We introduce a new principle for distance measurement in the terahertz-wave range using a resonant-tunneling-diode (RTD) oscillator as a source at 511 GHz and relying on the frequency-modulated continuous-wave (FMCW) radar technique. Unlike the usual FMCW radar, where the sawtooth frequency modulation is applied to the carrier, we propose applying it to a subcarrier obtained by amplitude modulation; this is advantageous when the source cannot be controlled precisely in oscillation frequency, but can easily be modulated in amplitude, as is the case of the RTD oscillator. The detailed principle and a series of proof-of-concept experimental results are presented.