Attention mechanisms have been widely integrated with various neural networks to boost performance. However, when an attention mechanism was applied to a radar ego-velocity estimation network, the importance of carefully handling the amplitude and phase of complex-valued tensor was revealed. Therefore, in this study, we present a self-attention mechanism designed to handle complexvalued tensors in order to capture the rich contextual relationships implied within amplitude and phase. To exploit the advantages of complex-valued attention (CA), we evaluated its impact while performing egovelocity estimation tasks based on radar data, whose amplitude and phase are related to the electromagnetic scattering of the target being observed. Radars are suitable sensors for such tasks as they are capable of long-range detection and instantaneous velocity measurement under variable weather and lighting conditions. In particular, we coupled our CA module with complex-valued neural networks, known to be particularly powerful for handling wave phenomena. The proposed method exhibits robust estimation performance, regardless of whether the Doppler ambiguity problem occurs and eliminates the dependence on preprocessing stages, including target detection and static target indication. Furthermore, it achieves improved stability during training via geometrical constraint regularization, and implicitly allows velocity conversion between the sensor and vehicle frames, even if the mount information of the sensor was not provided. Finally, ablation experiments conducted on extensive real-world datasets show noticeable improvement in estimation performance. INDEX TERMS Automotive radar; complex-valued attention; complex-valued neural network; deep learning; ego-velocity estimation This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.