Beyond White Noise: Integrating Spectral Gaussian Process into Diffusion Models for Wireless Signal Recognition Pre-training

Wireless signal recognition (WSR) aims to infer attributes of passively received wireless signals, and is widely used in radio system. Existing WSR models can learn dependencies among discrete wireless signal samples implicitly, but generally do not make the signal correlation structure an explicit target or prior during representation learning. Consequently, these dependencies must be discovered from the training data and architectural bias alone, without a direct covariance-aware learning objective. Therefore, we propose Spectral Gaussian Process Diffusion (SGP-Diff), a self-supervised framework that replaces isotropic white noise with length-scale-conditioned spectral GP noise that couples neighboring frequency bins. The model predicts this structured noise with a covariance-normalized denoising objective. A linear second-order analysis shows how the optimal denoiser depends jointly on the data and noise covariances. Across four datasets covering three WSR tasks, SGP-Diff obtains the best reported accuracy among the compared methods and exceeds the strongest baseline by 1.83% on average. Further analysis results have validated the effectiveness and practical efficiency of the designed module.