This paper presents a Joint Deep Probabilistic Subsampling framework with Cramér-Rao Bound (CRB) Integration (J-DPSC), which optimizes both transmit and receive antenna selection independently, enabling robust DoA estimation in mono-static and bi-static radar modes. Our method incorporates a differentiable worst-case CRB computation for end-to-end optimization. Additionally, sidelobe level (SLL) suppression is naturally integrated into the training process through data constraints, without requiring explicit penalty terms. Compared to prior methods, J-DPSC significantly reduces model complexity and the number of trainable parameters while maintaining high DoA estimation accuracy. Beampattern results demonstrate the effectiveness of our approach in improving performance with an acceptable SLL, making it well-suited for practical sparse array design in automotive radar applications.