白噪声中信号的样本容量认知检测
Sample size cognizant detection of signals in white noise
摘要：
在有噪声的有限数据中检测和估计信号是许多科学和工程界感兴趣的问题。我们提出了一个计算简单，样本特征值为基础的过程中估计的高维信号的白噪声时，有相对较少的样本的数量。我们突出了一个基本的渐近极限的样本特征值为基础的检测弱高维信号从有限的样本大小，并讨论其含义为两个紧密间隔的信号的检测。这激发了我们对“可识别信号的有效数量”的启发式定义。数值模拟被用来证明该算法相对于有效信号数的一致性以及该算法相对于Wax和Kailath的基于“渐近一致”MDL的估计器的优越性能。
英文摘要：
The detection and estimation of signals in noisy, limited data is a problem of interest to many scientific and engineering communities. We present a computationally simple, sample eigenvalue based procedure for estimating the number of high-dimensional signals in white noise when there are relatively few samples. We highlight a fundamental asymptotic limit of sample eigenvalue based detection of weak high-dimensional signals from a limited sample size and discuss its implication for the detection of two closely spaced signals. This motivates our heuristic definition of the 'effective number of identifiable signals.' Numerical simulations are used to demonstrate the consistency of the algorithm with respect to the effective number of signals and the superior performance of the algorithm with respect to Wax and Kailath's "asymptotically consistent" MDL based estimator.
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