Terahertz wave radar offers a higher resolution and smaller aperture compared with microwave radar. However, despite the emergence of terahertz sources and detectors suitable for radar front ends, the integration of a phased-array radar system remains challenging due to the lack of phase shifters and circulators, the basic components for beam steering and input–output isolation. Here we show that leaky-wave coherence tomography, which can integrate a terahertz radar system using a pair of reverse-connected leaky-wave antennas, can be used to implement beam steering and homodyne detection in one package. Our approach can detect direction and range without using phase shifters, circulators, half-mirrors, lenses or mechanical scanners, providing a compact, penetrating and high-resolution radar system suitable for mobile devices and drones. To illustrate the capabilities of the technique, we use it to create a remote heartbeat detector that can measure the chest displacement of a person through their clothes.