Nonlinear Digital Back Propagation compensator for coherent optical OFDM based on factorizing the Volterra Series Transfer Function

Abstract

We introduce an efficient and accurate nonlinear compensator (NLC) for digital back-propagation (DBP) of coherent optical OFDM receivers, based on a factorization procedure for the Volterra Series Transfer Function (VSTF) with 3N degrees of freedom for N frequency samples. The O(N2) nonlinear compensation complexity of generic Volterra evaluation (normalized per-subcarrier) is reduced to 28 + 6logN. Our analysis and simulations indicate that this NLC system outperforms previous VSTF-based non-linear compensation methods. Compared to a most recent VSTF-based method, the new method incurs 52% extra computational complexity in return for improved nonlinear tolerance of ~2 dB for the particular analyzed link.

Simplified Volterra Series Nonlinear Equalizer for Polarization-Multiplexed Coherent Optical Systems

“…(12) The time-domain nonlinearly equalized optical field, A NL x/y , is finally obtained by taking the inverse FFT (IFFT) ofà NL…”

“…However, the total number of complex multiplications per fast-Fourier transform (FFT) block evolves as O(N 3 ), with N being the FFT block length, thus limiting the applicability of the algorithm in scenarios with large accumulated chromatic dispersion that creates long memory effects. The VSTF complexity issues have been addressed in several recent publications [10]- [12]. In [10], the equivalence between the third-order VSTF and the firstorder regular perturbation method [17] is exploited to design a nonlinear compensation technique where each fiber span can be backpropagated in parallel.…”

“…In [10], the equivalence between the third-order VSTF and the firstorder regular perturbation method [17] is exploited to design a nonlinear compensation technique where each fiber span can be backpropagated in parallel. A factorized approximation for the single-polarization VSTF with overall O(N log(N )) complexity has been proposed in [11], [12], employing decisionfeedback [11] and feed-forward [12] equalizer structures. All these reduced complexity NLE algorithms [10]- [12] make use of time-frequency transformations, similarly to the SSF method, exploiting the convolution theorem to speed up the calculations.…”

“…A factorized approximation for the single-polarization VSTF with overall O(N log(N )) complexity has been proposed in [11], [12], employing decisionfeedback [11] and feed-forward [12] equalizer structures. All these reduced complexity NLE algorithms [10]- [12] make use of time-frequency transformations, similarly to the SSF method, exploiting the convolution theorem to speed up the calculations. In order to enable real-time estimation of the VSTF coefficients, an efficient nonlinear system identification strategy for singlepolarization transmission systems has been proposed in [18], using a compressed VSTF notation that significantly reduces the number of required probing tones.…”

“…It is worth stressing at this point that both the lossy and lossless compressions proposed in this paper differ from that proposed in [18], since we seek to avoid replication of operations by identifying common symmetries shared between the third-order VSNE kernel and the dual-polarization signal matrices, rather than focusing on maximum kernel compression. In addition, as opposed to [10]- [12], all VSNE-based algorithms proposed in this paper fully operate in frequency-domain.…”