A Two-User Cooperative Vortex Wave Communication Method

Abstract

The present invention discloses a two-user cooperative vortex wave communication method. First, by solving the intensity distribution with respect to the radial radius, a feasible radial radius and a waist radius are obtained. Subsequently, two cooperative users are selected using concentric circles at the base station. Finally, the waist radius is adjusted according to the communication distance between the two cooperative users to ensure that the two cooperative users have the maximum intensity. The simulation results verify that the two-user cooperative vortex wave communication method of the present invention has a higher communication capacity than the traditional scheme.

Description

Technical Field

[0001] The present invention belongs to the technical field of electrical communication. Background Art

[0002] Orbital Angular Momentum (OAM) has attracted the interest of many scholars in the field of high-capacity wireless communication. As a new orthogonal resource, the helical wavefront generated by the vortex wave mode can be used for multiplexing communication. The number of modes of the vortex wave is theoretically infinite, so vortex wave communication has the potential to significantly improve the spectral efficiency.

[0003] In 2011, the F. Tamburini team first successfully transmitted two vortex wave signals at the same time-frequency through a reflector antenna. To receive vortex wave signals, a general receiving scheme uses a reflector antenna and a centralized antenna array. The spatial multiplexing vortex wave communication with a 2×2 antenna aperture structure can achieve an information rate of 16 Gbits / s at 28 GHz using two modes. In 2018, NTT Corporation achieved a 10 m OAM multiplexing communication experiment based on a Uniform Circular Array (UCA). However, due to the limitation of the hollow divergence characteristic of vortex wave communication, it is difficult to achieve long-distance OAM multiplexing communication. Since the wavelength of radio frequency is much larger than that of optical frequency, the hollow divergence is a key and challenging problem for vortex wave communication.

[0004] The energy ring of the OAM beam will increase with the increase of the communication distance, resulting in an overly large size of the receiving-end UCA at long distances. The size of the user equipment is limited and it has only a single antenna, making it difficult to receive vortex wave signals propagating over long distances. Therefore, there is an urgent need for an easily implementable receiving scheme for vortex wave multiplexing communication. Summary of the Invention

[0005] Object of the Invention: To solve the problems existing in the above-mentioned prior art, the present invention provides a two-user cooperative vortex wave communication method.

[0006] Technical Solution: The present invention provides a two-user cooperative vortex wave communication method, which specifically includes the following steps:

[0007] Step 1: Set the cooperative user set as an empty set, and set the cooperative user conditions based on the principle of the maximum OAM beam intensity distribution.

[0008] Step 2: Set the initial value of the search radius r s to be ε;

[0009] Step 3: With the base station as the center, with r s -ε as the inner radius and r sA ring with an outer radius of +ε is set as the search ring area;

[0010] Step 4: Determine whether the number of users within the search ring area is greater than or equal to 2. If so, these users are regarded as potential users, and go to Step 5; otherwise, go to Step 7;

[0011] Step 5: Select two users with the shortest distance among the potential users, k 1 , k 2 ; Determine the distance between these two users Whether it meets the conditions for collaborative users. If so, add these two users to the set of collaborative users, and regard these two users as a group of collaborative users, and go to Step 6; otherwise, go to Step 7;

[0012] Step 6: Adjust the Laguerre-Gaussian beam emitted by the base station according to the distance So that the Laguerre-Gaussian beam covers these two collaborative users, and the search for collaborative users is completed;

[0013] Step 7: Update r s : r s = r s + 2ε, and determine whether the updated r s is greater than R max - ε. If not, go to Step 4; if so, go to Step 8;

[0014] Step 8: Update ε: ε = 2ε, and go to Step 2.

[0015] Furthermore, the specific conditions for collaborative users are: the distance between two users and 2r max (z) ∈ [2r fea (z c ), D max ; where z c represents the distance from the base station antenna to the midpoint of the line connecting the two users, D max is a preset maximum value, and r max (z c ) represents the radius of the Laguerre-Gaussian beam emitted by the base station when the distance between the base station antenna and the receiving surface of the Laguerre-Gaussian beam is z = z c , and the OAM beam intensity distribution is the largest; r max (z c ) and r fea (z c ) are expressed as follows:

[0016]

[0017] Among them, l is the azimuth index, w 0is the waist radius of the Laguerre-Gaussian beam, / λ is the Rayleigh range, and λ represents the wavelength of the Laguerre-Gaussian beam.

[0018] Further, step 7 is specifically as follows:

[0019] Calculate the waist radius of the Laguerre-Gaussian beam according to the distance between the two users:

[0020]

[0021] At this time, z = z c , where H represents the height of the base station;

[0022] The base station adjusts the Laguerre-Gaussian beam according to the waist radius w 0 so that the Laguerre-Gaussian beam covers the cooperative users.

[0023] Beneficial effects: According to the optimal intensity distribution regarding the radial radius, the present invention obtains the radial radius and the optional waist radius, and adjusts the waist radius according to the distance between the two users, enabling long-distance transmission between two cooperative users of the base station concentric circles and breaking through the communication distance constraint caused by hollow divergence. The present invention can achieve long-distance large-capacity transmission. The more the number of cooperative users, the greater the communication capacity. Moreover, the present invention can receive the vortex wave signal at the maximum intensity to maintain a stable communication capacity. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is the system model diagram of the present invention;

[0025] Figure 2 is the diagram of the selected cooperative users of the present invention;

[0026] Figure 3 is the curve graph of the capacity change of each communication scheme under different base station radii. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0027] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments and descriptions thereof of the present invention are used to explain the present invention and do not constitute an improper limitation to the present invention.

[0028] There is a base station and K users in the system considered by the present invention. The user set is represented by . The base station is configured with a uniform circular array, and there are M antenna elements in the array, represented by the set . All users are equipped with one antenna and are evenly distributed on the ground. The radius of the UCA (uniform circular array) is R, and the central angle between two adjacent antenna elements is This paper assumes that the channel is a line-of-sight-dominated free-space path loss model. In addition, the base station knows the user's location information.

[0029] In the three-dimensional cylindrical coordinate system, the base station is located at the origin (0, 0, 0), and the direction of the z-axis is the direction of the Laguerre-Gaussian beam emission, that is, the direction from the base station antenna to the center of the Laguerre-Gaussian beam receiving surface. The complex amplitude of the LG beam (Laguerre-Gaussian beam) propagates along the z-axis, as shown below:

[0030]

[0031] Where r represents the radius of the ring of the Laguerre-Gaussian beam incident on the receiving surface, θ is the azimuth angle, k is the wave number, represents the beam radius of the Laguerre-Gaussian beam at z, w 0 is the waist radius of the LG beam when the z-axis value is 0, / λ is the Rayleigh range, L p |l| (·) is the associated Laguerre polynomial, (2p+|l|+1)tan -1 (z / z R ) is the Gouy phase, l is the azimuthal index, p is the radial index, i is an imaginary number, and λ represents the wavelength of the LG beam. It can be found that the LG beam is related to two parameters: the azimuthal index l and the radial index p. The azimuthal index l is the topological charge, also known as the OAM mode or vortex wave mode. The radial index p is the number of radial nodes in the LG beam intensity cross section.

[0032] The OAM beam is the LG beam when p = 0, and the intensity distribution is as follows:

[0033]

[0034] The intensity distribution of the OAM beam is ring-shaped. From formula (2), we can see that U l (r,z) is a strictly convex function of the radial radius r of the Laguerre-Gaussian beam, so the maximum value U can be obtained l (r,z) corresponds to:

[0035]

[0036] At this time, the maximum strength values ​​are as follows:

[0037]

[0038] According to formula (3), the optimal radial radius r is derived max (z) corresponds to the beam waist radius w 0 As follows:

[0039]

[0040] The feasible radial radius should satisfy the waist radius w 0 for its existence.

[0041]

[0042] where is defined as.

[0043] Considering the size limitation of the base station, a small w is selected 0 as the optional waist radius:

[0044]

[0045] To achieve M OAM mode multiplexing communications, M antennas are uniformly distributed according to the radian (where a ∈ (0, 1] is a constant), and for different OAM modes l n (n = 1, 2, 3... M), it satisfies l n -l 0 = na, where l 0 is an integer constant. The device for a user to receive the vortex wave signal has size limitations, and generally only one antenna is used by one user. It can be found that M collaborative users are required to achieve M OAM mode multiplexing communications. Obviously, it is meaningless to achieve single-mode multiplexing communications. In addition, since users are randomly distributed, the more modes there are, the more difficult it is to achieve multiplexing communications. Therefore, choosing two collaborative users to achieve vortex wave communication is the most feasible case and can achieve two-mode multiplexing communications.

[0046] In the three-dimensional cylindrical coordinate system, the center of the UCA of the base station and the k-th user are located at the coordinates (0, 0, H) and (r k , θ k , 0) respectively, where H is the height of the base station, r k is the distance from the origin to the k-th user, and θ k is the angle rotated counterclockwise from the positive z-axis to the k-th user along the x-axis. Each user is uniformly distributed on the ground (i.e., the horizontal plane z = 0). The coordinate position of the m-th antenna element is (R, H), R is the radius of the transmitting antenna of the base station, is the angle rotated counterclockwise from the positive z-axis to the m-th antenna element in the transmitting antenna of the base station along the x-axis. Assume that the two collaborative users are the 1 k-th and the 2 k-th user. As Figure 1 shown, the distance between the two collaborative users is represented by . Based on formula (3), the distances from the two collaborative users to the base station and is the same and is located at both ends of the diameter of a circle with a radius of r max (z c ), that is z c represents the distance from the center of the base station transmitting antenna to the midpoint of the line connecting two cooperative users. In this embodiment, the maximum communication distance between the two cooperative users is set to D max .

[0047] The base station adjusts the waist radius w 0 to ensure that the two cooperative users are covered by the Laguerre-Gaussian beam. According to equation (6), it should satisfy and 2r max (z c ) ≥ 2r fea (z c ) to ensure the existence of the waist radius.

[0048] Let the set of cooperative users and the set of potential users be and and The cardinalities of and are max and max respectively, that is, they represent the number of users in the two sets. Set the interval of the search radius to (ε, R s -ε), where R s is the maximum value of the search radius (i.e., the maximum coverage radius of the base station). Through the iteratively updated r search ring, add the users falling within the r max search ring to the set of potential users If the number of potential users is not less than 2, select two users k c , k fea with the minimum distance among the potential users and satisfying c and 2r max (z 1 ) ∈ [2r 2 (z s ), D

[0049] To realize the vortex wave communication between two users, the two-user cooperative vortex wave communication method of this embodiment is implemented as follows:[[]]

[0050] Step 1, determine the user positions and initialize the parameters.[[]]

[0051] 1a. Obtain the user coordinates (r k , θ k, 0), set the collaborative users and the set of potential users

[0052] Step 2, select two collaborative users, specifically including the following steps:

[0053] 2a. Set the search radius r s = ε, set ε as a positive real number approaching 0;

[0054] 2b. If the set of collaborative users is an empty set, that is go to step 2c, otherwise go to step 2i;

[0055] 2c. When r s ≤ R max - ε, go to step 2d, otherwise go to step 2h;

[0056] 2d. Set the ring with the base station as the center, r s - ε as the inner radius and r s + ε as the outer radius as the search ring area; find the users falling within the search ring corresponding to r s as potential users, and add the potential user coordinates to the set of potential users (clear the set of potential users before each search within the search ring) ;

[0057] 2e. Judge whether the cardinality of the set of potential users is greater than or equal to 2, that is go to step 2f, otherwise go to step 2g;

[0058] 2f. Find the two users k with the shortest distance and satisfying and 2r max (z c ) ∈ [2r fea (z c ), D max in the set of potential users as collaborative users, and add the user coordinates of the collaborative users k 1 , k 2 to the set of collaborative users 1 , k 2 ; According to the two users in the set of collaborative users, r and the base station height H can be obtained, and substituting into formula (8) r s and the base station height H, the distance z from the base station transmitting antenna to the midpoint of the line connecting the two collaborative users can be obtained c . Then according to formula (7)

[0059] Let z = z c, obtain the waist radius w 0 , the base station adjusts the Laguerre-Gaussian beam according to the waist radius w 0 , so that the Laguerre-Gaussian beam covers the cooperative users, and go to step 2b;

[0060] 2g. Set r s = r s + 2ε, and go to step 2c;

[0061] 2h. Set ε = 2ε, and go to step 2a;

[0062] 2i. Select the users in the cooperative user set as the cooperative users.

[0063] Next, the capacity analysis of this embodiment is carried out.

[0064] In the two-user cooperative vortex wave communication scheme, the base station generates and transmits vortex wave signals. The two selected cooperative users are evenly located at the π-angle arc and can sample the vortex wave signals. The phase shift component is used to achieve two-mode multiplexing communication. Therefore, the received signal in the two-user cooperative vortex wave communication scheme is as follows:

[0065] y = Q H Gx + n, (9)

[0066] where is the received vector, represents the channel matrix, represents the demultiplexing matrix, is the transmitted information, is the noise. Q H Q is a 2×2 identity matrix. Based on formula (2), the (l,k)-th element in the channel matrix G is expressed as follows:

[0067]

[0068] The channel matrix in the two-user cooperative vortex wave communication can be further expressed as follows:

[0069] G = QΛ (11)

[0070] where is a diagonal matrix. The l-th diagonal element β l corresponds to the transmission gain of the l-th OAM channel. Based on equation (11), after rearrangement:

[0071]

[0072] The capacity formula of the two-user cooperative vortex wave communication is as follows:

[0073]

[0074] Among them, P l represents the power allocated to the l-th OAM channel according to the water-filling algorithm, and σ 2 represents the noise power, is the singular value corresponding to the l-th OAM channel.

[0075] The beneficial effects brought by the method of the present invention can be further illustrated by the following simulations.

[0076] I. Simulation conditions

[0077] Let the operating frequency be 1 GHz, the base station transmission power P = 30 dBm, and the noise power σ 2 = -90 dBm.

[0078] II. Simulation content and simulation results

[0079] Compare the two-user cooperative vortex wave communication scheme with the traditional fixed UCA scheme.

[0080] Simulation 1 shows the cooperative users selected by the two-user cooperative vortex wave communication scheme.

[0081] Simulation results: Figure 2 Show the users selected under the two-user cooperative vortex wave communication scheme. 50 users are distributed in a 200 m × 200 m area, marked by "ο". The dashed ring is the determined radius r s search ring. The 6 users located within the dashed ring are the potential user set, and "☆" are the selected cooperative users.

[0082] Simulation 2 compares the capacity performance of the communication schemes under different numbers of users and base station radii.

[0083] Simulation results: Figure 3 The middle shows the capacity change curves of each communication scheme under different base station radii. For the traditional fixed UCA scheme, there are two antennas to receive the vortex wave signal. It can be found that for 200 and 400 numbers of users, the two-user cooperative vortex wave communication scheme can achieve higher capacity than the traditional fixed UCA scheme. In addition, as the base station radius increases, the communication capacity of the fixed UCA scheme decreases rapidly, while the two-user cooperative vortex wave communication scheme can continue to maintain. Because compared with the traditional scheme, the two-user cooperative vortex wave communication scheme can receive the vortex wave signal at the maximum intensity, so it supports high-capacity transmission over long distances.

[0084] In addition, it should be noted that among the various specific technical features described in the above specific embodiments, they can be combined in any appropriate manner without contradiction. To avoid unnecessary repetition, the present invention does not further explain various possible combination methods.

Claims

1. A two-user cooperative vortex wave communication method, characterized in that: Specifically, it includes the following steps: Step 1: Set the cooperative user set as an empty set, and set the cooperative user conditions based on the principle of the maximum orbital angular momentum (OAM) beam intensity distribution; Step 2: Set the initial value of the search radius r s to be ε; Step 3: Set the circular ring with the base station as the center, with r s -ε as the inner radius and r s +ε as the outer radius as the search ring area; Step 4: Determine whether the number of users in the search ring area is greater than or equal to 2. If so, take these users as potential users and go to Step 5; otherwise, go to Step 7; Step 5: Select two users k with the shortest distance among potential users 1 , k 2 ; Determine the distance between these two users Whether it meets the conditions of collaborative users. If so, add these two users to the collaborative user set, and use these two users as a group of collaborative users, then go to Step 6; otherwise, go to Step 7; Step 6: According to the distance Adjust the Laguerre-Gaussian beam transmitted by the base station so that the Laguerre-Gaussian beam covers the two cooperative users, and the search for cooperative users is completed; Step 7: Update r s : r s = r s + 2ε, and determine whether the updated r s is greater than R max - ε. If not, go to Step 4; if so, go to Step 8; Step 8: Update ε: ε = 2ε, and go to Step 2; The specific conditions for the collaborating users are as follows: the distance between two users and 2r max (z) ∈ [2r fea (z c ), D max ; where z c represents the distance from the base station antenna to the midpoint of the line connecting the two users, D max is a preset maximum value, and r max (z c ) represents the radius of the Laguerre-Gaussian beam emitted by the base station when the distance z = z c between the base station antenna and the receiving surface of the Laguerre-Gaussian beam, and the OAM beam intensity distribution is maximum; r max (z c ) and r fea (z c ) are expressed as follows: where \(l\) is the azimuthal index, w 0 is the waist radius of the Laguerre-Gaussian beam, is the Rayleigh range, and \(\lambda\) represents the wavelength of the Laguerre-Gaussian beam.

2. A two-user cooperative vortex wave communication method according to claim 1, characterized in that: The specific content of Step 7 is: Calculate the waist radius of the Laguerre-Gaussian beam according to the distance between the two users: At this time, z = z c , where H represents the height of the base station; The base station adjusts the Laguerre-Gaussian beam according to the waist radius w 0 , so that the Laguerre-Gaussian beam covers the collaborative users.

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