  Progress made in optical references, including ultra-stable Fabry-Perot
cavities, optical frequency combs and optical atomic clocks, have driven the
need for ultra-stable optical fiber networks. Telecom-wavelength ultra-pure
optical signal transport has been demonstrated on distances ranging from the
laboratory scale to the continental scale. In this manuscript, we present a
Doppler-cancellation setup based on a digital phase-locked loop for
ultra-stable optical signal dissemination over fiber. The optical phase
stabilization setup is based on a usual heterodyne Michelson-interferometer
setup, while the Software Defined Radio (SDR) implementation of the
phase-locked loop is based on a compact commercial board embedding a field
programmable gate array, analog-to-digital and digital-to-analog converters.
Using three different configurations including an undersampling method, we
demonstrate a 20 m long fiber link with residual fractional frequency
instability as low as $10^{-18}$ at 1000 s, and an optical phase noise of $-70$
dBc/Hz at 1 Hz with a telecom frequency carrier.
