针对可由少量参数表示的低秩稀疏信号，本文推导压缩测量下参数估计的 CRB，给出有限方差无偏估计存在的样本数条件，并通过 DOA 与谱估计验证压缩对下界的影响。
摘要：
本文考虑具有低秩协方差矩阵的信号，这类信号位于低维子空间中，并可表示为有限（少量）个参数的形式。尽管此类信号在有限基下未必具有稀疏表示，但它们具备稀疏结构，从而使从压缩测量中恢复信号成为可能。我们研究了从压缩测量中对低秩信号模型进行参数估计的统计性能界。具体而言，我们推导了一般低秩模型的 Cramer-Rao 界（CRB），并表明：若要存在具有有限估计方差的无偏估计器，压缩样本数必须大于源数。我们进一步考虑了其在符合低秩信号模型的波达方向（DOA）估计和谱估计中的应用。我们还通过 DOA 估计场景的数值示例研究了压缩对 CRB 的影响，并说明 CRB 如何随压缩程度提高（等价于压缩样本数减少）而增大。
英文摘要：
In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse representation in a finite basis, they possess a sparse structure which makes it possible to recover the signal from compressed measurements. We study the statistical performance bound for parameter estimation in the low-rank signal model from compressed measurements. Specifically, we derive the Cramer-Rao bound (CRB) for a generic low-rank model and we show that the number of compressed samples needs to be larger than the number of sources for the existence of an unbiased estimator with finite estimation variance. We further consider the applications to direction-of-arrival (DOA) and spectral estimation which fit into the low-rank signal model. We also investigate the effect of compression on the CRB by considering numerical examples of the DOA estimation scenario, and show how the CRB increases by increasing the compression or equivalently reducing the number of compressed samples.
