Techniques and apparatuses are described that implement a smartphone-based radar system capable of detecting user gestures using coherent multi-look radar processing. Different approaches use a multi-look interferometer or a multi-look beamformer to coherently average multiple looks of a distributed target across two or more receive channels according to a window that spans one or more dimensions in time, range, or Doppler frequency. By coherently averaging the multiple looks, a radar system generates radar data with higher gain and less noise. This enables the radar system to achieve higher accuracies and be implemented within a variety of different devices. With these accuracies, the radar system can support a variety of different applications, including gesture recognition or presence detection.