Knowledge Graph-Based Multi-Objective Recommendation for a 6G Air Interface: A Digital Twin Empowered Approach

Abstract

In future sixth-generation (6G) communication systems, it is foreseen that complex communication scenarios and critical performance requirements will necessitate more flexible air interface configurations. Traditional air interface adaptation will no longer be applicable to 6G due to issues such as high computational complexity, sub-optimal trade-offs among multi-objective performance metrics, outdated configurations due to fast-varying channels, etc. In this paper, the relevant user behaviors, communication environment, and system are virtualized via the digital twinning technique. Then, a knowledge graph-based multi-objective recommendation framework is proposed to configure the digital twinning air interface to adapt to channel conditions, while balancing various service requirements. First, the knowledge graph is applied to reveal complex dependencies between the air interface and the service requirements, and more importantly, to reconcile possibly contradictory performance targets. Furthermore, the air interface configuration, empowered by the digital twin technique, is able to exploit predicted prior knowledge about user behavior and the channel characteristics, thus improving the utilization efficiency of wireless resources promptly. Moreover, the digital twin technique allows the candidate air interfaces to be virtually verified and compared with little effort. Finally, two case studies are presented to demonstrate the potential of the knowledge graph-based recommendation method for the digital twinning air interface.

1. Introduction

The evolution of mobile internet services and applications has led to diverse performance requirements for mobile communication systems. As depicted in Figure 1, the international telecommunication union (ITU) has defined three primary application scenarios for fifth-generation (5G) systems: enhanced mobile broadband (eMBB), massive machine-type communication (mMTC), and ultra-reliable and low-latency communications (URLLC) [1]. Recently, the IMT-2030 promotion group has outlined that the sixth generation (6G) will further investigate the original three typical scenarios of 5G while extending to three new scenarios [2] in order to support immersive communication, integrated artificial intelligence (AI) and communication, hyper-reliable and low-latency communication, massive communication, ubiquitous connectivity, and integrated sensing and communication (ISAC). The corresponding performance requirements are shown in Figure 1.

Air interface techniques significantly impact the performance of communication systems. Typically, the transceivers adapt the air interface with the communication links by adequately loading the information bits in resource domains including the following: the code domain, the time domain, the frequency domain, the beam domain, and the power domain [3]. These require adaptive selection and configuration of the modulation and coding, time and frequency resource scheduling, beam activation, power control schemes, etc., according to the state of the communication links and the user demands. However, it is difficult for the transceivers to acquire precise environment and user information while accomplishing the multi-domain adaptation. First, the modeling of the channel dynamics and the user behavior are typically data-driven, which requires a significant amount of unstructured data. Such data cannot be acquired and processed by a single or a few transceivers, but have to be acquired by the network and processed at the data center. Second, optimally configuring the 6G air interface becomes a complex multi-objective optimization problem due to the multi-purpose communication scenarios with massive connected user equipments (UEs). Traditional adaptation methods require optimizing and searching over a high-dimensional and (sometimes) discrete parameter space for each performance metric, which is time-consuming and unable to resolve conflicts among performance metrics as well as among different users. To address the above challenges, digital twin (DT) technology is adopted hereafter to model and forecast user behavior, environment dynamics, and the configuration of communication systems. In addition, in order to align the demands of the UEs and the capabilities of the communication systems, an air interface knowledge graph (KG) is constructed. It establishes the relationship between the channel conditions, the user demands, and the air interface configurations, thus transforming the complex optimization procedures into multi-objective recommendations or inferences from the KG.

Recently, DT technology has emerged as an innovative paradigm for designing, predicting, and managing complex systems. It lies in the precise modeling of physical systems and the bidirectional information exchange between physical and digital realms [4]. It finds widespread applications in various vertical domains such as the manufacturing industry, network security, healthcare, aerospace, intelligent systems, mobile communication systems, and so on [5,6,7,8]. The integration of DT with mobile communication networks represents a potential direction in the future that will enable cost-effective, adaptive, and fast network-wide optimization and design [9]. Specifically, DT technology utilizes the digital realm to develop and test novel signal processing and network optimization algorithms. Researchers, such as Van H. et al., have utilized DTs to virtualize computation-intensive networks [10], where the computation resource allocation is optimized within the DT framework. To address the challenges of neural network training at mobile user terminals with insufficient computation and storage resources, Liu T. et al. propose a DT edge network architecture to select mobile-edge servers and offload computation tasks intelligently [11]. The aforementioned works emphasize that DT provides a cost-effective platform for evaluating various system configurations, and out of those the optimum can be chosen. In addition, by acquiring massive network-wide environment and user data at the data center, DT is able to effectively predict the non-stationary stochastic variations of communication channels and user behaviors, which are difficult to model explicitly [12,13,14,15,16]. This is in contrast to the modeling and predicting algorithms of the transceiver-level channel and user, whose accuracy is inferior due to insufficient data. Indeed, the accuracy of these predicting variations is essential for improving the performance of communication systems.

The extensive information of the environment and the user behavior provided by the DT are mostly unstructured and cannot be directly utilized by the communication systems. On the other hand, KGs are an effective method for representing relationships between unstructured information and are widely used to recommend system configurations in the field of industrial manufacturing [17,18]. As a relation-sensitive artificial intelligence approach, KGs represent data optimally for efficient computation and storage, revealing hidden complex relationships; see [19]. In [20], a recommendation framework based on KGs is proposed to optimize the precision and diversity of multi-objective recommendation problems. This paper will utilize the existing air interface configurations as an expert database to form an initial air interface KG. The relationships among the performance requirements of the UEs, the condition of the communication links, and the configurations of the air interface are then comprehensively understood in the graph, so as to better balance different performance requirements in the air interface recommendation. Based on the existing relationships, additional relationships are inferred and complemented by the KG, which represents new air interface configuration strategies with new combinations of performance requirements.

The contributions of this paper are summarized as follows:

• First, we analyze the challenges of existing air interface adaptation methods in scenarios such as the high-dynamic environment of 6G systems. The advantages of KGs and DTs in addressing these challenges are discussed.
• Then, we propose a KG-based multi-objective recommendation method for the 6G air interface, which is empowered by DT technology. This is achieved by simulating and predicting the variations of communication links and user behavior in the digital realm of the DT, which are used to adaptively and promptly configure the air interface. Moreover, an air interface KG is constructed based on expert knowledge, which establishes the relationship among the entities, including the channel conditions, the user demands, and the system configurations. Based on the KG, additional air interface configurations are inferred by exploiting the existing relational information stored in the KG. Then, the traditional air interface adaptation that searches over the parameter space is replaced by relational reasoning via the KG.
• Finally, we provide two use cases to validate the performance of the proposed method. First, simulation results show that the proposed method can effectively balance the joint optimization of multiple performance metrics. Second, in fast-varying dynamic environments, we show that the proposed method effectively avoids the outdated air interface configuration and significantly reduces the complexity of the multi-objective optimization problem.

The remainder of this paper is organized as follows. In Section 2, we analyze the challenges of the traditional air interface adaptation method and discuss the advantages of using KGs and DTs. In Section 3, the air interface digital twin technology is introduced. To demonstrate the effectiveness of the proposed technology, two use cases are presented in Section 4. Finally, conclusions are drawn in Section 5.

2. Challenges of Traditional Methods and Opportunities of KGs and DTs

To illustrate the rationale for introducing KGs and DTs, we first discuss the challenges of traditional air interface adaptation methods for communication networks, as illustrated in Figure 2.

(1) The fast-varying channels result in an outdated air interface configuration. As the channel information is acquired via channel measurements based on pilot signals, there is a delay between the channel information acquired by the transceivers and the actual data transmission. Once the delay exceeds the channel coherence time, the measured channel information mismatches the actual channel, resulting in a degradation in communication performance. Furthermore, the performance degradation is exacerbated in a highly dynamic environment. For instance, communication links towards or from high-speed rail and airplanes are highly dynamic, which makes it difficult to maintain stable communication links, let alone more involved services, such as hyper-reliable and low-latency transmissions.

Traditional channel acquisition methods, such as periodic measurements, often fail to capture high-dynamic features. This limitation decreases the optimality of air interface adaptation and results in inefficient resource utilization, or even communication outages.

(2) Multi-objective performance requirements pose a challenge in air interface optimizations. As shown in Figure 1, the optimal configuration of the 6G air interface is complex because multiple performance metrics are simultaneously optimized. To name a few, in the integration sensing and communication (ISAC)-assisted vehicle-to-everything, vehicles exchange information with roadside units via communication services, while avoiding collisions with other vehicles via sensing services. However, these services share the same air interface resources, while having different service requirements. Then, multiple system parameters may conflict when configuring the air interface. Traditionally, communication systems have adopted a divide-and-conquer approach, where each functional module is individually optimized for one or a few performance metrics. Yet, there is no guarantee that each performance metric is optimized system-wisely or that the simultaneous optimization of a set of performance metrics for multiple services will be achieved. The complex relationship between air interfaces, channels, and performance requirements has failed to be explored by traditional adaptation methods, which cannot comprehensively address the conflicts.

(3) Random changes in service demands result in reduced resource utilization efficiency or the worst-case system configuration. This is because efficient energy control requires that the base station (BS) activates or hibernates intelligently in response to changes in service demands [21,22]. The movements of people lead to the significant migration of hotspot areas of service demands over time, which cannot be accurately predicted by the BS. It is difficult to dynamically control the power consumption and configure communication resources of BSs in real time according to the migration of hotspot areas of service demands. Thus, inadequate energy control leads to the idleness of communication resources or poor user experiences. Therefore, there remains a considerable performance gap in improving the precision of energy control and resource configuration in mobile communication systems.

The aforementioned challenges highlight that traditional air interface adaptation methods encounter issues, such as outdated adaptations and sub-optimal trade-offs among various performance metrics, as well as low efficiency of resource utilization. Resolving these issues requires the communication system to dynamically estimate and predict the channels of each user. It also needs to comprehend the complex relationships among performance metrics, channel characteristics, and diverse parameters of the 6G air interface. Therefore, this paper proposes a new paradigm of air interface recommendation based on KGs and DTs, whose main advantages are as follows:

(1) KGs can integrate and process multi-dimensional data. KGs can integrate multiple types of data, including user requirements, channel status, network load, device characteristics, etc., into the form of structured entities. Then, the complex relationships of the aforementioned entities can be established and inferred in the graph. This multi-dimensional data processing capability enables communication systems to take into account various complex factors when making air interface recommendations.

(2) DT technology has high-precision simulation and prediction capabilities. DT technology can realize high-fidelity simulations by dynamically interacting data with the physical communication system, including the BS, users, environment data, channel characteristics, etc. The real-time monitoring function enables DT technology to analyze users’ trajectories and predict the variations of wireless channels. For example, if a user passes through an obstacle, the trajectory analysis of DTs provides environment awareness for the channel prediction model, which can improve the accuracy of channel prediction. The accurate channel predictions and high-fidelity simulations of DT technology enable the DTs and KGs to configure air interfaces with greater precision.

(3) KGs and DTs can balance multiple optimization objectives. In communication systems, it is often necessary to optimize multiple objectives simultaneously, such as maximizing system throughput, minimizing delay, and reducing power consumption. KGs can provide a multi-objective optimization strategy by analyzing the interdependencies between multiple objectives, such as transmission rate, delay, and fairness, and various parameters, such as modulation schemes, transmission power, and resource allocation. In addition, DTs can find an optimal configuration by simulating multiple air interfaces in parallel and evaluating the performance of each air interface on different optimization objectives.

(4) KGs and DTs support dynamic and real-time decision-making. By dynamically updating the graph of a KG, the system can make corresponding adjustments according to the real-time network and user status. Dynamic adaptation ability enables KGs to respond quickly when dealing with the real-time varying environment. DT technology updates the virtual model based on real-time data from interactions with the physical world, ensuring the accuracy of the air interface tested on the virtual platform.

In Section 3, we will introduce in detail how to use DTs and KGs in air interface adaptation while satisfying the 6G requirements.

3. Multi-Objective Recommendation Design for Digital Twin of Air Interface

The air interface configuration based on a KG and DT is illustrated in Figure 3. In this figure, the DT consists of two core components: the virtual world and the prediction algorithm. The virtual world dynamically simulates the entire physical environment and communication links. It stores historical data and supports virtual testing of the performance of air interface configurations. The prediction algorithm, on the other hand, is designed to predict time-varying channels, which helps to address the issue of outdated air interface configurations. Additionally, the KG is utilized to uncover hidden relationships between diverse users and air interface configurations, enabling the recommendation of appropriate air interface configurations.

In more detail, in the first step, real-time data of the physical world are inputted to the DT. The real-time data include the dynamic environment and behaviors of users to construct the virtual counterpart, as well as channel information for the channel state prediction. Via interaction between the physical and digital realms, the virtual environment, the users’ moving trajectories, and the service requirements are constantly updated, which are then used to forecast the future network capacity and performance requirements. The channel information is used to forecast the future channel conditions of the user by the prediction algorithm to avoid outdated air interface adaptation due to user mobility. In the second step, the predictions are then forwarded to the KG. Based on the established relationship in the graph, the KG recommends suitable air interfaces for users. In the third step, the suitable air interfaces are tested in the virtual world of the DT. Finally, the optimal air interface that meets the users’ requirements is selected and configured in the physical world in the fourth step. Subsequent subsections will elucidate the principles of the prediction algorithm and the construction of the KG.

To establish the relationship of the KG, channel scenario, mobility, channel state information, the minimum transmission rate, and the maximum bit error rate (BER) are used as user attributes to form the structured user entity. The air interface attributes, such as information encoding schemes, channel encoding schemes, signal modulation schemes, air interface properties, power allocation, beam precoding designs, and channel encoding schemes, are used to form the structured air interface entity. Leveraging similarities among structured entities and the existing air interface configurations brought from the DT, the KG enables developing the nonlinear hidden relationship between users and air interfaces, and additional air interface configurations are then inferred.

Next, we will present details of the DT-based prediction algorithm and KG construction. It is worth noting that the virtual world is a foundational component for the standard DT and has been extensively studied in various references [23,24,25,26]. Therefore, the detailed construction of the virtual world is not provided in this work.

3.1. Digital Twin-Based Prediction Algorithm

The DT-based prediction algorithm consists of five layers: information input, feature extraction, prediction, convolution, and output, as illustrated in Figure 4. In the input layer, input features of the DT-based prediction algorithm are historic channel measurements and future channel gains inferred by the DT. The historic channel measurements are a standard input feature in traditional channel prediction algorithms, which can be obtained from physical-world observations. In contrast, future channel gains are novel a input feature provided by the virtual world of the DT, offering additional predictive channel information compared with the traditional prediction algorithm. Specifically, in the virtual world of the DT, user mobility patterns are monitored and recorded, enabling the prediction of user locations at subsequent time instances. Based on these predicted locations and environment-aware radio maps containing location-specific channel knowledge [27], future channel gains can be inferred. This approach is particularly effective in scenarios involving sudden changes in the communication environment, such as when users encounter obstacles. Under such cases, traditional prediction algorithms relying solely on historical channels often fail to capture the rapid variations in channel dynamics.

In the feature extraction layer, statistical channel features of historic channels, such as the delay spread ${\tau }_{DS}$, K-factor $K_f$, and power delay profile $PDP\left(\tau \right)$, can be calculated as

$${\tau }_{DS}=\sqrt{{\displaystyle \frac{{\sum }_i{P}_i{({\tau }_i-\frac{{\sum }_i{P}_i{\tau }_i}{{\sum }_i{P}_i})}^2}{{\sum }_i{P}_i}}},$$

(1)

$$K_f={\displaystyle \frac{P_{\mathrm{LOS}}}{P_{\mathrm{NLOS}}}},$$

(2)

$$PDP\left(\tau \right)=\sum _i{P}_i\delta (\tau -{\tau }_i),$$

(3)

where $P_i$ and ${\tau }_i$ denote power and delay of the i-th path, respectively, while $P_{\mathrm{LOS}}$ and $P_{\mathrm{NLOS}}$ denote power of the line-of-sight (LoS) component and power of the non-line-of-sight (NLoS) components, respectively. Here, $\delta$(_⬝) is the Dirac impulse function. In addition to these statistical features, hidden features of both historical channels and future channel gains are extracted using a $3\times 3$ convolution kernel. The hidden features are subsequently concatenated with the historic channels, future channel gains, and statistical channel features, forming the input data of the prediction layer.

Then, the prediction layers are designed to extract linear and non-linear hidden features in the time domain, ensuring a comprehensive representation of the channel dynamics. The DT-based prediction algorithm is powered by Long Short-Term Memory (LSTM) networks, which are known for their ability to capture long-range dependencies in sequential data. In this setup, LSTM is employed to predict the channel at the next moment. The predictive neural element adopts convolutional long short-term memory (Conv-LSTM). Conv-LSTM is composed of a forget gate, an input gate, and an output gate, structured as in Figure 5. Unlike traditional LSTMs that rely on fully connected layers, Conv-LSTM utilizes convolutional layers with a 5 × 5 convolution kernel, enabling more effective extraction and processing of data features.

The convolution layer in Figure 4 consists of a 5 × 5 convolution kernel-based network followed by a fully connected network. The convolution network is used to extract local features from the output of the prediction layer, while the fully connected network maps these local features to the channel space, generating the predicted channel. Subsequently, the predicted channel is inputted to the KG along with the performance requirements predicted by the virtual world of the DT. In the next subsection, we will describe in detail how to utilize the KG to dynamically recommend appropriate air interface configurations.

3.2. Knowledge Graph Construction

The establishment and application of the KG is elucidated in Figure 6. There are three stages in the establishment of the KG: entity formation, feature enhancement, and training adaptation relation.

Initially, during the entity formation, Trans-D and Word2Vec [28,29] adequately map both unstructured information and relations into vectors. Within the context of 6G communication, as shown in

Table 1. Entities of the knowledge graph system.

Concept Category	Entity
User ID	0, 1, 2, …
	Transmission Rate (bps)
	Bit Error Rate
	Energy Efficiency (bps/W)
	Spectral Efficiency (bps/Hz)
	Channel Scenario
	Line-of-Sight Type
User Properties	Channel Power
	The Number of paths
	Power Distribution of paths
	Delay Spread
	Power Angle Spectrum
	Angle Spread
	Mobility
Air Interface ID	0, 1, 2, …
	Information Encoding Schemes
	Channel Encoding Schemes
	Signal Modulation Schemes
Air Interface Properties	Allocation Schemes of Transmission Power
	Allocation Schemes of Receiving Power
	Beam Precoding Designs
	Channel Encoding Schemes

, both the user and air interface knowledge contains non-structural information, as well as numerical information, such as text descriptions of communication scenarios, types of transmission service, coverage area patterns of BSs, values of the bandwidth, values of channel state information, and so on. The non-structural information is firstly converted into structured vectors using Word2Vec. For any given non-structural entity $e_t$ in Table 1, the text is tokenized into individual words $\{w_1,w_2,\dots ,w_K\}$. Each word or value $w_k$ is mapped to a continuous vector ${\mathbf{v}}_{w_k}$ in a lower-dimensional embedding space, where semantically similar words or values have closer embeddings. Then, the structured entity corresponding to the non-structural entity $e_i$ can be represented as

$${\mathbf{e}}_{\mathbf{i}}={\displaystyle \frac{1}{K}}\sum _{k=1}^K{\mathbf{v}}_{w_k}.$$

(4)

Based on these structured entities, relationships between entities in

Table 2. Relations of entities.

Relation Type	Head Entity	Tail Entity
Belongs To	User Properties	User ID
Belongs To	Air Interface Properties	Air Interface ID
Similarity	User ID	User ID
Adaptation	User ID	Air Interface ID

can be embedded using TransD. Specifically, TransD, the head entity ${\mathbf{e}}_i$, and the tail entity ${\mathbf{e}}_j$ are associated with projection vectors ${\mathbf{p}}_i,{\mathbf{p}}_j$ that map two entities into a dynamic space specific to their relation as follows:

$${\mathbf{r}}_i={\mathbf{e}}_i+{\mathbf{p}}_i^{\top }\mathbf{r},{\mathbf{r}}_j={\mathbf{e}}_j+{\mathbf{p}}_j^{\top }{\mathbf{e}}_j.$$

(5)

${\mathbf{r}}_i$ and ${\mathbf{r}}_j$ are the transformed embeddings of the head and tail entities, respectively. Finally, the relation from the head entity ${\mathbf{e}}_i$ to the tail entity ${\mathbf{e}}_j$ is defined as

$$r({\mathbf{e}}_i,{\mathbf{e}}_j)={\parallel {\mathbf{r}}_i-{\mathbf{r}}_j\parallel }_2^2.$$

(6)

Moreover, considering that both the air interface and the user encompass multiple properties, the application of the multi-head attention mechanism [30] becomes imperative. In more detail, each attention head specializes in learning different features of the air interface or the user. Formally, an air interface ID entity or a user ID entity comprises multiple feature entities—e.g., an air interface ID entity contains transmit power, modulation method, coding efficiency, etc. Therefore, an air interface ID entity or a user ID entity can be denoted as $\mathbf{E}=[{\mathbf{e}}_1,{\mathbf{e}}_2,\cdots ,{\mathbf{e}}_n]$. The multi-head attention mechanism computes a weighted sum of features, expressed as

$$\mathbf{Z}=\mathrm{concat}(z_1,z_2,\cdots ,z_h){\mathbf{W}}_O,$$

(7)

where $z_i$ is the output of the i-th attention head, ${\mathbf{W}}_O$ is the learnable projection matrix applied to the concatenated outputs, and h is the number of attention heads. The output of each attention head $z_i$ is calculated as

$$z_i=\mathrm{Softmax}\left({\displaystyle \frac{{\mathbf{W}}_Q^i\mathbf{E}{\left({\mathbf{W}}_K^i\mathbf{E}\right)}^T}{\sqrt{d_i}}}\right){\mathbf{W}}_V^i\mathbf{E},$$

(8)

where ${\mathbf{W}}_Q^i$, ${\mathbf{W}}_K^i$, and ${\mathbf{W}}_V^i$ are learnable weight matrices corresponding to the query, key, and value projections for the i-th attention head, respectively. The term $d_i$ denotes the dimensionality of the keys and queries, and the Softmax function ensures that attention scores are normalized. This multi-head attention mechanism enhances the precision of representations for air interface ID and user ID entities by prioritizing significant features while suppressing irrelevant details, which are crucial for modeling complex properties associated with both air interfaces and users.

Furthermore, high-order cross layers for users and air interfaces are constructed. Each layer generates higher-order interactions based on the existing layer, leveraging a deep neural network to enhance the features of users and air interfaces.

Finally, to reduce the dimensionality of the augmented high-order cross features, two convolution layers and corresponding pooling layers are used. The convolutional layer first generates multiple two-dimensional activation maps by sliding a number of equally sized filters across the width and height of the input data. The activation maps are stacked up in the depth direction to form the output of the convolutional layer. Pooling essentially involves sampling. Dimension compression is performed by taking the maximum or average value of the input feature maps. This step eliminates redundancy and noise and retains the most expressive features.

Eventually, because the user entity and the air interface entity are heterogeneous, a multi-layer perceptron (MLP) is employed to train the adaptation relation between them. A MLP consists of an input layer, a fully connected layer, and an output layer [31]. The fully connected layer consists of three $LeakyRelu$ activation functions, the units of which are 100, 50, and 25, respectively. The input is the concatenated vector of air interface vectors and user vectors, and the output is normalized through the Softmax function.

After the KG is established, predictions from the DT are used as user attributes to form the new user entity through entity formation in the first and second step of Figure 6. The KG can deduce the relation between the new user entity and each air interface entity via feature enhancement and a well-trained MLP in the third and fourth step. Eventually, by comparing the relation between the user entity and each air interface entity, several candidate air interfaces are recommended to the user in the fifth step.

4. Application and Performance Evaluation

In this section, to demonstrate the advantages of the KG and the DT in the adaptation of air interface, two use cases are presented.

4.1. Link-Level Performance Trade-Off

We first select the communication between ground stations and satellites as a simulation scenario, focusing on balancing three performance requirements, including block error rate (BLER), transmission rate, and transmission power. These performance metrics are of significant interest in low-earth-orbit (LEO) satellite communications with remote sensing requirements. Compared to the terrestrial connectivity scenario with a fixed base station, the movement of the LEO satellites results in limited visible time between the satellite and the fixed ground station. Within this visibility constraint, achieving highly reliable and large-capacity data transmission is typical and challenging. Furthermore, compared to terrestrial communication equipment, the energy resources of satellites, such as transmission power, are more limited. Therefore, the three performance requirements, including block error rate (BLER), transmission rate, and transmission power, are significant for LEO satellite communication. However, the cost of testing air interface configurations in practical satellite communication networks is too high, while DTs can provide a virtual test platform. In addition, traditional communication systems have adopted a divide-and-conquer approach, where each functional module is individually optimized for one or a few performance metrics. Yet, there is no guarantee that each performance metric is optimized system-wisely. However, the proposed KG- and DT-based method can explore the complex relationship between air interfaces, channels, and performance metrics, which can comprehensively balance the three critical optimization objectives.

In this context, the three conflicting optimization objectives, i.e., transmission power ≤ 45 dBW [32], transmission rate ≥ 35 Mbps, and block error rate (BLER) ≤ 0.01, are assumed. The channels are generated according to the 3GPP TR 38.811 model [33]. The air interface configurations include modulation schemes (QPSK or 16QAM), and encoding efficiency ranging from 120/1024 to 616/1024. Other parameter settings are shown in

Table 3. Parameter settings of balancing multiple performance requirements.

Carrier Frequency	Subcarrier Spacing	Slots	RBs of Each Slot
30 GHz	120 kHz	2	21

.

Four methods for air interface adaptation are employed in this scenario: (1) minimizing BLER; (2) maximizing the transmission rate; (3) minimizing the transmission power; and (4) the proposed method based on a KG and DT.

Simulation results are illustrated in Figure 7. Traditional adaptation methods, such as methods (1)–(3), artificially select one performance requirement as the air interface adaptation criterion. This always leads to a failure to satisfy other performance requirements. The adaptation method (4) achieves the three performance requirements. Because the KG explores relations between multiple performance requirements and various air interface parameters through feature enhancement and MLP. It can balance multiple conflicting performance metrics. Additionally, the adaptation results can be cost-effectively validated in the virtual world of the DT, further ensuring the fulfillment of each requirement.

4.2. Network-Level Multi-User Scheduling

To evaluate the ability of the proposed scheme to recommend air interfaces with low complexity, we select a scenario involving a cell with multiple mobile users. In this case, traditional methods use convex optimization theory to solve for the optimal air interface configuration on a given random initial solution [34]. However, high-dimensional configurable parameters of the air interface and a larger number of users increase the optimization complexity. By mining the historical adaptions between user states and air interfaces, KGs can provide a better initial solution and then reduce the optimization complexity.

In this context, considering the downlink of an OFDMA cellular system, there are N mobile users randomly placed in a circular area with the BS located at the center and a radius of 500 m. The BS and the users are equipped with single antennas. The air interface configuration considered in this subsection involves power and frequency resource allocation. Specifically, F resource blocks (RBs) with a carrier frequency of 3.5 GHz are considered, and the maximum transmission power that the BS can allocate is denoted as $P_T$. The channel model employed in this subsection is the 3GPP 38.901 Uma model [35]. The BS is positioned at a height of 20 m, while the N users move along straight trajectories at a constant velocity of 3 m/s and a height of 1.5 m. In this scenario, user mobility leads to channel variations, necessitating accurate channel prediction and real-time adjustments of the resource allocation scheme. We denote the channel amplitude and noise power of user n on RB f as $H_{n,f}$ and ${\sigma }_{n,f}^2$, respectively. According to the Shannon formula in [36], the channel capacity of user n on an OFDM symbol can be calculated by

$$R_n=\sum _{f=1}^F{a}_{n,f}{B}_0{log}_2\left(1+{\displaystyle \frac{p_{n,f}{\left|H_{n,f}\right|}^2}{{\sigma }_{n,f}^2}}\right),$$

(9)

where $p_{n,f}$ is the transmit power of the BS when it transmits information to user n in RB f. $B_0$ is the bandwidth of an RB, while $a_{n,f}$ is the RB allocation indicator. If RB f is allocated to user n, $a_{n,f}=1$; otherwise, $a_{n,f}=0$. To improve spectral efficiency, the sum channel capacity of users ${\sum }_{n=1}^N{R}_n$ should be maximized. In addition, to avoid allocating most of the power and frequency resources to users with good channel states to improve the sum rate, we adopt a fair utility function as follows [37]:

$$u_{\alpha }\left(R_n\right)=\left\{\begin{array}{cc}ln\left(R_n\right),\hfill & \mathrm{if}\alpha =1,\hfill \\ {\displaystyle \frac{R_n^{1-\alpha }}{(1-\alpha )}},\hfill & \mathrm{if}\alpha \ne 1,\alpha \ge 0,\hfill \end{array}\right.$$

(10)

where the value of $\alpha$ represents different fairness levels. By increasing $\alpha$, the fairness among users during resource allocation improves. Therefore, maximizing the sum channel capacity ${\sum }_{n=1}^N{R}_n$ is transformed to maximizing the sum fair utility function ${\sum }_{n=1}^N{u}_{\alpha }\left(R_n\right)$.

In addition, to improve energy efficiency, the total consumption power $P_{\mathrm{total}}$ of the BS should be minimized, which can be calculated via the following [38]:

$$P_{\mathrm{total}}=P_0+{\displaystyle \frac{1}{\beta }}\sum _{n=1}^N\sum _{f=1}^F{a}_{n,f}{p}_{n,f}.$$

(11)

$P_0$ is the working power consumption of the BS, while $\beta$ is the amplifier efficiency.

Therefore, considering jointly maximizing spectral efficiency and minimizing energy efficiency, a multi-objective optimization problem is formulated as follows [34]:

$$\begin{array}{cc}\hfill \left(\mathrm{P}1\right)& \hfill \underset{{\alpha }_{n,f},p_{n,f}}{max}\left[\sum _{n=1}^N{u}_{\alpha }\left(R_n\right),-P_{\mathrm{total}}\right]\hfill \\ \hfill \mathrm{s}.\mathrm{t}.\mathrm{C}1:& \hfill \sum _{n=1}^N\sum _{f=1}^F{\alpha }_{n,f}{p}_{n,f}\le P_{\mathrm{T}},\hfill \\ \hfill \mathrm{C}2:& \hfill p_{n,f}\ge 0,\forall n,\forall f,\hfill \\ \hfill \mathrm{C}3:& \hfill \sum _{n=1}^N{\alpha }_{n,f}=1,\forall f,\hfill \\ \hfill \mathrm{C}4:& \hfill {\alpha }_{n,f}\in \{0,1\},\forall n,\forall f.\hfill \end{array}$$

(12)

where $P_{\mathrm{T}}$ is the maximum BS transmit power. In the above problem, the optimization variables are power resources and frequency resources.

In multi-objective optimization, there does not typically exist a feasible solution that maximizes all objective functions simultaneously. Explicitly, the improvement of one of the objectives may result in the degradation of other objectives [39]. Mathematically, a feasible solution ${\mathit{x}}_{\mathbf{1}}=\left({\alpha }_{n,f}^1,p_{n,f}^1\right)$ is said to dominate a feasible solution ${\mathit{x}}_{\mathbf{2}}=\left({\alpha }_{n,f}^2,p_{n,f}^2\right)$ if and only if

•  ${\displaystyle \sum _{n=1}^N}{u}_{\alpha }\left(R_n\left({\mathit{x}}_{\mathbf{1}}\right)\right)\ge \sum _{n=1}^N{u}_{\alpha }\left(R_n\left({\mathit{x}}_{\mathbf{2}}\right)\right)$, and $-P_{\mathrm{total}}\left({\mathit{x}}_{\mathbf{1}}\right)\ge -P_{\mathrm{total}}\left({\mathit{x}}_{\mathbf{2}}\right)$;
•  ${\displaystyle \sum _{n=1}^N}{u}_{\alpha }\left(R_n\left({\mathit{x}}_{\mathbf{1}}\right)\right)>\sum _{n=1}^N{u}_{\alpha }\left(R_n\left({\mathit{x}}_{\mathbf{2}}\right)\right)$, or $-P_{\mathrm{total}}\left({\mathit{x}}_{\mathbf{1}}\right)>-P_{\mathrm{total}}\left({\mathit{x}}_{\mathbf{2}}\right)$.

A feasible solution ${\mathit{x}}^{*}=\left({\alpha }_{n,f}^{*},p_{n,f}^{*}\right)$ is called Pareto optimal if there does not exist another solution that dominates it. The set of Pareto optimal outcomes, denoted ${\mathit{X}}^{*}$, is often called the Pareto front, Pareto frontier, or Pareto boundary [40].

The problem ($\mathrm{P}1$) is nonconvex and computationally expensive. Referring to [34], we transform the two optimization objectives of Problem ($\mathrm{P}1$) into a single-objective optimization problem by weighted summation. To be specific,

$$\begin{array}{cc}\hfill \left(\mathrm{P}2\right)& \hfill \underset{{\alpha }_{n,f},p_{n,f}}{max}{w}_r\sum _{n=1}^N{\displaystyle \frac{u_{\alpha }\left(R_n\right)}{1\mathrm{bit}/\mathrm{s}}}+\left(-\left(1-w_r\right){\displaystyle \frac{P_{\mathrm{total}}}{1\mathrm{mW}}}\right)\hfill \\ \hfill & \hfill \mathrm{s}.\mathrm{t}.\mathrm{C}1,\mathrm{C}2,\mathrm{C}3,\mathrm{C}4\mathrm{in}\left(12\right),\hfill \end{array}$$

(13)

where $w_r\in [0,1]$ is a weighting factor of optimization priority, which can be adjusted according to optimization priorities of spectral efficiency and energy efficiency. The larger $w_r$ is, the higher the priority of spectral efficient optimization. In this subsection, we take $w_r=0.5$.

In [34], the problem given in (13) is iteratively optimized by successive convex approximation algorithm based on random initialization variables $\{{\alpha }_{n,f},p_{n,f}\}$; thus, the optimal solution can be obtained. The parameter settings in the simulation are shown in

Table 4. The optimization processes corresponding to different methods of providing initial solutions.

N	F	F${\mathit{B}}_0$	$\mathit{\beta }$	${\mathit{P}}_{\mathbf{T}}$	The Power Spectral Density of Noise
20	128	25 MHz	38%	1 W	−174 dBm/Hz

. In this paper, the relationships between multiple sets of channel states and their corresponding optimal solutions can form a sample set. Based on different sample sets, we establish two KGs. A small-scale KG is constructed by training with a sample set consisting of 8000 relationships, while a large-scale KG is constructed by training with a sample set consisting of 15,000 relationships.

Before solving Problem (13), it is necessary to provide initial solutions. Three schemes are considered. The random initial solution in [34] serves as the baseline scheme, while the other two initial solutions are recommended by KGs. These three initial solutions are marked by the green dashed circles in Figure 8, where the vertical axis represents the weighted sum of energy efficiency (EE) and spectral efficiency (SE). As shown in Figure 8, the initial solutions recommended by both the large-scale KG and the small-scale KG significantly outperform the random initial solution. Based on the three initial solutions, we then use the algorithm in [34] to solve Problem (13). The optimization processes are shown in Figure 8, where the horizontal axis represents the number of required iterations to achieve convergence. We observe that the three initial solutions eventually converge to the same optimal solution. However, the random initial solution requires 10 iterations to achieve convergence, while the initial solution recommended by the large-scale KG converges to the optimal solution by just 3 iterations, reducing the number of iterations by 63.6% and thereby significantly decreasing the complexity to solve (13). Similarly, the small-scale KG reduces the number of iterations by 36.4%. Additionally, as shown in Figure 8, the performance of the initial solution recommended by the small-scale KG achieves 63.6% of the optimal solution performance, while the performance of the initial solution recommended by the large-scale KG achieves 86.6% of the optimal solution performance. Therefore, the larger the scale of the KG, the closer the initial solution recommended by the KG is to the optimal solution.

In addition, we simulate the optimization produces in a large-scale network with 40 users. The three initial solutions are marked by the green dashed circles in Figure 9. As shown in Figure 9, the initial solutions recommended by both the large-scale KG and the small-scale KG significantly outperform the random initial solution. Additionally, in this context, the small-scale KG and the large-scale KG reduce the number of iterations by 47.1% and 76.5%, respectively, which further demonstrate that KGs can effectively reduce the optimizing complexity. Meanwhile, as shown in Figure 9, the performance of the initial solutions recommended by the small-scale KG and the large-scale KG achieves 62.4% and 88.4% of the optimal solution performance, respectively. This further demonstrates that increasing the scale of the KG enhances the performance of the initial solution recommended by the KG.

Furthermore, considering the time-varying characteristics of channels caused by user movements in the network with 20 users, we provide the performance evaluation of the DT-based prediction algorithms, as shown in Figure 10. Two benchmarks are considered for comparison. The first benchmark involves no prediction, where out-data channels are directly used as the current channels. The second benchmark is a traditional prediction algorithm, where the inputs of the network consist only of historical channel data. It is worth noting that the channels measured in the physical world are imperfect, and thus the historic channels inputted into the prediction algorithm are measurement channels with errors. As shown in Figure 10, the channel amplitude predicted by the DT-based algorithm (the black dashed line) closely aligns with the ground-truth channel amplitude (the red line), outperforming both benchmarks. This remarkable accuracy is achieved by leveraging the rough channel information forecasted by the virtual world of the DT. In more detail, at time 80, the DT-based algorithm accurately predicts a sudden deterioration in channel conditions.

Finally, based on these predicted or out-data channels, we compare the SE and EE of the air interface configurations recommended by the KG. As shown in Figure 11, the accurate channels predicted by the DT-based prediction algorithm effectively improve the SE and EE, which demonstrate that the DT-based prediction algorithm enables better air interface configuration. Specifically, the timely prediction at time 80 enables real-time adjustments to the air interface configuration, as illustrated in Figure 11, where a high SE and EE are maintained despite the sudden deterioration in channel conditions.

5. Conclusions

This paper analyzed the importance of intelligent air interface adaptation for enhancing communication system performance. Subsequently, it summarized the challenges of the traditional adaptation of air interfaces in the emerging 6G communication scenarios. Then, based on a KG and DT, a novel air interface recommendation framework was proposed to resolve the multi-objective adaptation problem in a fast-varying dynamic environment. Two cases showcased that the proposed method can adequately balance multiple performance requirements and dynamically recommend suitable air interface configurations for users effectively in real time. In the future, we plan to use neural networks with stronger relationship-mining capabilities, such as transformers and GNNs, to construct a KG with enhanced inference ability. Additionally, leveraging DT and KG techniques, we aim to effectively recommend more complex air interface configurations, such as beamforming design and resource scheduling for multi-cell systems.