Pingyi Fan

Anbai Jiang, Wei-Qiang Zhang, Yufeng Deng et al.

Automatic detection of machine anomaly remains challenging for machine learning. We believe the capability of generative adversarial network (GAN) suits the need of machine audio anomaly detection, yet rarely has this been investigated by previous work. In this paper, we propose AEGAN-AD, a totally unsupervised approach in which the generator (also an autoencoder) is trained to reconstruct input spectrograms. It is pointed out that the denoising nature of reconstruction deprecates its capacity. Thus, the discriminator is redesigned to aid the generator during both training stage and detection stage. The performance of AEGAN-AD on the dataset of DCASE 2022 Challenge TASK 2 demonstrates the state-of-the-art result on five machine types. A novel anomaly localization method is also investigated. Source code available at: www.github.com/jianganbai/AEGAN-AD

Cui Zhang, Wenjun Zhang, Qiong Wu et al.

Federated Learning (FL) can protect the privacy of the vehicles in vehicle edge computing (VEC) to a certain extent through sharing the gradients of vehicles' local models instead of local data. The gradients of vehicles' local models are usually large for the vehicular artificial intelligence (AI) applications, thus transmitting such large gradients would cause large per-round latency. Gradient quantization has been proposed as one effective approach to reduce the per-round latency in FL enabled VEC through compressing gradients and reducing the number of bits, i.e., the quantization level, to transmit gradients. The selection of quantization level and thresholds determines the quantization error, which further affects the model accuracy and training time. To do so, the total training time and quantization error (QE) become two key metrics for the FL enabled VEC. It is critical to jointly optimize the total training time and QE for the FL enabled VEC. However, the time-varying channel condition causes more challenges to solve this problem. In this paper, we propose a distributed deep reinforcement learning (DRL)-based quantization level allocation scheme to optimize the long-term reward in terms of the total training time and QE. Extensive simulations identify the optimal weighted factors between the total training time and QE, and demonstrate the feasibility and effectiveness of the proposed scheme.

Maoxin Ji, Qiong Wu, Pingyi Fan et al.

In the rapidly evolving landscape of Internet of Vehicles (IoV) technology, Cellular Vehicle-to-Everything (C-V2X) communication has attracted much attention due to its superior performance in coverage, latency, and throughput. Resource allocation within C-V2X is crucial for ensuring the transmission of safety information and meeting the stringent requirements for ultra-low latency and high reliability in Vehicle-to-Vehicle (V2V) communication. This paper proposes a method that integrates Graph Neural Networks (GNN) with Deep Reinforcement Learning (DRL) to address this challenge. By constructing a dynamic graph with communication links as nodes and employing the Graph Sample and Aggregation (GraphSAGE) model to adapt to changes in graph structure, the model aims to ensure a high success rate for V2V communication while minimizing interference on Vehicle-to-Infrastructure (V2I) links, thereby ensuring the successful transmission of V2V link information and maintaining high transmission rates for V2I links. The proposed method retains the global feature learning capabilities of GNN and supports distributed network deployment, allowing vehicles to extract low-dimensional features that include structural information from the graph network based on local observations and to make independent resource allocation decisions. Simulation results indicate that the introduction of GNN, with a modest increase in computational load, effectively enhances the decision-making quality of agents, demonstrating superiority to other methods. This study not only provides a theoretically efficient resource allocation strategy for V2V and V2I communications but also paves a new technical path for resource management in practical IoV environments.

Qiong Wu, Yu Zhao, Qiang Fan et al.

The vehicular edge computing (VEC) can cache contents in different RSUs at the network edge to support the real-time vehicular applications. In VEC, owing to the high-mobility characteristics of vehicles, it is necessary to cache the user data in advance and learn the most popular and interesting contents for vehicular users. Since user data usually contains privacy information, users are reluctant to share their data with others. To solve this problem, traditional federated learning (FL) needs to update the global model synchronously through aggregating all users' local models to protect users' privacy. However, vehicles may frequently drive out of the coverage area of the VEC before they achieve their local model trainings and thus the local models cannot be uploaded as expected, which would reduce the accuracy of the global model. In addition, the caching capacity of the local RSU is limited and the popular contents are diverse, thus the size of the predicted popular contents usually exceeds the cache capacity of the local RSU. Hence, the VEC should cache the predicted popular contents in different RSUs while considering the content transmission delay. In this paper, we consider the mobility of vehicles and propose a cooperative Caching scheme in the VEC based on Asynchronous Federated and deep Reinforcement learning (CAFR). We first consider the mobility of vehicles and propose an asynchronous FL algorithm to obtain an accurate global model, and then propose an algorithm to predict the popular contents based on the global model. In addition, we consider the mobility of vehicles and propose a deep reinforcement learning algorithm to obtain the optimal cooperative caching location for the predicted popular contents in order to optimize the content transmission delay. Extensive experimental results have demonstrated that the CAFR scheme outperforms other baseline caching schemes.

Zheqi Zhu, Yuchen Shi, Jiajun Luo et al.

Federated learning (FL) has prevailed as an efficient and privacy-preserved scheme for distributed learning. In this work, we mainly focus on the optimization of computation and communication in FL from a view of pruning. By adopting layer-wise pruning in local training and federated updating, we formulate an explicit FL pruning framework, FedLP (Federated Layer-wise Pruning), which is model-agnostic and universal for different types of deep learning models. Two specific schemes of FedLP are designed for scenarios with homogeneous local models and heterogeneous ones. Both theoretical and experimental evaluations are developed to verify that FedLP relieves the system bottlenecks of communication and computation with marginal performance decay. To the best of our knowledge, FedLP is the first framework that formally introduces the layer-wise pruning into FL. Within the scope of federated learning, more variants and combinations can be further designed based on FedLP.

Zheqi Zhu, Yuchen Shi, Pingyi Fan et al.

As a promising learning paradigm integrating computation and communication, federated learning (FL) proceeds the local training and the periodic sharing from distributed clients. Due to the non-i.i.d. data distribution on clients, FL model suffers from the gradient diversity, poor performance, bad convergence, etc. In this work, we aim to tackle this key issue by adopting importance sampling (IS) for local training. We propose importance sampling federated learning (ISFL), an explicit framework with theoretical guarantees. Firstly, we derive the convergence theorem of ISFL to involve the effects of local importance sampling. Then, we formulate the problem of selecting optimal IS weights and obtain the theoretical solutions. We also employ a water-filling method to calculate the IS weights and develop the ISFL algorithms. The experimental results on CIFAR-10 fit the proposed theorems well and verify that ISFL reaps better performance, sampling efficiency, as well as explainability on non-i.i.d. data. To the best of our knowledge, ISFL is the first non-i.i.d. FL solution from the local sampling aspect which exhibits theoretical compatibility with neural network models. Furthermore, as a local sampling approach, ISFL can be easily migrated into other emerging FL frameworks.

Xueying Gu, Qiong Wu, Pingyi Fan et al.

Intelligent Transportation Systems (ITS) leverage Integrated Sensing and Communications (ISAC) to enhance data exchange between vehicles and infrastructure in the Internet of Vehicles (IoV). This integration inevitably increases computing demands, risking real-time system stability. Vehicle Edge Computing (VEC) addresses this by offloading tasks to Road Side Unit (RSU), ensuring timely services. Our previous work FLSimCo algorithm, which uses local resources for Federated Self-Supervised Learning (SSL), though vehicles often can't complete all iterations task. Our improved algorithm offloads partial task to RSU and optimizes energy consumption by adjusting transmission power, CPU frequency, and task assignment ratios, balancing local and RSU-based training. Meanwhile, setting an offloading threshold further prevents inefficiencies. Simulation results show that the enhanced algorithm reduces energy consumption, improves offloading efficiency and the accuracy of Federated SSL.

Xueying Gu, Qiong Wu, Pingyi Fan et al.

In the Internet of Vehicles (IoV), Federated Learning (FL) provides a privacy-preserving solution by aggregating local models without sharing data. Traditional supervised learning requires image data with labels, but data labeling involves significant manual effort. Federated Self-Supervised Learning (FSSL) utilizes Self-Supervised Learning (SSL) for local training in FL, eliminating the need for labels while protecting privacy. Compared to other SSL methods, Momentum Contrast (MoCo) reduces the demand for computing resources and storage space by creating a dictionary. However, using MoCo in FSSL requires uploading the local dictionary from vehicles to Base Station (BS), which poses a risk of privacy leakage. Simplified Contrast (SimCo) addresses the privacy leakage issue in MoCo-based FSSL by using dual temperature instead of a dictionary to control sample distribution. Additionally, considering the negative impact of motion blur on model aggregation, and based on SimCo, we propose a motion blur-resistant FSSL method, referred to as BFSSL. Furthermore, we address energy consumption and delay in the BFSSL process by proposing a Deep Reinforcement Learning (DRL)-based resource allocation scheme, called DRL-BFSSL. In this scheme, BS allocates the Central Processing Unit (CPU) frequency and transmission power of vehicles to minimize energy consumption and latency, while aggregating received models based on the motion blur level. Simulation results validate the effectiveness of our proposed aggregation and resource allocation methods.

Kangwei Qi, Qiong Wu, Pingyi Fan et al.

Vehicular edge computing (VEC) is an emerging technology with significant potential in the field of internet of vehicles (IoV), enabling vehicles to perform intensive computational tasks locally or offload them to nearby edge devices. However, the quality of communication links may be severely deteriorated due to obstacles such as buildings, impeding the offloading process. To address this challenge, we introduce the use of Reconfigurable Intelligent Surfaces (RIS), which provide alternative communication pathways to assist vehicular communication. By dynamically adjusting the phase-shift of the RIS, the performance of VEC systems can be substantially improved. In this work, we consider a RIS-assisted VEC system, and design an optimal scheme for local execution power, offloading power, and RIS phase-shift, where random task arrivals and channel variations are taken into account. To address the scheme, we propose an innovative deep reinforcement learning (DRL) framework that combines the Deep Deterministic Policy Gradient (DDPG) algorithm for optimizing RIS phase-shift coefficients and the Multi-Agent Deep Deterministic Policy Gradient (MADDPG) algorithm for optimizing the power allocation of vehicle user (VU). Simulation results show that our proposed scheme outperforms the traditional centralized DDPG, Twin Delayed Deep Deterministic Policy Gradient (TD3) and some typical stochastic schemes.

Wenhua Wang, Qiong Wu, Pingyi Fan et al.

With the rapid development of intelligent vehicles and Intelligent Transport Systems (ITS), the sensors such as cameras and LiDAR installed on intelligent vehicles provides higher capacity of executing computation-intensive and delay-sensitive tasks, thereby raising deployment costs. To address this issue, Vehicular Edge Computing (VEC) has been proposed to process data through Road Side Units (RSUs) to support real-time applications. This paper focuses on the Age of Information (AoI) as a key metric for data freshness and explores task offloading issues for vehicles under RSU communication resource constraints. We adopt a Multi-agent Deep Reinforcement Learning (MADRL) approach, allowing vehicles to autonomously make optimal data offloading decisions. However, MADRL poses risks of vehicle information leakage during communication learning and centralized training. To mitigate this, we employ a Federated Learning (FL) framework that shares model parameters instead of raw data to protect the privacy of vehicle users. Building on this, we propose an innovative distributed federated learning framework combining Graph Neural Networks (GNN), named Federated Graph Neural Network Multi-Agent Reinforcement Learning (FGNN-MADRL), to optimize AoI across the system. For the first time, road scenarios are constructed as graph data structures, and a GNN-based federated learning framework is proposed, effectively combining distributed and centralized federated aggregation. Furthermore, we propose a new MADRL algorithm that simplifies decision making and enhances offloading efficiency, further reducing the decision complexity. Simulation results demonstrate the superiority of our proposed approach to other methods through simulations.

Qiong Wu, Siyuan Wang, Pingyi Fan et al.

In the traditional vehicular network, computing tasks generated by the vehicles are usually uploaded to the cloud for processing. However, since task offloading toward the cloud will cause a large delay, vehicular edge computing (VEC) is introduced to avoid such a problem and improve the whole system performance, where a roadside unit (RSU) with certain computing capability is used to process the data of vehicles as an edge entity. Owing to the privacy and security issues, vehicles are reluctant to upload local data directly to the RSU, and thus federated learning (FL) becomes a promising technology for some machine learning tasks in VEC, where vehicles only need to upload the local model hyperparameters instead of transferring their local data to the nearby RSU. Furthermore, as vehicles have different local training time due to various sizes of local data and their different computing capabilities, asynchronous federated learning (AFL) is employed to facilitate the RSU to update the global model immediately after receiving a local model to reduce the aggregation delay. However, in AFL of VEC, different vehicles may have different impact on the global model updating because of their various local training delay, transmission delay and local data sizes. Also, if there are bad nodes among the vehicles, it will affect the global aggregation quality at the RSU. To solve the above problem, we shall propose a deep reinforcement learning (DRL) based vehicle selection scheme to improve the accuracy of the global model in AFL of vehicular network. In the scheme, we present the model including the state, action and reward in the DRL based to the specific problem. Simulation results demonstrate our scheme can effectively remove the bad nodes and improve the aggregation accuracy of the global model.

Gangtao Xin, Pingyi Fan

Semantic communication is not focused on improving the accuracy of transmitted symbols, but is concerned with expressing the expected meaning that the symbol sequence exactly carries. However, the measurement of semantic messages and their corresponding codebook generation are still open issues. Expansion, which integrates simple things into a complex system and even generates intelligence, is truly consistent with the evolution of the human language system. We apply this idea to the semantic communication system, quantifying semantic transmission by symbol sequences and investigating the semantic information system in a similar way as Shannon's method for digital communication systems. This work is the first to discuss semantic expansion and knowledge collision in the semantic information framework. Some important theoretical results are presented, including the relationship between semantic expansion and the transmission information rate. We believe such a semantic information framework may provide a new paradigm for semantic communications, and semantic expansion and knowledge collision will be the cornerstone of semantic information theory.

Yu Xie, Qiong Wu, Pingyi Fan et al.

As a promising technology, vehicular edge computing (VEC) can provide computing and caching services by deploying VEC servers near vehicles. However, VEC networks still face challenges such as high vehicle mobility. Digital twin (DT), an emerging technology, can predict, estimate, and analyze real-time states by digitally modeling objects in the physical world. By integrating DT with VEC, a virtual vehicle DT can be created in the VEC server to monitor the real-time operating status of vehicles. However, maintaining the vehicle DT model requires ongoing attention from the VEC server, which also needs to offer computing services for the vehicles. Therefore, effective allocation and scheduling of VEC server resources are crucial. This study focuses on a general VEC network with a single VEC service and multiple vehicles, examining the two types of delays caused by twin maintenance and computational processing within the network. By transforming the problem using satisfaction functions, we propose an optimization problem aimed at maximizing each vehicle's resource utility to determine the optimal resource allocation strategy. Given the non-convex nature of the issue, we employ multi-agent Markov decision processes to reformulate the problem. Subsequently, we propose the twin maintenance and computing task processing resource collaborative scheduling (MADRL-CSTC) algorithm, which leverages multi-agent deep reinforcement learning. Through experimental comparisons with alternative algorithms, it demonstrates that our proposed approach is effective in terms of resource allocation.

Rui She, Pingyi Fan

In order to introduce deep learning technologies into anomaly detection, Generative Adversarial Networks (GANs) are considered as important roles in the algorithm design and realistic applications. In terms of GANs, event probability reflected in the objective function, has an impact on the event generation which plays a crucial part in GAN-based anomaly detection. The information metric, e.g. Kullback-Leibler divergence in the original GAN, makes the objective function have different sensitivity on different event probability, which provides an opportunity to refine GAN-based anomaly detection by influencing data generation. In this paper, we introduce the exponential information metric into the GAN, referred to as MIM-based GAN, whose superior characteristics on data generation are discussed in theory. Furthermore, we propose an anomaly detection method with MIM-based GAN, as well as explain its principle for the unsupervised learning case from the viewpoint of probability event generation. Since this method is promising to detect anomalies in Internet of Things (IoT), such as environmental, medical and biochemical outliers, we make use of several datasets from the online ODDS repository to evaluate its performance and compare it with other methods.

Shanyun Liu, Rui She, Pingyi Fan

Data collection is a fundamental problem in the scenario of big data, where the size of sampling sets plays a very important role, especially in the characterization of data structure. This paper considers the information collection process by taking message importance into account, and gives a distribution-free criterion to determine how many samples are required in big data structure characterization. Similar to differential entropy, we define differential message importance measure (DMIM) as a measure of message importance for continuous random variable. The DMIM for many common densities is discussed, and high-precision approximate values for normal distribution are given. Moreover, it is proved that the change of DMIM can describe the gap between the distribution of a set of sample values and a theoretical distribution. In fact, the deviation of DMIM is equivalent to Kolmogorov-Smirnov statistic, but it offers a new way to characterize the distribution goodness-of-fit. Numerical results show some basic properties of DMIM and the accuracy of the proposed approximate values. Furthermore, it is also obtained that the empirical distribution approaches the real distribution with decreasing of the DMIM deviation, which contributes to the selection of suitable sampling points in actual system.

Hongbiao Zhu, Qiong Wu, Qiang Fan et al.

Multi-input multi-out and non-orthogonal multiple access (MIMO-NOMA) internet-of-things (IoT) systems can improve channel capacity and spectrum efficiency distinctly to support the real-time applications. Age of information (AoI) is an important metric for real-time application, but there is no literature have minimized AoI of the MIMO-NOMA IoT system, which motivates us to conduct this work. In MIMO-NOMA IoT system, the base station (BS) determines the sample collection requirements and allocates the transmission power for each IoT device. Each device determines whether to sample data according to the sample collection requirements and adopts the allocated power to transmit the sampled data to the BS over MIMO-NOMA channel. Afterwards, the BS employs successive interference cancelation (SIC) technique to decode the signal of the data transmitted by each device. The sample collection requirements and power allocation would affect AoI and energy consumption of the system. It is critical to determine the optimal policy including sample collection requirements and power allocation to minimize the AoI and energy consumption of MIMO-NOMA IoT system, where the transmission rate is not a constant in the SIC process and the noise is stochastic in the MIMO-NOMA channel. In this paper, we propose the optimal power allocation to minimize the AoI and energy consumption of MIMO- NOMA IoT system based on deep reinforcement learning (DRL). Extensive simulations are carried out to demonstrate the superiority of the optimal power allocation.

Xun Li, Qiong Wu, Pingyi Fan et al.

Vehicle edge caching is a promising technology that can significantly reduce the latency for vehicle users (VUs) to access content by pre-caching user-interested content at edge nodes. It is crucial to accurately predict the content that VUs are interested in without exposing their privacy. Traditional federated learning (FL) can protect user privacy by sharing models rather than raw data. However, the training of FL requires frequent model transmission, which can result in significant communication overhead. Additionally, vehicles may leave the road side unit (RSU) coverage area before training is completed, leading to training failures. To address these issues, in this letter, we propose a federated distillation-assisted vehicle edge caching scheme based on lightweight denoising diffusion probabilistic model (LDPM). The simulation results demonstrate that the proposed vehicle edge caching scheme has good robustness to variations in vehicle speed, significantly reducing communication overhead and improving cache hit percentage.

Cui Zhang, Wenjun Zhang, Qiong Wu et al.

The Internet of Vehicles (IoV) network can address the issue of limited computing resources and data processing capabilities of individual vehicles, but it also brings the risk of privacy leakage to vehicle users. Applying blockchain technology can establish secure data links within the IoV, solving the problems of insufficient computing resources for each vehicle and the security of data transmission over the network. However, with the development of the IoV, the amount of data interaction between multiple vehicles and between vehicles and base stations, roadside units, etc., is continuously increasing. There is a need to further reduce the interaction volume, and intelligent data compression is key to solving this problem. The VIB technique facilitates the training of encoding and decoding models, substantially diminishing the volume of data that needs to be transmitted. This paper introduces an innovative approach that integrates blockchain with VIB, referred to as BVIB, designed to lighten computational workloads and reinforce the security of the network. We first construct a new network framework by separating the encoding and decoding networks to address the computational burden issue, and then propose a new algorithm to enhance the security of IoV networks. We also discuss the impact of the data extraction rate on system latency to determine the most suitable data extraction rate. An experimental framework combining Python and C++ has been established to substantiate the efficacy of our BVIB approach. Comprehensive simulation studies indicate that the BVIB consistently excels in comparison to alternative foundational methodologies.

Shulin Song, Zheng Zhang, Qiong Wu et al.

Autonomous driving may be the most important application scenario of next generation, the development of wireless access technologies enabling reliable and low-latency vehicle communication becomes crucial. To address this, 3GPP has developed Vehicle-to-Everything (V2X) specifications based on 5G New Radio (NR) technology, where Mode 2 Side-Link (SL) communication resembles Mode 4 in LTE-V2X, allowing direct communication between vehicles. This supplements SL communication in LTE-V2X and represents the latest advancement in cellular V2X (C-V2X) with improved performance of NR-V2X. However, in NR-V2X Mode 2, resource collisions still occur, and thus degrade the age of information (AOI). Therefore, a interference cancellation method is employed to mitigate this impact by combining NR-V2X with Non-Orthogonal multiple access (NOMA) technology. In NR-V2X, when vehicles select smaller resource reservation interval (RRI), higher-frequency transmissions take ore energy to reduce AoI. Hence, it is important to jointly consider AoI and communication energy consumption based on NR-V2X communication. Then, we formulate such an optimization problem and employ the Deep Reinforcement Learning (DRL) algorithm to compute the optimal transmission RRI and transmission power for each transmitting vehicle to reduce the energy consumption of each transmitting vehicle and the AoI of each receiving vehicle. Extensive simulations have demonstrated the performance of our proposed algorithm.

Xueying Gu, Qiong Wu, Pingyi Fan et al.

Federated Learning (FL) is an advanced distributed machine learning approach, that protects the privacy of each vehicle by allowing the model to be trained on multiple devices simultaneously without the need to upload all data to a road side unit (RSU). This enables FL to handle scenarios with sensitive or widely distributed data. However, in these fields, it is well known that the labeling costs can be a significant expense, and models relying on labels are not suitable for these rapidly evolving fields especially in vehicular networks, or mobile internet of things (MIoT), where new data emerges constantly. To handle this issue, the self-supervised learning paves the way for training without labels. Additionally, for vehicles with high velocity, owing to blurred images, simple aggregation not only impacts the accuracy of the aggregated model but also reduces the convergence speed of FL. This paper proposes a FL algorithm based on image blur level to aggregation, called FLSimCo, which does not require labels and serves as a pre-training stage for self-supervised learning in the vehicular environment. Simulation results demonstrate that the proposed algorithm exhibits fast and stable convergence.

Yu Xie, Qiong Wu, Pingyi Fan

With the increasing demand for multiple applications on internet of vehicles. It requires vehicles to carry out multiple computing tasks in real time. However, due to the insufficient computing capability of vehicles themselves, offloading tasks to vehicular edge computing (VEC) servers and allocating computing resources to tasks becomes a challenge. In this paper, a multi task digital twin (DT) VEC network is established. By using DT to develop offloading strategies and resource allocation strategies for multiple tasks of each vehicle in a single slot, an optimization problem is constructed. To solve it, we propose a multi-agent reinforcement learning method on the task offloading and resource allocation. Numerous experiments demonstrate that our method is effective compared to other benchmark algorithms.

Jingbo Zhang, Maoxin Ji, Qiong Wu et al.

Semantic Communication (SC) combined with Vehicular edge computing (VEC) provides an efficient edge task processing paradigm for Internet of Vehicles (IoV). Focusing on highway scenarios, this paper proposes a Tripartite Cooperative Semantic Communication (TCSC) framework, which enables Vehicle Users (VUs) to perform semantic task offloading via Vehicle-to-Infrastructure (V2I) and Vehicle-to-Vehicle (V2V) communications. Considering task latency and the number of semantic symbols, the framework constructs a Mixed-Integer Nonlinear Programming (MINLP) problem, which is transformed into two subproblems. First, we innovatively propose a multi-agent proximal policy optimization task offloading optimization method based on parametric distribution noise (MAPPO-PDN) to solve the optimization problem of the number of semantic symbols; second, linear programming (LP) is used to solve offloading ratio. Simulations show that performance of this scheme is superior to that of other algorithms.

Xinhu Zheng, Anbai Jiang, Bing Han et al.

Anomalous Sound Detection (ASD) has gained significant interest through the application of various Artificial Intelligence (AI) technologies in industrial settings. Though possessing great potential, ASD systems can hardly be readily deployed in real production sites due to the generalization problem, which is primarily caused by the difficulty of data collection and the complexity of environmental factors. This paper introduces a robust ASD model that leverages audio pre-trained models. Specifically, we fine-tune these models using machine operation data, employing SpecAug as a data augmentation strategy. Additionally, we investigate the impact of utilizing Low-Rank Adaptation (LoRA) tuning instead of full fine-tuning to address the problem of limited data for fine-tuning. Our experiments on the DCASE2023 Task 2 dataset establish a new benchmark of 77.75% on the evaluation set, with a significant improvement of 6.48% compared with previous state-of-the-art (SOTA) models, including top-tier traditional convolutional networks and speech pre-trained models, which demonstrates the effectiveness of audio pre-trained models with LoRA tuning. Ablation studies are also conducted to showcase the efficacy of the proposed scheme.

Anbai Jiang, Yuchen Shi, Pingyi Fan et al.

Machine anomalous sound detection (ASD) has emerged as one of the most promising applications in the Industrial Internet of Things (IIoT) due to its unprecedented efficacy in mitigating risks of malfunctions and promoting production efficiency. Previous works mainly investigated the machine ASD task under centralized settings. However, developing the ASD system under decentralized settings is crucial in practice, since the machine data are dispersed in various factories and the data should not be explicitly shared due to privacy concerns. To enable these factories to cooperatively develop a scalable ASD model while preserving their privacy, we propose a novel framework named CoopASD, where each factory trains an ASD model on its local dataset, and a central server aggregates these local models periodically. We employ a pre-trained model as the backbone of the ASD model to improve its robustness and develop specialized techniques to stabilize the model under a completely non-iid and domain shift setting. Compared with previous state-of-the-art (SOTA) models trained in centralized settings, CoopASD showcases competitive results with negligible degradation of 0.08%. We also conduct extensive ablation studies to demonstrate the effectiveness of CoopASD.

Pingyi Fan, Anbai Jiang, Shuwei Zhang et al.

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

Zheng Zhang, Qiong Wu, Pingyi Fan et al.

To address communication latency issues, the Third Generation Partnership Project (3GPP) has defined Cellular-Vehicle to Everything (C-V2X) technology, which includes Vehicle-to-Vehicle (V2V) communication for direct vehicle-to-vehicle communication. However, this method requires vehicles to autonomously select communication resources based on the Semi-Persistent Scheduling (SPS) protocol, which may lead to collisions due to different vehicles sharing the same communication resources, thereby affecting communication effectiveness. Non-Orthogonal Multiple Access (NOMA) is considered a potential solution for handling large-scale vehicle communication, as it can enhance the Signal-to-Interference-plus-Noise Ratio (SINR) by employing Successive Interference Cancellation (SIC), thereby reducing the negative impact of communication collisions. When evaluating vehicle communication performance, traditional metrics such as reliability and transmission delay present certain contradictions. Introducing the new metric Age of Information (AoI) provides a more comprehensive evaluation of communication system. Additionally, to ensure service quality, user terminals need to possess high computational capabilities, which may lead to increased energy consumption, necessitating a trade-off between communication energy consumption and effectiveness. Given the complexity and dynamics of communication systems, Deep Reinforcement Learning (DRL) serves as an intelligent learning method capable of learning optimal strategies in dynamic environments. Therefore, this paper analyzes the effects of multi-priority queues and NOMA on AoI in the C-V2X vehicular communication system and proposes an energy consumption and AoI optimization method based on DRL. Finally, through comparative simulations with baseline methods, the proposed approach demonstrates its advances in terms of energy consumption and AoI.

Cui Zhang, Xiao Xu, Qiong Wu et al.

In vehicle edge computing (VEC), asynchronous federated learning (AFL) is used, where the edge receives a local model and updates the global model, effectively reducing the global aggregation latency.Due to different amounts of local data,computing capabilities and locations of the vehicles, renewing the global model with same weight is inappropriate.The above factors will affect the local calculation time and upload time of the local model, and the vehicle may also be affected by Byzantine attacks, leading to the deterioration of the vehicle data. However, based on deep reinforcement learning (DRL), we can consider these factors comprehensively to eliminate vehicles with poor performance as much as possible and exclude vehicles that have suffered Byzantine attacks before AFL. At the same time, when aggregating AFL, we can focus on those vehicles with better performance to improve the accuracy and safety of the system. In this paper, we proposed a vehicle selection scheme based on DRL in VEC. In this scheme, vehicle s mobility, channel conditions with temporal variations, computational resources with temporal variations, different data amount, transmission channel status of vehicles as well as Byzantine attacks were taken into account.Simulation results show that the proposed scheme effectively improves the safety and accuracy of the global model.

Sha Ye, Qiong Wu, Pingyi Fan et al.

Internet of Vehicles (IoV), as the core of intelligent transportation system, enables comprehensive interconnection between vehicles and their surroundings through multiple communication modes, which is significant for autonomous driving and intelligent traffic management. However, with the emergence of new applications, traditional communication technologies face the problems of scarce spectrum resources and high latency. Semantic communication, which focuses on extracting, transmitting, and recovering some useful semantic information from messages, can reduce redundant data transmission, improve spectrum utilization, and provide innovative solutions to communication challenges in the IoV. This paper systematically reviews state of art of semantic communications in the IoV, elaborates the technical background of IoV and semantic communications, and deeply discusses key technologies of semantic communications in IoV, including semantic information extraction, semantic communication architecture, resource allocation and management, and so on. Through specific case studies, it demonstrates that semantic communications can be effectively employed in the scenarios of traffic environment perception and understanding, intelligent driving decision support, IoV service optimization, and intelligent traffic management. Additionally, it analyzes the current challenges and future research directions. This survey reveals that semantic communications has broad application prospects in IoV, but it is necessary to solve the real existing problems by combining advanced technologies to promote its wide application in IoV and contributing to the development of intelligent transportation system.

Wenjun Zhang, Qiong Wu, Pingyi Fan et al.

Semantic communication transmits the extracted features of information rather than raw data, significantly reducing redundancy, which is crucial for addressing spectrum and energy challenges in 6G networks. In this paper, we introduce semantic communication into a cellular vehicle-to-everything (C-V2X)- based autonomous vehicle platoon system for the first time, aiming to achieve efficient management of communication resources in a dynamic environment. Firstly, we construct a mathematical model for semantic communication in platoon systems, in which the DeepSC model and MU-DeepSC model are used to semantically encode and decode unimodal and multi-modal data, respectively. Then, we propose the quality of experience (QoE) metric based on semantic similarity and semantic rate. Meanwhile, we consider the success rate of semantic information transmission (SRS) metric to ensure the fairness of channel resource allocation. Next, the optimization problem is posed with the aim of maximizing the QoE in vehicle-to-vehicle (V2V) links while improving SRS. To solve this mixed integer nonlinear programming problem (MINLP) and adapt to time-varying channel conditions, the paper proposes a distributed semantic-aware multi-modal resource allocation (SAMRA) algorithm based on multi-agent reinforcement learning (MARL), referred to as SAMRAMARL. The algorithm can dynamically allocate channels and power and determine semantic symbol length based on the contextual importance of the transmitted information, ensuring efficient resource utilization. Finally, extensive simulations have demonstrated that SAMRAMARL outperforms existing methods, achieving significant gains in QoE, SRS, and communication delay in C-V2X platooning scenarios.

Xiao Xu, Qiong Wu, Pingyi Fan et al.

Vehicle-to-Infrastructure (V2I) technology enables information exchange between vehicles and road infrastructure. Specifically, when a vehicle approaches a roadside unit (RSU), it can exchange information with the RSU to obtain accurate data that assists in driving. With the release of the 3rd Generation Partnership Project (3GPP) Release 16, which includes the 5G New Radio (NR) Vehicle-to-Everything (V2X) standards, vehicles typically adopt mode-2 communication using sensing-based semi-persistent scheduling (SPS) for resource allocation. In this approach, vehicles identify candidate resources within a selection window and exclude ineligible resources based on information from a sensing window. However, vehicles often drive at different speeds, resulting in varying amounts of data transmission with RSUs as they pass by, which leads to unfair access. Therefore, it is essential to design an access scheme that accounts for different vehicle speeds to achieve fair access across the network. This paper formulates an optimization problem for vehicular networks and proposes a multi-objective optimization scheme to address it by adjusting the selection window in the SPS mechanism of 5G NR V2I mode-2. Simulation results demonstrate the effectiveness of the proposed scheme

Qiong Wu, Maoxin Ji, Pingyi Fan et al.

On-ramp merging presents a critical challenge in autonomous driving, as vehicles from merging lanes need to dynamically adjust their positions and speeds while monitoring traffic on the main road to prevent collisions. To address this challenge, we propose a novel merging control scheme based on reinforcement learning, which integrates lateral control mechanisms. This approach ensures the smooth integration of vehicles from the merging lane onto the main road, optimizing both fuel efficiency and passenger comfort. Furthermore, we recognize the impact of vehicle-to-vehicle (V2V) communication on control strategies and introduce an enhanced protocol leveraging Cellular Vehicle-to-Everything (C-V2X) Mode 4. This protocol aims to reduce the Age of Information (AoI) and improve communication reliability. In our simulations, we employ two AoI-based metrics to rigorously assess the protocol's effectiveness in autonomous driving scenarios. By combining the NS3 network simulator with Python, we simulate V2V communication and vehicle control simultaneously. The results demonstrate that the enhanced C-V2X Mode 4 outperforms the standard version, while the proposed control scheme ensures safe and reliable vehicle operation during on-ramp merging.

Qiong Wu, Jiahou Chu, Pingyi Fan et al.

This paper investigates distributed computing and cooperative control of connected and automated vehicles (CAVs) in ramp merging scenario under transportation cyber-physical system. Firstly, a centralized cooperative trajectory planning problem is formulated subject to the safely constraints and traffic performance in ramp merging scenario, where the trajectories of all vehicles are jointly optimized. To get rid of the reliance on a central controller and reduce computation time, a distributed solution to this problem implemented among CAVs through Vehicles-to-Everything (V2X) communication is proposed. Unlike existing method, our method can distribute the computational task among CAVs and carry out parallel solving through V2X communication. Then, a multi-vehicles model predictive control (MPC) problem aimed at maximizing system stability and minimizing control input is formulated based on the solution of the first problem subject to strict safety constants and input limits. Due to these complex constraints, this problem becomes high-dimensional, centralized, and non-convex. To solve it in a short time, a decomposition and convex reformulation method, namely distributed cooperative iterative model predictive control (DCIMPC), is proposed. This method leverages the communication capability of CAVs to decompose the problem, making full use of the computational resources on vehicles to achieve fast solutions and distributed control. The two above problems with their corresponding solving methods form the systemic framework of the V2X assisted distributed computing and control. Simulations have been conducted to evaluate the framework's convergence, safety, and solving speed. Additionally, extra experiments are conducted to validate the performance of DCIMPC. The results show that our method can greatly improve computation speed without sacrificing system performance.

Maoxin Ji, Tong Wang, Qiong Wu et al.

Addressing the problem of Age of Information (AoI) deterioration caused by packet collisions and vehicle speed-related channel uncertainties in Semi-Persistent Scheduling (SPS) for the Internet of Vehicles (IoV), this letter proposes an optimization approach based on Large Language Models (LLM) and Deep Deterministic Policy Gradient (DDPG). First, an AoI calculation model influenced by vehicle speed, vehicle density, and Resource Reservation Interval (RRI) is established, followed by the design of a dual-path optimization scheme. The DDPG is guided by the state space and reward function, while the LLM leverages contextual learning to generate optimal parameter configurations. Experimental results demonstrate that LLM can significantly reduce AoI after accumulating a small number of exemplars without requiring model training, whereas the DDPG method achieves more stable performance after training.

Kangwei Qi, Qiong Wu, Pingyi Fan et al.

Vehicular edge computing (VEC) is an emerging technology that enables vehicles to perform high-intensity tasks by executing tasks locally or offloading them to nearby edge devices. However, obstacles such as buildings may degrade the communications and incur communication interruptions, and thus the vehicle may not meet the requirement for task offloading. Reconfigurable intelligent surfaces (RIS) is introduced to support vehicle communication and provide an alternative communication path. The system performance can be improved by flexibly adjusting the phase-shift of the RIS. For RIS-assisted VEC system where tasks arrive randomly, we design a control scheme that considers offloading power, local power allocation and phase-shift optimization. To solve this non-convex problem, we propose a new deep reinforcement learning (DRL) framework that employs modified multi-agent deep deterministic policy gradient (MADDPG) approach to optimize the power allocation for vehicle users (VUs) and block coordinate descent (BCD) algorithm to optimize the phase-shift of the RIS. Simulation results show that our proposed scheme outperforms the centralized deep deterministic policy gradient (DDPG) scheme and random scheme.

Kangwei Qi, Qiong Wu, Pingyi Fan et al.

Reconfigurable Intelligent Surface (RIS) is a pivotal technology in communication, offering an alternative path that significantly enhances the link quality in wireless communication environments. In this paper, we propose a RIS-assisted internet of vehicles (IoV) network, considering the vehicle-to-everything (V2X) communication method. In addition, in order to improve the timeliness of vehicle-to-infrastructure (V2I) links and the stability of vehicle-to-vehicle (V2V) links, we introduce the age of information (AoI) model and the payload transmission probability model. Therefore, with the objective of minimizing the AoI of V2I links and prioritizing transmission of V2V links payload, we construct this optimization problem as an Markov decision process (MDP) problem in which the BS serves as an agent to allocate resources and control phase-shift for the vehicles using the soft actor-critic (SAC) algorithm, which gradually converges and maintains a high stability. A AoI-aware joint vehicular resource allocation and RIS phase-shift control scheme based on SAC algorithm is proposed and simulation results show that its convergence speed, cumulative reward, AoI performance, and payload transmission probability outperforms those of proximal policy optimization (PPO), deep deterministic policy gradient (DDPG), twin delayed deep deterministic policy gradient (TD3) and stochastic algorithms.

Zhiyu Shao, Qiong Wu, Pingyi Fan et al.

This work aims to investigate semantic communication in high-speed mobile Internet of vehicles (IoV) environments, with a focus on the spectrum sharing between vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications. We specifically address spectrum scarcity and network traffic and then propose a semantic-aware spectrum sharing algorithm (SSS) based on the deep reinforcement learning (DRL) soft actor-critic (SAC) approach. Firstly, we delve into the extraction of semantic information. Secondly, we redefine metrics for semantic information in V2V and V2I spectrum sharing in IoV environments, introducing high-speed semantic spectrum efficiency (HSSE) and semantic transmission rate (HSR). Finally, we employ the SAC algorithm for decision optimization in V2V and V2I spectrum sharing based on semantic information. This optimization encompasses the optimal link of V2V and V2I sharing strategies, the transmission power for vehicles sending semantic information and the length of transmitted semantic symbols, aiming at maximizing HSSE of V2I and enhancing success rate of effective semantic information transmission (SRS) of V2V. Experimental results demonstrate that the SSS algorithm outperforms other baseline algorithms, including other traditional-communication-based spectrum sharing algorithms and spectrum sharing algorithm using other reinforcement learning approaches. The SSS algorithm exhibits a 15% increase in HSSE and approximately a 7% increase in SRS.

Qiong Wu, Wenhua Wang, Pingyi Fan et al.

Edge caching is a promising solution for next-generation networks by empowering caching units in small-cell base stations (SBSs), which allows user equipments (UEs) to fetch users' requested contents that have been pre-cached in SBSs. It is crucial for SBSs to predict accurate popular contents through learning while protecting users' personal information. Traditional federated learning (FL) can protect users' privacy but the data discrepancies among UEs can lead to a degradation in model quality. Therefore, it is necessary to train personalized local models for each UE to predict popular contents accurately. In addition, the cached contents can be shared among adjacent SBSs in next-generation networks, thus caching predicted popular contents in different SBSs may affect the cost to fetch contents. Hence, it is critical to determine where the popular contents are cached cooperatively. To address these issues, we propose a cooperative edge caching scheme based on elastic federated and multi-agent deep reinforcement learning (CEFMR) to optimize the cost in the network. We first propose an elastic FL algorithm to train the personalized model for each UE, where adversarial autoencoder (AAE) model is adopted for training to improve the prediction accuracy, then {a popular} content prediction algorithm is proposed to predict the popular contents for each SBS based on the trained AAE model. Finally, we propose a multi-agent deep reinforcement learning (MADRL) based algorithm to decide where the predicted popular contents are collaboratively cached among SBSs. Our experimental results demonstrate the superiority of our proposed scheme to existing baseline caching schemes.

Yuchen Shi, Zheqi Zhu, Pingyi Fan et al.

Federated Learning (FL) is a promising distributed learning mechanism which still faces two major challenges, namely privacy breaches and system efficiency. In this work, we reconceptualize the FL system from the perspective of network information theory, and formulate an original FL communication framework, FedNC, which is inspired by Network Coding (NC). The main idea of FedNC is mixing the information of the local models by making random linear combinations of the original parameters, before uploading for further aggregation. Due to the benefits of the coding scheme, both theoretical and experimental analysis indicate that FedNC improves the performance of traditional FL in several important ways, including security, efficiency, and robustness. To the best of our knowledge, this is the first framework where NC is introduced in FL. As FL continues to evolve within practical network frameworks, more variants can be further designed based on FedNC.

Shuo Wan, Jiaxun Lu, Pingyi Fan et al.

Federated learning (FL) has recently emerged as a transformative paradigm that jointly train a model with distributed data sets in IoT while avoiding the need for central data collection. Due to the limited observation range, such data sets can only reflect local information, which limits the quality of trained models. In practice, the global information and local observations would require a joint consideration for learning to make a reasonable policy. However, in horizontal FL, the central agency only acts as a model aggregator without utilizing its global observation to further improve the model. This could significantly degrade the performance in some missions such as traffic flow prediction in network systems, where the global information may enhance the accuracy. Meanwhile, the global feature may not be directly transmitted to agents for data security. How to utilize the global observation residing in the central agency while protecting its safety thus rises up as an important problem in FL. In this paper, we develop a vertical-horizontal federated learning (VHFL) process, where the global feature is shared with the agents in a procedure similar to that of vertical FL without any extra communication rounds. By considering the delay and packet loss, we will analyze VHFL convergence and validate its performance by experiments. It is shown that the proposed VHFL could enhance the accuracy compared with horizontal FL while still protecting the security of global data.

Shuo Wan, Jiaxun Lu, Pingyi Fan et al.

Federated learning (FL) has recently emerged as an important and promising learning scheme in IoT, enabling devices to jointly learn a model without sharing their raw data sets. However, as the training data in FL is not collected and stored centrally, FL training requires frequent model exchange, which is largely affected by the wireless communication network. Therein, limited bandwidth and random package loss restrict interactions in training. Meanwhile, the insufficient message synchronization among distributed clients could also affect FL convergence. In this paper, we analyze the convergence rate of FL training considering the joint impact of communication network and training settings. Further by considering the training costs in terms of time and power, the optimal scheduling problems for communication networks are formulated. The developed theoretical results can be used to assist the system parameter selections and explain the principle of how the wireless communication system could influence the distributed training process and network scheduling.

Pingyi Fan

It is well known that Hoeffding's inequality has a lot of applications in the signal and information processing fields. How to improve Hoeffding's inequality and find the refinements of its applications have always attracted much attentions. An improvement of Hoeffding inequality was recently given by Hertz \cite{r1}. Eventhough such an improvement is not so big, it still can be used to update many known results with original Hoeffding's inequality, especially for Hoeffding-Azuma inequality for martingales. However, the results in original Hoeffding's inequality and its refinement one by Hertz only considered the first order moment of random variables. In this paper, we present a new type of Hoeffding's inequalities, where the high order moments of random variables are taken into account. It can get some considerable improvements in the tail bounds evaluation compared with the known results. It is expected that the developed new type Hoeffding's inequalities could get more interesting applications in some related fields that use Hoeffding's results.

Gangtao Xin, Pingyi Fan

Soft compression is a lossless image compression method, which is committed to eliminating coding redundancy and spatial redundancy at the same time by adopting locations and shapes of codebook to encode an image from the perspective of information theory and statistical distribution. In this paper, we propose a new concept, compressible indicator function with regard to image, which gives a threshold about the average number of bits required to represent a location and can be used for revealing the performance of soft compression. We investigate and analyze soft compression for binary image, gray image and multi-component image by using specific algorithms and compressible indicator value. It is expected that the bandwidth and storage space needed when transmitting and storing the same kind of images can be greatly reduced by applying soft compression.

Rui She, Pingyi Fan

In terms of Generative Adversarial Networks (GANs), the information metric to discriminate the generative data from the real data, lies in the key point of generation efficiency, which plays an important role in GAN-based applications, especially in anomaly detection. As for the original GAN, there exist drawbacks for its hidden information measure based on KL divergence on rare events generation and training performance for adversarial networks. Therefore, it is significant to investigate the metrics used in GANs to improve the generation ability as well as bring gains in the training process. In this paper, we adopt the exponential form, referred from the information measure, i.e. MIM, to replace the logarithm form of the original GAN. This approach is called MIM-based GAN, has better performance on networks training and rare events generation. Specifically, we first discuss the characteristics of training process in this approach. Moreover, we also analyze its advantages on generating rare events in theory. In addition, we do simulations on the datasets of MNIST and ODDS to see that the MIM-based GAN achieves state-of-the-art performance on anomaly detection compared with some classical GANs.

Shuo Wan, Jiaxun Lu, Pingyi Fan et al.

Heavy data load and wide cover range have always been crucial problems for internet of things (IoT). However, in mobile-edge computing (MEC) network, the huge data can be partly processed at the edge. In this paper, a MEC-based big data analysis network is discussed. The raw data generated by distributed network terminals are collected and processed by edge servers. The edge servers split out a large sum of redundant data and transmit extracted information to the center cloud for further analysis. However, for consideration of limited edge computation ability, part of the raw data in huge data sources may be directly transmitted to the cloud. To manage limited resources online, we propose an algorithm based on Lyapunov optimization to jointly optimize the policy of edge processor frequency, transmission power and bandwidth allocation. The algorithm aims at stabilizing data processing delay and saving energy without knowing probability distributions of data sources. The proposed network management algorithm may contribute to big data processing in future IoT.

Zheqi Zhu, Pingyi Fan

With the rapid growth of the data volume and the fast increasing of the computational model complexity in the scenario of cloud computing, it becomes an important topic that how to handle users' requests by scheduling computational jobs and assigning the resources in data center. In order to have a better perception of the computing jobs and their requests of resources, we analyze its characteristics and focus on the prediction and classification of the computing jobs with some machine learning approaches. Specifically, we apply LSTM neural network to predict the arrival of the jobs and the aggregated requests for computing resources. Then we evaluate it on Google Cluster dataset and it shows that the accuracy has been improved compared to the current existing methods. Additionally, to have a better understanding of the computing jobs, we use an unsupervised hierarchical clustering algorithm, BIRCH, to make classification and get some interpretability of our results in the computing centers.

Shanyun Liu, Yunquan Dong, Pingyi Fan et al.

This paper focuses on the problem of finding a particular data recommendation strategy based on the user preferences and a system expected revenue. To this end, we formulate this problem as an optimization by designing the recommendation mechanism as close to the user behavior as possible with a certain revenue constraint. In fact, the optimal recommendation distribution is the one that is the closest to the utility distribution in the sense of relative entropy and satisfies expected revenue. We show that the optimal recommendation distribution follows the same form as the message importance measure (MIM) if the target revenue is reasonable, i.e., neither too small nor too large. Therefore, the optimal recommendation distribution can be regarded as the normalized MIM, where the parameter, called importance coefficient, presents the concern of the system and switches the attention of the system over data sets with different occurring probability. By adjusting the importance coefficient, our MIM based framework of data recommendation can then be applied to system with various system requirements and data distributions.Therefore,the obtained results illustrate the physical meaning of MIM from the data recommendation perspective and validate the rationality of MIM in one aspect.

Shuo Wan, Jiaxun Lu, Pingyi Fan et al.

Multi-robot formation control enables robots to cooperate as a working group in completing complex tasks, which has been widely used in both civilian and military scenarios. Before moving to reach a given formation, each robot should choose a position from the formation so that the whole system cost is minimized. To solve the problem, we formulate an optimization problem in terms of the total moving distance and give a solution by the Hungarian method. To analyze the deviation of the achieved formation from the ideal one, we obtain the lower bound of formation bias with respect to system's parameters based on notions in information theory. As an extension, we discuss methods of transformation between different formations. Some theoretical results are obtained to give a guidance of the system design.