CN113067618A - Multi-frequency spot beam forming method and system - Google Patents

Multi-frequency spot beam forming method and system Download PDF

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CN113067618A
CN113067618A CN202110292995.3A CN202110292995A CN113067618A CN 113067618 A CN113067618 A CN 113067618A CN 202110292995 A CN202110292995 A CN 202110292995A CN 113067618 A CN113067618 A CN 113067618A
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phase
frequency
directional diagram
amplitude
dimensional
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CN113067618B (en
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郑灵
曹军
李晓孟
程圣华
周围
丁文兵
强云飞
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CETC 38 Research Institute
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    • 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

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Abstract

The invention discloses a multi-frequency spot beam forming method and a system, wherein the method comprises the following steps: acquiring a phase function of an antenna array surface to be shaped; acquiring the phase of a typical frequency point in a forming direction; substituting each phase into a one-dimensional linear array directional diagram calculation formula for correction to obtain a corrected directional diagram formula; acquiring a medium-frequency amplitude-phase value meeting the requirement by utilizing an optimization algorithm according to the corrected directional diagram formula; expanding the amplitude and phase values of the intermediate frequency to amplitude and phase values of other frequency points; substituting the amplitude phase value of each frequency point into a two-dimensional array surface directional diagram formula, and solving a spatial directional diagram of an array surface, namely a beam forming directional diagram; judging whether the beam forming directional diagram meets the forming requirement, if not, encrypting the frequency point, and repeating the steps until the obtained beam forming directional diagram meets the forming requirement; the invention has the advantages that: the shaping is easier and the shaping efficiency is higher.

Description

Multi-frequency spot beam forming method and system
Technical Field
The invention relates to the field of array antenna design, in particular to a multi-frequency spot beam forming method and a multi-frequency spot beam forming system.
Background
The array antenna has wide application in the fields of radar, electronic warfare and the like. In many cases, radar, electronic warfare and the like require antenna beams with special shapes, such as cosecant square forming, beam broadening, flat-top beam and the like, and beam forming is an important link of phased array antenna design.
Most existing shaping methods are optimized for a single frequency point, when a shaping direction adopts power divider synthesis or antenna broadband work, if shaping is carried out only for intermediate frequency, due to the existence of dispersion effect, the phases of other frequency points can generate certain offset, and when the bandwidth is wider, the offset is larger, so that a directional diagram is deteriorated, and the shaping requirements cannot be met.
In a paper, "phase optimization method for realizing broadband beamforming" (penzhongwei, 2009 national antenna annual meeting introduction (lower), 1248-.
However, as the bandwidth of the antenna increases, even if the intermediate frequency phase distribution is limited to a certain range, the phase shift amount of the low frequency and the high frequency is large, resulting in poor shaping effect. In some cases, if the phase distribution is limited to a certain range, the degree of freedom of phase optimization is reduced, which makes the shaping difficult and the shaping efficiency low.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the existing wave beam shaping method has the problems of difficult shaping and low shaping efficiency when being applied to multiple frequency points.
The invention solves the technical problems through the following technical means: a method of multi-frequency spot beamforming, the method comprising:
step 1: acquiring a phase function of an antenna array surface to be shaped;
step 2: acquiring the phase of a typical frequency point in a forming direction;
and step 3: substituting each phase into a one-dimensional linear array directional diagram calculation formula for correction to obtain a corrected directional diagram formula;
and 4, step 4: acquiring a medium-frequency amplitude-phase value meeting the requirement by utilizing an optimization algorithm according to the corrected directional diagram formula;
and 5: expanding the amplitude and phase values of the intermediate frequency to amplitude and phase values of other frequency points;
step 6: substituting the amplitude phase value of each frequency point into a two-dimensional array surface directional diagram formula, and solving a spatial directional diagram of an array surface, namely a beam forming directional diagram;
and 7: and (3) judging whether the beam forming directional diagram obtained in the step (6) meets the forming requirement, if not, encrypting the frequency point in the step (2), and repeating the steps (2) to (7) until the obtained beam forming directional diagram meets the forming requirement.
The invention introduces a phase function, obtains the phase of a typical frequency point in the shaping direction according to the phase function, firstly obtains the intermediate frequency amplitude and phase value meeting the requirement, then expands the intermediate frequency amplitude and phase value into the amplitude and phase values of other frequency points, and converts the amplitude and phase value optimization of a multi-frequency point antenna unit into the amplitude and phase optimization of a single frequency point, thereby greatly reducing the optimization cost, reducing the shaping difficulty, improving the shaping efficiency, and the wider the bandwidth of an antenna array surface, the more obvious the optimization cost is reduced.
Further, the step 1 comprises:
for an M row by N column array plane, the antenna bandwidth is fL～fHAt an intermediate frequency of f0And obtaining a phase function:
Figure BDA0002983144840000031
wherein the content of the first and second substances,
Figure BDA0002983144840000032
is a frequency point fiThe phase of the corresponding phase is determined,
Figure BDA0002983144840000033
at an intermediate frequency f0The corresponding phase.
Further, the step 2 includes:
the value of the typical frequency point is determined by the shaped bandwidth and the phase function.
If the array surface is shaped by beams in the column direction
Figure BDA0002983144840000034
Wherein the content of the first and second substances,
Figure BDA0002983144840000035
is a frequency f1The phase of the corresponding M rows is,
Figure BDA0002983144840000036
is a frequency f2The phase of the corresponding M rows is,
Figure BDA0002983144840000037
is a frequency fqThe phase of the corresponding M rows is,
Figure BDA0002983144840000038
is a frequency f0The phase of the corresponding M rows;
if the array plane is shaped by beams in the row direction
Figure BDA0002983144840000039
Wherein the content of the first and second substances,
Figure BDA00029831448400000310
is a frequency f1The phase of the corresponding N columns,
Figure BDA00029831448400000311
is a frequency f2The phase of the corresponding N columns,
Figure BDA00029831448400000312
is a frequency fqThe phase of the corresponding N columns,
Figure BDA00029831448400000313
is a frequency f0The corresponding N columns of phases.
Still further, the step 3 includes:
will phase
Figure BDA00029831448400000314
Substituting into a one-dimensional linear array directional diagram formula for correction,
if the wave beam of the array surface is shaped in the column direction, the corrected directional diagram calculation formula is as follows:
Figure BDA00029831448400000315
wherein, amIs the amplitude, k, of a one-dimensional array antenna elementiThe wave number d corresponding to the ith frequency point in the one-dimensional array antenna unitmyThe coordinate of the one-dimensional linear array antenna unit is shown, and theta is the pitch angle of the one-dimensional linear array antenna unit;
if the wave beam of the array surface is shaped in the row direction, the corrected directional diagram calculation formula is as follows:
Figure BDA00029831448400000316
at this time, anIs the amplitude, k, of a one-dimensional row line array antenna elementiThe wave number d corresponding to the ith frequency point in the one-dimensional linear array antenna unitnxIs the coordinate of the one-dimensional linear array antenna unit, and phi is the azimuth angle of the one-dimensional linear array antenna unit.
Still further, the step 4 includes:
designing an optimization target F according to the directional diagram formula corrected in the step 31+F2+...+FgObtaining the amplitude and phase value a meeting the beam forming requirement by using an optimization algorithmm、
Figure BDA0002983144840000041
Or an、
Figure BDA0002983144840000042
Wherein the optimization algorithmAdopting a genetic algorithm or a particle swarm algorithm, and obtaining an amplitude-phase value a meeting the beam forming requirement when an optimization target convergesm、
Figure BDA0002983144840000043
Or an、
Figure BDA0002983144840000044
Still further, the step 6 includes:
and (3) bringing the amplitude and phase values of each frequency point into a two-dimensional array surface directional diagram calculation formula:
Figure BDA0002983144840000045
obtaining a beamforming directional pattern of the wavefront, wherein AmnRepresents the amplitude value of the m-th row and n-th column unit and Amn＝aman，ΦmnRepresents the phase of the m-th row and n-th column unit
Figure BDA0002983144840000046
k represents a wave number.
The invention also provides a multi-frequency spot beam forming system, which comprises:
the phase function acquisition module is used for acquiring a phase function of an antenna array surface to be shaped;
the phase acquisition module is used for acquiring the phase of a typical frequency point in the forming direction;
the directional diagram correction module is used for substituting each phase into a one-dimensional linear array directional diagram calculation formula for correction to obtain a corrected directional diagram formula;
the medium-frequency amplitude and phase value acquisition module is used for acquiring a medium-frequency amplitude and phase value meeting the requirement by utilizing an optimization algorithm according to the corrected directional diagram formula;
the amplitude-phase expansion module is used for expanding the intermediate frequency amplitude-phase value into amplitude-phase values of other frequency points;
the beam forming directional diagram acquisition module is used for substituting the amplitude phase value of each frequency point into a two-dimensional array surface directional diagram formula and solving a spatial directional diagram of an array surface, namely a beam forming directional diagram;
and the judging module is used for judging whether the beamforming directional diagram obtained by the beamforming directional diagram obtaining module meets the beamforming requirement, if not, encrypting the frequency point in the phase obtaining module, and repeatedly executing the phase obtaining module to the judging module until the obtained beamforming directional diagram meets the beamforming requirement.
Further, the phase function obtaining module is further configured to:
for an M row by N column array plane, the antenna bandwidth is fL～fHAt an intermediate frequency of f0And obtaining a phase function:
Figure BDA0002983144840000051
wherein the content of the first and second substances,
Figure BDA0002983144840000052
is a frequency point fiThe phase of the corresponding phase is determined,
Figure BDA0002983144840000053
at an intermediate frequency f0The corresponding phase.
Still further, the phase acquisition module is further configured to:
if the array surface is shaped by beams in the column direction
Figure BDA0002983144840000054
Wherein the content of the first and second substances,
Figure BDA0002983144840000055
is a frequency f1The phase of the corresponding M rows is,
Figure BDA0002983144840000056
is a frequency f2The phase of the corresponding M rows is,
Figure BDA0002983144840000057
is a frequency fqThe phase of the corresponding M rows is,
Figure BDA0002983144840000058
is a frequency f0The phase of the corresponding M rows;
if the array plane is shaped by beams in the row direction
Figure BDA0002983144840000059
Wherein the content of the first and second substances,
Figure BDA00029831448400000510
is a frequency f1The phase of the corresponding N columns,
Figure BDA00029831448400000511
is a frequency f2The phase of the corresponding N columns,
Figure BDA00029831448400000512
is a frequency fqThe phase of the corresponding N columns,
Figure BDA00029831448400000513
is a frequency f0The corresponding N columns of phases.
Still further, the pattern correction module is further configured to:
will phase
Figure BDA00029831448400000514
Substituting into a one-dimensional linear array directional diagram formula for correction,
if the wave beam of the array surface is shaped in the column direction, the corrected directional diagram calculation formula is as follows:
Figure BDA00029831448400000515
wherein, amIs the amplitude, k, of a one-dimensional array antenna elementiThe wave number d corresponding to the ith frequency point in the one-dimensional array antenna unitmyThe coordinate of the one-dimensional linear array antenna unit is shown, and theta is the pitch angle of the one-dimensional linear array antenna unit;
if the wave beam of the array surface is shaped in the row direction, the corrected directional diagram calculation formula is as follows:
Figure BDA0002983144840000061
at this time, anIs the amplitude, k, of a one-dimensional row line array antenna elementiThe wave number d corresponding to the ith frequency point in the one-dimensional linear array antenna unitnxIs the coordinate of the one-dimensional row line array antenna unit, and phi is the azimuth angle of the one-dimensional row line array antenna unit.
Further, the intermediate frequency amplitude and phase value obtaining module is further configured to:
according to the corrected directional diagram formula in the directional diagram correction module, an optimization target is designed to be F1+F2+...+FgObtaining the amplitude and phase value a meeting the beam forming requirement by using an optimization algorithmm、
Figure BDA0002983144840000062
Or an、
Figure BDA0002983144840000063
Wherein, the optimization algorithm adopts a genetic algorithm or a particle swarm algorithm, and when an optimization target converges, an amplitude-phase value a meeting the beam forming requirement is obtainedm、
Figure BDA0002983144840000064
Or an、
Figure BDA0002983144840000065
Further, the beamforming pattern obtaining module is further configured to:
and (3) bringing the amplitude and phase values of each frequency point into a two-dimensional array surface directional diagram calculation formula:
Figure BDA0002983144840000066
obtaining a beamforming directional pattern of the wavefront, wherein AmnRepresents the amplitude value of the m-th row and n-th column unit and Amn＝aman，ΦmnRepresents the phase of the m-th row and n-th column unit
Figure BDA0002983144840000067
k represents a wave number.
The invention has the advantages that: the invention introduces the phase function, obtains the phase of a typical frequency point in the shaping direction according to the phase function, firstly obtains the intermediate frequency amplitude and phase value meeting the requirement, then expands the intermediate frequency amplitude and phase value into the amplitude and phase value of other frequency points, and converts the amplitude and phase value optimization of a multi-frequency point antenna unit into the amplitude and phase optimization of a single frequency point, thereby greatly reducing the optimization cost, reducing the shaping difficulty, improving the shaping efficiency, and the wider the bandwidth of an antenna array surface, the more obvious the optimization cost is reduced.
Drawings
Fig. 1 is a flowchart of a multi-frequency spot beamforming method according to an embodiment of the present invention;
fig. 2 is a diagram of a column-direction cosecant squared forming effect in a multi-frequency spot beam forming method disclosed in the embodiment of the present invention, wherein (a) of fig. 2 is a diagram of a column-direction low-frequency cosecant squared forming effect; FIG. 2 (b) is a diagram of the effect of the intermediate frequency cosecant square forming in the column direction; FIG. 2 (c) is a column-direction high-frequency cosecant squared shaped effect diagram;
fig. 3 is a phase value corresponding to column direction cosecant squared forming in a multi-frequency spot beam forming method disclosed in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
As shown in fig. 1, a method for forming a multi-frequency spot beam includes:
step 1: acquiring a phase function of an antenna array surface to be shaped;
step 2: acquiring the phase of a typical frequency point in a forming direction;
and step 3: substituting each phase into a one-dimensional linear array directional diagram calculation formula for correction to obtain a corrected directional diagram formula;
and 4, step 4: acquiring a medium-frequency amplitude-phase value meeting the requirement by utilizing an optimization algorithm according to the corrected directional diagram formula;
and 5: expanding the amplitude and phase values of the intermediate frequency to amplitude and phase values of other frequency points;
step 6: substituting the amplitude phase value of each frequency point into a two-dimensional array surface directional diagram formula, and solving a spatial directional diagram of an array surface, namely a beam forming directional diagram;
and 7: and (3) judging whether the beam forming directional diagram obtained in the step (6) meets the forming requirement, if not, encrypting the frequency point in the step (2), and repeating the steps (2) to (7) until the obtained beam forming directional diagram meets the forming requirement.
The steps of the method provided by the invention are described in detail as follows:
step 1: for an M row by N column array plane, the antenna bandwidth is fL～fHAt an intermediate frequency of f0And obtaining a phase function:
Figure BDA0002983144840000081
wherein the content of the first and second substances,
Figure BDA0002983144840000082
is a frequency point fiThe phase of the corresponding phase is determined,
Figure BDA0002983144840000083
at an intermediate frequency f0The corresponding phase. Function giThe specific expression of (a) is related to the specific architecture of the system. For example, if the wavefront is synthesized by a microstrip power divider in the shaping direction
Figure BDA0002983144840000084
In this embodiment, the wavefront is at the shaping sideTo a phase function synthesized by a microstrip power divider
Figure BDA0002983144840000085
Step 2: if the array surface is shaped by beams in the column direction
Figure BDA0002983144840000086
Figure BDA0002983144840000087
Wherein the content of the first and second substances,
Figure BDA0002983144840000088
is a frequency f1The phase of the corresponding M rows is,
Figure BDA0002983144840000089
is a frequency f2The phase of the corresponding M rows is,
Figure BDA00029831448400000810
is a frequency fqThe phase of the corresponding M rows is,
Figure BDA00029831448400000811
is a frequency f0The phase of the corresponding M rows;
if the array plane is shaped by beams in the row direction
Figure BDA00029831448400000812
Wherein the content of the first and second substances,
Figure BDA00029831448400000813
is a frequency f1The phase of the corresponding N columns,
Figure BDA00029831448400000814
is a frequency f2The phase of the corresponding N columns,
Figure BDA00029831448400000815
is a frequency fqThe phase of the corresponding N columns,
Figure BDA00029831448400000816
is a frequency f0The corresponding N columns of phases.
In this embodiment, the phase factor in the forming direction is obtained
Figure BDA00029831448400000817
If the array surface is shaped by beams in the column direction
Figure BDA00029831448400000818
Wherein the content of the first and second substances,
Figure BDA0002983144840000091
at a low frequency of fLThe phase of the corresponding M rows is,
Figure BDA0002983144840000092
at an intermediate frequency f0The phase of the corresponding M rows is,
Figure BDA0002983144840000094
at a high frequency fHThe phase of the corresponding M rows.
Namely:
Figure BDA0002983144840000095
Figure BDA0002983144840000096
if the array plane is shaped by beams in the row direction
Figure BDA0002983144840000097
Wherein the content of the first and second substances,
Figure BDA0002983144840000098
at a low frequency of fLThe phase of the corresponding N columns,
Figure BDA0002983144840000099
at an intermediate frequency f0The phase of the corresponding N columns,
Figure BDA00029831448400000910
at a high frequency fHThe corresponding N columns of phases.
Namely:
Figure BDA00029831448400000911
Figure BDA00029831448400000912
and step 3: will phase
Figure BDA00029831448400000913
Substituting into a one-dimensional linear array directional diagram formula for correction,
if the wave beam of the array surface is shaped in the column direction, the corrected directional diagram calculation formula is as follows:
Figure BDA00029831448400000914
wherein, amIs the amplitude, k, of a one-dimensional array antenna elementiThe wave number d corresponding to the ith frequency point in the one-dimensional array antenna unitmyThe coordinate of the one-dimensional linear array antenna unit is shown, and theta is the pitch angle of the one-dimensional linear array antenna unit;
if the wave beam of the array surface is shaped in the row direction, the corrected directional diagram calculation formula is as follows:
Figure BDA00029831448400000915
at this time, anIs the amplitude, k, of a one-dimensional row line array antenna elementiThe wave number d corresponding to the ith frequency point in the one-dimensional linear array antenna unitnxIs the coordinate of the one-dimensional row line array antenna unit, and phi is the azimuth angle of the one-dimensional row line array antenna unit.
This implementationIn the example, the phase factor
Figure BDA0002983144840000101
Carrying in a one-dimensional linear array directional diagram formula for correction, and if the array surface carries out beam forming in the column direction, aiming at the frequency point fL、f0、fHIs provided with
Figure BDA0002983144840000102
Figure BDA0002983144840000103
Figure BDA0002983144840000104
If the wave beam of the array surface is shaped in the row direction, for the frequency point fL、f0、fHIs provided with
Figure BDA0002983144840000105
Figure BDA0002983144840000106
Figure BDA0002983144840000107
And 4, step 4: designing an optimization target F according to the directional diagram formula corrected in the step 31+F2+...+FgObtaining the amplitude and phase value a meeting the beam forming requirement by using an optimization algorithmm、
Figure BDA0002983144840000108
Or an、
Figure BDA0002983144840000109
Wherein, the optimization algorithm adopts a genetic algorithm or a particle swarm algorithm, and when an optimization target converges, an amplitude-phase value a meeting the beam forming requirement is obtainedm、
Figure BDA00029831448400001010
Or an、
Figure BDA00029831448400001011
In this embodiment, the optimization objective is FL+F0+FH。
And 5: and (4) expanding the amplitude and phase values of the antenna units of the one-dimensional linear array in the step (4) into the amplitude and phase values of other frequency points.
Step 6: and (3) bringing the amplitude and phase values of each frequency point into a two-dimensional array surface directional diagram calculation formula:
Figure BDA00029831448400001012
obtaining a beamforming directional pattern of the wavefront, wherein AmnRepresents the amplitude value of the m-th row and n-th column unit and Amn＝aman，ΦmnRepresents the phase of the m-th row and n-th column unit
Figure BDA0002983144840000111
k represents a wave number.
And 7: judging whether the shaped directional diagram obtained in the step 6 meets the shaped requirement, if not, encrypting the frequency points in the step 2 (if f is selected)L、
Figure BDA0002983144840000112
f0、
Figure BDA0002983144840000113
fH) And (5) repeating the step (2) to the step (7).
The invention was verified with the following parameters. The antenna array is 32 rows x 32 columns. The unit space is half wavelength, the pitching surface adopts the phase shaping microstrip power divider synthesis (namely a)m1) the array is required to shape the beam in the column directionIs a cosecant squared pattern.
As shown in connection with fig. 1, the phase function of the wavefront can be obtained
Figure BDA0002983144840000114
Further obtain the frequency point fL、f0、fHPhase of
Figure BDA0002983144840000115
The phase factor is brought into a directional diagram calculation formula of the one-dimensional linear array, and a phase value meeting the forming requirement is solved through an optimization algorithm
Figure BDA0002983144840000116
Then using the formula
Figure BDA0002983144840000117
And expanding the phase value of the central frequency point into the phase values of other frequency points, and bringing the phase values into a two-dimensional array surface directional diagram calculation formula to obtain a beam forming directional diagram of the array surface. Figure 2 shows the shaping effect, which confirms the feasibility of the method of the present invention, and the corresponding port phase value is shown in figure 3.
According to the technical scheme, the phase function is introduced, the phase of a typical frequency point in the shaping direction is obtained according to the phase function, the medium-frequency amplitude and phase value meeting the requirement is firstly obtained, then the medium-frequency amplitude and phase value is expanded to the amplitude and phase value of other frequency points, the amplitude and phase value optimization of the multi-frequency-point antenna unit is converted into the amplitude and phase optimization of a single frequency point, the optimization cost is greatly reduced, the shaping difficulty is reduced, the shaping efficiency is improved, and the more the bandwidth of an antenna array surface is, the more obvious the optimization cost is reduced.
Example 2
Corresponding to embodiment 1 of the present invention, embodiment 2 of the present invention further provides a multiple frequency spot beam forming system, where the system includes:
the phase function acquisition module is used for acquiring a phase function of an antenna array surface to be shaped;
the phase acquisition module is used for acquiring the phase of a typical frequency point in the forming direction;
the directional diagram correction module is used for substituting each phase into a one-dimensional linear array directional diagram calculation formula for correction to obtain a corrected directional diagram formula;
the medium-frequency amplitude and phase value acquisition module is used for acquiring a medium-frequency amplitude and phase value meeting the requirement by utilizing an optimization algorithm according to the corrected directional diagram formula;
the amplitude-phase expansion module is used for expanding the intermediate frequency amplitude-phase value into amplitude-phase values of other frequency points;
the beam forming directional diagram acquisition module is used for substituting the amplitude phase value of each frequency point into a two-dimensional array surface directional diagram formula and solving a spatial directional diagram of an array surface, namely a beam forming directional diagram;
and the judging module is used for judging whether the beamforming directional diagram obtained by the beamforming directional diagram obtaining module meets the beamforming requirement, if not, encrypting the frequency point in the phase obtaining module, and repeatedly executing the phase obtaining module to the judging module until the obtained beamforming directional diagram meets the beamforming requirement.
Specifically, the phase function obtaining module is further configured to:
for an M row by N column array plane, the antenna bandwidth is fL～fHAt an intermediate frequency of f0And obtaining a phase function:
Figure BDA0002983144840000121
wherein the content of the first and second substances,
Figure BDA0002983144840000122
is a frequency point fiThe phase of the corresponding phase is determined,
Figure BDA0002983144840000123
at an intermediate frequency f0The corresponding phase.
More specifically, the phase acquisition module is further configured to:
if the array surface is shaped by beams in the column direction
Figure BDA0002983144840000124
Wherein the content of the first and second substances,
Figure BDA0002983144840000125
is a frequency f1The phase of the corresponding M rows is,
Figure BDA0002983144840000126
is a frequency f2The phase of the corresponding M rows is,
Figure BDA0002983144840000127
is a frequency fqThe phase of the corresponding M rows is,
Figure BDA0002983144840000128
is a frequency f0The phase of the corresponding M rows;
if the array plane is shaped by beams in the row direction
Figure BDA0002983144840000131
Wherein the content of the first and second substances,
Figure BDA0002983144840000132
is a frequency f1The phase of the corresponding N columns,
Figure BDA0002983144840000133
is a frequency f2The phase of the corresponding N columns,
Figure BDA0002983144840000134
is a frequency fqThe phase of the corresponding N columns,
Figure BDA0002983144840000135
is a frequency f0The corresponding N columns of phases.
More specifically, the pattern correction module is further configured to:
will phase
Figure BDA0002983144840000136
Substituting into a one-dimensional linear array directional diagram formula for correction,
if the wave beam of the array surface is shaped in the column direction, the corrected directional diagram calculation formula is as follows:
Figure BDA0002983144840000137
wherein, amIs the amplitude, k, of a one-dimensional array antenna elementiThe wave number d corresponding to the ith frequency point in the one-dimensional array antenna unitmyThe coordinate of the one-dimensional linear array antenna unit is shown, and theta is the pitch angle of the one-dimensional linear array antenna unit;
if the wave beam of the array surface is shaped in the row direction, the corrected directional diagram calculation formula is as follows:
Figure BDA0002983144840000138
at this time, anIs the amplitude, k, of a one-dimensional row line array antenna elementiThe wave number d corresponding to the ith frequency point in the one-dimensional linear array antenna unitnxIs the coordinate of the one-dimensional row line array antenna unit, and phi is the azimuth angle of the one-dimensional row line array antenna unit.
More specifically, the intermediate frequency amplitude and phase value obtaining module is further configured to:
according to the corrected directional diagram formula in the directional diagram correction module, an optimization target is designed to be F1+F2+...+FgObtaining the amplitude and phase value a meeting the beam forming requirement by using an optimization algorithmm、
Figure BDA0002983144840000139
Or an、
Figure BDA00029831448400001310
Wherein, the optimization algorithm adopts a genetic algorithm or a particle swarm algorithm, and when an optimization target converges, an amplitude-phase value a meeting the beam forming requirement is obtainedm、
Figure BDA00029831448400001311
Or an、
Figure BDA00029831448400001312
More specifically, the beamforming pattern obtaining module is further configured to:
and (3) bringing the amplitude and phase values of each frequency point into a two-dimensional array surface directional diagram calculation formula:
Figure BDA0002983144840000141
obtaining a beamforming directional pattern of the wavefront, wherein AmnRepresents the amplitude value of the m-th row and n-th column unit and Amn＝aman，ΦmnRepresents the phase of the m-th row and n-th column unit
Figure BDA0002983144840000142
k represents a wave number.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. A method of multi-frequency spot beamforming, the method comprising:
step 1: acquiring a phase function of an antenna array surface to be shaped;
step 2: acquiring the phase of a typical frequency point in a forming direction;
and step 3: substituting each phase into a one-dimensional linear array directional diagram calculation formula for correction to obtain a corrected directional diagram formula;
and 4, step 4: acquiring a medium-frequency amplitude-phase value meeting the requirement by utilizing an optimization algorithm according to the corrected directional diagram formula;
and 5: expanding the amplitude and phase values of the intermediate frequency to amplitude and phase values of other frequency points;
step 6: substituting the amplitude phase value of each frequency point into a two-dimensional array surface directional diagram formula, and solving a spatial directional diagram of an array surface, namely a beam forming directional diagram;
and 7: and (3) judging whether the beam forming directional diagram obtained in the step (6) meets the forming requirement, if not, encrypting the frequency point in the step (2), and repeating the steps (2) to (7) until the obtained beam forming directional diagram meets the forming requirement.
2. The method of claim 1, wherein the step 1 comprises:
for an M row by N column array plane, the antenna bandwidth is fL～fHAt an intermediate frequency of f0And obtaining a phase function:
Figure FDA0002983144830000011
wherein the content of the first and second substances,
Figure FDA0002983144830000012
is a frequency point fiThe phase of the corresponding phase is determined,
Figure FDA0002983144830000013
at an intermediate frequency f0The corresponding phase.
3. The method of claim 2, wherein the step 2 comprises:
if the array surface is shaped by beams in the column direction
Figure FDA0002983144830000014
Wherein the content of the first and second substances,
Figure FDA0002983144830000015
is a frequency f1The phase of the corresponding M rows is,
Figure FDA0002983144830000016
is a frequency f2Corresponding phase of M rowsThe number of bits is,
Figure FDA0002983144830000021
is a frequency fqThe phase of the corresponding M rows is,
Figure FDA0002983144830000022
is a frequency f0The phase of the corresponding M rows;
if the array plane is shaped by beams in the row direction
Figure FDA0002983144830000023
Wherein the content of the first and second substances,
Figure FDA0002983144830000024
is a frequency f1The phase of the corresponding N columns,
Figure FDA0002983144830000025
is a frequency f2The phase of the corresponding N columns,
Figure FDA0002983144830000026
is a frequency fqThe phase of the corresponding N columns,
Figure FDA0002983144830000027
is a frequency f0The corresponding N columns of phases.
4. The method of claim 3, wherein the step 3 comprises:
will phase
Figure FDA0002983144830000028
Substituting into a one-dimensional linear array directional diagram formula for correction,
if the wave beam of the array surface is shaped in the column direction, the corrected directional diagram calculation formula is as follows:
Figure FDA0002983144830000029
wherein, amIs the amplitude, k, of a one-dimensional array antenna elementiThe wave number d corresponding to the ith frequency point in the one-dimensional array antenna unitmyThe coordinate of the one-dimensional linear array antenna unit is shown, and theta is the pitch angle of the one-dimensional linear array antenna unit;
if the wave beam of the array surface is shaped in the row direction, the corrected directional diagram calculation formula is as follows:
Figure FDA00029831448300000210
at this time, anIs the amplitude, k, of a one-dimensional row line array antenna elementiThe wave number d corresponding to the ith frequency point in the one-dimensional linear array antenna unitnxIs the coordinate of the one-dimensional row line array antenna unit, and phi is the azimuth angle of the one-dimensional row line array antenna unit.
5. The method of claim 4, wherein the step 4 comprises:
designing an optimization target F according to the directional diagram formula corrected in the step 31+F2+...+FgObtaining the amplitude and phase value a meeting the beam forming requirement by using an optimization algorithmm、
Figure FDA00029831448300000211
Or an、
Figure FDA00029831448300000212
Wherein, the optimization algorithm adopts a genetic algorithm or a particle swarm algorithm, and when an optimization target converges, an amplitude-phase value a meeting the beam forming requirement is obtainedm、
Figure FDA0002983144830000031
Or an、
Figure FDA0002983144830000032
6. The method of claim 5, wherein the step 6 comprises:
and (3) bringing the amplitude and phase values of each frequency point into a two-dimensional array surface directional diagram calculation formula:
Figure FDA0002983144830000033
obtaining a beamforming directional pattern of the wavefront, wherein AmnRepresents the amplitude value of the m-th row and n-th column unit and Amn＝aman，ΦmnRepresents the phase of the m-th row and n-th column unit
Figure FDA0002983144830000034
k represents a wave number.
7. A multiple frequency spot beamforming system, the system comprising:
the phase function acquisition module is used for acquiring a phase function of an antenna array surface to be shaped;
the phase acquisition module is used for acquiring the phase of a typical frequency point in the forming direction;
the directional diagram correction module is used for substituting each phase into a one-dimensional linear array directional diagram calculation formula for correction to obtain a corrected directional diagram formula;
the medium-frequency amplitude and phase value acquisition module is used for acquiring a medium-frequency amplitude and phase value meeting the requirement by utilizing an optimization algorithm according to the corrected directional diagram formula;
the amplitude-phase expansion module is used for expanding the intermediate frequency amplitude-phase value into amplitude-phase values of other frequency points;
the beam forming directional diagram acquisition module is used for substituting the amplitude phase value of each frequency point into a two-dimensional array surface directional diagram formula and solving a spatial directional diagram of an array surface, namely a beam forming directional diagram;
and the judging module is used for judging whether the beamforming directional diagram obtained by the beamforming directional diagram obtaining module meets the beamforming requirement, if not, encrypting the frequency point in the phase obtaining module, and repeatedly executing the phase obtaining module to the judging module until the obtained beamforming directional diagram meets the beamforming requirement.
8. The system of claim 7, wherein the phase function obtaining module is further configured to:
for an M row by N column array plane, the antenna bandwidth is fL～fHAt an intermediate frequency of f0And obtaining a phase function:
Figure FDA0002983144830000041
wherein the content of the first and second substances,
Figure FDA0002983144830000042
is a frequency point fiThe phase of the corresponding phase is determined,
Figure FDA0002983144830000043
at an intermediate frequency f0The corresponding phase.
9. The system of claim 8, wherein the phase acquisition module is further configured to:
if the array surface is shaped by beams in the column direction
Figure FDA0002983144830000044
Wherein the content of the first and second substances,
Figure FDA0002983144830000045
is a frequency f1The phase of the corresponding M rows is,
Figure FDA0002983144830000046
is a frequency f2The phase of the corresponding M rows is,
Figure FDA0002983144830000047
is a frequency fqThe phase of the corresponding M rows is,
Figure FDA0002983144830000048
is a frequency f0The phase of the corresponding M rows;
if the array plane is shaped by beams in the row direction
Figure FDA0002983144830000049
Wherein the content of the first and second substances,
Figure FDA00029831448300000410
is a frequency f1The phase of the corresponding N columns,
Figure FDA00029831448300000411
is a frequency f2The phase of the corresponding N columns,
Figure FDA00029831448300000412
is a frequency fqThe phase of the corresponding N columns,
Figure FDA00029831448300000413
is a frequency f0The corresponding N columns of phases.
10. The multi-frequency spot beamforming system of claim 9, wherein the pattern modification module is further configured to:
will phase
Figure FDA00029831448300000414
Substituting into a one-dimensional linear array directional diagram formula for correction,
if the wave beam of the array surface is shaped in the column direction, the corrected directional diagram calculation formula is as follows:
Figure FDA00029831448300000415
wherein, amBeing one-dimensional array antenna elementsAmplitude, kiThe wave number d corresponding to the ith frequency point in the one-dimensional array antenna unitmyThe coordinate of the one-dimensional linear array antenna unit is shown, and theta is the pitch angle of the one-dimensional linear array antenna unit;
if the wave beam of the array surface is shaped in the row direction, the corrected directional diagram calculation formula is as follows:
Figure FDA0002983144830000051
at this time, anIs the amplitude, k, of a one-dimensional row line array antenna elementiThe wave number d corresponding to the ith frequency point in the one-dimensional linear array antenna unitnxIs the coordinate of the one-dimensional row line array antenna unit, and phi is the azimuth angle of the one-dimensional row line array antenna unit.
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