CN113708804A - Whale algorithm-based user scheduling and simulated beam selection optimization method - Google Patents

Abstract

The invention discloses an optimization method for user scheduling and simulation beam selection based on whale algorithm. The method includes the following steps: transforming an optimization problem model into a non-convex NP-hard problem model; transforming the inequality constraints of the problem model into a penalty function The binary constraints are transformed into the characteristics of the algorithm search population; the transformed inequality constraints are multiplied by the indicator factor and the penalty coefficient, and then superimposed on the original optimization objective to construct a fitness function to obtain an analog beam set that matches the user set; Analog beam matching: select the best analog beam for each user; after matching the analog beam, determine whether all users in the user set have completed matching, and when all users are matched, perform channel scheduling according to the analog beam set that matches the user set . The invention solves the joint optimization problem of user scheduling and beam selection for the hybrid mmWave system, and further improves the performance of the system.

Description

User Scheduling and Simulation Beam Selection Optimization Method Based on Whale Algorithm

technical field

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

Background technique

For massive MIMO-mmWave systems, the traditional all-digital beamforming method is almost inapplicable 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 all-digital beamforming makes the system complexity and power consumption unbearable when the number of antennas is large. Hybrid beamforming, which divides beamforming into a low-dimensional digital part and an RF analog part, is a low-cost massive MIMO technology. In the RF analog part, each RF is connected to all antennas (a subset of all antennas) through an interface, a fully connected (partially connected) array structure. The design of analog beamforming is of great significance to improve system performance.

Generally, in a multi-user system, when the number of users is greater than the number of service resources, user scheduling needs to be performed to further improve the spectral efficiency of the system. Among the existing related studies, some have studied the joint design of user scheduling and beam selection in multi-user massive MIMO systems with lens antenna arrays; some have studied the joint design of user scheduling and analog beams in multi-user hybrid mmWave systems. , a local optimal solution based on differential convex function (DC) programming is derived. However, the local optimal scheme is iterative, and its solution is highly dependent on the initial iterative value; others have derived a low-complexity solution based on a greedy method, but its computational complexity is also high when the system is large. . Therefore, a new method for joint design of user scheduling and analog beams in hybrid mmWave systems is investigated to achieve a better trade-off between performance and complexity.

SUMMARY OF THE INVENTION

In order to overcome the defects and deficiencies existing in the prior art that the algorithm and the optimal performance are greatly different, the present invention provides an optimization method for user scheduling and analog beam selection based on the whale algorithm, which maximizes the optimization by combining user scheduling and analog beam selection. The reachability and rate of the system reduce the computing power required by the applicable large-scale system, have high compatibility, reduce the cost of communication system construction, and reduce the delay of users matching channels in the case of multiple users.

In order to achieve the above object, the present invention adopts the following technical solutions:

The present invention provides a user scheduling and simulation beam selection optimization method based on the whale algorithm, comprising the following steps:

Establish a problem model with joint optimization of user scheduling and simulation beam selection maximization and rate as the optimization goal, and transform it into a non-convex NP-hard problem model;

Transform the inequality constraints of the problem model into the form of penalty functions, and the binary constraints into the characteristics of the algorithm search population;

Multiply the transformed inequality constraint by the indicator factor and the penalty coefficient, superimpose it on the original optimization objective, construct a fitness function, and obtain an analog beam set matching the user set;

Analog beam matching: Use multiple beam classifiers to divide the downlink channel between the base station and the selected user into multiple different beam classes, and select the best analog beam for each user;

After the analog beams are matched, it is determined whether all the users in the user set have completed the matching, and when all the users are matched, the channel scheduling is performed according to the analog beam set matched with the user set.

As a preferred technical solution, the establishment of a problem model with joint optimization of user scheduling and simulation beam selection maximization and rate as the optimization goal, the optimization goal is expressed as:

The first constraint:

Second constraint:

The third constraint:

Fourth constraint:

是波束分配矩阵，

是Δ中的元素，用于标识波束分配矩阵中对用户k是否分配为波束b，

表示用户k信号干扰加噪声比。in,

is the beam allocation matrix,

is an element in Δ, used to identify whether user k is allocated as beam b in the beam allocation matrix,

represents the interference-plus-noise ratio of the user k signal.

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

The individual constraints are expressed as:

是波束分配矩阵，

是Δ中的元素，用于标识波束分配矩阵中对用户k是否分配为波束b，

表示用户k信号干扰加噪声比，F_i、H_j和G是指示函数，N_RF表示系统容量。where μ _i > 0, v _j > 0 and ω > 0 are penalty factors,

is the beam allocation matrix,

is an element in Δ, used to identify whether user k is allocated as beam b in the beam allocation matrix,

represents the interference-to-noise ratio of the user k signal, F _i , H _j and G are indicator functions, and N _RF represents the system capacity.

As a preferred technical solution, the binary constraints are converted into the characteristics of the algorithm search population, and the BWOA is used to process the binary constraints. The update position of the BWOA is a binary variable, and the position update of the search agent in the BWOA is expressed as:

where x ∈ {SEM, SUP, SFP}, p _WOA is a random number uniformly distributed in [0, 1], C( ) represents the complement operation, B _x is the step size calculated by the transfer function, based on the transfer function The function converts the continuous search space into binary behavior.

As a preferred technical solution, the transfer function adopts an s-shaped or v-shaped transfer function.

作为SEM阶段的传递函数，采用

作为SUP阶段的传递函数，采用

作为SFP阶段的传递函数，总的表示为：As the preferred technical solution, using

As the transfer function of the SEM stage, adopt

As the transfer function of the SUP stage, we use

As the transfer function of the SFP stage, the total expression is:

B _SEM = T ₁ (A·D)

B _SUP = T ₂ (A·D)

B _SFP = T ₃ (A·D)

where A is the coefficient vector and D represents the distance between 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

Among them, r is a random variable obeying the [0,1] distribution, C=2·r, a represents the nonlinear convergence factor, t and t _max are the iteration index and the maximum number of iterations.

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

表示用户k信号干扰加噪声比，

是波束分配矩阵，P表示基站处的传输功率，

表示码本。in,

represents the interference-to-noise ratio of the user k signal,

is the beam allocation matrix, P represents the transmission power at the base station,

represents the codebook.

The invention also provides a user scheduling and analog beam selection optimization system based on the whale algorithm, including: an optimization problem model conversion module, a constraint conversion module, an optimization target conversion module, an analog beam matching module, and a channel scheduling module;

The optimization problem model conversion module is used to establish a problem model with joint optimization of user scheduling and simulation beam selection maximization and rate as the optimization goal, and convert it into a non-convex NP-hard problem model;

The constraint conversion module is used to convert the inequality constraint of the problem model into the form of a penalty function, and the binary constraint is converted into the feature of the algorithm search population;

The optimization target conversion module is used to multiply the transformed inequality constraints by the indicator factor and the penalty coefficient, and then superimpose it on the original optimization target, construct a fitness function, and obtain an analog beam set matching the user set;

The analog beam matching module is configured to use multiple beam classifiers to divide the downlink channel between the base station and the selected user into multiple different beam classes, and select the best analog beam for each user;

The channel scheduling module is used to determine whether all users in the user set have completed matching after matching the analog beams, and when all users are matched, perform channel scheduling according to the analog beam set that matches the user set;

There is also a base station and a transmit precoder;

The base station is provided with N _BS antennas and N _RF radio frequency chains. The base station adopts a full-array hybrid structure. Each radio frequency chain is connected to the base station antenna through an analog phase shift network. The Saleh-Valenzuela channel model is used to describe the millimeter wave system. channel response;

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

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

是基站对用户k选择的模拟波束码字b，模拟波束码字b为码本

中第b个模拟波束，σ²表示方差。where P represents the transmission power at the base station,

is the analog beam codeword b selected by the base station for user k, and the analog beam codeword b is the codebook

In the b-th simulated beam, σ ² represents the variance.

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

(1) The global optimization scheme based on WOA of the present invention solves the joint optimization problem of user scheduling and beam selection for the hybrid mmWave system. Since the joint optimization problem of user scheduling and wave speed selection is a constrained integer programming problem, the integer variable adopts binary WOA The algorithm uses the penalty function method for constraint processing. In addition, a nonlinear convergence factor is introduced to balance the exploration and development of bubble net search in WOA, which further improves the performance of the system, maximizes the reachability and speed of the system, and reduces the applicable The computing power required by the large-scale system has high compatibility, reduces the cost of communication system construction, and reduces the delay of user matching channels in the case of multiple users.

(2) The binary WOA algorithm adopted by the present invention has fast convergence speed, low complexity and better performance than existing algorithms.

Description of drawings

1 is a schematic flowchart of the user scheduling and simulation beam selection optimization method based on the whale algorithm of the present invention;

Fig. 2 is a schematic diagram of an iterative optimization process based on whale algorithm of the present invention;

Figure 3 is a schematic diagram of the comparison of the average and rate changes of different schemes under different signal-to-noise ratios;

4 is a schematic diagram of the relationship between the computational complexity of the present invention and the number of served users;

5 is a schematic diagram of the effectiveness of the present invention under SNR=5dB;

6 is a schematic diagram of the relationship between the average sum rate and the number of service users when SNR=15dB according to the present invention;

7 is a schematic diagram showing the comparison of the convergence of the “WOA” scheme with a linear convergence factor and a nonlinear convergence factor of the present invention when SNR=-5dB;

FIG. 8 is a schematic diagram showing the variation of the average sum rate with the number of search agents in the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, 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, but not to limit the present invention.

As shown in FIG. 1 , this embodiment provides an optimization method for user scheduling and analog beam selection based on the whale algorithm, including the following steps:

Establish a problem model with joint optimization of user scheduling and simulation beam selection maximization and rate as the optimization goal, and transform it into a non-convex NP-hard problem model;

Transform the inequality constraints of the problem model into the form of penalty functions, and the binary constraints into the characteristics of the algorithm search population;

Multiply the transformed inequality constraint by the indicator factor and the penalty coefficient, superimpose it on the original optimization objective, construct a fitness function, and obtain an analog beam set matching the user set;

Analog beam matching: Use multiple beam classifiers to divide the downlink channel between the base station and the selected user into multiple different beam classes, and select the best analog beam for each user;

After the analog beams are matched, it is determined whether all the users in the user set have completed the matching, and when all the users are matched, the channel scheduling is performed 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 process of its analog beam scheduling. The downlink multi-user MIMO-mmWave system is provided with a base station (BS), and the base station is within its working range. Serve K users. The base station (BS) is equipped with N _BS antennas and N _RF radio frequency (RF) chains. The BS sends N _s data streams to the user, where N _s ≤ N _RF .

由L个有限的散射路径组成，可以表示为：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. Let each user be equipped with one antenna, and the number of users is greater than the system capacity, that is, K>N _RF . And the Saleh-Valenzuela channel model is used to describe the channel response of the mmWave system. Therefore, the channel between BS and user k

It consists of L finite scattering paths, which can be expressed as:

where α _k,m is the complex gain coefficient of the m-th path, ρ _k is the path loss between the base station and user k, φ _k,m is the transmit angle (AoD) of the m-th path at user k, and a _BS (φ _k,m ) ^H represents the transmit antenna array response vector of Uniform Linear Array (ULA), and H represents the conjugate transpose.

In this embodiment, a _BS (φ _k,m ) is specifically:

a _BS (φ _k,m ) is the response vector of the transmit antenna array of Uniform Linear Array (ULA), d is the antenna spacing, and λ is the signal wavelength.

和

分别为模拟预编码器和数字预编码器。模拟预编码器W_a通过移相网络在射频链上实现，数字预编码器W_d应用于基带数字数据。用户k处的接收信号表示如下：In a hybrid mmWave system, the transmit precoder W=W _a W _d , where

and

are an analog precoder and a digital precoder, respectively. The analog precoder W _a is implemented on the radio frequency chain through a phase shifting network, and the digital precoder W _d is applied to the baseband digital data. The received signal at user k is represented as follows:

为发射信号，

n_k～N(0,σ²)为加性复高斯噪声。in

to transmit a signal,

n _k to N(0,σ ² ) are additive complex Gaussian noise.

其中

表示

的基数，

并表示如下：The analog precoder W _a consists of a predefined codebook

in

express

the base,

and said as follows:

This embodiment considers that the baseband precoder W _d is an identity matrix. Therefore, the effective channel gain from the BS selecting the analog beam codeword b to the user k can be expressed as:

是BS对用户k选择的码本

中的第b个模拟波束。毫米波多用户下行链路MIMO系统的可达和速率可以表示为：where P represents the transmission power at the BS,

is the codebook selected by the BS for user k

The b-th analog beam in . The reachability and rate of the mmWave multi-user downlink MIMO system can be expressed as:

表示用户k信号干扰加噪声比(SINR)，以及：in

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

是用户间干扰，可定义为：in

is the inter-user interference, which can be defined as:

where ^wi is the analog beam selected at the BS side.

The optimization goal of this embodiment is to maximize the sum rate by jointly optimizing user scheduling and analog beam selection, and the formula is as follows:

In addition, four constraints must be met:

The first constraint:

Second constraint:

The third constraint:

Fourth constraint:

是波束分配矩阵，

是Δ中的元素，用于标识波束分配矩阵中对用户k是否分配为波束b。第一个约束条件表示

是二进制的。具体来说，如果波束b分配给用户k，

否则

第二个约束条件确保每个用户最多只能分配一个波束。第三个约束条件确保每个波束最多只能分配给一个用户。第四个约束条件表示从K个用户到

个模拟波束最多有N_RF个非重叠分配。in,

is the beam allocation matrix,

is an element in Δ, used to identify whether user k is allocated as beam b in the beam allocation matrix. The first constraint expresses

is binary. Specifically, if beam b is assigned to user k,

otherwise

The second constraint ensures that at most one beam can be assigned to each user. The third constraint ensures that each beam can be assigned to at most one user. The fourth constraint states that from K users to

There are at most N _RF non-overlapping assignments for an analog beam.

Combining the optimization goal and four constraints in this embodiment, it can be seen that the duality of the beam allocation matrix, and the base station's allocation of beams to users is a non-convex NP-hard problem, and the global optimization scheme based on exhaustive search has exponential computational complexity. degree, which is unacceptable when the scheduling scale is large. Furthermore, the local optimal solution based on successive convex approximation (SCA) is iterative, and its solution is highly dependent on the initial iterative value. In order to overcome the shortcomings of the traditional scheme, this embodiment first proposes a real-time application scheme based on machine learning, and then proposes a low-complexity approximation global optimal optimization scheme based on the whale optimization algorithm.

Firstly, a WOA-based method for solving non-convex NP-hard problems is proposed. The traditional WOA algorithm is divided into three stages: search for prey (SFP), shrinkage and surround mechanism (SEM) and spiral position update (SUP). In the SFP phase, each whale randomly selects a location and updates its location to the best search agent. The SEM and SUP phases are used for humpback whales' bubble-net attacks, continuously updating their position as they approach the position of their prey (the best search agent). SFP belongs to the exploratory stage, while SEM and SUP belong to the development stage. Since the WOA algorithm includes both the exploration phase and the development phase, the WOA algorithm can trade off between the exploration phase and the development phase, so as to obtain an approximate global optimal solution.

Since the traditional WOA method is for unconstrained continuous variable optimization problems, and the non-convex NP-hard problem is a constrained optimization problem, the application of the WOA method needs to deal with the constraints in the non-convex NP-hard problem. For the last three constraints , using a simple and effective constraint processing method: the penalty function method, which is converted into a penalty function through the penalty factor. Below, first rewrite the last three constraints as follows:

Then, the penalty function is expressed as:

where μ _i > 0, v _j > 0 and ω > 0 are penalty factors, and F _i , H _j and G are indicator functions. The index function Fi is defined as, Fi ( _fi ( _Δ ))=0 when _fi (Δ) _≤0 , and Fi _{( fi} (Δ))=1 when _fi (Δ)>0. Similarly, the index functions H _j and G.

The fitness function of the optimization objective value of a non-convex NP-hard problem can be written as:

In order to deal with the first binary constraint, the present embodiment adopts binary WOA (BWOA) instead of traditional WOA. Unlike traditional WOA, the update position of BWOA is a binary variable instead of a continuous variable. The location update of the search agent in BWOA is expressed as:

作为SEM阶段的传递函数，

作为SUP阶段的传递函数，

作为SFP阶段的传递函数。总的可以表示为：where x ∈ {SEM, SUP, SFP}, p _WOA is a random number uniformly distributed in [0, 1], and C( ) denotes the complement operation, which flips all bits of the position in the search agent. B _x is the step size calculated by the transfer function, which transforms the continuous search space into binary behavior. There are two main types of transfer functions: s-shaped and v-shaped. The choice of different transfer functions affects system performance. Therefore, choose

As the transfer function for the SEM stage,

As the transfer function of the SUP stage,

as the transfer function of the SFP stage. The total can be expressed as:

B _SEM = T ₁ (A·D)

B _SUP = T ₂ (A·D)

B _SFP = T ₃ (A·D)

where A is the coefficient vector and D represents the distance between 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)|

Among them, r is a random variable obeying the [0,1] distribution, C=2·r, a represents the convergence factor, and the convergence factor decreases linearly from 2 to 0. In order to achieve a good balance between development and exploration, this embodiment proposes a nonlinear convergence factor, namely:

where t and _tmax are the iteration index and the maximum number of iterations.

As shown in Figure 2, when the number of iterations is small (high probability exploration, ie SFP stage), the decline rate of the nonlinear convergence factor is slower than that of the linear convergence factor, which can improve the global search ability of WOA. When the number of iterations is large (high probability development, ie SEM and SUP stages), the nonlinear convergence factor decreases faster than the linear convergence factor, thus ensuring the convergence speed and accuracy. Therefore, the nonlinear convergence factor can control the balance between exploration and exploitation more effectively.

In this embodiment, a comparative experiment on the computational complexity of each optimization scheme is carried out, and the compared schemes specifically include: a global optimal algorithm based on exhaustive search, a local optimal algorithm based on D.c. (differential convex) programming, and the latest greedy method-based algorithm. low-complexity algorithms;

1. The scheme based on WOA:

假设最大迭代次数T_w，该算法的计算复杂度为：The complexity of the proposed algorithm based on WOA mainly comes from calculating the fitness function, and the computational complexity of the fitness function is

Assuming the maximum number of iterations _Tw , the computational complexity of the algorithm is:

2. Global optimal solution (ES) based on exhaustive search:

The ES scheme calculates the feasible set of all user and beam pairs, and the computational complexity is:

in,

3. Local optimal algorithm based on D.c. (differential convex) programming:

优化变量和

凸线性约束，因此每次迭代的计算复杂度为：The convex optimization problem at each iteration has

optimization variables and

Convex linear constraints, so the computational complexity of each iteration is:

Assuming that the maximum number of iterations is T _d , the computational complexity is:

4. The latest low-complexity scheme based on greedy methods:

计算复杂度为：The search space dimension of the greedy method scheme is

The computational complexity is:

It can be seen from the above that 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. ML methods have the lowest complexity. Therefore, the computational complexity of the two proposed solutions and the existing three solutions to the non-convex NP-hard problem can be ranked in descending order as follows:

CLT _e > CLT _d > CLT _w > CLT _g

较大时，本发明的优化方法具有更好的降低计算复杂度的效果，在减少调度时延上更具优势；Especially when N _BS , K and

When it is larger, the optimization method of the present invention has a better effect of reducing the computational complexity, and has more advantages in reducing the scheduling delay;

其中β是路径损耗指数，D_k表示BS与用户k之间的距离。设β＝3.76，D_k为均匀分布在10～15之间的随机变量值。本实施例还设置了N_RF＝4,N_BS＝16,K＝10和N_u＝4(如果没有指定)。对于毫米波信道，

＝5mm，φ_k,m均匀分布在0和2π之间。此外，本实施例将BS端的模拟波束码本数

提出的基于WOA方法的鲸鱼种群N＝5000，基于WOA方法的最大迭代次数I_max＝20，收敛阈值∈＝10^-7，惩罚因子{μ_i},{v_i},ω设置为10⁹。模拟结果来自montecarlo模拟，进行了1000个信道实现。In this embodiment, simulation results are provided to evaluate the performance of the optimization method proposed by the present invention, and the path loss of the kth user is

where β is the path loss index, and D _k represents the distance between the BS and user k. Let β=3.76, and D _k is a random variable value uniformly distributed between 10 and 15. This embodiment also sets N _RF = 4, N _BS = 16, K = 10 and _Nu = 4 (if not specified). For mmWave channels,

=5mm, φ _k,m is uniformly distributed between 0 and 2π. In addition, in this embodiment, the number of analog beam codebooks at the BS

The proposed whale population based on WOA method is N=5000, the maximum number of iterations based on WOA method I _max =20, the convergence threshold ∈=10 ^-7 , and the penalty factor {μ _i },{vi _} ,ω is set to 10 ⁹ . The simulation results are from a montecarlo simulation with 1000 channel implementations.

As shown in Figure 3, the average sum rate changes under different SNRs under five different schemes are given, the exhaustive search scheme (denoted as "ES" in the legend), the WOA-based scheme (denoted as "ES" in the legend) "WOA"), the d.c-based scheme (denoted as "D.c." in the legend), the greedy method scheme (denoted as "greedy" in the legend), and the naive method scheme in which the user randomly selects an analog beam (denoted as "" in the legend" naive”). The results show that the performance of all six schemes improves with the increase of SNR. It is also noted that the "ES" scheme has the best performance, the "Naive" scheme has the worst performance, and the "WOA" scheme outperforms the "D.c." scheme and the "Greedy" scheme.

As shown in Fig. 4, the complexity comparison of different schemes and the number of served users K is described, where SNR=5dB. It can be seen from Figure 4 that the complexity of the "WOA" scheme is lower than that of the "D.c." scheme and higher than that of the "Greedy" scheme. Furthermore, the complexity of the "WOA" scheme grows slowly with increasing K.

As shown in Figure 5, the effectiveness of the scheme proposed in this embodiment at SNR=5dB is verified, and the cumulative distribution function (CDF) is given; it can be seen from the figure that the CDF curve of the "WOA" scheme is close to " ES" scheme.

As shown in Figure 6, the relationship between the average sum rate and the number of users K is shown, where SNR=15dB. The average sum rate of the "WOA" and "Greedy" schemes increases with K. In addition, the "WOA" scheme has a larger performance advantage than the "greedy" scheme, so the "WOA" scheme has greater potential when dealing with large-scale systems.

As shown in Figure 7, the convergence of the "WOA" scheme with a linear convergence factor (denoted as "linear" in the legend) and the "WOA" scheme with a nonlinear convergence factor (denoted as "nonlinear" in the legend) is compared , where SNR=-5dB. As can be seen from Figure 7, the "WOA" scheme ("Linear" scheme) for the "Linear" factor converges when the number of iterations is 3, while the "WOA" scheme ("Nonlinear" scheme) for the "Nonlinear" factor converges at the iteration Convergence at times 7. Obviously, both the "linear" factorial scheme and the "non-linear" factorial scheme converge fast. Furthermore, the achievability and rate of the "non-linear" factorial scheme is significantly greater than that of the "linear" scheme. To sum up, when solving non-convex NP-hard problems, the "non-linear" factorial scheme is more beneficial to balance global search and local exploitation.

As shown in Figure 8, it is shown that the performance of the “WOA” scheme is highly dependent on the number of search agents, and 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-mentioned embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited by the above-mentioned embodiments, and any other changes, modifications, substitutions, combinations, The simplification should be equivalent replacement manners, which are all included in the protection scope of the present invention.

Claims (10)

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,

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 adopted

As a transfer function of the SEM stage, use is made of

As a transfer function of the SUP stage, adopt

As 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,

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 codebook

Middle (b) analog beam, σ²The variance is indicated.

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