论文标题
ESPRIT和空间平滑ESPRIT的非反应性能分析
Nonasymptotic performance analysis of ESPRIT and spatial-smoothing ESPRIT
论文作者
论文摘要
本文涉及来自多个SNAPSHOT数据的频率估计问题。众所周知，如果快照源或有限的快照，则ESPRIT（以及在存在有限的快照的情况下，空间平滑的ESPRIT）如果快照的数量或信噪比（SNR）接近Infinity，则可以找到真实的频率。在本文中，我们分析了具有有限的快照和有限的SNR的Esprit和空间平滑ESPRIT的非震荡性能。 We show that the absolute frequency estimation error of ESPRIT (or spatial-smoothing ESPRIT) is bounded from above by $C\frac{\max(σ, σ^2)}{\sqrt{L}}$ with overwhelming probability, where $σ^2$ denotes the Gaussian noise variance, $L$ is the number of snapshots and $C$ is a coefficient independent $ l $和$σ^2 $，并且只有在没有噪音或无限多个快照的情况下，才能通过Esprit（或空间平滑的Esprit）定位真实频率。我们的结果是通过得出新的矩阵扰动范围并概括经典的Schur产品定理，这可能是独立的。还制作了音乐和SS音乐的扩展。提供数值结果来证实我们的分析。
This paper is concerned with the problem of frequency estimation from multiple-snapshot data. It is well-known that ESPRIT (and spatial-smoothing ESPRIT in presence of coherent sources or given limited snapshots) can locate the true frequencies if either the number of snapshots or the signal-to-noise ratio (SNR) approaches infinity. In this paper, we analyze the nonasymptotic performance of ESPRIT and spatial-smoothing ESPRIT with finitely many snapshots and finite SNR. We show that the absolute frequency estimation error of ESPRIT (or spatial-smoothing ESPRIT) is bounded from above by $C\frac{\max(σ, σ^2)}{\sqrt{L}}$ with overwhelming probability, where $σ^2$ denotes the Gaussian noise variance, $L$ is the number of snapshots and $C$ is a coefficient independent of $L$ and $σ^2$, if and only if the true frequencies can be localized by ESPRIT (or spatial-smoothing ESPRIT) without noise or with infinitely many snapshots. Our results are obtained by deriving new matrix perturbation bounds and generalizing the classical Schur product theorem, which may be of independent interest. Extensions to MUSIC and SS-MUSIC are also made. Numerical results are provided corroborating our analysis.
