Diffusion-Enhanced Multidimensional Variational Line Spectral Estimation

Multidimensional line spectral estimation plays a fundamental role in communication and sensing systems, where it is often used for estimating channel parameters such as angles of arrival and time delays. Existing channel parameter estimation methods often suffer from limited resolution, high computational complexity, or strong sensitivity to noise, and the multidimensional variational line spectral estimation (MDVALSE) algorithm, although effective in off-grid estimation, degrades significantly under low signal-to-noise ratio (SNR) conditions. Recently, generative models, especially diffusion models, have demonstrated strong capabilities in prior-guided denoising and reconstruction of noise-contaminated signals by effectively learning the underlying data structure. Motivated by this, we propose a diffusion-enhanced multidimensional variational line spectral estimation algorithm for channel parameter extraction. Specifically, a diffusion model is first employed to denoise the estimated channel response and improve the observation quality. Then, considering that the residual error after diffusion-based denoising is generally colored rather than white, a colored-noise extension of MDVALSE, termed C-MDVALSE, is derived to better match the statistical structure of the denoised observations. Simulation results in various scenarios show that the proposed algorithm achieves more accurate channel reconstruction and channel parameter estimation than MDVALSE and other existing methods, with particularly significant improvements in low-SNR regimes.