We provide numerical verification of a feed-forward, heterodyne-based phase noise reduction scheme using single-sideband modulation that obviates the need for optical filtering at the output. The main benefit of a feed-forward heterodyne linewidth reduction scheme is the simultaneous reduction of the linewidth of all modes of a mode-locked laser (MLL) to that of a narrow-linewidth single-wavelength laser. At the heart of our simulator is an MLL model of reduced complexity. Importantly, the main issue being treated is the jitter of MLLs and we show how to create numerical waveforms that mimic the random-walk nature of timing jitter of pulses from MLLs. Thus, the model does not need to solve stochastic differential equations that describe the MLL dynamics, and the model calculates self-consistently the line-broadening of the modes of the MLL and shows good agreement with both the optical linewidth and jitter. The linewidth broadening of the MLL modes are calculated after the phase noise reduction scheme and we confirm that the phase noise contribution from the timing jitter still remains. Finally, we use the MLL model and phase noise reduction simulator within an optical communications system simulator and show that the phase noise reduction technique could enable MLLs as optical carriers for higher-order modulation formats, such as 16-state and 64-state quadrature amplitude modulation.