Stimulated Brillouin scattering (SBS) currently limits the power scaling of narrow-linewidth amplifiers. To date, several techniques have been employed to suppress SBS. Within these SBS suppressing techniques, the phase modulation technique is a preferable approach to obtaining kilowatt-level narrow-linewidth laser sources. In this manuscript, we numerically investigate the influence of phase modulation signals on linewidth and SBS threshold, and discuss how to choose an appropriate modulation signal for suppressing SBS with less linewidth broadening. Three types of signals are studied, including sinusoidal signal, white noise signal (WNS), and pseudo-random binary sequence signal (PRBS). Signal parameters such as modulation frequency and modulation depth are also optimized. It is found that the linewidth increases linearly with the modulation frequency, and the linewidth is largest for WNS modulation for the same modulation frequency. Specially, the linewidth is approximate to the modulation frequency for PRBS modulation. In the case of sinusoidal modulation, the spectra exhibit a series of discrete sidebands at integer multiples of the modulation frequency while the spectral power density is almost continuous for WNS modulation. In the case of PRBS modulation, the spectra contain periodic features that are distributed as a function of modulation frequency and pattern length. The SBS threshold grows to a maximum at~100 MHz modulation frequency for the case of sinusoidal signal modulation, which can be further increased by increasing the modulation depth. The SBS threshold can be further increased by implementing the cascade sinusoidal signal modulation. When WNS modulation is employed, the SBS threshold increases almost linearly with the modulation frequency and has an S-shaped increase with the modulation depth. For the PRBS modulation, the pattern length has an optimal value for SBS suppressing:the SBS threshold increases almost linearly below a frequency, but keeps stable above that frequency. The PRBSs with longer pattern lengths tend to suppress SBS more effectively in higher modulation frequency regime than those with the shorter ones. In the commonly used 1-2 GHz frequency regimes, the PRBS with a pattern length of 7 provides the best SBS mitigation, and the pattern length should be longer when the frequency is higher than 2 GHz. It should also be noted that the SBS threshold is highest when the modulation depth is close to the half-wave voltage (π). From the aspect of SBS suppression, the PRBS is superior to other two modulation signals, which can achieve higher SBS threshold with less linewidth broadening. The investigation can present a reference for the phase modulation signal designing in the power scaling of the narrow-linewidth fiber amplifiers.