A Joint Technique for Nonlinearity Compensation in CO-OFDM Superchannel Systems

O. S. Sunish Kumar, A. Amari, O. A. Dobre, R. Venkatesan, S. K. Wilson O. S. Sunish Kumar, A. Amari, O. A. Dobre, and R. Venkatesan are with the Faculty of Engineering and Applied Science, Memorial University, St. John’s, NL A1B 3X5, Canada (e-mail: [email protected]). S. K. Wilson is with Electrical Engineering Department, Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053, United States.

Abstract

We propose a technique combining the single-channel digital-back-propagation (SC-DBP) with phase-conjugated-twin-wave (PCTW) to compensate nonlinearities in CO-OFDM superchannel systems. This exhibits a similar performance as multi-channel DBP while providing increased transmission reach compared to SC-DBP, PCTW, and linear dispersion compensation (LDC).

Index Terms:

Fiber optics communications, coherent communications, optical communications.

I Introduction

The fiber Kerr nonlinearity imposes an upper limit on the maximum achievable transmission capacity in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems [1]. Over the past few decades, several techniques have been proposed to mitigate the fiber nonlinearities, ranging from optical techniques to advanced digital signal processing (DSP) algorithms [2]. The multi-channel digital-back-propagation (MC-DBP) is a DSP technique proposed in the context of the wavelength division multiplexed (WDM) transmission systems [3]. However, the large computational complexity and the unavailability of the information from the neighboring traffic channels make the implementation of the MC-DBP impractical in a dynamic optical network [4]. Several simplified intra-channel solutions based on the single-channel (SC) DBP have been considered in the literature; however, the reported gains are limited to $\sim 1$ dB [4]. Recently, a novel technique referred to as phase-conjugated-twin-wave (PCTW) has been proposed for the effective mitigation of the fiber nonlinearities [5]. The PCTW technique can compensate both intra- and inter-channel first-order nonlinear distortions with reduced complexity [5].

In this paper, we propose a joint technique which combines SC-DBP with the PCTW technique, referred to as SC-DBP-PCTW. We show through numerical simulations that the proposed scheme provides a performance gain higher than applying the SC-DBP and PCTW techniques individually in a $401.33$ Gbps $16$ -QAM-CO-OFDM superchannel system, at a transmission distance of $2000$ km. We further show that the joint scheme can achieve a similar performance as the MC-DBP with $16$ steps/span and also provides a substantial increase in the transmission reach when compared to SC-DBP, PCTW and the linear dispersion compensation (LDC) cases.

II The Joint SC-DBP-PCTW Technique

Refer to caption — Figure 1: Illustration showing the joint SC-DBP-PCTW technique for one channel. $E_{x}$ and $E_{y}$ represent the transmitted electric fields in the $x$ and $y$ polarizations, respectively; $\tilde{E}_{x}$ and $\tilde{E}_{y}$ are the received electric fields after SC-DBP; and $\tilde{E}$ represents the recovered field after the coherent superposition, $*$ stands for the complex conjugation operation. $N_{span}$ : number of fiber spans, EDFA: erbium doped fiber amplifier, SSMF: standard single mode fiber.

The concept of the joint SC-DBP-PCTW technique is depicted in Fig. 1. At the transmitter, the mutually phase conjugated twin waves are propagated on the two orthogonal polarization states of the fiber.

After the coherent detection at the receiver, the SC-DBP of the selected channel is carried out with $1$ step/span and then the coherent superposition of the PCTW technique is performed. Insets (a) and (b) show the signal constellations after the SC-DBP and the coherent superposition of the PCTW technique. Evidently, the constellation quality is much improved after the coherent superposition. The performance improvement of the joint technique comes from the individual abilities of the two constituent techniques in combating the impact of nonlinearities. The SC-DBP compensates for the deterministic intra-channel nonlinear distortions, while the PCTW technique compensates both intra- and inter-channel first-order nonlinear distortions [6], [5]. Thus, the joint SC-DBP-PCTW technique realizes a two-stage compensation for the intra-channel nonlinear distortions and a first-order cancellation for the inter-channel nonlinear distortions.

III Simulation Setup

Fig. 2 shows the simulation setup for the joint SC-DBP-PCTW technique. The transmission system consists of a WDM superchannel with four $37.5$ GHz spaced $32$ Gbaud 16-QAM-CO-OFDM signals employing the PCTW technique. The OFDM symbol consists of $3300$ data carrying subcarriers, and an inverse fast Fourier transform (IFFT) of size $4096$ is carried out to convert the signal into time-domain. There are four pilot subcarriers in each OFDM symbol and the cyclic prefix is $3$ %. Therefore, the net data rate is $401.33$ Gb/s. The long-haul fiber link consists of $25$ spans of standard single mode fiber (SSMF), each having a length of $80$ km, the attenuation coefficient of $0.2$ dB/km, the nonlinearity coefficient of $1.22$ /(W.km), the dispersion coefficient of $16$ ps/nm/km, and the polarization mode dispersion coefficient of $0.1$ ps/ $\sqrt{\mathrm{km}}$ . The optical power loss for each span is compensated by an erbium doped fiber amplifier (EDFA) with $16$ dB gain and $4$ dB noise figure. The transmitter and receiver lasers have the same linewidth of $100$ kHz. At the receiver, after the polarization diversity detector, the SC-DBP with $1$ step/span is carried out. The channel equalization and carrier phase recovery are carried out as in [7]. After that, the coherent superposition of the PCTW technique is performed. Finally, the recovered symbols are demapped in the binary form.

IV Results

We evaluate the performance of the proposed SC-DBP-PCTW scheme, which is compared with the MC-DBP, PCTW, SC-DBP, and LDC techniques in Fig. 3. It is evident from Fig. 3(a) that the proposed scheme improves the $Q$ -factor performances by $3$ dB, $2.3$ dB and $0.5$ dB when compared to the LDC, SC-DBP and PCTW schemes, respectively. It is interesting to note that the $Q$ -factor performance of the proposed SC-DBP-PCTW scheme is similar to that of the MC-DBP with $16$ steps/span, showing the effectiveness of the proposed technique in improving the performance-complexity trade-off. Fig. 3(b) shows an estimate of the maximum reach, including input power optimization for each propagation distance. It is observed that the maximum reach at the $20$ % overhead (OH) soft-decision (SD) forward error correction (FEC) limit of $2.7\times 10^{-2}$ [3] for the LDC, SC-DBP, PCTW, MC-DBP and SC-DBP-PCTW is $2380$ km, $3030$ km, $4380$ km, $5580$ km and $5600$ km, respectively. This indicates that the SC-DBP-PCTW scheme provides more than double transmission reach when compared to the LDC case and a similar reach as that of MC-DBP with $16$ steps/span. It also shows an $\sim 85\%$ and $\sim 28\%$ reach increase when compared to the SC-DBP and PCTW schemes, respectively. It should be noted that the implementation of the PCTW technique halves the spectral efficiency [5], and thereby the performance improvement of the proposed technique comes with a cost of spectral efficiency loss. In Fig. 4, the computational complexity of the proposed SC-DBP-PCTW technique has been compared in terms of the number of real multiplications per subcarrier with the LDC, SC-DBP, PCTW and MC-DBP schemes, as a function of the number of spans, $N_{span}$ . It is interesting to note that the complexity of the proposed SC-DBP-PCTW scheme is significantly lower than that of MC-DBP. Table $1$ shows the expressions for the number of real multiplications per subcarrier and the central processing unit (CPU) running time for the considered algorithms with N_FFT $=4096$ and $N_{span}=25.$ It is observed that the CPU running time for the proposed SC-DBP-PCTW technique is an order of magnitude lower than that of the MC-DBP. We also observe that the joint scheme has a complexity less than that of the sum of the individual complexities of the SC-DBP and PCTW techniques. The individual implementation of the SC-DBP and PCTW schemes involve a linear dispersion compensation followed by either a nonlinear compensation section or a coherent superposition. Thus, the technique combining SC-DBP with the PCTW scheme has a slightly increased complexity when compared to its individual implementations and the additional complexities are from the nonlinear compensation section or the coherent superposition.

V Conclusion

We have proposed a low-complexity joint technique for fiber nonlinearity compensation, which combines the SC-DBP and PCTW. The new technique shows a similar performance as the MC-DBP with $16$ steps/span in a $401.33$ Gbps CO-OFDM based superchannel system, at a transmission distance of $2000$ km. It also almost double the transmission reach when compared to the LDC case and provides about $28\%$ increase compared to PCTW.

References

[1] R. Essiambre et al., “Capacity limits of optical fiber networks,” J. Lightw. Technol. 28 (4), 662–701 (2010).
[2] A. Amari et al., “A survey on fiber nonlinearity compensation for 400 Gb/s and beyond optical communication systems”, IEEE Commun. Surveys Tuts.18 (3), 2017.
[3] F. P. Guiomar et al., “Multicarrier digital backpropagation for 400G optical superchannels,” J. Lightw. Technol. 34 (8), 1896–1907 (2016).
[4] L. Dou et al., “A low complexity pre-distortion method for intrachannel nonlinearity,” Proc. OFC, Paper OThF5, (2011).
[5] X. Liu et al., “Fiber-nonlinearity-tolerant superchannel transmission via nonlinear noise squeezing and generalized phase-conjugated twin waves,” J. Lightw. Technol. 32 (4), 766–775, (2014).
[6] E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightw. Technol. 26 (20), 3416–3425, (2008).
[7] S. T. Le et al., “Demonstration of phase-conjugated subcarrier coding for fiber nonlinearity compensation in CO-OFDM transmission”, J. Lightw. Technol. 33 (11), 2206–2212, (2015).