We introduce an analytical model describing the statistical and spectral properties of laser phase noise induced intensity noise in ring-resonator-based modulation. The model is validated with single sideband orthogonal frequency division multiplexing (SSB-OFDM) implemented with a silicon photonics resonantly-assisted Mach-Zehnder modulator (RA-MZM). Excellent agreement of experimental data with full link simulations, in which phase noise conversion is treated with the analytical model, confirms its validity. Moreover, we demonstrate 30 Gb/s raw data rate transmission with SSB-OFDM over 20 km of single-mode fiber with a bit error ratio below the 20% forward error correction (FEC) limit for three independently run channels of the RA-MZM, each supplied with off-the-shelf 1 MHz linewidth distributed feedback lasers.