Abstract
We consider the capacity optimization of submarine links when including
a realistic model of the gain-flattened constant-pump erbium doped fiber
amplifiers (EDFA). While Perin et al. [1] numerically attacked this
optimization for Constant-Gain (CG) amplified links, we extend the
analysis also to more realistic submarine constant
power-spectral-density (CPSD) links. As in [1], we concentrate on a
single spatial mode of a spatial division multiplexed (SDM) link at low
EDFA pump power Pp, and thus consider only the impairments of amplified
spontaneous emission noise. Here we adopt a novel semi-analytical
approach which consists of fixing the inversion x1 of the first EDFA
(the state-variable of the link) and analytically finding capacity C(x1)
by searching over the x1-feasible input wavelength division multiplexed
(WDM) PSD distributions. Then the optimum inversion x1 that maximizes
C(x1) is numerically obtained. This approach enables us to get both
approximate (for CG links) and exact (for CPSD links)
capacity-maximizing WDM input distributions, which vary inversely with
the EDFA gain profile. For CG links the optimal WDM allocation is called
the gain-shaped water-filling. Other practical allocations are analyzed,
such as the signal to noise ratio equalizing allocation (CSNR), and the
constant input power (CIP) allocation which uses a flat WDM
distribution. We find that, for typical submarine span attenuations
around 10dB and when the link works at the optimal inversion x1, CIP and
CSNR achieve essentially the same capacity as the optimal allocation. At
sufficiently large pump Pp (>= 30 mW) the optimal inversion
x1 is such that the EDFA gain at 1538nm equals the span attenuation, for
EDFA emission and absorption as in [1]. When span attenuations
increase to 20dB, then we start seeing an advantage of the optimal
allocation. Another key finding is that optimized CG and CPSD links
behave roughly the same, with a slightly superior capacity for CPSD.