As typical application scenarios for autonomous vehicles, intersections pose severe challenges to the prediction systems of autonomous driving due to the complex interaction patterns of traffic participants and multi-modal behavioral trajectory features. In view of the problems of existing map-free trajectory prediction methods, such as insufficient accuracy in modeling vehicle interactions, coarse characterization of motion direction features, and limited stability in long-term predictions, a multi-vehicle trajectory prediction method based on spatio-temporal feature enhancement (wave-enhanced spatio-temporal transformer, WAGT) was proposed. Firstly, a spatial interaction modeling framework based on graph neural networks was constructed to characterize the interaction intensity among vehicles through weighted adjacency matrices. Secondly, a dual-channel feature enhancement module based on a wave superposition mechanism was introduced to adaptively model the differences in lateral and longitudinal vehicle motions from the perspectives of amplitude and phase. Finally, a Transformer encoder-decoder integrating time-aware positional encoding was designed to alleviate the problems of position confusion and error accumulation in long-sequence prediction. Quantitative evaluation of the method performance was conducted based on the SIND dataset of Chinese signalized intersections, and comparisons with various map-free trajectory prediction models were performed. Experimental results indicate that the method achieves optimal performance in different prediction horizons. Compared with the representative graph interaction model GRIP, the average displacement error (ADE) and final displacement error (FDE) of the method are improved by 39.70% and 22.90%, respectively, which verifies the advantages of the model in prediction accuracy and robustness under complex intersection scenarios.