In this paper, we address the problem of direction of arrival (DOA) estimation for multiple targets in the presence of sensor failures in a sparse array. Generally, sparse arrays are known with very high-resolution capabilities, where N physical sensors can resolve up to $\mathcal{O}(N^2)$ uncorrelated sources. However, among the many configurations introduced in the literature, the arrays that provide the largest hole-free co-array are the most susceptible to sensor failures. We propose here two machine learning (ML) methods to mitigate the effect of sensor failures and maintain the DOA estimation performance and resolution. The first method enhances the conventional spatial smoothing using deep neural network (DNN), while the second one is an end-to-end data-driven method. Numerical results show that both approaches can significantly improve the performance of MRA with two failed sensors. The data-driven method can maintain the performance of the array with no failures at high signal-tonoise ratio (SNR). Moreover, both approaches can even perform better than the original array at low SNR thanks to the denoising effect of the proposed DNN

翻译：本文针对稀疏阵列中传感器失效情况下的多目标波达方向（DOA）估计问题展开研究。通常，稀疏阵列具有超高分辨能力，N个物理传感器可解析多达$\mathcal{O}(N^2)$个非相干信源。然而，在文献提出的多种阵列构型中，提供最大无空洞共阵的阵列对传感器失效最为敏感。本文提出两种机器学习方法以抑制传感器失效影响，维持DOA估计性能与分辨率：第一种方法利用深度神经网络（DNN）增强传统空间平滑技术，第二种方法采用端到端数据驱动方案。数值结果表明，两种方法均能显著提升含两个故障传感器的最大冗余阵列（MRA）性能。在高信噪比（SNR）条件下，数据驱动方法可维持无故障阵列的估计性能。此外，得益于所提DNN的去噪效应，两种方法在低SNR区域的性能甚至优于原始阵列。