Performance of direction of arrival (DOA) estimation is one of the most important issues in array signal processing. Subspace-based algorithms provide a good compromise between the estimation accuracy and computational complexity. However, these methods are exposed to performance breakdown at low SNR scenarios. A major reason for such performance breakdown is the subspace swap phenomenon (intersubspace leakage). In this article, we elaborate on a novel modified signal subspace model through exploiting a supervised index for the estimation of DOA. With the developed model we refine the signal subspace so as to enhance the performance of the DOA estimation. In the proposed scheme, we define a fuzzy similarity matrix for the eigenvalues of the array output correlation matrix to capture the distribution of the eigenvalues. Then, we build up a transformation matrix between the fuzzy similarity matrix and the eigenspace of the correlation matrix, and construct a nonlinear transformation function to adjust the fuzzy similarity matrix. Subsequently, we define a supervised evaluation index named signal subspace reconstruction error for DOA estimation and construct a cost function of the signal subspace to develop a supervised model for the signal subspace. The signal subspace can be modified through adjusting the parameter in the nonlinear transformation function and optimizing the abovementioned cost function. Finally, the performance of DOA estimation can be enhanced with the modified signal subspace. The main characteristic of the proposed model is circularly applied feedback of the estimated DOA for refining the estimated subspace. It is a closed loop and supervised method not reported before. This article opens a specific way for improving the performance of the DOA estimation in array signal processing by a supervised index. However, the proposed method is still unsatisfying in some scopes of signal-to-noise ratio. We believe that exploiting a validity index for DOA estimation in array signal processing is still a general and interesting problem.

中文翻译：

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基于监督指标的低信噪比高精度DOA估计算法

波达方向（DOA）估计的性能是阵列信号处理中最重要的问题之一。基于子空间的算法在估计精度和计算复杂度之间提供了很好的折衷。但是，这些方法在低 SNR 场景下会出现性能故障。这种性能下降的一个主要原因是子空间交换现象（子空间间泄漏）。在本文中，我们通过利用监督指标估计 DOA 来详细阐述一种新的修正信号子空间模型。通过开发的模型，我们细化了信号子空间，以提高 DOA 估计的性能。在所提出的方案中，我们为数组输出相关矩阵的特征值定义了一个模糊相似度矩阵，以捕捉特征值的分布。然后，我们在模糊相似矩阵和相关矩阵的特征空间之间建立一个变换矩阵，并构造一个非线性变换函数来调整模糊相似矩阵。随后，我们定义了一个名为信号子空间重构误差的监督评价指标，用于DOA估计，并构建了信号子空间的成本函数，以开发信号子空间的监督模型。可以通过调整非线性变换函数中的参数和优化上述代价函数来修改信号子空间。最后，DOA估计的性能可以通过修改后的信号子空间来增强。所提出模型的主要特点是循环应用估计的 DOA 反馈来细化估计的子空间。这是一种以前没有报道过的闭环和监督方法。本文为通过监督索引提高阵列信号处理中 DOA 估计的性能开辟了一条具体途径。然而，所提出的方法在信噪比的某些范围内仍然不能令人满意。我们认为，在阵列信号处理中利用 DOA 估计的有效性指标仍然是一个普遍而有趣的问题。