In this work we experimentally demonstrate the compensation of nonlinearities introduced by a semiconductor optical amplifier (SOA) operating as a power booster in a field-modulated direct detection fiber-optic system transmitter. We show that a combination of digital pre-compensation to deal with SOA nonlinearities, and digital post-compensation after Kramers-Kronig receiver for mitigating the impacts of chromatic dispersion and signal-signal beat interference (SSBI) is an effective scheme to gain similar to 3dB in ROSNR in presence of SOA nonlinearity at 3dB of gain compression.