Multi-user precoding method based on super-directive antenna array, and device and medium

Abstract

The present invention belongs to the field of wireless communications. Disclosed are a multi-user precoding method based on a super-directive antenna array, and a device and a medium. The method comprises: for a user u, constructing a unitary matrix [formula 1], wherein the last N (N≤K-1) columns of the unitary matrix U are respectively standard orthogonal bases of an interfered user channel space span{hi, i=1, ..., K, i≠u}, N is the number of dimensions of the interfered user channel space, and [formula 2] represents channel state information of an i-th terminal user, M is the total number of antennas on a network device side, K is the total number of terminal users that perform communications, and M≥K; capturing the first M-N rows of a matrix UHhu, so as to obtain a matrix ηu, wherein [formula 3], hu represents channel state information of a u-th terminal user, and the superscript H represents conjugate transposition; capturing the first M-N rows and the first M-N columns of a matrix UHZU, so as to obtain a matrix Ξ, wherein [formula 4], a matrix [formula 5], and an element in Z represents a coupling coefficient of any two antennas; and performing calculation to obtain a precoding matrix [formula 6] of the u-th terminal user, wherein [formula 7]. The spectral efficiency and capacity of a system can be significantly improved, thereby meeting the increasing communication requirements.

Description

Super-directional antenna array multi-user precoding method, device and medium

Technical field

[0001] The present invention belongs to the field of wireless communications, and more specifically, relates to a super-directional antenna array multi-user precoding method, device, and medium. [Background Technology]

[0002] Early research on Massive MIMO focused on analyzing channel characteristics when the number of base station antennas approaches an infinite number. However, in practice, due to the immaturity of both technology and theory, the distance between antennas is still limited to half a wavelength. Therefore, deploying a large number of antennas on a fixed-size antenna panel to approach theoretical channel capacity remains challenging. In recent years, with the further maturity of Massive MIMO technology and the increasing demand for spectral efficiency in communication systems, achieving increased system throughput through the deployment of ultra-dense antenna arrays has become a major challenge in the wireless communications field.

[0003] In the context of 5G, facing the defects of large signal attenuation and the inability to deploy ultra-large-scale antenna arrays, super-directional antenna arrays, as a narrow-beam super-directional array, have the potential to become a key technology for the next generation of wireless communication systems. In traditional antenna arrays, in order to reduce the mutual coupling between antennas, an antenna spacing of about half a wavelength is usually used, but this also means that the array gain is only proportional to the number of antennas M. In super-directional antenna arrays, by reducing the antenna spacing and making full use of the strong mutual coupling between antennas, the antenna array gain can be proportional to M. 2 Proportional performance improvement.

[0004] However, research on the application of super-directional antenna arrays in wireless communication systems has yet to be fully explored. Traditional MIMO arrays can achieve spatial multiplexing through beamforming, significantly improving system throughput. However, there is currently no solution for utilizing super-directional antenna arrays in multi-user wireless communication scenarios while taking into account coupling effects.

[0005] [Summary of the invention]

[0006] In response to the above defects or improvement needs, the present invention provides a super-directional antenna array multi-user precoding method, device and medium, aiming to solve the technical problem that the existing traditional multi-user beamforming scheme ignores the coupling effect between antennas, resulting in the inability to achieve the super-directivity of the array, and thus cannot improve the system spectrum efficiency when the base station is a compact array.

[0007] To achieve the above objectives, in a first aspect, the present invention provides a super-directional antenna array multi-user precoding method, comprising:

[0008] For the terminal user u, construct the unitary matrix The last N (N≤K-1) columns of the unitary matrix U are the interfering user channel space span{h i , i=1,...,K,i≠u}, where N is the dimension of the interfering user channel space, represents the channel state information of the i-th terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M ≥ K;

[0009] Truncation matrix U H h u The first MN rows of the matrix η are obtained u ,in h u represents the channel state information of the u-th terminal user, and the superscript H represents the conjugate transpose;

[0010] Truncation matrix U H The first MN rows and columns of ZU are used to obtain the matrix Ξ, where matrix The elements in Z represent the coupling coefficients between any two antennas;

[0011] Calculate the precoding matrix of the u-th terminal user in The superscript * indicates conjugation.

[0012] Furthermore, when intercepting the matrix U H Before obtaining the matrix Ξ from the first MN rows and the first MN columns of ZU, the method further includes: updating the matrix Z to Z+Λ, where is the regularization matrix of the matrix Z.

[0013] Furthermore, the regularization matrix Λ is:

[0014] R rad ≈24.7(kL / 2) 2.5

[0015] Among them, r loss and R rad are the loss and radiation impedance of the antenna, I M is an M×M unit matrix, L, a, f, μ, σ, and k are the length, radius, operating frequency, magnetic permeability, electrical conductivity, and wave number of the antenna, respectively.

[0016] Furthermore, the regularization matrix Λ is:

[0017] Among them, ∈2 is the Gaussian noise power, k(θ, φ) is the antenna pattern function, θ and φ are the far-field coordinate components in the spherical coordinate system, I M is the M×M identity matrix.

[0018] Furthermore, the regularization matrix Λ is:

[0019] R rad ≈24.7(kL / 2) 2.5

[0020] Among them, r loss and R rad are the loss and radiation impedance of the antenna, I M is an M×M unit matrix, L, a, f, μ, σ and k are the length, radius, operating frequency, magnetic permeability, electrical conductivity and wave number of the antenna respectively, ∈ 2 is the Gaussian noise power, k(θ, φ) is the antenna pattern function, θ and φ are the far-field coordinate components in the spherical coordinate system.

[0021] Furthermore, the unitary matrix is ​​constructed Specifically:

[0022] Construct the total interference covariance matrix:

[0023] R int Do SVD decomposition:

[0024] R int =W H ΛW

[0025] The unitary matrix U is:

[0026] U = [MN columns after W, N columns before W].

[0027] Furthermore, the matrix

[0028] Among them, z mn represents the coupling coefficient between the mth and nth antennas, k(θ, φ) is the antenna pattern function, θ and φ are the far-field coordinate components in the spherical coordinate system, k is the wave number of the antenna, is the unit vector in the spherical coordinate system, r m and r n are the coordinates of the mth and nth antennas respectively, m=1,…,M, n=1,…,M.

[0029] Furthermore, the last N (N≤K-1) columns of the unitary matrix U are the interfering user channel space span{h i, i=1,...,K,i≠u}, including:

[0030] make is a matrix composed of interfering user channel vectors. If N=K-1, the last K-1 columns of the unitary matrix U are in:

[0031] If N<K-1, calculate Then N non-zero vectors will be obtained, and the N non-zero vectors are selected as the last N columns of U.

[0032] In a second aspect, the present invention provides a super-directional antenna array multi-user precoding method, comprising:

[0033] For the terminal user u, construct the unitary matrix The first N (N≤K-1) columns of the unitary matrix W are the interfering user channel space span {h i , i=1,...,K,i≠u}, where N is the dimension of the interfering user channel space, represents the channel state information of the i-th terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M ≥ K;

[0034] The matrix R is obtained by cutting the last MN columns of the unitary matrix W, where

[0035] Calculate the precoding matrix of the u-th terminal user in The superscript * indicates conjugation, h u Represents the channel state information of the u-th terminal user, the matrix The elements in Z represent the coupling coefficients between any two antennas, and the superscript H represents the conjugate transpose.

[0036] In a third aspect, the present invention provides a network device, comprising:

[0037] Construction unit, used to construct a unitary matrix for the terminal user u The last N (N≤K-1) columns of the unitary matrix U are the interfering user channel space span{h i , i=1,...,K,i≠u}, where N is the dimension of the interfering user channel space, represents the channel state information of the i-th terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M ≥ K;

[0038] The first interception unit is used to intercept the matrix U H hu The first MN rows of the matrix η are obtained u ,in h u represents the channel state information of the u-th terminal user, and the superscript H represents the conjugate transpose;

[0039] The second interception unit is used to intercept the matrix U H The first MN rows and columns of ZU are used to obtain the matrix Ξ, where matrix The elements in Z represent the coupling coefficients between any two antennas;

[0040] The calculation unit is used to calculate the precoding matrix of the u-th terminal user in The superscript * indicates conjugation.

[0041] In a fourth aspect, the present invention provides a network device, comprising:

[0042] Construction unit, used to construct a unitary matrix for the terminal user u The first N (N≤K-1) columns of the unitary matrix W are the interfering user channel space span {h i , i=1,...,K,i≠u}, where N is the dimension of the interfering user channel space, represents the channel state information of the i-th terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M ≥ K;

[0043] The truncation unit is used to truncate the last MN columns of the unitary matrix W to obtain the matrix R, where

[0044] The calculation unit is used to calculate the precoding matrix of the u-th terminal user in The superscript * indicates conjugation, h u Represents the channel state information of the u-th terminal user, the matrix The elements in Z represent the coupling coefficients between any two antennas, and the superscript H represents the conjugate transpose.

[0045] In a fifth aspect, the present invention provides an electronic device, comprising:

[0046] processor; and

[0047] a memory for storing executable instructions of the processor;

[0048] The processor is configured to execute the super-directional antenna array multi-user precoding method described in the first aspect or the second aspect by executing the executable instructions.

[0049] In a sixth aspect, the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer execution instructions. When a processor executes the computer execution instructions, the super-directional antenna array multi-user precoding method as described in the first aspect or the second aspect is implemented.

[0050] In general, the above technical solutions proposed by the present invention can achieve the following beneficial effects compared with the prior art:

[0051] (1) This invention utilizes the progressive orthogonality of different user channels to propose a low-complexity solution to the convex optimization problem. By constructing a unitary matrix and performing appropriate mathematical transformations, the precoding matrix for each end user is obtained. This solution fully considers the coupling between antennas and can better distinguish and process the communication signals between different end users, thereby significantly improving the system's spectral efficiency and capacity to meet the growing communication needs.

[0052] (2) The present invention introduces a regularization matrix to overcome the problem of system capacity reduction in actual super-directional multi-user communication systems due to ohmic loss and inaccurate channel estimation.

[0053] (3) The present invention proposes a simplified solution to solve the convex optimization problem, specifically: first find the optimal solution of the objective function, and then project this optimal solution onto the null space of the interfering user; thereby avoiding multiple matrix operations.

Brief Description of the Drawings

[0054] FIG1 is a directional pattern obtained by performing super-directional zero-forcing beamforming on a target user in a simulation according to the present invention;

[0055] 2 is a spectrum efficiency SE-SNR comparison diagram of the invention scheme 1 and the invention scheme 2, the traditional maximum ratio transmission, and the zero-forcing transmission scheme under the simulated multi-user situation provided by the present invention;

[0056] FIG3 is a spectrum efficiency SE-SNR comparison diagram of the first and third invention solutions, the traditional maximum ratio transmission, and the zero-forcing transmission solution under the simulated multi-user situation provided by the present invention. [Specific implementation method]

[0057] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0058] The present invention can be applied to wireless communication systems. It should be noted that the wireless communication systems mentioned in the embodiments of the present application include but are not limited to: Narrow Band-Internet of Things (NB-IoT) system, Global System for Mobile Communications (GSM), Enhanced Data rate for GSM Evolution (EDGE), Wideband Code Division Multiple Access (WCDMA), Code Division Multiple Access 2000 (CDMA2000), Time Division-Synchronization Code Division Multiple Access (TD-SCDMA), Long Term Evolution (LTE) and three major application scenarios of 5G mobile communication systems: Enhanced Mobile Broad Band (eMBB), Ultra-reliable and Low Latency Communications (URLLC) and Massive Machine-Type Communications (mMTC).

[0059] The communication device involved in the present invention mainly includes a network side device or a terminal device. In the present invention, the sending end is a network side device, and the receiving end is a terminal device; or, in the present invention, the sending end is a terminal device, and the receiving end is a network side device.

[0060] The terminal device of the present invention may be a wireless terminal. A wireless terminal may be a device that provides voice and / or other service data connectivity to a user, a handheld device with wireless connection capabilities, or other processing devices connected to a wireless modem. A wireless terminal may communicate with one or more core networks via a radio access network (RAN). A wireless terminal may be a mobile terminal, such as a mobile phone (or "cellular" phone) and a computer with a mobile terminal. For example, a wireless terminal may be a portable, pocket-sized, handheld, computer-built-in, or vehicle-mounted mobile device that exchanges voice and / or data with a radio access network. Examples include personal communication service (PCS) phones, cordless phones, session initiation protocol (SIP) phones, wireless local loop (WLL) stations, personal digital assistants (PDAs), and other devices. A wireless terminal may also be referred to as a system, a subscriber unit, a subscriber station, a mobile station, a mobile station, a remote station, a remote terminal, an access terminal, a user terminal, a user agent, or a user device or user equipment, without limitation herein.

[0061] The network side device of the present invention can be a device for communicating with a terminal device, for example, it can be a base station (base transceiver station, BTS) in a GSM system or CDMA, it can be a base station (nodeB, NB) in a WCDMA system, it can also be an evolved base station (eNB or eNodeB) in an LTE system, it can also be a next generation base station (next generation eNodeB, ngeNB) in an LTE system, or the network side device can be a relay station, an access point (AP), a vehicle-mounted device, a wearable device, and a network side device in a 5G network or a network side device in a future evolved public land mobile network (PLMN), etc., for example, it can be a new generation base station (generation nodeB, gNB or gNodeB).

[0062] The following first describes the current state of the art of multi-user precoding methods for super-directional antenna arrays.

[0063] 1.1 System Model

[0064] The channel between the sth antenna of the base station and the uth terminal user can be expressed as:

[0065] where β p and τ p are the complex amplitude and time delay of the pth path respectively; λ0 is the wavelength of the center frequency; θ p,ZOD 、φ p,AOD ,θ p,ZOA 、φ p,AOA It represents the pitch departure angle, horizontal departure angle, pitch arrival angle, and horizontal arrival angle of the p-th path.

[0066] is a horizontal arrival angle φ p,AOA and the pitch arrival angle θ p,ZOA The spherical unit vector of :

[0067] is the pitch departure angle θ p,ZOD and horizontal departure angle φ p,AOD The spherical unit vector of :

[0068] in, is the position vector of the i-th end user in the 3D rectangular coordinate system; similarly, is the position vector of the sth antenna of the base station; the exponential term is the Doppler of the pth path, where t represents time; ω p for in Represents the terminal user UE velocity vector:

[0069] Among them, v, φ v ,θ v They are UE moving speed, horizontal angle, and pitch angle.

[0070] The base station contains N v Row N h Antennas, the number of base station antennas is N t Indicates that N t =N v N h ; Replace the number of UE antennas with N r Indicates that the entire bandwidth includes N f subcarriers, and the interval between adjacent subcarriers is Δf.

[0071] use Represents the channel from all antennas of the base station to the u-th terminal user UE at time t and frequency f; f The channel on the subcarriers is written in matrix form:

[0072] Among them, f i is the frequency of the i-th subcarrier and satisfies 1≤i≤N f .

[0073] The signal received by the u-th terminal user UE at time t and subcarrier f is

[0074] in is the beamforming precoding vector of the base station for the u-th terminal user UE, h is a zero-mean and variance σ 2 Gaussian white noise. Consider a certain time t and frequency f i , Simply expressed as

[0075] 1.2. Traditional Multi-User Beamforming Solution 1: Maximum Ratio Transmission

[0076] Maximum Ratio Transmission (MRT) is a multi-antenna technology that uses the channel state information at the receiving end to optimize the antenna weights at the transmitting end, thereby maximizing the signal-to-noise ratio of the received signal.

[0077] The mathematical expression of the maximum ratio transmission beamforming vector can be expressed as: MRT =βh * (7)

[0078] Where β is the power constraint coefficient of the base station on the beamforming vector, h is the channel state information (CSI) of the target user measured by the base station, and h * is its conjugate. By assigning different beamforming vectors to different users based on their channel state information, multi-user communication is achieved. In traditional MIMO systems, MRT solutions focus on maximizing user signal gain. However, in multi-user systems, as transmission channel correlation increases, this solution fails to address inter-user interference, leading to a rapid decline in overall system performance.

[0079] 1.3 Traditional Multi-User Beamforming Solution 2: Zero-Forcing Transmission

[0080] Maximum ratio transmission (MRT) focuses solely on the desired signal for the target user, ignoring interference from other users. In contrast, zero-forcing (ZF) eliminates interference between different users without considering the effects of noise. Specifically, the precoding matrix for MRT can be expressed as the product of the normalized value of the target user's channel vector and the transmitted signal, while the precoding matrix for ZF can be expressed as the product of the pseudo-inverse of the channel transmission matrix and the received signal vector. This eliminates interference between different users and obtains the desired signal.

[0081] where H = [h1, h2, ..., h K ] is the matrix composed of the channel state information of K terminal users, W ZF The kth column in is the precoding vector for the kth end user. The ZF scheme can achieve good system sum rates in areas with high signal-to-noise ratios. However, in areas with low signal-to-noise ratios, the total system rate is not as high as the MRT scheme because it ignores the effects of noise.

[0082] 1.4 Super-directional Beamforming

[0083] For ease of analysis, assume an antenna array consisting of M antennas with a spacing of d, where the pattern function of each antenna is k(θ, φ), where θ and φ are the far-field coordinate components in the spherical coordinate system. The far-field pattern function f(θ, φ) of this array is:

[0084] where a m is the excitation coefficient of the mth antenna, k is the wave number, is the unit vector in the spherical coordinate system, r mare the coordinates of the mth antenna, m=1,…,M.

[0085] The directivity coefficient D(θ0, φ0) in the direction (θ0, φ0) is defined as:

[0086] Simplify the denominator in the above formula:

[0087] For the integral term in the above formula, let:

[0088] So formula (11) can be rewritten as:

[0089] For the convenience of expression, formula (10) can be simplified as

[0090] Where, a=[a1,a2,…,a M ] T , (15)

[0091] and

[0092] Z is the normalized real impedance matrix:

[0093] The beamforming vector a that maximizes Equation (14) can be solved as:

[0094] a=Z -1 e * , (18)

[0095] The maximized directivity coefficient is:

[0096] D max =e H Z -1 e. (19)

[0097] Based on the above description, it can be seen that current research on super-directional arrays only explores how to maximize directional gain from the perspective of antenna arrays and has not yet been integrated into actual communication systems. Improving the spectral efficiency of the entire system remains a challenge. Traditional multi-user beamforming schemes, however, ignore the coupling between antennas, making it impossible to achieve super-directional arrays and, consequently, unable to improve system spectral efficiency when using compact base station arrays.

[0098] To address this issue, a multi-user super-directional beamforming algorithm needs to be developed. This algorithm should account for the coupling between antennas and better distinguish and process the communication signals between different users. By using this algorithm, the system's spectral efficiency and capacity can be significantly improved to meet the growing communication needs.

[0099] To this end, the present invention incorporates the coupling effect between antennas into the analysis model in a compact antenna array, and provides a multi-user beamforming precoding algorithm to achieve improved spectrum efficiency.

[0100] Example 1

[0101] 2.1 Solution 1 of the present invention: Super-directional zero-forcing multi-user transmission

[0102] Consider that there are M antennas on the base station side, communicating with K end users at the same time, and their respective channel state information is [h1, h2, ..., h K ], satisfying M ≥ K. According to formula (14), the directivity coefficient D of the u-th terminal user is u for:

[0103] where a u is the beamforming vector of u terminal users. In order to suppress the interference of other users and maximize the directional gain of the target user, the present invention proposes the following optimization problem:

[0104] This problem is a convex optimization problem with linear constraints. It can be solved using optimization toolboxes such as CVX and Gurobi. However, it requires multiple iterations, resulting in high complexity and inability to meet the real-time communication requirements of base stations. This paper proposes an optimal, low-complexity solution by leveraging the progressive orthogonality of different user channels.

[0105] First, orthogonalize the interference user channel, is the matrix composed of the interference user channel vector, then the orthogonalized interference user standard orthogonal basis is in:

[0106] Consider constructing a unitary matrix Meet U H U=I M , the last N (N≤K-1) columns of the unitary matrix U are the interfering user channel space span{h i , i=1,...,K,i≠u} Where N is the dimension of the interfering user channel space. If N < K-1, then the standard orthogonal basis is N non-zero column vectors, and these N non-zero column vectors are selected as the last N columns of U. It should be noted that in the last N columns of the unitary matrix U, the first column does not need to be Column 2 is The order can be disrupted as long as any two columns are different.

[0107] make

[0108] in To satisfy the linear constraints in the optimization problem, let

[0109] in

[0110] make

[0111] in Ψ and Υ are also block matrices.

[0112] but

[0113] So the optimization problem (21) can be transformed into

[0114] Analogous to formula (18), the closed-form solution of this problem is

[0115] According to formula (23), we can get

[0116] For the construction of the unitary matrix U, only the last N (N≤K-1) columns of U are needed to be the interfering user channel space span {h i , i=1, ..., K, i≠u}. This embodiment adopts the following scheme. Of course, other schemes are also acceptable as long as they meet the condition of U, such as Schmidt orthogonalization.

[0117] First construct the total interference covariance matrix:

[0118] R int Do SVD decomposition to get R int =W H ΛW (31)

[0119] The first N columns of W are the unit orthogonalized channels of the interfering users, that is, Since W itself is a unitary matrix, U can be constructed as: U = [MN columns after W, N columns before W] (32)

[0120] The steps to obtain the super-directional zero-forcing precoding matrix for each terminal user are as follows:

[0121] S1, loop 1: u=1,…,K;

[0122] S2. Calculate the interference covariance matrix according to formula (30);

[0123] S3. Calculate the SVD decomposition of the interference covariance matrix, as shown in formula (31);

[0124] S4. Construct a unitary matrix U according to formula (32);

[0125] S5. Refer to formula (24) to obtain η u ;

[0126] S6. Refer to formula (25) to obtain the matrix Ξ;

[0127] S7, refer to formula (28) to obtain α u ;

[0128] S8. Refer to formula (29) to obtain the precoding matrix a of the u-th terminal user u ;

[0129] End loop 1.

[0130] Therefore, the present invention proposes a super-directional antenna array multi-user precoding method, comprising:

[0131] For the terminal user u, construct the unitary matrix The last N (N≤K-1) columns of the unitary matrix U are the interfering user channel space span{h i , i=1,...,K,i≠u}, where N is the dimension of the interfering user channel space, represents the channel state information of the i-th terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M ≥ K;

[0132] Truncation matrix U H h u The first MN rows of the matrix η are obtained u ,in h u represents the channel state information of the u-th terminal user, and the superscript H represents the conjugate transpose;

[0133] Truncation matrix U H The first MN rows and columns of ZU are used to obtain the matrix Ξ, where matrix The elements in Z represent the coupling coefficients between any two antennas;

[0134] Calculate the precoding matrix of the u-th terminal user in Superscripts indicate conjugation.

[0135] 2.2 Solution 2 of the present invention: Super-directional interference null space projection method

[0136] Considering that the first solution requires multiple matrix operations, the present invention proposes a simplified solution of the first solution: a super-directional interference null space projection method.

[0137] Consider the optimization problem again

[0138] The solution to this optimization problem in this scheme is to first find the optimal solution of the objective function, and then project this optimal solution onto the null space of the interfering user.

[0139] According to formula (18), the optimal solution of the objective function is:

[0140] The null space of the interfering user can be obtained using equation (32), and after defining R = W, the MN column (35)

[0141] Then the projection of the optimal solution on the null space of the interfering user is

[0142] Therefore, the present invention proposes another super-directional antenna array multi-user precoding method, comprising:

[0143] For the terminal user u, construct the unitary matrix The first N (N≤K-1) columns of the unitary matrix W are the standard orthogonal basis of the interference user channel space span {hi, i=1, ..., K, i≠u}, where N is the dimension of the interference user channel space, represents the channel state information of the i-th terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M ≥ K;

[0144] The matrix R is obtained by cutting the last MN columns of the unitary matrix W, where

[0145] Calculate the precoding matrix of the u-th terminal user in Represents the channel state information of the u-th terminal user, the matrix The elements in Z represent the coupling coefficients between any two antennas, the superscript H represents conjugate transpose, and the superscript * represents conjugate.

[0146] 2.3 Solution 3 of the Invention: Regularized Super-Directional Zero-Forcing Multi-User Transmission

[0147] In actual super-directional multi-user communication systems, system capacity can decrease due to factors such as ohmic loss and inaccurate channel estimation. This paper proposes a third solution: regularized super-directional zero-forcing multi-user transmission. This solves the following optimization problem:

[0148] where Z R =Z+Λ (38)

[0149] Λ is the regularization matrix. Note that the solution to optimization problem (37) is the same as that of optimization problem (21). Here are three methods for determining Λ.

[0150] In the first method, Λ is determined by the material and structure of the antenna unit. Consider the radiation resistance of the antenna to be R rad , in the array, the radiation resistance of the entire antenna array is affected by coupling and becomes: R rad =R rad Z. Therefore, the radiation efficiency of the antenna is:

[0151] The gain of an antenna is the product of its radiation efficiency and directivity:

[0152] Substituting into formula (39), G can be expressed as

[0153] Available

[0154] For a dipole antenna, the antenna loss r loss for

[0155] Where a is the radius of the dipole antenna, L is the length, f is the operating frequency, μ is the magnetic permeability of the material, and σ is the electrical conductivity of the material.

[0156] Radiation resistance R rad Then:

[0157] R rad ≈24.7(kL / 2) 2.5 (43)

[0158] In the second approach, Λ is determined by the inaccuracy of the channel estimate. Consider that the channel estimate for each user has zero mean and variance σ 2 Gaussian white noise, that is, the channel estimate of the u-th terminal user for:

[0159] where n uTo estimate Gaussian noise, satisfy n u ~C(0,∈ 2 ), that is, n u Obey zero mean and variance ∈ 2 Complex Gaussian distribution, ||h u ||=1. According to the calculation method of the elements in Z in formula (12), Z R The calculation method of the elements is

[0160] in is the expectation operator. Then

[0161] Among them I M is an M×M matrix.

[0162] The third method is to consider both ohmic loss and channel estimation error at the same time.

[0163] 3.1 Specific application steps

[0164] Through the schemes 1 to 3 proposed in the present invention, the precoding matrix a of the u-th terminal user can be calculated. u .

[0165] Further, let P tot is the base station transmission power, each user has equal power distribution, and the Gaussian white noise power is σ 2 . Then the transmit signal-to-noise ratio is:

[0166] Consider K as the total number of terminal users communicating, and the precoding matrix of the u-th terminal user is a u , the channel state information is h u , then the total system throughput SE is

[0167] Each beamforming vector is subject to a power constraint such that the transmit power of each user is (When considering ohmic loss or channel estimation error, ).

[0168] 3.2 Simulation results

[0169] First, we simulated the signal enhancement effect of the proposed solution on the target user and the signal suppression effect on other users. Without loss of generality, the number of antennas in this simulation was set to 20, the spacing was 0.25 wavelengths, the number of users was 4, the target user was located at 76°, and the other users were located at -51°, 9°, and 39°, respectively. The resulting pattern of super-directional zero-forcing beamforming for the target user is shown in Figure 1.

[0170] As can be seen from FIG1 , the signal strength at the perspective of the target user is the strongest, while the signal strength at the perspectives of other users is close to 0, indicating that the first solution of the present invention can effectively enhance the signal of the target user while reducing interference to other users.

[0171] Next, a spectrum efficiency-SNR comparison chart of Scheme 1 of the present invention, Scheme 2 of the present invention, traditional maximum ratio transmission, and zero-forcing transmission schemes is simulated under a multi-user scenario. In this simulation, the number of antennas is set to 20, the spacing is 0.25 times the wavelength, and the number of users is 8. The simulation results are shown in Figure 2.

[0172] As can be seen from Figure 2, the present invention achieves a significant improvement in spectrum efficiency compared to traditional maximum ratio transmission and zero-forcing transmission schemes by considering the coupling in the compact array and utilizing its super-directivity. In the entire SNR range, the first scheme of the present invention performs best because it not only utilizes the enhancement of user signals by super-directivity but also considers the influence of interference from other users. The second scheme of the present invention does not perform as well as the first scheme of the present invention because it simply projects the optimal solution of super-directivity shaping onto the null space of the interfering user, but is worse than the traditional maximum ratio transmission and zero-forcing schemes. However, since maximum ratio transmission and zero-forcing transmission ignore the coupling of the antenna array and do not utilize its super-directivity, their performance is inferior to the scheme proposed by the present invention at all SNRs.

[0173] Next, the system spectrum efficiency is simulated considering ohmic loss, and the comparison of the third solution of the present invention is added. Considering that each antenna works in the 1.6 GHz frequency band, the material is copper, the radius is 0.75 mm, the length is 85 mm, and the magnetic permeability is 4π×10 -7 , the conductivity is 5.8×10 7 , the number of antennas is 20, the spacing is 0.25 wavelength, the number of users is 8, and the simulation results are shown in Figure 3.

[0174] As can be seen from FIG3 , since the ohmic loss is not taken into account, the first solution of the present invention performs poorly, while the third solution of the present invention improves the spectrum efficiency by introducing the regularization matrix and performs the best among all the solutions.

[0175] Example 2

[0176] A network device, comprising:

[0177] Construction unit, used to construct a unitary matrix for the terminal user u The last N (N≤K-1) columns of the unitary matrix U are the interfering user channel space span{h i , i=1,...,K,i≠u}, where N is the dimension of the interfering user channel space, represents the channel state information of the i-th terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M ≥ K;

[0178] The first interception unit is used to intercept the matrix U H h u The first MN rows of the matrix η are obtained u ,in h u represents the channel state information of the u-th terminal user, and the superscript H represents the conjugate transpose;

[0179] The second interception unit is used to intercept the matrix U H The first MN rows and columns of ZU are used to obtain the matrix Ξ, where matrix The elements in Z represent the coupling coefficients between any two antennas;

[0180] The calculation unit is used to calculate the precoding matrix of the u-th terminal user in The superscript * indicates conjugation.

[0181] The relevant technical solutions are the same as those in Example 1 and will not be described again here.

[0182] Another network device, comprising:

[0183] Construction unit, used to construct a unitary matrix for the terminal user u The first N (N≤K-1) columns of the unitary matrix W are the interfering user channel space span {h i , i=1,...,K,i≠u}, where N is the dimension of the interfering user channel space, represents the channel state information of the i-th terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M ≥ K;

[0184] The truncation unit is used to truncate the last MN columns of the unitary matrix W to obtain the matrix R, where

[0185] The calculation unit is used to calculate the precoding matrix of the u-th terminal user in The superscript * indicates conjugation, h u Represents the channel state information of the u-th terminal user, the matrix The elements in Z represent the coupling coefficients between any two antennas, and the superscript H represents the conjugate transpose.

[0186] The relevant technical solutions are the same as those in Example 1 and will not be described again here.

[0187] Example 3

[0188] An electronic device, comprising:

[0189] processor; and

[0190] a memory for storing executable instructions of the processor;

[0191] The processor is configured to execute the super-directional antenna array multi-user precoding method described in embodiment 1 by executing the executable instructions.

[0192] The relevant technical solutions are the same as those in Example 1 and will not be described again here.

[0193] Example 4

[0194] A computer-readable storage medium stores computer-executable instructions. When a processor executes the computer-executable instructions, the super-directional antenna array multi-user precoding method as described in Example 1 is implemented.

[0195] The relevant technical solutions are the same as those in Example 1 and will not be described again here.

[0196] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A super-directional antenna array multi-user precoding method, characterized in that: include: For end user u, construct a unitary matrix The last N (N≤K-1) columns of the unitary matrix U are the interfering user channel space span{h i , i=1,...,K,i≠u}, where N is the dimension of the interfering user channel space, represents the channel state information of the ith terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M≥K is satisfied; Intercept matrix U H h u The first MN rows of the matrix η u ,in h u represents the channel state information of the u-th terminal user, and the superscript H represents the conjugate transpose; Intercept matrix U H The first MN rows and columns of ZU are used to obtain the matrix Ξ, where matrix The elements in Z represent the coupling coefficients between any two antennas; Calculate the precoding matrix of the u-th terminal user in The superscript * indicates conjugation.

2. The super-directional antenna array multi-user precoding method according to claim 1, characterized in that: In the intercept matrix U H Before obtaining the matrix Ξ from the first MN rows and the first MN columns of ZU, the method further includes: updating the matrix Z to Z+Λ, where is the regularization matrix of the matrix Z.

3. The super-directional antenna array multi-user precoding method according to claim 2, characterized in that: The regularization matrix Λ is: R rad ≈24.7(kL / 2) 2.5 Among them, r loss and R rad are the loss and radiation impedance of the antenna, I M is an M×M unit matrix, L, a, f, μ, σ, and k are the length, radius, operating frequency, magnetic permeability, electrical conductivity, and wave number of the antenna, respectively.

4. The super-directional antenna array multi-user precoding method according to claim 2, characterized in that: The regularization matrix Λ is: Among them, ε 2 is the Gaussian noise power, k(θ, φ) is the antenna pattern function, θ and φ are the far-field coordinate components in the spherical coordinate system, and I M is the M×M identity matrix.

5. The super-directional antenna array multi-user precoding method according to claim 2, characterized in that: The regularization matrix Λ is: R rad ≈24.7(kL / 2) 2.5 Among them, r loss and R rad are the loss and radiation impedance of the antenna, I M is an M×M unit matrix, L, a, f, μ, σ and k are the length, radius, operating frequency, magnetic permeability, electrical conductivity and wave number of the antenna respectively, ε 2 is the Gaussian noise power, k(θ, φ) is the antenna pattern function, θ and φ are the far-field coordinate components in the spherical coordinate system.

6. The super-directional antenna array multi-user precoding method according to any one of claims 1 to 5, characterized in that: The constructed unitary matrix Specifically: Construct the total interference covariance matrix: R int Do SVD decomposition to get: R int =In H ΛW The unitary matrix U is: U = [MN columns after W, N columns before W].

7. The super-directional antenna array multi-user precoding method according to claim 1, characterized in that: matrix Among them, z mn represents the coupling coefficient between the mth and nth antennas, k(θ, φ) is the antenna pattern function, θ and φ are the far-field coordinate components in the spherical coordinate system, k is the wave number of the antenna, is the unit vector in the spherical coordinate system, r m and r n are the coordinates of the mth and nth antennas respectively, m=1,…,M, n=1,…,M.

8. The super-directional antenna array multi-user precoding method according to claim 1, characterized in that: The last N (N≤K-1) columns of the unitary matrix U are the interfering user channel space span{h i , i=1,...,K,i≠u}, including: make is a matrix composed of interfering user channel vectors. If N=K-1, the last K-1 columns of the unitary matrix U are in: If N<K-1, calculate Then N non-zero vectors will be obtained, and the N non-zero vectors are selected as the last N columns of U.

9. A super-directional antenna array multi-user precoding method, characterized in that: include: For end user u, construct a unitary matrix The first N (N≤K-1) columns of the unitary matrix W are the interfering user channel space span {h i , i=1,...,K,i≠u}, where N is the dimension of the interfering user channel space, represents the channel state information of the ith terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M≥K is satisfied; The matrix R is obtained by cutting the last MN columns of the unitary matrix W, where Calculate the precoding matrix of the u-th terminal user in h u represents the channel state information of the u-th terminal user, the matrix The elements in Z represent the coupling coefficients between any two antennas, the superscript H represents conjugate transpose, and the superscript * represents conjugation.

10. A network device, characterized in that: include: Construction unit, used to construct a unitary matrix for the terminal user u The last N (N≤K-1) columns of the unitary matrix U are the interfering user channel space span{h i , i=1,...,K,i≠u}, where N is the dimension of the interfering user channel space, represents the channel state information of the ith terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M≥K is satisfied; The first interception unit is used to intercept the matrix U H h u The first MN rows of the matrix η u ,in h u represents the channel state information of the u-th terminal user, and the superscript H represents the conjugate transpose; The second interception unit is used to intercept the matrix U H The first MN rows and columns of ZU are used to obtain the matrix Ξ, where matrix The elements in Z represent the coupling coefficients between any two antennas; A calculation unit, used to calculate the precoding matrix of the u-th terminal user in The superscript * indicates conjugation.

11. A network device, characterized in that: include: Construction unit, used to construct a unitary matrix for the terminal user u The first N (N≤K-1) columns of the unitary matrix W are the interfering user channel space span {h i , i=1,...,K,i≠u}, where N is the dimension of the interfering user channel space, represents the channel state information of the ith terminal user, M is the total number of antennas on the network device side, K is the total number of terminal users communicating, and M≥K is satisfied; The truncation unit is used to truncate the last MN columns of the unitary matrix W to obtain the matrix R, where A calculation unit, used to calculate the precoding matrix of the u-th terminal user in The superscript * indicates conjugation, h u represents the channel state information of the u-th terminal user, the matrix The elements in Z represent the coupling coefficients between any two antennas, and the superscript H represents the conjugate transpose.

12. An electronic device, characterized in that: include: processor; as well as A memory, configured to store executable instructions of the processor; The processor is configured to execute the super-directional antenna array multi-user precoding method according to any one of claims 1 to 9 by executing the executable instructions.

13. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions. When the processor executes the computer-executable instructions, the super-directional antenna array multi-user precoding method as described in any one of claims 1 to 9 is implemented.

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