空间平滑方案在大阵列中的性能分析
Performance analysis of spatial smoothing schemes in the context of large arrays
摘要：
本文讨论了在观测数$N$明显小于传感器数$M$，且平滑参数$L$使得$M$和$NL$具有相同数量级的情况下，利用传感器阵列的空间平滑子空间DOA估计方案的统计特性。该上下文由渐进机制建模，其中$NL$和$M$都以相同的速率向$\infty$收敛。在最近的作品致力于研究（未平滑）子空间方法的情况下，$M$和$N$是相同的数量级，它表明，它仍然是可能的，以获得改进的DOA估计称为广义MUSIC与空间平滑（G-MUSIC SS）。这项工作的关键成分是一个技术性的结果表明，最大的奇异值和相应的奇异向量的低秩确定性扰动的某些高斯块汉克尔大随机矩阵的行为，如果后者的随机矩阵的条目是独立同分布。这允许得出结论，当源的数量和它们的DoA不与$M,N,L,$成比例时，建模宽间隔DoA场景的情况，则传统和广义空间平滑子空间方法都提供一致的DoA估计，其收敛速度比$\frac{1}{M}$快。DoA的情况下，间隔的波束宽度的顺序，模型紧密间隔的源，也被认为是。结果表明，G-MUSIC SS估计的收敛速度是不变的，但它不再是MUSIC SS的情况。
英文摘要：
This paper adresses the statistical behaviour of spatial smoothing subspace DoA estimation schemes using a sensor array in the case where the number of observations $N$ is significantly smaller than the number of sensors $M$, and that the smoothing parameter $L$ is such that $M$ and $NL$ are of the same order of magnitude. This context is modelled by an asymptotic regime in which $NL$ and $M$ both converge towards $\infty$ at the same rate. As in recent works devoted to the study of (unsmoothed) subspace methods in the case where $M$ and $N$ are of the same order of magnitude, it is shown that it is still possible to derive improved DoA estimators termed as Generalized-MUSIC with spatial smoothing (G-MUSIC SS). The key ingredient of this work is a technical result showing that the largest singular values and corresponding singular vectors of low rank deterministic perturbation of certain Gaussian block-Hankel large random matrices behave as if the entries of the latter random matrices were independent identically distributed. This allows to conclude that when the number of sources and their DoA do not scale with $M,N,L,$ a situation modelling widely spaced DoA scenarios, then both traditional and Generalized spatial smoothing subspace methods provide consistent DoA estimators whose convergence speed is faster than $\frac{1}{M}$. The case of DoA that are spaced of the order of a beamwidth, which models closely spaced sources, is also considered. It is shown that the convergence speed of G-MUSIC SS estimates is unchanged, but that it is no longer the case for MUSIC SS ones.
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