Based on the self-mixing and heterodyne mixing effects of antenna-coupled AlGaN/GaN HEMT terahertz detectors, two receiving front-ends, namely homodyne receiver and heterodyne receiver, were designed and tested in 340 GHz frequency band, respectively. The equivalent noise powers of two receivers were calculated through measuring the signal-noise ratio (SNR) of the signal and the received power. The experimental result indicates that the responsivity of detectors is about 20 mA/W for homodyne receiver, the noise equivalent power is about -64.6 dBm/Hz^1/2 for homodyne receiver and -114.79 dBm/Hz for heterodyne receiver, respectively. With the same carrier power and the signal bandwidth, the SNR of the heterodyne receiver is greater than that of the homodyne receiver when the local terahertz source power is greater than -7 dBm. The heterodyne receiver exhibits excellent demodulation characteristics: a local terahertz source power above 0 dBm boosts the SNR by more than 10 dB compared with the homodyne receiver.