Method for obtaining electromagnetic effective degrees of freedom of MIMO system in non-free space

Abstract

The present invention provides a method for obtaining the electromagnetic effective degrees of freedom of a MIMO system in a non-free space, the method comprising S1: establishing a MIMO communication system model in a non-free space including a reflective ground; S2: performing electromagnetic simulation by respectively changing the number of array units, the communication distance, the array height, and the dielectric constant of the reflective ground; S3: obtaining a corresponding channel matrix according to the simulated receiving electric field, and establishing a full polarization electromagnetic channel model; S4: calculating the electromagnetic effective degrees of freedom using the obtained simulation results, and drawing an electromagnetic effective degrees of freedom curve. The generated channel correlation matrix is ​​subjected to singular value decomposition, and the electromagnetic effective degrees of freedom calculated can more comprehensively characterize the performance of the communication channel. The present invention can assist in analyzing the performance of a communication system in a non-free space through the electromagnetic effective degrees of freedom, and thus can serve as an effective basis for designing and laying out indoor and outdoor antenna arrays that assist wireless communications.

Description

Technical Field

[0001] The invention relates to a method for acquiring electromagnetic effective degrees of freedom of a MIMO (multiple input multiple output) system in a non-free space, which is a channel performance simulation analysis technology and belongs to the technical field of electromagnetic information. Background Art

[0002] Modern wireless communication technology is in a stage of rapid development towards higher frequencies. However, the lack of consideration of the underlying physical constraints in the traditional communication theory that supports its development has become one of the important reasons that hinder the development of practical engineering technology. Therefore, the concept of electromagnetic information theory came into being. In the past, in traditional single-channel communications, Shannon information theory, as its underlying theoretical basis, used a probability model to analyze the channel capacity and communication bit error rate of the communication system, and provided the performance upper limit of the single-channel communication system. As the basic theory guiding the development of a new generation of communications, electromagnetic information theory takes into account the actual physical constraints in electromagnetic theory on the basis of traditional Shannon information theory. It can provide a performance upper limit of the communication system that is more in line with actual high-frequency communication technology and engineering, and also lays a solid theoretical foundation for the optimization and improvement of existing communication technologies and the development of emerging communication technologies in the future.

[0003] Effective degrees of freedom is a very important concept in information theory, which is equivalent to the number of independent single-input single-output (SISO) systems equivalent to the communication system. In the past, when analyzing the effective degrees of freedom of communication systems, the channel matrix used to obtain the communication degrees of freedom belonged to the scalar channel matrix, which only considered the scalar output current signal and the received electric field signal. However, as modern communication signals are rapidly developing towards higher frequencies and even terahertz, near-field communication has gradually occupied an important position in recent years. The previous scalar channel matrix is ​​not only not applicable in the near-field region, but also cannot capture the full-wave physical information of the communication electromagnetic waves. Therefore, it is necessary to establish a fully polarized channel matrix containing all the information of the transmitting and receiving polarization directions, so that the system performance of high-frequency near-field communication can be analyzed more comprehensively and accurately.

[0004] According to the paper "Electromagnetic Effective Degree of Freedom of a MIMO System in Free Space", a fully polarized channel model of a communication system can be established based on the vector Green's function, but it only considers the communication system in free space and ignores the impact of the actual environment on the system. However, high-frequency signals are susceptible to the influence of complex electromagnetic environments, resulting in multipath effects and other phenomena that lead to rapid signal fading. Therefore, placing the communication system in a non-free space to study and analyze the system performance can better guide the system design in actual engineering. Based on the fully polarized channel matrix, the present invention proposes a method for analyzing the electromagnetic effective degrees of freedom of a MIMO system in non-free space. Summary of the invention

[0005] Technical problem: The purpose of the present invention is to provide a method for obtaining the electromagnetic effective degrees of freedom of a MIMO system in a non-free space. For a MIMO communication system in a non-free space, the electromagnetic effective degrees of freedom of the system are obtained through the corresponding fully polarized channel matrix, and the performance of the system and the impact of the environment on it are analyzed, thereby guiding the design and layout of the system.

[0006] Technical solution: In order to achieve the above-mentioned purpose, the technical solution steps adopted by the method for obtaining the electromagnetic effective degrees of freedom of a MIMO system in a non-free space of the present invention are as follows:

[0007] S1: Establish a MIMO communication system model in non-free space including a reflective ground;

[0008] S2: Perform electromagnetic simulation by changing the number of array units, communication distance, array height, and dielectric constant of the reflecting ground respectively;

[0009] S3: Obtain the corresponding channel matrix according to the simulated receiving electric field and establish a full polarization electromagnetic channel model;

[0010] S4: Calculate the electromagnetic effective degrees of freedom using the obtained simulation results and draw an electromagnetic effective degrees of freedom curve.

[0011] in,

[0012] The step S1 specifically includes:

[0013] S11: The units of the transmitting array are modeled as M×M unit electric dipoles, and are evenly distributed in a square area of ​​fixed size;

[0014] S12: The units of the receiving array are modeled as M×M ideal receiving points, which are evenly distributed in a square area of ​​a fixed size. The straight-line distance between the receiving array and the transmitting array is D.

[0015] S13: Set a dielectric constant of ε below the transceiver array at a height H with an area larger than the projected area of ​​the MIMO system. r reflective ground.

[0016] The step S2 specifically includes:

[0017] S21: After the MIMO system communication model is set in the electromagnetic simulation software, the software is run to perform simulation, and the generated file containing all modeling information is found, and a program is written to use the file to call the simulation software to perform simulation;

[0018] S22: by programming to change the coordinate values ​​of the unit electric dipole and the coordinate values ​​of the receiving point in the simulation to perform simulation, a full polarization channel matrix corresponding to different numbers of MIMO unit arrays can be obtained;

[0019] S23: By programming to change the value of the distance parameter D between the transceiver arrays for simulation, a full polarization channel matrix corresponding to different communication distances can be obtained;

[0020] S24: by programming to change the value of the height parameter H of the transceiver array relative to the ground for simulation, a full polarization channel matrix corresponding to different array heights can be obtained;

[0021] S25: Using programming to change the dielectric constant ε of the reflecting ground r By simulating the value of , the full polarization channel matrix corresponding to different reflective ground materials can be obtained.

[0022] The step S3 specifically includes:

[0023] S31: Establishing the electromagnetic channel matrix as a fully polarized channel matrix

[0024]

[0025] It is necessary to obtain 9 single-polarization channel matrices through simulation;

[0026] S32: For the single-polarization channel matrix, only one unit electric dipole is set at the i-th point on the source plane for each simulation, and then the electric fields in the x, y, and z directions at M×M points on the receiving plane are obtained through simulation, and the i-th column vectors of the corresponding single-polarization channel matrices of three different receiving array polarization directions are obtained respectively. The position of the unit electric dipole is changed, and after M×M simulations, three complete single-polarization channel matrices are obtained;

[0027] S33: changing the direction of the unit electric dipole and performing the simulation in step S32 again. Finally, after 3 (M×M) simulations in total, 9 single-polarization channel matrices can be obtained, and the corresponding full-polarization channel matrix can be obtained.

[0028] The step S4 specifically includes:

[0029] S41: For the full polarization channel matrix H obtained by simulation, the corresponding channel correlation matrix is ​​obtained Then perform singular value decomposition on R to obtain the singular value σ i . Then the expression of electromagnetic effective degree of freedom is:

[0030]

[0031] S42: After solving the electromagnetic effective degree of freedom for the full polarization channel matrix corresponding to different M by programming, M is used as the abscissa and the electromagnetic effective degree of freedom is used as the ordinate, and the corresponding electromagnetic effective degree of freedom curve is drawn;

[0032] S43: For different parameters D, H and ε r , while fixing two of them, changing the value of the remaining parameter, so as to draw multiple electromagnetic effective degree of freedom curves. These curves are plotted on the same coordinate axis and are used to analyze the influence of the parameter on the electromagnetic effective degree of freedom.

[0033] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0034] First, compared with the previous single-polarization channel matrix, the present invention uses a full-polarization channel matrix including x, y, and z directions to analyze channel performance. The electromagnetic effective degree of freedom studied is about twice the electromagnetic effective degree of freedom corresponding to the single-polarization channel matrix in the near field area, and gradually approaches 2 times in the far field area. In addition, the present invention proposes a method for automatically calling electromagnetic simulation software for simulation and obtaining the corresponding electromagnetic effective degree of freedom, thereby solving the problem of too many simulation times required for the electromagnetic effective degree of freedom curve.

[0035] Second, the electromagnetic wave propagation environment considered by the present invention is a non-free space including a reflective ground, and the influence of the propagation environment on electromagnetic waves is taken into account. Compared with the free space research background of previous communication models, the communication model research in non-free space takes into account practical issues such as array height and environmental reflective materials, which is more practical and has engineering significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is the basic model of a non-free space MIMO system including a reflecting ground.

[0037] Figure 2 It is the electromagnetic effective degree of freedom curve under different communication distances.

[0038] Figure 3 It is the electromagnetic effective degree of freedom curve at different array heights.

[0039] Figure 4 It is the electromagnetic effective degree of freedom curve under different reflective ground materials. DETAILED DESCRIPTION

[0040] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0041] The MIMO communication model in non-free space established by simulation is shown in the attached Figure 1 , where the source plane and the receiving plane are square areas of the same size, with a fixed side length of L, and M×M points are evenly distributed in the transceiver area, corresponding to the ideal point source and the ideal receiving point. The straight-line distance between the transceiver arrays is D, defined as the communication distance of the system, and the reflective ground is set at a distance H from the transceiver array, where the dielectric constant of the reflective ground is ε r In this communication model, the electromagnetic waves emitted by a point source will have two propagation paths, namely the direct line of sight path and the reflected path. The total electric field received by an ideal receiving point in the receiving array should be the superposition of the electric fields generated by all point sources at the receiving point through all paths. The signal amplitudes of the transmitting array and the receiving array are regarded as vectors t = [t 1 ,t 2 ,…,t N ] T and r = [r 1 ,r 2 ,…,r N ] T , where N = M × M, then there is a channel matrix H connecting the two:

[0042] r=Ht (1)

[0043] The single-polarization channel matrix H is an N×N matrix, and the matrix element h ij It is the projection coefficient from the jth source of the transmitting array to the i-th receiving point of the receiving array.

[0044] Based on the above single-polarization channel matrix, the corresponding full-polarization channel matrix G can be obtained, which is composed of 9 single-polarization channel matrices:

[0045]

[0046] G is a 3N×3N matrix, in which the submatrix H ij Corresponding to a single-polarization channel matrix, the corresponding transmit array polarization direction is j, and the receive array polarization direction is i.

[0047] In order to easily obtain the corresponding channel matrix through simulation software, simulation can be performed through the following steps:

[0048] S1: Set a unit electric dipole with a fixed direction at the i-th unit of the transmitting array, and leave the rest of the positions empty. Set electric field receiving points at the M×M unit positions of the receiving array. After a simulation, the electric field distribution at the receiving point in this case is obtained in the x, y, and z directions respectively. The electric field values ​​in different polarization directions are respectively composed of three vectors, corresponding to the i-th column of the single-polarization channel matrix with the same polarization direction of the three transmitting arrays and different polarization directions of the receiving arrays.

[0049] S2: Change the position of the unit electric dipole at the transmitting array in turn according to the coordinates of the array unit, repeat the operation simulation of S1 M×M times, and the received electric field vectors can form 3 N×N single-polarization channel matrices, whose corresponding transmitting array polarization directions are consistent, and the receiving array polarization directions are x, y, and z respectively.

[0050] S3: Change the direction of the unit electric dipole at the transmitting array and repeat steps S1 and S2 to perform simulation. Finally, 9 different single-polarization channel matrices can be obtained. Then, the corresponding full-polarization channel matrix is ​​formed according to formula (2).

[0051] After the full polarization channel matrix is ​​obtained through simulation, in order to obtain the corresponding electromagnetic effective degrees of freedom, it is necessary to first calculate the correlation matrix of the channel. Perform singular value decomposition and obtain the corresponding singular value σ i Then the system's effective electromagnetic degree of freedom Ψ can be calculated. e :

[0052]

[0053] By changing the number of array units N for simulation, different electromagnetic effective degrees of freedom can be obtained. Based on multiple sets of data, an electromagnetic effective degree of freedom curve about the variable M can be drawn. Since one electromagnetic effective degree of freedom needs to be simulated 3N times, in order to obtain an electromagnetic effective degree of freedom curve, the number of simulations will be very large, so it is necessary to use programming to automatically call the electromagnetic simulation software for simulation. For the electromagnetic simulation software used, after finding the file that stores all the modeling parameters, the simulation software can be called up with this file for simulation. By using this, programming can be performed to achieve automatic simulation to obtain an electromagnetic effective degree of freedom curve. The steps are as follows:

[0054] S1: Set up the MIMO system communication model in the electromagnetic simulation software. After running the software for simulation, you need to find the file that stores all the modeling parameters. Use Notepad to open the file to understand the settings of each parameter.

[0055] S2: Use programming to change different parameters according to the file obtained in S1, and then use this file to automatically call the simulation software for simulation.

[0056] S21: By using programming to change the coordinate value and direction of the unit electric dipole and the coordinate value of the receiving point in the file and perform 3N simulations, a full polarization channel matrix corresponding to different numbers of MIMO unit arrays can be obtained.

[0057] S22: By changing the value of the distance parameter D between the transceiver arrays in the file by programming for simulation, a full polarization channel matrix corresponding to different communication distances can be obtained.

[0058] S23: By changing the value of the height parameter H of the transceiver array relative to the ground in the file by programming to perform simulation, a full polarization channel matrix corresponding to different array heights can be obtained.

[0059] S24: Using programming to change the dielectric constant ε of the reflecting ground in the file r By simulating the value of , the full polarization channel matrix corresponding to different reflective ground materials can be obtained.

[0060] The above descriptions are only partial embodiments of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

[0061] Embodiment 1:

[0062] 1. Establishment of basic MIMO communication system model

[0063] In the present invention, electromagnetic simulation software is used to establish a non-free space MIMO communication model containing a reflective ground. Figure 1 , and a full polarization channel matrix was established based on the simulation results, so that the characteristics of the electromagnetic channel of the communication system can be discussed more comprehensively.

[0064] The operating frequency is set to 2.6 GHz, corresponding to a wavelength of about 11.5 cm, and the side length of the square area of ​​the transceiver array is fixed to 5 times the wavelength. The total number of transceiver array units is M×M, and the simulation studies the electromagnetic effective degrees of freedom corresponding to m from 2 to 10.

[0065] 2. Drawing of electromagnetic effective degree of freedom curves at different communication distances

[0066] The relative height H of the transceiver array is fixed to 8 times the wavelength, reflecting the dielectric constant ε of the ground. r The value is fixed at 10, and the communication distance D is changed to 1 times the wavelength, 7 times the wavelength, 13 times the wavelength, and 19 times the wavelength. The electromagnetic effective degree of freedom curve obtained by simulation is shown in the attached figure. Figure 2 .

[0067] First, it can be seen from the figure that when the number of units in the system array is less than the optimal number, the effective electromagnetic degrees of freedom will increase rapidly. This is because as the number of antennas increases, the system can capture more independent channels at the same time. On the other hand, when the number of units reaches and exceeds the optimal number, the effective electromagnetic degrees of freedom will slowly decrease as the number of units increases. This is because the upper limit of the effective degrees of freedom of the communication system is only related to the antenna aperture and transmission distance, but not to the antenna structure or the number of antenna units. Therefore, when the number of units is greater than the optimal number, the mutual interference between the units is serious, causing the corresponding effective electromagnetic degrees of freedom to decrease and be less than the maximum effective electromagnetic degrees of freedom of the system.

[0068] In addition, it can be seen that the maximum effective electromagnetic degree of freedom of the system decreases with the increase of communication distance. There are three main reasons for this. First, when the communication distance increases beyond the near-field range, the degree of freedom corresponding to the z-polarization will tend to disappear, resulting in a decrease in the effective electromagnetic degree of freedom of the fully polarized channel matrix solution. In addition, electromagnetic waves will degenerate into plane waves under long-distance transmission, which means that the amplitude of the received electric field will tend to be the same at all receiving points, resulting in fewer effective electromagnetic degrees of freedom. Finally, changes in communication distance will also affect the incident angle of the electromagnetic wave and the length of the propagation path, resulting in greater power loss of the electromagnetic wave and smaller corresponding effective degrees of freedom.

[0069] 3. Plotting the electromagnetic effective degree of freedom curves at different array heights

[0070] The communication distance D is fixed at 10 times the wavelength, and the dielectric constant ε of the reflecting ground is r The value is fixed at 10, and the array height H is changed to 3 times the wavelength, 6 times the wavelength, 10 times the wavelength, 15 times the wavelength and infinity (i.e. free space). The curve of electromagnetic effective degree of freedom obtained by simulation is shown in the attached figure. Figure 3 .

[0071] It can be seen that when M is greater than the critical value of 7, the effective electromagnetic degrees of freedom decrease as H increases, and reach a minimum value in free space, which reflects the effect of ground reflection on the degree of freedom of the communication system. Specifically, the reflection path will introduce additional spatial degrees of freedom, resulting in an increase in the total degree of freedom of the system. At the same time, as H increases, the reflection path length increases, the power loss of the reflected wave will be greater, and the corresponding additional electromagnetic effective degrees of freedom will be smaller.

[0072] On the other hand, in the attached Figure 3From the range of M from 4 to 7, it can be seen that the trend of the electromagnetic effective degree of freedom curve is relatively complex. The electromagnetic effective degree of freedom corresponding to some array heights shows a trend that the lower the height, the smaller the electromagnetic effective degree of freedom. This shows that when the number of units does not reach the critical value, the additional degrees of freedom brought by ground reflection are not obvious. This is caused by the complex interference between the transmitting and receiving arrays. In addition, under some altitude conditions, the curve will have an abnormal inflection point before reaching the optimal number. This is because the full polarization channel model corresponds to very strict full-wave physical information, captures very complex vector near-field electromagnetic waves in the near field, and leads to the complexity of the corresponding electromagnetic effective degree of freedom.

[0073] 4. Rendering of electromagnetic effective degrees of freedom for different reflective ground materials

[0074] The communication distance d and array height H are fixed at 10 times the wavelength, and the relative dielectric constant εr of the reflecting ground is changed to 1 (i.e. free space), 10, 100 and infinity (i.e. PEC). The electromagnetic effective degree of freedom curve obtained by simulation is shown in the attached figure. Figure 4 .

[0075] It can be seen that when m is greater than the critical value of 8, the effective electromagnetic degree of freedom decreases as the relative dielectric constant of the reflecting ground decreases, and reaches a minimum value in free space. This is because the larger the relative dielectric constant of the reflecting ground, the smaller the reflection loss of the electromagnetic wave, and the larger the corresponding effective electromagnetic degree of freedom.

Claims

1. A method for obtaining electromagnetic effective degrees of freedom of a MIMO system in non-free space, characterized in that: The following steps are involved: S1: Establish a MIMO communication system model in non-free space including a reflective ground; S2: Perform electromagnetic simulation by changing the number of array units, communication distance, array height, and dielectric constant of the reflecting ground respectively; S3: Obtain the corresponding channel matrix according to the simulated receiving electric field and establish a full polarization electromagnetic channel model; S4: Calculate the electromagnetic effective degrees of freedom using the obtained simulation results and draw an electromagnetic effective degrees of freedom curve; The step S1 specifically includes: S11: The units of the transmitting array are modeled as M×M unit electric dipoles, and are evenly distributed in a square area of ​​fixed size; S12: The units of the receiving array are modeled as M×M ideal receiving points, which are evenly distributed in a square area of ​​a fixed size. The straight-line distance between the receiving array and the transmitting array is D. S13: Set a dielectric constant of ε below the transceiver array at a height H with an area larger than the projected area of ​​the MIMO system. r reflective ground; The step S2 specifically includes: S21: After the MIMO system communication model is set in the electromagnetic simulation software, the software is run to perform simulation, and the generated file containing all modeling information is found, and a program is written to use the file to call the simulation software to perform simulation; S22: by programming to change the coordinate values ​​of the unit electric dipole and the coordinate values ​​of the receiving point in the simulation to perform simulation, a full polarization channel matrix corresponding to different numbers of MIMO unit arrays can be obtained; S23: By programming to change the value of the distance parameter D between the transceiver arrays for simulation, a full polarization channel matrix corresponding to different communication distances can be obtained; S24: by programming to change the value of the height parameter H of the transceiver array relative to the ground for simulation, a full polarization channel matrix corresponding to different array heights can be obtained; S25: By changing the value of the dielectric constant εr of the reflecting ground through programming for simulation, a full polarization channel matrix corresponding to different reflecting ground materials can be obtained; The step S3 specifically includes: S31: Establishing the electromagnetic channel matrix as a fully polarized channel matrix It is necessary to obtain 9 single-polarization channel matrices through simulation; S32: For the single-polarization channel matrix, only one unit electric dipole is set at the i-th point of the source plane for each simulation, and then the electric fields in the x, y, and z directions at M×M points on the receiving plane are obtained through simulation, and the i-th column vectors of the corresponding single-polarization channel matrices of three different receiving array polarization directions are obtained respectively. The position of the unit electric dipole is changed, and after M×M simulations, three complete single-polarization channel matrices are obtained; S33: changing the direction of the unit electric dipole and performing the simulation in step S32 again, and finally simulating 3 (M×M) times in total to obtain 9 single-polarization channel matrices, that is, the corresponding full-polarization channel matrix; The step S4 specifically includes: S41: For the full polarization channel matrix H obtained by simulation, the corresponding channel correlation matrix is ​​obtained Then perform singular value decomposition on R to obtain the singular value σ i ; Then the expression of electromagnetic effective degree of freedom is: S42: After solving the electromagnetic effective degree of freedom for the full polarization channel matrix corresponding to different M by programming, M is used as the abscissa and the electromagnetic effective degree of freedom is used as the ordinate, and the corresponding electromagnetic effective degree of freedom curve is drawn; S43: For different parameters D, H and ε r , while fixing two of them, changing the value of the remaining parameter, so as to draw multiple electromagnetic effective degree of freedom curves. These curves are plotted on the same coordinate axis and are used to analyze the influence of the parameter on the electromagnetic effective degree of freedom.

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