Having in mind the capacity optimization of power-constrained submarine links, by following the work in [1] we first compare the achievable information rate (AIR) of gain-flattened and un-flattened blocks of N b ≤ 12 spans with span loss 16.5dB and with end-span single-stage co-pumped erbium-doped fiber amplifiers (EDFA) when the transmitted wavelength division multiplexed (WDM) channels all have the same transmitted power. All EDFAs have the same pump power and the same physical parameters. In the flattened case, each EDFA is followed by an ideal gain-flattening filter (GFF) that chops off the EDFA gain exceeding the span loss. No GFFs are used in the un-flattended case. We show that, for block length Nb > 7, at large-enough input power the AIR of the GFF block exceeds that of the no-GFF block, while for Nb ≤ 7 at large input power the AIR is about the same. We next build a long submarine link by concatenating the Nb-span no-GFF blocks, and placing a GFF at the last EDFA of each block in order to flatten the block gain down to the Nb-span loss, and calculate the AIR of the resulting sparse-GFF submarine link, accounting also for nonlinear interference. For the 287-span case-study link with span loss 9.5dB used in [5], [9], we show that the best power efficiency is achieved by blocks of size Nb = 6 (i.e., one GFF every 6 spans) when the pump is around 12 mW. When the GFF excess loss is 0.3dB the top-AIR gain over the standard all GFF system is 9.5%, a value that decreases to 4% when the excess loss is zero. Considering that modern submarine-grade GFFs have almost zero excess loss, and that the most efficient pump power is likely too low to operate with, we conclude that sparse-GFF links offer little advantage in practice over the current design.

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.