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Prediction of proton-induced SEE error rates for the VATA160 ASIC 被引量:1
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作者 Kai Xi Di Jiang +7 位作者 Shan-Shan Gao Jie Kong Hong-Yun Zhao Hai-Bo Yang Tian-Qi Liu Bin Wang Bing Ye Jie Liu 《Nuclear Science and Techniques》 SCIE CAS CSCD 2017年第1期88-93,共6页
We predict proton single event effect(SEE)error rates for the VATA160 ASIC chip on the Dark Matter Particle Explorer(DAMPE) to evaluate its radiation tolerance.Lacking proton test facilities,we built a Monte Carlo sim... We predict proton single event effect(SEE)error rates for the VATA160 ASIC chip on the Dark Matter Particle Explorer(DAMPE) to evaluate its radiation tolerance.Lacking proton test facilities,we built a Monte Carlo simulation tool named PRESTAGE to calculate the proton SEE cross-sections.PRESTAGE is based on the particle transport toolkit Geant4.It adopts a location-dependent strategy to derive the SEE sensitivity of the device from heavy-ion test data,which have been measured at the HI-13 tandem accelerator of the China Institute of Atomic Energy and the heavy-ion research facility in Lanzhou.The AP-8,SOLPRO,and August 1972 worst-case models are used to predict the average and peak proton fluxes on the DAMPE orbit.Calculation results show that the averaged proton SEE error rate for the VATA160 chip is approximately 2.17×10^(-5)/device/day.Worst-case error rates for the Van Allen belts and solar energetic particle events are 1-3 orders of magnitude higher than the averaged error rate. 展开更多
关键词 PROTON ASIC SINGLE EVENT effects error rates
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Symbol Error Rate Performance Analysis of Non-Orthogonal Multiple Access for Visible Light Communications 被引量:3
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作者 Hongji Huang Jinyuan Wang +3 位作者 Jie Wang Jie Yang Jian Xiong Guan Gui 《China Communications》 SCIE CSCD 2017年第12期153-161,共9页
Non-orthogonal multiple access(NOMA) is considered as one of promising radio access techniques for visible light communications(VLC) in next-generation wireless communications systems.In order to provide theoretical s... Non-orthogonal multiple access(NOMA) is considered as one of promising radio access techniques for visible light communications(VLC) in next-generation wireless communications systems.In order to provide theoretical support for designing VLC-NOMA,we derive its analytic expressions for the symbol error rate(SER).Specifically,NOMA is first incorporated with appropriate VLC to establish a VLC-NOMA framework.Afterwards,mathematical expressions of the SER for the VLC-NOMA are developed.Moreover,numerical results are provided carefully to demonstrate that the proposed VLC-NOMA scheme outperforms than state-of-the-art orthogonal frequency division multiple access(OFDMA) one in terms of SER performance.Finally,relationships between the SER performance and the number of users,power allocation coefficient and semi-angle are well investigated,which can give us a scientific guide to devise the VLC-NOMA system for achieving better SER performance. 展开更多
关键词 VISIBLE light communication(VLC) non-orthogonal multiple access(NOMA) SYMBOL error rate (SER)
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Reducing the Internal Difference Error Rate in Hospital Pharmacies:From the Angle of Quality Control Circle 被引量:1
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作者 Wang Shuling Lei Yingzi +2 位作者 Liu Linchuan Wang Ruili He Yalan 《Asian Journal of Social Pharmacy》 2020年第2期73-82,共10页
Objective To improve the management level of pharmacy dispensing center,reduce dispensing errors and promote the safety of drug use.Methods Hospital pharmacies could be managed according to the theory of quality contr... Objective To improve the management level of pharmacy dispensing center,reduce dispensing errors and promote the safety of drug use.Methods Hospital pharmacies could be managed according to the theory of quality control circle(QCC).Based on the ten steps of QCC,the internal difference error rate in pharmacies could be reduced.Results and Conclusion The error rate of pharmacies was reduced from 2.74‰to 0.57‰,and the goal achievement rate was 108.466.Besides,the progress rate reached 84.82%.The abilities of circle members were improved,and the operation of pharmacy was more standardized.The activity of QCC is helpful to reduce the internal difference error rate,improve the operation level of pharmacy and ensure the safety of drug use. 展开更多
关键词 quality control circle(QCC) medical institution internal difference error rate
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CLOSED-FORM ERROR RATES OF STBC SYSTEMS AND ITS PERFORMANCE ANALYSIS
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作者 Hu Xianbin Gao Yuanyuan Yi Xiaoxin 《Journal of Electronics(China)》 2006年第1期39-43,共5页
The closed-form solutions for error rates of Space-Time Block Code (STBC) Multiple Phase Shift Keying (MPSK) systems are derived in this paper. With characteristic function based method and the partial integration bas... The closed-form solutions for error rates of Space-Time Block Code (STBC) Multiple Phase Shift Keying (MPSK) systems are derived in this paper. With characteristic function based method and the partial integration based respectively, the exact expressions of error rates are obtained for (2,1) STBC with and without channel estimation error. Simulations show that the practical error rates accord with the theoretical ones, so closed-form error rates are accurate references for STBC performance evaluation. For the error of pilot assisted channel estimation, the performance of a (2,1) STBC system is deteriorated about 3dB. 展开更多
关键词 Wireless communication Space-Time Block Code(STBC) Channel estimation error error rates calculation Transmitter diversity
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Performance Analysis of Outage Probability and Error Rate of Square M-QAM in Mobile Wireless Communication Systems over Generalized α-μ Fading Channels with Non-Gaussian Noise
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作者 Fares S. Aimehmadi Osamah S. Badarneh 《China Communications》 SCIE CSCD 2018年第1期62-71,共10页
This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels sub... This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels subject to an additive non-Gaussian noise. The obtained expressions take into account static and mobile wireless receivers. In addition, a closed-form expression for the outage probability in mobile networks is obtained. Please note that all derived expressions in this paper a valid for integer and non-integer values of the fading parameters. Analytical results are presented to study the impact of noise shaping parameter, severity of fading, and mobility on the average SER. Monte-Carlo simulations results are also provided to validate the accuracy of the analytical results. 展开更多
关键词 α-μ FADING SYMBOL error rate NON-GAUSSIAN noise random WAYPOINT mobili-ty model
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A Simulation Based Comparison of Correlation Coefficients with Regard to Type I Error Rate and Power
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作者 Elif Tugran Mehmet Kocak +2 位作者 Hamit Mirtagioglu Soner Yigit Mehmet Mendes 《Journal of Data Analysis and Information Processing》 2015年第3期87-101,共15页
In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where t... In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where the underlying distributions of the variables of interest, sample sizes and correlation patterns were varied. Simulation results showed that the Type I error rate and power of Pearson correlation coefficient were negatively affected by the distribution shapes especially for small sample sizes, which was much more pronounced for Spearman Rank and Kendal Tau correlation coefficients especially when sample sizes were small. In general, Permutation-based and Winsorized correlation coefficients are more robust to distribution shapes and correlation patterns, regardless of sample size. In conclusion, when assumptions of Pearson correlation coefficient are not satisfied, Permutation-based and Winsorized correlation coefficients seem to be better alternatives. 展开更多
关键词 Correlation Coefficient ROBUSTNESS Type I error rate Test Power NON-NORMALITY SIMULATION
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Arbitrary Decode-Forward Relaying with Re-Encoded Bits Selection Strategy for Polar Codes
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作者 Di Guan Kai Niu Chao Dong 《China Communications》 SCIE CSCD 2023年第8期153-162,共10页
In this paper,we propose an arbitrary decode-forward single-relay scheme for finite blocklength polar codes,which can be applied to the general symmetric discrete memoryless relay channel with orthogonal receiver comp... In this paper,we propose an arbitrary decode-forward single-relay scheme for finite blocklength polar codes,which can be applied to the general symmetric discrete memoryless relay channel with orthogonal receiver components.The relay node decodes the received message.The relay node selectively re-encodes the message and transmits it to the destination node.Furthermore,in order to minimize the upper-bound of the block error probability,we propose a selection strategy to decide the proper re-encoded bit set by the relay.Simulation results are presented to illustrate the improvement in decoding performance of the proposed scheme compared to conventional relay schemes in both additive white Gaussian noise(AWGN)channel and Rayleigh fading channel(RFC). 展开更多
关键词 polar codes decode-and-forward relaying arbitrary relay channel block error rate estimation
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ADS-B Reception Error Correction Based on the LSTM Neural-Network Model
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作者 Jamal Habibi Markani Syed Ibtehaj Raza Rizvi +2 位作者 Abdessamad Amrhar Jean-Marc Gagné René Jr. Landry 《Communications and Network》 2023年第2期25-42,共18页
Standard automatic dependent surveillance broadcast (ADS-B) reception algorithms offer considerable performance at high signal-to-noise ratios (SNRs). However, the performance of ADS-B algorithms in applications can b... Standard automatic dependent surveillance broadcast (ADS-B) reception algorithms offer considerable performance at high signal-to-noise ratios (SNRs). However, the performance of ADS-B algorithms in applications can be problematic at low SNRs and in high interference situations, as detecting and decoding techniques may not perform correctly in such circumstances. In addition, conventional error correction algorithms have limitations in their ability to correct errors in ADS-B messages, as the bit and confidence values may be declared inaccurately in the event of low SNRs and high interference. The principal goal of this paper is to deploy a Long Short-Term Memory (LSTM) recurrent neural network model for error correction in conjunction with a conventional algorithm. The data of various flights are collected and cleaned in an initial stage. The clean data is divided randomly into training and test sets. Next, the LSTM model is trained based on the training dataset, and then the model is evaluated based on the test dataset. The proposed model not only improves the ADS-B In packet error correction rate (PECR), but it also enhances the ADS-B In terms of sensitivity. The performance evaluation results reveal that the proposed scheme is achievable and efficient for the avionics industry. It is worth noting that the proposed algorithm is not dependent on conventional algorithms’ prerequisites. 展开更多
关键词 ADS-B Long Short-Term Memory Packet error Correction rate error Correction Bit error rate
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Bit Error Rate (BER) Performance Evaluation of Various Space-time Block Codes in MIMO Wireless Communications
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作者 Sanjay Kumar Sharma Syed Naseem Ahmad 《通讯和计算机(中英文版)》 2010年第3期32-38,共7页
关键词 空时分组码 无线通信 MIMO BER 误码率 评价 性能
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CNN-AE在超奈奎斯特无线光通信端到端系统中的性能 被引量:1
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作者 曹明华 王瑞 +2 位作者 张悦 张星宇 王惠琴 《重庆邮电大学学报(自然科学版)》 CSCD 北大核心 2024年第1期181-190,共10页
符号间干扰的存在使超奈奎斯特(faster-than-Nyquist, FTN)速率无线光通信系统的性能受到严重影响,针对此问题,提出了一种基于卷积神经网络自编码器的端到端通信系统来消除符号间干扰的影响并完成信号的恢复。针对超奈奎斯特信号非正交... 符号间干扰的存在使超奈奎斯特(faster-than-Nyquist, FTN)速率无线光通信系统的性能受到严重影响,针对此问题,提出了一种基于卷积神经网络自编码器的端到端通信系统来消除符号间干扰的影响并完成信号的恢复。针对超奈奎斯特信号非正交的特性,采用交替训练算法分别训练发射机和接收机权重,解决监督训练中模型输入输出数据尺寸不匹配的问题。在此基础上,分析了该系统在Gamma-Gamma大气信道中的误码率(bit error rate, BER)性能。仿真结果证明,与采用最大似然估计的传统系统相比,该系统的误码率性能在各种条件因素影响下都有不同程度的提高。当加速因子在Mazo限内时,该系统可以消除FTN成型和湍流信道带来的复杂混合码间干扰,其误码性能几乎与正交传输系统相等。 展开更多
关键词 无线光通信 超奈奎斯特(FTN) 端到端通信 大气湍流信道 误码率性能
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基于DVB-S2X协议的低轨卫星通信性能仿真分析 被引量:1
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作者 王磊 王勇 +1 位作者 赵青松 虞海秀 《航天电子对抗》 2024年第2期43-47,共5页
介绍了DVB-S2X标准,重点分析了其中高阶调制技术的基本原理和星座映射,在进行星地链路分析的基础上,构建了DVB-S2X标准低轨卫星通信仿真模型,针对DVB-S2X标准中16APSK、32APSK、64APSK调制信号开展仿真试验,以误码率和丢帧率为指标进行... 介绍了DVB-S2X标准,重点分析了其中高阶调制技术的基本原理和星座映射,在进行星地链路分析的基础上,构建了DVB-S2X标准低轨卫星通信仿真模型,针对DVB-S2X标准中16APSK、32APSK、64APSK调制信号开展仿真试验,以误码率和丢帧率为指标进行通信性能分析。 展开更多
关键词 DVB-S2X 低轨卫星 通信性能 误码率 丢帧率
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时间反转直扩通信系统及性能分析
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作者 雷维嘉 邹梦婷 +1 位作者 雷宏江 唐宏 《电子学报》 EI CAS CSCD 北大核心 2024年第1期69-80,共12页
时间反转传输技术的空时聚焦特性能够有效地提升通信系统的性能.本文设计了一种将时间反转技术应用于直扩通信系统的方案,并对多径衰落信道下单用户和多用户系统的接收信干噪比、系统容量、误比特率等性能进行了理论分析与仿真验证.理... 时间反转传输技术的空时聚焦特性能够有效地提升通信系统的性能.本文设计了一种将时间反转技术应用于直扩通信系统的方案,并对多径衰落信道下单用户和多用户系统的接收信干噪比、系统容量、误比特率等性能进行了理论分析与仿真验证.理论与仿真结果表明,通过时间反转预处理,直扩通信系统的性能得到了改善,且优于复杂度较高的多通道Rake接收的系统,且多径数目越多,优势越明显. 展开更多
关键词 直接序列扩频 时间反转 RAKE接收机 系统容量 误比特率
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一种支持向量机的相干解调系统误码率模拟预测算法
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作者 孙培刚 李美丽 张全禹 《电子设计工程》 2024年第10期74-77,82,共5页
针对信道中高斯加性噪声引起接收端相干解调系统的误码问题,提出了一种支持向量机的相干解调系统误码率模拟预测算法,为提高通信系统的抗噪特性提供研究基础。文中采用差分进化算法与支持向量机SVM算法相结合的方法,通过差分进化算法优... 针对信道中高斯加性噪声引起接收端相干解调系统的误码问题,提出了一种支持向量机的相干解调系统误码率模拟预测算法,为提高通信系统的抗噪特性提供研究基础。文中采用差分进化算法与支持向量机SVM算法相结合的方法,通过差分进化算法优化SVM算法中的惩罚因子与高斯径向基的核函数参数,并对模拟环境下相干解调系统受高斯加性噪声影响所产生的误码数据进行了预测。实验结果表明,基于差分进化的SVM算法预测模型相比经典遗传算法预测精度提高了3.7%,预测精度基本满足误码率数据的预测要求,并具有较强的泛化能力。 展开更多
关键词 误码率 支持向量机 差分进化算法 缺一个 相干解调系统
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联合RIS子块与接收天线的索引调制方案性能分析
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作者 景小荣 万宇 +2 位作者 曾裕 于江 陈前斌 《信号处理》 CSCD 北大核心 2024年第7期1318-1328,共11页
利用大量无源反射器件设计的可重构智能表面(RIS),具有拓展无线通信覆盖范围、降低系统成本/功耗和提升未来通信系统性能的优势;而索引调制(IM),通过激活通信资源的子集可实现信息的隐性传输,有望为无线通信带来更高的频谱效率和能量效... 利用大量无源反射器件设计的可重构智能表面(RIS),具有拓展无线通信覆盖范围、降低系统成本/功耗和提升未来通信系统性能的优势;而索引调制(IM),通过激活通信资源的子集可实现信息的隐性传输,有望为无线通信带来更高的频谱效率和能量效率,因此,为进一步提升未来无线通信系统的性能,该论文融合RIS与IM技术,提出一种联合RIS子块与接收天线的IM方案。在该方案中,按照相邻原则,将RIS反射元件分割为若干子块,进而利用RIS子块索引与接收天线索引同时实现附加信息传递,即对待传输比特序列,将其分割为三部分,其中第一部比特被调制为星座符号,第二部分用于指示RIS子块划分,第三部分用于指示接收天线索引;在此基础上,根据最大似然(ML)检测的成对错误概率(PEP)解析形式,分四种情况,从理论上推导出对应的矩母函数(MGF),得到无条件PEP的解析表达式,最后得到该方案ML检测的平均误码率(ABER)性能上界。仿真结果表明,与现有RIS辅助的IM方案相比,无须增加额外频谱资源,所提方案的系统可达速率和系统差错性能方面均具有一定优势;同时,验证了ML检测的ABER上界具备严格一致性。 展开更多
关键词 可重构智能表面 索引调制 最大似然检测 理论误码率
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外界干扰下车对车2×2 MIMO-VLC系统研究
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作者 尹荣荣 沈兴悦 +3 位作者 桑军 秦豪 翟萌发 贾宽宽 《电子学报》 EI CAS CSCD 北大核心 2024年第4期1269-1281,共13页
为了研究干扰车辆和穿越道路行人对车对车可见光通信系统的影响,本文提出了带有外界干扰的车对车2×2 MIMO可见光通信模型.该模型以基于市场加权灯束模型的汽车前照灯作为2个发射器,以光电探测器作为2个接收器,考虑了间隔车道车辆... 为了研究干扰车辆和穿越道路行人对车对车可见光通信系统的影响,本文提出了带有外界干扰的车对车2×2 MIMO可见光通信模型.该模型以基于市场加权灯束模型的汽车前照灯作为2个发射器,以光电探测器作为2个接收器,考虑了间隔车道车辆和过道行人对系统性能的影响.研究结果表明:当误码率小于为10^(−4)时,同道、邻道和间隔车道车辆的纵向通信距离分别为:28 m、5~18 m、0 m;间隔车道的两车不能直接通信,但其前照灯发射光线会进入信号接收车辆从而对正常通信两车产生影响;行人穿越道路会使正常通信两车的误码率产生较大波动且存在积极影响,正常通信两车横向距离越大积极影响占比越高;本文提出的模型考虑了行人和车辆的干扰,为改善可见光通信在复杂交通网的应用效果提供了理论依据. 展开更多
关键词 外界干扰 车对车 可见光通信 误码率
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基于全概率公式的M-APSK误码率分析模型
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作者 郇浩 任科学 《通信学报》 EI CSCD 北大核心 2024年第7期127-137,共11页
为有效评估加性白高斯噪声信道中M-APSK的性能,提出了一种基于全概率公式的理论误码率分析模型。首先根据星座点分布及其编码特点对星座平面进行区域划分,然后由接收符号落在相应区域的概率推导出各比特的判决错误概率表达式,最后得到... 为有效评估加性白高斯噪声信道中M-APSK的性能,提出了一种基于全概率公式的理论误码率分析模型。首先根据星座点分布及其编码特点对星座平面进行区域划分,然后由接收符号落在相应区域的概率推导出各比特的判决错误概率表达式,最后得到理论误码率的精确闭式解。以16APSK和32APSK为例,推导出了其各类星座图的理论误码率计算公式,与Monte Carlo仿真结果非常吻合。模型具有通用性,PSK、QAM、PAM、APSK等调制方式均可利用该模型得到理论误码率的精确闭式解。相较于依赖大量数值计算的复杂二维概率积分方法,所提模型能够更方便地给出M-APSK的误码率性能。 展开更多
关键词 幅相调制 理论误码率 计算公式 闭式解
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基于可逆元胞自动机加密的扩展码索引调制方案
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作者 赵耿 黄思婕 +2 位作者 马英杰 董有恒 吴锐 《计算机科学》 CSCD 北大核心 2024年第6期416-422,共7页
针对直接序列扩频系统伪随机(Pseudo Noise,PN)码资源有限且码索引调制系统误码率性能下降的问题,提出了一种基于可逆的初等元胞自动机加密的扩展码索引调制方案。首先,针对PN码资源有限的问题,提出使用混沌规则的初等元胞自动机对PN码... 针对直接序列扩频系统伪随机(Pseudo Noise,PN)码资源有限且码索引调制系统误码率性能下降的问题,提出了一种基于可逆的初等元胞自动机加密的扩展码索引调制方案。首先,针对PN码资源有限的问题,提出使用混沌规则的初等元胞自动机对PN码进行迭代的方案,从而实现扩展PN码的目的;其次,针对码索引调制误码率性能下降的问题,提出了一种可逆元胞自动机加密的码索引调制方案,在发射端,把信息比特切割成调制比特和映射比特,并分别映射为调制符号和扩频码索引,使用对应索引的扩频码对同相分量进行扩频,同时使用可逆元胞自动机对映射比特进行加密,加密后的映射比特为调制符号的正交分量选取对应索引的扩频码进行扩频。仿真与分析结果表明,在相同频谱效率条件下,在加性高斯白噪声信道中,当误码率为10-5时,扩展码索引调制方案的误码率性能优于码索引调制和广义码索引调制方案约2~4 dB,优于非正交码移键控码索引调制方案约0.5 dB。 展开更多
关键词 直接序列扩频 码索引调制 初等元胞自动机 误比特率
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无线紫外光与射频混合链路中继协作方案性能分析
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作者 邵军虎 史魏征 +1 位作者 刘依朔 刘再平 《电子测量与仪器学报》 CSCD 北大核心 2024年第1期160-167,共8页
将无线紫外光通信与传统射频通信进行优势互补结合,针对双链路异构组网时的中继协作混合传输问题,采用建模与数值计算分析的方法,对比分析了不同策略和参数条件下系统的中断概率和误码率性能。基于无线紫外非直视散射信道和射频无线衰... 将无线紫外光通信与传统射频通信进行优势互补结合,针对双链路异构组网时的中继协作混合传输问题,采用建模与数值计算分析的方法,对比分析了不同策略和参数条件下系统的中断概率和误码率性能。基于无线紫外非直视散射信道和射频无线衰落信道的各自特点,建立了描述双链路并行传输中继与协作问题的模型,给出了3种典型情况下的传输策略。通过理论分析和数值计算的方法,给出了不同策略下混合链路中继的中断概率和误码率表达式,并在不同信道参数条件下对系统性能进行了对比分析。研究结果表明,相比于无线紫外光单链路传输,混合链路的中继协作策略在不同距离和不同参量条件下获得更低的系统中断概率。在误码率为1×10^(-6)条件下,双链路中继传输可以在不同湍流强度和不同莱斯因子情况下可获得约0.4~6.1 dB的信噪比增益改善。 展开更多
关键词 紫外光通信 射频通信 中继协作 中断概率 误码率
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基于马尔科夫模型的双站激光微波混合链路性能分析
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作者 邵军虎 杜旭晓 +1 位作者 庞健 史魏征 《电子学报》 EI CAS CSCD 北大核心 2024年第2期468-476,共9页
针对气象变化对自由空间光(Free Space Optical,FSO)通信链路和毫米波射频(Radio Frequency,RF)通信链路可用率的影响问题,采用马尔科夫建模与稳态概率求解计算方法,分析不同天气条件下FSO/RF混合链路的双接收站分集与中断概率性能.基于... 针对气象变化对自由空间光(Free Space Optical,FSO)通信链路和毫米波射频(Radio Frequency,RF)通信链路可用率的影响问题,采用马尔科夫建模与稳态概率求解计算方法,分析不同天气条件下FSO/RF混合链路的双接收站分集与中断概率性能.基于FSO链路和RF链路的信道模型,采用有限状态马尔科夫链(Finite State Markov Chain,FSMC)分别对单双站FSO/RF混合链路的切换选择进行建模,推导得出不同参数和天气情况下系统稳态的中断概率表达式.数值计算结果表明,当中断概率达到10^(-6),雨雾天气链路距离为1~7 km时,双站FSO/RF混合链路相比单站可获得4~25 dB的增益. 展开更多
关键词 FSO/RF混合链路 多站分集 马尔科夫模型 中断概率 误码率
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Error Estimations, Error Computations, and Convergence Rates in FEM for BVPs
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作者 Karan S. Surana A. D. Joy J. N. Reddy 《Applied Mathematics》 2016年第12期1359-1407,共49页
This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential o... This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential operators. A posteriori error estimates are discussed in context with local approximations in higher order scalar product spaces. A posteriori error computational framework (without the knowledge of theoretical solution) is presented for all BVPs regardless of the method of approximation employed in constructing the integral form. This enables computations of local errors as well as the global errors in the computed finite element solutions. The two most significant and essential aspects of the research presented in this paper that enable all of the features described above are: 1) ensuring variational consistency of the integral form(s) resulting from the methods of approximation for self adjoint, non-self adjoint, and nonlinear differential operators and 2) choosing local approximations for the elements of a discretization in a subspace of a higher order scalar product space that is minimally conforming, hence ensuring desired global differentiability of the approximations over the discretizations. It is shown that when the theoretical solution of a BVP is analytic, the a priori error estimate (in the asymptotic range, discussed in a later section of the paper) is independent of the method of approximation or the nature of the differential operator provided the resulting integral form is variationally consistent. Thus, the finite element processes utilizing integral forms based on different methods of approximation but resulting in VC integral forms result in the same a priori error estimate and convergence rate. It is shown that a variationally consistent (VC) integral form has best approximation property in some norm, conversely an integral form with best approximation property in some norm is variationally consistent. That is best approximation property of the integral form and the VC of the integral form is equivalent, one cannot exist without the other, hence can be used interchangeably. Dimensional model problems consisting of diffusion equation, convection-diffusion equation, and Burgers equation described by self adjoint, non-self adjoint, and nonlinear differential operators are considered to present extensive numerical studies using Galerkin method with weak form (GM/WF) and least squares process (LSP) to determine computed convergence rates of various error norms and present comparisons with the theoretical convergence rates. 展开更多
关键词 Finite Element error Estimation Convergence rate A Priori A Posteriori BVP Variationally Consistent Integral Form Variationally Inconsistent Integral Form Differential Operator Classification SELF-ADJOINT NON-SELF-ADJOINT Nonlinear
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