CN110176953B - Plane frequency control array beam forming method based on generalized eigenvalue decomposition - Google Patents

Plane frequency control array beam forming method based on generalized eigenvalue decomposition Download PDF

Info

Publication number
CN110176953B
CN110176953B CN201910450444.8A CN201910450444A CN110176953B CN 110176953 B CN110176953 B CN 110176953B CN 201910450444 A CN201910450444 A CN 201910450444A CN 110176953 B CN110176953 B CN 110176953B
Authority
CN
China
Prior art keywords
representing
array
elements
antenna
frequency control
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.)
Expired - Fee Related
Application number
CN201910450444.8A
Other languages
Chinese (zh)
Other versions
CN110176953A (en
Inventor
陈慧
程婕
万珂妙
王文钦
廖轶
张顺生
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.)
University of Electronic Science and Technology of China
Original Assignee
University of Electronic Science and Technology of China
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 University of Electronic Science and Technology of China filed Critical University of Electronic Science and Technology of China
Priority to CN201910450444.8A priority Critical patent/CN110176953B/en
Publication of CN110176953A publication Critical patent/CN110176953A/en
Application granted granted Critical
Publication of CN110176953B publication Critical patent/CN110176953B/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0619—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
    • H04B7/0621—Feedback content
    • H04B7/0634—Antenna weights or vector/matrix coefficients

Abstract

The invention provides a plane frequency control array beam forming method based on generalized eigenvalue decomposition, which comprises the following steps: constructing a planar frequency control array according to the number of the antenna array elements, the carrier frequency, the frequency offset value between the adjacent antenna array elements and the space between the adjacent antenna array elements; constructing a corresponding far-field emission beam pattern according to the planar frequency control array; and respectively solving the eigenvalue and the eigenvector of the far-field emission beam pattern by using an energy aggregation algorithm (BCE) to obtain an optimal weight matrix of the far-field emission beam pattern, thereby forming a beam of the planar frequency control array. The invention solves the optimal transmitting weight by utilizing generalized eigenvalue decomposition, can form a focusing point beam in an expected area, and solves the problem that a linear frequency control array cannot form a good point beam.

Description

Plane frequency control array beam forming method based on generalized eigenvalue decomposition
Technical Field
The invention belongs to the technical field of frequency control array radars, and particularly relates to a plane frequency control array beam forming method based on generalized eigenvalue decomposition.
Background
The frequency control array radar has very wide application in the fields of radar systems, wireless communication, radar imaging, target estimation and tracking, interference resistance and the like due to the specific distance-angle dependence of the frequency control array radar. The uniform linear frequency control array can form a transmitting beam with angle-distance dependency, but the distance and azimuth coupling of the beam pattern of the uniform linear frequency control array is in an S-shaped peak ridge shape in a distance-angle two-dimensional plane, and is not an ideal unimodal beam, namely a spot beam. In order to form a spot beam, angle dimension and distance dimension decoupling is required, while a linear frequency control array cannot generate a spot beam in a true sense, even if an approximate spot beam can be formed by configuring parameters of the linear frequency control array, such as frequency offset, array element interval and the like, the cost is the loss of beam resolution. At present, the beam forming method aiming at the planar frequency control array can adopt an ant colony algorithm to optimize frequency deviation, but the calculation process of the method is relatively complex.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a plane frequency control array beam forming method based on generalized eigenvalue decomposition, which solves the optimal transmitting weight by utilizing generalized eigenvalue decomposition, can form a focusing point beam in an expected area and solves the problem that a linear frequency control array cannot form a good point beam.
In order to achieve the above purpose, the invention adopts the technical scheme that:
the scheme provides a plane frequency control array beam forming method based on generalized eigenvalue decomposition, which comprises the following steps:
s1, constructing a planar frequency control array according to the number of the antenna array elements, the carrier frequency, the frequency offset value between the adjacent antenna array elements and the distance between the adjacent antenna array elements;
s2, constructing a corresponding far-field emission beam pattern according to the planar frequency control array;
and S3, respectively solving the eigenvalue and the eigenvector of the far-field emission beam pattern by using an energy clustering algorithm BCE to obtain an optimal weight matrix of the far-field emission beam pattern, thereby forming the beam of the plane frequency control array.
Still further, in step S1, the antenna is an omni-directional antenna.
Still further, the planar frequency control array is composed of M × N antenna elements, and the carrier frequency f of the first antenna0Is 10GHz, wherein,
the x direction of the antenna array element is at equal interval dxDistributing M antenna elements, and frequency offset value delta f between adjacent antenna elementsxSequentially increasing according to linear increment;
the y direction of the antenna array element is at equal interval dyN antenna elements are distributed, and the frequency offset value delta f between adjacent antenna elementsySequentially increasing linearly.
Still further, the frequency offset values of the adjacent antennas in the x direction and the y direction are both 30 KHz.
Still further, the distance between the adjacent antennas in the x direction and the y direction is 0.03 m.
Still further, the far field transmit beam pattern
Figure BDA0002074970390000021
Expression (2)The following were used:
Figure BDA0002074970390000022
Figure BDA0002074970390000023
and is
Figure BDA0002074970390000024
Wherein exp {. cndot } represents an exponential function with a natural constant e as the base, j represents a complex unit, f0The method comprises the steps of representing the center frequency of a transmitted signal, t representing time, r representing the distance from a reference array element to a target point, c representing the speed of light, W representing a transmission weight matrix of an antenna array element, M representing the number of the antenna array elements in the x direction, N representing the number of the antenna array elements in the y direction, M representing the sequence number of the antenna array element in the x direction, M being 0,1,2,. eta.M, N representing the sequence number of the array element in the y direction, N being 0,1,2,. eta.N, W*Denotes the conjugate of the transmit matrix W, ⊙ denotes the Hadamard product, A denotes the array factor, WM-1,N-1Representing an element of an emission matrix, aM-1,N-1Representing an array factor element, amnArray factor, Δ f, representing the mn array elementmnIndicating the frequency offset value of the mn-th array element, dmnThe array element spacing of the mn-th array element is shown, theta represents the inverted angle of the target point,
Figure BDA0002074970390000031
indicating the azimuth of the target point.
Still further, the optimal weight matrix vec (W) of the far-field transmit beam pattern in the step S3opt) The expression of (a) is as follows:
Figure BDA0002074970390000032
wherein the content of the first and second substances,
Figure BDA0002074970390000033
represents solving for the maximum weight vector, vec (W))HThe conjugate transpose of the matrix vectorization representing the transmit weights, vec (w) represents the transmit weight matrix vectorization, a represents the power in the desired radiation range, and B represents the power in the total radiation range.
The invention has the beneficial effects that:
according to the method, a planar frequency control array is constructed according to the number of the array elements of the antenna, the carrier frequency, the frequency offset value between the adjacent antenna array elements and the distance between the adjacent antenna array elements; constructing a corresponding far-field emission beam pattern according to the planar frequency control array; respectively solving the eigenvalue and the eigenvector of the far-field transmitting beam pattern by using an energy clustering algorithm BCE to obtain an optimal weight matrix of the far-field transmitting beam pattern so as to form a beam of a planar frequency control array
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of a planar frequency control array model in this embodiment.
Fig. 3 is a three-dimensional spatial emission model diagram of the planar frequency control array in this embodiment.
Fig. 4 is a normalized three-dimensional beam pattern of the planar frequency control array corresponding to the unused optimized weight matrix in this embodiment.
Fig. 5 is a normalized two-dimensional plane beam pattern of the plane frequency control matrix corresponding to the unused optimized weight matrix in this embodiment.
Fig. 6 is a plane frequency control lattice spot beam diagram of the target area a in this embodiment.
Fig. 7 is a plane frequency control lattice spot beam diagram of the target area b in this embodiment.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Examples
As shown in fig. 1, the invention discloses a planar frequency-controlled array beam forming method based on generalized eigenvalue decomposition, which is implemented as follows:
s1, constructing a plane frequency control array according to the number of the antenna array elements, the carrier frequency of the antenna array elements, the frequency offset value between the adjacent antenna array elements and the distance between the adjacent antenna array elements, specifically, as shown in figures 2-3, a plane frequency control array is formed by M × N array elements, and the x-direction array elements are according to dxM array elements are distributed at equal intervals, and the frequency deviation of each array element is in turn according to delta fxLinearly increasing, y-direction array elements by dyN array elements are distributed at equal intervals, and the frequency deviation of each array element is in turn according to delta fyLinearly increasing, transmitting signal by a planar frequency control array, and obtaining the spherical coordinate of an observation point at a far field
Figure BDA0002074970390000041
Wherein the content of the first and second substances,
Figure BDA0002074970390000042
is the azimuth angle of the target point, and the value range is [0,2 pi ]; theta is the pitch angle of the target point, and the value range is [0, pi ]; r is the distance from the observation point to the reference point, and the value range is [ R ]minInfinity), wherein RminIn the embodiment of the present invention, the antennas in the assumed planar frequency-controlled array model all use omnidirectional antennas, and under the condition that the energy attenuation along with the distance is not considered, the number of omnidirectional antenna elements is set to be M-N-10, and the carrier frequency of the first omnidirectional antenna (reference element) is f0Frequency offset value of delta f for adjacent omnidirectional antennas at 10GHzx＝Δfy30KHz, with spacing of adjacent omnidirectional antennas dx＝dyThe pitch angle theta is equal to 90 degrees, namely the plane of the array is located;
s2, constructing a corresponding far-field emission beam pattern according to the plane frequency control array, wherein in the specific embodiment, the far-field emission beam pattern is assumed to be located at the origin of a coordinate systemThe array element at the position is the first omnidirectional antenna (reference array element) and is marked as e00Then the array elements at other positions can be marked as emnWherein, M represents the serial number of the antenna array element along the x direction, M is 0,1,2,. M, N represents the serial number of the array element along the y direction, N is 0,1,2,. N, and the array element emnFor transmitting a single frequency signal smn(t) is represented by the formula (1):
smn(t)＝exp(j2πfmnt) (1)
far field observation point
Figure BDA0002074970390000051
To the received signal
Figure BDA0002074970390000052
As shown in formula (2):
Figure BDA0002074970390000053
wherein exp {. cndot } represents an exponential function with a natural constant e as the base, fmnRepresenting the operating frequency of the mn-th array element, t represents time,
Figure BDA0002074970390000054
representing the conjugate of the weight of the mn-th array element, rmnDenotes the tilt distance of the mn-th array element, W ═ Wmn}M×NIs a matrix of transmit weights for the antenna elements,
Figure BDA0002074970390000055
as an array element emnThe antenna directional pattern of (1) assumes that the array antenna has good consistency, each array element antenna is an isotropic point source, and the frequency domain response is at the carrier frequency f0The vicinity is flat, then there are
Figure BDA0002074970390000056
exp {. is } represents an exponential function with a natural constant e as the base, an array element emnCarrier frequency f ofmn＝f0+mΔfx+nΔfy，m＝0,1,2,...,M-1,n＝0,1,2,...,N-1，f0As a reference array element e00Carrier frequency of far field observation point to array element emnIs a distance of
Figure BDA0002074970390000057
M-0, 1,2, M-1, N-0, 1,2, N-1, and simplified formula (2) is:
Figure BDA0002074970390000061
wherein, Δ fmn＝mΔfx+nΔfy，
Figure BDA0002074970390000062
ΔfxRepresenting the frequency offset, Δ f, of adjacent antenna elements in the x-directionyIndicating the frequency offset, Δ f, of adjacent antenna elements in the y-directionmnIndicating the frequency offset value of the mn-th array element, dmnThe array element interval of the mn-th array element is shown, theta represents the inverted angle of the target point,
Figure BDA0002074970390000063
representing an azimuth of the target point;
assuming frequency offset values Δ f of adjacent antennasxAnd Δ fySpacing d between adjacent antenna elementsxAnd dyThe following conditions are satisfied:
Figure BDA0002074970390000064
then the formula (4) is further simplified:
Figure BDA0002074970390000065
wherein, AFxAs linear frequency-controlled array factors, AF, on the x-axisyThe linear frequency control array factors on the y axis can be respectively expressed as:
Figure BDA0002074970390000066
Figure BDA0002074970390000067
wherein the content of the first and second substances,
Figure BDA0002074970390000068
representing the conjugate of the weight in the x-direction,
Figure BDA0002074970390000069
representing the weight conjugate in the y-direction, the weight w of the frequency-controlled array in the x-axisx＝{wxm}M×1And the weight w of the frequency control array on the y-axisy＝{wyn}N×1Expressed as:
W＝wx Twy＝{wxm·wyn}M×N(8)
wherein, wx TRepresenting the transpose of the weight vector in the x direction, wyRepresenting the weight vector in the y direction, wxmDenotes the weight in the x direction, wynThe representation represents the weight in the y-direction,M×Nthe method is characterized in that a plane frequency control array model is represented, a transmitting weight matrix of the plane frequency control array is decomposed into two linear array frequency control array transmitting weight vectors, and a transmitting beam pattern of the plane frequency control array can be written into the following matrix form:
Figure BDA0002074970390000071
wherein:
Figure BDA0002074970390000072
and is
Figure BDA0002074970390000073
Wherein exp {. cndot } represents an exponential function with a natural constant e as the base, j represents a complex unit, f0Representing the center frequency of the transmitted signal, t representing time, r representing the distance of the reference array element to the target pointC represents the speed of light, W represents the transmit weight matrix of the antenna elements, M represents the number of antenna elements in the x direction, N represents the number of antenna elements in the y direction, M represents the serial number of the antenna elements in the x direction, M is 0,1,2,. eta.m, N represents the serial number of the elements in the y direction, N is 0,1,2,. eta.n, W*Denotes the conjugate of the transmit matrix W, ⊙ denotes the Hadamard product, A denotes the array factor, WM-1,N-1Representing an element of an emission matrix, aM-1,N-1Representing an array factor element, amnArray factor, Δ f, representing the mn array elementmnIndicating the frequency offset value of the mn-th array element, dmnThe array element spacing of the mn-th array element is shown, theta represents the inverted angle of the target point,
Figure BDA0002074970390000074
representing an azimuth of the target point;
s3, respectively solving the eigenvalue and the eigenvector of the far-field emission beam pattern by using an energy clustering algorithm BCE to obtain an optimal weight matrix of the far-field emission beam pattern, so as to form the beam of the planar frequency control array, in the specific embodiment, the far-field emission beam pattern is combined with the energy clustering algorithm BCE, and the method for forming the dot beam of the planar frequency control array based on the generalized eigenvalue decomposition is provided:
in a specific embodiment, the transmit beam pattern of the planar frequency control array
Figure BDA0002074970390000081
Expressed as:
Figure BDA0002074970390000082
the further derivation is:
Figure BDA0002074970390000083
wherein A represents an array factor, wx HRepresenting the conjugate transpose of the weight vector in the x-direction, ax(. denotes the array factor in the x-direction, wy HRepresenting sum of weight vectors in the y-directionYoke transfer, ay(. cndot.) represents the weight vector in the y direction, W represents the emission weight matrix, H represents the conjugate transpose, vec (. cndot.) represents the vectorization of the matrix;
defining an energy-aggregating algorithm BCE to transmit power within a desired range
Figure BDA0002074970390000084
And total transmission power PΩThe expression of the ratio of (a) to (b) is:
Figure BDA0002074970390000085
wherein the content of the first and second substances,
Figure BDA0002074970390000086
Ω0and omega respectively denote a desired beam radiation range and a total beam radiation range,
Figure BDA0002074970390000087
represents the integral over the desired radiation range, [ integral ] orΩDenotes the integral over the total radiation range, d denotes the differential sign, theta denotes the angle of the target point's inversion,
Figure BDA0002074970390000088
representing the azimuth of the target point, r represents the distance from the reference array element to the target point, then
Figure BDA0002074970390000091
Wherein the content of the first and second substances,
Figure BDA0002074970390000092
Figure BDA0002074970390000093
Figure BDA0002074970390000094
in the above formula, the first and second carbon atoms are,
Figure BDA0002074970390000095
represents the triple integral, integral ^ integral within the expected radiation rangeΩRepresenting the triple integral, theta, over the total radiation range1And theta2Each representing a range boundary of the desired range of angles,
Figure BDA0002074970390000096
and
Figure BDA0002074970390000097
all represent the azimuth angle range boundary of the expected range, for the distance dimension, because of its periodicity, r is taken within a range of a distance period, and for any transmit aperture and target area beam forming problem, a generalized eigenvalue decomposition problem can be constructed, and the eigenvalue and eigenvector of the far-field transmit beam pattern are solved to obtain an explicit expression of the optimal transmit array weight of the maximum energy aggregation algorithm BCE:
Figure BDA0002074970390000098
wherein the content of the first and second substances,
Figure BDA0002074970390000099
representing the solving for the maximum weight vector, vec (W)HConjugate transpose of matrix vectorization representing the transmission weights vec (W) represents the transmission weight matrix vectorization, a represents the power in the desired radiation range, B represents the power in the total radiation range, weight vector vec (W) that maximizes the maximum energy aggregation algorithm BCE if a and B are Hermitian matrices and have positive definite propertiesopt) The eigenvector corresponding to the largest eigenvalue of the generalized eigenvalue problem is equal, after the items A and B are determined, the optimal solution vec (W) is obtained by calculating the largest eigenvalue and the corresponding eigenvector in the formula (14)opt) The result in equation (14) is substituted into equation (13), and the ratio of the transmission power to the total transmission power in the desired range is finally obtained:
Figure BDA00020749703900000910
in the present embodiment, as shown in fig. 6 and 7, a Ω for the target region is obtained based on the result of the decomposition based on the generalized eigenvalue1:[70°,90°],[29km,32km]And target area b Ω2:[30°,50°],[39km,42km]The corresponding 10 × 10 weight matrix elements are 0.5274, 0.5972, 0.8933, 0.9558, 0.9966, 0.9966, 0.9558, 0.8933, 0.5972, 0.5274 (only diagonal elements are given.) and 0.2826, 0.4692, 0.7590, 0.9193, 0.9893, 0.9893, 0.9193, 0.7590, 0.4692, 0.2826 (only diagonal elements are given.), respectively, and the corresponding planar frequency control array forms a two-dimensional transmit spot beam pattern at two target regions, where Ω is the number of transmit spots in the two target regions1Representing the target area a, omega2When the transmission weight matrix is an all-1 matrix, that is, the optimized weight matrix is not used, the normalized three-dimensional beam pattern of the corresponding planar frequency control array is shown in fig. 4, the two-dimensional plane pattern is shown in fig. 5, fig. 4 shows the normalized three-dimensional beam pattern of the planar frequency control array without using the energy focusing beam forming algorithm, fig. 5 shows the corresponding two-dimensional beam pattern, and it can be seen by comparing with fig. 6 and 7 (fig. 6 and 7 use the energy focusing beam forming algorithm) that the energy focusing beam forming algorithm used at this time can control the focusing position of the spot beam by setting the required focusing range.

Claims (6)

1. A plane frequency control array beam forming method based on generalized eigenvalue decomposition is characterized by comprising the following steps:
s1, constructing a planar frequency control array according to the number of the antenna array elements, the carrier frequency, the frequency offset value between the adjacent antenna array elements and the distance between the adjacent antenna array elements;
s2, constructing a corresponding far-field emission beam pattern according to the planar frequency control array;
s3, respectively solving the eigenvalue and the eigenvector of the far-field emission beam pattern by using an energy clustering algorithm BCE to obtain an optimal weight matrix of the far-field emission beam pattern, thereby forming a beam of the planar frequency control array;
the expression of the energy aggregation algorithm BCE in step S3 is:
Figure FDA0002497872190000011
wherein, BCEoptRepresenting the energy focusing algorithm BCE, vec (W)opt)HOptimal weight matrix vec (W) representing far field transmit beam patternopt) A denotes the power in the desired radiation range, B denotes the power in the total radiation range;
the optimal weight matrix vec (W) of the far-field transmit beam pattern in said step S3opt) The expression of (a) is as follows:
Figure FDA0002497872190000012
wherein the content of the first and second substances,
Figure FDA0002497872190000013
representing the solving for the maximum weight vector, vec (W)HThe conjugate transpose of the matrix vectorization representing the transmit weights, vec (w) represents the transmit weight matrix vectorization.
2. The method for forming planar frequency steering array beam based on generalized eigenvalue decomposition of claim 1 wherein, in step S1, the antenna is an omnidirectional antenna.
3. The method as claimed in claim 1, wherein the planar frequency control array is composed of M × N antenna elements, and the carrier frequency f of the first antenna is0The frequency is 10GHz, wherein M represents the number of antenna elements in the x direction, and N represents the number of antenna elements in the y direction;
the x direction of the antenna array element is at equal interval dxDistributing M antenna elements, and frequency offset value delta f between adjacent antenna elementsxSequentially increasing according to linear increment;
the y direction of the antenna array element is at equal interval dyN antenna elements are distributed, and the frequency offset value delta f between adjacent antenna elementsySequentially increasing linearly.
4. The method as claimed in claim 3, wherein the frequency offset values of the adjacent antennas in x and y directions are both 30 KHz.
5. The method according to claim 3, wherein the distances between adjacent antennas in the x-direction and the y-direction are both 0.03 m.
6. The method of claim 1, wherein the far-field transmit beam pattern is formed by using a planar frequency-controlled array based on generalized eigenvalue decomposition
Figure FDA0002497872190000021
The expression of (a) is as follows:
Figure FDA0002497872190000022
Figure FDA0002497872190000023
and is
Figure FDA0002497872190000024
Wherein exp {. cndot } represents an exponential function with a natural constant e as the base, j represents a complex unit, f0The method comprises the steps of representing the center frequency of a transmitted signal, t representing time, r representing the distance from a reference array element to a target point, c representing the speed of light, W representing a transmission weight matrix of an antenna array element, M representing the number of the antenna array elements in the x direction, N representing the number of the antenna array elements in the y direction, M representing the sequence number of the antenna array elements in the x direction, and M being 0,1,2N-1, W, indicating the number of the array elements in the y-direction, N being 0,1,2*Denotes the conjugate of the transmit matrix W, ⊙ denotes the Hadamard product, Y denotes the array factor, WM-1,N-1Representing elements in a transmit weight matrix, aM-1,N-1Representing an array factor element, amnRepresenting the array factor of the mn-th array element, theta representing the inversion angle of the target point,
Figure FDA0002497872190000031
indicating the azimuth angle of the target point, Δ fxRepresenting the value of the frequency offset, af, between adjacent antenna elements in the x-directionyRepresenting the frequency offset value between adjacent antenna array elements along the y direction; dxRepresenting the spacing between adjacent antenna elements in the x-direction, dyIndicating the spacing between adjacent antenna elements in the y-direction.
CN201910450444.8A 2019-05-28 2019-05-28 Plane frequency control array beam forming method based on generalized eigenvalue decomposition Expired - Fee Related CN110176953B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910450444.8A CN110176953B (en) 2019-05-28 2019-05-28 Plane frequency control array beam forming method based on generalized eigenvalue decomposition

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910450444.8A CN110176953B (en) 2019-05-28 2019-05-28 Plane frequency control array beam forming method based on generalized eigenvalue decomposition

Publications (2)

Publication Number Publication Date
CN110176953A CN110176953A (en) 2019-08-27
CN110176953B true CN110176953B (en) 2020-07-07

Family

ID=67696398

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910450444.8A Expired - Fee Related CN110176953B (en) 2019-05-28 2019-05-28 Plane frequency control array beam forming method based on generalized eigenvalue decomposition

Country Status (1)

Country Link
CN (1) CN110176953B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111355517B (en) * 2020-03-17 2021-04-06 电子科技大学 Frequency control array base station cooperative transmission method for high-speed mobile user

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107346986A (en) * 2017-07-12 2017-11-14 电子科技大学 A kind of Multibeam synthesis method based on sparse frequency control sensor antenna array

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7075485B2 (en) * 2003-11-24 2006-07-11 Hong Kong Applied Science And Technology Research Institute Co., Ltd. Low cost multi-beam, multi-band and multi-diversity antenna systems and methods for wireless communications
CN106656293B (en) * 2016-12-21 2020-07-28 电子科技大学 Physical layer secure communication method based on frequency control array beam forming
CN106646394B (en) * 2017-02-28 2018-03-02 湖北工业大学 A kind of launching beam matrix design method based on loop optimization in FDA MIMO radars
CN108896983B (en) * 2018-05-10 2022-09-20 电子科技大学 Time-invariant space focusing beam forming method based on frequency control array

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107346986A (en) * 2017-07-12 2017-11-14 电子科技大学 A kind of Multibeam synthesis method based on sparse frequency control sensor antenna array

Also Published As

Publication number Publication date
CN110176953A (en) 2019-08-27

Similar Documents

Publication Publication Date Title
Liao et al. Transmit beampattern synthesis for frequency diverse array with particle swarm frequency offset optimization
CN108896983B (en) Time-invariant space focusing beam forming method based on frequency control array
CN109633526B (en) Direction finding ambiguity resolving method of non-uniform circular array phase interferometer based on direction function
CN110221293B (en) Pitching angle imaging method based on vortex electromagnetic waves
CN108919174B (en) Short wave radio direction finding system and method of irregular antenna array structure
CN108196239B (en) Unambiguous parameter estimation method for frequency diversity MIMO radar
CN113115205B (en) Distributed cooperative positioning method based on angle measurement
CN110176953B (en) Plane frequency control array beam forming method based on generalized eigenvalue decomposition
CN108459301B (en) Heterogeneous array-based MIMO radar waveform design method
CN113068195A (en) Intelligent super-surface position design method based on user speed maximization
CN110764059A (en) Three-coordinate phased array radar technology for transmitting and receiving vertical beams
CN113917461B (en) MIMO radar imaging method and system
CN110995331B (en) Beam forming method based on multipoint accurate control
KR20170127939A (en) Apparatus for estimating direction of arrival based on a circularly arraying antenna compensating intermutual interference and method therefor
CN113075649A (en) Signal level direct positioning method suitable for distributed networked radar
CN112072295A (en) Miniaturized multi-beam vortex beam generating device
CN109639329A (en) The only quick shaping method of phase weighting wave beam
CN114499615B (en) Near-far field unified transmitting beam forming method in terahertz communication system
Guo et al. Synthesis of Planar Array Antenna for Wireless Power Transmission
CN108761414B (en) S-shaped interference wave beam testing method based on frequency control array
CN102664691B (en) Virtual source theory-based modeling approach for six-polarized MIMO (multi-input multi-output) channel
Cao et al. Direct Self-Position Awareness Based on Array-Sensing Multiple Source Data Fitting
CN112162240A (en) Sparse frequency waveform generation method and device based on co-prime array and storage medium
CN111276805A (en) Method for generating structural electromagnetic wave beams based on partial circular ring traveling wave antenna theory
CN110907926A (en) Bistatic EMVS-MIMO radar rapid target positioning algorithm and device based on propagation operator

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
CF01 Termination of patent right due to non-payment of annual fee
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20200707

Termination date: 20210528