CN106888059B - Off-axis detection method for vortex beam orbital angular momentum mode - Google Patents

Off-axis detection method for vortex beam orbital angular momentum mode Download PDF

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CN106888059B
CN106888059B CN201710047500.4A CN201710047500A CN106888059B CN 106888059 B CN106888059 B CN 106888059B CN 201710047500 A CN201710047500 A CN 201710047500A CN 106888059 B CN106888059 B CN 106888059B
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张朝阳
武华阳
袁裕清
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Zhejiang University ZJU
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
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    • H04B17/10—Monitoring; Testing of transmitters
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Abstract

The invention discloses an off-axis detection method of a vortex beam orbit angular momentum mode. The invention provides an OAM mode off-axis detection method based on a uniform annular array (UCA) aiming at the detection problem of a vortex beam Orbital Angular Momentum (OAM) mode when a detection array has a transverse offset relative to a vortex beam axis. Compared with the traditional two-antenna phase gradient method, the method provided by the invention does not need to completely align the detection array and the beam axis, and has lower error mode rate, thereby having important significance for the practicability of a wireless OAM communication system.

Description

Off-axis detection method for vortex beam orbital angular momentum mode
Technical Field
The invention relates to the field of wireless orbital angular momentum communication, in particular to an off-axis detection method of a vortex beam orbital angular momentum mode based on a uniform circular antenna array.
Background
The rapid development of the wireless communication technology provides great convenience for the efficient and rapid information exchange of the modern society. In order to enable a plurality of different broadcasting stations to transmit signals simultaneously under the condition that radio signals are not overlapped, the total available frequency band of a radio frequency spectrum is divided into a plurality of frequency sub-bands which are not overlapped, so that the communication capacity is greatly improved. However, the rapid increase in mobile device usage, the constant emergence of new services, makes it inevitable to cause spectrum congestion problems with limited spectrum resources even if techniques for increasing communication capacity, such as multiport, channel reuse, etc., are employed. Therefore, research into new wireless communication technologies with high spectral efficiency is becoming increasingly important.
Communication services in radio communication have hitherto been based on various forms of phase, frequency and amplitude modulation of electromagnetic radiation, i.e. the linear momentum of an electromagnetic field. However, it is now known that classical electromagnetic fields can carry not only linear momentum but also angular momentum, and it is obvious that information transmission in a communication system using only linear momentum does not take full advantage of the physical properties of electromagnetic fields. Studies have shown that the capacity of a communication system can be further improved by using electromagnetic Orbital Angular Momentum (OAM), which has not been applied in current wireless communication systems. OAM, which is a basic physical quantity of an electromagnetic field, has been widely used in an optical frequency band including microscopic manipulation of atoms, molecules, optical imaging, etc. for the last two decades, which is well known. In the radio frequency band, until recently, studies have been made on how to perform wireless communication by OAM so as to improve the information transmission capacity of a channel. The OAM has been more widely and mature applied in the optical frequency band than in the radio frequency band because in the optical frequency band, the related processing of the optical beam OAM, including the generation, transmission and reception of the optical beam carrying OAM and the corresponding information extraction, can be accomplished by using various cheap optical instruments. However, in the radio frequency domain, the method is not so simple, and many processing methods for optical beams in the optical domain are not applicable in the low frequency domain, so that the discussion of the related processing method for OAM in the radio frequency domain has important significance for the practical application of the wireless OAM communication technology.
In the radio frequency band, the beam carrying the OAM is also called vortex beam. Research shows that orthogonality exists between different OAM eigenmodes carried by vortex beams, and independent information flow can be transmitted in each OAM eigenmode, so that two visual methods exist in consideration of applying the characteristic of the vortex beams to the field of wireless communication: one method is to use the orthogonality among different OAM eigenmodes and use the vortex wave beams of different OAM modes as the carrier wave of multiplex signal multiplexing; another method is to encode the message signal into different OAM modes directly, and after the receiving end detects the OAM mode carried by the beam, the sent message signal can be recovered according to the preset encoding rule. The former needs the receiving end to have OAM demultiplexing capability, so that independent signal streams transmitted on each OAM mode can be recovered; the latter is similar to the techniques of amplitude modulation, phase modulation and the like in the traditional wireless communication, and because the message signals are coded and modulated into different OAM modes, a receiving end is required to be capable of detecting the OAM mode carried by the vortex beam in real time, which puts requirements on the detection method of the OAM mode.
For the detection problem of the vortex beam OAM mode, a widely known OAM mode detection method is called as a phase gradient method, and the method only needs two antennas to perform field phase detection and perform phase gradient operation at a receiving end to obtain an OAM mode value. Subsequently, another scholars proposed a multi-antenna phase gradient method based on this, aiming to improve the accuracy of OAM mode detection and reduce the Mode Error Rate (MER). However, no matter two antennas or multiple antennas, the conventional OAM mode detection method based on phase gradient needs to completely align the center of the detection antenna array with the beam axis, and if the detection array has a lateral offset with respect to the beam axis, the accuracy of OAM mode detection will be sharply reduced or even impossible to detect, which severely restricts the application scenario of wireless OAM communication. Therefore, it is important to study how to accurately detect the OAM mode of the vortex beam when the detection array is laterally offset from the beam axis for the practical application of radio frequency OAM.
Disclosure of Invention
The invention provides an off-axis detection method of a vortex beam orbital angular momentum mode, and aims to achieve the purpose that when a detection array has a certain transverse offset relative to a vortex beam axis, a correct orbital angular momentum mode detection value can still be obtained.
The purpose of the invention is realized by the following technical scheme:
the radius of N antenna elements of the vortex wave beam OAM mode detection array is R0The circular array (UCA) is formed by arranging Uniform Circular Arrays (UCAs) at equal intervals, and the UCAs in the case can also be regarded as regular N-polygon arrays with antennas at the vertexes, as shown in fig. 1. Angular separation between two adjacent antennas in a UCA
Figure GDA0002441668770000031
The vortex beam axis is perpendicular to the plane x ' o ' y ' of the detection array and intersects at a point o ', and the offset vector of the detection array relative to the position o ' of the beam axis is
Figure GDA0002441668770000032
Where deltax 'and deltay' are offsets along the x 'axis and along the y' axis respectively,
Figure GDA0002441668770000033
and
Figure GDA0002441668770000034
respectively representing unit vectors along the x 'axis and along the y' axis, the offset vector, respectively
Figure GDA0002441668770000035
The corresponding offset is of the magnitude
Figure GDA0002441668770000036
When the position o' of the beam axis is located in a positive N-polygon formed by array elements in the UCA array, the off-axis detection of the vortex beam OAM mode can be realized through the following steps:
(1) the phases of vortex beam fields detected by N antenna elements in UCA are respectively phin(N ═ 1, 2.,. N) indicates that every two adjacent array elements of N array elements form a group, the group is totally divided into N groups, each group of array elements respectively detects the OAM value of the wave beam according to the traditional two-antenna phase gradient method, and the detected values of N OAM modes in total are obtained, namely, the detected values are represented
Figure GDA0002441668770000041
(2) Detecting values l of N OAM modes obtained in step (1)nAveraging (N ═ 1, 2., N), to obtain a final OAM mode detection value l of the vortex beam, i.e. the final OAM mode detection value l of the vortex beam is obtained
Figure GDA0002441668770000042
The OAM mode of the vortex beam is detectedIn the process, to avoid the angular distance of array elements
Figure GDA0002441668770000043
Ambiguity problem of OAM mode detection value caused by oversize, the number N of array elements of UCA and maximum absolute value | l! y of OAM mode capable of being detectedmaxSatisfy the relation
Figure GDA0002441668770000044
The invention has the beneficial effects that: compared with the traditional two-antenna phase gradient method, the off-axis detection method for the vortex beam orbital angular momentum mode provided by the invention has the advantages that when a detection array has a certain transverse offset relative to a beam axis, the OAM mode value of the beam can be correctly detected as long as the beam axis is still positioned in a regular polygon formed by array elements in the UCA, meanwhile, under the same signal-to-noise ratio detection condition, the method can obtain a lower error mode rate, and the detection performance is not influenced by the offset. When the OAM mode of the vortex wave beam is detected, the detection array does not need to be completely aligned with the wave beam axis, so that the application scene of a future wireless OAM communication system is greatly widened, and the method has important significance for the practicability of the wireless OAM communication system.
Drawings
Fig. 1 is a uniform perimeter antenna array structure (N ═ 8) for OAM mode off-axis detection;
fig. 2 shows N-8 sets of detection values and their average values obtained when the vortex beam OAM mode is l-0 and l-1, respectively;
FIG. 3 is a graph showing the relationship between the error mode rate of OAM mode detection by the method and the conventional two-antenna phase gradient method and the variation of the error mode rate with the detection signal-to-noise ratio under different offsets;
fig. 4 illustrates OAM mode detection values obtained by the method at different offsets, where l is 1.
Detailed Description
The invention is described in further detail below with reference to the figures and specific examples.
The invention provides an off-axis detection method of a vortex beam orbit angular momentum mode, which comprises the following specific embodiments:
the UCA for OAM mode off-axis detection is formed by N-8 antenna elements along the radius of R0λ, where λ is the wavelength of the vortex beam, and λ is 125mm, then 8 array elements in the UCA form a regular octagon, as shown in fig. 1. Angular separation between two adjacent antennas in a UCA
Figure GDA0002441668770000051
The vortex beam axis is perpendicular to the plane x ' o ' y ' of the detection array and intersects at a point o ', and the offset vector of the detection array relative to the position o ' of the beam axis is
Figure GDA0002441668770000052
The offset vector
Figure GDA0002441668770000053
The corresponding offset is of the magnitude
Figure GDA0002441668770000054
When the position o' of the beam axis is located in the area covered by the regular octagon, the off-axis detection of the vortex beam OAM mode can be realized through the following steps:
(1) the phases of vortex beam fields detected by 8 antenna elements in UCA are respectively phin(n ═ 1, 2., 8.) shows that every two adjacent array elements of 8 array elements form a group, the group is totally divided into 8 groups, each group of array elements respectively detects the OAM value of the wave beam according to the traditional two-antenna phase gradient method, and the detected values of 8 OAM modes in total are obtained, namely, the detected values are
Figure GDA0002441668770000055
(2) For the 8 OAM mode detection values l obtained in the step (1)n(n ═ 1, 2.., 8) is averaged, i.e.The final OAM mode detection value l of the vortex beam can be obtained, namely
Figure GDA0002441668770000061
It should also be noted that the angular distance between the array elements is avoided
Figure GDA0002441668770000062
The maximum absolute value | l of the OAM mode that can be detected is the shortest distance in the UCA composed of 8 array elements due to the ambiguity problem of the OAM mode detection value caused by overlarge sizemaxIs limited by
Figure GDA0002441668770000063
That is, for an 8-element UCA, the detected OAM mode values are l ═ 0, ± 1, ± 2, ± 3, respectively.
Fig. 2 shows N-8 sets of detection values and their average values obtained when the vortex beam OAM mode is l-0 and l-1, respectively. The detection signal-to-noise ratio is 20 db, taking the detection result of OAM mode l ═ 1 as an example, as can be seen from the figure, due to the existence of offset vectors, for the detection result obtained by the traditional two-antenna phase gradient method, the obtained detection values all have deviation from the true values, however, the detection values obtained by each group are averaged by using the circular symmetry of UCA, the positive deviation and the negative deviation of the detection values of each group are cancelled out, the averaged value is exactly equal to the true value of the OAM mode, and for the OAM mode l ═ 0, there are similar detection results. Therefore, when the detection array has a certain transverse offset relative to the beam axis, the method (the method for short) provided by the invention can still obtain a correct OAM mode detection value.
Fig. 3 is a graph showing the relationship between the error mode rate of OAM mode detection and the signal-to-noise ratio of detection under different offsets. The offset is respectively determined by adopting Monte Carlo (Monte Carlo) simulation method
Figure GDA0002441668770000064
The method and the traditional method carry out the error mode rate of OAM mode (l is 1), namely the mode error probability, and the simulation is carried out, and the simulation result shows that: first, the detection array is perfectly aligned with the beam axis, i.e.
Figure GDA0002441668770000065
In the conventional method, the error mode rate is high when the signal-to-noise ratio is low, and the signal-to-noise ratio of the receiving end must be increased in order to obtain a reliable mode detection result. Different from the above, under the same signal-to-noise ratio, the detection error mode rate of the method is far lower than that of the traditional method, and along with the increase of the signal-to-noise ratio, the error mode rate is rapidly reduced, and the error mode rate reaches 10 when the signal-to-noise ratio is 15 dB-6In order of magnitude, for a larger signal-to-noise ratio, the obtained error pattern rate is already small enough, so that only the detection result when the signal-to-noise ratio is lower than 15 db is shown in fig. 3; secondly, for the situation when the detection array is laterally shifted from the beam axis, it can be seen that the mode error rate increases with the increase of the shift amount in the conventional method, and when Δ r is 0.3 λ, the mode error rate is already large to the extent that the wireless communication system cannot accept it. On the contrary, the method is not sensitive to the beam axis shift, and although the shift amount deltar is increased, the error mode rate is basically unchanged and can still be maintained at a lower level. Therefore, when the detection array has lateral deviation relative to the beam axis, the detection result of the vortex beam OAM mode obtained by the traditional method is no longer reliable, and the method can still obtain a reliable detection result when the signal-to-noise ratio is relatively low.
Fig. 4 illustrates OAM mode detection values obtained by the method at different offsets, where l is 1. Wherein, the detection signal-to-noise ratio is 20 dB, and it can be seen that as long as the beam axis o' is positioned in the regular octagon formed by the array elements in the UCA, the detection values of l are all close to 1, thereby obtaining the correct detection result, and when the offset delta R is more than R0The values of l all go to zero without exception. Thus, for the case when the detection array is laterally offset relative to the beam axis, the vortex beam axis remains within the regular octagonal coverage area of the detection arrayIn addition, the method can still correctly detect the OAM mode carried by the wave beam, and the detection array is not required to be completely aligned with the wave beam axis.
The foregoing detailed description is intended to illustrate and not limit the invention, which is intended to be within the spirit and scope of the appended claims, and any changes and modifications that fall within the true spirit and scope of the invention are intended to be covered by the following claims.

Claims (1)

1. An off-axis detection method of a vortex beam orbital angular momentum mode is characterized by comprising the following steps:
n antenna elements with radius R0The uniform annular array UCA formed by the circular equal-interval arrangement of the UCA is used as a detection array of the vortex beam OAM mode, the UCA can be regarded as a regular N-edge array with the antenna positioned at the vertex, and the angular distance between two adjacent antennas in the UCA
Figure FDA0002459576430000011
The vortex beam axis is perpendicular to the plane x ' o ' y ' of the detection array and intersects with the point o ', when o ' is positioned in the positive N-polygon formed by the array elements in the UCA array, the vortex beam field phases detected by the N antenna array elements in the UCA are respectively phinIndicating that N is 1, 2.. multidot.n, each two adjacent array elements of N array elements are in one group, the two adjacent array elements are totally divided into N groups, each group of array elements respectively detect the OAM mode value of the wave beam according to the traditional two-antenna phase gradient method to obtain the detection values of N OAM modes in total, namely, the detection values of N OAM modes are obtained, namely, the two adjacent array elements are in one group
Figure FDA0002459576430000012
For the obtained detection values l of N OAM modesnTaking an average value N, 1,2, N, to obtain a final detection value l of the vortex beam OAM mode, that is, obtaining a final detection value l of the vortex beam OAM mode
Figure FDA0002459576430000013
The maximum absolute value of the detection value in the OAM mode|l|maxThe number N of array elements of the UCA needs to satisfy the relational expression
Figure FDA0002459576430000014
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