While tensor-based methods excel at Direction-of-Arrival (DOA) estimation, their performance degrades severely with faulty or sparse arrays that violate the required manifold structure. To address this challenge, we propose Tensor Completion for Defective Arrays (TCDA), a robust algorithm that reformulates the physical imperfection problem as a data recovery task within a virtual tensor space. We present a detailed derivation for constructing an incomplete third-order Parallel Factor Analysis (PARAFAC) tensor from the faulty array signals via subarray partitioning, cross-correlation, and dimensional reshaping. Leveraging the tensor's inherent low-rank structure, an Alternating Least Squares (ALS)-based algorithm directly recovers the factor matrices embedding the DOA parameters from the incomplete observations. This approach provides a software-defined 'self-healing' capability, demonstrating exceptional robustness against random element failures without requiring additional processing steps for DOA estimation.

翻译：尽管基于张量的方法在波达方向（DOA）估计中表现出色，但当阵列存在缺陷或稀疏性而破坏所需流形结构时，其性能会严重下降。为应对这一挑战，我们提出针对缺陷阵列的张量补全算法（TCDA），该鲁棒算法将物理缺陷问题重新表述为虚拟张量空间内的数据恢复任务。我们详细推导了如何通过子阵划分、互相关和维度重塑，从缺陷阵列信号构建不完整的三阶平行因子分析（PARAFAC）张量。利用张量固有的低秩结构，一种基于交替最小二乘法（ALS）的算法直接从非完整观测中恢复嵌入DOA参数的因子矩阵。该方法提供了一种软件定义的“自修复”能力，在无需额外DOA估计处理步骤的情况下，展现出对随机阵元故障的卓越鲁棒性。