Techniques and apparatuses are described that implement a smart-device-based radar system capable of detecting a frame-of-reference change. In particular, a radar system includes a frame-of-reference machine-learned module trained to recognize whether or not the radar system's frame of reference changes. The frame-of-reference machine-learned module analyzes complex radar data generated from at least one chirp of a reflected radar signal to analyze a relative motion of at least one object over time. By analyzing the complex radar data directly using machine learning, the radar system can operate as a motion sensor without relying on non-radar-based sensors, such as gyroscopes, inertial sensors, or accelerometers. With knowledge of whether the frame-of-reference is stationary or moving, the radar system can determine whether or not a gesture is likely to occur and, in some cases, compensate for the relative motion of the radar system itself.