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Photonic microwave downconversion based on an optoelectronic oscillator (OEO) is interesting because the local oscillator signal is directly extracted from the RF signal, but some of the frequency components in the RF signal would leak to the oscillation signal due to the limited rejection ratio of the electrical bandpass filter in the OEO, which degrades the downconverted signal. In this paper, a high-performance photonic microwave downconverter based on a frequency-doubling OEO (FD-OEO) is proposed and demonstrated to avoid the direct degradation from the RF signal. A 20-GHz RF signal with 1-Gb/s data modulation is successfully downconverted by the FD-OEO. The phase noise at 10-kHz frequency offset of the extracted RF carrier by the FD-OEO is 14 dB lower than that extracted by a conventional OEO, and the receiver sensitivity of the downconverted signal has a 1.173-dB improvement. The downconverter needs only low-frequency devices, which may find application in phased-array antenna arrays, electronic warfare receivers, avionics, and wireless communication systems.