With the emergence of AI technologies in next-generation communication systems, machine learning plays a pivotal role due to its ability to address high-dimensional, non-stationary optimization problems within dynamic environments while maintaining computational efficiency. One such application is directional beamforming, achieved through learning-based blind beamforming techniques that utilize already existing radio frequency (RF) fingerprints of the user equipment obtained from the base stations and eliminate the need for additional hardware or channel and angle estimations. However, as the number of users and antenna dimensions increase, thereby expanding the problem's complexity, the learning process becomes increasingly challenging, and the performance of the learning-based method cannot match that of the optimal solution. In such a scenario, we propose a deep reinforcement learning-based blind beamforming technique using a learnable Dolph-Tschebyscheff antenna array that can change its beam pattern to accommodate mobile users. Our simulation results show that the proposed method can support data rates very close to the best possible values.