Autonomous driving requires very accurate perception of the surrounding environment. Multiple sensors are used to achieve highly accurate object detection and environment perception. Among all types of sensors, cameras and automotive radars are two major sensors used in most high-end commercial vehicles. To achieve good performance in perception tasks, machine learning and deep neural networks are utilized and have shown the advantages of robustness and generalization. Although deep neural networks were largely developed in the context of image processing, they are rarely seen in radar perception systems. In this dissertation, a new radar perception neural network with several new methods and techniques is proposed. In recent years, the sampling methods applied in neural networks have attracted much research interest. Sampling increases the flexibility of rigid convolution kernels inside convolutional neural networks. It samples the feature map of intermediate output based on a pre-defined or dynamic data-dependent sampling grid to re-arrange the location of feature vectors. Several new approaches and designs were proposed in previous works to further utilize sampling methods in advanced neural network architectures. These approaches have shown good performance in both image perception task and radar perception tasks. Many challenges and issues are discussed and solved through the proposal of new methods, network designs or processing techniques. These applications and solutions are general, and as they are instructive in automotive use cases, they can be easily extended to other use cases.