Simplified high-order Volterra series transfer function for optical transmission links

We develop a simplified high-order multi-span Volterra series transfer function (SHMS-
VSTF), basing our derivation on the well-known third-order Volterra series transfer function
(VSTF). We notice that when applying an approach based on a recursive method and considering
the phased-array factor, the order of the expression for the transfer function grows as 3 raised to
the number of considered spans. By imposing a frequency-flat approximation to the higher-order
terms that are usually neglected in the commonly used VSTF approach, we are able to reduce
the overall expression order to the typical third-order plus a complex correction factor. We carry
on performance comparisons between the purposed SH-MS-VSTF, the well-known split-step
Fourier method (SSFM), and the third-order VSTF. The SH-MS-VSTF exhibits a uniform
improvement of about two orders of magnitude in the normalized mean squared deviation with
respect to the other methods. This can be translated in a reduction of the overall number of steps
required to fully analyze the transmission link up to 99.75% with respect to the SSFM, and
98.75% with respect to the third-order VSTF, respectively, for the same numerical accuracy.