1. Introduction

Multi-core fiber (MCF) has been used to support space-division-multiplexed (SDM) transmission with record per-fiber capacities [1–3] and spectral efficiencies (SEs) [4]. Aggregate capacities of 112 Tb/s and 1.01 Pb/s were demonstrated [2,3] in a 76.8-km seven-core-fiber and a 10.1-km 19-core-fiber, respectively, using polarization-division multiplexed quadrature phase-shift keyed (PDM-QPSK) signals. Recently, digital coherent superposition (DCS) [5] has been proposed to improve the signal performance in MCF-based SDM transmission, by trading capacity for performance. This may be desirable in transmission links where link performance rather than link capacity is of primary concern. DCS was experimentally demonstrated in a 2688-km SDM transmission link with 128-Gb/s differentially-encoded PDM-QPSK signals, using an additional phase alignment technique to match the phases of the recovered SDM copies at the receiver [5]. It was later found that in the nonlinear transmission regime, the nonlinear distortions on identical signal copies are highly correlated, which diminishes the benefit of DCS [6]. It was also shown that scrambled coherent superposition (SCS), in which the signal constellations are scrambled at the transmitter and unscrambled at the received prior to coherent superposition, can effectively eliminate the correlation among the nonlinear distortions of the superimposing signals and thus retain the full benefit of coherent superposition even in the nonlinear regime [6]. More recently, we demonstrated DCS in a coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system where phase alignment among different SDM copies is automatically achieved through the use of pilot subcarriers [7]. With 16-ary quadrature amplitude modulation (16-QAM) for subcarrier modulation, about 4 dB reduction in the required optical signal-to-noise ratio (OSNR) at a bit error ratio (BER) of 10⁻³ was obtained by using only two SDM copies, enabling SDM 676-Gb/s OFDM-16QAM superchannel transmission over 1075 km (14x76.8km) of a seven-core-fiber with an effective aggregate spectral efficiency of 23.7 b/s/Hz [7]. Here, we present the experimental setup and results in more depth. Furthermore, we show the use of a series of simple scrambling functions to effectively realize SCS to nearly obtain the full benefit of coherent superposition in the nonlinear transmission regime.

2. Experimental setup

Figure 1 shows the schematic of the experimental setup. Eight 100-GHz spaced external cavity lasers were separated into odd and even channels. Wavelengths within each group were passively combined and modulated by multicarrier generators (MCGs) based on a Mach-Zehnder modulator (MZM) driven by a 19.45-GHz sine-wave with ~3Vπ amplitude. Five 19.45-GHz-spaced frequency-locked carriers were thus generated for each of the eight input wavelengths. A wavelength-selective switch (WSS), configured to have a 3-dB bandwidth of 100 GHz, was used to reject the unwanted harmonics generated by each MCG. Two I/Q modulators were then used to modulate even and odd channels to generate eight OFDM-16QAM superchannels. The two drive signals for the first modulator were provided by two 30-GS/s digital-to-analog converters (DACs) with 6-bit resolution. The two drive signals for the second modulator were the complementary outputs from the same two DACs but with > 4 ns delay for de-correlation. The DAC outputs were filtered by RF anti-aliasing low-pass filters (LPFs) with 12.5-GHz 3-dB bandwidth. The inputs to the DACs were provided by a field-programmable gate array (FPGA) based real-time logic circuit with stored OFDM-16QAM waveforms. To generate the signal waveforms, pseudo-random bit sequences (PRBS) of length 2¹⁵-1 were first encoded and mapped to 16-QAM symbols. The IFFT size was 128, and the guard-interval (GI) was 2 samples. Each component of an OFDM symbol contained 79 data subcarriers (SCs), 3 pilot SCs, 1 unfilled center SC, and 45 unfilled edge SCs. Four correlated training symbols were used for every 508 payload OFDM symbols. The modulated odd and even channels were passively combined by a 2 × 2 optical coupler (OC), followed by polarization multiplexing, which was achieved by separating the signals into two paths, delaying one by one OFDM symbol (or 4.33 ns), and recombining them in a polarization beam combiner (PBC). Assuming 7% forward-error-correction (FEC) overhead, the net payload data rate for each superchannel was 676 Gb/s, occupying a null-to-null spectrum bandwidth of 97.3 GHz. The optical spectrum of eight wavelength-division multiplexed (WDM) superchannels is shown as inset (a) in Fig. 1.

 

Fig. 1 Schematic of the experimental setup. Insets: (a) measured optical spectrum of the eight WDM superchannels; (b) measured optical spectrum of a 676-Gb/s superchannel; and (c) typical recovered subcarrier constellation of the superchannel in back-to-back configuration. MCG: multi-carrier generator; WSS: wavelength-selective switch; OC: optical coupler; PDM: polarization-division multiplexer; SW: switch; EDFA: Erbium-doped fiber amplifier, TMC: tapered multi-core coupler; OLO: optical local oscillator; ADC: analog-to-digital converter.

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For SDM transmission, the eight WDM superchannels were launched into seven parallel and synchronized re-circulating loops, which were connected to the seven cores of a seven-core-fiber [5,8]. Different from the setup used in Refs. 5 and 6, all the seven cores of the MCF were backward Raman pumped with an average Raman gain of about 10 dB, provided by single-wavelength pumps at ~1455 nm. A 7x7 wavelength blocker array was used to equalize the powers across the channels. A cyclic core-to-core rotation scheme was used to equalize the transmission characteristics of the seven cores. At the output, a 1x7 optical switch was used to sequentially direct the received signal from each of the seven re-circulating loops to a wavelength selective switch (WSS), where only the center WDM superchannel (λ4) was selected for DCS processing. This superchannel was then sent to a digital coherent receiver with offline digital signal processing (DSP), which sampled and processed each of the five subbands of the superchannel individually. To aid the banded detection, the signal components after the four balanced detectors (BDs) were first electrically filtered using RF LPFs with 14.6-GHz 3-dB bandwidth. As all the SDM copies of the center superchannel exiting from the seven cores were periodic with the same patterns, although delayed differently, they were individually stored before being synchronized and recovered in offline DSP. The signal recovery process includes electronic dispersion compensation, OFDM channel estimation and compensation, and frequency and phase compensation [9]. Unlike differentially encoded PDM-QPSK [5], all the SDM copies of the OFDM-16QAM signals are automatically phase-aligned through the pilot subcarriers, so DCS can be readily performed after the OFDM symbol recovery.

3. Experimental results

Figure 2 shows the back-to-back BER performance without DCS and with DCS of two SDM copies from two of the seven cores of the MCF. Remarkably, the DCS of two SDM copies offers ~4 dB reduction in the required OSNR at BER = 4.6 × 10⁻³, the threshold of a 7%-overhead hard-decision FEC [10]. We attribute the large OSNR gain to the fact that DCS not only averages optical noise (which would result in a 3-dB OSNR gain) but also other noise sources, such as ADC quantization noise.

 

Fig. 2 Measured back-to-back BER performance of a 676-Gb/s superchannel without DCS and with DCS of two SDM copies. Insets: (a) recovered subcarrier constellations without DCS; and (b) recovered subcarrier constellations with DCS at 22-dB and 26-dB OSNR.

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Figure 3 shows the measured Q² factor, derived from the BER, as a function of the superchannel launch power per core (Pin) at a distance of 1075 km (or 14 spans of 76.8-km MCF) without and with DCS. At P_in = 0 dBm, the received OSNR of the superchannel under test is ~28 dB, and DCS with two SDM copies provides a Q² factor improvement of ~2.5 dB. The improvement becomes smaller as the signal launch power increases beyond 2 dBm, as the SDM signal copies experience similar pattern-dependent intra-channel nonlinear distortions in the high-power region, and these correlated impairments do not “average out” among the 2 DCS-processed signal copies as do the uncorrelated optical and quantization noise realizations in the low-power region [5]. The optimum Q² factor without DCS is 6.15 dB, below the threshold of a practically implementable 20.5%-overhead soft-decision FEC [11] (6.4 dB). The optimum Q² factor with the DCS is 8.5 dB, above the threshold of the 7%-overhead hard-decision FEC [10] (8.3 dB). In the nonlinear transmission regime, the performance improvement obtained by DCS is reduced, especially when P_in is higher than 2 dBm. This is expected from Ref [6].

 

Fig. 3 Measured Q² factor as a function of superchannel launch power per per core at a distance of 1075 km without and with DCS. The results obtained by SCS are also shown.

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To retain the performance gain in the nonlinear transmission regime, we implemented SCS [6] using a series of simple scrambling functions, S_n(t), as shown in Fig. 3 (and later in Fig. 5). Since only one modulator was used in our proof-of-concept experiment to modulate the signals to be transmitted over the seven cores of the MCF (see Fig. 1), we had to specially design the modulation and detection schemes in the following way. We first transmitted a series of scrambled versions of a given original signal sequence (E(t)) in each OFDM frame, i.e., E_n(t) = S_n(t)E(t), where t is the modulation symbol index. At the receiver, we received signals from all the fiber cores and digitally stored them for further processing. We then used the OFDM frame headers to align all the received signals. For SCS, the superimposing signals from different fiber cores were taken from different scrambled sections, unscrambled based on their corresponding scrambling functions, and coherently superimposed. The mathematical expression for the above process is, $E^{RX}(t)={\displaystyle {\sum }_{n=1}^m{S}_n^{}{(t)}^{-1}{E}_n^{RX}(t)}$, where $E^{RX}(t)$ is the final recovered signal field, $E_n^{RX}(t)$ is the n-th recovered signal field right before the coherent superposition, and m is the number of signals used in the SCS process. As shown in Fig. 3, SCS noticeably outperforms DCS in the nonlinear regime (e.g., P_in>0 dBm), as also demonstrated in Ref [6].

Figure 4 shows the Q² factor improvement as a function of the number of superimposed SDM copies in the DCS process after 1075-km transmission at P_in = 0 dBm (in the moderately nonlinear transmission regime). Insets (a-c) show typical recovered subcarrier constellations without DCS, with DCS of two SDM copies, and with DCS of seven SDM copies, respectively, clearly indicating that the signal quality continues to improve with the number of superimposed SDM copies. To fully utilize an M-core fiber for DCS-based transmission of any number of superimposed signal copies, one can break the signal intended for transmission into equal-length blocks, make copies for each block, and send the duplicate blocks to M cores of the MCF at M blocks a time. Note that the performance improvement comes at the expense of reduced MCF transmission capacity. DCS may provide the flexibility to trade link capacity for link performance or transmission distance. The performance of a QSPK signal can also be improved by DCS [5], but the use of OFDM-16QAM provides higher maximum capacity and finer granularity in the supported capacities.

 

Fig. 4 Measured Q² factor improvement vs. number of superimposed signals (m) after 1075-km transmission with 0-dBm signal launch power. Insets: typical recovered constellations at different m-values.

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In the highly nonlinear regime, SCS needs to be used to retain the performance gain of coherent superposition. Figure 5 shows the recovered signal constellations without DCS and with SCS using the outputs from 4 fiber cores. The scrambling functions [6] used for different cores are also shown in Fig. 5. Evidently, SCS enables substantial performance improvement even in this highly nonlinear transmission scenario.

 

Fig. 5 Recovered signal constellations after 1075-km transmission with 4-dBm signal launch power without DCS and with SCS using the outputs from 4 fiber cores. The scrambling functions used for different cores are shown in the right subplot.

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4. Conclusions

We have experimentally demonstrated digital coherent superposition (DCS) for improving the performance of SDM OFDM signals, whose phase alignment is readily achievable through the use of pilot subcarriers. Using DCS of two SDM copies, SDM/WDM transmission of 676-Gb/s OFDM-16QAM superchannels over 1075-km seven-core fiber with an aggregate spectral efficiency of 23.7 b/s/Hz is achieved. This represents the longest transmission distance for SDM transmission with an aggregate SE of over 20 b/s/Hz. In the linear transmission regime, the performance gain of DCS is similar to the diversity gain of wireless single-input-multiple-output (SIMO) systems. In the nonlinear optical fiber transmission regime, however, the gain of DCS is reduced. We have also experimentally shown that scrambled coherent superposition (SCS), based on a series of simple scrambling functions, allows the gain of DCS to be nearly fully retained even in the nonlinear transmission regime.