The Amplified Spontaneous Emission (ASE) noise, equivalent spontaneous emission factor and equivalent noise factor for the Raman Amplifier (RA) as well as the respective impacts of the the ASE noise, Rayleigh noise, optical fiber length and the switching gain in the RA on the Signal Noise Ratio (SNR) of optical receivers are theoretically analyzed, and then the Double Rayleigh Backscattering (DRB) noise are also theoretically analyzed and calculated. Furthermore, the numerically related simulations are also implemented. The calculation and simulation results show that, compared with the Erbium-Doped Fiber Amplifier (EDFA),the RA can improve the SNR of optical receivers under the condition of the same input signal; the equivalent spontaneous emission factor is less than 1 and decreases with the increase of the switching gain, so this characteristics of the RA are superior to that of the EDFA.Moreover,when the gain of the RA is less than 15 dB the Rayleigh noise of the RA can be ignored. Also, some other significant conclusions to play the important roles in guiding the optimal design of the RA are obtained.