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Automotive perception systems are obligated to meet high requirements. While optical sensors such as Camera and Lidar struggle in adverse weather conditions, Radar provides a more robust perception performance, effectively penetrating fog, rain, and snow. Since full Radar tensors have large data sizes and very few datasets provide them, most Radar-based approaches work with sparse point clouds or 2D projections, which can result in information loss. Additionally, deep learning methods show potential to extract richer and more dense features from low level Radar data and therefore significantly increase the perception performance. Therefore, we propose a 3D projection method for fast-Fourier-transformed 4D Range-Azimuth-Doppler-Elevation (RADE) tensors. Our method preserves rich Doppler and Elevation features while reducing the required data size for a single frame by 91.9% compared to a full tensor, thus achieving higher training and inference speed as well as lower model complexity. We introduce RADE-Net, a lightweight model tailored to 3D projections of the RADE tensor. The backbone enables exploitation of low-level and high-level cues of Radar tensors with spatial and channel-attention. The decoupled detection heads predict object center-points directly in the Range-Azimuth domain and regress rotated 3D bounding boxes from rich feature maps in the cartesian scene. We evaluate the model on scenes with multiple different road users and under various weather conditions on the large-scale K-Radar dataset and achieve a 16.7% improvement compared to their baseline, as well as 6.5% improvement over current Radar-only models. Additionally, we outperform several Lidar approaches in scenarios with adverse weather conditions. The code is available under this https URL.