Ultra-large scale MIMO system optimal antenna spacing design method based on effective degree of freedom

Abstract

The invention discloses a super-large scale MIMO system optimal antenna spacing design method based on effective degree of freedom, and belongs to the field of wireless communication physical layers. The method comprises the following steps: performing channel modeling on a super-large-scale MIMO system based on an electromagnetic field theory to obtain a channel coefficient represented based on a Green function; considering that a transmitting array of the system is focused on a certain antenna position of a receiving array, and obtaining a corresponding guiding phase shift by an expression of array gain; calculating interference received at an antenna closest to the focusing antenna in the receiving array by utilizing the guiding phase deviation; and calculating the antenna spacing when the interference on the adjacent antenna is minimum, namely the effective freedom degree of the channel is maximum, so as to obtain the optimal antenna spacing. According to the method, the effective degree of freedom of the super-large-scale MIMO system is effectively improved by increasing the antenna spacing, the expression of the optimal antenna spacing of the system, which enables the effective degree of freedom of the channel to be maximum, is deduced theoretically, and guidance is provided for the design of the super-large-scale MIMO system.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless communication physical layer, and in particular to a method for designing optimal antenna spacing of a very large-scale MIMO system based on effective degrees of freedom. Background Art

[0002] In recent years, in order to meet the requirements of ultra-reliability, high capacity density, extremely low latency and low energy consumption for future sixth-generation communications, ultra-large-scale MIMO technology has attracted extensive research attention. Compared with traditional massive MIMO, ultra-large-scale MIMO deploys orders of magnitude more antennas to achieve extremely high spectral efficiency. The increase in the number of antennas not only expands the array scale, but also pushes the system's working environment from the traditional far-field region to the near-field region. Therefore, ultra-large-scale MIMO systems need to consider new channel characteristics, such as spherical wavefront, spatial non-stationarity, etc. Among them, the spherical wavefront characteristics of near-field ultra-large-scale MIMO systems have attracted the attention of the academic community. For traditional far-field channels, due to the single spatial angle of the plane wavefront, the freedom of the line-of-sight path is extremely limited. On the contrary, in the near-field scenario, considering the spherical wavefront, the spatial angle varies across the entire transmit / receive array, which greatly increases the freedom of the ultra-large-scale MIMO system, thereby significantly improving the channel capacity. On the other hand, since the channel capacity mainly depends on the orthogonal sub-channels with large singular values, existing research works are more concerned with the so-called effective degrees of freedom, that is, the number of large singular values ​​of the channel matrix.

[0003] Existing literature shows that increasing the effective degrees of freedom can significantly improve the channel capacity of very large-scale MIMO systems. It should be pointed out that although the effective degrees of freedom can be increased by increasing the number of antennas or reducing the distance between the transmit and receive arrays, the effective degrees of freedom increased by these means are very limited. This means that only when more or even excessive antennas are deployed or the distance between the transmit and receive arrays is very close can the system have a larger effective degree of freedom, but this is not practical. Therefore, for the existing very large-scale MIMO systems, there is an urgent need for a solution that can effectively increase the effective degrees of freedom to fully utilize the near-field characteristics of the spherical wavefront to increase the system capacity. Summary of the invention

[0004] The present invention provides a method for designing optimal antenna spacing of a very large-scale MIMO system based on effective degrees of freedom. The effective degrees of freedom of the very large-scale MIMO system are effectively improved by increasing the antenna spacing, and an expression for the optimal antenna spacing of the system that maximizes the effective degrees of freedom of the channel is theoretically derived, providing guidance for the design of the very large-scale MIMO system.

[0005] The embodiment of the present invention provides a method for designing optimal antenna spacing of a very large-scale MIMO system based on effective degrees of freedom, comprising the following steps:

[0006] Step S1, performing channel modeling on a very large-scale MIMO system based on electromagnetic field theory to obtain a channel coefficient represented by a Green's function;

[0007] Step S2, considering that the system transmit array is focused on a certain antenna position of the receive array, the corresponding steering phase offset is obtained according to the array gain expression of the focused antenna position;

[0008] Step S3, using the steering phase offset, calculating the interference received at the receiving antenna closest to the focus antenna position in the receiving array;

[0009] Step S4, calculating the antenna spacing when the interference to the adjacent antenna is minimal, that is, when the effective degree of freedom of the channel is maximized, to obtain the optimal antenna spacing.

[0010] Optionally, in one embodiment of the present invention, step S1 specifically includes the following steps:

[0011] Step S101, for a single frequency source ψ(r) on the transmitting array, where r is a position vector, the corresponding Helmholtz wave equation is:

[0012]

[0013] in, is the Laplace operator, k is the wave number, and φ(r) is the generated wave;

[0014] Step S102, expressing the solution of the wave equation in step S101 by the corresponding Green's function:

[0015]

[0016] Among them, S S is the area of ​​the transmitting array, r R is the position vector on the receiving array, r S is the position vector on the transmitting array, G(·; ·) is the Green function, expressed as:

[0017]

[0018] Where i is the imaginary unit, r and r′ are position vectors;

[0019] Step S103: Considering that both the system transmitting array and the receiving array are configured with point source antenna arrays, then N S The signal transmitted by the point source transmitting antenna is received by the point source receiving antenna r Ri The signal wave generated at is:

[0020]

[0021] Among them, the position of each transmitting antenna is denoted as r Sj , j = 1, 2, ..., N S , the position of each receiving antenna is denoted as r Ri , i = 1, 2, ..., N R , N R is the number of receiving antennas, s j is the transmitting antenna r Sj The source of the transmitted signal; g ij represents the position of the transmitting antenna r Sj and the receiving antenna position r Ri The Green's function between is defined as:

[0022]

[0023] Step S104: Based on step S103, receiving a received signal on the array plane It is expressed as:

[0024] f=Gs+n,

[0025] Among them, the transmitted signal s and the received signal f are expressed as:

[0026]

[0027] Among them, s i is the transmitted signal of the i-th transmitting antenna, i = 1, 2, ..., N S , f j is the received signal of the jth receiving antenna, j = 1, 2, ..., N R ; Vector n is additive Gaussian white noise, and its elements follow the distribution variance is the noise power; matrix G is the channel matrix, expressed as:

[0028]

[0029] Optionally, in one embodiment of the present invention, step S2 specifically includes the following steps:

[0030] Step S201, consider that the transmitting end and the receiving end use a uniform planar array with the same parameters, the number of antennas is N, and the antenna spacing is d; the transmitting array is located in the XY plane, and each side is parallel to a coordinate axis, and the position coordinate of the center antenna is (0, 0, 0); the receiving array position is the transmitting array position translated along the Z axis, and the position coordinate of the center antenna is (0, 0, L), recorded as r0, where L is the distance between the center antenna of the transmitting array and the center antenna of the receiving array;

[0031] In step S202, it is considered that the transmitting array is focused on the receiving antenna r0, and each transmitting antenna transmits the same transmitting signal s, and the power is P / N. Then the receiving signal at the receiving antenna r0 is expressed as:

[0032]

[0033] Where P is the total power of the signal transmitted by the transmitting array, The steering phase offset applied to the transmitting antenna (m, n) to focus the transmitting array on the receiving antenna r0, where n is additive white Gaussian noise and follows the distribution is the channel coefficient corresponding to the receiving antenna r0, and the expression is as follows:

[0034]

[0035] The index subscript (m, n) is the relative position of the transmitting antenna on the transmitting array. The transmitting antenna in the fourth quadrant at the lower left corner is the first row and the first column, denoted as (1, 1). From left to right and from bottom to top, the antenna in the mth row and nth column is denoted by the subscript (m, n); i is the imaginary unit, k = 2π / λ is the wave number, and λ is the wavelength; and are the X-axis and Y-axis coordinates of the transmitting antenna (m, n), respectively:

[0036]

[0037] Step S203, according to the expression of the received signal f0 given in step S202, when the transmitting array is focused on the receiving antenna r0, the signal-to-noise ratio of the received signal at the receiving antenna r0 is obtained as follows:

[0038]

[0039] Where ρ0 is the array gain of the transmitting array at r0, expressed as:

[0040]

[0041] Since the transmit array is focused on the receive antenna r0, the steering phase shift The array gain ρ0 should be maximized, so its value is:

[0042]

[0043] Optionally, in one embodiment of the present invention, step S3 specifically includes the following steps:

[0044] Step S301, when the transmitting array is focused on the receiving antenna r0 (0, 0, L), the interference signal received at the receiving antenna r1 (d, 0, L) closest to the receiving antenna r0 is:

[0045]

[0046] in, represents the channel coefficient corresponding to the receiving antenna r1, which is approximately:

[0047]

[0048] Step S302: According to the expression of the interference signal given in step S301, the signal-to-noise ratio expression of the receiving antenna r1 is:

[0049]

[0050] Where ρ1 represents the array gain of the transmitting array at the receiving antenna r1, expressed as:

[0051]

[0052] Step S303: offset the steering phase obtained in step S2 Substituting into the array gain ρ1 in step S302, and simplifying the calculation of ρ1, we obtain:

[0053]

[0054] The approximation step uses the first-order Taylor approximation x→0, step is substituted into x in step S202 n Expression of

[0055] Step S304, further simplify the summation term in step S303 to obtain:

[0056]

[0057] Step S305, substituting the calculation result of step S304 into the expression of array gain ρ1 in step S303, obtains:

[0058]

[0059] Optionally, in one embodiment of the present invention, step S4 specifically includes the following steps:

[0060] Step S401, according to step S3, when the transmitting array is focused on the receiving antenna r0 (0, 0, L), the size of the interference signal received at the receiving antenna r1 (d, 0, L) closest to the receiving antenna r0 is proportional to the size of the array gain ρ1; when the interference to the adjacent antenna is minimized, that is, when the effective degree of freedom of the channel is maximized, therefore, to maximize the effective degree of freedom of the channel, only the zero point of the array gain ρ1 needs to be considered;

[0061] Step S402, considering ρ1 = 0, then Given the system's operating frequency, the distance between the transmit and receive arrays, and the number of transmit and receive antennas, the antenna spacing that maximizes the channel's effective degrees of freedom is expressed as:

[0062]

[0063] The method for designing the optimal antenna spacing of a very large-scale MIMO system based on effective degrees of freedom in an embodiment of the present invention is more effective than the solution in the existing literature that increases the effective degrees of freedom of a very large-scale MIMO system by increasing the number of antennas or reducing the distance between the transmitting and receiving arrays. In addition, the present invention theoretically derives a closed-form expression for the optimal antenna spacing when the effective degrees of freedom of the system are maximized, which has important guiding value for the design of future very large-scale MIMO systems.

[0064] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0066] Figure 1 A flowchart of a method for designing optimal antenna spacing for a very large-scale MIMO system based on effective degrees of freedom according to an embodiment of the present invention;

[0067] Figure 2 A schematic diagram of a very large-scale MIMO system according to an embodiment of the present invention;

[0068] Figure 3 Graph showing the relationship among array gain ρ1, effective degrees of freedom, and optimal antenna spacing obtained according to an embodiment of the present invention. DETAILED DESCRIPTION

[0069] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0070] Figure 1 The present invention provides a flowchart of a method for designing optimal antenna spacing for a very large-scale MIMO system based on effective degrees of freedom according to an embodiment of the present invention.

[0071] like Figure 1 As shown, the optimal antenna spacing design method for a very large-scale MIMO system based on effective degrees of freedom includes the following steps:

[0072] Step S1, based on electromagnetic field theory Figure 2 The ultra-large-scale MIMO system shown is subjected to channel modeling to obtain channel coefficients based on Green's function representation.

[0073] In an embodiment of the present invention, step S1 specifically includes the following steps:

[0074] Step S101: For a single-frequency source ψ(r) on the transmitting array, where r is a position vector, the corresponding Helmholtz wave equation is:

[0075]

[0076] in, represents the Laplace operator, k represents the wave number, and φ(r) represents the generated wave;

[0077] Step S102: The solution of the wave equation in step S101 is expressed by the corresponding Green's function:

[0078]

[0079] Among them, S S is the area of ​​the transmitting array, r R is the position vector on the receiving array, r S is the position vector on the transmitting array, G(·; ·) is the Green function, which can be expressed as:

[0080]

[0081] Where i is the imaginary unit, r and r′ are position vectors;

[0082] Step S103: Considering that both the system transmitting array and the receiving array are configured with point source antenna arrays, then N S The signal transmitted by the point source transmitting antenna is received by the point source receiving antenna r RiThe signal wave generated at is:

[0083]

[0084] Among them, the position of each transmitting antenna is denoted as r Sj , j = 1, 2, ..., N S , the position of each receiving antenna is denoted as r Ri , i = 1, 2, ..., N R , N R is the number of receiving antennas, s j is the transmitting antenna r Sj The source of the transmitted signal; g ij represents the position of the transmitting antenna r Sj and the receiving antenna position r Ri The Green's function between is defined as:

[0085]

[0086] Step S104: Based on step S103, receiving the received signal on the receiving plane It can be expressed as:

[0087] f=Gs+n,

[0088] Among them, the transmitted signal s and the received signal f are expressed as:

[0089]

[0090] Among them, s i is the transmitted signal of the i-th transmitting antenna, i = 1, 2, ..., N S , f j is the received signal of the jth receiving antenna, j = 1, 2, ..., N R ; Vector n represents additive Gaussian white noise, whose elements follow the distribution variance represents the noise power; the matrix G represents the channel matrix, which is expressed as:

[0091]

[0092] Among them, g ij Given by step S103.

[0093] Furthermore, in this embodiment of the present invention, the autocorrelation matrix GG of the channel matrix G obtained in step S104 is H Perform eigenvalue decomposition to obtain a set of eigenvalues ​​in descending order:

[0094]

[0095] The effective degrees of freedom of the channel can be calculated as follows:

[0096]

[0097] Consider the example system operating frequency f = 30GHz (λ = 0.01m), the number of antennas N S =N R =25×25, the distance between the transmitting and receiving arrays is L=4000λ, then the effective degree of freedom varies with the antenna spacing d of the array as follows: Figure 3 shown.

[0098] Step S2, considering that the system transmitting array is focused on a certain antenna position of the receiving array, the corresponding steering phase offset is obtained according to the array gain expression of the focused antenna position.

[0099] In an embodiment of the present invention, step S2 specifically includes the following steps:

[0100] Step S201: Consider that the transmitting end and the receiving end use a uniform planar array with the same parameters, the number of antennas is N, and the antenna spacing is d; the transmitting array is located in the XY plane, and each side is parallel to a coordinate axis, and the position coordinate of the center antenna is (0, 0, 0); the receiving array position is the position of the transmitting array translated along the Z axis, and the position coordinate of the center antenna is (0, 0, L), denoted as r0, where L is the distance between the center antenna of the transmitting array and the center antenna of the receiving array;

[0101] Step S202: Considering that the transmitting array is focused at r0, and each transmitting antenna transmits the same transmitting signal s, with a power of P / N, the receiving signal at the receiving antenna r0 is expressed as:

[0102]

[0103] Where P is the total power of the signal transmitted by the transmitting array, The steering phase offset applied to the transmitting antenna (m, n) to focus the transmitting array on the receiving antenna r0, where n is additive white Gaussian noise and follows the distribution represents the channel coefficient corresponding to the receiving antenna r0, which is g in step S103 ij A renumbered version of In order to facilitate subsequent analysis, the expression is as follows:

[0104]

[0105] The approximation in the expression is because in the radiated near field considered by the system, the signal energy change caused by the distance change can be ignored compared with the signal energy change caused by the phase change; the index subscript (m, n) is the relative position of the transmitting antenna on the transmitting array, The transmitting antenna in the fourth quadrant at the lower left corner is the first row and the first column, denoted as (1, 1). From left to right and from bottom to top, the antenna in the mth row and nth column is denoted by the subscript (m, n); i is the imaginary unit, k = 2π / λ is the wave number, and λ is the wavelength; and are the X-axis and Y-axis coordinates of the transmitting antenna (m, n), respectively:

[0106]

[0107] Step S203: According to the received signal expression given in step S202, when the transmitting array is focused on the receiving antenna r0, the signal-to-noise ratio of the received signal at r0 is:

[0108]

[0109] Where ρ0 represents the array gain of the transmitting array at r0, expressed as:

[0110]

[0111] Since the transmitting array is focused at r0, the steering phase shift The array gain ρ0 should be maximized, so its value is

[0112]

[0113] Step S3, using the steering phase offset Calculate the array gain of the receiving antenna closest to the focused antenna position in the receiving array, that is, the interference received by the closest antenna.

[0114] In an embodiment of the present invention, step S3 specifically includes the following steps:

[0115] Step S301: When the transmitting array is focused on the receiving antenna r0 (0, 0, L), the interference signal received at the receiving antenna r1 (d, 0, L) closest to r0 is:

[0116]

[0117] in, represents the channel coefficient corresponding to the receiving antenna r1, which can be approximated as:

[0118]

[0119] Step S302: According to the expression of the interference signal given in step S301, the signal-to-noise ratio expression of the receiving antenna r1 is:

[0120]

[0121] Where ρ1 represents the array gain of the transmitting array at r1, expressed as:

[0122]

[0123] Step S303: offset the steering phase obtained in step S2 Substituting the array gain ρ1 in step S302 and then simplifying the calculation of ρ1, we can obtain:

[0124]

[0125] The approximation step uses the first-order Taylor approximation x→0; Step is substituted into the value given in step S202 Expression of

[0126] Step S304: Further simplify the summation term in step S303 to obtain:

[0127]

[0128] Step S305: Substitute the calculation result of step S304 into the expression of array gain ρ1 in step S303 to obtain:

[0129]

[0130] Consider the example system operating frequency f = 30GHz (λ = 0.01m), the number of antennas N S =N R =N=25×25, the distance between the transmitting and receiving arrays is L=4000λ, then the array gain ρ1 varies with the array antenna spacing d as follows: Figure 3 shown.

[0131] Step S4, calculating the antenna spacing when the interference to the adjacent antenna is minimal, that is, when the effective degree of freedom of the channel is maximized, to obtain the optimal antenna spacing.

[0132] In one embodiment of the present invention, step S4 specifically includes the following steps:

[0133] Step S401: According to step S3, when the transmitting array is focused on the receiving antenna r0 (0, 0, L), the interference signal received at the receiving antenna r1 (d, 0, L) closest to r0 is proportional to the size of the array gain ρ1; when the interference to the adjacent antenna is minimized, the effective degree of freedom of the channel is maximized; therefore, to maximize the effective degree of freedom of the channel, only the zero point of the array gain ρ1 needs to be considered;

[0134] Step S402: Consider ρ1=0, then Given the system's operating frequency, the distance between the transmit and receive arrays, and the number of transmit and receive antennas, the antenna spacing that maximizes the channel's effective degrees of freedom is expressed as:

[0135]

[0136] Consider the example system operating frequency f = 30GHz (λ = 0.01m), the number of antennas N S =N R =N=25×25, the distance between the transmitting and receiving arrays is L=4000λ, then the optimal antenna spacing of the array can be calculated as

[0137]

[0138] The results are as follows Figure 3 as shown in .

[0139] According to the method for designing the optimal antenna spacing of a very large-scale MIMO system based on effective degrees of freedom proposed in an embodiment of the present invention, first, based on electromagnetic field theory, the channel modeling of the very large-scale MIMO system is performed to obtain the channel coefficient represented by the Green's function; secondly, considering that the system transmit array is focused on a certain antenna position of the receiving array, the corresponding guided phase offset is obtained from the expression of the array gain here; then, the guided phase offset is used to calculate the interference received at the antenna closest to the focused antenna in the receiving array; finally, the antenna spacing is calculated when the interference to the adjacent antenna is minimized, that is, when the effective degrees of freedom of the channel is maximized, thereby obtaining the optimal antenna spacing. The present invention effectively improves the effective degrees of freedom of the very large-scale MIMO system by increasing the antenna spacing, and theoretically derives the expression of the optimal antenna spacing of the system that maximizes the effective degrees of freedom of the channel, providing guidance for the design of very large-scale MIMO systems.

[0140] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0141] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0142] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

Claims

1. A method for designing optimal antenna spacing for a very large-scale MIMO system based on effective degrees of freedom, characterized in that: The following steps are involved: Step S1, performing channel modeling on a very large-scale MIMO system based on electromagnetic field theory to obtain a channel coefficient represented by a Green's function; Step S2, considering that the system transmit array is focused on a certain antenna position of the receive array, the corresponding steering phase offset is obtained according to the array gain expression of the focused antenna position; Step S3, using the steering phase offset, calculating the interference received at the receiving antenna closest to the focus antenna position in the receiving array; Step S4, calculating the antenna spacing when the interference to the adjacent antenna is minimal, that is, when the effective degree of freedom of the channel is maximized, to obtain the optimal antenna spacing.

2. The method according to claim 1, characterized in that Step S1 specifically includes the following steps: Step S101, for a single frequency source ψ(r) on the transmitting array, where r is a position vector, the corresponding Helmholtz wave equation is: in, is the Laplace operator, k is the wave number, and φ(r) is the generated wave; Step S102, expressing the solution of the wave equation in step S101 by the corresponding Green's function: Among them, S s is the area of ​​the transmitting array, r R is the position vector on the receiving array, r S is the position vector on the transmitting array, G(·,·) is the Green function, expressed as: Where i is the imaginary unit, r and r′ are position vectors; Step S103: Considering that both the system transmitting array and the receiving array are configured with point source antenna arrays, then N s The signal transmitted by the point source transmitting antenna is received by the point source receiving antenna r Ri The signal wave generated at is: Among them, the position of each transmitting antenna is denoted as r Sj , j = 1, 2, ..., N S , the position of each receiving antenna is denoted as r Ri , i = 1, 2, ..., N R , N R is the number of receiving antennas, s j is the transmitting antenna r Sj The source of the transmitted signal; g ij represents the position of the transmitting antenna r Sj and the receiving antenna position r Ri The Green's function between is defined as: Step S104: Based on step S103, receiving a received signal on the array plane It is expressed as: f=Gs+n, Among them, the transmitted signal s and the received signal f are expressed as: Among them, s i is the transmitted signal of the i-th transmitting antenna, i = 1, 2, ..., N s , f j is the received signal of the jth receiving antenna, j = 1, 2, ..., N R ; Vector n is additive Gaussian white noise, and its elements follow the distribution variance is the noise power; matrix G is the channel matrix, expressed as:

3. The method according to claim 1, characterized in that: Step S2 specifically includes the following steps: Step S201, consider that the transmitting end and the receiving end use a uniform planar array with the same parameters, the number of antennas is N, and the antenna spacing is d; the transmitting array is located in the XY plane, and each side is parallel to a coordinate axis, and the position coordinate of the center antenna is (0, 0, 0); the receiving array position is the transmitting array position translated along the Z axis, and the position coordinate of the center antenna is (0, 0, L), recorded as r0, where L is the distance between the center antenna of the transmitting array and the center antenna of the receiving array; In step S202, it is considered that the transmitting array is focused on the receiving antenna r0, and each transmitting antenna transmits the same transmitting signal s, and the power is P / N. Then the receiving signal at the receiving antenna r0 is expressed as: Where P is the total power of the signal transmitted by the transmitting array, The steering phase offset applied to the transmitting antenna (m, n) to focus the transmitting array on the receiving antenna r0, where n is additive white Gaussian noise and follows the distribution is the channel coefficient corresponding to the receiving antenna r0, and the expression is as follows: The index subscript (m, n) is the relative position of the transmitting antenna on the transmitting array. The transmitting antenna in the fourth quadrant at the lower left corner is the first row and first column, denoted as (1,1). From left to right and from bottom to top, the antenna in the mth row and nth column is denoted by the subscript (m, n); i is the imaginary unit, k = 2π / λ is the wave number, and λ is the wavelength; and are the X-axis and Y-axis coordinates of the transmitting antenna (m, n), respectively: Step S203, according to the expression of the received signal f0 given in step S202, when the transmitting array is focused on the receiving antenna r0, the signal-to-noise ratio of the received signal at the receiving antenna r0 is obtained as follows: Where ρ0 is the array gain of the transmitting array at r0, expressed as: Since the transmit array is focused on the receive antenna r0, the steering phase shift The array gain ρ0 should be maximized, so its value is:

4. The method according to claim 3, characterized in that Step S3 specifically includes the following steps: Step S301, when the transmitting array is focused on the receiving antenna r0 (0, 0, L), the interference signal received at the receiving antenna r1 (d, 0, L) closest to the receiving antenna r0 is: in, represents the channel coefficient corresponding to the receiving antenna r1, which is approximately: Step S302: According to the expression of the interference signal given in step S301, the signal-to-noise ratio expression of the receiving antenna r1 is: Where ρ1 represents the array gain of the transmitting array at the receiving antenna r1, expressed as: Step S303: offset the steering phase obtained in step S2 Substituting into the array gain ρ1 in step S302, and simplifying the calculation of ρ1, we obtain: The approximation step uses the first-order Taylor approximation step is substituted into x in step S202 n Expression of Step S304, further simplify the summation term in step S303 to obtain: Step S305, substituting the calculation result of step S304 into the expression of array gain ρ1 in step S303, obtains:

5. The method according to claim 4, characterized in that Step S4 specifically includes the following steps: Step S401, according to step S3, when the transmitting array is focused on the receiving antenna r0 (0, 0, L), the size of the interference signal received at the receiving antenna r1 (d, 0, L) closest to the receiving antenna r0 is proportional to the size of the array gain ρ1; when the interference to the adjacent antenna is minimized, that is, when the effective degree of freedom of the channel is maximized, therefore, to maximize the effective degree of freedom of the channel, only the zero point of the array gain ρ1 needs to be considered; Step S402, considering ρ1 = 0, then Given the system's operating frequency, the distance between the transmit and receive arrays, and the number of transmit and receive antennas, the antenna spacing that maximizes the channel's effective degrees of freedom is expressed as:

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