A Comparative Study of Invariance-Aware Loss Functions for Deep Learning-based Gridless Direction-of-Arrival Estimation
Year: 2025
Type: conference-paper
Abstract: (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.
Authors: Kuan-Lin Chen, Bhaskar D. Rao
Institution: University of California San Diego
Language: English
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408352449