In this paper, we demonstrate a self-homodyne coherent system with a significantly narrowed effective linewidth using optical carrier recovery based on stimulated Brillouin scattering (SBS), employing only coarse path length matching. The effective linewidth of the SBS-based receiver system is reduced from 75 kHz to less than 2 kHz, which is estimated by Lorentzian fitting of power spectra, and confirmed by simulation results of the tolerance window length for phase noise compensation (PNC) with different linewidth. Both experimental and numerical studies on the tracking requirements on PNC algorithms confirm effective linewidth reduction to this level, and show a 32x relaxation of the phase recovery tracking window length. This highlights the potential to significantly reduce the computational complexity of PNC even in coarsely optimized SBS-based self-homodyne coherent systems, providing an alternative to using demanding ultra-low linewidth lasers.