摘要翻译：
最大特征值检测(MED)是随机矩阵理论在频谱感知和信号检测中的一个重要应用。而在小信噪比环境下，代表信号的最大特征值位于Marchenko-Pastur（M-P）定律体的边缘，满足Tracy-Widom分布。由于Tracy-Widom的分布没有封闭形式的表达式，给处理带来了很大的困难。本文提出了一种移动最大特征值(SMED)算法，该算法通过结合与待检测信号相关的辅助信号将最大特征值从M-P律体中移出。根据随机矩阵理论，移位的最大特征值符合高斯分布。提出的SMED不仅简化了检测算法，而且大大提高了检测性能。本文分析了SMED、MED和跟踪(FMD)算法的性能，并进行了理论性能比较。在不同的信号环境下进行了仿真，验证了算法和理论结果。
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英文标题：
《Shifting Maximum Eigenvalue Detection in Low SNR Environment》
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作者：
Lin Zheng, Robert C. Qiu, Qing Feng, Xuebin Li
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最新提交年份：
2018
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分类信息：

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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英文摘要：
  Maximum eigenvalue detection (MED) is an important application of random matrix theory in spectrum sensing and signal detection. However, in small signal-to-noise ratio environment, the maximum eigenvalue of the representative signal is at the edge of Marchenko-Pastur (M-P) law bulk and meets the Tracy-Widom distribution. Since the distribution of Tracy-Widom has no closed-form expression, it brings great difficulty in processing. In this paper, we propose a shifting maximum eigenvalue (SMED) algorithm, which shifts the maximum eigenvalue out of the M-P law bulk by combining an auxiliary signal associated with the signal to be detected. According to the random matrix theory, the shifted maximum eigenvalue is consistent with Gaussian distribution. The proposed SMED not only simplifies the detection algorithm, but also greatly improve the detection performance. In this paper, the performance of SMED, MED and trace (FMD) algorithm is analyzed and the theoretical performance comparisons are obtained. The algorithm and theoretical results are verified by the simulations in different signal environments.
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PDF链接：
https://arxiv.org/pdf/1802.10325