Adaptive Bandwidth Allocation for Massive MIMO Systems Based on Multiple Services

Abstract

Aiming at the characteristics of resource periodicity in massive MIMO systems and bandwidth allocation without comprehensive consideration of user service QoS and channel state information, resulting in poor user satisfaction and low bandwidth utilization, this paper proposes an adaptive bandwidth allocation method based on user services. This method comprehensively considers factors, such as user service QoS, channel state information, and resource periodicity, to adaptively allocate bandwidth for users using different services. Firstly, based on the service priority, the user priority is dynamically adjusted according to the current channel state information and the continuous periodicity of the allocation, and the user is scheduled.; Secondly, the dynamic priority is combined with the minimum guaranteed time slot to establish the objective function of adaptive bandwidth allocation. Finally, chaos theory, Levy flight, and reverse learning are integrated to improve the bald eagle optimization algorithm. The improved bald eagle algorithm is used to solve the problem, and the optimal solution to bandwidth allocation is obtained. The simulation shows that compared with the traditional bandwidth allocation method based on user service quality perception, the bandwidth allocation algorithm based on the minimum rate requirement, and the ant colony-based allocation algorithm, the bandwidth allocation method proposed in this paper improves the system utility value, bandwidth utilization rate, throughput, and user satisfaction by 23.70%, 4.22%, 6.55%, and 4.28%, respectively, and better meets the business needs of users.

1. Introduction

Multiple-input multiple-output (MIMO) technology is one of the core technologies of 5G communication [1]. By configuring a large number of antennas at the base station transmitting end, it can effectively improve spectrum utilization, energy efficiency, transmission rate, and communication quality [2,3], which has the potential to meet the rising demand for mobile communication in the future. With the improvement of the quality of life, the types of services are also increasing. In order to enable the massive MIMO system to provide different services for various application scenarios, it is urgent to carry out research on bandwidth allocation that comprehensively considers multiple requirements, such as resource allocation efficiency, throughput, and fairness [4]. Massive MIMO systems transmit a wide variety of data and limited bandwidth resources, making it difficult to guarantee user service requirements. Therefore, reasonable bandwidth allocation has become a major factor limiting the performance of massive MIMO. To sum up, when performing the bandwidth allocation in a massive MIMO system, it is necessary to take business as the premise and comprehensively consider multiple requirements.

Bandwidth allocation is mainly divided into channel-aware schemes and other schemes [5]. The former gives priority to users with good channel conditions when allocating bandwidth, while users with poor channel conditions are likely to be starved to death, and the allocation result is unfair. The latter generally allocates bandwidth under ideal channel conditions to ensure minimum traffic, maximum delay boundary, and fairness. Literature [6] proposed a bandwidth allocation method based on user quality of service (QoS) awareness (IHQB), which transformed the optimal scheduling problem into a mixed integer nonlinear programming problem and solved the problem using a heuristic algorithm. It has good performance in terms of the weighted sum of flows and system throughput, but the method simply takes the reciprocal of traffic priority as the weight, ignoring the impact of channel state information on the results. Literature [7] studies the efficient multiplexing of massive multi-user MIMO downlink eMBB and URLLC services. When URLLC data packets arrive, the base station reallocates bandwidth resources but does not consider channel state information. Literature [8] proposes a bandwidth allocation algorithm based on minimum rate requirements to maximize energy efficiency (BABEE), which uses each user’s energy efficiency and minimum rate requirements to determine user bandwidth allocation. However, this method only considers the user’s minimum rate requirement in the allocation process and does not consider the service type, so it is difficult to meet the user’s QoS requirements. Literature [9] proposes a joint optimization framework for wireless networks, which can satisfy more user transmissions, thereby achieving higher link capacity utilization, but only considering the throughput of the system, it is difficult to meet the requirements of the user end. Literature [10] proposes an intelligent dynamic bandwidth allocation algorithm based on machine learning, which divides bandwidth utilization devices into three categories: key programs, medium-level, and low-level, and shows better reliability in a low-bandwidth environment. However, this method only starts from a single cycle, and the fairness of users cannot be guaranteed. Facts have proved that only considering service information or channel information cannot really meet the needs of users, and joint service and channel information allocation has become the focus of research [11,12,13,14,15]. Literature [16] pointed out that the resource allocation effect of MIMO system is affected by the user’s channel conditions and QoS requirements. Literature [17] proposed a bandwidth allocation method combining channel information and user service information and used the improved genetic algorithm to solve the problem. This method reduces the average delay of users on the basis of effectively improving system performance but does not consider the minimum bandwidth request of the service, resulting in some users not being served and reducing user satisfaction. Literature [18] builds a bandwidth allocation framework by considering factors, such as user business information and channel state information, and proposes a bee colony-based bandwidth allocation method (BO-CL-DBA). This method can achieve high allocation efficiency but ignores the minimum bandwidth request of the business and does not consider the bandwidth allocation of users in the previous cycle so that the fairness among users cannot be satisfied. Literature [19] proposes a cross layer dynamic bandwidth allocation method that balances fairness and utility, applying the resource allocation results of the previous service as an influencing factor in the next allocation to ensure fair allocation of business resources. However, the algorithm complexity is high, and the default number of users meets antenna constraints, which does not meet the access situation of users in practical applications. Reference [20] used swarm intelligence optimization algorithms to study resource allocation problems in communication systems, and the results showed that swarm intelligence optimization algorithms performed well in the field of resource allocation. Literature [21] proposed a bald eagle search algorithm (BES), which can effectively solve various complex numerical optimization problems. Compared with the bee colony algorithm and genetic algorithm, it has faster convergence speed and search ability, but it has the disadvantages of incoordination between local search and global optimization and is easy to fall into local optimum.

Aiming at the above problems, this paper proposes a multi-service based adaptive bandwidth allocation method for massive MIMO systems, which combines service information, channel state information, and user bandwidth allocation in the previous cycle. First, it uses factors, such as QoS delay requirements and channel state information, to set dynamic priorities for users and then performs user scheduling according to the dynamic priorities. Then, it considers the minimum guaranteed time slot, assigns the minimum guaranteed time slot to each user first, and then allocates bandwidth according to the principle of maximizing the objective function. Finally, the improved bald eagle search algorithm (IBES) is used to solve the problem, taking into account both system throughput and fairness in user allocation while considering utility.

Comparing the above literature with the algorithm proposed in this article, and the comparison results are summarized in

Table 1. Comparison between relevant literature and the algorithm in this article.

	Whether to Consider This Factor	Traffic Priority	Channel State Information	Resource Periodicity	User Minimum Request
Work
[6]		Yes	No	No	Yes
[7]		Yes	No	No	Yes
[8]		No	Yes	No	Yes
[9]		No	Yes	No	Yes
[10]		Yes	Yes	No	Yes
[16]		Yes	Yes	No	Yes
[17]		Yes	Yes	No	No
[18]		Yes	Yes	No	No
[19]		Yes	Yes, but ignore transfer rate	Yes	Yes
Algorithm in this article		Yes	Yes	Yes	Yes

.

The main contributions of this article are as follows: introducing business priority, channel state information, and the number of unsatisfied request time slots in the previous scheduling cycle to calculate the dynamic priority of users, and scheduling users based on this to improve satisfaction. reassign bandwidth to selected users while ensuring the minimum user demand and establish an objective function to maximize system utility value; introducing chaos theory in the initialization phase of the bald eagle algorithm to make the population search the space more comprehensively and solve the problem that the search time is prolonged due to inappropriate initial value selection; introducing Levy flight in the important stage of optimization to improve the global search and local optimization capabilities of the bald eagle algorithm; introducing reverse learning after the dive phase to improve the quality of the final solution; applying the improved bald eagle algorithm to the bandwidth allocation process to improve the system’s throughput, bandwidth utilization, and user relative fairness.

2. Optimization Model of Massive MIMO System

Firstly, the priority of different services is analyzed, and on this basis, channel state information and the number of unsatisfied user request slots in the previous scheduling cycle are introduced to calculate the dynamic priority of users, and user scheduling is performed based on the dynamic priority. Then, under the requirement of guaranteeing the minimum time slot of users, the bandwidth redistribution is carried out to the selected users, and the objective function of adaptive bandwidth distribution is established to optimize the system utility value.

2.1. User Scheduling

As shown in Figure 1, in a downlink single-cell massive MIMO system, it includes a base station (BS) located in the center of the cell and N uniformly distributed single-antenna users.

In practical applications, due to the burstiness of user traffic, the number of users accessing the system will be greater than the limited number of antennas on the base station side. Therefore, bandwidth allocation first requires user scheduling. According to the service priority of the user, channel state information, and the amount of bandwidth resources allocated by the user terminal in the previous scheduling period, the dynamic priority of the user is obtained, and user scheduling is performed according to the obtained priority.

Literature [22] divides users into groups according to the types of services used. On this basis, this paper discusses four main types of services, namely conversational services (voice, videophone, etc.), stream services (video streams, audio streams, etc.), interactive services (web browsing, online games, etc.), and background services (E-mail reception, SMS, FTP, etc.). Conversational services strictly limit the transmission delay. Severe delay jitter will cause the conversation to fail normally, but certain voice pauses and picture blurring can be allowed. In order to ensure the delay index of conversational services, this service is set as the highest priority; streaming services also requires real-time performance, but because of the one-way transmission characteristics, the requirements for transmission delay are not as strict as session services, and a certain packet loss rate is allowed; interactive services have low requirements on transmission delay but strict restrictions on packet loss rate; background services have no restrictions on transmission delay and delay jitter but generally require zero packet loss rate. Therefore, this paper regards transmission delay and delay jitter as the key indicators for evaluating service priority and summarizes the requirements of the four types of services for each QoS parameter in

Table 2. QoS requirements for different services.

Types of Services	Transmission Delay	Transmission Delay Jitter	Throughput	Packet Loss Rate	Priority
Conversational services	Strict restrictions	Strict restrictions	Largest	A certain range	Highest
Stream services	Limit	Limit	Larger	Smaller	Higher
Interactive services	Loose	Loose	Smaller	Approaching 0	Lower
Background services	Unlimited	Unlimited	Smallest	Approaching 0	Lowest

.

Simply taking the service priority as the user’s dynamic priority does not meet the actual needs, and the priority scheduling of users with high service priority but poor channel status may reduce the system throughput. Therefore, channel state information and the number of unsatisfied user request time slots in the previous scheduling cycle are introduced on the basis of service priority to improve user scheduling efficiency while ensuring user fairness as much as possible. Drawing in the form of the correction function in reference [18] and combining with the research elements of this article, the dynamic priority of user i is represented as:

$$f_i=w_1.\frac{q_i}{{\displaystyle \sum _{i=1}^N{q}_i}}+w_2.\frac{M_i.R_i.V_i}{{\displaystyle \sum _{i=1}^N{M}_i.R_i.V_i}}+w_3.\frac{g_i}{{\displaystyle \sum _{i=1}^N{g}_i}}$$

(1)

Among them, $N$ represents the number of users, $q_i$ represents the service priority of user $i$ ($i\in N$), $M_i$ represents the modulation order, $R_i$ represents the coding efficiency, and $V_i$ represents the transmission rate, $g_i$ represents the number of unsatisfied requested time slots of the $i$-th user in the previous cycle. $w$ is a weight coefficient, $w_1$, $w_2$, $w_3$, respectively, reflect the relative importance of service QoS parameters, channel state information, and the weight of the number of unsatisfied user slots in the previous period, and $w_1+w_2+w_3=1$. The formula is divided into three parts. The first part reflects the urgency of the business. The higher the business priority, the greater the proportion of this part. The second part represents the channel state information. The better the channel state, the greater the value of this part. The third part guarantees the fairness of users from the periodic point of view and makes up for users who are not satisfied due to lower service priority and poor channel quality to a certain extent.

Calculate the dynamic priority of all users, sort by numerical value, and prioritize scheduling for users with large numerical values. If the number of accessed users is greater than the limited number of antennas, end user scheduling and update the current user set to R.

2.2. Objective Function Establishment

In the wireless communication network, the utility function is often used to measure the user’s satisfaction with the service, and the best result of bandwidth allocation can be obtained by solving the optimal value of the utility function. Introducing the logarithmic utility function in [23], the utility function of the $i$-th user is shown in (2):

$$\mathrm{u}(x_i)=s_i\times \ln (1+\frac{x_i}{x_{{\max }_i}})$$

(2)

Among them, $\mathrm{u}(x_i)$ represents the utility of the $i$-th user, $x_i$ represents the number of time slots allocated to user $i$, $s_i$ represents the service priority of user $i$, and $x_{{\max }_i}$ represents the number of time slots requested by user $i$.

First, consider the user’s business priorities $s_i$. The traditional utility function shown in (2) ignores the user’s channel state information and the number of unsatisfied time slots of the user in the previous scheduling cycle and cannot fully express the user’s characteristics. Therefore, this paper introduces the aforementioned dynamic priority $f_i$.

Then, considering the minimum guaranteed time slot, if the needs of low dynamic priority users are not met for a long time, it is easy to cause the user to be starved to death. Therefore, in order to ensure the basic communication of users, it is necessary to assign the minimum guaranteed time slot to each user first and then allocate bandwidth according to the principle of maximizing the total utility function. The improved utility function is shown in (3):

$$\mathrm{u}(x_i)=f_i\times \ln (1+\frac{x_i-x_{{\min }_i}}{x_{{\max }_i}-x_{{\min }_i}})+\mathrm{u}(x_{{\min }_i})$$

(3)

Among them, $\mathrm{u}(x_{{\min }_i})$ represents the utility value generated by allocating the minimum guaranteed time slot $x_{{\min }_i}$ for user $i$, which is used to compensate for the neglected utility value due to the priority allocation of the minimum guaranteed time slot for each service, expressed as:

$$\mathrm{u}(x_{{\min }_i})=\ln (1+\frac{x_{{\min }_i}}{x_{{\max }_i}})$$

(4)

The total utility function of the system is expressed as:

$$\max {\displaystyle \sum _{i\in R}\mathrm{u}(x_i)=\max }{\displaystyle \sum _{i\in R}[f_i\times \ln (1+\frac{x_i-x_{{\min }_i}}{x_{{\max }_i}-x_{{\min }_i}})+}\ln (1+\frac{x_{{\min }_i}}{x_{{\max }_i}})]$$

(5)

$$\mathrm{s}.\mathrm{t} x_{{\min }_i}\le x_i\le x_{{\max }_i}$$

$${\displaystyle \sum _{i\in R}{x}_i\le x_{all}}$$

Among them, $x_{{\min }_i}$ and $x_{{\max }_i}$, respectively, represent the minimum number of time slots to ensure the normal communication of user $i$ and the number of time slots requested by user $i$, and $x_{all}$ represents the total number of time slots that can be allocated by the system.

3. Adaptive Bandwidth Allocation Algorithm for Improved Bald Eagle Optimization

3.1. Improved Bald Eagle Optimization Algorithm

The above-mentioned bandwidth allocation problem is an NP-hard nonlinear optimization problem, and it is more complicated to solve it by traditional mathematical methods. Therefore, this paper uses the bald eagle optimization algorithm to solve this problem. The global search ability of the bald eagle optimization algorithm is inconsistent with the local optimization ability, and it is easy to fall into the local optimum. Therefore, this paper improves the bald eagle algorithm in the following aspects:

• Chaos initialization

The original bald eagle algorithm uses random initialization to generate populations, which may cause uneven distribution of bald eagles and prolong the search time of the algorithm. In order to avoid this problem as much as possible, inspired by reference [24], this paper uses the Sin chaotic strategy to initialize the population. The Sin chaotic mapping is as follows:

$$x_{n+1}=\sin (\frac{2}{x_n}),n=0,1,\dots ,N$$

(6)

Among them, $x_n$ is randomly generated, $-1\le x_n\le 1, x_n\ne 0$, and $N$ is the total number of individuals in the population.

2.

Levy Flight

The control position change parameter $\alpha$ and random parameter $\gamma$ in the selection stage are prone to premature convergence of the solution and falling into local optima. Inspired by reference [25], the Levi flight strategy can be introduced to expand the search range of the population and improve the problem of the original algorithm being prone to falling into local optima. At this time, the position of the selection stage is updated to:

$$P_{i,new}=P_{best}+\alpha \ast \gamma (P_{mean}-P_i)\ast Levy$$

(7)

Among them, $\alpha$ is a parameter to control the position change, and the value is between [1.5, 2]. $\gamma$ is a random number between [0, 1]. $P_{best}$ is the current optimal position, $P_{mean}$ is the average position, $P_i$ is the position of the $i$-th vulture, and $Levy$ is the Levy flight function.

3.

Reverse Learning

If the bald eagle falls into a local optimum when searching the solution space, it will lead to the inability to obtain the optimal solution in the predation phase. Therefore, the perturbation strategy can be used after the predation phase to improve the quality of the solution and improve the problem of falling into local optimum. This article introduces the dynamic reverse learning strategy from reference [26] and takes the latest position of the bald eagle in the stage diving to capture the prey as the individual reverse learning. The formula is as follows:

$$P_{i,new}^{\prime }=rand\times (\max (P_{i,new})+\min (P_{i,new})-P_{i,new})$$

(8)

Among them, $rand$ is a random number between [0, 1], which is the position of the bald eagle in the dive stage.

3.2. Adaptive Bandwidth Allocation Algorithm Based on Improved Bald Eagle Optimization

The original bald eagle search algorithm does not involve the processing constraints, but the objective function of this paper is proposed under the constraints of Formula (5). In order to deal with constraints, a penalty function is introduced to transform the constrained objective function into an unconstrained penalty function. This paper designs the following penalty function:

$$\begin{array}{l}z=\max {\displaystyle \sum _{i\in R}\mathrm{u}(x_i)-{\eta }_1}{\displaystyle \sum _{i\in R}[\max (0,x_{{\min }_i}-x_i}){]}^2\\ -{\eta }_2{\displaystyle \sum _{i\in R}[\max (0,x_i-x_{{\max }_i}}){]}^2-{\eta }_3{[\max (0,{\displaystyle \sum _{i\in R}{x}_i-x_{all}})]}^2\end{array}$$

(9)

Among them, ${\eta }_1$, ${\eta }_2$, and ${\eta }_3$ represent penalty factors, indicating the penalty weight for violating the corresponding constraints. Generally, in order to highlight the impact of infeasible solutions, the penalty factors are set to larger values. In ${\eta }_1$ penalty item, if the number of time slots allocated to user $i$ is not lower than the minimum guaranteed number of time slots, no penalty will be given, otherwise, punishment will be imposed. In ${\eta }_2$ penalty item, the condition for not giving penalty is that the number of time slots allocated to user $i$ is not greater than the number of time slots requested. ${\eta }_3$ corresponds to the second constraint in (5).

The specific steps of the improved bald eagle search for adaptive bandwidth allocation algorithm (IBES-ABA) are as follows:

(1)

User business arrives and receives business parameters, including business priority, number of user requested time slots, minimum guaranteed time slot, modulation order, coding efficiency, and transmission rate.

(2)

Calculate the dynamic priority of the user and perform user scheduling.

(3)

Allocate the minimum guaranteed time slot for the user to ensure the basic communication of the user.

(4)

Calculate the number of remaining time slots $X^{\prime }$, the number of scheduled users who have not yet met the time slot request $R^{\prime }$, and the number of unscheduled users who have not yet met the time slot request $S^{\prime }$. If $X^{\prime }=0$, it means that there is no unallocated time slot under the system, and the bandwidth allocation process ends; if $R^{\prime }=0$ and $X^{\prime }\ne 0$, then assign the number of time slots to the users in the set S = N − R in sequence according to the priority and continue to perform step (5) until $X^{\prime }=0$ or $S^{\prime }=0$.

(5)

Generate an initial solution according to the number of remaining time slots and the value range of the number of time slots that can be allocated to each user.

(6)

Using Formula (9) as the fitness function, calculate the fitness function value of the above initial solution, and sort from large to small.

(7)

According to the improved bald eagle search algorithm, the position update strategy is implemented. If the fitness function value of the new position is greater than the value of the original position, the position is updated.

(8)

Return to step (4).

(9)

Output the result.

The flowchart is shown in Figure 2:

4. Experimental Simulation and Analysis

4.1. Simulation Parameter Settings

In order to analyze the performance of the IBES-ABA algorithm under different conditions, the user parameters, service priority, and modulation scheme are set as

Table 3. User simulation parameters.

$\mathit{i}$	${\mathit{M}}_{\mathit{i}}$	${\mathit{R}}_{\mathit{i}}$	${\mathit{V}}_{\mathit{i}}$	$x_{{\max }_i}$	${\mathit{x}}_{{\mathbf{min}}_{\mathit{i}}}$	${\mathit{q}}_{\mathit{i}}$
1–35	1	2/3	4	[15,16,9,19,14,5,17,13,4,5,13,13,8,12,10,2,2,7,1,8,14,3,2,13,12,6,16,15,3,8,11,15,7,6,15]	[2,0,0,1,2,0,1,2,2,2,0,1,1,1,0,2,2,2,1,2,0,1,2,3,0,1,2,0,2,2,1,2,0,1,2]	[1.75,1.25,1.25,2,1.25,1.75,1.75,2,1.25,2,1.25,1.75,1.25,1.25,1.75,1.75,1.75,2,1.25,1.25,2,1.75,1.25,1.75,1.25,1.25,1.25,1.75,2,1.25,1.75,1.25,1.25,1.75,2]
36–70	2	3/4	6	[17,13,4,5,13,13,8,14,5,15,2,7,2,3,17,15,8,20,2,10,9,16,17,5,11,10,14,15,16,7,14,14,5,4,11]	[1,2,2,2,0,1,1,3,1,2,0,3,1,2,2,3,3,2,0,0,1,3,1,3,0,3,1,0,1,2,1,1,3,2,2]	[1.75,2,1.25,2,1.25,1.75,1.25,1.25,1,1.25,1.75,2,1,1,1.75,1,1.25,1.25,1.75,1,1,2,1.25,2,1,1.75,1.25,1.25,1.75,2,1,1.75,1.25,1,1]
71–105	3	4/5	8	[12,10,2,2,7,1,8,6,19,4,17,12,20,3,10,4,20,2,16,17,18,3,9,6,17,10,9,5,7,4,4,18,13,12,4]	[1,0,2,2,2,1,2,3,1,3,3,1,2,0,0,2,3,3,0,2,1,0,1,0,3,1,2,0,2,1,2,2,2,1,0]	[1.25,1.75,1.75,1.75,2,1.25,1,1.25,1.75,2,1.75,1.25,1,1.75,1,2,1.25,1.25,1,2,1.75,1.25,1,1,2,1,25,1.25,1.75,1,1.25,1,1.75,1,2,1.25]
106–140	4	7/8	10	[14,3,2,13,8,17,2,2,5,14,15,14,10,12,7,16,5,15,5,9,13,16,3,19,16,11,10,10,7,11,11,17,17,14,9]	[0,1,2,3,3,2,1,2,1,0,0,1,2,1,1,0,3,3,1,1,1,3,1,0,3,1,0,1,0,0,3,3,2,0,0]	[1.25,2,1,1.75,1.75,1,2,1.25,1.25,1.75,1,1,1.25,2,2,1.25,1.25,1.25,1.75,1.25,1.25,1.75,1,1.25,1.75,1.75,2,1,1.25,2,1.25,1.75,2,1,1]

,

Table 4. Business priority parameters.

Type of Service	Business Priority q
Conversational services	2
Stream services	1.75
Interactive services	1.25
Background services	1

and

Table 5. Modulation scheme and related parameters.

Modulation	$\mathbf{Modulation} \mathbf{Order} {\mathit{M}}_{\mathit{i}}$	$\mathbf{Coding} \mathbf{Efficiency} {\mathit{R}}_{\mathit{i}}$
QPSK	1	2/3
16QAM	2	3/4
64QAM	3	4/5
256QAM	4	7/8

respectively. Suppose there are 140 users in the system, that is, N = 140, the total number of time slots is 700, and the number of base station antennas is 128 [27].

4.2. Simulation Result Analysis

Compare the IBES-ABA algorithm proposed in this paper with the bald eagle search for adaptive bandwidth allocation algorithm (BES-ABA) and the IHQB, BABEE, and BO-CL-DBA mentioned above.

4.2.1. Performance Index

(1)

System utility value

System utility value refers to the benefits obtained by the system when users communicate using bandwidth resources allocated by algorithms. As shown in Equation (5).

(2)

Bandwidth utilization

Bandwidth utilization rate refers to the ratio of the actual bandwidth of data transmission of the total available bandwidth, expressed as:

$$\eta =\frac{{\displaystyle \sum _{i=1}^N{x}_i}}{x_{all}}$$

(10)

(3)

System throughput

System throughput refers to the number of successful transactions processed by the system per unit of time, expressed as:

$$\mathrm{T}={\displaystyle \sum _{i=1}^N{x}_i}.M_i.R_i$$

(11)

(4)

User satisfaction

The indicators that reflect the fairness of distribution results mainly include absolute fairness and relative fairness. Absolute fairness refers to the equal allocation of bandwidth to every user as much as possible, only considering the absolute amount of bandwidth allocated by users, ignoring the bandwidth needs of users with different priority levels. Therefore, considering relative fairness and utilizing user satisfaction to reflect the relative fairness of bandwidth allocation, the ratio of the actual number of time slots allocated to users to the number of requested time slots is defined as user satisfaction. The calculation method is shown in (12):

$$c=\frac{{\displaystyle \sum _{i=1}^N\frac{x_i}{x_{{\max }_i}}}}{N}$$

(12)

4.2.2. Simulation Results and Analysis

In order to verify the optimizing ability of the IBES algorithm proposed in this paper, the BES algorithm and the IBES algorithm are compared on the basis of using the same experimental parameters. To avoid lengthy articles, six representative functions were selected for experiments, namely: unimodal benchmark function ($F_1$,$F_2$), multimodal benchmark function ($F_3$,$F_4$), and fixed-dimensional multimodal benchmark function ($F_5$,$F_6$). See

Table 6. Benchmark function.

Benchmark Function	Dimension	Search Scope	Theoretical Minimum
$F_1(x)={\displaystyle \sum _{i=1}^n(x_i}-90{)}^2$	30	[−100, 100]	0
$F_2(x)={\displaystyle \sum _{i=1}^n(|x_i}+0.5|{)}^2$	30	[−100, 100]	0
$F_3(x)={\displaystyle \sum _{i=1}^n-x_i}\sin (\sqrt{\left|x_i\right|})$	30	[−500, 500]	−12,569.46
$\begin{array}{c}{F}_4(x)=\frac{\pi }{n}\left\{10\sin (\right.\pi y_1)+{\displaystyle \sum _{i=1}^{n-1}(y_i}-1{)}^2[1+10{\sin }^2(\pi y_{i+1})]+\left.{(y_n-1)}^2\right\}+{\displaystyle \sum _{i=1}^{n}u(x_i},10,100,4)\\ y_i=1+\frac{x_i+1}{4}\end{array}$	30	[−50, 50]	0
$F_5(x)={\displaystyle \sum _{i=1}^{11}{[a_i-\frac{x_1(b_i{}^2+b_i{x}_2)}{b_i{}^2+b_i{x}_3+x_4}]}^2}$	4	[−5, 5]	0.00030
$F_6(x)=-{\displaystyle \sum _{i=1}^4{c}_i\exp (-{\displaystyle \sum _{j=1}^6{a}_{ij}{(x_j-p_{ij})}^2})}$	6	[0, 1]	−3.32

for details. Using the convergence curves of different objective functions to compare the performance of the two algorithms, the convergence curves are shown in Figure 3.

From Figure 3a,b, it can be seen that when dealing with unimodal reference functions, the IBES algorithm can achieve convergence faster and has the stronger optimization ability compared to the original algorithm. Figure 3c,d show that the IBES algorithm has better performance when dealing with multimodal reference functions as the introduced Levy flight and reverse learning strategies can help the algorithm jump out of local optima. It can be seen from Figure 3e,f that the IBES algorithm still has a faster rate of convergence and stronger search ability in the face of fixed dimensional multimodal reference function. Therefore, the bald eagle optimization algorithm improved by chaos initialization, Levy flight, and reverse learning strategy in this paper has a faster rate of convergence and stronger optimization ability when facing different types of benchmark functions.

When the number of available time slots in the system is 700, analyze the number of time slots allocated by the five algorithms for each user. Because the number of users is large, it is difficult to visually present the allocation results of different algorithms, so the top six users are selected from the four groups of users in Table 3 for analysis, and the results are shown in Figure 4.

From Figure 4, it can be seen that when the number of available time slots is 700, the five algorithms allocate a different number of time slots for each user. The IHQB algorithm allocates more time slots for users 4, 37, and 39, while allocating fewer time slots for users 108 and 111. This is because the algorithm only considers the user’s business priority and ignores the impact of channel state information in the process of allocating resources to users, thereby allocating too much bandwidth to some users with poor channel state. The BABEE algorithm allocates a relatively average number of time slots to users as it only considers the user’s minimum rate constraint during the allocation process and ignores the bandwidth requirements of users with different priority levels. The BO-CL-DBA algorithm allocates fewer time slots for users 4, 36, and 75. Although this method considers channel conditions, it ignores the user’s request time slots and user priority. The BES-ABA algorithm allocates more time slots for users with higher modulation orders. The IBES-ABA algorithm proposed in this article allocates more time slots for users 4, 36, and 109 as the algorithm takes into account the priority of user services and channel conditions during resource allocation.

When the number of time slots that can be allocated by the system is 700, the performance parameters of the five algorithms are shown in

Table 7. Performance analysis of five algorithms when the number of allocatable time slots in the system is 700.

Algorithm Name	Utility Value	Throughput	Bandwidth Utilization	User Satisfaction
IBES-ABA	58.8	1513	0.997	0.76
BES-ABA	54.6	1388	0.993	0.74
IHQB	45.6	1200	0.98	0.71
BABEE	38.6	1190	0.989	0.69
BO-CL-DBA	50.4	1310	0.985	0.73

.

From Table 7, it can be seen that the utility value and throughput of BABEE algorithm is the lowest. Due to not considering business QoS and channel state information, the user satisfaction of this algorithm is also the lowest. The utility value, throughput, and user satisfaction of the BO-CL-DBA algorithm are higher than those of the IHQB algorithm. The bandwidth utilization of all algorithms does not differ significantly. The IBES-ABA algorithm proposed in this article has the highest system utility value, throughput, and user satisfaction and overall performs well.

To more intuitively and comprehensively reflect the performance of the five algorithms, the number of allocated time slots in the system has been expanded from 300 to 1200. Figure 5, Figure 6, Figure 7 and Figure 8 represent the system utility values, bandwidth utilization, throughput, and user satisfaction of the five algorithms under different time slots.

As shown in Figure 5, the system utility values of the five algorithms are positively correlated with the number of time slots because as the total bandwidth resources that users can allocate increase, the cumulative utility values of all users also increase. The BABEE algorithm has the lowest utility value because it ignores the impact of user channel state information and business QoS on allocation results. The IBES-ABA algorithm proposed in this article performs best because it comprehensively considers the priority of user services and channel state information during the allocation process, and the objective function of this article is to maximize the system utility value, reflecting the feasibility of this algorithm. By calculating the average system utility value of each algorithm under all time slots and comparing the differences among the five algorithms, it can be concluded that the algorithm proposed in this paper has improved the system utility value by at least 23.70% compared to the IHQB algorithm, BABEE algorithm, and BO-CL-DBA algorithm.

As shown in Figure 6, when bandwidth resources are insufficient, the bandwidth utilization rate is high, and the difference in bandwidth utilization rates among the five algorithms is very small. When bandwidth resources are sufficient, the bandwidth utilization rate decreases and the bandwidth utilization rates of different algorithms begin to show differences because with sufficient bandwidth, the needs of users are already met. The algorithm proposed in this article has the highest bandwidth utilization rate because during the allocation process, the lowest guaranteed bandwidth is first allocated to users and then allocate the remaining bandwidth according to the user’s dynamic priority, and there is no situation that the remaining bandwidth cannot even satisfy the lowest bandwidth resource application so that the bandwidth can be maximized. By calculating the average bandwidth utilization of each algorithm under all time slots, it can be concluded that the proposed algorithm in this paper has improved by at least 4.22% compared to the IHQB algorithm, BABEE algorithm, and BO-CL-DBA algorithm.

As shown in Figure 7, the system throughput of all five algorithms shows an upward trend with the increase of the number of allocatable time slots because the more bandwidth resources can be allocated, the more services each user can transmit and the higher the system throughput. When the number of time slots is 300–450, the throughput of the five algorithms does not differ significantly as the relatively limited available resources result in a less significant difference in allocation schemes. When the number of time slots is 450~900, the throughput of the IBES-ABA algorithm is much higher than other algorithms because it fully utilizes transmission rate, encoding efficiency, and modulation order to characterize the channel state. Poor channel state corresponds to lower modulation order and encoding efficiency, thereby improving system throughput. When the number of time slots is between 900 and 1200, the gap between several algorithms begins to narrow and gradually stabilizes. At this time, the number of time slots is sufficient, and most of the user’s requests have been met, so the gap in allocation schemes gradually narrows. Due to the neglect of channel status and business QoS information during the allocation process by the BABEE algorithm, the throughput is significantly lower than other algorithms. By calculating the average system throughput of each algorithm under different time slots, it can be concluded that the algorithm proposed in this paper has improved the system throughput by at least 6.55% compared to the IHQB algorithm, BABEE algorithm, and BO-CL-DBA algorithm.

As shown in Figure 8, as the number of time slots increases, the user satisfaction of all five algorithms increases. Among them, the user satisfaction of the IBES-ABA algorithm and the BES-ABA algorithm is relatively close and always higher than other algorithms. This is because the algorithm proposed in this article comprehensively considers factors, such as business QoS, channel state information, and the number of user time slots, that were not satisfied in the previous cycle, which can better meet the needs of various users and improve user satisfaction. The BABEE algorithm focuses on allocating the same bandwidth resources to different users. Although this algorithm improves the absolute fairness of bandwidth allocation, it ignores the bandwidth needs of users with different priorities, resulting in the lowest user satisfaction under this algorithm. By calculating the average user satisfaction of each algorithm under different time slots, it can be concluded that the algorithm proposed in this paper has improved user satisfaction by at least 4.28% compared to the IHQB algorithm, BABEE algorithm, and BO-CL-DBA algorithm.

5. Conclusions

Aiming at the characteristics of resource periodicity in massive MIMO system and bandwidth allocation without comprehensive consideration of user service QoS and channel state information, resulting in poor user satisfaction and low bandwidth utilization, an adaptive bandwidth allocation method based on user service is proposed. The method is mainly divided into the following steps. Firstly, dynamic priorities are created for different users according to factors, such as user service priority, channel state information, and continuous periodicity of allocation, and user scheduling is performed according to the priority. Then, the minimum guaranteed time slot is set for the selected users, and the objective function is established. Finally, the improved bald eagle algorithm is used to solve the problem. The simulation results show that the algorithm proposed in this paper has improved system utility value, bandwidth utilization, system throughput, and user satisfaction by 23.70%, 4.22%, 6.55%, and 4.28%, respectively, compared to the algorithms proposed in other literature. The algorithm in this article can improve the utility value, bandwidth utilization, and throughput to a certain extent while ensuring user QoS requirements and improving user satisfaction.

This article only focuses on the allocation of bandwidth resources in massive MIMO systems. In the future, multiple resources will be jointly allocated, such as bandwidth, power, number of antennas, etc., to optimize them from both user and system perspectives.