Noise properties of a bidirectional optical fiber transmission system using Raman amplification are analyzed. Analytical expressions for both forward and backward amplified spontaneous emission (ASE) noise are established in terms of system parameters. The signal to ASE noise ratio (SNR) and the achievable repeater length are discussed. Based on the results, we find that there exist optimum pump and initial power levels for the maximum SNR and repeater spacing. The maximum system transmission length and accumulated ASE noise for a multiple‐amplifier system are calculated. A maximum system transmission length up to 5,000 km with 12 dB SNR is then predicted.