Starting from a previously proposed frequency-domain Volterra series nonlinear equalizer (VSNE), whose complexity evolves as $O(N^3)$, with $N$ being the frequency-domain block length, we derive a symmetric VSNE filter array formulation for polarization-multiplexed (PM) signals, whose full VSNE equivalent is up to 3 $\times$ more computationally efficient, with zero performance penalty. By gradually reconstructing the third-order kernel from its column/diagonal components, the full VSNE can be reduced to a restrict set of $N_k$ frequency-domain filters, leading to $O(N_k N^2)$ complexity, associated with negligible performance loss. Finally, a simplified VSNE approach with invariant Kernel coefficients is proposed, delivering $O(N_k N)$ complexity at the expense of controlled performance penalty. The proposed array of symmetric VSNE filters significantly increases the scalability of the previous matrix-based VSNE, providing a more flexible balance between performance and complexity, which can be freely adjusted to match the available computational resources. Performing a direct comparison between the simplified VSNE and the widely used split-step Fourier method in a long-haul 224 Gb/s PM-16QAM transmission system, we demonstrate a reduction of over 60% in terms of computational effort and 90% in terms of equalization latency.
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