We present a theoretical model that fully supports the recently disclosed generalized droop formula (GDF) for calculating the signal-to-noise ratio (SNR) of constant-output power (COP) amplified coherent links operated at a very low SNR. For single-mode nonlinear COP links we compare the GDF-SNR to the better known generalized SNR (GSNR) that uses the Gaussian noise (GN) model for constant-gain (CG) amplifiers. We find that at all medium to large SNRs the GSNR well matches with the GDF, while at GSNR below 6 dB the GSNR over-estimates the correct GDF-SNR by more than 0.5 dB. Fortunately, the GDF-SNR turns out to be approximately a simple function of the GSNR, which allows adaptation of the widespread GSNR also to very low SNR links. A key finding of this article is that the end-to-end model underlying the GDF is a concatenation of per-span first-order regular perturbation (RP1) models with end-span power renormalization. This fact allows the GDF to well reproduce the SNR of highly nonlinear systems, well beyond the RP1 limit underlying the GN model. The GDF is successfully extended to the case where the bandwidth/modes of the COP amplifiers are not entirely filled by the transmitted multiplex. Finally, the GDF is extended to CG amplified links and is shown to improve on known GN models of highly nonlinear propagation with CG amplifiers.

中文翻译：

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低信噪比光链路的广义下垂公式

我们提出了一个理论模型，该模型完全支持最近公开的广义下垂公式 (GDF)，用于计算以非常低的 SNR 运行的恒定输出功率 (COP) 放大相干链路的信噪比 (SNR)。对于单模非线性 COP 链路，我们将 GDF-SNR 与更广为人知的广义 SNR (GSNR) 进行比较，后者将高斯噪声 (GN) 模型用于恒定增益 (CG) 放大器。我们发现，在所有中到大 SNR 下，GSNR 与 GDF 都很好地匹配，而在 GSNR 低于 6 dB 时，GSNR 高估了正确的 GDF-SNR 超过 0.5 dB。幸运的是，GDF-SNR 大约是 GSNR 的一个简单函数，它允许广泛的 GSNR 也适用于非常低的 SNR 链路。本文的一个关键发现是 GDF 底层的端到端模型是每跨一阶正则扰动 (RP1) 模型与端跨功率重整化的串联。这一事实使 GDF 能够很好地再现高度非线性系统的 SNR，远远超出 GN 模型下的 RP1 限制。GDF 成功地扩展到 COP 放大器的带宽/模式没有完全被传输的多路复用填充的情况。最后，GDF 被扩展到 CG 放大链路，并被证明可以改进已知的具有 CG 放大器的高度非线性传播的 GN 模型。GDF 成功地扩展到 COP 放大器的带宽/模式没有完全被传输的多路复用填充的情况。最后，GDF 被扩展到 CG 放大链路，并被证明可以改进已知的具有 CG 放大器的高度非线性传播的 GN 模型。GDF 成功地扩展到 COP 放大器的带宽/模式没有完全被传输的多路复用填充的情况。最后，GDF 被扩展到 CG 放大链路，并被证明可以改进已知的具有 CG 放大器的高度非线性传播的 GN 模型。