CA Energy Saving Joint Resource Optimization Scheme Based on 5G Channel Information Prediction of Machine Learning

Abstract

Carrier aggregation (CA) is considered as a key enabling technology to provide higher rates for users in LTE/5G networks. However, the increased transmission rate is accompanied by higher energy consumption. The existing CA energy efficiency resource optimization allocation scheme in 5G does not fully consider the following two issues, namely, the impact of delayed channel state information feedback on the rationality of resource allocation and the increasing in energy consumption caused by frequent switching of component carriers (CCs) by narrowband users; this paper proposed a CA energy-efficient joint resource optimization allocation (PEJA) scheme based on channel information prediction. The proposed scheme (PEJA) fully considers the above two issues. Firstly, the algorithm of random forest predicting channel state information is designed. On the basis, the CA energy-efficient joint resource optimization allocation (PEJA) scheme based on channel information prediction is proposed. The simulation results show that the proposed algorithm PEJA has a higher energy efficiency and throughput than the comparison algorithm under different numbers of users and different transmission powers. The PEJA algorithm is more energy efficient than the PEJA-NC algorithm, which does not consider the CC handover of narrowband users. To sum up, the proposed PEJA energy-efficient resource allocation scheme maximizes system energy efficiency and achieves a higher throughput.

1. Introduction

Due to the introduction of many new technologies and the expansion of communication systems, the energy consumption of communication systems has increased rapidly. On the basis of the rational use of wireless resources, improving energy efficiency and advocating green communication are the inevitable requirements in future communication systems. Green or energy conservation has become an important trend in the design of wireless communication networks. Radio resource allocation (RRA) is one of the energy conservation methods in LTE or 5G networks [1,2]. This paper studied the optimal radio resource allocation based on carrier aggregation technology for improving the energy efficiency in 5G communication networks.

Carrier aggregation (CA) technology is proposed in LTE/5G networks. An user device can aggregate two or more component carriers (CCs) for supporting high-data-rate transmission over a wide bandwidth [3]. An LTE-advanced device can aggregate up to five CCs at most, each up to 20 MHz. With the largest configuration, this implies a total bandwidth of 100 MHz. The contiguous and non-contiguous CCs with different bandwidths can also be aggregated. Therefore, CA can not only increase the bandwidth but also offer significant flexibility for efficient spectrum utilization. In the LTE/5G system, CA is considered as one of the key technologies to improve capacity and reduce interference. Based on these facts, CA technology can significantly improve the throughput of the communication system [4]. However, without a scientific and reasonable resource management scheme, CA technology will increase the energy consumption of base stations and users [5].

Recently, many works have been devoted to the energy-efficient resource optimization in wireless communication networks [6,7], such as orthogonal frequency division multiple access (OFDMA) systems [8], cooperative multipoint (COMP) systems [9], cooperative relay networks [10], non-orthogonal multiple access (NOMA)-based satellite terrestrial integrated network [11], multi-user multiple input multiple output (MIMO) systems [12], and Rate-Splitting Multiple Access in Satellite and Aerial-Integrated Network [13]. The energy-efficient optimization with CA technology has also attracted much attention. The main research is as follows: paper [14] proposed to allocate resources for users on a small subset of component carriers to reduce energy consumption in LTE-advanced. Paper [15] proposed algorithms based on cross entropy to effectively solve the problem of resource allocation to maximize energy efficiency. The allocated radio resources include the user association between equipment and base station (BS), CC configuration, resource block (RB) allocation, and power allocation under QoS constraints. In addition, the sleep strategy is adopted for the BS with low traffic, which further improves the system energy efficiency. Paper [16] studied the CA energy-efficient resource allocation problem in cognitive radio systems and proposed a sub-optimal resource allocation algorithm considering energy efficiency, fairness, and system capacity. The above studies focus on the optimal allocation with CA energy-efficient resources but ignore the choice of modulation and coding scheme (MCS). Paper [17] studied the energy-efficient resource allocation for RB, CC, and MCS considering the downlink in LTE-advanced system with CA technology and adopted a proportional fairness energy scheduling strategy. However, this study does not consider power allocation. In [18], considering the downlink transmission system in LTE-advanced networks, the problem of maximizing system energy efficiency with QoS was studied and a joint resource allocation algorithm considering RB, power, and MCS was proposed. In [19], Xiao et al. solved the problem of RB and power allocation in LTE networks using fractional planning to maximize energy efficiency but ignored the selection of MCS and the CA capability of users. In [20], Liao et al. proposed an energy-efficient resource allocation algorithm using CA technology in LTE-advanced downlink transmission systems, considering joint CC selection, MCS allocation, and RB allocation. The optimal joint CC selection and RB allocation methods performed disjoint schemes due to a comprehensive view on the available resources [21,22]. Paper [22] proposed QoS-aware joint CC and RB allocation satisfying the delay requirement of users in 5G.

The above energy-efficient resource optimization allocation with CA mainly focused on the energy efficiency in the downlink. Since multi-carrier transmission needed to increase the uplink power consumption of user equipment, Liu et al. proposed a new dynamic carrier aggregation (DCA) scheduling scheme in [23] to improve the energy efficiency of uplink and designed two scheduling algorithms, the longest serving the queue and the priority polling, so as to reduce the transmission power and maximize the utilization of radio resources. However, these studies did not comprehensively consider the impact of the uplink and downlink using CA technology on the system energy efficiency. In response to this problem, paper [24] studied the joint energy-efficient resource allocation between base stations and users, balanced the energy efficiency between uplink and downlink, each user, the jointly allocated CC, and power, but this study ignored the choice of MCS.

At present, the research on the optimal energy-efficient resources allocation in CA still has the following shortcomings: under the condition that different users have different carrier aggregation capabilities and fairness, there is no related examples in the literature for the optimal energy-efficient resource allocation comprehensively considering joint CC, RB, power allocation, and MCS selection. Even if the energy-efficient resources allocation with MCS is considered, the selection of MCS is mostly based on receiving ideal channel state information and the influence of delayed channel state information feedback on system performance and resource scheduling rationality is not fully considered. In the CA energy-efficient resource scheduling scheme, the influences of signal overhead and energy consumption caused by frequent CC switching by narrowband users have not been considered.

In view of the above issues, we can carry out the research work of this paper and the main contributions are as follows:

(1)

A mathematical model for the optimal CA energy-efficient resources allocation is established, which comprehensively considers many factors, including the carrier aggregation capability of different users, the delayed channel information, and the selection of MCS, CC, RB, and power allocation. Since the established energy-efficient optimization model is a mixed-integer nonlinear programming (MINLP), the power, RB allocation sub-algorithm, and CC allocation sub-algorithm of energy efficiency optimization are designed to solve the problem iteratively.

(2)

Aiming at the problem that CQI with delayed feedback causes the resource allocation performance to be worse, the random forest algorithm is used to predict the SINR online to obtain the current SINR and its corresponding real-time CQI and MCS.

(3)

Under the assumption that both the CC allocation and the predicted channel information are known, the energy-efficiency optimized RB and power allocation algorithms (ERPA) are proposed. The ERPA algorithm transforms RB and power allocation problem into a fractional programming problem P₃ by introducing relaxation variables. The Dinkelbach theory and Lagrangian dual method are applied to solve P₃. The sufficient and necessary conditions for obtaining the maximum energy efficiency are proved and P₃ is converted to non-fractional subtraction P₄₋₁ and we obtain P₄₋₁ as the corollary of convex optimization.

(4)

The CC allocation algorithm (DDJBNBC) is proposed, which combines the iterative pruning method and the algorithm to avoid the frequent handover of narrowband users and then the criteria for CC deletion and the energy-efficient CC handover of narrowband users is formulated. Based on ERPA and DDJBNBC sub algorithms, an energy efficiency joint resource allocation algorithm (PEJA) based on channel information prediction is proposed.

The rest of the paper is organized as follows. Section 2 contains the energy-efficient optimization model. Section 3 introduces the fast channel information prediction method based random forest. Additionally, Section 4 describes the energy-efficient resource optimization allocation algorithm based on channel information prediction. Section 5 is the experience results and analysis. Section 6 is the conclusion.

As there are many symbols in paper, please refer to Appendix A for main symbols and definitions.

2. Energy-Efficient Optimization Model

In the LTE/5G system using CA, we study the energy-efficient optimization allocation for CC, RB, and power considering MCS. The system adopts an adaptive MCS according to the CQI feedback by the user and allocates CC, RB, and power. CQI is usually obtained by measuring the signal-to-interference-noise ratio (SINR) in the downlink. Suppose that a base station eNB (evolved Node B) provides communication services for K users through n component carriers (CCs) and different users can support different bandwidths, ${\mathrm{C}}_{\mathrm{k}}$ represents the number of component carriers that user K can support and ${\displaystyle \tilde{\mathrm{C}}}=\left[{\mathrm{C}}_1,{\mathrm{C}}_2,\dots ,{\mathrm{C}}_{\mathrm{k}}\right]$ is the vector representing the number of CCs that can be supported by different users. One CC contains M resource blocks (RBs) where $\mathrm{n}\in \left\{1,2,\dots ,\mathrm{N}\right\}$ represents n represents the nth CC, $\mathrm{k}\in \left\{1,2,\dots ,\mathrm{K}\right\}$ represents the kth end user, and $\mathrm{m}\in \left\{1,2,\dots ,\mathrm{M}\right\}$ represents the mth resource block. Assuming that the CQI feedback of the user is available on RBs of all CCs, ${\mathrm{C}}_{\mathrm{n},\mathrm{m},\mathrm{k}}$ represents the CQI index value when the mth RB in the nth CC is allocated to user k and${\mathrm{C}}_{\mathrm{n},\mathrm{m},\mathrm{k}}\in \left\{1,2,\dots ,\mathrm{J}\right\}$,$\mathrm{J}=31$.

When the mth RB in the nth component carrier is allocated to user k, the rate that user k can achieve in time slot t is ${\mathrm{r}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\left(\mathrm{t}\right)$, its expression is:

$${\mathrm{r}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\left(\mathrm{t}\right)={\mathrm{B}}_{\mathrm{RB}}{\log }_2\left(1+{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\left(\mathrm{t}\right){\mathsf{\gamma }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\left(\mathrm{t}\right)\right)$$

(1)

where ${\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\left(\mathrm{t}\right)$ represents the transmission power allocated on the resource block when the mth RB in the nth CC is allocated to user k in time slot t; ${\mathrm{B}}_{\mathrm{RB}}$ represents the bandwidth of the resource block; ${\mathsf{\gamma }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\left(\mathrm{t}\right)$ represents the channel state information when the mth Rb in the nth component carrier of time slot t is allocated to user k (it is assumed that the base station can obtain all the channel state information in current time through CQI feedback),

$${\mathsf{\gamma }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\left(\mathrm{t}\right)={\mathrm{H}}_{\mathrm{n},\mathrm{m},\mathrm{k}}^2\left(\mathrm{t}\right)/{\mathrm{N}}_0{\mathrm{B}}_{\mathrm{RB}}$$

(2)

where${\mathrm{H}}_{\mathrm{n},\mathrm{m},\mathrm{k}}^2\left(\mathrm{t}\right)$ represents the channel power gain when the mth RB in the nth CC in time slot t is allocated to user k and ${\mathrm{N}}_0$ is the single-sided power spectral density of additive white Gaussian noise.

For simplicity of description, the user k of the corresponding MCS when the CQI index is j is simply referred to as the user k using MCS$\mathrm{j}$. When the mth RB in the nth component carrier is allocated to user k, the rate ${\mathrm{r}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)$ that can be reached by user k using MCS$\mathrm{j}$ in time slot t, the expression is:

$${\mathrm{r}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)=\{\begin{array}{c}0,{\mathrm{C}}_{\mathrm{n},\mathrm{m},\mathrm{k}}<\mathrm{j}\\ {\mathrm{r}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\left(\mathrm{t}\right),{\mathrm{C}}_{\mathrm{n},\mathrm{m},\mathrm{k}}\ge \mathrm{j}\end{array}$$

(3)

Equation (3) indicates that when the CQI value of RB is lower than the CQI value corresponding to the target MCS, the RB cannot be used. Because according to TR 36.912 [25], on each CC, all the RBs allocated to designated users must use the same MCS and satisfy the block error rate BLER ≤ 10%, otherwise the RB cannot be used.

Let ${\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)$ represent the resource block allocation identifier. When the mth RB on the nth CC in time slot t is allocated to user k using MCS$\mathrm{j}$, ${\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)=1$, otherwise, ${\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)=0$. At the same time, Formula (4) needs to be satisfied:

$${\displaystyle \sum }_{\mathrm{k}=1}^{\mathrm{K}}{\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{J}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)\le 1,\forall \mathrm{n},\forall \mathrm{m}$$

(4)

Let ${\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)$ represent the CC allocation identifier. When the nth CC in time slot t is allocated to user k using mcsj, ${\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)=1$, otherwise, ${\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)=0$. At the same time, the constraint condition of Formula (5) needs to be satisfied:

$${\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{J}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)\le {\mathrm{C}}_{\mathrm{k}},\forall \mathrm{k}$$

(5)

where ${\mathrm{C}}_{\mathrm{k}}$ is the carrier aggregation capability of user k, including narrowband users and broadband users. The carrier aggregation capability of narrowband users is equal to 1 and the carrier aggregation capability of broadband users is an integer in the interval [2,5].

${\mathrm{P}}_{\mathrm{T}}$ represents the total power transmitted by the base station. The base station allocates the power transmitted by the system to each resource block, ${\mathrm{P}}_{\mathrm{s}}$ is the sum of transmission power consumed on all the resource blocks and the following power constraint conditions need to be satisfied:

$${\mathrm{P}}_{\mathrm{s}}={\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{m}=1}^{\mathrm{M}}{\displaystyle \sum }_{\mathrm{k}=1}^{\mathrm{K}}{\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{J}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right){\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right){\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)\le {\mathrm{P}}_{\mathrm{T}}$$

(6)

where ${\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)$ indicates the transmit power that the mth resource block on the nth CC is allocated to user k using MCSj in the time slot.

Let ${\mathrm{R}}_{\mathrm{k}}\left(\mathrm{t}\right)$ denote the total rate obtained by user k in time slot t and the expression is Formula (7):

$${\mathrm{R}}_{\mathrm{k}}\left(\mathrm{t}\right)={\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{m}=1}^{\mathrm{M}}{\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{J}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right){\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right){\mathrm{r}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)$$

(7)

The energy efficiency (EE) of the system is defined as the ratio of the user’s transmission rate to the total energy consumption (unit is bits/J), which has been used by many scholars as a performance criterion for energy-efficient resource allocation [24] and which reflects the system performance gain brought by energy consumption. The larger the EE value, the greater the system performance gain brought by the energy consumption, otherwise, the smaller the value is. We define the EE in the downlink of the LTE/5G system using CA technology as ${\mathsf{\eta }}_{\mathrm{EE}}$ and its expression is:

$${\mathsf{\eta }}_{\mathrm{EE}}=\frac{\mathrm{R}}{{\mathsf{\zeta }\mathrm{P}}_{\mathrm{s}}+{\mathrm{P}}_{\mathrm{C}}}$$

(8)

where, $\mathsf{\zeta }$ is the reciprocal of the efficiency of the transmission power amplifier; $\mathrm{R}$ is the total user transmission rate; ${\mathrm{P}}_{\mathrm{C}}$ is the static power consumed by the circuit and is set as a fixed value.

The optimization model ${\mathrm{P}}_1$ for maximizing the energy efficiency of the system is defined as follows (the time slot variable t is omitted for simplicity):

$${\mathrm{P}}_1:{\mathsf{\eta }}_{\mathrm{EE}}^{\ast }\triangleq \max \frac{{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{K}}{\mathrm{R}}_{\mathrm{k}}}{\mathsf{\zeta }{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{K}}{{\displaystyle \sum }}_{\mathrm{n}=1}^{\mathrm{N}}{{\displaystyle \sum }}_{\mathrm{m}=1}^{\mathrm{M}}{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{J}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}+{\mathrm{P}}_{\mathrm{C}}}$$

(9)

$${\displaystyle \sum }_{\mathrm{k}=1}^{\mathrm{K}}{\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{J}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\le 1,\forall \mathrm{n},\forall \mathrm{m}$$

(9a)

$${\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{J}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\le {\mathrm{C}}_{\mathrm{k}},\forall \mathrm{k}$$

(9b)

$${\displaystyle \sum }_{\mathrm{k}=1}^{\mathrm{K}}{\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{m}=1}^{\mathrm{M}}{\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{J}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\le {\mathrm{P}}_{\mathrm{T}}$$

(9c)

$${\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{J}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\le 1,\forall \mathrm{n},\forall \mathrm{k}$$

(9d)

$${\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\in \left\{0,1\right\},{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\in \left\{0,1\right\},{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\ge 0,\forall \mathrm{n},\forall \mathrm{m},\forall \mathrm{k}$$

(9e)

$${\mathrm{C}}_{\mathrm{n},\mathrm{m},\mathrm{k}}\in \left\{1,2,\dots ,31\right\}$$

(9f)

where the constraint condition (9a) indicates that one RB can only be allocated to one user in the same time slot; the constraint condition (9b) indicates that the number of carriers allocated to different users must satisfy the limit condition of the maximum number of CCs supported by the users that have different carrier aggregation capabilities; the constraint condition (9c) indicates that the transmission power actually allocated should be less than or equal to the total transmission power; the constraint condition (9d) indicates that for each CC, all the RBs allocated to the specified user must use the same MCS; the constraint condition (9e) indicates that the CC identifier and the RB identifier are 0 or 1 and the power allocated to each RB is non-negative; and the constraint condition (9f) indicates that the value of CQI is an integer between 1 and 31.

3. Fast Channel Information Prediction Based Random Forest

3.1. Basis for Channel Information Prediction

The channel quality indication (CQI) is a key index to describe channel information and allocate appropriate MCS. The base station determines which RBs are allocated to the user according to the CQI value fed back by the user and adopts the corresponding adaptive modulation coding (AMC) scheme. This requires obtaining accurate and real-time CQI values. Most downlink resource scheduling schemes of LTE/5G systems are based on receiving ideal CQI, without considering the delay CQI. However, the scheduler actually uses the delayed CQI [26] and the delay of CQI will reduce the rationality of scheduling RBs, which will significantly degrade the system performance.

The existing channel information prediction methods include the regression model, Kalman filter, artificial neural network, and wavelet support vector machine (wt-svm) [27,28,29,30,31]. The existing channel information prediction methods mentioned above have problems such as high computational complexity, low prediction accuracy, and inability to process nonlinear data. Moreover, these channel information prediction methods are not used to solve the problem of energy-efficient resources optimal allocation in specific communication scenarios. According to the shortcomings of the existing research, this paper proposes to use random forest to predict SINR to obtain real-time SINR and its corresponding CQI and MCS.

3.2. Random Forest Prediction SINR

The CART in a random forest is composed of a bagging algorithm and random subspace method (RSM). Among them, CART is a dichotomous recursive segmentation technique proposed by Breiman et al. in 1984. At each node (except the leaf node), the current sample set is divided into two subsets. For the regression problem, the minimum mean square error is used to partition the data set. For any partition feature T, two sides of the corresponding partition point s are divided into the left data set Dl and the right data set Dr [32]. The expression is:

$${\min }_{\mathrm{T},\mathrm{s}}\left[{\displaystyle \sum }_{{\mathrm{x}}_{\mathrm{i}}\in {\mathrm{D}}_{\mathrm{l}}\mathrm{T},\mathrm{s}}^{}{\left({\mathrm{y}}_{\mathrm{i}}-{\mathrm{c}}_{\mathrm{i}}\right)}^2+{\displaystyle \sum }_{{\mathrm{x}}_{\mathrm{i}}\in {\mathrm{D}}_{\mathrm{r}}\mathrm{T},\mathrm{s}}^{}{\left({\mathrm{y}}_{\mathrm{i}}-{\mathrm{c}}_{\mathrm{i}}\right)}^2\right]$$

(10)

where c1 and c2 are the output mean values of the data sets Dl and Dr. This principle is used to divide continuously at each branch node until the set threshold is reached.

Bagging (bootstrap aggregating) is an ensemble learning algorithm. In random forest, Bagging specifically expresses that multiple samples are randomly selected with replacement from the original training sample set to generate a new training sample set. Then, multiple decision trees are constructed to form the random forest. Finally, the random forest averages the output of each decision tree to determine the final result. Additionally, then, the remaining samples that have not been drawn are called out-of-bag samples (out of bag, OOB), these OOB samples can be used as verification samples for the internal evaluation of the model and the final model prediction results are determined by “voting”. In this paper, the average result of each CART model is used as the prediction results of the random forest regression model.

In the fields of statistical analysis and machine learning, K-fold cross validation is commonly used to evaluate the generalization ability of the model. The K-fold cross validation means that the training set is divided into K disjoint subsets, in which K-1 subsets data are used for training and the remaining one is used for validation to obtain the accuracy results. Train K times in this way and use the average value of each training as the final result of cross validation model. The grid search algorithm is an exhaustive search parameter adjustment method, which obtains the optimal parameters by looping through the range of candidate parameters and using the cross-validation results as indicators. This method has generality and is simple and efficient. In order to facilitate model comparison, this method is used as a model parameter selection method. Select historical CQI, MCS, and SINR as input variables to predict the SINR of the current channel.

According to the principle of random forest, the algorithm process for building an SINR model of random forest prediction channel is Algorithm 1. The specific steps are as follows:

Algorithm 1: Random forest prediction channel SINR

① Input: Pre-treatment the original data. Select historical CQI, MCS, and SINR Output: the prediction results ② Output: current channel SINR; ③ Divide the sample set into test set and training set and divide the training set into K parts; ④ Set the grid search range for the number of decision regression trees as n, the maximum eigenvalue as m, and the maximum tree depth as D; ⑤ Select a set of parameters for the grid search range and use the selected K-1 fold subsets data as the sample of the single decision tree; ⑥ For i = 1, i < k, i++; ⑦         While j <= n do ⑧                     Select m features from the feature set using the selection method in the grid search parameters. When the depth of the tree is less than the maximum depth of the tree d, the optimal branch characteristics and split points are computed, and the node sample is branched into two nodes in the next level; ⑨         End while ⑩ End for ⑪ calculate the mean of the evaluation indexes of K-1 test sets as the evaluation indexes of the prediction model; ⑫ Calculate the evaluation index of the predicted data as with the remaining one-fold data; ⑬ Input the test set data to each tree to receive the regression results of each tree and use the average value to obtain the prediction results of the model.

The flowchart of Algorithm 1 (random forest prediction) is shown in Figure 1.

4. Energy-Efficient Resource Optimization Allocation Algorithm Based on Channel Information Prediction

The mathematical model of energy-efficient optimization established according to Section 2 ${\mathrm{P}}_1$ and its constraints,${\mathrm{P}}_1$ is a mixed integer nonlinear programming (MINLP) problem. In order to obtain accurate channel information, we use the proposed random forest prediction channel SINR for obtaining real-time CQI and MCS and design the optimal energy-efficient resource allocation scheme on this basis. Define the CQI index set allocated on the available RB as ${\mathbb{J}}_{\mathrm{m}}=\left\{{\mathrm{j}|\mathrm{C}}_{\mathrm{n},\mathrm{m},\mathrm{k}}\ge \mathrm{j},\forall \mathrm{j},\forall \mathrm{k}\right\}$. In order to obtain the optimal energy-efficient resource allocation scheme, according to the mathematical model of energy-efficient optimization${\mathrm{P}}_1$ and its constraints, redefine the expressions of the total user rate and total power consumption, which are, respectively, Formulas (11) and (12):

$$\mathrm{R}\mathfrak{a},\mathfrak{b},\mathfrak{p}={\displaystyle \sum }_{\mathrm{k}=1}^{\mathrm{K}}{\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{m}=1}^{\mathrm{M}}{\displaystyle \sum }_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}{\mathrm{B}}_{\mathrm{RB}}{\log }_2\left(1+{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}{\mathsf{\gamma }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\right)$$

(11)

$$\mathrm{P}\left(\mathfrak{a},\mathfrak{b},\mathfrak{p}\right)=\mathsf{\zeta }{\displaystyle \sum }_{\mathrm{k}=1}^{\mathrm{K}}{\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{m}=1}^{\mathrm{M}}{\displaystyle \sum }_{\mathrm{j}ϵ{\mathbb{J}}_{\mathrm{m}}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}+{\mathrm{P}}_{\mathrm{C}}$$

(12)

where $\mathfrak{a}$, $\mathfrak{b}$, $\mathfrak{p}$ represents the CC allocation scheme, the RB allocation scheme, and the power allocation scheme, respectively. Therefore, the energy-efficient optimization mathematical model ${\mathrm{P}}_1$ is simplified to ${\mathrm{P}}_2$:

$${\mathrm{P}}_2:\max \mathrm{R}\left(\mathfrak{a},\mathfrak{b},\mathfrak{p}\right)/\mathrm{R}\left(\mathfrak{a},\mathfrak{b},\mathfrak{p}\right)$$

(13)

$${\displaystyle \sum }_{\mathrm{k}=1}^{\mathrm{K}}{\displaystyle \sum }_{\mathrm{j}ϵ{\mathbb{J}}_{\mathrm{m}}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\le 1,\forall \mathrm{n}\in {ℂ}_{\mathrm{k}},\forall \mathrm{m}$$

(13a)

$${\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\le {\mathrm{C}}_{\mathrm{k}},\forall \mathrm{k}$$

(13b)

$${\displaystyle \sum }_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\le 1,\forall \mathrm{n},\forall \mathrm{k}$$

(13c)

$${\displaystyle \sum }_{\mathrm{k}=1}^{\mathrm{K}}{\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{m}=1}^{\mathrm{M}}{\displaystyle \sum }_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\le {\mathrm{P}}_{\mathrm{T}}$$

(13d)

$${\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\in \left\{0,1\right\},{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\in \left\{0,1\right\},{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\ge 0,\forall \mathrm{k},\forall \mathrm{n},\forall \mathrm{m}$$

(13e)

4.1. RB and Power Allocation Algorithm for Energy-Efficient Optimization

In order to facilitate the analysis and solution of the energy-efficiency optimization problem ${\mathrm{P}}_2$, the RB and power allocation are performed when the predicted SINR and CC allocation (${\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)$ or $\mathfrak{a}$ is known) are known. The set of component carriers allocated to user k with MCS$\mathrm{j}$ is defined as ${ℂ}_{\mathrm{k}}=\left\{{\mathrm{n}|\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}=1,\forall \mathrm{n},\forall \mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}\right\}$ and the set of users with MCS$\mathrm{j}$ allocated carrier n is defined as ${\mathbb{U}}_{\mathrm{n}}=\left\{{\mathrm{k}|\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}=1,\forall \mathrm{k},\forall \mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}\right\}$. In order to ensure the RB and power allocation problems can be solved by fractional programming theory, we first relax the 0–1 discrete variable ${\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}\right)$ to a real variable in the interval [0, 1] and introduce the slack variable ${\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$ and ${\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$, then the RB and power allocation optimization are equivalent to the optimization problem ${\mathrm{P}}_3$ with ${\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$ and ${\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$ as independent variables:

$${\mathrm{P}}_3:\max \frac{\widehat{\mathrm{R}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)}{\widehat{\mathrm{P}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)}=\max \frac{{{\displaystyle \sum }}_{\mathrm{n}=1}^{\mathrm{N}}{{\displaystyle \sum }}_{\mathrm{m}=1}^{\mathrm{M}}{{\displaystyle \sum }}_{\mathrm{k}\in {\mathbb{U}}_{\mathrm{n}}}{{\displaystyle \sum }}_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}{\mathrm{B}}_{\mathrm{RB}}{\log }_2\left(1+\frac{{\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}}{{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}}{\mathsf{\gamma }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\right)}{\mathsf{\zeta }{{\displaystyle \sum }}_{\mathrm{n}=1}^{\mathrm{N}}{{\displaystyle \sum }}_{\mathrm{m}=1}^{\mathrm{M}}{{\displaystyle \sum }}_{\mathrm{k}\in {\mathbb{U}}_{\mathrm{n}}}{{\displaystyle \sum }}_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}+{\mathrm{P}}_{\mathrm{C}}}$$

(14)

$${\displaystyle \sum }_{\mathrm{k}\in {\mathbb{U}}_{\mathrm{n}}}{\displaystyle \sum }_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\le 1,\forall \mathrm{m},\forall \mathrm{n}\in {ℂ}_{\mathrm{k}}$$

(14a)

$${\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{m}=1}^{\mathrm{M}}{\displaystyle \sum }_{\mathrm{k}\in {\mathbb{U}}_{\mathrm{n}}}{\displaystyle \sum }_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\le {\mathrm{P}}_{\mathrm{T}}$$

(14b)

$$0\le {\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\le 1,\forall \mathrm{n},\forall \mathrm{m},\forall \mathrm{k},\forall \mathrm{j}$$

(14c)

$${\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\ge 0,\forall \mathrm{n},\forall \mathrm{m},\forall \mathrm{k},\forall \mathrm{j}$$

(14d)

P₃ is a fractional programming problem whose numerator $\widehat{\mathrm{R}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)$ is a concave function and its denominator $\widehat{\mathrm{P}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)$ is a positive affine function. According to the nonlinear fractional programming theory, Formula (14) is a quasi-concave function, which can be solved by converting P₃ into a non-fractional subtraction form using Dinkelbach theory. Therefore, the optimization problem P₃ is transformed into a non-fractional subtraction form P₄ and the ${\mathsf{\rho }}_{\mathrm{i}}$ series is constructed to approximate the optimal energy efficiency ${\mathsf{\rho }}^{\ast }$. When the component carrier allocation is known, it is assumed that the energy efficiency $\mathsf{\rho }=\frac{\widehat{\mathrm{R}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)}{\widehat{\mathrm{P}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)}$, the objective function, and constraints of P₄ are as follows:

$${\mathrm{P}}_4:\mathrm{f}\left(\mathsf{\rho }\right)={\max }_{\mathfrak{b},{\displaystyle \widehat{\mathfrak{p}}}}[\widehat{\mathrm{R}}\left(\mathfrak{b},{\displaystyle \widehat{\mathfrak{p}}}\right)-\mathsf{\rho }\widehat{\mathrm{P}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)]$$

(15)

s.t. Formulas (14a), (14b), (14c), (14d)

Theorem 1. 

The necessary and sufficient condition for$f\left(\rho \right)$to obtain the maximum energy efficiency${\rho }^{\ast }$is to satisfy:$ma{x}_{\mathfrak{b},\widehat{\mathfrak{p}}} \left[\widehat{R}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)-{\rho }^{\ast }\widehat{P}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)\right]=\widehat{R}\left({\mathfrak{b}}^{\ast },{\widehat{\mathfrak{p}}}^{\ast }\right)-{\rho }^{\ast }\widehat{P}\left({\mathfrak{b}}^{\ast },{\widehat{\mathfrak{p}}}^{\ast }\right)=0$and when the maximum energy efficiency is ${\rho }^{\ast }$, the optimal value$\left\{{\mathfrak{b}}^{\ast },{\widehat{\mathfrak{p}}}^{\ast }\right\}$of the independent variable corresponding to the problem$P_4$is also the optimal solution of problem$P_3$.

Proof. 

 

With the CC allocation known, let S be the set of feasible solutions for the RB and power allocation scheme $\left\{\mathfrak{b},\widehat{\mathfrak{p}}\right\}$ of the ${\mathrm{P}}_3$, so it satisfies the constraints Formulas (14a), (14b), (14c), and (14d); definition $\mathrm{x}=\left\{\mathfrak{b},\widehat{\mathfrak{p}}\right\}$ is any feasible solution in the set S, $\forall \mathrm{x}\in \mathrm{S}$.

Sufficient condition: In the case of known CC allocation, if ${\mathrm{x}}^{\ast }=\left\{{\mathfrak{b}}^{\ast },{\widehat{\mathfrak{p}}}^{\ast }\right\}$ is a feasible solution for optimal RB and power allocation, then ${\mathsf{\rho }}^{\ast }=\frac{\widehat{\mathrm{R}}\left({\mathrm{x}}^{\ast }\right)}{\hat{\mathrm{P}}\left({\mathrm{x}}^{\ast }\right)}\ge \frac{\hat{\mathrm{R}}\left(\mathrm{x}\right)}{\hat{\mathrm{P}}\left(\mathrm{x}\right)}$, so we obtain the following conclusion: (a): $\hat{\mathrm{R}}\left(\mathrm{x}\right)-{\mathsf{\rho }}^{\ast }\hat{\mathrm{P}}\left(\mathrm{x}\right)\le 0$; and (b): $\widehat{\mathrm{R}}\left({\mathrm{x}}^{\ast }\right)-{\mathsf{\rho }}^{\ast }\hat{\mathrm{P}}\left({\mathrm{x}}^{\ast }\right)=0$.

From (a) we can obtain ${\max }_{\mathrm{x}}\left\{\hat{\mathrm{R}}\left(\mathrm{x}\right)-{\mathsf{\rho }}^{\ast }\hat{\mathrm{P}}\left(\mathrm{x}\right)|\forall \mathrm{x}\in \mathrm{S}\right\}=0$; from (b) the maximum value is obtained when $\mathrm{x}={\mathrm{x}}^{\ast }$.

Necessary condition: if ${\mathrm{x}}^{\ast }=\left\{{\mathfrak{b}}^{\ast },{\widehat{\mathfrak{p}}}^{\ast }\right\}$ is a solution of ${\max }_{\mathrm{x}}\left\{\hat{\mathrm{R}}\left(\mathrm{x}\right)-{\mathsf{\rho }}^{\ast }\hat{\mathrm{P}}\left(\mathrm{x}\right)|\forall \mathrm{x}\in \mathrm{S}\right\}$, namely $\hat{\mathrm{R}}\left({\mathrm{x}}^{\ast }\right)-{\mathsf{\rho }}^{\ast }\hat{\mathrm{P}}\left({\mathrm{x}}^{\ast }\right)=0$, then $\hat{\mathrm{R}}\left(\mathrm{x}\right)-{\mathsf{\rho }}^{\ast }\hat{\mathrm{P}}\left(\mathrm{x}\right)\le \hat{\mathrm{R}}\left({\mathrm{x}}^{\ast }\right)-{\mathsf{\rho }}^{\ast }\hat{\mathrm{P}}\left({\mathrm{x}}^{\ast }\right)=0$, therefore, we can obtain (c): $\left\{\hat{\mathrm{R}}\left(\mathrm{x}\right)-{\mathsf{\rho }}^{\ast }\hat{\mathrm{P}}\left(\mathrm{x}\right)|\forall \mathrm{x}\in \mathrm{S}\right\}\le 0$; and (d): $\hat{\mathrm{R}}\left({\mathrm{x}}^{\ast }\right)-{\mathsf{\rho }}^{\ast }\hat{\mathrm{P}}\left({\mathrm{x}}^{\ast }\right)=0$.

From (c), we can obtain${\mathsf{\rho }}^{\ast }\ge \frac{\hat{\mathrm{R}}\left(\mathrm{x}\right)}{\hat{\mathrm{P}}\left(\mathrm{x}\right)},\forall \mathrm{x}\in \mathrm{S}$, namely, ${\mathsf{\rho }}^{\ast }$ is the maximum energy efficiency; from (d),we can obtain${\mathsf{\rho }}^{\ast }=\frac{\hat{\mathrm{R}}\left({\mathrm{x}}^{\ast }\right)}{\hat{\mathrm{P}}\left({\mathrm{x}}^{\ast }\right)}$, namely, ${\mathrm{x}}^{\ast }$ is the optimal RB and power allocation scheme.

Therefore, Theorem 1 is proved.

The proof is over. □

According to Theorem 1, the Dinkelbach method or dichotomy method can be used to obtain the optimal energy efficiency ${\mathsf{\rho }}^{\ast }$. Both the Dinkelbach method and the bisection method obtain the optimal parameter ρ by iterating and updating ρ until the convergence conditions are satisfied. The two methods have the same convergence speed, but the Dinkelbach method does not need to set the upper limit of ρ in advance, so we use the Dinkelbach method to find the optimal energy efficiency ${\mathsf{\rho }}^{\ast }$. See Algorithm 2 for the specific steps.

Algorithm 2: Dinkelbach algorithm

① $\mathrm{Initialization}\mathrm{i}\leftarrow 0;{\mathsf{\rho }}^0\leftarrow 0$, convergence condition $\mathsf{\epsilon }={10}^{-4}$ ② $\mathrm{while}\parallel {\mathsf{\rho }}^i-{\mathsf{\rho }}^{i-1}\parallel \ge \mathsf{\epsilon }$ do ③ $\mathrm{i}\leftarrow \mathrm{i}+1$; ④ $\mathrm{update}{\mathsf{\rho }}^i$ using the Newton iterative method; ⑤ end while ⑥ ${\mathsf{\rho }}^{\ast }\leftarrow \frac{\widehat{R}\left({\mathfrak{b}}^{\ast },{\widehat{\mathfrak{p}}}^{\ast }\right)}{\widehat{P}\left({\mathfrak{b}}^{\ast },{\widehat{\mathfrak{p}}}^{\ast }\right)}$.

Next, we are to assume that ρ ≥ 0 for solving the optimization problem ${\mathrm{P}}_4$. For the convenience of analysis, the ${\mathrm{P}}_4$ is rewritten as ${\mathrm{P}}_{4-1}$,

$${\mathrm{P}}_{4-1}:{\max }_{\mathfrak{b},\widehat{\mathfrak{p}}}[\hat{\mathrm{R}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)-{\mathsf{\rho }}^{\mathrm{i}-1}\hat{\mathrm{P}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)]$$

(16)

s.t. Formulas (14a), (14b), (14c), (14d)

Where ${\mathsf{\rho }}^{\mathrm{i}-1}$ is the energy efficiency of the previous iteration, assuming that ${\mathsf{\rho }}^{\mathrm{i}-1}\ge 0$ is a constant. $\hat{\mathrm{R}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)$ is a concave function, $\hat{\mathrm{P}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)$ is an affine function, and the constraints are all linear combinations. We can obtain that ${\mathrm{P}}_{4-1}$ is a convex optimization problem. Therefore, corollary 1 can be obtained.

Inference 1. 

If the optimization problem$P_{4-1}$is feasible, then$P_{4-1}$is a convex optimization problem for feasible solutions of all the variables$\left\{\mathfrak{b},\widehat{\mathfrak{p}}\right\}$.

Since ${\mathrm{P}}_{4-1}$ is a convex optimization problem, ${\mathrm{P}}_{4-1}$ can be solved using a Lagrangian dual method and the optimal solution can be obtained. For the optimization problem ${\mathrm{P}}_{4-1}$, the Lagrangian function we constructed is as follows:

$$ℒ\left(\mathfrak{b},\widehat{\mathfrak{p}},\mathsf{\lambda },\mathsf{\mu }\right)=\hat{\mathrm{R}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)-\mathsf{\rho }\hat{\mathrm{P}}\left(\mathfrak{b},\widehat{\mathfrak{p}}\right)+\mathsf{\lambda }\left({\mathrm{P}}_{\mathrm{T}}-{\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{m}=1}^{\mathrm{M}}{\displaystyle \sum }_{\mathrm{k}\in {\mathbb{U}}_{\mathrm{n}}}{\displaystyle \sum }_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\right)+\mathsf{\mu }\left(1-{\displaystyle \sum }_{\mathrm{k}\in {\mathbb{U}}_{\mathrm{n}}}{\displaystyle \sum }_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\right)$$

(17)

where λ ≥ 0 is the Lagrangian multiplier related to the constraint of ${\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$; $\mathsf{\mu }\ge 0$ is the Lagrangian multipliers related to the constraint conditions ${\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$; and $\mathsf{\rho }$ is a shorthand for ${\mathsf{\rho }}^{\mathrm{i}-1}$. See Algorithm 3 for the update $\mathsf{\rho }$.

The constructed Lagrangian dual function is:

$$\mathrm{g}\left(\mathsf{\lambda },\mathsf{\mu }\right)=\underset{\mathfrak{b},\widehat{\mathfrak{p}}}{\max }ℒ\left(\mathfrak{b},\widehat{\mathfrak{p}},\mathsf{\lambda },\mathsf{\mu }\right)$$

(18)

The dual optimization problem of the original optimization problem ${\mathrm{P}}_{4-1}$ is:

$$\min \mathrm{g}\left(\mathsf{\lambda },\mathsf{\mu }\right)=\underset{\mathsf{\lambda }>0,\mathsf{\mu }>0}{\min }\underset{\mathfrak{b},\widehat{\mathfrak{p}}}{\max }ℒ\left(\mathfrak{b},\widehat{\mathfrak{p}},\mathsf{\lambda },\mathsf{\mu }\right)=\underset{\mathsf{\lambda }>0,\mathsf{\mu }>0}{\min }{{\displaystyle \sum }}_{\mathrm{n},\mathrm{m}}{\mathrm{g}}_{\mathrm{k}}\left(\mathsf{\lambda }\right)+{\mathsf{\lambda }\mathrm{P}}_{\mathrm{T}}+\mathsf{\mu }$$

(19)

where

$${\mathrm{g}}_{\mathrm{k}}\left(\mathsf{\lambda },\mathsf{\mu }\right)=\max ({\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}{\mathrm{B}}_{\mathrm{RB}}{\log }_2\left(1+\frac{{\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}}{{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}}{\mathsf{\gamma }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\right)-\mathsf{\rho }\left({\mathsf{\zeta }\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}-{\mathrm{P}}_{\mathrm{C}}\right)-{\mathsf{\lambda }\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}-{\mathsf{\mu }\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$$

To solve the minimum value of ${\mathrm{g}}_{\mathrm{k}}\left(\mathsf{\lambda },\mathsf{\mu }\right)$, according to the KKT conditions, using the method of finding partial derivatives of ${\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}$ and ${\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$, we can obtain:

$${\mathrm{S}}^{\ast }{}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}={[(\frac{{\mathrm{B}}_{\mathrm{RB}}/\ln 2}{\mathsf{\rho }\mathsf{\zeta }+\mathsf{\lambda }}-\frac{1}{{\mathsf{\gamma }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}})]}^{+}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$$

(20)

${\mathrm{p}}^{\ast }{}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}={\mathrm{S}}^{\ast }{}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}/{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$, so the optimal power solution is:

$${\mathrm{p}}^{\ast }{}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}={\left[\left(\frac{{\mathrm{B}}_{\mathrm{RB}}/\ln 2}{\mathsf{\rho }\mathsf{\zeta }+\mathsf{\lambda }}-\frac{1}{{\mathsf{\gamma }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}}\right)\right]}^{+}$$

(21)

where${\left[\mathrm{x}\right]}^{+}=\max \left(0,\mathrm{x}\right)$, we obtain that the optimal solution of RB is ${\mathsf{\eta }}^{\ast }{}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$,

$${\mathsf{\eta }}^{\ast }{}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}={\left[{\mathrm{B}}_{\mathrm{RB}}{\log }_2\left(1+{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}{\mathsf{\gamma }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\right)+\mathsf{\mu }\right]}^{+}$$

(22)

As the value of ${\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$ in the original optimization problem ${\mathrm{P}}_2$ is an integer “0” or “1”, with $\mathsf{\mu }$ known, the RB identifier ${\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}$ assigned to user k is obtained by the following formula:

$${\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}=\{\begin{array}{c}1,\mathrm{k}\in {\mathbb{U}}_{\mathrm{n}}=\mathrm{argmax}\left({\mathrm{r}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}/{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\right), \forall \mathrm{n}\in {ℂ}_{\mathrm{k}},\forall \mathrm{m})\\ 0, \mathrm{otherwise}\end{array}$$

(23)

The RB and power allocation of the optimal energy efficiency is carried out on the premise that the Lagrangian multipliers $\mathsf{\lambda }$,$\mathsf{\mu }$ are known. Therefore, the optimal value of the Lagrangian multipliers $\mathsf{\lambda }$,$\mathsf{\mu }$ should also be obtained by searching. Since the dual problem Equation (19) of ${\mathrm{P}}_{4-1}$ is an unconstrained convex optimization problem, we adopt the sub-gradient method in [33] to update $\mathsf{\lambda }$ and $\mathsf{\mu }$. The update method is shown in Equations (24) and (25):

$${\mathsf{\lambda }}^{\mathrm{i}+1}={\left[{\mathsf{\lambda }}^{\mathrm{i}}-\frac{1}{\mathrm{i}}\left({\mathrm{P}}_{\mathrm{T}}-{\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\displaystyle \sum }_{\mathrm{m}=1}^{\mathrm{M}}{{\displaystyle \sum }}_{\mathrm{k}\in {\mathbb{U}}_{\mathrm{n}}}{\displaystyle \sum }_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathrm{S}}_{\mathrm{n},\mathrm{m}}^{\ast \mathrm{k},\mathrm{j}}\right)\right]}^{+}$$

(24)

$${\mathsf{\mu }}^{\mathrm{i}+1}={\left[{\mathsf{\mu }}^{\mathrm{i}}-\frac{1}{\mathrm{i}}\left(1-{\displaystyle \sum }_{\mathrm{k}\in {\mathbb{U}}_{\mathrm{n}}}{\displaystyle \sum }_{\mathrm{j}\in {\mathbb{J}}_{\mathrm{m}}}{\mathsf{\eta }}_{\mathrm{n},\mathrm{m}}^{\ast \mathrm{k},\mathrm{j}}\right)\right]}^{+}$$

(25)

where i is the current iteration number.

The optimal energy-efficient RB and power allocation algorithm is defined as the ERPA algorithm. For the specific ERPA algorithm steps is shown in Algorithm 3.

Algorithm 3: ERPA Algorithm

Input: the set ${ℂ}_{k }\forall k$ of component carrier assigned to each user; obtained CQI index and MCS by predicted SINR in Section 3.2;$P_T$;$P_C$; Output: RB allocation scheme $\mathfrak{b}$, power allocation scheme $\widehat{\mathfrak{p}}$

① $\mathrm{Initialization}\mathrm{i}\leftarrow 0;{\mathsf{\rho }}^0\leftarrow 0$, convergence condition $\mathsf{\epsilon }={10}^{-4}$ ② $\mathrm{while}\parallel {\mathsf{\rho }}^i-{\mathsf{\rho }}^{i-1}\parallel \ge \mathsf{\epsilon }$ do ③ $\mathrm{Use}\mathrm{the}\mathrm{Lagrangian}\mathrm{dual}\mathrm{to}\mathrm{perform}\mathrm{power}\mathrm{and}\mathrm{RB}\mathrm{allocation}\mathrm{of}{P}_{5-4-1}$; ④ $\mathrm{update}{\lambda }^i$ and ${\mu }^i$ by (24) and (25); ⑤ $\mathrm{update}{\mathsf{\rho }}^i$ by Newton iterative method; ⑥ $\mathrm{i}\leftarrow \mathrm{i}+1$; ⑦ end while ⑧ $\mathrm{obtain}{p}^{\ast }{}_{n,m}^{k,j}$, ${\eta }^{\ast }{}_{n,m}^{k,j}$ and ${\mathfrak{b}}^{\ast }$, ${\widehat{\mathfrak{p}}}^{\ast }$; ⑨ ${\mathsf{\rho }}^{\ast }\leftarrow \frac{\widehat{R}\left({\mathfrak{b}}^{\ast },{\widehat{\mathfrak{p}}}^{\ast }\right)}{\widehat{P}\left({\mathfrak{b}}^{\ast },{\widehat{\mathfrak{p}}}^{\ast }\right)}$.

4.2. CC Allocation Algorithm for Energy-Efficient Optimization

The premise of executing the RB and power allocation algorithm ERPA in Section 4.1 is to assume that the user’s CC allocation is known and the allocation scheme $\mathfrak{a}$ of the CCs in the original energy-efficient optimization problem ${\mathrm{P}}_2$ still needs to be further determined. To this end, the CC allocation algorithm combining iterative pruning and avoiding frequent handover of narrowband users is proposed and this CC allocation algorithm is defined as a DDJBNBC algorithm. The CC set ${ℂ}_{\mathrm{k}}$ allocated to each user is randomly generated in the interval [1,5]. In order to ensure that the CCs used by the users can satisfy the constraints of their carrier aggregation capabilities and energy efficiency requirements, each iteration will search for CCs that do not satisfy the requirements and remove them. The criterion for deleting CC is that when $\left|{ℂ}_{\mathrm{k}}\right|>{\mathrm{C}}_{\mathrm{k}}$, and Formula (26) is satisfied, then delete the corresponding CC:

$$\mathrm{n}\prime ,\mathrm{k}\prime =\mathrm{argmax}\left\{{\mathrm{E}}_{\mathrm{n},\mathrm{k}}=\frac{{\mathrm{R}}_{\mathrm{k}}}{{{\displaystyle \sum }}_{\mathrm{n}\in {ℂ}_{\mathrm{k}}-\mathrm{n}″}^{}{{\displaystyle \sum }}_{\mathrm{m}}^{}{{\displaystyle \sum }}_{\mathrm{j}}^{}{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}},\forall \mathrm{n}\in {ℂ}_{\mathrm{k}}-\mathrm{n}″,\mathrm{k}\in {\mathrm{K}}_{\mathrm{del}}\right\}$$

(26)

where ${\mathrm{K}}_{\mathrm{del}}=\left\{\mathrm{k}|{\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{N}}{\mathsf{\eta }}_{\mathrm{n}}^{\mathrm{k}}>{\mathrm{C}}_{\mathrm{k}}\right\}$ represents the set of users that do not satisfy the limit conditions of carrier aggregation capability; ${\mathrm{E}}_{\mathrm{n},\mathrm{k}}$ indicates that the component carrier assigned to user k does not contain the energy efficiency of $\mathrm{n}″$and $\mathrm{n}″$ is component carrier to be deleted. The component carrier and user pair $\mathrm{n}\prime ,\mathrm{k}\prime$ are obtained according to Equation (26), from the CC set ${ℂ}_{\mathrm{k}}$ delete the carrier $\mathrm{n}\prime$ and update ${ℂ}_{\mathrm{k}}$,${ℂ}_{\mathrm{k}}={ℂ}_{\mathrm{k}}-\mathrm{n}\prime$. Repeat the iteration until all the constraints are satisfied.

After all the users are allocated CCs that satisfy their carrier aggregation capabilities, in the next scheduling time slot, as broadband users can use all CCs that meet their aggregation capabilities, while narrowband users can only be allocated one CC, when broadband users need to aggregate narrowband users’ CC that the CC is using, the CC on the narrowband user may need to be switched to other CCs, so the frequent CC switching of the narrowband user will cause a lot of signal overhead and energy consumption, resulting in reduced system energy efficiency. In order to balance the signal overhead and energy consumption, in the next scheduling time slot, firstly keep the original CC allocation scheme unchanged, evaluate whether the CC needs to be switched for each narrowband user, and calculate the energy efficiency obtained by each narrowband user in the previous scheduling time slot; if the obtained energy efficiency is less than or equal to the energy efficiency threshold (${\mathrm{EE}}_{\mathrm{t}h}$) set in advance, switch the working CC of the narrowband user, otherwise the narrowband user keeps the original working CC unchanged. The switching criteria are as follows:

$$\{\begin{array}{c}{\mathrm{EE}}_{\mathrm{k}}^{\mathrm{t}}\le {\mathrm{EE}}_{\mathrm{t}h}\\ {\mathrm{EE}}_{\mathrm{k}}^{\mathrm{t}}=\frac{{\mathrm{B}}_{\mathrm{RB}}{\log }_2\left(1+{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}-1\right){\mathsf{\gamma }}_{\mathrm{n},\mathrm{m}}^{\mathrm{k}}\left(\mathrm{t}-1\right)\right)}{{\mathrm{p}}_{\mathrm{n},\mathrm{m}}^{\mathrm{k},\mathrm{j}}\left(\mathrm{t}-1\right)}\end{array}\mathrm{k}\in {\mathrm{K}}_1=\left\{\mathrm{k}|{\displaystyle \sum }_{\mathrm{n}\in {ℂ}_{\mathrm{k}}}{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{J}}{\mathsf{\chi }}_{\mathrm{n}}^{\mathrm{k},\mathrm{j}}=1\right\}$$

(27)

where ${\mathrm{K}}_1$ is the set of narrowband users and ${\mathrm{EE}}_{\mathrm{k}}^{\mathrm{t}}$ is the energy efficiency in time slot t-1 of narrowband user k calculated at time slot t. First, determine the CC set of narrowband users as $\{\mathrm{m}{\left(\mathrm{k}\right)}_{\mathrm{pre}},\forall \mathrm{k}\in {\mathrm{K}}_1\}$. If ${\mathrm{EE}}_{\mathrm{k}}^{\mathrm{t}}\le {\mathrm{EE}}_{\mathrm{t}h}$, the narrowband user switches CC, the CC set of narrowband users is updated to $\mathrm{m}{\left(\mathrm{k}\right)}_{\mathrm{update}}$, then the narrowband user set in time slot t is $\mathrm{m}{\left(\mathrm{k}\right)}_{\mathrm{new}}\leftarrow \mathrm{m}{\left(\mathrm{k}\right)}_{\mathrm{update}}$; otherwise, the narrowband user keeps the working CC in the last scheduled time slot unchanged, $\mathrm{m}{\left(\mathrm{k}\right)}_{\mathrm{new}}\leftarrow \mathrm{m}{\left(\mathrm{k}\right)}_{\mathrm{pre}}$.

The proposed CC allocation (DDJBNBC) algorithm that combines the iterative pruning method and the algorithm to avoid frequent handover of narrowband users. The specific process of the DDJBNBC algorithm is shown in Algorithm 4. The flow chart of Algorithm 4 (DDJBNBC) is shown in Figure 2.

Algorithm 4: DDJBNBC Algorithm

① $\mathrm{Input}:\mathrm{the}\mathrm{random}\mathrm{set}{ℂ}_{\mathrm{k}}\forall \mathrm{k}$; user number $\mathrm{k}$; maximum slot ${\mathrm{T}}_{\mathrm{slot}}$; ${\mathrm{EE}}_{\mathrm{t}h}$; ② $\mathrm{Output}:\mathrm{CC}\mathrm{allocation}\mathrm{scheme}\mathfrak{a}$; ③      $\mathrm{for}\mathrm{t}=1\mathrm{to}{\mathrm{T}}_{\mathrm{slot}}$ do ④         $\mathrm{compute}\mathrm{narrowband}\mathrm{user}\text{’}\mathrm{s}\mathrm{CC}\mathrm{set}\left\{\mathrm{m}{\left(\mathrm{k}\right)}_{\mathrm{pre}},\forall \mathrm{k}\in {\mathrm{K}}_1\right\}$; ⑤           for $\mathrm{k}=1$ to $\mathrm{K}$ do ⑥                  $\mathrm{while}\left|{ℂ}_{\mathrm{k}}\right|>{\mathrm{C}}_{\mathrm{k}}\mathrm{do}$ ⑦                             $\mathrm{obtain}\mathrm{n}\prime ,\mathrm{k}\prime$ by Equation (26); ⑧                              $\mathrm{update}{ℂ}_{\mathrm{k}}$, namely ${ℂ}_{\mathrm{k}}={ℂ}_{\mathrm{k}}-\mathrm{n}\prime$; ⑨                 end while ⑩                  $\mathrm{for}\mathrm{k}\in {\mathrm{K}}_1$ do ⑪                       $\mathrm{if}{\mathrm{EE}}_{\mathrm{k}}^{\mathrm{t}}\le {\mathrm{EE}}_{\mathrm{t}h}$ then ⑫                         $\mathrm{m}{\left(\mathrm{k}\right)}_{\mathrm{new}}\leftarrow \mathrm{m}{\left(\mathrm{k}\right)}_{\mathrm{update}}$; ⑬                         $\mathrm{else}\mathrm{m}{\left(\mathrm{k}\right)}_{\mathrm{new}}\leftarrow \mathrm{m}{\left(\mathrm{k}\right)}_{\mathrm{pre}}$ ⑭                       end if ⑮                 end for ⑯               end for ⑰              $\mathfrak{a}=\left\{{ℂ}_1,{ℂ}_2, \dots ,{ℂ}_{\mathrm{k}}\right\}\mathrm{end}\mathrm{for}$; ⑱        end for

4.3. Energy-Efficient Optimization Joint Resource Allocation Algorithm (PEJA) Based on Channel Information Prediction

On the basis of energy-efficient optimized RB and power allocation algorithm ERPA and CC allocation algorithm DDJBNBC, the energy efficiency joint resource optimization allocation (PEJA) algorithm based on channel information prediction is proposed. The PEJA algorithm uses the online predicted channel information and iterates the ERPA algorithm and the DDJBNBC algorithm. The detailed PEJA algorithm steps are shown in Algorithm 5.

Algorithm 5: PEJA algorithm

Input: the random set ${ℂ}_{k }\forall k$; user number n; maximum slot ${\mathrm{T}}_{slot }$Output: CC allocation scheme $\mathfrak{a}$; RB allocation scheme $\mathfrak{b}$; power allocation scheme $\mathfrak{p}$; maximal ${\eta }_{EE}^{\ast }$.

①  $\mathrm{for}t=1$$\mathrm{to}{\mathrm{T}}_{slot}$do ②      $\mathrm{while}(\mathrm{the}\mathrm{value}\mathrm{of}{P}_2$$$$$$\mathrm{than}\mathrm{in}t-1$ slot) do ③           $\mathrm{for}k=1$$$ do ④                  call for Algorithm 1 ⑤                  call for Algorithm 3 ERPA algorithm; ⑥                  call for Algorithm 4 DDJBNBC algorithm; ⑦            end for ⑧      end while ⑨    end for.

Algorithm 5 PEJA is the optimal energy-efficient resources allocation algorithm, which includes the iteration of two sub algorithms, they are Algorithm 3 EERPA and Algorithm 4 DDJBNBC separately. Algorithm 3 EERPA is the RB and power allocation sub algorithm and Algorithm 4 DDJBNBC is the CC allocation sub algorithm. Figure 3 shows the flow chart of PEJA algorithm 5.

5. Experiment Results and Analysis

In order to further analyze the performance of the proposed CA energy-efficient Joint Resource Allocation Algorithm (PEJA) based on channel information prediction, we established a communication simulation system for 5G with carrier aggregation. The communication network structure is that a base station eNB provide communication services for k uses by N component carriers, k uses are randomly distributed, and the downlink communication system is simulated. The main simulation parameters are set as shown in

Table 1. Main simulation parameters and settings.

Parameter	Settings
Number of CCs; bandwidth per CC	3 CCs; bandwidth of each CC is 10MHz
Subcarrier spacing	15KHz
Carrier frequency	3.5GHz
Path loss	PL(d) = 137.74 + 5.22log(d)
Thermal noise power spectral density	−174 dBm/Hz
Standard deviation of shadow fading	7 db
Small-scale fading distribution	Rayleigh fading

.

The standardized energy efficiency, standardized throughput, and cumulative distribution function of standardized energy efficiency are used to evaluate the performance of the proposed scheme and algorithm. Compared with the proposed algorithm, there are the greedy resource allocation (GA) algorithm without considering energy efficiency in [20], energy efficiency greedy (EGA) algorithm with the goal of maximizing energy efficiency after the modified greedy algorithm in [20], energy efficiency resource block allocation (ERAA) algorithm, and NP-EJA algorithm in [17]. The NP-EJA algorithm does not use predicted channel information on the basis of the PEJA algorithm proposed in this chapter, the measured CQI and its mapped channel state information are directly used for the joint allocation of energy efficiency resources. As shown in Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, and Figure 10, they are the average values of 50 experiments results.

The following expression is used for the standardization of evaluation indicators:

$${\mathrm{x}}_{\mathrm{i}}{}^{\prime }=\frac{{\mathrm{x}}_{\mathrm{i}}-\min \left(\mathrm{X}\right)}{\max \left(\mathrm{X}\right)-\min \left(\mathrm{X}\right)}$$

(28)

where ${\mathrm{x}}_{\mathrm{i}}$ is the standardized variable value; ${\mathrm{x}}_{\mathrm{i}}{}^{\prime }$ is the variable value after standardization; $\min \left(\mathrm{X}\right)$ is the minimum value of variable sequence X; $\max \left(\mathrm{X}\right)$ is the maximum value of the variable sequence X. The average carrier aggregation capability of users is defined as $\widehat{\mathrm{Ca}}={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{K}}{\mathrm{C}}_{\mathrm{k}}/\mathrm{K}$.

As shown in Figure 4, as the number of users increases, the power consumed by the system increases and the standardized energy efficiency of the four algorithms decreases steadily. It is obvious that the PEJA algorithm has the highest energy efficiency and the EGA algorithm has the lowest energy efficiency. The energy efficiency curves of NP-EJA and ERAA are close to each other but lower than those of the PEJA algorithm. The main reason is that both NP-EJA and ERAA algorithms directly use the delayed CQI of user feedback for modulation and coding, which affects the system performance. Although the ERAA algorithm can achieve the minimum energy consumption, its energy efficiency performance is lower than the PEJA algorithm.

As shown in Figure 5 with the maximum transmission power ${\mathrm{P}}_{\mathrm{T}}$ increasing, the standardized energy efficiency of most algorithms tends to increase, among which the PEJA algorithm is the most efficient. From the standardized energy efficiency curve in Figure 5, we can obtain the following rule: the maximum transmission power ${\mathrm{P}}_{\mathrm{T}}=35$ of the base station is the turning point of energy efficiency of the three algorithms (PEJA, NP-EJA, and ERAA). When ${\mathrm{P}}_{\mathrm{T}}<35$, the energy efficiency curves of the three algorithms rise rapidly with the P increasing. When ${\mathrm{P}}_{\mathrm{T}}>35$, the standardized energy efficiency curves of the PEJA algorithm, NP-EJA algorithm, and ERAA algorithm tend to be stable with the increase of the maximum transmission power. This is mainly because the power ${\mathrm{P}}_{\mathrm{T}}=35$, the transmission power of the base station can meet the power demand of the system, and increasing the maximum transmission power of the base station will not improve the system energy efficiency. Furthermore, the system has limited the maximum power constraint, which is also the reason why the system energy efficiency will not increase when increasing the maximum transmission power of the base station. The energy efficiency of the GA algorithm increases with the increase in transmission power until ${\mathrm{P}}_{\mathrm{T}}=25$ and the energy efficiency decreases rapidly with the increase in transmission power. The main reason is that the optimization goal of the GA algorithm is to maximize the utility function of the throughput. When the transmission power satisfies the user’s needs, the energy efficiency will reduce with increasing the transmission power.

As shown in Figure 6 and Figure 7, in the case of different carrier aggregation capabilities ($\widehat{\mathrm{Ca}}$), the throughputs of the four comparison algorithms increase with the number of cell users. The PEJA algorithm obtains the highest throughput. Because the PEJA algorithm uses the predicted channel information, it can better schedule system resources, so the throughput obtained is greater than the NP-EJA algorithm, ERAA algorithm, and EGA algorithm using the delayed channel information. The throughput of the ERAA algorithm is larger than that of the NP-EJA algorithm, which does not use predicted channel information. Since the ERAA algorithm does not consider power allocation and the NP-EJA algorithm considers power allocation to increase the complexity of the algorithm, the throughput of the NP-EJA algorithm is slightly lower than that of ERAA algorithm.

As shown in Figure 6 (($\widehat{\mathrm{Ca}}=2$) and Figure 7 ($\widehat{\mathrm{Ca}}=3$), we can see that the greater the average carrier aggregation capacity of users, the greater the system throughput they will obtain.

The cumulative distribution function (CDF) value represents the proportion of users less than or equal to the corresponding current EE value. In the case of the same EE, the lower the CDF function value is, the larger the user EE is.

From the average energy efficiency CDF curve ($\widehat{\mathrm{Ca}}=3$, $\mathrm{K}=15$) shown in Figure 8, it can be seen that the standardized energy efficiency of 82% users in the EGA algorithm are less than 0.6, the standardized energy efficiency of 60% users in the ERRA algorithm are less than 0.6, the standardized energy efficiency of 43% users in the NP-EJA algorithm are less than 0.6, and only the standardized energy efficiency of 32% users in the proposed PEJA algorithm is less than 0.6. It can be seen that the proposed energy efficiency of PEJA algorithm is the highest.

From the average energy efficiency CDF curve ($\widehat{\mathrm{Ca}}=2$, $\mathrm{K}=15$) shown in Figure 9, it can be seen that the normalized EE of 86% of the users in the EGA algorithm are less than 0.6, the normalized EE of 70% of the users in the ERRA algorithm are less than 0.6, the normalized EE of 44% of the users in the NP-EJA algorithm are less than 0.6, and only the normalized EE of 35% of the users in the proposed PEJA algorithm is less than 0.6. It can be seen that the proposed EE of the PEJA algorithm is the highest.

From the statical results shown in Figure 8 (($\widehat{\mathrm{Ca}}=3$) and Figure 9 ($\widehat{\mathrm{Ca}}=2$), we can see that the greater the average carrier aggregation capacity of users, the lower the EE they will obtain. However, compared with the EGA, ERAA, and NP-EJA algorithm, the PEJA algorithm has the highest EE.

In order to verify the performance of the proposed CC allocation algorithm (DDJBNBC algorithm), the proposed PEJA algorithm and PEJA-NC algorithm are compared. The PEJA-NC algorithm is the same as the PEJA algorithm, except that the PEJA-NC algorithm does not consider the signal overhead and energy consumption generated by narrowband user handover during CC allocation, namely, the CC allocation process does not control the handover of narrowband users. Figure 10 shows the comparison of the standardized energy efficiency of the two algorithms. Suppose the average carrier aggregation capacity ($\widehat{\mathrm{Ca}}=3$) of the user.

6. Conclusions

This paper mainly studied the optimal radio resource allocation based on carrier aggregation technology for improving the energy efficiency in 5G system.

The proposed energy-efficient sustainable resource optimization allocation scheme PEJA is verified through system simulation experiments. Compared with the NP-EJA, ERAA, EGA, and GA algorithms, PEJA achieves better energy-efficient performance in different user numbers and different maximum transmission powers and is also better than the comparison algorithm in throughput performance; PEJA algorithm has higher energy efficiency than PEJA-NC algorithm, which does not consider the CC handover of narrowband users. In conclusion, the proposed PEJA energy efficiency resource allocation scheme maximizes the system energy efficiency and achieves high throughput.