Simplified high-order Volterra series transfer function for optical transmission links. 
We develop a simplified high-order multi-span Volterra series transfer function (SH-MS-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.