In wireless communication and edge computing networks, fractional programming (FP) and multiplicative programming (MP) are fundamental methodologies widely employed in solving non-convex optimization problems. Prior work introduced a remarkable method to solve non-convex functions with multiple ratios by deriving novel tight upper bounds, which we formalize as the UpperBound transform in this paper. However, the UpperBound transform faces critical limitations, particularly when directly extended to MP problems involving non-negative functions or discrete optimization variables. In this paper, we introduce a generalized transform termed the UP transform to overcome these limitations.We rigorously prove that the UP transform guarantees convergence to a Karush-Kuhn-Tucker (KKT) point for a broader class of MP problems, including scenarios where variables can be zero or discrete. We comprehensively illustrate the UP transform’s utility through two practical applications: partial task offloading in mobile edge computing, optimizing computation and energy efficiency; and user association coupled with resource allocation in heterogeneous networks, addressing mixed discrete-continuous optimization challenges. Comparative evaluations against conventional methods demonstrate superior convergence speed, efficiency, solution quality, and reduced computational complexity of the proposed UP transform based algorithms.

Semantic communication (SemCom) has recently gained attention for its ability to achieve high transmission efficiency with minimal data distortion under limited communication resources. However, the strong correlation between source data and channel input leaves SemCom schemes vulnerable to eavesdropping. Additionally, advances in quantum computing threaten traditional cryptographic methods such as RSA due to Shor’s algorithm. To address these risks, a secure SemCom framework with post-quantum protection is essential. This paper presents a post-quantum secure semantic communication (PQSC) framework by integrating learning with errors (LWE) encryption (widely regarded as quantum-resistant) into a VQ-VAE-based SemCom system. The proposed PQSC framework not only resists quantum attacks but also defends against chosen-plaintext attacks. Experiments show that PQSC consistently outperforms baseline methods across various datasets, channel conditions, and SNR levels. To simulate practical wireless environments, we implement channel coding and modulation using Nvidia Sionna, a GPU-accelerated library for physical layer research. We further examine the trade-off between compression efficiency and computational cost. A downlink use case is modeled to analyze recovery quality, energy consumption, and latency. Our mathematical analysis offers insights into system design and parameter selection for real-world deployment.

With the evolution of artificial intelligence-generated content (AIGC) techniques and the development of space-air-ground integrated networks (SAGIN), there will be a growing opportunity to enhance mobile user experiences with customized AIGC applications. This is enabled by combining parameter-efficient fine-tuning (PEFT) with mobile edge computing. In this paper, we formulate the optimization problem of maximizing the parameter training efficiency of the SAGIN system over wireless networks under limited resource constraints. We propose theParameter training efficiencyAwareResourceAllocation (PARA) technique to jointly optimize user association, data offloading, and communication and computational resource allocation. Detailed derivations are presented to solve this difficult sum of ratios problem based on quadratically constrained quadratic programming (QCQP), semidefinite programming (SDP), graph theory, and fractional programming (FP) techniques. Our proposed PARA technique is effective in finding a stationary point of this non-convex problem. The simulation results demonstrate that the proposed PARA method outperforms other baselines.

In the rapidly evolving landscape of the Metaverse, enhanced by blockchain technology, the efficient processing of data has emerged as a critical challenge, especially in wireless communication systems. Addressing this challenge, our paper introduces the innovative concept of data processing efficiency (DPE), aiming to maximize processed bits per unit of resource consumption in blockchain-empowered Metaverse environments. To achieve this, we propose the DPE-Aware User Association and Resource Allocation (DAUR) algorithm, a tailored optimization framework for blockchain-enabled Metaverse wireless communication systems characterized by joint computing and communication resource constraints. The DAUR algorithm transforms the nonconvex problem of maximizing the sum of DPE ratios into a solvable convex optimization problem. It alternates the optimization of key variables, including user association, work offloading ratios, task-specific computing resource distribution, bandwidth allocation, user power usage ratios, and server computing resource allocation ratios. Our extensive numerical results demonstrate the DAUR algorithm's effectiveness in DPE.

The rapid proliferation of emerging applications, such as the Metaverse and Artificial Intelligence Generated Content (AIGC), demands extensive computational resources, ultra-low latency, and scalable user support. Traditional terrestrial Mobile Edge Computing (MEC) systems cannot fully satisfy these stringent requirements due to limited coverage and constrained resources. This paper proposes a Satellite-Terrestrial Integrated Network-based Mobile Edge Computing (SMEC) system explicitly positioned within an innovative edge-satellite-cloud continuum, incorporating terrestrial edge servers, satellite servers, and terrestrial cloud servers into a unified resource allocation framework. Unlike previous works, which typically oversimplify system complexities, our heterogeneous SMEC architecture explicitly models diverse user-server interactions, satellite energy constraints, and realistic multi-objective trade-offs among latency, energy consumption, and user experience, which, however, introduces challenging non-convex and discrete variables. We formulate this realistic and complex resource allocation problem as a Mixed-Integer Non-Convex Problem (MINCP) and propose the Connection-constrained SMEC Resource Allocation (CSRA) algorithm. CSRA innovatively integrates Block Coordinate Descent (BCD), Successive Convex Approximation (SCA), and advanced Fractional Programming (FP) techniques with significant algorithmic enhancements to accelerate the convergence speed and reduce the computational overhead. Simulation results demonstrate that the CSRA algorithm significantly outperforms benchmark methods, underscoring its practical effectiveness and methodological robustness.

Ensuring secure and efficient data processing in mobile edge computing (MEC) systems is a critical challenge. While quantum key distribution (QKD) offers unconditionally secure key exchange and homomorphic encryption (HE) enables privacy-preserving data processing, existing research fails to address the comprehensive trade-offs among QKD utility, HE security, and system costs. This paper proposes a novel framework integrating QKD, transciphering, and HE for secure and efficient MEC. QKD distributes symmetric keys, transciphering bridges symmetric encryption, and HE processes encrypted data at the server. We formulate an optimization problem balancing QKD utility, HE security, processing and wireless transmission costs. However, the formulated optimization is non-convex and NPhard. To solve it efficiently, we propose the Quantum-enhanced Homomorphic Encryption resource allocation (QuHE) algorithm. Theoretical analysis proves the proposed QuHE algorithm’s convergence and optimality, and simulations demonstrate its effectiveness across multiple performance metrics.

This paper proposes a framework for applying a novel multi-domain modulation scheme, orthogonal chirp division multiplexing with index modulation (OCDM-IM), in integrated sensing and communication (ISAC) systems by combining OCDM and index modulation (IM). To support simple SISO-ISAC applications, a low-complexity fast Fourier transform (FFT)-based sensing algorithm is developed for the sake of the superior performance of OCDM-IM over traditional OCDM. Building on this, the framework is further extended to more attractive MIMO-ISAC systems in order to achieve improved bit error rate (BER) and a lower peak-to-average power ratio (PAPR) compared to the conventional MIMO-OCDM scheme. For sensing, it enables distance, velocity, and angle estimation by formulating the OCDM-IM waveform within a compressed sensing framework, which is then efficiently solved using the proposed orthogonal matching pursuit (OMP) algorithm. Simulation results confirm that the OCDM-IM waveform enhances communication performance through IM while preserving the promising sensing performance.

The emergence of 5G technology has enabled the development of Metaverse applications that provide users with immersive experiences through augmented reality (AR) devices, and the integration of federated learning (FL) with the Metaverse AR (MAR) systems can enable many edge intelligence services in 5G. However, the presence of nonindependent and identically distributed (Non-IID) data across all AR users' devices, coupled with limited edge communication resources, makes it challenging to achieve human-centric Metaverse-related applications such as target detection or image classification that combine virtual content with real-world. To address these challenges, we propose a novel adaptive resource-efficient Metaverse-based FL (AMFL) algorithm for AR applications that mitigates the negative effect of Non-IID data and reduces resource costs as well as improves the quality of experience (QoE). We first analyze the impact of wireless communication factors such as CPU frequency, bandwidth, and transmission power on FL training performance by a toy example in the MAR systems. Based on this analysis, furthermore, we establish a Non-IID degree, model accuracy, and resource consumption-related QoE maximization problem under given resource budgets, which is a stochastic optimization problem with strongly coupled variables, including bandwidth, CPU frequency, and transmission power. Guided by the theoretical analysis, to solve this issue, AMFL employs a deep reinforcement learning (DRL)-based method to adaptively allocate resources. Numerical results demonstrate that AMFL can significantly improve the QoE by up to 30.28%, and reduce communication round and energy costs by up to 81.08% and 72.20%, respectively, even under the worst Non-IID case, compared to benchmarks.

The convergence of blockchain, Metaverse, and non-fungible tokens (NFTs) brings transformative digital opportunities alongside challenges like privacy and resource management. Addressing these, we focus on optimizing user connectivity and resource allocation in an NFT-centric and blockchain-enabled Metaverse in this paper. Through user work-offloading, we optimize data tasks, user connection parameters, and server computing frequency division. In the resource allocation phase, we optimize communication-computation resource distributions, including bandwidth, transmit power, and computing frequency. We introduce the trust-cost ratio (TCR), a pivotal measure combining trust scores from users’ resources and server history with delay and energy costs. This balance ensures sustained user engagement and trust. The DASHF algorithm, central to our approach, encapsulates the Dinkelbach algorithm, alternating optimization, semidefinite relaxation (SDR), the Hungarian method, and a novel fractional programming technique from a recent IEEE JSAC paper [2]. The most challenging part of DASHF is to rewrite an optimization problem as Quadratically Constrained Quadratic Programming (QCQP) via carefully designed transformations, in order to be solved by SDR and the Hungarian algorithm. Extensive simulations validate the DASHF algorithm’s efficacy, revealing critical insights for enhancing blockchain-Metaverse applications, especially with NFTs.

Semantic communication (SemCom) is an emerging way that aims to improve communication efficiency based on the semantics of content, which relies on the knowledge base (KB) and is usually dedicated to specific tasks or datasets. To improve the adaptability of SemCom systems on unknown datasets, we propose a post-deployment Fine-Tunable Semantic Communication (FTSC) system for image transmission. Towards an adaptive and efficient SemCom system, our research consists of the framework design of FTSC and its system optimization study. Firstly, the generalizability study is conducted based on a two-layer hierarchical vector quantized-variational autoencoder (VQ-VAE-2). Unlike traditional SemCom that can work on limited pretrained datasets, FTSC adapts to varied input data post-deployment, enhancing practicality in diverse communication scenarios. This system incorporates two novel fine-tuning methods: Decoder Fine-Tuning (DFT) and Latent Space-based Decoder Fine-Tuning (LSDFT). DFT updates the decoder for new images post-deployment without transmitting gradients, while LSDFT eliminates the need for raw image transmission during fine-tuning. Secondly, we study the system optimization of the proposed FTSC framework to improve the efficiency of communication resource allocation with the concern of recovery quality, time delay, and energy cost in downlink transmissions. Extensive experiments demonstrate the superiority of FTSC over Joint Photographic Experts Group (JPEG) and Joint Source-Channel Coding (JSCC) across various datasets and noise levels, and both DFT and LSDFT significantly enhance image recovery on unfamiliar datasets compared to pre-trained models.

In the rapidly evolving landscape of the Metaverse, enhanced by blockchain technology, the efficient processing of data has emerged as a critical challenge, especially in wireless communication systems. Addressing this need, our paper introduces the innovative concept of data processing efficiency (DPE), aiming to maximize processed bits per unit of resource consumption in blockchain-empowered Metaverse environments. To achieve this, we propose the DPE-Aware User Association and Resource Allocation (DAUR) algorithm, a tailored solution for these complex systems. The DAUR algorithm transforms the challenging task of optimizing the sum of DPE ratios into a solvable convex optimization problem. It uniquely alternates the optimization of key variables like user association, work offloading ratios, task-specific computing resource distribution, bandwidth allocation, user power usage ratios, and server computing resource allocation ratios. Our extensive numerical results demonstrate the DAUR algorithm's effectiveness in DPE.

In the rapidly evolving landscape of large language models (LLMs) and mobile edge computing for 6G, the need for efficient service delivery to mobile users with constrained computational resources has become paramount. Addressing this, our paper delves into a collaborative framework for model training where user data and model adapters are shared with servers to optimize performance. Within this framework, users initially update the first several layers of the adapters while freezing the other layers of them, leveraging their local datasets. Once this step is complete, these partially trained parameters are transmitted to servers. The servers, equipped with more robust computational capabilities, then update the subsequent layers. After this training, they send the enhanced parameters back to the users. This collaborative training approach ensures that mobile users with limited computational capacities can still benefit from advanced LLM services without being burdened by exhaustive computations. Central to our methodology is the DASHF algorithm, which encapsulates the Dinkelbach algorithm, alternating optimization, semidefinite relaxation (SDR), the Hungarian method, and a pioneering fractional programming technique from a recent IEEE JSAC paper [1]. The crux of DASHF is its capability to reformulate an optimization problem as Quadratically Constrained Quadratic Programming (QCQP) via meticulously crafted transformations, making it solvable by SDR and the Hungarian algorithm. Through extensive simulations, we demonstrate the effectiveness of the DASHF algorithm, offering significant insights for the advancement of collaborative LLM service deployments.

The Metaverse will provide numerous immersive applications for human users, by consolidating technologies like extended reality (XR), video streaming, and cellular networks. Optimizing wireless communications to enable the human-centric Metaverse is important to satisfy the demands of mobile users. In this paper, we formulate the optimization of the system utility-cost ratio (UCR) for the Metaverse over wireless networks. Our human-centric utility measure for virtual reality (VR) applications of the Metaverse represents users’ perceptual assessment of the VR video quality as a function of the data rate and the video resolution and is learned from real datasets. The variables jointly optimized in our problem include the allocation of both communication and computation resources as well as VR video resolutions. The system cost in our problem comprises the energy consumption and delay and is non-convex with respect to the optimization variables. To solve the non-convex optimization, we develop a novel fractional programming technique, which contributes to optimization theory and has broad applicability beyond our paper. Our proposed algorithm for the system UCR optimization is computationally efficient and finds a stationary point to the constrained optimization. Through extensive simulations, our algorithm is demonstrated to outperform other approaches.

In this paper, we study an unmanned aerial vehicle (UAV) assisted data collection (DC) system and consider the interference caused by malicious nodes. To ensure sustainable communication, a bi-objective optimization problem is proposed to jointly optimize the maximization of the total data throughput and the minimization of the UAV energy consumption. To this end, a proximal policy optimization (PPO) based framework is proposed. Specifically, under a realistic probabilistic line-of-sight (LoS) channel model, we derive the maximum achievable data transmission rate under interference and express its lower bound explicitly, considering coverage and sensing constraints. In order to tackle the non-convex dilemma and optimize communication throughput and energy utilization, the issue at hand is conceptualized as a Markov decision process (MDP) and a multidimensional reward function is set. Extensive numerical simulations demonstrate the effectiveness of the proposed frame-work in handling the data transmission task while reducing overall network energy consumption. The results indicate a total throughput improvement of 19.7% and a reduction of 46.3% in energy consumption compared to the baseline algorithm.

The Metaverse, an emerging digital space, is expected to offer various services mirroring the real world. Wireless communications for mobile Metaverse users should be tailored to meet the following user characteristics: 1) emphasizing application-specific perceptual utility instead of simply the transmission rate, 2) concerned with energy efficiency due to the limited device battery and energy intensiveness of some applications, and 3) caring about security as the applications may involve sensitive personal data. To this end, this paper incorporates application-specific utility, energy efficiency, and physical-layer security (PLS) into the studied optimization in a wireless network for the Metaverse. Specifically, after introducing utility-energy efficiency (UEE) to represent each Metaverse user's application-specific objective under PLS, we formulate an optimization to maximize the network's weighted sum-UEE by deciding users' transmission powers and communication bandwidths. The formulated problem belongs to the sum-of-ratios optimization, for which prior studies have demonstrated its difficulty. Nevertheless, our proposed algorithm 1) obtains the global optimum for the weighted sum-UEE optimization, via a transform to parametric convex optimization problems, 2) applies to any utility function which is concave, increasing, and twice differentiable, and 3) achieves a linear time complexity in the number of users (the optimal complexity in the order sense). Simulations confirm the superiority of our algorithm over other approaches. We explain that our technique for solving the sum-of-ratios optimization is applicable to other optimization problems in wireless networks and mobile computing.