We present a general treatment of multispan effects on Shannon channel capacity for dispersion-free nonlinear optical fiber transmission. We have derived a closed-form formula that is exact and applicable for arbitrary input signal power and noise power. The nonlinear interference among the accumulated Kerr nonlinear noises and the amplifier noises along each span will be investigated. The dependence of the channel capacity on various operating conditions and system parameters will be studied. We have derived a simple scaling law for the Shannon capacity as given by log2[1 + C Ns-4/3 Nc-2/3 -2/3 PW-2/3] for Ns spans and Nc channels, where is the Kerr nonlinearity coefficient and PW is the average noise power density for each amplifier.
Jau Tang, "The Multispan Effects of Kerr Nonlinearity and Amplifier Noises on Shannon Channel Capacity of a Dispersion-Free Nonlinear Optical Fiber," J. Lightwave Technol. 19, 1110- (2001)