High-resolution automotive radar sensors are required to meet the high bar of autonomous vehicle needs and regulations. However, current radar systems are limited in their angular resolution, causing a technological gap. An industry and academic trend to improve angular resolution by increasing the number of physical channels also increases system complexity, requires sensitive calibration processes, lowers robustness to hardware malfunctions, and drives higher costs. We offer an alternative approach, named Radar signal Reconstruction using Self Supervision (R2S2), which substantially improves the angular resolution of a given radar array without increasing the number of physical channels. R2S2 is a family of algorithms that use a deep neural network (DNN) with complex range-Doppler radar data as input and trained in a self-supervised method using a loss function that operates in multiple data representation spaces. Improvement of 4× in angular resolution was demonstrated using a real-world dataset collected in urban and highway environments during clear and rainy weather conditions.