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Proportional-Integral Observer Design for Multi-Rate Systems Under Decode-and-Forward Relays:Tackling Power-Dependent Packet Dropouts 认领 引用
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作者 Di Zhao Zidong Wang +2 位作者 Derui Ding Qing-Long Han Guoliang Wei 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2026年第7期1558-1571,共14页
In this paper,the problem of proportional-integral observer(PIO)design is investigated for a class of discrete-time multi-rate systems with multiple sensors,with the sensor sampling periods being allowed to differ fro... In this paper,the problem of proportional-integral observer(PIO)design is investigated for a class of discrete-time multi-rate systems with multiple sensors,with the sensor sampling periods being allowed to differ from the system updating periods.The facilitation of communication between sensors and the remote PIO through wireless networks,which are subject to probabilistic packet dropouts,is achieved through the utilization of a decode-and-forward relay-based strategy.The occurrence of packet dropouts is governed by a Bernoulli-distributed random variable whose probability is dependent on the available transmission power.A decode-and-forward relay-based strategy,developed based on different components,is capable of processing information from different encoders at different physical locations.For the convenience of observer design,the lifting technique is employed with aim to cast the multi-rate system into a single-rate one.By establishing sufficient conditions,the combined effect of external noises and relaying-aided communication on estimation performance is intuitively illustrated.Subsequently,a PIO with an adjustable parameter is designed by solving certain optimization problems.A simulation example is finally provided to validate the theoretical results. 展开更多
关键词 Decode-and-forward relay multi-rate systems networked systems proportional-integral observer design power-dependent packet dropouts
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Cubature Kalman Fusion Filtering Under Amplify-and-Forward Relays With Randomly Varying Channel Parameters 认领 引用 被引量：2
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作者 Jiaxing Li Zidong Wang +2 位作者 Jun Hu Hongli Dong Hongjian Liu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2025年第2期356-368,共13页
In this paper, the problem of cubature Kalman fusion filtering(CKFF) is addressed for multi-sensor systems under amplify-and-forward(AaF) relays. For the purpose of facilitating data transmission, AaF relays are utili... In this paper, the problem of cubature Kalman fusion filtering(CKFF) is addressed for multi-sensor systems under amplify-and-forward(AaF) relays. For the purpose of facilitating data transmission, AaF relays are utilized to regulate signal communication between sensors and filters. Here, the randomly varying channel parameters are represented by a set of stochastic variables whose occurring probabilities are permitted to exhibit bounded uncertainty. Employing the spherical-radial cubature principle, a local filter under AaF relays is initially constructed. This construction ensures and minimizes an upper bound of the filtering error covariance by designing an appropriate filter gain. Subsequently, the local filters are fused through the application of the covariance intersection fusion rule. Furthermore, the uniform boundedness of the filtering error covariance's upper bound is investigated through establishing certain sufficient conditions. The effectiveness of the proposed CKFF scheme is ultimately validated via a simulation experiment concentrating on a three-phase induction machine. 展开更多
关键词 Amplify-and-forward(AaF)relays covariance intersection fusion cubature Kalman filtering multi-sensor systems uniform boundedness
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Research on Feature Extraction of Remnant Particles of Aerospace Relays 认领 引用 被引量：7
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作者 WANG Shu-juan GAO Hong-liang ZHAI Guo-fu 《Chinese Journal of Aeronautics》 SCIE EI CAS 2007年第3期253-259,共7页
The existence of remnant particles, which significantly reduce the reliability of relays, is a serious problem for aerospace relays. The traditional method for detecting remnant particles-particle impact noise detecti... The existence of remnant particles, which significantly reduce the reliability of relays, is a serious problem for aerospace relays. The traditional method for detecting remnant particles-particle impact noise detection （PIND）-can be used merely to detect the existence of the particle; it is not able to provide any information about the particles＇ material. However, information on the material of the particles is very helpful for analyzing the causes of remnants. By analyzing the output acoustic signals from a PIND tester, this paper proposes three feature extraction methods： unit energy average pulse durative time, shape parameter of signal power spectral density （PSD）, and pulse linear predictive coding coefficient sequence. These methods allow identified remnants to be classified into four categories based on their material. Furthermore, we prove the validity of this new method by processing P1ND signals from actual tests. 展开更多
关键词 feature extraction aerospace relays remnant particles particle impact noise detection
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Placement of unmanned aerial vehicles as communication relays in two-tiered multi-agent system:clustering based methods 认领 引用 被引量：3
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作者 WU Gaofeng WAN Kaifang +1 位作者 GAO Xiaoguang FU Xiaowei 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2020年第2期231-242,共12页
The network performance and the unmanned aerial vehicle(UAV)number are important objectives when UAVs are placed as communication relays to enhance the multi-agent information exchange.The problem is a non-determinist... The network performance and the unmanned aerial vehicle(UAV)number are important objectives when UAVs are placed as communication relays to enhance the multi-agent information exchange.The problem is a non-deterministic polynomial hard(NP-hard)multi-objective optimization problem,instead of generating a Pareto solution,this work focuses on considering both objectives at the same level so as to achieve a balanced solution between them.Based on the property that agents connected to the same UAV are a cluster,two clustering-based algorithms,M-K-means(MKM)and modified fast search and find density of peaks(MFSFDP)methods,are first proposed.Since the former algorithm requires too much computational time and the latter one requires too many relays,an algorithm for the balanced network performance and relay number(BPN)is proposed by discretizing the area to avoid missing the optimal relay positions and defining a new local density function to reflect the network performance metric.Simulation results demonstrate that the proposed algorithms are feasible and effective.Comparisons between these algorithms show that the BPN algorithm uses fewer relay UAVs than the MFSFDP and classic set-covering based algorithm,and its computational time is far less than the MKM algorithm. 展开更多
关键词 unmanned aerial vehicle(UAV) relay communication clustering relay node placement wireless network
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Influence of the Inverse-Time Protection Relays on the Voltage Dip Index 认领 引用 被引量：2
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作者 高新科 刘玡朋 《Journal of Shanghai Jiaotong university(Science)》 EI 2014年第3期354-360,共7页
The probability-assessment analyses on the characteristic value of voltage dip by using Monte Carlo stochastic modeling method to stimulate the randomness of the short circuit fault are introduced. Using Matlab and Po... The probability-assessment analyses on the characteristic value of voltage dip by using Monte Carlo stochastic modeling method to stimulate the randomness of the short circuit fault are introduced. Using Matlab and Power Systems CAD(PSCAD), we design control interface which combines the electromagnetic transient simulation with the Monte Carlo method. Specifically, the designing of interface which is meant to employ the method of Matlab programming to control the electromagnetic transients including direct current(EMTDC)simulation is introduced. Furthermore, the influences of the protection devices on the voltage dip to ensure the authenticity and the referential reliability are simulated. A system with the inverse-time protection devices equipped on each line which can coordinate together is designed to cut off the short-circuit fault. The voltage dip of the designed system is assessed by the pre- and post-system average root mean square(RMS) variation frequency index, and the voltage dip index is compared with the Information Technology Industry Council(ITIC)curves. The simulation results demonstrate that the inverse-time relay protection equipments are well-coordinated,and the severity and the range of the voltage dip are influenced by the cooperation of the equipped inverse-time protection devices. 展开更多
关键词 power quality voltage dip inverse-time protection relay Monte Carlo algorithm simulation
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Interference and Spectral Efficiency Analysis in Two-hop Cellular Network with Fixed Relays in FDD Mode 认领 引用 被引量：1
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作者 李平 戎蒙恬 +1 位作者 黄磊 喻丹 《Journal of Shanghai Jiaotong university(Science)》 EI 2006年第3期361-367,共7页
This paper presented a scheme of two-hop cellular network with fixed relay nodes (FRN). Based on this scheme, co-channel interference and signal interference ratio(SIR) received by base station(BS) and FRN were analyz... This paper presented a scheme of two-hop cellular network with fixed relay nodes (FRN). Based on this scheme, co-channel interference and signal interference ratio(SIR) received by base station(BS) and FRN were analyzed. Both the theoretical analysis and simulation results show that the SIR can be improved significantly when relays are employed in the network. The higher spectral efficiency can be obtained due to the improved two-hop link quality through the use of adaptive modulation and coding (AMC). The antenna height of FRN and the cell radius of BS and that of FRN influence SIR received by BS and FRN and the system spectral efficiency greatly. The proper antenna height of FRN and cell radius of BS and that of FRN were also given to get the highest spectral efficiency. 展开更多
关键词 fixed relay nodes （FRN） signal interference ratio （SIR） two-hop cellular network frequency division diplex（FDD）
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Uplink Power Saving Potential of Cellular System with Fixed Relays 认领 引用
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作者 史宏逵 戎蒙恬 +1 位作者 刘涛 喻丹 《Journal of Shanghai Jiaotong university(Science)》 EI 2007年第2期223-228,233,共6页
This paper presented a scheme of relayed cellular mobile telecommunication network,which only employs fixed digital relays and not more than two-hop relay routes.Power saving potential of the network is deeply studied... This paper presented a scheme of relayed cellular mobile telecommunication network,which only employs fixed digital relays and not more than two-hop relay routes.Power saving potential of the network is deeply studied under the assumption of not occupying additional frequency bands(i.e.relays share the same frequency bands as used by the base stations).Theoretical analysis and simulation results have both shown that,with the same radio coverage requirement,the necessary effective transmission powers in such a relayed network have greatly decreased compared to conventional cellular network. 展开更多
关键词 digital relay fixed relay two-hop cellular system power saving
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Optimal Number of Relays in Cooperative Communication in Wireless Sensor Networks 认领 引用 被引量：1
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作者 Wail Mardini Yaser Khamayseh Shorouq AL-Eide 《Communications and Network》 2012年第2期101-110,共10页
Wireless Sensor Networks (WSN) typically consist of resource constrained micro sensors that organize itself into multihop wireless network. Sensors collect data and send it directly, or through intermediate hops in co... Wireless Sensor Networks (WSN) typically consist of resource constrained micro sensors that organize itself into multihop wireless network. Sensors collect data and send it directly, or through intermediate hops in cooperative communication system, to the collection point. These sensors are powered up by batteries, for which the replacement or recharging is very difficult. With finite energy, we can transmit a finite amount of information. Therefore, minimizing the power consumption for data transmission becomes a most important design consideration for wireless sensor networks. In this paper, we discuss the optimal power consumption in cooperative wireless sensor network that are placed on a grid. We study different cases for the optimal power consumption in such grids by varying the grid distance and number of nodes in the grid. We assume the cases of grids from 2 × 2 up to 5 × 5 in increasing complexity of calculations. The results show that the optimal path that consumes the least power is the path along the diagonal using of the grid when the source and the destination and the furthest two nodes in the grid. This path takes intermediate nodes (relays) along it based on some threshold distances. For example, in 5 × 5 cases;the first threshold between the direct distance and between using one relay in the middle is 31.6 m the second threshold distance is 63.3 m after which using three relays is the best in power consumption between the source and the destination. 展开更多
关键词 Power Consumption Wireless Sensor Networks Optimal Number of Relays
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Behavior Prediction of Untrusted Relays Based on Nonzero-Sum Game 认领 引用
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作者 付晓梅 吴晓 汪清 《Transactions of Tianjin University》 EI CAS 2015年第4期371-376,共6页
To keep the secrecy performance from being badly influenced by untrusted relay(UR), a multi-UR network through amplify-and-forward(AF) cooperative scheme is put forward, which takes relay weight and harmful factor int... To keep the secrecy performance from being badly influenced by untrusted relay(UR), a multi-UR network through amplify-and-forward(AF) cooperative scheme is put forward, which takes relay weight and harmful factor into account. A nonzero-sum game is established to capture the interaction among URs and detection strategies. Secrecy capacity is investigated as game payoff to indicate the untrusted behaviors of the relays. The maximum probabilities of the behaviors of relay and the optimal system detection strategy can be obtained by using the proposed algorithm. 展开更多
关键词 physical layer security cooperative communication untrusted relay secrecy capacity nonzero-sum game
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A Niche-Based Evolutionary Tabu Search Algorithm for Optimal Coordination of Protection Relays in Power Networks 认领 引用
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作者 YUAN Rongxiang ZOU Xiufen XU Chunlin 《Wuhan University Journal of Natural Sciences》 CAS 2009年第3期215-222,共8页
In this paper, refusal of operation and the degree of constraint violation are considered as one part of the objective function for optimizing the protection relay setting coordination of over current relays in power ... In this paper, refusal of operation and the degree of constraint violation are considered as one part of the objective function for optimizing the protection relay setting coordination of over current relays in power systems; a new expression of objective function in this optimization problem is proposed. To combine the advantages of both Tabu search （TS） and evolutionary algorithms （EAs）, a new niche-based evolutionary Tabu search algorithm （named NETS） is presented to solve this optimization problem. Moreover, in two cases of power networks, comparisons between NETS and two published algorithms are given. Experimental results show the expression of the objective function for protection relay setting is feasible and reasonable, and the proposed algorithm NETS exhibits a good performance. 展开更多
关键词 evolutionary algorithm Tabu search power system protection relay coordination
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Method to deploy wireless relays in industrial wireless monitoring 认领 引用
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作者 翁浩 Gao Jinji 《High Technology Letters》 EI CAS 2014年第2期161-165,共5页
In light of demands for wireless monitoring and the characteristics of wireless channel,a complete deployment method containing channel survey,path loss estimation,and gradient grade of wireless relay nodes is propose... In light of demands for wireless monitoring and the characteristics of wireless channel,a complete deployment method containing channel survey,path loss estimation,and gradient grade of wireless relay nodes is proposed.It can be proved by experiments that under the premise of meeting the requirements of real-time and redundant-topology,the total number of relay nodes could be minimized by using the proposed method. 展开更多
关键词 industrial wireless monitoring relay node deployment site survey path loss factor greedy randomized adaptive search procedure
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Directional Overcurrent Relays Coordination Restoration by Reducing Minimum Fault Current Limiter Impedance 认领 引用
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作者 Saadoun Abdel Aziz Mostafa DoaaKhalil Ibrahim Essam El-Din Abo El-Zahab 《Journal of Energy and Power Engineering》 CAS 2014年第6期1132-1141,共10页
FCL （fault current limiter） is used to solve relays miscoordination problem arises from DG （distributed generation） installation. In most published researches, different optimization methods are developed to obtai... FCL （fault current limiter） is used to solve relays miscoordination problem arises from DG （distributed generation） installation. In most published researches, different optimization methods are developed to obtain optimal relay settings to achieve coordination in case of not installing DG, then depending on the achieved optimal obtained relay settings, FCL impedance is deduced to ensure relays coordination restoration in case of installing DG. Based on original optimal relay settings, obtained FCL impedance is not the minimum one required to achieve relay coordination. The contribution of this paper is the generation of multi sets of original relay settings that increase the possibility of finding FCL impedance of minimum value which is lower than the calculated value based on original optimal relay settings. The proposed method achieves better economic target by reducing FCL impedance. The proposed approach is implemented and tested on IEEE-39 bus test system. 展开更多
关键词 FCL （fault current limiter） IP （pickup current setting） relays coordination TDS （time-dial setting）.
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Performance of AF Relay Networks with Multiple Relays and Multiple Antennas at Destination Using MRC Combining 认领 引用
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作者 Solimanzoy Fayeqa Haider Cong Li Yasunori Iwanami 《International Journal of Communications, Network and System Sciences》 2013年第5期197-203,共7页
Cooperative networking schemes in wireless networks provide cooperative diversity gain using differently located antennas that combat fadings induced by multipath propagation. In this paper, we present the optimal wei... Cooperative networking schemes in wireless networks provide cooperative diversity gain using differently located antennas that combat fadings induced by multipath propagation. In this paper, we present the optimal weight design for the destination in AF (Amplify and Forward) relay system, where the optimally designed MRC (Maximum Ratio Combining) is employed at the destination for S→D link (direct link between source and destination) and R→D links (indirect links between relays and destination). We investigate the BER performance of 1S→NR→LD system composed of one source, N relay nodes equipped with single antenna and one destination node equipped with L antennas, which also includes 1S→1R→LD and 1S→NR→1D. Simulation and numerical results are presented to verify our analysis. 展开更多
关键词 AF Relay MRC Diversity Multiple Relays Multiple Antennas
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Energy Efficiency Analysis of Cellular Networks with Cooperative Relays via Stochastic Geometry 认领 引用 被引量：1
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作者 Zhang Zhiwei Li Yunzhou +2 位作者 Huang Kaizhi Zhou Shidong Wang Jing 《China Communications》 SCIE CSCD 2015年第9期112-121,共10页
Cooperative relaying is a promising technology that can improve the spectral and energy efficiency of cellular networks. However, the deployed relays consume a lot of energy and system resources. To improve the energy... Cooperative relaying is a promising technology that can improve the spectral and energy efficiency of cellular networks. However, the deployed relays consume a lot of energy and system resources. To improve the energy efficiency of the relay-assisted cellular networks, this paper considers the use of energy harvesting(EH) on relay nodes. A random sleeping strategy is also introduced in macro base stations(MBS) as a possible method to reduce energy consumption. In this paper, an analytical model is proposed to investigate the energy efficiency of cellular networks with EH relays and sleep mode strategy. Numerical results confirm a significant energy efficiency gain of the proposed networks comparing to the cellular networks with non-EH relays and MBSs without sleep mode strategy. The effects of the density and transmit power of MBSs on energy efficiency are also given through simulations. 展开更多
关键词 cooperative relay energy efficiency stochastic geometry energy harvesting
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Designing a Protection Scheme in Micro-Grid Systems with DG Using Central Protection Unite and Multiple Setting Group Protection Relays 认领 引用 被引量：1
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作者 Mostafa I. Saleh Gaber El-Saady +1 位作者 Ali M. Yousef El-Noby A. Ibrahim 《Journal of Power and Energy Engineering》 2024年第9期37-49,共13页
Distributed generators now is widely used in electrical power networks, in some cases it works seasonally, and some types works at special weather conditions like photo voltaic systems and wind energy, and due to this... Distributed generators now is widely used in electrical power networks, in some cases it works seasonally, and some types works at special weather conditions like photo voltaic systems and wind energy, and due to this continuous changes in generation condition, the fault current level in network will be affected, this changes in fault current level will affect in the coordination between protection relays and to keep the coordination at right way, an adaptive protection system is required that can adaptive its setting according to generation changes, the fault current level in each case is evaluated using ETAP software, and the required relay setting in each case is also evaluated using Grey Wolf Optimizer (GWO) algorithm, and to select suitable setting which required in each condition, to select the active setting group of protection relay according to generation capacity, central protection unite can be used, and to improve protection stability and minimizing relays tripping time, a proposed method for selecting suitable backup relay is used, which leads to decrease relays tripping time and increase system stability, output settings for relays in all cases achieved our constrains. 展开更多
关键词 Directional Overcurrent Relay Protection Coordination Distributed Generators Central Protection Unite Multiple Setting Group Protection Relay
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Textbook Relays 认领 引用
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《小学生时代（大嘴英语）》 2026年第7期59-59,共1页
Recently(最近),some Chinese people left their English textbooks near Big Ben.They hid textbooks in secret spots and shared clues(线索)online.Soon,many Chinese joined in the textbook relays.They found the books,wrote w... Recently(最近),some Chinese people left their English textbooks near Big Ben.They hid textbooks in secret spots and shared clues(线索)online.Soon,many Chinese joined in the textbook relays.They found the books,wrote wishes,and left small gifts.Some foreigners joined in as well.The textbooks helped Chinese students learn about the world.Now they are helping people make new friends. 展开更多
关键词 english textbooks textbook relays Big Ben friends clues
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Teledyne Relays公司6引脚DIP固态继电器 认领 引用
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《电子产品世界》 2004年第10B期41-41,共1页
关键词 Teledyne Relays公司 6引脚 DIP 固态继电器 ZD20CF ZD24CC 温度范围 过载保护 筛选选项
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Online Transient Stability Assessment Implementing the Weighted Least-square Support Vector Machine with the Consideration of Protection Relays 认领 引用 被引量：7
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作者 Amir Hossein Poursaeed Farhad Namdari 《Protection and Control of Modern Power Systems》 SCIE EI CSCD 2025年第1期1-17,共17页
Weighted least-square support vector machine(WLS-SVM)is proposed in this research as a real-time transient stability evaluation method using the synchrophasor measurement received from phasor measurement units(PMUs).T... Weighted least-square support vector machine(WLS-SVM)is proposed in this research as a real-time transient stability evaluation method using the synchrophasor measurement received from phasor measurement units(PMUs).This method considers the directional overcurrent relays(DOCRs)for the transmission system,whereas in previous studies,the effect of protective mechanisms on the transient stability was largely ignored.When protective relays are activated in power system,the configuration of the power system is altered to mitigate the risk of the power system becoming unstable.The present study considers the operation of DOCRs in transmission lines for the transient stability so that the proposed method can respond to changes in the configuration of the case study system.In addition,WLS-SVM is employed for an online assessment of the transient stability.WLS-SVM not only is effective in response due to its faster speed,but also is resistant to noise and has excellent performance against the measurement errors of PMUs.To extract the characteristics of the vectors that are fed into the WLS-SVM algorithm,principal component analysis is used.The findings of the suggested technique reveal that it has higher accuracy and optimum performance,as compared to the extreme learning machine method,the adaptive neuro-fuzzy inference system method,and the back-propagation neural network method.The proposed technique is validated in the New England 39-bus system and the IEEE 118-bus system. 展开更多
关键词 Transient stability assessment weighted least-square support vector machine directional over-current relay phasor measurement unit
A Wideband Amplifying and Filtering Reconfigurable Intelligent Surface for Wireless Relay 认领 引用
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作者 Lijie Wu Qun Yan Zhou +11 位作者 Jun Yan Dai Siran Wang Junwei Zhang Zhen Jie Qi Hanqing Yang Ruizhe Jiang Zheng Xing Wang Huidong Li Zhen Zhang Jiang Luo Qiang Cheng Tie Jun Cui 《Engineering》 SCIE EI CSCD 2026年第1期120-129,共10页
Programmable metasurfaces have garnered significant attention due to their exceptional ability to manipulate electromagnetic(EM)waves in real time,propelling the emergence of reconfigurable intelligent surfaces(RISs)a... Programmable metasurfaces have garnered significant attention due to their exceptional ability to manipulate electromagnetic(EM)waves in real time,propelling the emergence of reconfigurable intelligent surfaces(RISs)as a transformative advancement in wireless communication for controlling signal propagation and coverage.However,conventional RISs often suffer from a limited operational range and spectral interference,hindering their practical deployment in wireless relay and communication systems.To overcome this limitation,we propose an amplifying and filtering RIS(AF-RIS)to enhance the inband signal energy and filter the out-of-band signal of the incident EM waves,thereby achieving RIS array miniaturization and improved anti-interference capability.Furthermore,each AF-RIS element features 2-bit phase control,significantly improving the array's beamforming performance.A meticulously designed4×8 AF-RIS array is presented by integrating the power dividing and combining networks,which substantially reduces the number of amplifiers and filters,drastically decreasing the hardware costs and power consumption.The experimental results demonstrate the powerful capabilities of the AF-RIS in beam-steering,frequency selectivity,and signal amplification.Thus,the proposed AF-RIS offers significant potential for critical wireless relay applications by improving frequency selectivity,expanding signal coverage,and minimizing hardware size. 展开更多
关键词 Reconfigurable intelligent surface Programmable metasurface Wireless relay Signal filtering Signal energy enhancement
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Power allocation of cooperative amplify-and-forward communications with multiple relays 认领 引用 被引量：5
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作者 WU Zhuo YANG Hong-bing 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2011年第4期65-69,共5页
Cooperative diversity is one of the most effective ways to mitigate the fading effect of wireless channels and obtain the spatial gain in wireless networks. In this paper, an optimal power allocation （OPA） scheme fo... Cooperative diversity is one of the most effective ways to mitigate the fading effect of wireless channels and obtain the spatial gain in wireless networks. In this paper, an optimal power allocation （OPA） scheme for a cooperative communication system using the amplify-and-forward （AF） transmit strategy with multiple relay users is proposed by minimizing the bit-error-rate （BER） at the destination under the constraint of the total transmit power of both the source user and the relay users. Simutation resutts indicate that the proposed power allocation method can achieve significant BER performance improvement than using the equal power allocation （EPA） scheme, while still attains low complexity. The system performance is improved significantly with the increasing of the number of relay users at high signal-noise ratio （SNR）. However, at low SNR, the system performance decreases when the relay number increases. Thus, an adaptive relay selection scheme may be used to choose the appropriate relay numbers in different transmission scenarios to provide system performance improvement and keep the power allocation scheme with low complexity. 展开更多
关键词 cooperative communication AF EPA PA multiple relays BER
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