Direction augmentation (DA) and spatial smoothing (SS), followed by a subspace method such as ESPRIT or MUSIC, are two simple and successful approaches that enable localization of more uncorrelated sources than sensors with a proper sparse array. In this paper, we carry out nonasymptotic performance analyses of DA-ESPRIT and SS-ESPRIT in the practical finite-snapshot regime. We show that their absolute localization errors are bounded from above by $C_1\frac{\max\{\sigma^2, C_2\}}{\sqrt{L}}$ with overwhelming probability, where $L$ is the snapshot number, $\sigma^2$ is the Gaussian noise power, and $C_1,C_2$ are constants independent of $L$ and $\sigma^2$, if and only if they can do exact source localization with infinitely many snapshots. We also show that their resolution increases with the snapshot number, without a substantial limit. Numerical results corroborating our analysis are provided.

翻译：方向增强（DA）和空间平滑（SS）结合子空间方法（如ESPRIT或MUSIC），是两种简单有效的途径，能够利用适当稀疏阵列实现比传感器数量更多的非相干信源定位。本文针对实际有限快拍场景下DA-ESPRIT和SS-ESPRIT算法开展非渐近性能分析。我们证明，当且仅当算法在无限快拍下能够实现精确信源定位时，其绝对定位误差以压倒性概率被$C_1\frac{\max\{\sigma^2, C_2\}}{\sqrt{L}}$上界约束，其中$L$为快拍数，$\sigma^2$为高斯噪声功率，$C_1,C_2$为与$L$和$\sigma^2$无关的常数。同时证明，算法的分辨率随快拍数增加而提升，且不存在实质性上限。文中还提供了验证理论分析的数值结果。