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CN109446477B - An Arbitrary Sampling Reception Method for Multimodal Orbital Angular Momentum Vortex Waves - Google Patents

An Arbitrary Sampling Reception Method for Multimodal Orbital Angular Momentum Vortex Waves Download PDF

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CN109446477B
CN109446477B CN201811246293.6A CN201811246293A CN109446477B CN 109446477 B CN109446477 B CN 109446477B CN 201811246293 A CN201811246293 A CN 201811246293A CN 109446477 B CN109446477 B CN 109446477B
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李龙
冯强
阳棂均
郑雨珊
薛浩
邵庆瑶
刘永杰
席瑞
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Abstract

本发明提出了一种多模态轨道角动量涡旋波的任意采样接收方法，用于在空间环境存在障碍物限制的情况下，在保证远距离传输接收孔径较小和实现连续阶模态值的涡旋波接收的同时，提高多模态轨道角动量涡旋波模态信息的准确性。实现步骤为：确定每个天线单元的方位角；构建多模态轨道角动量涡旋波的场表达式

Figure DDA0001840588800000011
根据采样定理构建M个模态涡旋波的能量幅度向量c与N个天线单元采样接收的多模态涡旋波信号向量b之间的系数矩阵A；采样接收装置获取多模态涡旋波信号向量b；获取多模态轨道角动量涡旋波中第i个模态涡旋波能量幅度Fi的值。本发明实现了对连续阶模态值的涡旋波的灵活接收，提高了轨道角动量的利用率。

Figure 201811246293

The present invention proposes an arbitrary sampling and receiving method for multi-modal orbital angular momentum vortex waves, which is used to ensure a small receiving aperture for long-distance transmission and realize continuous-order modal values under the circumstance that there are obstacles in the space environment. While receiving the vortex wave, the accuracy of the multimodal orbital angular momentum vortex wave modal information is improved. The realization steps are: determine the azimuth angle of each antenna element; construct the field expression of the multimodal orbital angular momentum vortex wave

Figure DDA0001840588800000011
According to the sampling theorem, the coefficient matrix A between the energy amplitude vector c of M modal vortex waves and the multi-modal vortex wave signal vector b sampled and received by N antenna elements is constructed; the sampling receiving device obtains the multi-modal vortex wave Signal vector b; obtains the value of the energy amplitude F i of the ith mode vortex wave in the multimodal orbital angular momentum vortex wave. The invention realizes flexible reception of the vortex wave of continuous order mode value, and improves the utilization rate of orbital angular momentum.

Figure 201811246293

Description

Random sampling receiving method for multi-modal orbital angular momentum vortex waves
Technical Field
The invention belongs to the technical field of wireless communication, relates to a receiving method of orbital angular momentum vortex waves, in particular to a random sampling receiving method of multi-mode orbital angular momentum vortex waves aiming at receiving environment limitation, and can be used for radio frequency and microwave band wireless communication systems.
Background
With the wide application of wireless communication technology, the channel congestion problem becomes a research difficulty of the technology at the present stage, and the modal characteristic of orbital angular momentum vortex waves (OAM) brings a new multiplexing mode for information transmission, which provides possibility for expanding the channel capacity. Until 2007, the B.Thide teaching team in Sweden successfully generated orbital angular momentum vortex waves by means of array antennas, the field expression of the vortex waves carrying
Figure GDA0002963007610000011
The term (wherein l represents a modal number) makes the transmission characteristic of the vortex wave be an equiphase plane with spiral distribution, which is the first realization of the vortex wave in the field of radio frequency wireless communication, so that the application of the vortex wave in wireless communication gradually becomes a research hotspot at present. Research shows that the modal value of the orbital angular momentum vortex beam determines the specific distribution of the phase. And the orbital angular momentum vortex waves of different modes have orthogonality, a plurality of independent channels which are easy to demodulate can be transmitted, the mode number of vortex beams is not limited theoretically, and the mode multiplexing characteristic of the multi-mode vortex waves brings infinite possibility for the development of the wireless communication technology.
In order to realize the communication application of the vortex beam, the receiving of the orbital angular momentum and the mode demodulation method become one of the important points of the electromagnetic vortex technology. Due to the transmission characteristic of the vortex wave, the center of the wave beam is provided with a dark area with zero amplitude, and the radius of the dark area increases as the transmission distance becomes longer. Therefore, when the transmission distance is long, a large receiving aperture is also needed to effectively implement modal demultiplexing, and the existing non-sampling receiving methods are as follows: holographic Plate (HP), Spiral Phase Plate (SPP), refractive element transformation methods are very difficult to implement. In wireless communication, the antenna sampling method is more flexible in receiving compared with the traditional method. In 2011, an 2.414GHz vortex electromagnetic wave communication experiment is successfully realized by a full-aperture uniform sampling receiving method, and vortex beams are transmitted and received by placing two yagi antennas with a distance of 4.5 meters. The full aperture uniform sampling receiving method can receive vortex waves with continuous order modal values, but under the condition of long-distance transmission, the full aperture size is too large to be suitable for practical application. For reception under long-distance transmission conditions, partial aperture uniform sampling reception was proposed in 2016. The method requires that the receiving antenna units are uniformly distributed in a 1/P (P is an integer) sector area, the receiving aperture of the antenna is reduced during vortex wave long-distance transmission, and the partial aperture sampling receiving method requires that two received vortex wave modal values l meet a certain interval, namely, vortex beams with continuous low-order modal values cannot communicate, so that the utilization rate of orbital angular momentum is reduced. The uniform distribution of the receiving antennas of the full-aperture and partial-aperture sampling receiving method may be affected by obstacles in the space, which may affect the amplitude of the received vortex wave energy and cause inaccurate multimode orbital angular momentum vortex wave mode information.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a random sampling and receiving method of multi-mode orbital angular momentum vortex waves, which is used for improving the accuracy of modal information of the multi-mode orbital angular momentum vortex waves while ensuring that a long-distance transmission receiving aperture is small and vortex waves of continuous order modal values are received under the condition that a space environment is limited by obstacles.
The technical idea of the invention is as follows: firstly, a field expression of multi-mode vortex waves is deduced according to the relation between a direction angle domain and a modal number domain of vortex electromagnetic waves, then a coefficient matrix between the energy amplitude of each modal vortex wave and multi-mode vortex wave signals sampled and received by an antenna unit is constructed by combining a sampling theorem and the distribution of sampling receiving antenna units, and finally the modal energy amplitude distribution of the multi-mode vortex waves is obtained through the calculation of the coefficient matrix and the multi-mode vortex wave receiving signals.
In order to achieve the purpose, the invention realizes arbitrary sampling and receiving of the multi-modal orbital angular momentum vortex wave beam through a sampling and receiving device, the sampling and receiving device comprises an antenna array formed by N antenna units distributed on a ring with the radius of R, N is more than or equal to M, M is the modal number of the multi-modal orbital angular momentum vortex wave to be received, M is more than or equal to 2, the antenna units are uniformly or non-uniformly distributed, the transmission center of the multi-modal orbital angular momentum vortex wave vertically passes through the center of the plane where the antenna array is located, and the implementation steps are as follows:
(1) determining the azimuth angle of each antenna element:
(1a) determining a mode set L of multi-mode orbital angular momentum vortex waves to be received: l ═ LiE.z | i ═ 1,2, …, M }, and the number N of antenna elements is determined from L, where LiIs the modal value of the ith single-mode vortex wave, and Z is an integer collection;
(1b) determining azimuth angles of N antenna units according to environmental limits of the antenna array
Figure GDA0002963007610000021
Wherein
Figure GDA0002963007610000022
Is the azimuth angle of the kth antenna element;
(2) constructing a field expression of multi-modal orbital angular momentum vortex waves
Figure GDA0002963007610000023
Setting the energy amplitude of the ith modal vortex wave in the multi-modal orbital angular momentum vortex waves to be FiAnd according to FiAnd a mode set L, constructing a field expression of the multi-mode orbital angular momentum vortex wave
Figure GDA0002963007610000031
Wherein
Figure GDA0002963007610000032
J is an imaginary number unit, and is the azimuth angle of the plane where the sampling receiving antenna is located;
(3) according to the sampling theorem, a coefficient matrix A between an energy amplitude vector c of M modal vortex waves and a multi-modal vortex wave signal vector b sampled and received by N antenna units is constructed:
(3a) setting the vector formed by the energy amplitudes of M modal vortex waves as c, and sampling and receiving a multi-modal vortex wave signal by a kth antenna unit as
Figure GDA0002963007610000033
A vector formed by the N multi-mode vortex wave signals is b;
(3b) according to the sampling theorem and by using the azimuth angle of the kth antenna unit determined in the step (1)
Figure GDA0002963007610000034
And (3) constructing a field expression of the multi-modal vortex waves in the step (2)
Figure GDA0002963007610000035
Obtaining multi-mode vortex wave signals sampled and received by the kth antenna unit
Figure GDA0002963007610000036
Then the vector expression b of the multi-mode vortex wave signals sampled and received by the N antenna units is:
Figure GDA0002963007610000037
convert it to matrix form: if b is Ac, the coefficient matrix a between the energy amplitude vector c of the M modal vortex waves and the multi-modal vortex wave signal vector b sampled and received by the N antenna units is:
Figure GDA0002963007610000038
(4) the sampling receiving device acquires a multi-mode vortex wave signal vector b:
multimode vortex wave signals generated by k antenna unit in sampling receiving device to transmitting device
Figure GDA0002963007610000039
Sampling and receiving are carried out, and N multimode vortex wave signals sampled and received by N antenna units form a vector b:
Figure GDA0002963007610000041
wherein [. ]' represents transposing the vector;
(5) obtaining energy amplitude F of ith modal vortex wave in multi-modal orbital angular momentum vortex waveiThe value of (c):
(5a) deforming a multi-mode vortex wave signal vector expression b ═ Ac sampled and received by the N antenna units to obtain an M-mode vortex wave energy amplitude vector expression c ═ A-1b；
(5b) Calculating M modal vortex wave energy amplitude vectors c ═ F according to the coefficient matrix A constructed in the step (3) and the multi-modal vortex wave signal vector b obtained in the step (4)1 F2…FM]′。
Compared with the prior art, the invention has the following advantages:
according to the method, through combination of the relation between the direction angular domain and the modal number domain of the multi-modal vortex electromagnetic wave and the sampling theorem, a coefficient matrix between the energy amplitude of each modal vortex wave to be received and the multi-modal vortex wave signal to be sampled and received is obtained, and through changing the distribution azimuth angle of the receiving antenna unit in the coefficient matrix and the mode set of the vortex wave to be received, the accuracy of receiving the multi-modal orbital angular momentum vortex wave mode information under the condition that the space environment is limited by obstacles is achieved while the remote transmission receiving aperture is small and the vortex wave receiving of continuous order mode values is guaranteed. The invention reduces the receiving caliber of the far field of the vortex electromagnetic wave, realizes flexible receiving of the continuous-order multi-mode vortex wave and effectively improves the utilization rate of orbital angular momentum.
Drawings
FIG. 1 is a schematic diagram of a sample receiving device used in the present invention;
FIG. 2 is a flow chart of an implementation of the present invention;
FIG. 3 is a schematic diagram of a four environment-limited downsampling reception scheme in an embodiment of the present invention;
FIG. 4 is a diagram of an HFSS simulation of a transmitting and receiving apparatus according to an embodiment of the invention;
fig. 5 is a diagram of simulation results of modal energy amplitudes of four modal sets under four environmental constraints in the embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Referring to fig. 1, a receiving antenna array is composed of 5 antenna units distributed on a circular ring with a radius R of 50mm, the mode sets of four multi-mode orbital angular momentum vortex waves to be received are set to L-2, L-1, 1, and L-1, 1,2, respectively, and the antenna units are distributed as
Figure GDA0002963007610000042
The transmission center of the multi-mode orbital angular momentum vortex wave vertically passes through the center of the antenna array, wherein a sector area (1) represents the complete environmental limit, a sector area (2) represents the partial environmental limit, sampling receiving antennas cannot be placed on the sector area (1) and the sector area (2), and sampling receiving antennas can be placed on other areas.
Referring to fig. 2, an arbitrary sampling and receiving method for a multi-modal orbital angular momentum vortex wave includes the following steps:
step 1) determining the azimuth angle of each antenna unit:
step 1a) has determined that a set of four modes L ═ { L ] of multi-modal orbital angular momentum vortex waves to be receivediE.z | i ═ 1,2, …, M }: l { -2, L { -1,1} and L { -1,1, -2}, wherein L { -2, L { -1,1, -2}, and a pharmaceutically acceptable salt thereofiIs the modal value of the ith single-mode vortex wave and is based onL determines the number of antenna elements N to be 5, and M has values of 1,1,2, and 3, respectively.
Step 1b) according to the restriction condition that the antenna unit cannot be placed because of the existence of the obstacle in the space where the antenna array is located, an arbitrary sampling receiving scheme under four environment restriction conditions is proposed as shown in fig. 3. Wherein fig. 3(a) is a schematic diagram of a scheme, and the sampling receiving antennas are uniformly distributed on the whole aperture surface, which is the same as the existing full aperture sampling receiving scheme. Fig. 3(b) is a schematic diagram of a scheme two, the environment is limited to a part of the environment in the sector area (2), and the sampling receiving antennas are arbitrarily distributed in an area outside the sector area (2) for sampling reception. Fig. 3(c) is a schematic diagram of a scheme three, the environment limitation is complete environment limitation of the sector area (1), and the sampling receiving antennas are uniformly distributed in the area outside the sector area (1) for sampling reception, which is the same as the existing partial aperture sampling reception scheme. Fig. 3(d) is a schematic diagram of a scheme four, the environment limitation is complete environment limitation of the sector area (1) and partial environment limitation of the sector area (2), and the sampling receiving antennas are randomly distributed in the area outside the limited area for sampling reception. The four environmental constraints are denoted as I, II, III and IV, respectively, where the sample receiving antenna unit azimuth distribution
Figure GDA0002963007610000051
As shown in table 1;
TABLE 1 (Unit: degree)
Figure GDA0002963007610000052
Step 2) constructing a field expression of multi-modal orbital angular momentum vortex waves
Figure GDA0002963007610000061
Setting the energy amplitude of the ith modal vortex wave in the multi-modal orbital angular momentum vortex waves to be FiAnd according to FiAnd a mode set L, constructing a field expression of the multi-mode orbital angular momentum vortex wave
Figure GDA0002963007610000062
Wherein
Figure GDA0002963007610000063
J is an imaginary number unit, and is the azimuth angle of the plane where the sampling receiving antenna is located;
step 3) constructing a coefficient matrix A between energy amplitude vectors c of M modal vortex waves and multi-modal vortex wave signal vectors b sampled and received by 5 antenna units according to a sampling theorem:
step 3a) setting a vector formed by the energy amplitudes of M modal vortex waves as c, and sampling and receiving multi-modal vortex wave signals by the kth antenna unit as
Figure GDA0002963007610000064
The vector formed by the 5 multi-mode vortex wave signals is b;
step 3b) according to the sampling theorem, and utilizing the azimuth angle of the kth antenna unit determined in step 1
Figure GDA0002963007610000065
And 2, constructing a field expression of the multi-mode vortex wave
Figure GDA0002963007610000066
Obtaining multi-mode vortex wave signals sampled and received by the kth antenna unit
Figure GDA0002963007610000067
Then the vector expression b of the multi-mode vortex wave signals sampled and received by the 5 antenna units is:
Figure GDA0002963007610000068
convert it to matrix form: if b is Ac, the coefficient matrix a between the energy amplitude vector c of the M modal vortex waves and the multi-modal vortex wave signal vector b sampled and received by the 5 antenna units is:
Figure GDA0002963007610000069
step 4), acquiring a multi-modal vortex wave signal vector b by a sampling receiving device:
multimode vortex wave signals generated by k antenna unit in sampling receiving device to transmitting device
Figure GDA0002963007610000071
Sampling and receiving are carried out, and M multi-mode vortex wave signals sampled and received by 5 antenna units form a vector b:
Figure GDA0002963007610000072
wherein [. ]' represents transposing the vector;
step 5) obtaining the energy amplitude F of the ith modal vortex wave in the multi-modal orbital angular momentum vortex waveiThe value of (c):
step 5a) deforming a multi-mode vortex wave signal vector expression b ═ Ac sampled and received by the 5 antenna units to obtain M modal vortex wave energy amplitude vector expressions c ═ A-1b；
Step 5b) calculating M modal vortex wave energy amplitude vectors c ═ F according to the coefficient matrix A constructed in the step 3 and the multi-modal vortex wave signal vector b obtained in the step 41 F2 … FM]′。
The technical effects of the invention are explained in combination with simulation experiments as follows:
1. simulation conditions and contents:
the experiment of the present invention is performed on HFSS15 software, and an HFSS simulation diagram of the transmitting and receiving device in this embodiment refers to fig. 4, where fig. 4(a) is a transmitting device, an octave array with a radius R of 50mm is used to generate a multi-modal orbital angular momentum vortex wave, fig. 4(b) is a receiving device, a transmission distance D from the transmitting device to the receiving device is 200mm, and a receiving antenna is consistent with an operating frequency band of the multi-modal vortex wave and polarization-matched. And simulation realizes random sampling and receiving of the four-mode set multi-mode orbital angular momentum vortex waves under the four environmental limitation conditions, the simulation result is a multi-mode vortex wave signal vector sampled and received by the receiving device, and a modal energy amplitude vector is obtained through calculation. Fig. 5 is a diagram of simulation results of modal energy amplitudes of four modal sets under four environmental constraints.
2. And (3) simulation result analysis:
fig. 5(a), 5(b), 5(c), and 5(d) are graphs of modal energy amplitude simulation results of the mode sets of the four environmental constraints, i.e., L-2, L-1, 1, and L-1, 1-2, respectively, where the four environmental constraints are represented as i, II, iii, and iv, respectively. The receiving result of any sampling in the figure is obvious that the modal value is liThe amplitude of the vortex wave energy is obviously higher than that of the non-transmitted vortex wave mode and is consistent with the mode set L of the transmitting end, which shows that the sampling and receiving of the orbital angular momentum vortex waves with the mode sets L-2, L-1, 1 and L-1, 1, -2 can be realized under four environment limiting conditions. The method can complete random sampling and receiving of the multi-mode orbital angular momentum vortex waves under the condition of environmental limitation.
The above description is only one specific embodiment of the present invention and should not be construed as limiting the invention in any way, and it will be apparent to those skilled in the art that various modifications and variations in form and detail may be made without departing from the spirit and principle of the invention, but these modifications and variations are within the scope of the invention as defined in the appended claims.

Claims (2)

1.一种多模态轨道角动量涡旋波的任意采样接收方法，其特征在于，是通过采样接收装置实现的，所述采样接收装置包括分布在半径为R的圆环上的N个天线单元组成的天线阵列，N≥M，M为待接收的多模态轨道角动量涡旋波的模态个数，M≥2，天线单元为均匀分布或不均匀分布，多模态轨道角动量涡旋波的传输中心垂直通过天线阵列所在平面的中心，实现步骤为：1. an arbitrary sampling receiving method of a multimodal orbital angular momentum vortex wave, is characterized in that, is realized by sampling receiving device, and described sampling receiving device comprises N antennas that are distributed on the ring that radius is R Antenna array composed of elements, N≥M, M is the number of modes of the multimodal orbital angular momentum vortex wave to be received, M≥2, the antenna elements are uniformly distributed or non-uniformly distributed, and the multimodal orbital angular momentum The transmission center of the vortex wave passes vertically through the center of the plane where the antenna array is located. The implementation steps are: (1)确定每个天线单元的方位角：(1) Determine the azimuth of each antenna element: (1a)确定待接收的多模态轨道角动量涡旋波的模态集合L：L＝{li∈Z|i＝1,2,…,M}，并根据L确定天线单元的个数N，其中li为第i个单模态涡旋波的模态值，Z为整数合集；(1a) Determine the modal set L of the multimodal orbital angular momentum vortex wave to be received: L={l i ∈ Z|i=1,2,...,M}, and determine the number of antenna elements according to L N, where li is the modal value of the i -th single-mode vortex wave, and Z is a set of integers; (1b)根据天线阵列所在的环境限制，确定N个天线单元的方位角
Figure FDA0001840588770000011
其中
Figure FDA0001840588770000012
为第k个天线单元的方位角；(1b) Determine the azimuth angles of N antenna elements according to the environmental constraints where the antenna array is located
Figure FDA0001840588770000011
in
Figure FDA0001840588770000012
is the azimuth angle of the kth antenna element; (2)构建多模态轨道角动量涡旋波的场表达式
Figure FDA0001840588770000013
(2) Constructing the field expression of the multimodal orbital angular momentum vortex wave
Figure FDA0001840588770000013
 设定多模态轨道角动量涡旋波中第i个模态涡旋波的能量幅度为Fi，并根据Fi和模态集合L，构建多模态轨道角动量涡旋波的场表达式
Figure FDA0001840588770000014
其中
Figure FDA0001840588770000015
为采样接收天线所在平面的方位角，j为虚数单位；Set the energy amplitude of the ith mode vortex wave in the multimodal orbital vortex wave as F i , and construct the field expression of the multimodal orbital angular momentum vortex wave according to F i and the mode set L Mode
Figure FDA0001840588770000014
in
Figure FDA0001840588770000015
is the azimuth angle of the plane where the sampling receiving antenna is located, and j is the imaginary unit; (3)根据采样定理构建M个模态涡旋波的能量幅度向量c与N个天线单元采样接收的多模态涡旋波信号向量b之间的系数矩阵A：(3) According to the sampling theorem, construct the coefficient matrix A between the energy amplitude vector c of the M modal vortex waves and the multi-modal vortex wave signal vector b sampled and received by the N antenna units: (3a)设定M个模态涡旋波能量幅度组成的向量为c，第k个天线单元采样接收多模态涡旋波信号为
Figure FDA0001840588770000016
N个多模态涡旋波信号组成的向量为b；(3a) Set the vector composed of M modal vortex wave energy amplitudes as c, and the kth antenna unit samples the received multi-modal vortex wave signal as
Figure FDA0001840588770000016
The vector composed of N multimodal vortex wave signals is b; (3b)根据采样定理，并利用步骤(1)确定的第k个天线单元的方位角
Figure FDA0001840588770000017
和步骤(2)构建的多模态涡旋波的场表达式
Figure FDA0001840588770000018
获取第k个天线单元采样接收的多模态涡旋波信号
Figure FDA0001840588770000019
则N个天线单元采样接收的多模态涡旋波信号的向量表达式b为：(3b) According to the sampling theorem, and use the azimuth angle of the kth antenna element determined in step (1)
Figure FDA0001840588770000017
and the field expression of the multimodal vortex wave constructed in step (2)
Figure FDA0001840588770000018
Obtain the multimodal vortex wave signal sampled and received by the kth antenna element
Figure FDA0001840588770000019
Then the vector expression b of the multimodal vortex wave signal sampled and received by N antenna units is:
Figure FDA0001840588770000021
Figure FDA0001840588770000021
 将其转化为矩阵形式：b＝Ac，则M个模态涡旋波的能量幅度向量c与N个天线单元采样接收的多模态涡旋波信号向量b之间的系数矩阵A为：Convert it into a matrix form: b=Ac, then the coefficient matrix A between the energy amplitude vector c of the M modal vortex waves and the multi-modal vortex wave signal vector b sampled and received by the N antenna units is:
Figure FDA0001840588770000022
Figure FDA0001840588770000022
 (4)采样接收装置获取多模态涡旋波信号向量b：(4) The sampling receiving device obtains the multimodal vortex wave signal vector b: 采样接收装置中的第k个天线单元对发射装置产生的多模态涡旋波信号
Figure FDA0001840588770000023
进行采样接收，并将N个天线单元采样接收的N个多模态涡旋波信号组成向量b：Sampling the multi-mode vortex wave signal generated by the kth antenna element in the receiving device to the transmitting device
Figure FDA0001840588770000023
Perform sampling reception, and form a vector b of N multi-mode vortex wave signals sampled and received by N antenna units:
Figure FDA0001840588770000024
Figure FDA0001840588770000024
 其中，[·]′代表对向量进行转置；Among them, [ ]' represents the transpose of the vector; (5)获取多模态轨道角动量涡旋波中第i个模态涡旋波能量幅度Fi的值：(5) Obtain the value of the energy amplitude F i of the ith modal vortex wave in the multimodal orbital angular momentum vortex wave: (5a)对N个天线单元采样接收的多模态涡旋波信号向量表达式b＝Ac进行变形，得到M个模态涡旋波能量幅度向量表达式c＝A-1b；(5a) Deform the multi-modal vortex wave signal vector expression b=Ac sampled and received by the N antenna units to obtain the M modal vortex wave energy amplitude vector expression c=A −1 b; (5b)根据步骤(3)构建的系数矩阵A和步骤(4)获取的多模态涡旋波信号向量b，计算M个模态涡旋波能量幅度向量c＝[F1 F2 … FM]′。(5b) According to the coefficient matrix A constructed in step (3) and the multimodal vortex wave signal vector b obtained in step (4), calculate M modal vortex wave energy amplitude vectors c=[F 1 F 2 … F M ]'. 2.根据权利要求1所述的多模态轨道角动量涡旋波的任意采样接收方法，其特征在于，步骤(1b)中所述的天线阵列所在的环境限制，是指空间中存在障碍物而无法放置天线单元的限制条件。2. the arbitrary sampling receiving method of the multi-modal orbital angular momentum vortex wave according to claim 1, is characterized in that, the environment restriction where the antenna array described in the step (1b) is located means that there is an obstacle in the space and the restriction that the antenna unit cannot be placed.
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