论文标题
连续空间SSFM光纤模型的下限
Lower Bound on the Capacity of the Continuous-Space SSFM Model of Optical Fiber
论文作者
论文摘要
由拆分步骤傅立叶方法（SSFM）描述的光纤的离散时间模型的容量是信噪比$ \ text {snr} $的函数，距离$ k $中的段数。结果表明，如果$ k \ geq \ text {snr}^{2/3} $和$ \ text {snr} \ rightarrow \ infty \ infty $，则由此产生的连续空间模型的能力由$ \ \\ frac {1} {1} {2} {2} {2} {2} \ log_2 {1+ \ frac} {1+ \ fr} o（1）$，其中$ o（1）$倾向于用$ \ text {snr} $零。由于$ k \ rightArrow \ infty $，由于数量大的定律，符号间干扰（ISI）平均为零，而SSFM模型倾向于对角相噪声模型。因此，与离散空间模型相比，高功率只有一个信号自由度（DOF），连续空间模型中的DOF数量至少是输入维度$ n $的一半。强度调节和直接检测达到了这一速率。当$ k = \ sqrt [δ] {\ text {snr}} $通常以$δ$为特征时，下限的前log。 结果表明，如果非线性参数$γ\ rightarrow \ infty $，则连续空间模型的容量为$ \ frac {1} {2} {2} {2} \ log_2（1+ \ text {snr}）+ o（1）$。 当分散矩阵不取决于$ K $时，SSFM模型被考虑。结果表明，当$ k = \ sqrt [δ] {\ text {snr}} $，$Δ> 3 $和$ \ text {snr} \ rightarrow \ infty $ is $ \ frac {1} {1} {2n} {2n} {2n} {2n} \ log_2（1+ \ fext {snr}）时，该模型的容量表明。因此，此模型中只有一个DOF。 最后，发现使用数值模拟获得的后传播均衡的SSFM模型的最大可实现信息率（AIRS）遵循双重呈曲线。
The capacity of a discrete-time model of optical fiber described by the split-step Fourier method (SSFM) as a function of the signal-to-noise ratio $\text{SNR}$ and the number of segments in distance $K$ is considered. It is shown that if $K\geq \text{SNR}^{2/3}$ and $\text{SNR} \rightarrow \infty$, the capacity of the resulting continuous-space lossless model is lower bounded by $\frac{1}{2}\log_2(1+\text{SNR}) - \frac{1}{2}+ o(1)$, where $o(1)$ tends to zero with $\text{SNR}$. As $K\rightarrow \infty$, the inter-symbol interference (ISI) averages out to zero due to the law of large numbers and the SSFM model tends to a diagonal phase noise model. It follows that, in contrast to the discrete-space model where there is only one signal degree-of-freedom (DoF) at high powers, the number of DoFs in the continuous-space model is at least half of the input dimension $n$. Intensity-modulation and direct detection achieves this rate. The pre-log in the lower bound when $K= \sqrt[δ]{\text{SNR}}$ is generally characterized in terms of $δ$. It is shown that if the nonlinearity parameter $γ\rightarrow \infty$, the capacity of the continuous-space model is $\frac{1}{2}\log_2(1+\text{SNR})+ o(1)$. The SSFM model when the dispersion matrix does not depend on $K$ is considered. It is shown that the capacity of this model when $K= \sqrt[δ]{\text{SNR}}$, $δ>3$, and $\text{SNR} \rightarrow \infty$ is $\frac{1}{2n}\log_2(1+\text{SNR})+ O(1)$. Thus, there is only one DoF in this model. Finally, it is found that the maximum achievable information rates (AIRs) of the SSFM model with back-propagation equalization obtained using numerical simulation follows a double-ascent curve.
