OS-CFAR thresholding in decentralized radar systems

In a decentralized detection scheme, several sensors perform a binary (hard) decision and send the resulting data to a fusion center for the final decision. If each local decision has a constant false alarm rate (CFAR), the final decision is ensured to be CFAR. We consider the case that each local decision is a threshold decision, and the threshold is proportional, through a suitable multiplier, to a linear combination of order statistics (OS) from a reference set (a generalization of the concept of OS thresholding). We address the following problem: given the fusion rule and the relevant system parameters, select each threshold multiplier and the coefficients of each linear combination so as to maximize the overall probability of detection for constrained probability of false alarm. By a Lagrangian maximization approach, we obtain a general solution to this problem and closed-form solutions for the AND and OR fusion logics. A performance assessment is carried on, showing a global superiority of the OR fusion rule in terms of detection probability (for operating conditions matching the design assumptions) and of robustness (when these do not match). We also investigate the effect of the hard quantization performed at the local sensors, by comparing the said performance to those achievable by the same fusion rule in the limiting case of no quantization     

Explicit solutions for some simple decentralized detection problems

A decentralized detection problem is considered in which a number of identical sensors transmit a finite-valued function of their observations to a fusion center which makes a final decision on one of M alternative hypotheses. The authors consider the case in which the number of sensors is large, and they derive (asymptotically) optimal rules for determining the messages of the sensors when the observations are generated from a simple and symmetrical set of discrete distributions. They also consider the tradeoff between the number of sensors and the communication rate of each sensor when there is a constraint on the total communication rate from the sensors to the fusion center. The results suggest that it is preferable to have several independent sensors transmitting low-rate (coarse) information instead of a few sensors transmitting high-rate (very detailed) information. They also suggest that an M-ary hypothesis testing problem can be viewed as a collection of M(M-1)/2 binary hypothesis testing problems. From this point of view the most useful messages (decision rules) are those that provide information to the fusion center that is relevant to the largest possible numbers of these binary hypothesis testing problems     

Decentralized CFAR signal detection

The authors develop the theory of CA-CFAR (cell-averaging constant false-alarm rate) detection using multiple sensors and data fusion, where detection decisions are transmitted from each CA-CFAR detector to the data fusion center. The overall decision is obtained at the data fusion center based on some k out of n fusion rule. For a Swerling target model I embedded in white Gaussian noise of unknown level, the authors obtain the optimum threshold multipliers of the individual detectors. At the data fusion center, they derive an expression for the overall probability of detection while the overall probability of false alarm is maintained at the desired value for the given fusion rules. An example is presented showing numerical results     

Optimum multisensor fusion of correlated local decisions

A distributed detection system consisting of a number of local detectors and a fusion center is considered. Each detector makes a decision for the underlying binary hypothesis testing problem based on its own observation and transmits its decision to the fusion center where the global decision is derived. The local decision rules are assumed to be given, but the local decisions are correlated. The correlation is generally characterized by a finite number of conditional probabilities. The optimum decision fusion rule in the Neyman-Pearson sense is derived and analyzed. The performance of the distributed detection system versus the degree of correlation between the local decisions is analyzed for a correlation structure that can be indexed by a single parameter. System performance as well as the performance advantage of using a larger number of local detectors degrade as the degree of correlation between local decisions increases     

Distributed binary integration

A distributed radar detection system that employs binary integration at each local detector is studied. Local decisions are transmitted to the fusion center where they are combined to yield a global decision. The optimum values of the two thresholds at each local processor are determined so as to maximize the detection probability under a given probability of false alarm constraint. Using an important channel model, performance comparisons are made to determine the integration loss     

Relay selection in cooperative communication systems over continuous time-varying fading channel

In this paper, we study relay selection under outdated channel state information (CSI) in a decode-and-forward (DF) cooperative system. Unlike previous researches on cooperative commu-nication under outdated CSI, we consider that the channel varies continuously over time, i.e., the channel not only changes between relay selection and data transmission but also changes during data transmission. Thus the level of accuracy of the CSI used in relay selection degrades with data transmission. We first evaluate the packet error rate (PER) of the cooperative system under contin-uous time-varying fading channel, and find that the PER performance deteriorates more seriously under continuous time-varying fading channel than when the channel is assumed to be constant during data transmission. Then, we propose a repeated relay selection (RRS) strategy to improve the PER performance, in which the forwarded data is divided into multiple segments and relay is reselected before the transmission of each segment based on the updated CSI. Finally, we propose a combined relay selection (CRS) strategy which takes advantage of three different relay selection strategies to further mitigate the impact of outdated CSI.     

Blind adaptive decision fusion for distributed detection

We consider the problem of decision fusion in a distributed detection system. In this system, each detector makes a binary decision based on its own observation, and then communicates its binary decision to a fusion center. The objective of the fusion center is to optimally fuse the local decisions in order to minimize the final error probability. To implement such an optimal fusion center, the performance parameters of each detector (i.e., its probabilities of false alarm and missed detection) as well as the a priori probabilities of the hypotheses must be known. However, in practical applications these statistics may be unknown or may vary with time. We develop a recursive algorithm that approximates these unknown values on-line. We then use these approximations to adapt the fusion center. Our algorithm is based on an explicit analytic relation between the unknown probabilities and the joint probabilities of the local decisions. Under the assumption that the local observations are conditionally independent, the estimates given by our algorithm are shown to be asymptotically unbiased and converge to their true values at the rate of O(1/k/sup 1/2/) in the rms error sense, where k is the number of iterations. Simulation results indicate that our algorithm is substantially more reliable than two existing (asymptotically biased) algorithms, and performs at least as well as those algorithms when they work.     

Optimal m-ary data fusion with distributed sensors

An optimal data fusion rule is derived for an m-ary detection problem. Each detector determines a local decision using a local decision rule and transmits the local decision to the fusion center. Considering the reliability of local detectors, local decisions are combined to produce the final decision. In this study, based upon the maximum posterior probability concept, optimal decision rules for m-ary detection problems are proposed for the local detector and the data fusion center     

无人机中继平台覆盖区域统计模型简

 针对中继信号覆盖区域确定性模型没有考虑信道随机衰落影响的问题,提出了一种基于中断概率的无人机（UAVs）中继平台信号覆盖半径统计模型。通过将中继链路建模为包含路径损耗、阴影衰落和多径衰落的复合分布模型,推导获得中继信号覆盖半径的概率分布,并给出一种利用中断概率数值求解覆盖半径的方法。仿真结果表明,信道衰落对覆盖半径影响非常大,当中断概率小于10%时,覆盖半径仅为无衰落信道时的一半。研究结果对移动自组织网络（MANETs）中的中继网络的无人机最优布置、飞行策略以及网络性能评估等具有重要的参考价值。     

无人机中继平台覆盖区域统计模型

针对中继信号覆盖区域确定性模型没有考虑信道随机衰落影响的问题,提出了一种基于中断概率的无人机（UAVs）中继平台信号覆盖半径统计模型。通过将中继链路建模为包含路径损耗、阴影衰落和多径衰落的复合分布模型,推导获得中继信号覆盖半径的概率分布,并给出一种利用中断概率数值求解覆盖半径的方法。仿真结果表明,信道衰落对覆盖半径影响非常大,当中断概率小于10%时,覆盖半径仅为无衰落信道时的一半。研究结果对移动自组织网络（MANETs）中的中继网络的无人机最优布置、飞行策略以及网络性能评估等具有重要的参考价值。     

Asynchronous distributed detection

Binary parallel distributed-detection architectures employ a bank of local detectors to observe a common volume of surveillance, and form binary local decisions about the existence or nonexistence of a target in that volume. The local decisions are transmitted to a central detector, the data fusion center (DEC), which integrates them to a global target or no target decision. Most studies of distributed-detection systems assume that the local detectors are synchronized. In practice local decisions are made asynchronously and the DFC has to update its global decision continually. In this study the number of local decisions observed by the central detector within any observation period is Poisson distributed. An optimal fusion rule is developed and the sufficient statistic is shown to be a weighted sum of the local decisions collected by the DFC within the observation interval. The weights are functions of the individual local detector performance probabilities (i.e., probabilities of false alarm and detection). In this respect the decision rule is similar to the one developed by Chair and Varshney for the synchronized system. Unlike the Chair-Varshney rule, however, the DFC's decision threshold in the asynchronous system is time varying. Exact expressions and asymptotic approximations are developed for the detection performance with the optimal rule. These expressions allow performance prediction and assessment of tradeoffs in realistic decision fusion architectures which operate over modern communication networks     

CFAR data fusion center with inhomogeneous receivers

Detection systems with distributed sensors and data fusion are increasingly used by surveillance systems. A system formed by N inhomogeneous constant false alarm rate (CFAR) detectors (cell-averaging (CA) and ordered statistic (OS) CFAR detectors) is studied. A recursive formulation of an algorithm that permits a fixed level of false alarms in the data fusion center is presented, to set the optimum individual threshold levels in the CFAR receivers and the optimum `K out of N' decision rule in order to maximize the total probability of detection. The algorithm also considers receivers of different quality or with different communication channel qualities connecting them with the fusion center. This procedure has been applied to several hypothetical networks with distributed CA-CFAR and OS-CFAR receivers and for Rayleigh targets and interference, and it was seen that in general the fusion decision OR rule is not always the best     

Optimum local decision space partitioning for distributed detection

A distributed detection system is considered that consists of a number of independent local detectors and a fusion center. The decision statistics and performance characteristics (i.e. the false alarm probabilities and detection probabilities) of the local detectors are assumed as given. Communication is assumed only between each local detector and the fusion center and is one-way from the former to the latter. The fusion center receives decisions from the local detectors and combines them for a global decision. Instead of a one-bit hard decision, the authors propose that each local detector provides the fusion center with multiple-bit decision value which represents its decision and, conceptually, its degree of confidence on that decision. Generating a multiple-bit local decision entails a subpartitioning of the local decision space the optimization of which is studied. It is shown that the proposed system significantly outperforms one in which each local detector provides only a hard decision. Based on optimum subpartitioning of local decision space, the detection performance is shown to increase monotonically with the number of partitions     

Reliability Analysis of Aircraft Condition Monitoring Network Using an Enhanced BDD Algorithm

The aircraft condition monitoring network is responsible for collecting the status of each component in aircraft. The reliability of this network has a significant effect on safety of the aircraft. The aircraft condition monitoring network works in a real-time manner that all the data should be transmitted within the deadline to ensure that the control center makes proper decision in time. Only the connectedness between the source node and destination cannot guarantee the data to be transmitted in time. In this paper, we take the time deadline into account and build the task-based reliability model. The binary decision diagram (BDD), which has the merit of efficiency in computing and storage space, is introduced when calculating the reliability of the network and addressing the essential variable. A case is analyzed using the algorithm proposed in this paper. The experimental results show that our method is efficient and proper for the reliability analysis of the real-time network.     

Optimal Decision Fusion in Multiple Sensor Systems

The problem of optimal data fusion in the sense of the Neyman-pearson (N-P) test in a centralized fusion center is considered. The fusion center receives data from various distributed sensors. Each sensor implements a N-P test individually and independently of the other sensors. Due to limitations in channel capacity, the sensors transmit their decision instead of raw data. In addition to their decisions, the sensors may transmit one or more bits of quality information. The optimal, in the N-P sense, decision scheme at the fusion center is derived and it is seen that an improvement in the performance of the system beyond that of the most reliable sensor is feasible, even without quality information, for a system of three or more sensors. If quality information bits are also available at the fusion center, the performance of the distributed decision scheme is comparable to that of the centralized N-P test. Several examples are provided and an algorithm for adjusting the threshold level at the fusion center is provided.     

非对称衰落信道下无人机中继传输方案及性能分析

 无人机(UAV)作为中继传输平台受到了国内外研究人员的广泛关注。本文研究了非对称衰落信道下的无人机中继传输系统,提出了输出信噪比最大化准则下的波束形成(BF)优化方案,并推导出系统中断概率、遍历容量和平均误符号率等无线通信系统主要性能指标的理论表达式。通过计算机仿真验证了本文提出的中继传输方案及性能分析的正确性,并定量分析了天线数量、信道参数以及功率分配对系统性能的影响,为无人机中继传输系统的设计及性能评估提供了参考和依据。     

Relay selection based on MAP estimation for cooperative communication with outdated channel state information

In this paper, we consider an amplify-and-forward (AF) cooperative communication system when the channel state information (CSI) used in relay selection differs from that during data transmission, i.e., the CSI used in relay selection is outdated. The selected relay may not be actually the best for data transmission and the outage performance of the cooperative system will deteriorate. To improve its performance, we propose a relay selection strategy based on maximum a posteriori (MAP) estimation, where relay is selected based on predicted signal-to-noise ratio (SNR). To reduce the computation complexity, we approximate the a posteriori probability density of SNR and obtain a closed-form predicted SNR, and a relay selection strategy based on the approximate MAP estimation (RS-AMAP) is proposed. The simulation results show that this approximation leads to trivial performance loss from the perspective of outage probability. Compared with relay selection strategies given in the literature, the outage probability is reduced largely through RS-AMAP for medium-to-large transmitting powers and medium-to-high channel correlation coefficients.     

基于粗糙集理论的证券分析系统数据融合

将粗糙集理论应用于证券分析系统,探讨了相容状况下基于粗糙集理论的数据处理方法,并给出了系统结构和融合方法。该方法以局部决策作为条件属性,融合中心采用粗集理论方法对局部决策进行处理,包括知识表达、化简,最后给出决策规则。从结果来看,采用该方法不需要先验概率,也不需要隶属函数,同时还可以去除冗余的局部决策,使系统的配置最优化、提高了系统的运行速度。     

Phase-Locked-Loop Detection of Binary PSK Signals Utilizing Decision Feedback

A modified quadrature channel phase-locked-loop demodulator for binary phase-shift-keyed signals is presented. The modification, called decision feedback, is a practical implementation of decisiondirected channel measurement. Noise analyses are carried out for both additive and phase noise. An optimum loop filter is derived and the analyses include determination of probability of error for the system. The results of an analog simulation of the decision feedback technique are also included.     

频率选择性衰落信道DS-CDMA无人机中继通信系统航迹规划

无人机中继通信是实现远距离无线通信的一种重要技术手段，无人机的飞行航迹对无人机中继通信系统的链路传输可靠性存在显著的影响，在频率选择性衰落信道环境下研究了基于直序列码分多址（DS-CDMA）的无人机中继通信系统的航迹优化的问题。首先，给出了基于DS-CDMA的译码转发无人机中继通信系统的模型，并理论分析给出无人机中继通信系统的链路中断概率及平均误码率计算公式，以此为基础，基于链路中断概率最小化准则提出了中继无人机的航迹规划方法，最后通过仿真验证了所提出方法的正确性与有效性。研究表明：最大比值合并DS-CDMA无人机中继通信系统可充分获取频率选择性衰落信道提供的分集增益，显著改善链路传输的可靠性。