1. Introduction

A 69.4 GBd carrier launched into a transpacific cable at −0.78 dBm arrives 10,800 km later carrying three noise terms that a coherent receiver cannot tell apart. Amplified spontaneous emission (ASE) from 180 erbium-doped fibre amplifiers (EDFAs) contributes 77.2% of the received noise variance, nonlinear interference (NLI) generated by the Kerr effect contributes 12.2%, and guided acoustic-wave Brillouin scattering (GAWBS) contributes the remaining 10.6% (GN-model result on reference link S1, derived in Section 8). The receiver's digital signal processing (DSP) sees one Gaussian noise floor and reports one signal-to-noise ratio. That indifference is not a limitation of the instrument. It is a property of the channel, and the whole commercial architecture of the open cable rests on it.

The property has a physical cause with a measurable onset. Chromatic dispersion in a fibre with no inline compensation spreads every symbol across its neighbours and randomises the relative phases of the wavelength-division multiplexing (WDM) comb. On reference link S1 a symbol overlaps 47 neighbours after one 60 km span, 95 after two, and 8,546 by the time it reaches the far shore (derived from the accumulated dispersion, Section 4.2). Once several tens of independent contributions add at each instant, the central limit theorem applies to the resulting distortion and the Kerr-generated field takes circular Gaussian statistics. The distortion then has no structure the DSP can exploit, and its variance becomes the only quantity that matters.

The Gaussian Noise (GN) model turns that observation into a closed-form estimate of the variance. It treats the transmitted WDM signal as a stationary Gaussian process, computes the power spectral density of the four-wave mixing products that fall inside the carrier of interest, and accumulates them span by span. What comes out is a nonlinear signal-to-noise ratio, SNR_NLI, that composes with the amplifier noise term by the reciprocal sum rule. The composed quantity is the generalized signal-to-noise ratio (GSNR), and ITU-T G.977.1 defines it for exactly this purpose: a figure that describes the cable and nothing else, measurable before any transponder is bought (standard-specified).

Submarine links sit further inside the model's validity region than any other system class. Span lengths of 50 to 80 km, local dispersion above 20 ps/(nm·km) on pure silica core fibre (PSCF), amplifier counts in the hundreds, and no dispersion compensation modules anywhere in the wet plant combine to produce the strongest decorrelation in commercial optical transmission. That is why GSNR became a contractual parameter on subsea cables years before terrestrial planning tools adopted the same arithmetic, and why an open cable can be accepted, sold in spectrum blocks, and upgraded by a third-party terminal vendor on the strength of one measured number per frequency.

1.1 Scope and Boundary Conditions

This article covers the Gaussian description of nonlinear interference on repeatered, dispersion-unmanaged submarine cable systems: the physical condition that produces Gaussian statistics, the closed-form GN estimate of NLI variance, the aggregation of ASE, NLI and GAWBS into GSNR under both the additive and generalized droop rules, the measurement procedure that recovers GSNR from a modem Q-factor, and the two conditions under which the description degrades. Enhanced GN (EGN) and time-domain variants appear where they change a design decision, not as a derivation. Unrepeatered systems, dispersion-managed legacy cables and multicore crosstalk are named where they bound the argument and are otherwise outside the scope. The companion treatment of the model in its terrestrial form is available in the Gaussian Noise model reference, and the relationship between the modelled quantity and the instrument reading is set out in GOSNR versus OSNR.

1.2 Reference Link S1

Every calculation in this article uses one link, so a capacity quoted in Section 9 traces back to a launch power in Section 6. Reference link S1 is a transpacific-class open cable of the kind built since the middle of the last decade: PSCF throughout, C-band only, EDFA repeaters on 60 km spacing, and a fibre pair count high enough that each pair is operated below its own nonlinear threshold.

The nonlinear coefficient follows from the effective area alone. With γ = 2πn₂/(λA_eff), an effective nonlinear index of 2.22 × 10⁻²⁰ m²/W at 1550 nm and a 150 µm² effective area give 0.60 W⁻¹km⁻¹, roughly half the 1.3 W⁻¹km⁻¹ of terrestrial ITU-T G.652.D fibre (derived). Halving γ divides the NLI power spectral density by four at fixed launch power, which is the first-order reason large-effective-area fibre reaches the sea floor and small-effective-area fibre does not. Fibre selection and its effect on the nonlinear budget is developed further in the optical fibre parameter reference.

1.3 Three Statements That Organise the Argument

The Gaussian description holds because dispersion destroys the phase structure of the signal, not because the Kerr effect is weak; the strongest nonlinear regimes on S1 are also the most Gaussian. The GSNR that follows describes the cable independently of the transponder, which is what makes an acceptance contract possible without a transponder. And the description degrades along two axes only, local dispersion and symbol rate, both of which enter through the same overlap criterion, which is why one number in picoseconds per nanometre bounds the whole validity region. Sections 4, 7 and 11 develop the three in turn.