分布式向量的贝叶斯Fisher信息最大化 估算

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摘要翻译：
研究了具有线性观测模型的高斯向量的分布估计问题。每个传感器对未知矢量进行标量噪声观测，量化其观测结果，将其映射到数字调制符号，并通过正交功率约束衰落信道将该符号传输到融合中心(FC)。模糊控制器的任务是对传感器接收到的信号进行融合并估计未知向量。我们推导了三类接收机的贝叶斯-费雪信息矩阵(FIM)：(i)相干接收机，(ii)信道包络已知的非相干接收机，(iii)信道统计量已知的非相干接收机。我们还导出了Weiss-Weinstein界(WWB)。以传感器发射功率为优化变量，提出了网络发射功率约束下贝叶斯FIM的跟踪最大化和对数行列式两个约束优化问题。我们证明了对于相干接收机，这些问题是凹的。然而，对于非相干接收机，它们不一定是凹的。贝叶斯FIM最大跟踪问题的求解可以以分布式的方式实现。数值研究了传感器间FIM-max功率分配与传感器观测质量、物理层参数以及网络发射功率约束的关系。此外，我们用FIM-max方案的解来评估系统的MSE性能，并与LMMSE估计器的MSE最小化方案（MSE-min方案）以及均匀功率分配方案的MSE最小化方案进行了比较。这些比较表明，尽管WWB比Bayesian FIM的逆算法更紧，但由于LMMSE估计器的MSE性能损失不大，因此仍然适合使用FIM-max方案。
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英文标题：
《On Bayesian Fisher Information Maximization for Distributed Vector
  Estimation》
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作者：
Mojtaba Shirazi and Azadeh Vosoughi
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最新提交年份：
2020
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Information Theory        信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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一级分类：Mathematics        数学
二级分类：Information Theory        信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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英文摘要：
  We consider the problem of distributed estimation of a Gaussian vector with linear observation model. Each sensor makes a scalar noisy observation of the unknown vector, quantizes its observation, maps it to a digitally modulated symbol, and transmits the symbol over orthogonal power-constrained fading channels to a fusion center (FC). The FC is tasked with fusing the received signals from sensors and estimating the unknown vector. We derive the Bayesian Fisher Information Matrix (FIM) for three types of receivers: (i) coherent receiver (ii) noncoherent receiver with known channel envelopes (iii) noncoherent receiver with known channel statistics only. We also derive the Weiss-Weinstein bound (WWB). We formulate two constrained optimization problems, namely maximizing trace and log-determinant of Bayesian FIM under network transmit power constraint, with sensors transmit powers being the optimization variables. We show that for coherent receiver, these problems are concave. However, for noncoherent receivers, they are not necessarily concave. The solution to the trace of Bayesian FIM maximization problem can be implemented in a distributed fashion. We numerically investigate how the FIM-max power allocation across sensors depends on the sensors observation qualities and physical layer parameters as well as the network transmit power constraint. Moreover, we evaluate the system performance in terms of MSE using the solutions of FIM-max schemes, and compare it with the solution obtained from minimizing the MSE of the LMMSE estimator (MSE-min scheme), and that of uniform power allocation. These comparisons illustrate that, although the WWB is tighter than the inverse of Bayesian FIM, it is still suitable to use FIM-max schemes, since the performance loss in terms of the MSE of the LMMSE estimator is not significant.
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PDF链接：
https://arxiv.org/pdf/1705.00803

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关键词：Fisher Fish 分布式 贝叶斯 SHE 方案 receiver 进行 传感器 未知