The rise of privacy-preserving applications, such as medical diagnostics and the Metaverse, highlights the importance of federated learning (FL) for distributed model training at the wireless edge. These applications often rely on multimodal data (e.g., text, images, audio), necessitating advances in multimodal federated learning (MMFL). However, MMFL faces challenges like energy efficiency, multimodal fusion, and heterogeneity. To address these, a scheduling and fusion-based MMFL framework (SFMMFL) is proposed that focuses on improving both the scheduling mechanism and aggregation strategy. To improve the training performance under energy constraint, a Lyapunov-based scheduling algorithm is proposed, in which long-term optimization is transformed into immediate optimization. After that, to tackle the issue of model separation caused by multimodal datasets, a multimodal model aggregation strategy based on Knowledge Distillation (KD) is introduced for multimodal fusion. Convergence analysis proves its feasibility, and simulation results demonstrate that it can achieve faster and more stable convergence performance while improving model training accuracy. Specifically, our proposed SFMMFL can lower the energy consumption of the system by about$20\%$for computing and$16.67\%$for transmission.

Integrated sensing and communication (ISAC) is emerging as a key enabler for vehicle-to-everything (V2X) systems. However, designing efficient beamforming schemes for ISAC signals to achieve accurate sensing and enhance communication performance in the dynamic and uncertain environments of V2X networks presents significant challenges. While artificial intelligence technologies offer promising solutions, the energy-intensive nature of neural networks imposes substantial burdens on communication infrastructures. To address these challenges, this work proposes an energy-efficient and intelligent ISAC system for V2X networks. Specifically, we first leverage a Markov Decision Process framework to model the dynamic and uncertain nature of V2X networks. This framework allows the roadside unit to develop beamforming schemes relying solely on its current sensing information, eliminating the need for numerous pilot signals and extensive CSI acquisition. We then introduce an advanced deep reinforcement learning (DRL) algorithm, enabling the joint optimization of beamforming and power allocation to guarantee both communication rate and sensing accuracy in dynamic and uncertain V2X scenario. To alleviate the energy demands of neural networks, we integrate spiking neural networks (SNNs) into the DRL algorithm. The event-driven, sparse spike-based processing of SNNs significantly improves energy efficiency while maintaining strong performance. Extensive simulation results validate the effectiveness of the proposed scheme with lower energy consumption, superior communication performance, and improved sensing accuracy.

Dynamic resource allocation in mobile wireless networks involves complex, time-varying optimization problems, motivating the adoption of deep reinforcement learning (DRL). However, most existing works rely on pre-trained policies, overlooking dynamic environmental changes that rapidly invalidate the policies. Periodic retraining becomes inevitable but incurs prohibitive computational costs and energy consumption-critical concerns for resource-constrained wireless systems. We identify three root causes of inefficient retraining: high-dimensional state spaces, suboptimal action spaces exploration-exploitation trade-offs, and reward design limitations. To overcome these limitations, we propose Diffusion-based Deep Reinforcement Learning (D2RL), which leverages generative diffusion models (GDMs) to holistically enhance all three DRL components. GDMs’ iterative refinement process and distribution modelling enable (1) the generation of diverse state samples to improve environmental understanding, (2) balanced action space exploration to escape local optima, and (3) the design of discriminative reward functions that better evaluate action quality. Our framework operates in two modes: Mode I leverages GDMs to explore reward spaces and design discriminative reward functions that rigorously evaluate action quality, while Mode II synthesizes diverse state samples to enhance environmental understanding and generalization. Extensive experiments demonstrate that D2RL achieves faster convergence and reduced computational costs over conventional DRL methods for resource allocation in wireless communications while maintaining competitive policy performance. This work underscores the transformative potential of GDMs in overcoming fundamental DRL training bottlenecks for wireless networks, paving the way for practical, real-time deployments.

This paper investigates resource allocation for providing heterogeneous users with customized virtual reality (VR) streaming services in a mobile edge computing (MEC) system. We introduce a quality of experience (QoE) metric that considers system latency, user attention levels, and preferred resolutions to measure user experience based on the Weber-Fechner Law. A QoE maximization problem is then formulated for resource allocation to optimize user experience. It is cast as a reinforcement learning problem, aiming to learn a generalized policy applicable across diverse user environments of different MEC servers. To solve the problem, we propose a FedPromptDT framework, which employs federated learning (FL) and prompt-based generative sequence modeling to pre-train a common decision model across MEC servers. FL addresses the issue of insufficient local MEC data while protecting user privacy during offline training. Meanwhile, by integrating user-environment cues and user-preferred allocation, the design of prompts enhances the model’s adaptability to various user environments during online execution. Extensive experimental evaluations demonstrate that FedPromptDT outperforms baseline methods, exhibiting remarkable adaptability and maintaining superior performance across various user environments.

This work proposes an energy-efficient, learning-based beamforming scheme for integrated sensing and communication (ISAC)-enabled V2X networks. Specifically, we first model the dynamic and uncertain nature of V2X environments as a Markov Decision Process. This formulation allows the roadside unit to generate beamforming decisions based solely on current sensing information, thereby eliminating the need for frequent pilot transmissions and extensive channel state information acquisition. We then develop a deep reinforcement learning (DRL) algorithm to jointly optimize beamforming and power allocation, ensuring both communication throughput and sensing accuracy in highly dynamic scenario. To address the high energy demands of conventional learning-based schemes, we embed spiking neural networks (SNNs) into the DRL framework. Leveraging their event-driven and sparsely activated architecture, SNNs significantly enhance energy efficiency while maintaining robust performance. Simulation results confirm that the proposed method achieves substantial energy savings and superior communication performance, demonstrating its potential to support green and sustainable connectivity in future V2X systems.

The emergence of intelligent, privacy-preserving applications—such as medical diagnostics and the Metaverse—at the wireless network edge has made federated learning (FL) a promising approach for supporting distributed model training. Given that these applications rely on multimodal data (e.g., text, images, audio) collected from users, there is a growing need for research on multimodal federated learning (MMFL) to enable more robust and comprehensive learning. However, MMFL in wireless edge networks introduces unique challenges beyond traditional FL, particularly in managing the fusion of multimodal data and coordinating user scheduling across various data modalities. To address these issues, we propose a knowledge distillation-based MMFL (KD-MMFL) which considers unimodal model aggregation and adaptive multimodal aggregation via multi-teacher knowledge distillation (MTKD), to build a robust multimodal global model that effectively integrates insights from diverse data sources. Furthermore, to tackle the challenges of device heterogeneity in terms of data distribution and energy availability, we introduce a Lyapunov-based scheduling algorithm to map the long-term optimal problem that maximizes the training performance while considering users’ energy constraints into an immediate optimization problem. Experiment results demonstrate that the KD-MMFL framework successfully learns a robust multimodal global model from distributed multimodal datasets, while the Lyapunov-based scheduling method achieves an improvement of approximately 25% or more in energy efficiency compared to other scheduling methods.

The rapid expansion of multi-user virtual reality (VR) applications, such as VR gaming and the Metaverse, has heightened the demand for bandwidth-efficient, immersive experiences. This paper introduces a customized Quality of Experience (QoE) framework tailored to VR interactions in a sub-6 GHz communication environment, integrating attention-based interaction, keyframe extraction, and principles from the Weber-Fechner Law. The QoE maximization problem is formulated as a Mixed Integer Programming (MIP) problem that jointly optimizes keyframe extraction ratio and resource allocation (i.e., bandwidth and CPU frequency), incorporating fairness. We employ the Deep Deterministic Policy Gradient (DDPG) algorithm as a reinforcement learning strategy. Evaluation with the Motion Capture Database demonstrates that our framework significantly reduces interactive latency, enhances QoE, and maintains fairness, achieving superior performance compared to baseline methods.

In the era of the Internet of Vehicles (IoV), Digital Twins (DTs) serve as a critical bridge between physical vehicles and the digital world, enabling real-time virtualization, simulation, and data-driven decision-making. While Cloud Computing (CC) and Mobile Edge Computing (MEC) provide foundational support for low-latency services, the dynamic nature of IoV environments-characterized by fluctuating resource availability, heterogeneous infrastructures, and stringent quality-of-service requirements-poses significant challenges for efficient DT deployment. To address this, we propose a novel DT system framework tailored for heterogeneous MEC/CC environments, where DTs are dynamically maintained across distributed servers using multisource data collected from vehicular networks. Central to our approach is a DT placement optimization problem that jointly minimizes latency and energy consumption under resource constraints. We design a Distributed Deep Learning (DDL)-based offloading scheme to adaptively optimize DT placement, ensuring scalability and responsiveness to real-time environmental changes. Extensive simulations demonstrate that our solution shows superior performance compared to heuristic benchmarks.

Due to the massive computing demands of the Internet of Things, mobile edge computing (MEC) has been extensively investigated as a means of providing computation-intensive and latency-sensitive services at the network edge. With increasing density of base stations (BSs), users are simultaneously served by multiple BSs, leading to the multicell MEC environment. Intelligent reflecting surface (IRS) provides a promising solution for constructing the virtual Line-of-Sight (LoS) links between cell-edge users (CEUs) and BSs. In this article, we investigate the joint channel estimation and resource allocation in the IRS-aided multicell MEC system. Instead of assuming the perfect channel state information (CSI), we propose a three-phase channel estimation method to obtain the CSI. Our purpose is to minimize the total joint energy and latency cost (JELC) in terms of both task-execution latency and energy consumption in the IRS-aided multicell MEC problem by jointly optimizing the task offloading volume, precoding matrix, and IRS phase shifts. We propose a quadratically constrained program (QCP)-assisted proximal policy optimization (PPO) reinforcement learning algorithm with two modules (i.e., QCP optimizer and PPO agent) execute iteratively. The QCP optimizer is utilized to compute the offloading decision variables, and the PPO agent is adapted to determine the optimal channel precoding matrix and the phase shifts of IRS. Numerical results validate that our QCP-assisted PPO algorithm executes more rapidly than benchmarks. Moreover, the proposed QCP-assisted PPO algorithm delivers the best performance compared to benchmarks. Furthermore, the multicell IRS-aided MEC framework yields additional performance gains compared to those without IRS.

Metaverse applications such as virtual reality (VR) content streaming, require optimal resource allocation strategies for mobile edge computing (MEC) to ensure a high-quality user experience. In contrast to online reinforcement learning (RL) algorithms, which can incur substantial communication overheads and longer delays, the majority of existing works employ offline-trained RL algorithms for resource allocation decisions in MEC systems. However, they neglect the impact of desynchronization between the physical and digital worlds on the effectiveness of the allocation strategy. In this paper, we tackle this desynchronization using a continual RL (CRL) framework that facilitates the resource allocation dynamically for MEC-enabled VR content streaming. We first design a digital twin-empowered edge computing (DTEC) system and formulate a quality of experience (QoE) maximization problem based on attention-based resolution perception. This problem optimizes the allocation of computing and bandwidth resources while adapting the attention-based resolution of the VR content. The CRL framework in DTEC enables adaptive online execution in a time-varying environment. We propose three variants of CRL, namely Continual Deep Deterministic Policy Gradient (CDDPG), Prioritized Experience Replay - CDDPG (PER-CDDPG), and Freshness Prioritized Experience Replay - CDDPG (FPER-CDDPG). We evaluate these algorithms, including two other benchmarks, using extensive experiments. FPER-CDDPG shows superior performance in terms of average latency, QoE, and successful delivery rate as well as meeting the hfQoE requirements over long-term execution while ensuring system scalability with the increasing number of users.

Mobile edge computing (MEC) resource allocation for remote rendering in virtual reality (VR) content streaming is critical for user experience. However, resource allocation becomes challenging due to the desynchronization between the physical and digital worlds in digital twin-empowered MEC. This paper presents our continual RL framework that facilitates dynamic resource allocation for MEC-enabled VR content streaming. We first design a digital twin-empowered edge computing (DTEC) system and formulate a maximization problem that considers attention-based resolution perception to maximize the quality of experience (QoE). This problem optimizes the allocation of computing and bandwidth resources while adapting the attention-based resolution of the VR content. We then apply continual reinforcement learning (CRL) to enable adaptive attention-based resolution VR streaming in a time-varying environment. We base the CRL's reward function on the QoE and horizon-fairness QoE (hfQoE) constraints. We support CRL with prioritized experience replay - continual deep deterministic policy gradient (PER-CDDPG) to enhance the performance of continual learning in the presence of time-varying DT updates. We test PER-CDDPG using extensive experiments and evaluation. PER-CDDPG outperforms the benchmarks in terms of average latency, QoE, and successful delivery rate as well as meeting the hfQoE requirements and performance over long-term execution while ensuring system scalability with the increasing number of users.

Non-orthogonal multiple access (NOMA)-aided mobile edge computing (MEC) system can enhance the spectral-efficiency with massive tasks offloading. However, with more dynamic devices and the uncontrollable stochastic channel environment, it is even desirable to deploy appealing technique, i.e., intelligent reflecting surfaces (IRS), in the MEC system to flexibly adjust the communication environment and improve the system energy-efficiency. In this paper, we investigate the joint offloading, communication and computation resource allocation for IRS-assisted NOMA-aided MEC system. We firstly formulate a mixed integer energy-efficiency maximization problem with the system queue stability constraint. We then propose a Het-erogeneous Multi-agent Lyapunov-function-based Mixed Integer Deep Deterministic Policy Gradient (HMA-LMIDDPG) algorithm which is based on the multi-agent reinforcement learning (MARL) framework with homogeneous edge devices (EDs) and heterogeneous base station (BS) as heterogeneous multi-agent. Numerical results show that our proposed algorithms can achieve superior energy-efficiency performance to the benchmark algorithms while maintaining the queue stability.

By employing powerful edge servers for data processing, mobile edge computing (MEC) has been recognized as a promising technology to support emerging computation-intensive applications. Besides, non-orthogonal multiple access (NOMA)-aided MEC system can further enhance the spectral efficiency with massive tasks offloading. However, with more dynamic devices brought online and the uncontrollable stochastic channel environment, it is even desirable to deploy appealing technique, i.e., intelligent reflecting surfaces (IRS), in the MEC system to flexibly tune the communication environment and improve the system energy efficiency. In this paper, we investigate the joint offloading, communication and computation resource allocation for the IRS-assisted NOMA MEC system. We first formulate a mixed integer energy efficiency maximization problem with system queue stability constraint. We then propose the Lyapunov-function-based Mixed Integer Deep Deterministic Policy Gradient (LMIDDPG) algorithm which is based on the centralized reinforcement learning (RL) framework. To be specific, we design the mixed integer action space mapping which contains both continuous mapping and integer mapping. Moreover, the award function is defined as the upper-bound of the Lyapunov drift-plus-penalty function. To enable end devices (EDs) to choose actions independently at the execution stage, we further propose the Heterogeneous Multi-agent LMIDDPG (HMA-LMIDDPG) algorithm based on distributed RL framework with homogeneous EDs and heterogeneous base station (BS) as heterogeneous multi-agent. Numerical results show that our proposed algorithms can achieve superior energy efficiency performance to the benchmark algorithms while maintaining the queue stability. Specially, the distributed structure HMA-LMIDDPG can acquire more energy efficiency gain than the centralized structure LMIDDPG.

The space-air-ground integrated network (SAGIN) has drawn increasing attention for its benefits, such as wide coverage, high throughput for 5G and 6G communications. As one of the links, space-air communications between multiple unmanned aerial vehicles (UAVs) and Ka-band orbiting low earth orbit (LEO) satellites face a crucial challenge in tracking the 3D dynamic channel information. This paper exploits a statistical dynamic channel model called the multi-dimensional Markov model (MD-MM), which investigates the more realistic spatial and temporal correlation in the sparse UAVs-satellite channel. Specifically, the spatial and temporal probabilistic relationships of multi-user (MU) hidden support vector, single-user (SU) joint hidden support vector, and SU hidden value vector are investigated. The specific transition probabilities that connect the SU and MU hidden support vector for both azimuth and elevation directions are defined. Moreover, based on the proposed MD-MM, we derive a novel multi-dimensional dynamic turbo approximate message passing (MD-DTAMP) algorithm for tracking the 3D dynamic channel in multiple UAVs systems. Furthermore, we also develop a gradient update scheme to recursively find the azimuth and elevation offset for 3D off-grid estimation. Numerical results verify that the proposed algorithm shows superior 3D channel tracking performance with smaller pilot overhead and comparable complexity.

To boost the performance of wireless communication networks, unmanned aerial vehicles (UAVs) aided communications have drawn dramatically attention due to their flexibility in establishing the line of sight (LoS) communications. However, with the blockage in the complex urban environment, and due to the movement of UAVs and mobile users, the directional paths can be occasionally blocked by trees and high-rise buildings. Intelligent reflection surfaces (IRSs) that can reflect signals to generate virtual LoS paths are capable of providing stable communications and serving wider coverage. This is the first paper that exploits a three-dimensional geometry dynamic channel model in IRS- assisted UAV-enabled communication system. Moreover, we develop a novel deep learning based channel tracking algorithm consisting of two modules: channel pre-estimation and channel tracking. A deep neural network with off-line training is designed for denoising in the pre-estimation module. Moreover, for channel tracking, a stacked bi-directional long short term memory (Stacked Bi-LSTM) is developed based on a framework that can trace back historical time sequence together with bidirectional structure over multiple stacked layers. Simulations have shown that the proposed channel tracking algorithm requires fewer epochs to convergence compared to benchmark algorithms. It also demonstrates that the proposed algorithm is superior to different benchmarks with small pilot overheads and comparable computation complexity.

In this article, we investigate resource allocation with edge computing in Internet-of-Things (IoT) networks via machine learning approaches. Edge computing is playing a promising role in IoT networks by providing computing capabilities close to users. However, the massive number of users in IoT networks requires sufficient spectrum resource to transmit their computation tasks to an edge server, while the IoT users were developed to have more powerful computation ability recently, which makes it possible for them to execute some tasks locally. Then, the design of computation task offloading policies for such IoT edge computing systems remains challenging. In this article, centralized user clustering is explored to group the IoT users into different clusters according to users' priorities. The cluster with the highest priority is assigned to offload computation tasks and executed at the edge server, while the lowest priority cluster executes computation tasks locally. For the other clusters, the design of distributed task offloading policies for the IoT users is modeled by a Markov decision process, where each IoT user is considered as an agent which makes a series of decisions on task offloading by minimizing the system cost based on the environment dynamics. To deal with the curse of high dimensionality, we use a deep Q-network to learn the optimal policy in which deep neural network is used to approximate the Q-function in Q-learning. Simulations show that users are grouped into clusters with optimal number of clusters. Moreover, our proposed computation offloading algorithm outperforms the other baseline schemes under the same system costs.

The space-air-ground integrated network (SAGIN) aims to provide seamless wide-area connections, high throughput and strong resilience for 5G and beyond communications. Acting as a crucial link segment of the SAGIN, unmanned aerial vehicle (UAV)-satellite communication has drawn much attention. However, it is a key challenge to track dynamic channel information due to the low earth orbit (LEO) satellite orbiting and three-dimensional (3D) UAV trajectory. In this paper, we explore the 3D channel tracking for a Ka-band UAV-satellite communication system. We firstly propose a statistical dynamic channel model called 3D two-dimensional Markov model (3D-2D-MM) for the UAV-satellite communication system by exploiting the probabilistic insight relationship of both hidden value vector and joint hidden support vector. Specifically, for the joint hidden support vector, we consider a more realistic 3D support vector in both azimuth and elevation direction. Moreover, the spatial sparsity structure and the time-varying probabilistic relationship between degree patterns named the spatial and temporal correlation, respectively, are studied for each direction. Furthermore, we derive a novel 3D dynamic turbo approximate message passing (3D-DTAMP) algorithm to recursively track the dynamic channel with the 3D-2D-MM priors. Numerical results show that our proposed algorithm achieves superior channel tracking performance to the state-of-the-art algorithms with lower pilot overhead and comparable complexity.

Channel estimation is crucial to beamforming techniques in directional millimetre wave (mmWave) communications, which is generally designed based on channel state information with the assumption that the channel is static. However, due to the Doppler effect caused by the mobility of the users in highly mobile applications, the mmWave channel is changing rapidly. Spatial channel covariance, defined by long-term statistic information of channels, is a promising solution to reduce channel estimation frequency, and which can be used to design hybrid precoders. In this paper, we investigate compressive sensing based spatial channel covariance estimation for hybrid mmWave multiuser (MU) multiple input multiple output (MIMO) system. The updated sparse Bayesian learning (Updated-SBL) algorithm is proposed which is achieved by reducing the total squared mutual coherence of the sensing matrix in it. Simulations demonstrate that the total squared mutual coherence of the proposed Updated-SBL algorithm is dramatically reduced and the superiority of the proposed algorithm is validated by comparing to the other benchmark methods.

Compressive sensing has been applied in wideband spectrum sensing to achieve sub-Nyquist sampling. Prior information of the multiband spectrum occupancy, e.g. from geo-location database, can be utilized by compressive spectrum sensing (CSS) to enhance the sensing performance. However, these priors are prone to be partially missing and may also contain incorrect information. We hereby propose a CSS scheme aided by priors and robust to priors imperfections, and moreover, a novel and practical algorithm to provide robust channel sparsity estimation needed by the CSS scheme. Simulations show prominent enhancement of detection performance and lower iteration counts by employing priors in the proposed CSS scheme.

In this paper we study the problem of sorting unsigned genomes by double-cut-and-join operations, where genomes allow a mix of linear and circular chromosomes to be present. First, we formulate an equivalent optimization problem, called maximum cycle/path decomposition, which is aimed at finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths in a breakpoint graph. Then, we show that the problem of finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length no more than l can be reduced to the well-known degree-bounded k-set packing problem with k = 2l. Finally, a polynomial-time approximation algorithm for the problem of sorting unsigned genomes by double-cut-and-join operations is devised, which achieves the approximation ratio 13/9 + ε ≈ 1.4444 + ε, for any positive ε. For the restricted variation where each genome contains only one linear chromosome, the approximation ratio can be further improved to 69/49 + ε ≈ 1.4082 + ε.