论文标题
无均匀阵列的无网状DOA估计和根部音乐
Gridless DOA Estimation and Root-MUSIC for Non-Uniform Arrays
论文作者
论文摘要
在非均匀阵列（NUA）情况下解决了无网向到达方向（DOA）估计的问题。传统上，无网状的DOA估计和根本音乐仅适用于均匀线性阵列（ULA）的测量。这是因为ULA测量的样品协方差矩阵具有toeplitz结构，并且这两种算法均基于toeplitz矩阵的Vandermonde分解。 Vandermonde的分解将toeplitz基质分解为其谐波组件，从中估算了DOA。首先，我们介绍“不规则” toeplitz矩阵和不规则的Vandermonde分解（IVD），该分解（IVD）概括了Vandermonde分解以应用于更通用的矩阵集。结果表明，IVD与音乐和根本算法有关。接下来，使用IVD概括为NUA案例。使用交替的投影（AP）解决了最终的非凸优化问题。对基于AP的解决方案进行了数值分析，该解决方案表明，对NUAS的概括与传统无网状DOA具有相似的性能。
The problem of gridless direction of arrival (DOA) estimation is addressed in the non-uniform array (NUA) case. Traditionally, gridless DOA estimation and root-MUSIC are only applicable for measurements from a uniform linear array (ULA). This is because the sample covariance matrix of ULA measurements has Toeplitz structure, and both algorithms are based on the Vandermonde decomposition of a Toeplitz matrix. The Vandermonde decomposition breaks a Toeplitz matrix into its harmonic components, from which the DOAs are estimated. First, we present the `irregular' Toeplitz matrix and irregular Vandermonde decomposition (IVD), which generalizes the Vandermonde decomposition to apply to a more general set of matrices. It is shown that the IVD is related to the MUSIC and root-MUSIC algorithms. Next, gridless DOA is generalized to the NUA case using IVD. The resulting non-convex optimization problem is solved using alternating projections (AP). A numerical analysis is performed on the AP based solution which shows that the generalization to NUAs has similar performance to traditional gridless DOA.
