阅读说明：本技术 基于鲸鱼算法的用户调度和模拟波束选择优化方法 (Whale algorithm-based user scheduling and simulated beam selection optimization method ) 是由 赵赛 邹章晨 唐冬 黄高飞 于 2021-07-28 设计创作，主要内容包括：本发明公开了一种基于鲸鱼算法的用户调度和模拟波束选择优化方法,该方法包括下述步骤：将优化问题模型转化为非凸的NP难问题模型；将问题模型的不等式约束转化为罚函数的形式,二进制约束转化为算法搜索种群的特征；将转化后的不等式约束乘以指示因子和惩罚系数后,叠加到原优化目标上,构建适应度函数,得到与用户集匹配的模拟波束集；模拟波束匹配：为每个用户选择最佳的模拟波束；经过匹配模拟波束后,判断用户集中所有用户是否完成匹配,当所有用户匹配完成时,根据与用户集匹配的模拟波束集进行信道的调度。本发明解决针对混合mmWave系统的用户调度和波束选择的联合优化问题,进一步提高了系统的性能。(The invention discloses a whale algorithm-based user scheduling and simulated beam selection optimization method, which comprises the following steps: converting the optimization problem model into a non-convex NP difficult problem model; converting inequality constraints of the problem model into a form of a penalty function, and converting binary constraints into characteristics of an algorithm search population; after multiplying the converted inequality constraints by an indicator factor and a penalty coefficient, superposing the inequality constraints on an original optimization target, and constructing a fitness function to obtain a simulated beam set matched with the user set; and (3) analog beam matching: selecting an optimal analog beam for each user; and after the analog beams are matched, judging whether all the users in the user set finish matching or not, and when all the users finish matching, scheduling channels according to the analog beam set matched with the user set. The invention solves the problem of joint optimization of user scheduling and beam selection aiming at the hybrid mmWave system, and further improves the performance of the system.)

1. A user scheduling and simulated beam selection optimization method based on a whale algorithm is characterized by comprising the following steps:

establishing a problem model taking joint optimization user scheduling and simulation beam selection maximization and rate as optimization targets, and converting the problem model into a non-convex NP difficult problem model;

converting inequality constraints of the problem model into a form of a penalty function, and converting binary constraints into characteristics of an algorithm search population;

after multiplying the converted inequality constraints by an indicator factor and a penalty coefficient, superposing the inequality constraints on an original optimization target, and constructing a fitness function to obtain a simulated beam set matched with the user set;

and (3) analog beam matching: dividing a downlink channel between a base station and a selected user into a plurality of different beam classes by using a plurality of beam classifiers, and selecting an optimal analog beam for each user;

and after the analog beams are matched, judging whether all the users in the user set finish matching or not, and when all the users finish matching, scheduling channels according to the analog beam set matched with the user set.

2. The whale algorithm based user scheduling and simulated beam selection optimization method according to claim 1, wherein the problem model is established with a joint optimization of user scheduling and simulated beam selection maximization and rate as an optimization objective, and the optimization objective is expressed as:

the first constraint condition is:

the second constraint condition is as follows:

the third constraint condition is as follows:

the fourth constraint condition is as follows:

wherein the content of the first and second substances,is a matrix of beam assignments made of,is an element in delta that identifies whether user k is assigned as beam b in the beam assignment matrix,representing the user k signal to interference plus noise ratio.

3. The whale algorithm based user scheduling and simulated beam selection optimization method according to claim 1, wherein the inequality constraints of the problem model are converted into the form of a penalty function expressed as:

the constraints are expressed as:

wherein, mu_i＞0，v_j> 0 and ω > 0 are penalty factors,is a matrix of beam assignments made of,is an element in delta that identifies whether user k is assigned as beam b in the beam assignment matrix,representing the signal-to-interference-plus-noise ratio, F, of user k_i、H_jAnd G is an indicator function, N_RFRepresenting the system capacity.

4. The whale algorithm-based user scheduling and simulated beam selection optimization method according to claim 1, wherein the binary constraint is transformed into a characteristic of an algorithm search population, and the binary constraint is processed by using BWOA, an updated position of the BWOA is a binary variable, and a position update of a search agent in the BWOA is represented as:

wherein x ∈ { SEM, SUP, SFP }, p_WOAIs uniformly distributed in [0,1]]Wherein C (-) represents a complement operation, B_xIs the step size calculated by the transfer function based on which the continuous search space is converted into a binary behavior.

5. The whale algorithm based user scheduling and simulated beam selection optimization method according to claim 4, wherein the transfer function is an s-shaped or v-shaped transfer function.

6. The whale algorithm based user scheduling and analog beam selection optimization method of claim 4, wherein the optimization method is adoptedAs a transfer function of the SEM stage, use is made ofAs a transfer function of the SUP stage, adoptAs a transfer function of the SFP stage, the overall representation is:

B_SEM＝T₁(A·D)

B_SUP＝T₂(A·D)

B_SFP＝T₃(A·D)

where A is the coefficient vector and D represents the current best search agent Δ^*(t) and the current search agent Δ (t).

7. The whale algorithm based user scheduling and simulated beam selection optimization method as claimed in claim 6, wherein a non-linear convergence factor is constructed in the calculation of the system vector A, specifically expressed as:

A＝2a·r-a

wherein r is obedient [0,1]]A random variable of distribution, C ═ 2 · r, a denotes a nonlinear convergence factor, t and t_maxIs the iteration index and the maximum number of iterations.

8. The whale algorithm-based user scheduling and simulated beam selection optimization method according to claim 1, wherein the fitness function is constructed by:

wherein the content of the first and second substances,representing the signal-to-interference-plus-noise ratio for user k,is a beam allocation matrix, P denotes the transmission power at the base station,representing a codebook.

9. A whale algorithm based user scheduling and simulated beam selection optimization system, comprising: the system comprises an optimization problem model conversion module, a constraint conversion module, an optimization target conversion module, a simulation beam matching module and a channel scheduling module;

the optimization problem model conversion module is used for establishing a problem model taking the maximization and the rate of the joint optimization user scheduling and the simulation beam selection as optimization targets and converting the problem model into a non-convex NP difficult problem model;

the constraint conversion module is used for converting inequality constraints of the problem model into a form of a penalty function, and binary constraints are converted into characteristics of an algorithm search population;

the optimization target transformation module is used for superposing the transformed inequality constraint multiplied by an indicator factor and a penalty coefficient to the original optimization target to construct a fitness function to obtain a simulation beam set matched with the user set;

the analog beam matching module is used for dividing a downlink channel between the base station and the selected user into a plurality of different beam classes by utilizing a plurality of beam classifiers and selecting the optimal analog beam for each user;

the channel scheduling module is used for judging whether all users in the user set finish matching after the matched analog wave beams pass through, and when all users finish matching, scheduling the channels according to the analog wave beam set matched with the user set;

a base station and a transmitting precoder are also arranged;

the base station is provided with N_BSAn antenna and N_RFThe base station adopts a full-array mixed structure, each radio frequency chain is connected with a base station antenna through an analog phase shift network, and a Saleh-Vallenzuela channel model is adopted to describe the channel response of the millimeter wave system;

the transmit precoder comprises an analog precoder and a digital precoder, the analog precoder is implemented on a radio frequency chain through a phase shift network, a predefined codebook is employed, and the digital precoder is applied to baseband digital data.

10. The whale algorithm based user scheduling and analog beam selection optimization system of claim 9, wherein the effective channel gain of a base station selecting an analog beam codeword b to user k is expressed as:

where, P denotes the transmission power at the base station,is the analog beam code word b selected by the base station for the user k, and the analog beam code word b is a codebookMiddle (b) analog beam, σ²The variance is indicated.

Technical Field

The invention relates to the technical field of user scheduling and beam selection, in particular to a user scheduling and simulated beam selection optimization method based on a whale algorithm.

Background

For massive MIMO-mmWave systems, the traditional all-digital beamforming method is hardly applicable in practical applications, because in all-digital beamforming, each antenna is equipped with a Radio Frequency (RF) chain, and each RF chain occupies a dedicated baseband processor, so that all-digital beamforming makes the complexity and power consumption of the system difficult to bear in the case of a large number of antennas. Hybrid beamforming, which divides beamforming into a low-dimensional digital part and a radio frequency analog part, is a low-cost massive MIMO technique. In the RF analog part, each RF is connected to all antennas (a subset of all antennas) through one interface, i.e. a fully connected (partially connected) array structure. The design of analog beamforming has important significance for improving the system performance.

Generally, in a multi-user system, when the number of users is greater than the number of service resources, user scheduling is required to further improve the spectrum efficiency of the system. In the existing related researches, some researches the problem of the joint design of user scheduling and beam selection in a lens antenna array multi-user large-scale MIMO system; some researches the joint design of user scheduling and analog beams in a multi-user hybrid mmWave system, and derives a local optimal solution based on differential convex function (DC) planning. However, the local optimal solution is iterative, with the solution highly dependent on the initial iteration value; a low-complexity solution based on a greedy method is also derived, but the calculation complexity is higher when the system size is larger. Therefore, new methods for user scheduling and analog beam joint design in hybrid mmWave systems are studied to achieve better performance and complexity tradeoffs.

Disclosure of Invention

In order to overcome the defect and the defect that the algorithm is greatly different from the optimal performance in the prior art, the invention provides the whale algorithm-based user scheduling and analog beam selection optimization method.

In order to achieve the purpose, the invention adopts the following technical scheme:

the invention provides a whale algorithm-based user scheduling and simulated beam selection optimization method, which comprises the following steps:

establishing a problem model taking joint optimization user scheduling and simulation beam selection maximization and rate as optimization targets, and converting the problem model into a non-convex NP difficult problem model;

converting inequality constraints of the problem model into a form of a penalty function, and converting binary constraints into characteristics of an algorithm search population;

after multiplying the converted inequality constraints by an indicator factor and a penalty coefficient, superposing the inequality constraints on an original optimization target, and constructing a fitness function to obtain a simulated beam set matched with the user set;

and (3) analog beam matching: dividing a downlink channel between a base station and a selected user into a plurality of different beam classes by using a plurality of beam classifiers, and selecting an optimal analog beam for each user;

and after the analog beams are matched, judging whether all the users in the user set finish matching or not, and when all the users finish matching, scheduling channels according to the analog beam set matched with the user set.

As a preferred technical solution, the problem model with the joint optimization of user scheduling and maximization of simulated beam selection and rate as optimization objectives is established, and the optimization objectives are expressed as:

the first constraint condition is:

the second constraint condition is as follows:

the third constraint condition is as follows:

the fourth constraint condition is as follows:

wherein the content of the first and second substances,is a matrix of beam assignments made of,is an element in delta that identifies whether user k is assigned as beam b in the beam assignment matrix,representing the user k signal to interference plus noise ratio.

As a preferred technical solution, the inequality constraint of the problem model is converted into a form of a penalty function, and the penalty function is expressed as:

the constraints are expressed as:

wherein, mu_i＞0,v_j> 0 and ω > 0 are penalty factors,is a matrix of beam assignments made of,is an element in delta that identifies whether user k is assigned as beam b in the beam assignment matrix,representing the signal-to-interference-plus-noise ratio, F, of user k_i、H_jAnd G is an indicator function, N_RFRepresenting the system capacity.

As a preferred technical solution, the binary constraint is converted into a feature of an algorithm search population, specifically, BWOA is used to process the binary constraint, an updated position of the BWOA is a binary variable, and a position update of a search agent in the BWOA is represented as:

wherein x ∈ { SEM, SUP, SFP }, p_WOAIs uniformly distributed in [0,1]]Wherein C (-) represents a complement operation, B_xIs the step size calculated by the transfer function based on which the continuous search space is converted into a binary behavior.

Preferably, the transfer function is an s-shaped or v-shaped transfer function.

As a preferred technical solution, use is made ofAs a transfer function of the SEM stage, use is made ofAs a transfer function of the SUP stage, adoptAs a transfer function of the SFP stage, the overall representation is:

B_SEM＝T₁(A·D)

B_SUP＝T₂(A·D)

B_SFP＝T₃(A·D)

where A is the coefficient vector and D represents the current best search agent Δ^*(t) and the current search agent Δ (t).

As a preferred technical solution, a nonlinear convergence factor is constructed in the calculation of the system vector a, which is specifically expressed as:

A＝2a·r-a

wherein r is obedient [0,1]]A random variable of distribution, C ═ 2 · r, a denotes a nonlinear convergence factor, t and t_maxIs the iteration index and the maximum number of iterations.

As a preferred technical solution, the constructing a fitness function is specifically expressed as:

wherein the content of the first and second substances,representing the signal-to-interference-plus-noise ratio for user k,is a beam allocation matrix, P denotes the transmission power at the base station,representing a codebook.

The invention also provides a whale algorithm-based user scheduling and simulated beam selection optimization system, which comprises the following steps: the system comprises an optimization problem model conversion module, a constraint conversion module, an optimization target conversion module, a simulation beam matching module and a channel scheduling module;

the optimization problem model conversion module is used for establishing a problem model taking the maximization and the rate of the joint optimization user scheduling and the simulation beam selection as optimization targets and converting the problem model into a non-convex NP difficult problem model;

the constraint conversion module is used for converting inequality constraints of the problem model into a form of a penalty function, and binary constraints are converted into characteristics of an algorithm search population;

the optimization target transformation module is used for superposing the transformed inequality constraint multiplied by an indicator factor and a penalty coefficient to the original optimization target to construct a fitness function to obtain a simulation beam set matched with the user set;

the analog beam matching module is used for dividing a downlink channel between the base station and the selected user into a plurality of different beam classes by utilizing a plurality of beam classifiers and selecting the optimal analog beam for each user;

the channel scheduling module is used for judging whether all users in the user set finish matching after the matched analog wave beams pass through, and when all users finish matching, scheduling the channels according to the analog wave beam set matched with the user set;

a base station and a transmitting precoder are also arranged;

the base station is provided with N_BSAn antenna and N_RFThe base station adopts a full-array mixed structure, and each radio frequency chain passes through a moduleThe quasi-phase shift network is connected with a base station antenna, and a Saleh-Vallenzuela channel model is adopted to describe the channel response of the millimeter wave system;

the transmit precoder comprises an analog precoder and a digital precoder, the analog precoder is implemented on a radio frequency chain through a phase shift network, a predefined codebook is employed, and the digital precoder is applied to baseband digital data.

As a preferred technical solution, the effective channel gain from the base station to select the analog beam codeword b to the user k is represented as:

where, P denotes the transmission power at the base station,is the analog beam code word b selected by the base station for the user k, and the analog beam code word b is a codebookMiddle (b) analog beam, σ²The variance is indicated.

Compared with the prior art, the invention has the following advantages and beneficial effects:

(1) the invention solves the joint optimization problem of user scheduling and wave beam selection aiming at a hybrid mmWave system based on a global optimization scheme of WOA, and because the joint optimization user scheduling and wave speed selection problem is a constrained integer programming problem, an integer variable adopts a binary WOA algorithm, constraint processing adopts a penalty function method, in addition, a nonlinear convergence factor is introduced to balance exploration and development of bubble network search in WOA, the performance of the system is further improved, the reachable rate and the speed of the system are maximized, the computing capacity required by the applicable large-scale system is reduced, the compatibility is higher, the cost of building a communication system is reduced, and the time delay of a user matched with a channel under the condition of multiple users is reduced.

(2) The binary WOA algorithm adopted by the invention has the advantages of high convergence speed, low complexity and better performance than the existing algorithm.

Drawings

FIG. 1 is a schematic flow chart of a user scheduling and simulated beam selection optimization method based on whale algorithm according to the present invention;

FIG. 2 is a schematic diagram of an optimization iteration flow based on whale algorithm;

FIG. 3 is a graph showing the average and rate variation of different schemes in comparison with different signal-to-noise ratios;

FIG. 4 is a diagram illustrating the relationship between the computational complexity and the number of served users according to the present invention;

FIG. 5 is a graphical illustration of the effectiveness of the present invention at a SNR of 5 dB;

fig. 6 is a diagram illustrating the relationship between the average sum rate and the number of service users when the SNR is 15 dB;

FIG. 7 is a graph showing the comparison of the convergence of the "WOA" scheme with linear convergence factor and non-linear convergence factor of the present invention at SNR of-5 dB;

FIG. 8 is a graph illustrating the variation of the average sum rate with the number of search agents according to the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

As shown in fig. 1, the present embodiment provides a whale algorithm-based user scheduling and analog beam selection optimization method, which includes the following steps:

establishing a problem model taking joint optimization user scheduling and simulation beam selection maximization and rate as optimization targets, and converting the problem model into a non-convex NP difficult problem model;

converting inequality constraints of the problem model into a form of a penalty function, and converting binary constraints into characteristics of an algorithm search population;

after multiplying the converted inequality constraints by an indicator factor and a penalty coefficient, superposing the inequality constraints on an original optimization target, and constructing a fitness function to obtain a simulated beam set matched with the user set;

and (3) analog beam matching: dividing a downlink channel between a base station and a selected user into a plurality of different beam classes by using a plurality of beam classifiers, and selecting an optimal analog beam for each user;

and after the analog beams are matched, judging whether all the users in the user set finish matching or not, and when all the users finish matching, scheduling channels according to the analog beam set matched with the user set.

This embodiment takes a downlink multi-user MIMO-mmWave system as an example to illustrate the procedure of analog beam scheduling, and the downlink multi-user MIMO-mmWave system is provided with a Base Station (BS) which serves K users in its working range. Base Station (BS) is equipped with N_BSAntenna and N_RFA Radio Frequency (RF) chain. BS sends N to user_sA data stream of which N_s≤N_RF。

In this embodiment, the base station adopts a full-array hybrid structure, and each radio frequency chain is connected to the base station antenna through an analog phase shift network. Each user is provided with an antenna, and the number of users is larger than the system capacity, i.e. K > N_RF. And the Saleh-valencuela channel model is used to describe the channel response of the millimeter wave system. Thus, the channel between the BS and user kConsists of L finite scattering paths, which can be expressed as:

wherein alpha is_k,mIs the complex gain coefficient, p, of the mth path_kIs the path loss between the base station and user k, phi_k,mRepresents the launch angle (AoD), a, of the mth path at user k_BS(φ_k,m)^HRepresenting the transmit antenna array response vector of a Uniform Line Array (ULA) and H representing the conjugate transpose.

In this embodiment, a_BS(φ_k,m) The method specifically comprises the following steps:

a_BS(φ_k,m) Is the transmit antenna array response vector of a Uniform Linear Array (ULA), d represents the antenna spacing, and λ represents the signal wavelength.

In a hybrid millimeter wave system, the transmit precoder W ═ W_aW_dWhereinAndrespectively, an analog precoder and a digital precoder. Analog precoder W_aDigital precoder W implemented on a radio frequency chain through a phase shift network_dApplied to baseband digital data. The received signal at user k is represented as follows:

whereinIn order to transmit the signal(s),n_k～N(0,σ²) Is additive complex gaussian noise.

Analog precoder W_aFrom a predefined codebookWhereinTo representThe base number of (c) is,and is represented as follows:

this embodiment considers the baseband precoder W_dIs an identity matrix. Thus, the effective channel gain for BS to select analog beam codeword b to user k can be expressed as:

where P denotes the transmission power at the BS,is the codebook selected by the BS for user kThe b-th analog beam of (1). The achievable sum rate for a millimeter wave multi-user downlink MIMO system can be expressed as:

whereinRepresents the user k signal-to-interference-plus-noise ratio (SINR), and:

whereinIs inter-user interference and can be defined as:

wherein wⁱIs an analog beam selected at the BS side.

The optimization goal of this embodiment is to maximize sum rate by jointly optimizing user scheduling and analog beam selection, whose formula is shown below:

in addition, four constraints are required to be satisfied:

the first constraint condition is:

the second constraint condition is as follows:

the third constraint condition is as follows:

the fourth constraint condition is as follows:

wherein the content of the first and second substances,is a matrix of beam assignments made of,is an element in Δ, for identifying a beamWhether user k is assigned as beam b in the assignment matrix. First constraint representationIs binary. In particular, if beam b is assigned to user k,otherwiseThe second constraint ensures that each user can only be allocated a maximum of one beam. A third constraint ensures that each beam can only be allocated to one user at most. The fourth constraint represents the number of users from K toWith a maximum of N analog beams_RFNon-overlapping allocations.

Combining the optimization target and the four constraint conditions of the embodiment, it can be seen that the duality of the beam allocation matrix and the problem that the base station is not convex NP-hard to allocate beams to users, and the global optimization scheme based on exhaustive search has exponential computational complexity, which is not acceptable when the scheduling scale is large. Furthermore, the locally optimal solution based on Successive Convex Approximation (SCA) is iterative, the solution of which is highly dependent on the initial iteration values. In order to overcome the defects of the conventional scheme, the embodiment firstly provides a real-time application scheme based on machine learning, and then provides a low-complexity approximate global optimal optimization scheme based on a while optimization algorithm.

Firstly, a method for solving a non-convex NP difficult problem based on WOA is provided, and the traditional WOA algorithm is divided into three stages: search prey (SFP), shrink wrap-around mechanism (SEM), and spiral position update (SUP). During the SFP phase, each whale randomly selects a location and updates its location to the best search agent. SEM and SUP stages are used for bubble net attacks by whales with their location constantly updated as they approach the location of the prey (best search agent). SFP belongs to the exploration phase and SEM and SUP to the development phase. Because the WOA algorithm comprises an exploration phase and a development phase, the WOA algorithm can be balanced between the exploration phase and the development phase, and therefore an approximately global optimal solution is obtained.

Because the traditional WOA method aims at the unconstrained continuous variable optimization problem, but the non-convex NP difficult problem is a constrained optimization problem, the application of the WOA method needs to process the constraints in the non-convex NP difficult problem, and for the last three constraints, a simple and effective constraint processing method, namely a penalty function method, is adopted to convert the non-convex NP difficult problem into a penalty function through a penalty factor. In the following, the last three constraints are first rewritten as follows:

the penalty function is then expressed as:

wherein, mu_i＞0,v_j> 0 and ω > 0 are penalty factors, F_i、H_jAnd G is an indicator function. Index function F_iIs defined as F_i(f_i(Δ)) -0 when f_i(Δ)≤0，F_i(f_i(Δ)) -1 when f_i(Delta) > 0. Similarly, index function H_jAnd G.

The fitness function for the optimal target value of a non-convex NP-hard problem can be written as:

to handle the first binary constraint, the present embodiment replaces the conventional WOA with Binary WOA (BWOA). Unlike conventional WOA, the update location of BWOA is a binary variable rather than a continuous variable. The location update of the search agent in BWOA is represented as:

wherein x is formed by { SEM, SUP, SFP }, and p_WOAIs uniformly distributed in [0,1]]The random number in (1), C (-), represents a complement operation that flips all bits of the position in the search agent. B is_xIs the step size calculated by the transfer function, which is used to convert the continuous search space into a binary behavior. The transfer functions mainly comprise an s-shape and a v-shape, and the selection of different transfer functions influences the system performance. Thus, selectingAs a function of the transfer at the SEM stage,as a function of the transfer of the SUP phase,as a transfer function of the SFP stage. The sum can be expressed as:

B_SEM＝T₁(A·D)

B_SUP＝T₂(A·D)

B_SFP＝T₃(A·D)

where A is the coefficient vector and D represents the current best search agent Δ^*(t) and the current search agent Δ (t). And:

A＝2a·r-a

D＝|C·Δ^*(t)-Δ(t)|

where r is a random variable following the [0,1] distribution, C ═ 2 · r, a denotes the convergence factor, which decreases linearly from 2 to 0. In order to achieve a good balance between development and exploration, the present embodiment proposes a nonlinear convergence factor, namely:

wherein t and t_maxIs the iteration index and the maximum number of iterations.

As shown in fig. 2, when the number of iterations is small (a rough search, that is, SFP stage), the lowering rate of the nonlinear convergence factor is slower than that of the linear convergence factor, and the global search capability of the WOA can be improved. When the iteration number is larger (probably developed, namely SEM and SUP stages), the nonlinear convergence factor is reduced faster than the linear convergence factor, thereby ensuring the convergence speed and precision. Thus, the nonlinear convergence factor can more effectively control the balance between exploration exploitation.

In this embodiment, a comparison experiment of the calculation complexity is performed on each optimization scheme, and the comparison scheme specifically includes: a global optimization algorithm based on exhaustive search, a local optimization algorithm based on D.c. (differential convex) planning and a latest low complexity algorithm based on a greedy method;

1. WOA-based schemes:

the complexity of the proposed WOA-based algorithm mainly comes from the computation of a fitness function with a computational complexity ofAssuming a maximum number of iterations T_wThe computational complexity of the algorithm is:

2. global optimum (ES) based on exhaustive search:

the ES scheme calculates a feasible set of all users and beam pairs, and the calculation complexity is as follows:

wherein the content of the first and second substances,

3. local optimization algorithm based on D.c (differential convex) planning:

the convex optimization problem of each iteration isOptimizing variables andconvex linear constraints, so the computational complexity per iteration is:

assuming that the maximum number of iterations is T_dThen the computational complexity is:

4. the latest low complexity scheme based on greedy approach:

the search space dimension of the greedy approach isThe computational complexity is:

from the above, the exhaustive search method has the highest complexity. The WOA-based method is less complex than the DC method and more complex than the greedy method. The ML method has the lowest complexity. Thus, the computational complexity of the two solutions proposed for the non-convex NP-hard problem and the existing three solutions can be arranged in descending order as follows:

CLT_e＞CLT_d＞CLT_w＞CLT_g

especially when N is_BSK andwhen the scheduling delay is larger, the optimization method has the effect of better reducing the calculation complexity and has more advantages in reducing the scheduling delay;

in this embodiment, a simulation result is provided to evaluate the performance of the optimization method provided by the present invention, and the path loss of the kth user isWhere beta is the path loss exponent, D_kRepresenting the distance between the BS and user k. Let beta be 3.76, D_kThe random variable values are uniformly distributed between 10-15. This embodiment also sets up N_RF＝4,N_BS16, K10 and N_u4 (if not specified). For the millimeter-wave channel,＝5mm，φ_k,mevenly distributed between 0 and 2 pi. In addition, in this embodiment, the number of analog beam codebooks at the BS end is usedThe proposed whale population N is 5000 based on the WOA method, and the maximum iteration number I is based on the WOA method_max20, the convergence threshold e is 10^-7Penalty factor μ_i},{v_iω is set to 10⁹. Simulation results were from montearlo simulations, with 1000 channel realizations.

As shown in fig. 3, the average and rate variation at different signal-to-noise ratios for five different schemes are given, an exhaustive search scheme (denoted as "ES" in the legend), a WOA-based scheme (denoted as "WOA" in the legend), a d.c-based scheme (denoted as "d.c.") a greedy approach scheme (denoted as "greedy" in the legend), and a naive approach scheme (denoted as "naive" in the legend) where the user randomly selects an analog beam. The results show that the performance of all six schemes improves as the signal-to-noise ratio increases. It is also noted that the "ES" scheme performs best, the "Naive" scheme performs worst, and the "WOA" scheme performs better than the "d.c." scheme and the "Greedy" scheme.

As shown in fig. 4, a comparison of the complexity of the different schemes with the number K of served users is described, where SNR is 5 dB. As can be seen from fig. 4, the "WOA" scheme is less complex than the "d.c." scheme and higher than the "Greedy" scheme. Furthermore, the complexity of the "WOA" scheme slowly grows as K increases.

As shown in fig. 5, the effectiveness of the scheme proposed in this embodiment is verified under SNR of 5dB, where a Cumulative Distribution Function (CDF) is given; it can be seen from the figure that the CDF curve of the "WOA" scheme is close to the "ES" scheme.

As shown in fig. 6, the average sum rate is shown in relation to the number K of users, where SNR is 15 dB. The average sum rate of the "WOA" and "Greedy" schemes increases as K increases. Furthermore, the "WOA" scheme has a greater performance advantage than the "greedy" scheme, and thus has greater potential in dealing with large-scale systems.

As shown in fig. 7, the convergence of the "WOA" scheme with a linear convergence factor (denoted "linear" in the legend) is compared with the "WOA" scheme with a non-linear convergence factor (denoted "non-linear" in the legend), where SNR is-5 dB. As can be seen from fig. 7, the "WOA" scheme of the "linear" factor ("linear" scheme) converges at a number of iterations of 3, while the "WOA" scheme of the "non-linear" factor ("non-linear" scheme) converges at a number of iterations of 7. Clearly, both the "linear" factor scheme and the "non-linear" factor scheme converge very fast. Furthermore, the realizations and rates of the "non-linear" factor schemes are significantly greater than the "linear" schemes. In summary, the "non-linear" factor approach is more conducive to balancing global search and local development when solving the non-convex NP-hard problem.

As shown in fig. 8, showing that the "WOA" scheme performance is highly dependent on the number of search agents, by increasing the number of whale populations and the signal-to-noise ratio, performance very close to the optimal solution can be obtained.

The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.