Autocorrelation Function for Dispersion-Free Fiber Channels with Distributed Amplification

Abstract

Optical fiber signals with high power exhibit spectral broadening that seems to limit capacity. To study spectral broadening, the autocorrelation function of the output signal given the input signal is derived for a simplified fiber model that has zero dispersion, distributed optical amplification (OA), and idealized spatial noise processes. 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 one-half 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.

Accepted for publication in the IEEE Trans. Inf. Theory. The main changes are in Sec. III-D: the noise (35), which is based on (33), does not give jointly Wiener spatial processes that are needed for analysis. However, Appendix A points out that the noise in (33) is itself an idealization. We suspect that the capacity bounds for the idealized case provide insight on the general case