Design of inline amplifier gains and spacings to minimize the phase noise in optical transmission systems

In optical fiber transmission systems using inline amplifiers, the interaction of a signal and an amplifier noise through the Kerr effect leads to a nonlinear phase noise that can impair detection of phase-modulated signals. The authors show how to minimize the variance of the total phase noise (linear plus nonlinear) by a choice of the number of inline amplifiers N and their spacings and gains, assuming a fixed total system length L and an overall compensation of the fiber loss. In the case of a uniform amplifier spacing and a per-span loss compensation, there exists a finite N that minimizes the total phase noise. This contrasts with the well-known observation that a linear phase noise alone is minimized by a choice of an infinite N. Relaxing the constraints of the uniform spacing and/or the per-span loss compensation leads to further reduction of the total phase noise. The optimization of the spacings and the gains can be approximately formulated as a convex problem. In typical terrestrial and transoceanic systems, the total-phase-noise variance can be reduced by up to 45% and 83%.