In recent years, the application of neural networks (NNs) in wireless communication has garnered widespread attention and proven successful. However, conventional learning-based NNs often suffer from poor calibration, meaning that they struggle to reliably quantify prediction confidence and lack proper uncertainty estimation. This limitation becomes especially critical for next generation communication systems, particularly in complex industrial scenarios with stringent reliability requirements. Previous efforts to enhance model calibration have primarily centered on modifying NNs’ training processes. However, these methods often demand significant computing resources, making them impractical for resource-constrained scenarios. In this paper, we investigate a distributed wireless communication system involving multiple users and propose a novel approach to improve model calibration. Our method focuses on enhancing calibration during the inference stage of NNs by introducing a power control mechanism. Notably, existing research indicates that many NNs exhibit overconfidence, i.e., the NN’s confidence exceeds its actual accuracy. Leveraging this insight, we exploit the inherent noise and fading in wireless systems to naturally reduce the NN’s confidence while preserving accuracy. To achieve this, we employ linear relaxation-based perturbation analysis (LiRPA) to approximate the relationship between the perturbed output and the input perturbation of the NN. Subsequently, we devise an optimization problem by leveraging the analyzed relationship and the definition of perfect calibration. It is aimed at finding the input perturbation that maximizes the probability of the model achieving perfect calibration. Finally, considering different channel conditions and a given specific modulation method, we derive the optimal transmission power based on bit error rate (BER) formula. Simulation results demonstrate that our proposed power control method exhibits significant advantages in model calibration compared to several traditional approaches.

As an efficient neural network model for graph data, graph neural networks (GNNs) recently find successful applications for various wireless optimization problems. Given that the inference stage of GNNs can be naturally implemented in a decentralized manner, GNN is a potential enabler for decentralized control/management in the next-generation wireless communications. Privacy leakage, however, may occur due to the information exchanges among neighbors during decentralized inference with GNNs. To deal with this issue, in this paper, we analyze and enhance the privacy of decentralized inference with GNNs in wireless networks. Specifically, we adopt local differential privacy as the metric, and design novel privacy-preserving signals as well as privacy-guaranteed training algorithms to achieve privacy-preserving inference. We also define the SNR-privacy trade-off function to analyze the performance upper bound of decentralized inference with GNNs in wireless networks. To further enhance the communication and computation efficiency, we adopt the over-the-air computation technique and theoretically demonstrate its advantage in privacy preservation. Through extensive simulations on the synthetic graph data, we validate our theoretical analysis, verify the effectiveness of proposed privacy-preserving wireless signaling and privacy-guaranteed training algorithm, and offer some guidance on practical implementation.

With the great success of deep learning (DL) in image classification, speech recognition, and other fields, more and more studies have applied various neural networks (NNs) to wireless resource allocation. Generally speaking, these artificial intelligent (AI) models are trained under some special learning hypotheses, especially that the statistics of the training data are static during the training stage. However, the distribution of channel state information (CSI) is constantly changing in the real-world wireless communication environment. Therefore, it is essential to study effective dynamic DL technologies to solve wireless resource allocation problems. In this paper, we propose a novel framework, named meta-gating, for solving resource allocation problems in an episodically dynamic wireless environment, where the CSI distribution changes over periods and remains constant within each period. The proposed framework, consisting of an inner network and an outer network, aims to adapt to the dynamic wireless environment by achieving three important goals, i.e., seamlessness, quickness and continuity. Specifically, for the former two goals, we propose a training method by combining a model-agnostic meta-learning (MAML) algorithm with an unsupervised learning mechanism. With this training method, the inner network is able to fast adapt to different channel distributions because of the good initialization. As for the goal of ‘continuity’, the outer network can learn to evaluate the importance of inner network’s parameters under different CSI distributions, and then decide which subset of the inner network should be activated through the gating operation. Additionally, we theoretically analyze the performance of the proposed meta-gating framework. Simulation results demonstrate that the proposed meta-gating framework can well achieve the three important goals compared with existing state-of-the-art algorithms.

Graph neural network (GNN) is an efficient neural network model for graph data and is widely used in different fields, including wireless communications. Different from other neural network models, GNN can be implemented in a decentralized manner during the inference stage with information exchanges among neighbors, making it a potentially powerful tool for decentralized control in wireless communication systems. The main bottleneck, however, is wireless channel impairments that deteriorate the prediction robustness of GNN. To overcome this obstacle, we analyze and enhance the robustness of the decentralized GNN during the inference stage in different wireless communication systems in this paper. Specifically, using a GNN binary classifier as an example, we first develop a methodology to verify whether the predictions are robust. Then, we analyze the performance of the decentralized GNN binary classifier in both uncoded and coded wireless communication systems. To remedy imperfect wireless transmission and enhance the prediction robustness, we further propose novel retransmission mechanisms for the above two communication systems, respectively. Through simulations on the synthetic graph data, we validate our analysis, verify the effectiveness of the proposed retransmission mechanisms, and provide some insights for practical implementation.

As an important part of the fifth generation (5G) mobile networks, unmanned aerial vehicles (UAVs) have been applied in various communication scenarios due to their high operability and low cost. In this paper, we investigate a multi-UAV communication system with moving users and consider the co-channel interference caused by the transmissions of all other UAVs. To ensure the fairness, we maximize the minimum average user rate during the observed time by jointly optimizing UAVs’ trajectories, transmission power, and user association. Considering that UAVs can cover a large area for communications, UAVs do not need to move as soon as the users move. Therefore, a two-timescale structure is proposed for the considered scenario, where the UAVs’ trajectories are optimized based on the channel state information (CSI) in a long timescale, while the transmission power and the user association are optimized based on the instantaneous CSI in a short timescale. To effectively tackle this challenging non-convex problem with both discrete and continuous variables, we propose a joint neural network (NN) design, where a deep reinforcement learning based Pointer Network named advantage pointer-critic (APC) is applied to optimize discrete variables and a deep-unfolding NN is used to optimize the continuous variables. Specifically, we first formulate a Markov decision process to model the user association, and then employ the APC network trained by the advantage actor-critic algorithm to address it. The APC network consists of a Pointer Network and a Multilayer Perceptron. As for the deep-unfolding NN, we first develop a block coordinate descent based algorithm to optimize the UAVs’ trajectories and transmission power, and then unfold the algorithm into a layer-wise NN with introduced trainable parameters. These two networks are jointly trained in an unsupervised fashion. Simulation results validate that the proposed joint NN significantly outperforms the optimization algorithm with much lower complexity, and achieves good performances on scalability and generalization ability.

Graph neural network (GNN) is widely applied in various fields, especially for graph data. Moreover, it is an effective technique for decentralized inference tasks, where information exchange among neighbors relies on wireless communications. However, wireless channel impairments and noise decrease the accuracy of prediction. To remedy imperfect wireless transmission and enhance the prediction robustness, we propose a novel retransmission mechanism with adaptive modulation that could select the appropriate modulation order adaptively for each retransmission. Compared to the traditional method that determines the modulation order based on bit error ratio (BER), we bring in a new indicator called robust prediction to select an appropriate modulation order for each transmission. Under the requirement of prediction robustness, the error-tolerance of GNNs is exploited and a higher modulation order can be used in the proposed mechanism compared with the traditional method, thus reducing the communication overhead and improving the data rate. Meanwhile, we combine the signals of different retransmission with the soft-bit maximum ratio combine (SBMRC) technique. Simulation results verify the effectiveness of the proposed retransmission mechanism.

In this paper, we investigate a multi-UAV communication system with moving users and consider the co-channel interference caused by the transmissions of all other UAVs. To ensure the fairness of moving users, we maximize the minimum average user rate during the observed time by jointly optimizing UAVs' trajectories, transmission power, and user association. To effectively tackle this non-convex problem with both discrete and continuous variables, we propose a joint neural network (NN) design, where a network named advantage pointer-critic (APC) is applied to optimize discrete variables and a deep-unfolding NN is used to optimize continuous variables. Specifically, we first elaborately formulate a Markov decision process to model the user association, and then use the APC network trained by the advantage actor-critic algorithm to address it. As for the deep-unfolding NN, we first develop a block coordinate descent based algorithm to optimize UAVs' trajectories and transmission power, and then unfold this algorithm into a layer-wise NN with introduced trainable parameters. These two networks are jointly trained in an unsupervised fashion. Simulation results validate that the proposed joint NN significantly outperforms the mathematical optimization algorithm with much lower complexity.

The combinatorial auction (CA) is an efficient mechanism for resource allocation in different fields, including cloud computing. It can obtain high economic efficiency and user flexibility by allowing bidders to submit bids for combinations of different items instead of only for individual items. However, the problem of allocating items among the bidders to maximize the auctioneers’ revenue, i.e., the winner determination problem (WDP), is NP-complete to solve and inapproximable. Existing works for WDPs are generally based on mathematical optimization techniques and most of them focus on the single-unit WDP, where each item only has one unit. On the contrary, few works consider the multi-unit WDP in which each item may have multiple units. Given that the multi-unit WDP is more complicated but prevalent in cloud computing, we propose leveraging machine learning (ML) techniques to develop a novel low-complexity algorithm for solving this problem with negligible revenue loss. Specifically, we model the multi-unit WDP as an augmented bipartite bid-item graph and use a graph neural network (GNN) with half-convolution operations to learn the probability of each bid belonging to the optimal allocation. To improve the sample generation efficiency and decrease the number of needed labeled instances, we propose two different sample generation processes. We also develop two novel graph-based post-processing algorithms to transform the outputs of the GNN into feasible solutions. Through simulations on both synthetic instances and a specific virtual machine (VM) allocation problem in a cloud computing platform, we validate that our proposed method can approach optimal performance with low complexity and has good generalization ability in terms of problem size and user-type distribution.

The conventional federated learning (FedL) architecture distributes machine learning (ML) across worker devices by having them train local models that are periodically aggregated by a server. FedL ignores two important characteristics of contemporary wireless networks, however: (i) the network may contain heterogeneous communication/computation resources, while (ii) there may be significant overlaps in devices' local data distributions. In this work, we develop a novel optimization methodology that jointly accounts for these factors via intelligent device sampling complemented by device-to-device (D2D) offloading. Our optimization aims to select the best combination of sampled nodes and data offloading configuration to maximize FedL training accuracy subject to realistic constraints on the network topology and device capabilities. Theoretical analysis of the D2D offloading subproblem leads to new FedL convergence bounds and an efficient sequential convex optimizer. Using this result, we develop a sampling methodology based on graph convolutional networks (GCNs) which learns the relationship between network attributes, sampled nodes, and resulting offloading that maximizes FedL accuracy. Through evaluation on real-world datasets and network measurements from our IoT testbed, we find that our methodology while sampling less than 5% of all devices outperforms conventional FedL substantially both in terms of trained model accuracy and required resource utilization.

Generalized Benders decomposition (GBD) is a globally optimal algorithm for mixed integer nonlinear programming (MINLP) problems, which are NP-hard and can be widely found in the area of wireless resource allocation. The main idea of GBD is decomposing an MINLP problem into a primal problem and a master problem, which are iteratively solved until their solutions converge. However, a direct implementation of GBD is time- and memory-consuming. The main bottleneck is the high complexity of the master problem, which increases over the iterations. Therefore, we propose to leverage machine learning (ML) techniques to accelerate GBD aiming at decreasing the complexity of the master problem. Specifically, we utilize two different ML techniques, classification and regression, to deal with this acceleration task. In this way, a cut classifier and a cut regressor are learned, respectively, to distinguish between useful and useless cuts. Only useful cuts are added to the master problem and thus the complexity of the master problem is reduced. By using a resource allocation problem in device-to-device communication networks as an example, we validate that the proposed method can reduce the computational complexity of GBD without loss of optimality and has good generalization ability. The proposed method is applicable for solving various MINLP problems in wireless networks since the designs are invariant for different problems.

Link scheduling in device-to-device (D2D) networks is usually formulated as a non-convex combinatorial problem, which is generally NP-hard and difficult to get the optimal solution. Traditional methods to solve this problem are mainly based on mathematical optimization techniques, where accurate channel state information (CSI), usually obtained through channel estimation and feedback, is needed. To overcome the high computational complexity of the traditional methods and eliminate the costly channel estimation stage, machine leaning (ML) has been introduced recently to address the wireless link scheduling problems. In this article, we propose a novel graph embedding based method for link scheduling in D2D networks. We first construct a fully-connected directed graph for the D2D network, where each D2D pair is a node while interference links among D2D pairs are the edges. Then we compute a low-dimensional feature vector for each node in the graph. The graph embedding process is based on the distances of both communication and interference links, therefore without requiring the accurate CSI. By utilizing a multi-layer classifier, a scheduling strategy can be learned in a supervised manner based on the graph embedding results for each node. We also propose an unsupervised manner to train the graph embedding based method to further reinforce the scalability and develop a K-nearest neighbor graph representation method to reduce the computational complexity. Extensive simulation demonstrates that the proposed method is near-optimal compared with the existing state-of-art methods but is with only hundreds of training network layouts. It is also competitive in terms of scalability and generalizability to more complicated scenarios.

Link scheduling for device-to-device (D2D) communications is usually formulated as an NP-hard non-convex combinatorial problem, which is difficult to get the optimal solution. Traditional methods are mainly based on mathematical optimization techniques with the help of accurate channel state information (CSI), which is costly to obtain. In this paper, we propose a graph embedding based method to achieve link scheduling without CSI for D2D communications. We first construct a fully-connected directed graph for the D2D network, and then compute a low-dimensional feature vector for each node in the graph based on the distances of both communication and interference links. Finally, a scheduling strategy can be learned based on the graph embedding results by utilizing a multi-layer classifier. Extensive simulation demonstrates that the proposed method is near-optimal compared with the existing state-of-art methods and only needs hundreds of training network layouts. It is also competitive in terms of scalability and generalizability to more complicated scenarios.

Wireless link scheduling in D2D communication systems aims at maximizing the weighted sum rate of D2D pairs by determining which subset of D2D pairs should be activated. However, it is a non-convex combinatorial optimization problem, which is generally NP-hard and difficult to achieve the optimal solution. Inspired by the recent attempt of introducing machine learning and graph embedding to reach the general goal, we propose an efficient method to solve the weighted sum rate maximization problem. We first model the system as a one-nearest neighbor graph, in which each D2D pair is a node and the strongest interference link for each node is an edge. Then we compute the feature vectors of both weights and nodes by graph embedding and use the feature vectors as the input of a subsequent multi-layer classifier. The parameters of classifier and graph embedding are trained jointly in a supervised manner. Simulation result shows that the proposed method can obtain near-optimal performance with only hundreds of training samples and is capable to be generalized to more complicated scenarios.

Millimeter-wave (mmWave) communication has been regarded as one of the most promising means to improve the cellular system capacity in the fifth-generation (5G) era. Compared with the conventional microwave communication networks, mmWave terminals should connect with multiple base stations (BSs) simultaneously to prevent the signal blockage. Meanwhile, the accurate instantaneous channel state information (CSI) is difficult to estimate and collect due to the densification of mmWave BSs. These unique characteristics pose stiff challenges to user association in mmWave networks. To deal with these issues, we develop a novel machine learning based user association approach to support multi-connectivity in mmWave networks. Specifically, we first formulate the mmWave user association problem as a multi-label classification problem, which is then transformed into a series of single-label classification problems through efficient multi-label classification algorithms. To further reduce the requirement on the amount of training samples, we utilize graphical model to represent the user association scenario and adopt novel feature extraction methods to obtain appropriate features from both geographical location information and topological information. With appropriate features, each single-label classification problem can be trained in a supervised manner. Test results show that the proposed approach can achieve a good performance with only a few training samples and without the need of CSI.

Resource allocation for device-to-device (D2D) communications is usually formulated as mixed integer nonlinear programming (MINLP) problems, which are generally NP-hard and difficult to solve. Traditional methods are based on mathematical optimization techniques, which suffer from forbidding computational complexity or unsatisfactory optimality. In this paper, we introduce a machine leaning (ML) technique, imitation learning, to address the resource allocation in D2D communications. The key idea is learning a good prune policy to speed up the widely-used globally optimal algorithm for the MINLP problems, the branch- and-bound (B&B) algorithm. With appropriate feature selection, imitation learning can be converted into a binary classification problem, which can be solved by the classical support vector machine (SVM). Extensive simulation demonstrates that the proposed method can achieve good optimality and reduce computational complexity simultaneously. It only needs hundreds of training samples and has a good generalization ability. Our proposed method can be also applied to the MINLP problems in other wireless communication networks.