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11766182B2 (en) * 2015-06-05 2023-09-26 The Arizona Board Of Regents On Behalf Of The University Of Arizona Systems and methods for real-time signal processing and fitting

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104898113A (en) * 2015-06-19 2015-09-09 哈尔滨工业大学 Multiple-input-multiple-output radar waveform design method
CN105467365A (en) * 2015-12-08 2016-04-06 中国人民解放军信息工程大学 A low-sidelobe emission directional diagram design method improving DOA estimated performance of a MIMO radar
CN107024681A (en) * 2017-05-05 2017-08-08 大连大学 MIMO radar transmit-receive combination optimization method under the conditions of not known based on clutter knowledge
CN110082731A (en) * 2019-04-28 2019-08-02 北京理工大学 A kind of MIMO radar optimum waveform design method of continuous phase

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Polyphase Waveform Design for MIMO Radar Space Time Adaptive Processing;Bo Tang et al.;《IEEE TRANSACTIONS ON SIGNAL PROCESSING》;20201231;全文 *
干扰环境下MIMO雷达波形与接收滤波联合优化算法;李玉翔等;《太赫兹科学与电子信息学报》;20170625(第03期);全文 *

Also Published As

Publication number Publication date
CN113050078A (en) 2021-06-29

Similar Documents

Publication Publication Date Title
Qi et al. Integrating sensing, computing, and communication in 6G wireless networks: Design and optimization
Zhong et al. MmWave beamforming for UAV communications with unstable beam pointing
CN107395255B (en) Robust hybrid beam forming method based on convex optimization
CN109560849B (en) Beam forming robustness self-adaptive algorithm based on second-order cone planning
CN114675238B (en) Radar communication integrated waveform direct optimization method and system
CN107302391A (en) Adaptive beamforming method based on relatively prime array
Loshakov et al. Adaptive space-time and polarisation-time signal processing in mobile communication systems of next generations
CN113030931B (en) MIMO radar waveform generation method based on manifold optimization
CN112564754A (en) Wave beam selection method based on self-adaptive cross entropy under millimeter wave Massive MIMO system
Sidharth et al. Deep learning based hybrid precoding for mmWave massive MIMO system using comcepNet
CN113050079B (en) Joint generation method for radar transmitting waveform and receiving filter weight vector
CN112668155B (en) Steady beam forming method and system based on secondary reconstruction
CN106960083A (en) A kind of robust adaptive beamforming method optimized based on main lobe beam pattern
CN113050078B (en) MIMO radar waveform generation method based on convex relaxation
Yin et al. Joint active and passive beamforming optimization for multi-IRS-assisted wireless communication systems: A covariance matrix adaptation evolution strategy
CN117290996A (en) MIMO radar constant mode waveform design method based on Riemann self-adaptive gradient
CN108037487A (en) A kind of distributed MIMO radar emission signal optimum design method stealthy based on radio frequency
CN111740766A (en) Codebook-based beam design method and device
Zhang et al. Training beam sequence design for mmWave tracking systems with and without environmental knowledge
CN110518944A (en) Antenna selecting method and system in a kind of millimeter wave MIMO communication system
CN114839604A (en) Orthogonal waveform design method and system for MIMO radar
CN115133969A (en) Performance improving method of millimeter wave large-scale MIMO-NOMA system
CN113642181A (en) MIMO radar waveform optimization method for rapid manifold modeling
CN114499612A (en) Beam forming processing method and device and readable storage medium
CN114978264B (en) Mixed precoding method based on terahertz MIMO system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant