A heterodyne correlation radiometer is considered for the sensitive detection of radiating species whose Doppler shift is known, but whose presence we wish to affirm. Such radiation (which may be actively induced) can arise, for example, from remote molecular emitters, impurities and pollutants, trace minerals, chemical agents, or a general multiline source. A radiating sample of the species to be detected is physically made a part of the laboratory receiver, and serves as a kind of frequency-domain template with which the remote radiation is correlated, after heterodyne detection. The system is expected to be especially useful for the detection of sources whose radiated energy is distributed over a large number of lines, with frequencies that are not necessarily known. Requirements for local oscillator stability and tunability are less stringent than in the conventional heterodyne system and the use of a multiline local oscillator may be advantageous. It is shown that the minimum detectable power is expressible in a form similar to that for conventional heterodyning (for both quantum-noise-limited and Johnson-noise-limited detectors). The notable distinction is that the performance of the proposed system improves with increasing density of detected remotely radiating signal lines and increasing radiation power from the local sample. Performance degradation due to undesired impurity radiation is considered and shown to be tolerable in most cases. The technique should be applicable over a broad frequency range from the microwave to the optical, with its most likely use in the infrared.