Three-dimensional non-uniform antenna array design method, device and storage medium for Massive MIMO system

Abstract

The present invention discloses a three-dimensional non-uniform antenna array design method, device, and storage medium for a Massive MIMO system, including the following steps: Step 1: constructing a distance relationship between array element positions and user positions and a spatial correlation matrix between array elements based on the arrangement characteristics of the three-dimensional non-uniform antenna array; Step 2: constructing a channel model based on the distance relationship and the spatial correlation matrix between array elements; Step 3: constructing and approximating a system traversal and rate model based on the channel model to obtain an approximated system traversal and rate model; Step 4: establishing an optimization problem with the goal of maximizing the approximated system traversal and rate model, using antenna layout as the optimization variable, and constrained by limited spatial resources and antenna element spacing greater than half a wavelength; Step 5: solving the optimization problem using an enhanced particle swarm optimization algorithm to obtain a three-dimensional non-uniform antenna array topology. This invention can improve the traversal and rate of a communication system.

Description

Technical Field

[0001] The present invention belongs to the field of mobile communication technology, and in particular relates to a three-dimensional non-uniform antenna array design method, device and storage medium for a Massive MIMO system. Background Art

[0002] With the rapid development of technologies such as the Internet of Things, the internet, big data, and cloud computing, the information and communications sector continues to grow and develop. In a fully interconnected, intelligent information world, everything needs to be connected, including people and vehicles, sensors, data, cloud resources, and even robotic agents. However, currently deployed 5G networks are insufficient to meet all the connectivity needs of the future information society. In particular, applications such as remote holographic telepresence, virtual reality (VR), and high-fidelity augmented reality (AR) require data transmission rates of up to 1Tbps, far exceeding the 20Gbps target defined by 5G. To achieve the convergence of information from different mobile networks, the industry has accelerated research on B5G and 6G networks to further deepen mobile connectivity. 6G will provide higher data transmission efficiency, energy efficiency, reliability, and broader, deeper communication coverage than 5G.

[0003] 5G communication system performance improvements in modulation and channel coding have reached their limits. To achieve higher energy and spectral efficiency in B5G / 6G communications, hopes are placed on the spatial dimension. Massive MIMO, a key core technology of 5G, can deeply exploit spatial resources, achieve higher spatial resolution and spectral efficiency, and meet certain capacity gains. Since large-scale antenna arrays are often constrained by limited physical space resources in practical deployments, non-uniform array structures can achieve the same system performance as uniform array structures with fewer antenna elements within the same deployment area, reducing costs while also reducing system complexity and power consumption. On the other hand, three-dimensional antenna array structures can significantly increase the number of ports and expand the size of the antenna array within a limited deployment area. They can also adaptively adjust the radiation angle in both the horizontal and vertical dimensions, providing omnidirectional transmission capabilities. While improving system performance such as channel capacity and spectral efficiency, they overcome the angular blind spots in user differentiation inherent in lower-dimensional arrays. These structures can address the diverse receiver types and user locations expected in typical 6G application scenarios such as the Internet of Things and massive machine-to-machine communications.

[0004] In summary, the existing technology faces the following challenges: Currently, optimization design for one-dimensional linear and two-dimensional planar non-uniform arrays is limited, lacking optimization for three-dimensional non-uniform arrays. Furthermore, existing conclusions regarding the topological characteristics of three-dimensional arrays are mostly derived from analysis of simulation results of given array structures in specific application scenarios, without providing more instructive design guidelines for antenna array topology optimization. Therefore, designing three-dimensional non-uniform antenna arrays for Massive MIMO systems remains a key challenge in the existing technology. Summary of the Invention

[0005] To overcome the shortcomings of the above-mentioned prior art, the present invention aims to provide a method, device, and storage medium for designing a three-dimensional non-uniform antenna array for a Massive MIMO system. The method implements array design by analyzing the analytical relationship between the array element positions of the three-dimensional non-uniform antenna array and the system traversal and rate, thereby improving the traversal and rate of the communication system.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for designing a three-dimensional non-uniform antenna array for a Massive MIMO system includes the following steps:

[0008] Step 1: Based on the layout characteristics of the 3D non-uniform antenna array, construct the distance relationship between the array element position and the user position, as well as the spatial correlation matrix between the array elements;

[0009] Step 2: Construct a channel model based on the distance relationship and the spatial correlation matrix between array elements;

[0010] Step 3: constructing and approximating a system ergodic and rate model based on the channel model to obtain an approximated system ergodic and rate model;

[0011] Step 4: Establish an optimization problem with the goal of maximizing the approximate system traversal and rate model, antenna layout as the optimization variable, and spatial resource limitations and antenna element spacing greater than half a wavelength as constraints.

[0012] Step 5: Use the enhanced particle swarm optimization algorithm to solve the optimization problem and obtain the three-dimensional non-uniform antenna array topology.

[0013] The step 1 is specifically as follows:

[0014] Step 1.1, set the base station to be equipped with N t The distance between the mth transmitting antenna of the base station and the kth user is r. m,k Expressed as:

[0015]

[0016] Among them, ||·|| represents the norm operation, p m =[x m ,y m ,z m ] T ,m=1,…,N t Indicates the position of the mth transmitting element, x m 、y m With z m Corresponding to the positions of the x-axis, y-axis, and z-axis in the rectangular coordinate system, [·] T represents the matrix transpose operation, u k =[r k Ψ k ,r k Φ k ,r k Ω k ] T represents the location of the kth user, r k (k=1,…,K) represents the distance from user k to the coordinate origin, θ k ∈[0,2π] represents the azimuth angle of user k, φ k ∈[-π / 2,π / 2] represents the elevation angle of user k,

[0017] Step 1.2: For any two positions at the base station, m =(x m ,y m ,z m ) and p n =(x n ,y n ,z n ) for the transmitting antennas m and n, the antenna correlation coefficient in the three-dimensional spatial domain can be expressed as:

[0018]

[0019] Where e is the natural index, λ is the wavelength of electromagnetic wave, P a (θ) and P e (φ) represents the horizontal angle power spectrum function (PAS) and vertical angle power spectrum function (PES) of each multipath energy in the horizontal direction and vertical direction, respectively. θ and They represent the azimuth and elevation angles of the electromagnetic wave, respectively. a (θ) and P e (φ) has an independent probability distribution. pn =[x n ,y n ,z n ] T ,n=1,…,N t Indicates the position of the nth transmitting element, x n 、y n With z n They correspond to the positions of the x-axis, y-axis, and z-axis in the rectangular coordinate system. When in a uniform scattering wireless propagation environment, PAS and PES obey uniform distribution, then P a (θ) and P e (φ) are respectively expressed as:

[0020] θ∈[-Δ θ +θ0,Δ θ +θ0]

[0021] θ∈[-Δ φ +φ0,Δ φ +φ0]

[0022] Where θ0 and φ0 represent the mean of the azimuth and elevation angles, respectively; Δ θ and Δ φ Represents the angular distribution range of azimuth and elevation angles respectively;

[0023] Therefore, the spatial correlation matrix R of the three-dimensional antenna array is T It can be expressed as:

[0024]

[0025] The step 2 is specifically as follows:

[0026] Assume that the channel h from the base station to the kth user k Following the spatially correlated Rice fading distribution, h k It can be expressed as:

[0027]

[0028] Among them, K R is the Rice factor, represents the LOS component, represents the NLOS component;

[0029] For the LOS component, in order to reflect the near-field spherical wavefront characteristics, Modeled as:

[0030]

[0031] in,[·]H Represents the conjugate transpose operation of the matrix, r m,k (m=1,…,N t ,k=1,…,K) represents the distance between the mth transmitting antenna of the base station and the kth user.

[0032] For the NLOS component, The statistical method is used to model the model, which is specifically expressed as:

[0033]

[0034] in, Obeys a complex Gaussian distribution with a mean of 0 and a variance of 1, R T Represents the spatial correlation matrix of a 3D antenna array.

[0035] The step 3 is specifically as follows:

[0036] Step 3.1: System traversal and rate R sum It can be expressed as:

[0037]

[0038] in, β k =ρ k Xξ1(r0 / r k ) α is the power received by user k from the base station, X is the unit-decreasing constant of geometric attenuation at the reference distance r0, α is the attenuation exponent, and ξ1 is the shadow fading effect following the log-normal distribution, i.e. is the transmission power of the kth user, P is the total transmission power, is the precoding normalization parameter so that E{||w k || 2}=1,W=[w1,w2,…,w K ];

[0039] Step 3.2: Use Jensen’s inequality to derive the deterministic approximate expression of the system’s ergodic and rate. The system’s ergodic and rate R sum A preliminary approximation is:

[0040]

[0041] in,

[0042] Step 3.3: To simplify the mathematical representation, let Signal power E{|h k w k |2} and interference power E{|h k w j | 2 The approximate solutions of} are expressed as:

[0043]

[0044]

[0045] Finally, the system traverses and the approximation of the rate It can be expressed as:

[0046]

[0047] The step 4 is specifically as follows:

[0048] The base station antenna layout is defined as N t The set of root antenna position vectors: With the optimization goal of maximizing the traversal system and rate approximation, the antenna layout is used as the optimization variable, and the limited space resources and the spacing between transmitting array elements are used as constraints. A three-dimensional antenna array topology optimization problem is established. The optimization problem is expressed as:

[0049] P1:

[0050] stP∈A

[0051]

[0052] Wherein, A represents the limitation of the base station antenna array deployment area.

[0053] The step 5 is specifically as follows:

[0054] Step 5.1: Use enhanced particle swarm optimization to search for the optimal antenna layout. Particles represent antenna layouts P, and the fitness function is defined as:

[0055]

[0056] Among them, f(P) is the fitness function, P represents the base station antenna layout, Represents an approximation of the system ergodic sum rate.

[0057] Step 5.2: Initialize the particle population and calculate the fitness value of each particle;

[0058] Step 5.3: Set the position P that each particle has experienced i Sort by their fitness values to obtain the current individual optimal position and update the current global optimal particle P g ;

[0059] Step 5.4: According to P i Sort all particles in descending order by fitness value and update their speed and position. The update expressions of speed and position are:

[0060]

[0061]

[0062] Where i = 1, 2, ..., S, S is the total number of particles; n = 1, 2, ..., N represents the n-th dimension, N = 3; t is the current iteration number; represents the velocity of the n-dimensional space of the i-th particle at the t-th iteration; represents the position of the n-dimensional space of the i-th particle at the t-th iteration; represents the individual optimal position of the i-th particle in the n-dimensional space at the t-th iteration; represents the global optimal position of the n-dimensional space of the i-th particle at the t-th iteration; c1 and c2 are learning factors, r1 and r2 are random numbers uniformly distributed between [0,1], and w is the inertia weight factor, which is expressed as follows:

[0063]

[0064]

[0065] Among them, w max and w min are the maximum and minimum values of the inertia weight factor, respectively, f i 、 f max and f min are the particle’s current fitness value, average fitness value, maximum fitness value, and minimum fitness value, respectively. s is the standard inertia weight value;

[0066] Step 5.5: Perturb the global optimal particle so that it can jump out of the local optimal solution to explore more areas, so that the global optimal particle can play its maximum value. The perturbation expression of the global optimal particle is:

[0067]

[0068] Where r is a random number that follows the [0,1] distribution, and T is the maximum number of iterations;

[0069] Step 5.6: Loop through steps 5.3 to 5.5 to determine whether the performance requirement is met or the number of iterations reaches the preset maximum iteration value. If the termination condition is met, the optimal solution is directly output.

[0070] A three-dimensional non-uniform antenna array design device for a Massive MIMO system, comprising:

[0071] The first construction module is used to construct a distance relationship between array element positions and users and a spatial correlation matrix between array elements according to the arrangement characteristics of the three-dimensional non-uniform antenna array;

[0072] A second construction module is used to construct a channel model based on the distance relationship and the spatial correlation matrix between array elements;

[0073] An approximation module, configured to construct and approximate a system ergodic and rate model based on the channel model to obtain an approximated system ergodic and rate model;

[0074] Establish a module for maximizing the approximated system traversal and rate model as the goal, using antenna layout as the optimization variable, and constraining spatial resources and antenna element spacing greater than half a wavelength to establish an optimization problem.

[0075] The solution module is used to solve the optimization problem using the enhanced particle swarm algorithm to obtain the three-dimensional non-uniform antenna array topology structure.

[0076] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for designing a three-dimensional non-uniform antenna array for a Massive MIMO system is implemented.

[0077] A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements a three-dimensional non-uniform antenna array design method for a Massive MIMO system according to any one of claims 1 to 6.

[0078] Beneficial effects of the present invention:

[0079] The present invention uses the arrangement characteristics of a three-dimensional non-uniform antenna array to construct a distance relationship between the array element position and the user position and a spatial correlation matrix between the array elements to obtain a channel model and characterize the system traversal and rate model. Then, the system traversal and rate are approximated using the Jensen inequality to obtain a deterministic approximate expression for the system traversal and rate, and further obtains a mathematical relationship between the array element position of the three-dimensional non-uniform antenna array and the system traversal and rate. With the goal of maximizing the approximate system traversal and rate model, the antenna layout is used as the optimization variable, and the optimization problem is established with the constraints of limited spatial resources and the antenna array element spacing being greater than half a wavelength. The enhanced particle swarm algorithm is used to solve the optimization problem to obtain a three-dimensional non-uniform antenna array topology structure. The obtained three-dimensional non-uniform antenna array topology structure can increase the system traversal and rate by at least 10% compared with the traditional antenna array topology structure, further improving system performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 This is a flow chart of a method for designing a three-dimensional non-uniform antenna array for a Massive MIMO system according to an embodiment of the present invention.

[0081] Figure 2 FIG. 4 is a schematic diagram of a three-dimensional non-uniform array Massive MIMO multi-user downlink transmission model according to an embodiment of the present invention.

[0082] Figure 3 The figure is a schematic diagram of the arrangement of elements of a three-dimensional non-uniform antenna array obtained by solving the method according to an embodiment of the present invention.

[0083] Figure 4 Schematic diagram comparing the effects of the method according to the embodiment of the present invention and other methods.

[0084] Figure 5 FIG4 is a structural diagram of a device for designing a three-dimensional non-uniform antenna array for a Massive MIMO system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0085] The present invention will be described in further detail below with reference to the accompanying drawings.

[0086] The present invention discloses a three-dimensional non-uniform antenna array design method for a Massive MIMO system, such as Figure 1 As shown, the following steps are included:

[0087] Step S110: constructing a distance relationship between array element positions and user positions and a spatial correlation matrix between array elements based on the arrangement characteristics of the three-dimensional non-uniform antenna array;

[0088] Step S120: constructing a channel model based on the distance relationship and the spatial correlation matrix between array elements;

[0089] Step S130: constructing and approximating a system ergodic and rate model based on the channel model to obtain an approximated system ergodic and rate model;

[0090] Step S140: Establish an optimization problem with the goal of maximizing the approximated system traversal and rate model, antenna layout as the optimization variable, and spatial resource limitations and antenna element spacing greater than half a wavelength as constraints;

[0091] Step S150: Utilize the enhanced particle swarm optimization algorithm to solve the optimization problem and obtain a three-dimensional non-uniform antenna array topology structure.

[0092] The present invention uses the arrangement characteristics of a three-dimensional non-uniform antenna array to sequentially construct a distance relationship between array element positions and user positions, a spatial correlation matrix between array elements, a channel model, and an approximate model of a system traversal and rate model. The present invention takes maximizing the approximate system traversal and rate model as the goal, uses antenna layout as the optimization variable, and establishes an optimization problem with the constraints of limited spatial resources and antenna element spacing greater than half a wavelength. The enhanced particle swarm algorithm is used to solve the optimization problem and obtain a three-dimensional non-uniform antenna array topology structure, thereby further improving the system traversal and rate.

[0093] like Figure 2 As shown in FIG, a schematic diagram of a three-dimensional non-uniform array Massive MIMO multi-user downlink transmission model in an embodiment of the present invention is shown. Considering a single-cell multi-user Massive MIMO downlink communication scenario equipped with a three-dimensional non-uniform array, assuming that the base station is equipped with N t transmit antennas, and simultaneously communicate with K users equipped with single antennas in a given coverage area. Assume that the number of users is not greater than the number of transmit antennas, that is, N t ≥K, and in N t If an equal power allocation scheme is used on the transmitting antennas, the received signal at the kth user can be expressed as:

[0094]

[0095] Among them, β k is the power received from the base station at user k, β k =ρ k Xξ1(r0 / r k ) α , X is the unit decreasing constant of geometric attenuation at the reference distance r0, α is the attenuation exponent, and ξ1 is the shadow fading effect following the log-normal distribution, that is, is the transmission power of the kth user, and P is the total transmission power; is the precoding normalization parameter so that E{||w k || 2}=1,W=[w1,w2,…,wK ];h k represents the channel from the base station to the kth user; s k and s j represents the transmission symbols of user k and user j, satisfying E{|s k | 2}=E{|s j | 2}=1;w k and w j Represent the precoding vectors from the base station to user k and user j respectively, using the MRT precoding method, then (Symbols are garbled) represents complex Gaussian additive noise at the kth user.

[0096] The distance r between the mth transmitting antenna of the base station and the kth user m,k It can be expressed as:

[0097]

[0098] Among them, ||·|| represents the norm operation, p m =[x m ,y m ,z m ] T ,m=1,…,N t Indicates the position of the mth transmitting element, x m 、y m With z m Corresponding to the positions of the x-axis, y-axis, and z-axis in the rectangular coordinate system, [·] T represents the matrix transpose operation, u k =[r k Ψ k ,r k Φ k ,r k Ω k ] T represents the location of the kth user, r k (k=1,…,K) represents the distance from user k to the coordinate origin, θ k ∈[0,2π] represents the azimuth angle of user k, φ k ∈[-π / 2,π / 2] represents the elevation angle of user k,

[0099] For any two positions at the base station, respectively, p m =(x m ,y m ,z m ) and p n =(x n,y n ,z n ) for the transmitting antennas m and n, the antenna correlation coefficient in the three-dimensional spatial domain can be expressed as:

[0100]

[0101] Where e is the natural index, λ is the wavelength of electromagnetic wave, P a (θ) and P e (φ) represents the horizontal angle power spectrum function (PAS) and vertical angle power spectrum function (PES) of each multipath energy in the horizontal direction and vertical direction, respectively. They represent the azimuth and elevation angles of the electromagnetic wave, respectively. a (θ) and P e (φ) has an independent probability distribution. p n =[x n ,y n ,z n ] T ,n=1,…,N t Indicates the position of the nth transmitting element, x n 、y n With z n They correspond to the positions of the x-axis, y-axis, and z-axis in the rectangular coordinate system. When in a uniform scattering wireless propagation environment, PAS and PES obey uniform distribution, then P a (θ) and P e (φ) are respectively expressed as:

[0102] θ∈[-Δ θ +θ0,Δ θ +θ0]

[0103] θ∈[-Δ φ +φ0,Δ φ +φ0]

[0104] Where θ0 and φ0 represent the mean of the azimuth and elevation angles, respectively; Δ θ and Δ φ Represent the angular distribution range of azimuth and elevation angles respectively.

[0105] The spatial correlation matrix R of the three-dimensional antenna array T It can be expressed as:

[0106]

[0107] Assume that the channel h from the base station to the kth userk Following the spatially correlated Rice fading distribution, h k It can be expressed as:

[0108]

[0109] Among them, K R is the Rice factor, represents the LOS component, Represents the NLOS component.

[0110] For the LOS component, in order to reflect the near-field spherical wavefront characteristics, Modeled as:

[0111]

[0112] in,[·] H Represents the conjugate transpose operation of the matrix, r m,k (m=1,…,N t ,k=1,…,K) represents the distance between the mth transmitting antenna of the base station and the kth user.

[0113] For the NLOS component, The model can be modeled using statistical methods, specifically expressed as:

[0114]

[0115] in, Obeys a complex Gaussian distribution with a mean of 0 and a variance of 1, R T Represents the spatial correlation matrix of a 3D antenna array.

[0116] Since the channel h between the base station and the kth user k If is a random variable, then the system and rate are also random variables. The study of random variables usually adopts statistical methods, so the system traversal and rate are introduced.

[0117] Signal to Interference plus Noise Ratio (SINR) of user k k It can be expressed as:

[0118]

[0119] Furthermore, the instantaneous achievable rate R of user k is k It can be expressed as:

[0120] R k =E{log2(1+SINR k )}

[0121] Finally, the system's traversal and rate R sum It can be expressed as:

[0122]

[0123] Since solving the ergodic sum rate requires a lot of data collection and statistical work, which is operationally complex, the deterministic approximate expressions of the ergodic sum rate of the system are derived using Jensen inequality.

[0124] First, to simplify the mathematical representation, let Then the traversal rate R of user k is k can be re-characterized as:

[0125]

[0126] Then, using Jensen's inequality, we can get the following bounds:

[0127]

[0128]

[0129] Combining the above formula, we can obtain the following boundary inequality, which is specifically expressed as:

[0130]

[0131] Using E{1 / (M+N)}≥1 / E{M+N} and E{1 / N}≥1 / E{N}, we can obtain:

[0132] Then, the above inequality can be further written as:

[0133]

[0134] Finally, we can get:

[0135]

[0136] therefore, Then the system's ergodic and rate R sum A preliminary approximation is:

[0137]

[0138] in,

[0139] In order to simplify the mathematical representation, Then the channel h k It can be further characterized as:

[0140] h k =u k +v k

[0141] Next, the signal power E{|h k w k | 2} and interference power E{|h k w j | 2 The approximate solutions of} are expressed as:

[0142]

[0143]

[0144] Finally, the system traverses and the approximation of the rate It can be expressed as:

[0145]

[0146] The base station antenna layout is defined as N t The set of root antenna position vectors: With the optimization goal of maximizing the traversal system and rate approximation, the antenna layout is used as the optimization variable, and the limited space resources and the spacing between transmitting array elements are used as constraints to establish the three-dimensional antenna array topology optimization problem. The optimization problem can be expressed as:

[0147] P1:

[0148] stP∈A

[0149]

[0150] Wherein, A represents the limitation of the base station antenna array deployment area.

[0151] Since the objective function of the modeled optimization problem is highly nonlinear, has multiple extreme values and is not differentiable, it is impossible to solve the optimization problem using theoretical analytical methods. Therefore, an enhanced particle swarm algorithm is used to solve the modeled optimization problem. The specific steps are as follows:

[0152] (1) The enhanced particle swarm algorithm is used to search for the optimal antenna layout. The particles represent the antenna layout P, and the fitness function is defined as:

[0153]

[0154] Among them, f(P) is the fitness function, P represents the base station antenna layout, Represents the approximate value of the system traversal and rate. (2) Initialize the number of particle populations and calculate the fitness value of each particle.

[0155] (3) The position P that each particle has experienced i Sort by their fitness values to obtain the current individual optimal position and update the current global optimal particle P g .

[0156] (4) According to P i Sort all particles in descending order by fitness value and update their speed and position. The update expressions of speed and position are:

[0157]

[0158]

[0159] Where i = 1, 2, ..., S, S is the total number of particles; n = 1, 2, ..., N represents the n-th dimension, N = 3; t is the current iteration number; represents the velocity of the n-dimensional space of the i-th particle at the t-th iteration; represents the position of the n-dimensional space of the i-th particle at the t-th iteration; represents the individual optimal position of the i-th particle in the n-dimensional space at the t-th iteration; represents the global optimal position of the n-dimensional space of the i-th particle at the t-th iteration; c1 and c2 are learning factors, r1 and r2 are random numbers uniformly distributed between [0,1], and w is the inertia weight factor, which is expressed as follows:

[0160]

[0161]

[0162] Among them, w max and w min are the maximum and minimum values of the inertia weight factor, respectively, f i 、 f max and f min are the particle’s current fitness value, average fitness value, maximum fitness value, and minimum fitness value, respectively. s is the standard inertia weight value.

[0163] (5) The global optimal particle is perturbed so that it can jump out of the local optimal solution to explore more areas, so that the global optimal particle can play its maximum value. The perturbation expression of the global optimal particle is:

[0164]

[0165] Where r is a random number distributed in [0,1], and T is the maximum number of iterations.

[0166] (6) Loop through steps (3) to (5) to determine whether the performance requirement is met or the number of iterations reaches the preset maximum iteration value. If the termination condition is met, the optimal solution is directly output.

[0167] like Figure 3 As shown in FIG, a schematic diagram of the arrangement of elements of a three-dimensional non-uniform antenna array is obtained by solving the optimization problem using an enhanced particle swarm algorithm.

[0168] In addition, the method of the embodiment of the present invention is verified. Assume that the number of users is 4, the number of base station antennas is 64, the center frequency of the signal is f = 28GHz, the base station antenna constraint area is a cube with a side length of 9cm, and PAS and PES obey uniform distribution. The four users are randomly and uniformly distributed in areas 1 to 4 on the surface of a sphere with a radius of 5m. The azimuth angle range of area 1 is 60 degrees to 75 degrees, and the elevation angle range is 20 degrees to 35 degrees; the azimuth angle range of area 2 is 285 degrees to 300 degrees, and the elevation angle range is 20 degrees to 35 degrees; the azimuth angle range of area 3 is 120 degrees to 135 degrees, and the elevation angle range is -35 degrees to -20 degrees; the azimuth angle range of area 4 is 225 degrees to 240 degrees, and the elevation angle range is -35 degrees to -20 degrees. (Symbols are displayed in garbled characters)

[0169] like Figure 4 As shown, the comparison method adopted by the present invention is: a uniform array structure with the same number of antenna elements under the same transmission conditions. It can be seen from the figure that under the same circumstances, the method proposed in the embodiment of the present invention further improves the system traversal and rate by changing the arrangement position of the antenna elements. Specifically, when the signal-to-noise ratio is 15dB, the traversal and rate corresponding to the three-dimensional non-uniform array topology structure obtained by the enhanced particle swarm algorithm can be improved by at least 10% compared with three-dimensional uniform array topologies such as cylindrical arrays, cubic arrays and spherical arrays, and can be improved by more than 40% compared with two-dimensional planar arrays, and can be improved by more than 80% compared with one-dimensional linear arrays.

[0170] The present invention uses the proposed three-dimensional non-uniform antenna array during transmission in a single-cell multi-user Massive MIMO system to effectively improve system traversal and rate performance. Based on the geometric structure of the array elements of the three-dimensional non-uniform array, the present invention establishes an analytical relationship between the arrangement position of the three-dimensional non-uniform antenna array topology and the system traversal and rate. The optimization problem is established with the goal of maximizing the system traversal and rate model, the antenna layout as the optimization variable, and the constraints of limited spatial resources and antenna element spacing greater than half a wavelength. The enhanced particle swarm algorithm is used to solve the optimization problem, and ultimately a three-dimensional non-uniform antenna array arrangement is designed for the base station, which further improves the system traversal and rate.

[0171] The present invention also discloses a three-dimensional non-uniform antenna array design device for a Massive MIMO system, such as Figure 5 As shown, it includes: a first construction module 210, which is used to construct a distance relationship between the array element position and the user position and a spatial correlation matrix between the array elements according to the arrangement characteristics of the three-dimensional non-uniform antenna array; a second construction module 220, which is used to construct a channel model based on the distance relationship and the spatial correlation matrix between the array elements; an approximation module 230, which is used to construct and approximate a system traversal and rate model based on the channel model to obtain an approximate system traversal and rate model; an establishment module 240, which is used to establish an optimization problem with the goal of maximizing the approximate system traversal and rate model, using antenna layout as an optimization variable, and using spatial resource limitations and the antenna element spacing being greater than half a wavelength as constraints; and a solution module 250, which is used to solve the optimization problem using an enhanced particle swarm algorithm to obtain a three-dimensional non-uniform antenna array topology.

[0172] It should be noted that the information interaction, execution process, etc. between the modules of the above-mentioned device are based on the same concept as the method embodiment of the present application. Their specific functions and technical effects can be found in the method embodiment part and will not be repeated here.

[0173] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the division of the above-mentioned functional modules is used as an example for illustration. In actual applications, the above-mentioned functions can be distributed and completed by different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. The functional modules in the embodiment can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of a software functional unit. In addition, the specific names of the functional modules are only for the convenience of distinguishing each other and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here.

[0174] The present invention also discloses a three-dimensional non-uniform antenna array design device for a Massive MIMO system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the three-dimensional non-uniform antenna array design method for a Massive MIMO system is implemented.

[0175] The device may be a computing device such as a desktop computer, laptop, PDA, or cloud server. The device may include, but is not limited to, a processor and memory. Those skilled in the art will appreciate that the device may include more or fewer components, or a combination of certain components, or different components, and may also include, for example, input / output devices, network access devices, etc.

[0176] The processor may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc.

[0177] In some embodiments, the memory may be an internal storage unit of the device, such as a hard disk or memory of the device. In other embodiments, the memory may also be an external storage device of the device, such as a plug-in hard disk equipped on the device, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card, etc. Furthermore, the memory may include both an internal storage unit of the device and an external storage device. The memory is used to store an operating system, an application program, a boot loader (BootLoader), data, and other programs, such as the program code of the computer program. The memory may also be used to temporarily store data that has been output or is about to be output.

[0178] The present invention also discloses a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the computer program implements the above-mentioned three-dimensional non-uniform antenna array design method for a Massive MIMO system.

[0179] Computer-readable media may include at least any entity or device capable of carrying computer program code to a camera / terminal device, recording media, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signals, telecommunications signals, and software distribution media. Examples include USB flash drives, external hard drives, magnetic disks, or optical disks. In some jurisdictions, due to legislation and patent practice, computer-readable media cannot include electric carrier signals or telecommunications signals.

Claims

1. A three-dimensional non-uniform antenna array design method for a Massive MIMO system, characterized in that: The following steps are included: Step 1: Based on the layout characteristics of the 3D non-uniform antenna array, construct the distance relationship between the array element position and the user position, as well as the spatial correlation matrix between the array elements; Step 2: Construct a channel model based on the distance relationship and the spatial correlation matrix between array elements; Step 3: constructing and approximating a system ergodic and rate model based on the channel model to obtain an approximated system ergodic and rate model; Step 4: Establish an optimization problem with the goal of maximizing the approximate system traversal and rate model, antenna layout as the optimization variable, and spatial resource limitations and antenna element spacing greater than half a wavelength as constraints. Step 5: Use the enhanced particle swarm optimization algorithm to solve the optimization problem and obtain the three-dimensional non-uniform antenna array topology; The step 1 is specifically as follows: Step 1.1: Assume that the base station is equipped with N t The distance between the mth transmitting antenna of the base station and the kth user is r. m,k Expressed as: Among them, ||·|| represents the norm operation, p m =[x m ,y m ,z m ] T ,m=1,…,N t Indicates the position of the mth transmitting element, x m 、y m With z m Corresponding to the positions of the x-axis, y-axis, and z-axis in the rectangular coordinate system, [·] T represents the matrix transpose operation, u k =[r k Ψ k ,r k Φ k ,r k Ω k ] T represents the location of the kth user, r k represents the distance from user k to the coordinate origin, k = 1, ..., K, θ k ∈[0,2π] represents the azimuth angle of user k, φ k ∈[-π / 2,π / 2] represents the elevation angle of user k, Step 1.2: For any two positions at the base station, m =(x m ,y m ,z m ) and p n =(x n ,y n ,z n ) for the transmitting antennas m and n, the antenna correlation coefficient in the three-dimensional spatial domain is expressed as: Where e is the natural index, λ is the wavelength of electromagnetic wave, P a (θ) and P e (φ) represents the horizontal angle power spectrum function PAS and vertical angle power spectrum function PES of each multipath energy in the horizontal and vertical directions, respectively, θ and They represent the azimuth and elevation angles of the electromagnetic wave, respectively. a (θ) and P e (φ) has an independent probability distribution; p n =[x n ,y n ,z n ] T ,n=1,…,N t Indicates the position of the nth transmitting element, x n 、y n With z n They correspond to the positions of the x-axis, y-axis, and z-axis in the rectangular coordinate system. When in a uniform scattering wireless propagation environment, PAS and PES obey uniform distribution, then P a (θ) and P e (φ) are respectively expressed as: Where θ0 and φ0 represent the mean of the azimuth and elevation angles, respectively; Δ θ and Δ φ Represents the angular distribution range of azimuth and elevation angles respectively; Therefore, the spatial correlation moment R between array elements is T Can be expressed as: The step 2 is specifically as follows: Assume that the channel h from the base station to the kth user k Following the spatially correlated Rice fading distribution, h k Expressed as: Among them, K R is the Rice factor, represents the LOS component, represents the NLOS component; For the LOS component, in order to reflect the near-field spherical wavefront characteristics, Modeled as: in,[·] H Represents the conjugate transpose operation of the matrix, r m，k represents the distance between the mth transmitting antenna of the base station and the kth user, m = 1, ..., N t , k=1,...,K; For the NLOS component, The statistical method is used to model the model, which is specifically expressed as: in, Obeys a complex Gaussian distribution with a mean of 0 and a variance of 1, R T Represents the spatial correlation moment between array elements; i = 1, ... N t ; The step 5 is specifically as follows: Step 5.1: Use the enhanced particle swarm algorithm to search for the optimal antenna layout. The particles represent the antenna layout P, and the fitness function is defined as: Among them, f(P) is the fitness function, P represents the base station antenna layout, Represents an approximation of the system traversal and rate; Step 5.2: Initialize the particle population and calculate the fitness value of each particle; Step 5.3: Set the position P that each particle has experienced i Sort by their fitness values to obtain the current individual optimal position and update the current global optimal particle P g ; Step 5.4: According to P i Sort all particles in descending order by fitness value and update their speed and position. The update expressions of speed and position are: Where i = 1, 2, ..., S, S is the total number of particles; n = 1, 2, ..., N represents the n-th dimension, N = 3; t is the current iteration number; represents the velocity of the n-dimensional space of the i-th particle at the t-th iteration; represents the position of the n-dimensional space of the i-th particle at the t-th iteration; represents the individual optimal position of the i-th particle in the n-dimensional space at the t-th iteration; represents the global optimal position of the n-dimensional space of the i-th particle at the t-th iteration; c1 and c2 are learning factors, r1 and r2 are random numbers uniformly distributed between [0,1], and w is the inertia weight factor, which is expressed as follows: Among them, w max and w min are the maximum and minimum values of the inertia weight factor, respectively, f i 、 f max and f min are the particle’s current fitness value, average fitness value, maximum fitness value, and minimum fitness value, respectively. s is the standard inertia weight value; Step 5.5: Perturb the global optimal particle so that it can jump out of the local optimal solution to explore more areas, so that the global optimal particle can play its maximum value. The perturbation expression of the global optimal particle is: Where r is a random number that follows the [0,1] distribution, and T is the maximum number of iterations; Step 5.6: Loop through steps 5.3 to 5.5 to determine whether the performance requirement is met or the number of iterations reaches the preset maximum iteration value. If the termination condition is met, the optimal solution is directly output.

2. The method for designing a three-dimensional non-uniform antenna array for a Massive MIMO system according to claim 1, wherein: The step 3 is specifically as follows: Step 3.1: System traversal and rate R sum Expressed as: in, β k =ρ k Xξ1(r0 / r k ) α is the power received by user k from the base station, X is the unit-decreasing constant of geometric attenuation at the reference distance r0, α is the attenuation exponent, and ξ1 is the shadow fading effect following the log-normal distribution, i.e. is the transmission power of the kth user, P is the total transmission power, is the precoding normalization parameter so that E{||w k || 2 }=1,W=[w1,w2,...,w K ]; Step 3.2: Use Jensen’s inequality to derive the deterministic approximate expression of the system’s ergodic and rate. The system’s ergodic and rate R sum It can be roughly approximated as: in, Step 3.3: To simplify the mathematical representation, let Signal power E{|h k w k | 2 } and interference power E{|h k w j | 2 The approximate solutions of} are expressed as: Finally, the system traverses and the approximation of the rate Can be expressed as:

3. The method for designing a three-dimensional non-uniform antenna array for a Massive MIMO system according to claim 1, wherein: The step 4 is specifically as follows: The base station antenna layout is defined as N t The set of root antenna position vectors: With the optimization goal of maximizing the traversal system and rate approximation, the antenna layout is used as the optimization variable, and the limited space resources and the spacing between transmitting array elements are used as constraints. A three-dimensional antenna array topology optimization problem is established. The optimization problem is expressed as: stP∈A Wherein, A represents the limitation of the base station antenna array deployment area.

4. A device for designing a three-dimensional non-uniform antenna array for a Massive MIMO system, executing the method according to any one of claims 1 to 3, characterized in that: include: A first construction module is used to construct a distance relationship between array element positions and user positions and a spatial correlation matrix between array elements based on the arrangement characteristics of the three-dimensional non-uniform antenna array; A second construction module is used to construct a channel model based on the distance relationship and the spatial correlation matrix between array elements; An approximation module, configured to construct and approximate a system ergodic and rate model based on the channel model to obtain an approximated system ergodic and rate model; Establish a module for maximizing the approximated system traversal and rate model as the goal, using antenna layout as the optimization variable, and constraining spatial resources and antenna element spacing greater than half a wavelength to establish an optimization problem. The solution module is used to solve the optimization problem using the enhanced particle swarm algorithm to obtain the three-dimensional non-uniform antenna array topology structure.

5. An electronic device, characterized in that: The invention comprises a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for designing a three-dimensional non-uniform antenna array for a Massive MIMO system as described in any one of claims 1 to 3 is implemented.

6. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for designing a three-dimensional non-uniform antenna array for a Massive MIMO system according to any one of claims 1 to 3 is implemented.

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