提出可缩放不变的损失函数，提升无网格波达方向估计精度。
A Comparative Study of Invariance-Aware Loss Functions for Deep Learning-based Gridless Direction-of-Arrival Estimation
- 基于信号与预测矩阵间尺度不变信干比设计新损失函数。
- 缩放不变损失优于非不变损失，但逊于基变换不变的子空间损失。
- 适合做阵列信号处理与深度学习结合的研究者参考。
协方差矩阵重构是稀疏线性阵列无网格波达方向（DoA）估计中最广泛使用的指导目标，许多基于半定规划（SDP）的方法均属此类。尽管深度学习方法能构建更复杂的损失函数，多数仍依赖协方差矩阵重构。本文提出新型损失函数，具备矩阵缩放不变性，并对不同不变性程度的损失函数进行对比研究。所提损失函数基于目标矩阵与预测矩阵格拉姆矩阵间的尺度不变信干比（SIR）。数值结果表明，缩放不变损失优于非不变损失，但劣于近期提出的基变换不变子空间损失。该结果表明，在深度学习驱动的无网格DoA估计中，设计更高阶不变性的损失函数更具优势。
原文摘要 · Abstract (English)
Covariance matrix reconstruction has been the most widely used guiding objective in gridless direction-of-arrival (DoA) estimation for sparse linear arrays. Many semidefinite programming (SDP)-based methods fall under this category. Although deep learning-based approaches enable the construction of more sophisticated objective functions, most methods still rely on covariance matrix reconstruction. In this paper, we propose new loss functions that are invariant to the scaling of the matrices and provide a comparative study of losses with varying degrees of invariance. The proposed loss functions are formulated based on the scale-invariant signal-to-distortion ratio between the target matrix and the Gram matrix of the prediction. Numerical results show that a scale-invariant loss outperforms its non-invariant counterpart but is inferior to the recently proposed subspace loss that is invariant to the change of basis. These results provide evidence that designing loss functions with greater degrees of invariance is advantageous in deep learning-based gridless DoA estimation.
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