Autocorrelation Function for Dispersion-Free Fiber Channels with Distributed Amplification

The autocorrelation function of the output signal given the input signal is derived in closed form for dispersion-free fiber channels with distributed optical amplification (OA). The autocorrelation function is used to upper bound the output power of bandlimited or time-resolution limited receivers, and thereby to bound spectral broadening and the capacity of receivers with thermal noise. The output power scales at most as the square-root of the launch power, and thus capacity scales at most as onehalf the logarithm of the launch power. The propagating signal bandwidth scales at least as the square-root of the launch power. However, in practice the OA bandwidth should exceed the signal bandwidth to compensate attenuation. Hence, there is a launch power threshold beyond which the fiber model loses practical relevance. Nevertheless, for the mathematical model an upper bound on capacity is developed when the OA bandwidth scales as the square-root of the launch power, in which case capacity scales at most as the inverse fourth root of the launch power.