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An effective attention and residual network for malware detection 用于恶意软件检测的有效注意力和残留物网络
IF 1.6 4区 计算机科学 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2024-04-27 DOI: 10.1049/cmu2.12754
Wei Gu, Hongyan Xing, Tianhao Hou

Due to its open source and large user base, Android has emerged as the most popular operating system. Android's popularity and openness have made it a prime target for malicious attackers. Permissions have received great attention from researchers because of their effectiveness in restricting applications’ access to sensitive resources. However, existing malware detection methods based on permissions are easily bypassed by inter-application resource access. To address these issues, we combine inter-application resource access-related intent features with permission features. Besides, we designed a customized convolutional neural network using two squeeze-and-excitation blocks to learn the inherent relationships between multi-type features. The two basic SE blocks perform squeezing operations based on average pooling and max pooling, respectively, to compute channel-wise attention from multiple perspectives. We designed a series of experiments based on real-world samples to evaluate the efficacy of the proposed framework. Empirical results demonstrate that our framework outperforms state-of-the-art methods, achieving an accuracy of 96.29%, precision of 97.52%, recall of 94.63%, F1-score of 96.06% and MCC of 92.60%. These promising experimental results consistently demonstrate that AMERDroid is an effective approach for Android malware detection.

由于其开放源代码和庞大的用户群,安卓已成为最流行的操作系统。安卓的普及性和开放性使其成为恶意攻击者的主要目标。由于权限能有效限制应用程序对敏感资源的访问,因此受到了研究人员的极大关注。然而,现有的基于权限的恶意软件检测方法很容易被应用程序间的资源访问绕过。为了解决这些问题,我们将应用程序间资源访问相关的意图特征与权限特征相结合。此外,我们还设计了一个定制的卷积神经网络,使用两个挤压-激发块来学习多类型特征之间的内在关系。这两个基本 SE 模块分别执行基于平均池化和最大池化的挤压操作,从多个角度计算渠道关注度。我们设计了一系列基于真实世界样本的实验来评估所提出框架的功效。实证结果表明,我们的框架优于最先进的方法,准确率达 96.29%,精确率达 97.52%,召回率达 94.63%,F1 分数达 96.06%,MCC 达 92.60%。这些令人鼓舞的实验结果一致证明,AMERDroid 是一种有效的安卓恶意软件检测方法。
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引用次数: 0
Survey of research on confidential computing 保密计算研究调查
IF 1.6 4区 计算机科学 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2024-04-23 DOI: 10.1049/cmu2.12759
Dengguo Feng, Yu Qin, Wei Feng, Wei Li, Ketong Shang, Hongzhan Ma

As the global data strategy deepens and data elements accelerate integrating and flowing more rapidly, the demand for data security and privacy protection has become increasingly prominent. Confidential computing emerges as a crucial security technology to solve security and privacy problem, and it is also a hot subject of in contemporary security technologies. Leveraging collaborative security in both hardware and software, it builds a trusted execution environment to ensure confidentiality and integrity protection for data in use. This paper provides a comprehensive overview of the development process of confidential computing, summarizing its current research status and issues, which focuses on the security requirements for data security and privacy protection. Furthermore, it deeply analyses the common technical features of confidential computing, and proposes a trusted confidential computing architecture based on collaborative hardware and software trust. Then, it elaborates on the research status and issues of confidential computing from four aspects: hardware security, architecture and key technologies, applications, and standards and evaluation. Finally, this paper provides a synthesis and outlook for the future development of confidential computing. In summary, confidential computing is currently in a rapidly developing stage and will play an important role in cyber security in the future.

随着全球数据战略的不断深化,数据要素加速融合和流动,数据安全和隐私保护的需求日益凸显。保密计算作为解决安全和隐私问题的重要安全技术应运而生,也是当代安全技术的热门话题。保密计算利用硬件和软件的协同安全,构建可信的执行环境,确保使用中数据的机密性和完整性。本文全面概述了保密计算的发展过程,总结了其研究现状和问题,重点介绍了数据安全和隐私保护的安全要求。此外,本文还深入分析了保密计算的共性技术特征,提出了基于软硬件协同信任的可信保密计算体系结构。然后,从硬件安全、体系结构与关键技术、应用、标准与评估四个方面阐述了保密计算的研究现状与问题。最后,本文对保密计算的未来发展进行了总结和展望。综上所述,保密计算目前正处于快速发展阶段,未来将在网络安全领域发挥重要作用。
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引用次数: 0
Resource allocation and passive beamforming for IRS-assisted short packet systems IRS 辅助短数据包系统的资源分配和无源波束成形
IF 1.6 4区 计算机科学 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2024-04-23 DOI: 10.1049/cmu2.12763
Yangyi Zhang, Xinrong Guan, Qingqing Wu, Zhi Ji, Yueming Cai

This paper investigates an intelligent reflecting surface (IRS) assisted downlink short packet transmission system, where an access point sends short packets to multiple devices with the help of an IRS. Specifically, a performance comparison between the frequency division multiple access and time division multiple access is conducted for the considered system, from the perspective of average age of information (AoI). To minimize the maximum average AoI among all devices, the resource allocation and passive beamforming are jointly optimized. However, the formulated problem is difficult to solve due to the non-convex objective function and coupled variables. Thus, an alternating optimization based algorithm is proposed by exploiting the semidefinite relaxation and bisection search techniques. Simulation results show that time division multiple access can achieve lower AoI by exploiting the time-selective passive beamforming of IRS for maximizing the signal to noise ratio of each device consecutively. Moreover, it also shows that as the length of information bits becomes sufficiently large as compared to the available bandwidth, the proposed frequency division multiple access transmission scheme becomes more favourable due to more flexible power allocation.

本文研究了一种智能反射面(IRS)辅助下行链路短数据包传输系统,在该系统中,一个接入点借助 IRS 向多个设备发送短数据包。具体而言,从平均信息年龄(AoI)的角度,对所考虑的系统进行了频分多址和时分多址的性能比较。为了最小化所有设备的最大平均 AoI,对资源分配和无源波束成形进行了联合优化。然而,由于目标函数的非凸性和耦合变量,所提出的问题很难解决。因此,利用半无限松弛和分段搜索技术,提出了一种基于交替优化的算法。仿真结果表明,利用 IRS 的时间选择性无源波束成形技术,可以连续实现每个设备的信噪比最大化,从而降低时分多址的 AoI。此外,仿真结果还表明,当信息比特的长度与可用带宽相比变得足够大时,由于功率分配更加灵活,拟议的频分多址传输方案变得更加有利。
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引用次数: 0
On a class of column-weight 3 decomposable LDPC codes with the analysis of elementary trapping sets 关于一类列重 3 可分解 LDPC 码与基本陷波组的分析
IF 1.6 4区 计算机科学 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2024-04-22 DOI: 10.1049/cmu2.12762
G. Raeisi, M. Gholami

A column-weight k$k$ LDPC code with the parity-check matrix H$H$ is called decomposable if there exists a permutation π$pi$ on the rows of H$H$, such that π(H)${pi }(H)$ can be decomposed into k$k$ column-weight one matrix. In this paper, some variations of edge coloring of graphs are used to construct some column-weight three decomposable LDPC codes with girths at least six and eight. Applying the presented method on several known classes of bipartite graphs, some classes of column-weight three decomposable LDPC codes are derived having flexibility in length and rate. Interestingly, the constructed parity-check matrices based on the proper edge coloring of graphs can be considered as the base matrix of some high rate column-weight three quasi-cyclic (QC) LDPC codes with maximum-achievable girth 20. The paper also leads to a simple characterization of elementary trapping sets of the decomposable codes based on the chromatic index of the corresponding normal graphs. This characterization corresponds to a simple search algorithm finds all possible existing elementary trapping sets in a girth-6 or girth-8 column-weight 3 LDPC code which are layered super set of a short cycle in the Tanner graph of the code. Simulation results indicate that the QC-LDPC codes with large girths lifted from the constructed base matrices have good performances over AWGN channel.

如果奇偶校验矩阵 , 的行上存在一种排列组合,从而可以分解成列重为一的矩阵,那么这种具有奇偶校验矩阵的列重 LDPC 码称为可分解码。本文利用图边着色的一些变化来构造一些列重为三的可分解 LDPC 码,其周长至少为六和八。将本文提出的方法应用于几类已知的双方形图,得出了几类在长度和速率上具有灵活性的列重三可分解 LDPC 码。有趣的是,基于图的适当边着色所构建的奇偶校验矩阵可被视为某些最大周长为 20 的高速率列重三准循环 (QC) LDPC 码的基矩阵。本文还根据相应法线图的色度指数,对可分解代码的基本陷阱集进行了简单的表征。这种表征相当于一种简单的搜索算法,可以找到周长为 6 或周长为 8 的列重 3 LDPC 码中所有可能存在的基本陷波集,这些陷波集是该码坦纳图中一个短周期的分层超集。仿真结果表明,在 AWGN 信道上,从构建的基矩阵中提取的大周长 QC-LDPC 码具有良好的性能。
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引用次数: 0
Energy efficient RF chains selection based on integrated Hungarian and genetic approaches for uplink cell-free millimetre-wave massive MIMO systems 基于匈牙利和遗传综合方法的高效射频链选择,适用于上行链路无蜂窝毫米波大规模多输入多输出系统
IF 1.6 4区 计算机科学 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2024-04-19 DOI: 10.1049/cmu2.12761
Abdulrahman Al Ayidh, Mohammed M. Alammar

The purpose of this work is to explore the decrease of total used power in cell-free millimetre-wave (mm-Wave) massive multiple-input multiple-output (MIMO) systems, which can be regarded an essential technology for future wireless generations to improve system performance. One of the most important strategies for reducing total power consumption is to activate and deactivate radio frequency (RF) chains at each access point (AP) in the coverage region. Nonetheless, the optimization issue for this methodology is NP-hard, and an exhaustive search method may be used to determine the ideal number of RF chains at each AP in the cell-free network. Unfortunately, the exhaustive searching approach is prohibitively complicated, indicating that it is unworkable when there are a significant number of APs in the service region. Furthermore, present RF chain selection approaches prioritize decreasing consumed power and complexity at the price of system performance in terms of total possible rate. This research solves this issue by introducing a unique RF chain selection approach that combines Hungarian and genetic algorithms. The fact that the genetic algorithm (GA) can readily determine the ideal number of active RF chains, yet this technique generally entails significant complexity in large-scale cell-free networks, prompted this notion. As a result, the Hungarian method is used early in the GA to overcome the complexity problem while still retaining system performance. In addition, the suggested system employs a semi-centralized hybrid beamforming architecture in which all analogue combiners for all APs are operated at a central processing unit using channel state information. In addition, each AP has a fully linked phase shifters network and restricted RF chains connecting to its antennas. Finally, simulation findings reveal that, when compared to state-of-the-art techniques, the suggested approach achieves the maximum attainable rate and overall energy efficiency with a tolerable computational complexity.

这项工作的目的是探索如何降低无蜂窝毫米波(mm-Wave)大规模多输入多输出(MIMO)系统的总功耗。降低总功耗的最重要策略之一是激活和关闭覆盖区域内每个接入点(AP)的射频(RF)链。然而,这种方法的优化问题是 NP-hard,可采用穷举搜索法来确定无小区网络中每个接入点的理想射频链数量。遗憾的是,穷举搜索法过于复杂,表明当服务区域内有大量接入点时,这种方法是行不通的。此外,目前的射频链选择方法以降低功耗和复杂性为优先考虑,而以总可能速率的系统性能为代价。本研究通过引入一种结合匈牙利算法和遗传算法的独特射频链选择方法来解决这一问题。事实上,遗传算法(GA)可以轻松确定活动射频链的理想数量,但在大规模无细胞网络中,这种技术通常会带来极大的复杂性,因此提出了这一概念。因此,匈牙利法在遗传算法的早期使用,以克服复杂性问题,同时保持系统性能。此外,建议的系统还采用了半集中式混合波束成形架构,所有接入点的模拟合路器都在中央处理器上使用信道状态信息进行操作。此外,每个接入点都有一个完全链接的移相器网络和连接其天线的受限射频链。最后,仿真结果表明,与最先进的技术相比,所建议的方法以可承受的计算复杂度实现了最大速率和总体能效。
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引用次数: 0
Optimizing secure power allocation in massive MIMO systems with an eavesdropper under imperfect CSI conditions 在不完美 CSI 条件下优化有窃听者的大规模 MIMO 系统中的安全功率分配
IF 1.6 4区 计算机科学 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2024-04-18 DOI: 10.1049/cmu2.12769
Abdolrasoul Sakhaei Gharagezlou, Mahdi Nangir, Nima Imani

This paper discusses the operation of a massive multiple-input multiple-output (MIMO) system from a different perspective. The system is performed in the presence of an eavesdropper who is trying to disrupt the message being transmitted between the base station (BS) and the users. An attempt has been made to maximize the secure energy efficiency (EE) of the system by allocating appropriate power to each user. The channel state information (CSI) between users and the BS is considered imperfect and the employed precoding scheme is the zero forcing (ZF). The CSI related to the eavesdropper is considered to be perfect and its precoding is assumed to be the maximum ratio transmission (MRT). The problem of optimization that is for maximizing the EE has two constraints including the maximum transmission power and the minimum user data rate. To improve the performance of system, the cell division technique is applied, which results in approaching the performance of system to the without eavesdropper scenario. Five various scenarios have been investigated in this research, and it is proved that the proposed method improves the system performance in all cases. The numerical and simulation results obtained from implementation of the proposed algorithm confirm the claim.

本文从另一个角度讨论了大规模多输入多输出(MIMO)系统的运行。该系统在存在窃听者的情况下运行,窃听者试图破坏基站(BS)和用户之间传输的信息。通过为每个用户分配适当的功率,试图最大限度地提高系统的安全能效(EE)。用户和基站之间的信道状态信息(CSI)被认为是不完美的,采用的预编码方案是零强迫(ZF)。与窃听者相关的 CSI 被认为是完美的,其预编码假定为最大比率传输(MRT)。最大化 EE 的优化问题有两个约束条件,包括最大传输功率和最小用户数据速率。为提高系统性能,采用了小区划分技术,从而使系统性能接近无窃听器情况。本研究调查了五种不同的情况,结果证明所提出的方法在所有情况下都能提高系统性能。实施所提算法得到的数值和模拟结果证实了这一说法。
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引用次数: 0
Burst traffic: Congestion management and performance optimization strategies in heterogeneous cognitive radio networks 突发流量:异构认知无线电网络中的拥塞管理和性能优化策略
IF 1.6 4区 计算机科学 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2024-04-17 DOI: 10.1049/cmu2.12753
Jie Yan, Bo Zhang, Shi Wang, Hao Lan, Xin Wang

In order to solve the network congestion problem caused by burst service flows in heterogeneous cognitive radio networks (Het-CRN), a two-stage dual-threshold random early detection (TD-RED) control mechanism is proposed here. Meanwhile, a three-state Markov modulated Poisson process (MMPP-3) is used to model the burst service to analyze its arrival in depth. Moreover, a performance evaluation system (PES) is proposed to quantify the interference of burst services to different classes of services and their quality of service, which can comprehensively evaluate the performance enhancement of the TD-RED control mechanism for each service. The system examines performance metrics such as packet loss rate, average delay, average captain etc. PES simulation results show that TD-RED significantly reduces the packet rejection rate and transmission delay compared to the no congestion control (NCC) and random early detection (RED) methods, thus providing superior quality of service to all services. thereby providing a superior quality of service to cognitive users. Its lower average captain fully proves that TD-RED can effectively alleviate congestion.

为了解决异构认知无线电网络(Het-CRN)中突发业务流引起的网络拥塞问题,本文提出了一种两阶段双阈值随机早期检测(TD-RED)控制机制。同时,采用三态马尔可夫调制泊松过程(MMPP-3)对突发业务进行建模,以深入分析其到达情况。此外,还提出了一个性能评估系统(PES)来量化突发业务对不同类业务的干扰及其服务质量,从而全面评估 TD-RED 控制机制对每种业务的性能提升。该系统考察了丢包率、平均延迟、平均队长等性能指标。PES 仿真结果表明,与无拥塞控制(NCC)和随机早期检测(RED)方法相比,TD-RED 能显著降低丢包率和传输延迟,从而为所有业务提供更优的服务质量。其较低的平均队长充分证明了 TD-RED 可以有效缓解拥塞。
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引用次数: 0
Distributed MA-IDDPG-OLSR based stable routing protocol for unmanned aerial vehicle ad-hoc network 基于分布式 MA-IDDPG-OLSR 的无人机 ad-hoc 网络稳定路由协议
IF 1.6 4区 计算机科学 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2024-04-14 DOI: 10.1049/cmu2.12757
Youjun Zeng, Jie Zhou, Youjiang Liu, Tao Cao, Dalong Yang, Yu Liu, Xianhua Shi

In unmanned aerial vehicle ad-hoc network (UANET), the node speed of unmanned aerial vehicles (UAVs) may reach up to 400 km/h. The fast or slow movement of UAV nodes leads to different speeds of topology change of the nodes. Traditional optimized link state routing (OLSR) protocol cannot adaptively adjust the routing update period when the network topology changes, which may lead to the nodes calculating incorrect routing tables. This increases the average end-to-end delay and packet loss rate for packet transmission. To enhance the adaptability of OLSR routing protocol to network topology changes, this paper proposes a multi-agent independent deep deterministic policy gradient-OLSR (MA-IDDPG-OLSR) routing protocol based on distributed multi-agent reinforcement learning. The protocol deploys DDPG algorithm on each UAV node, and each UAV node adaptively adjusts the Hello and TC message sending intervals, according to the one-hop neighbouring nodes as well as its own state. Simulation results show that the proposed protocol is able to improve the throughput and reduce the packet loss rate as compared to traditional AODV, GRP, OLSR, and distributed multiple-agent independent proximal policy optimization-OLSR (MA-IPPO-OLSR), distributed multiple-agent independent twin delayed deep deterministic policy gradient-OLSR (MA-ITD3-OLSR) routing protocols. Since MA-IDDPG-OLSR relies only on local information, there is a minor performance degradation in MA-IDDPG-OLSR compared to centralized single-agent DQN-OLSR routing protocol. But it is more suitable to a completely distributed UAV network without a centralized node.

在无人飞行器 ad-hoc 网络(UANET)中,无人飞行器(UAV)的节点速度最高可达 400 km/h。无人飞行器节点移动的快慢导致节点拓扑变化的速度不同。传统的优化链路状态路由(OLSR)协议无法在网络拓扑发生变化时自适应地调整路由更新周期,这可能会导致节点计算出错误的路由表。这会增加数据包传输的平均端到端延迟和数据包丢失率。为了增强 OLSR 路由协议对网络拓扑变化的适应性,本文提出了一种基于分布式多代理强化学习的多代理独立深度确定性策略梯度-OLSR(MA-IDDPG-OLSR)路由协议。该协议在每个无人机节点上部署了 DDPG 算法,每个无人机节点根据单跳邻居节点和自身状态自适应地调整 Hello 和 TC 消息的发送间隔。仿真结果表明,与传统的 AODV、GRP、OLSR 和分布式多代理独立近端策略优化-OLSR(MA-IPPO-OLSR)、分布式多代理独立双延迟深度确定性策略梯度-OLSR(MA-ITD3-OLSR)路由协议相比,所提出的协议能够提高吞吐量并降低丢包率。由于 MA-IDDPG-OLSR 只依赖本地信息,因此与集中式单代理 DQN-OLSR 路由协议相比,MA-IDDPG-OLSR 的性能略有下降。但它更适用于没有集中节点的完全分布式无人机网络。
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引用次数: 0
Construction of secure adaptive frequency hopping sequence sets based on AES algorithm 基于 AES 算法构建安全自适应跳频序列集
IF 1.6 4区 计算机科学 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2024-04-10 DOI: 10.1049/cmu2.12756
Dongpo Song, Peng Wei, Yongming Fu, Shilian Wang

Communication security has become particularly crucial with the rapid development of the Internet of Things (IoT). Frequency hopping spread spectrum (FHSS) technology, a prevalent method in wireless communication, has a wide range of applications in the Internet of Things. Enhancing the security of frequency hopping sequences is an essential means to improve the security of frequency hopping communication in the Internet of Things, as the performance of frequency hopping sequences plays a crucial role in frequency hopping systems. This paper proposes constructing secure adaptive frequency hopping sequence sets based on the advanced encryption standard (AES) algorithm. As a block cipher algorithm with superior security, the AES algorithm can provide a fundamental guarantee for the security of the proposed frequency hopping sequences. The mapping methods from ciphertext sequences to frequency hopping sequences proposed in this paper can achieve the construction of frequency hopping sequences of any frequency set size to meet the requirements of adaptive frequency hopping. In addition, we also model and analyse the problem of overlapping spectrum band of the IoT groups in the industrial, scientific, and medical (ISM) band, aiming to achieve better packet transmission performance by adjusting the frequency set size.

随着物联网(IoT)的快速发展,通信安全变得尤为重要。跳频扩频(FHSS)技术是无线通信中的一种普遍方法,在物联网中有着广泛的应用。由于跳频序列的性能在跳频系统中起着至关重要的作用,因此增强跳频序列的安全性是提高物联网跳频通信安全性的重要手段。本文提出基于高级加密标准(AES)算法构建安全的自适应跳频序列集。作为一种安全性极高的块密码算法,AES 算法可以为所提出的跳频序列的安全性提供根本保证。本文提出的从密文序列到跳频序列的映射方法可以实现任意频率集大小的跳频序列的构建,以满足自适应跳频的要求。此外,我们还对工业、科学和医疗(ISM)频段中的物联网群组频带重叠问题进行了建模和分析,旨在通过调整频率集大小实现更好的数据包传输性能。
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引用次数: 0
Asymptotic performance of reconfigurable intelligent surface assisted MIMO communication for large systems using random matrix theory 利用随机矩阵理论实现大型系统中可重构智能面辅助多输入多输出通信的渐近性能
IF 1.6 4区 计算机科学 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2024-04-10 DOI: 10.1049/cmu2.12755
Feng Hu, Hongliu Zhang, ShuTing Chen, Libiao Jin, Jinhao Zhang, Yunfei Feng

Reconfigurable intelligent surface (RIS) can provide unprecedented spectral efficiency gains and excellent ability to manipulate electromagnetic waves. This article considered a RIS-assisted multiuser multiple-input multiple-output (MIMO) downlink system, where the beamforming at the base station and RIS are jointly designed to maximize the sum-rate. For the large dimension scenario and high-rank beamforming matrix, the accurate deterministic approximations from random matrix theory are then utilized to simplify the RIS-assisted MIMO systems. The asymptotical signal-to-interference-plus-noise ratio values obtained through random matrix theory is infinitely close to the theoretical limits calculated by accurately iteration. And the performance of the proposed algorithm computed via the sharing second-order channel statistics matches that of the RIS algorithm with sharing full channel state information asymptotically. The deterministic approximations are instrumental to get improvement into the structure of the optimal beamforming and to reduce the implementation complexity in large-scale MIMO system. Numerical simulations results are provided to evaluate and verify the accuracy of the asymptotic results obtained from the proposed algorithm in the finite system regime. With the complex operation process of large dimension matrix reducing to the deterministic approximations, a lower computational complexity can be obtained compared with other methods.

可重构智能表面(RIS)可提供前所未有的频谱效率提升和出色的电磁波操控能力。本文研究了一个由 RIS 辅助的多用户多输入多输出(MIMO)下行链路系统,其中基站和 RIS 的波束成形是为最大化总速率而联合设计的。针对大维度场景和高阶波束成形矩阵,利用随机矩阵理论的精确确定性近似来简化 RIS 辅助 MIMO 系统。通过随机矩阵理论得到的渐近信号干扰加噪声比值与精确迭代计算出的理论极限值无限接近。通过共享二阶信道统计计算得出的拟议算法的性能与共享完整信道状态信息的 RIS 算法的性能渐近匹配。确定性近似有助于改进最优波束成形的结构,降低大规模多输入多输出系统的实现复杂度。本文提供了数值模拟结果,以评估和验证所提算法在有限系统机制下得到的渐近结果的准确性。通过将大维度矩阵的复杂运算过程还原为确定性近似,可以获得比其他方法更低的计算复杂度。
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