## Abstract

We propose a novel energy-efficient coherent-optical OFDM transmission scheme based on hybrid optical-electronic signal processing. We demonstrate transmission of a 0.26-Tb/s OFDM superchannel, consisting of 13 x 20-Gb/s polarization-multiplexed QPSK subcarrier channels, over 400-km standard single-mode fiber (SSMF) with BER less than 6.3x10^{−4} using all-optical Fourier transform processing and electronic 7-tap blind digital equalization per subchannel. We further explore long-haul transmission over up to 960 km SSMF and show that the electronic signal processing is capable of compensating chromatic dispersion up to 16,000 ps/nm using only 15 taps per subchannel, even in the presence of strong inter-carrier interference.

©2012 Optical Society of America

## 1. Introduction

Advances in electronic signal processing have enabled recent breakthroughs in increasing the spectral efficiency and reach of coherent optical transmission. Especially, compensation of transmission impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD) by digital signal processing (DSP) has proven to be highly versatile and powerful. For example, tunable optical devices for compensating chromatic and polarization mode dispersion that were necessary for 40-Gb/s direct-detection-based transmission systems are being replaced by electronic equalizers for 100-Gb/s coherent-detection-based transmission. However, the capability is achieved at the expense of high power consumption and majority of the complexity and power consumption of the processing circuits are due to the processing for CD/PMD mitigation [1].

All-optical signal processing techniques are of interest as a potentially energy-efficient alternative to their electronic counterpart. Lately, optical OFDM transmission using passive-optical discrete Fourier transform (DFT) devices for demultiplexing orthogonally-multiplexed subcarriers have attracted much attention [2–5]. However, it has been considered that the energy saving obtained by the passive-optical DFT is diminished by the extra complexity and energy consumption associated with operating a high-speed modulator per subcarrier for time-gating the inter-(sub)carrier interference (ICI) and tunable optical dispersion compensation on a per-channel basis. In addition, the benefit of the energy savings needs to be weighed in consideration of any degradation in performance, such as penalty due to uncompensated residual chromatic dispersion. We have recently addressed the aforementioned shortcomings by implementation of an all-optical (AO) OFDM system without using energy-consuming time gating that is also highly dispersion tolerant: specifically, we used a photonic-integrated DFT circuit to support *non-coherent* reception of 35-Gb/s (7 x 5 Gb/s NRZ-OOK) data having near-unity spectral efficiency with 1-dB dispersion margin of ~1000 ps/nm [6], and further demonstrated long-haul dispersion-managed transmission without using tunable dispersion compensation [7].

In this paper, we show how the all-optical DFT method can be employed to reduce the complexity and power consumption of coherent optical (CO)-OFDM signal processing. We demonstrate that a hybrid signal processing method, comprising the all-optical DFT and electronic time-domain tap-and-delay finite-impulse-response (FIR) equalization, can substantially reduce the overall complexity in comparison to all-electronic signal processing without sacrificing the flexible dispersion compensation capability, which is the main benefit of the electronic DSP. In high-speed coherent optical communication, the most widely-used strategy for compensating gross chromatic dispersion (>10,000 ps/nm) is frequency-domain equalization (FDE) consisting of FFT, complex multiplication to cancel the quadratic frequency-dependent phase accumulated owing to the chromatic dispersion, followed by IFFT. For both single-carrier and multi-carrier coherent optical communication, the FDE is the first step in the digital signal processing chain, which includes additional time-domain equalization to address time-varying CD and PMD and subchannel demultiplexing in the case of OFDM transmission [1, 8, 9]. The FDE is typically the most complex and energy-consuming step in the digital signal processing in coherent optical communication. In an analogy to the electronic signal processing, optical chromatic dispersion compensation preceded optical DFT in prior all-optical OFDM experiments, with limited flexibility in dispersion compensation as a result. On the contrary, we propose a hybrid method wherein all-optical DFT is used first to demultiplex the OFDM superchannel into individual subchannels, each of which is coherently detected. The detected subchannels contain impairments from uncompensated CD and PMD, as well as ICI. We then recover information by applying electronic time-domain FIR equalization with a small number of taps. For example, we demonstrate OFDM transmission of 0.26 Tb/s superchannel composed of 13 x 20-Gb/s polarization-multiplexed NRZ-QPSK subchannels over 400-km SSMF (6800 ps/nm) with bit-error-ratio (BER) less than 6.3x10^{−4} without using any *optical* dispersion compensation. We achieve this using only 7 taps per subchannel with fractional spacing (1/3 of the symbol period) in the presence of CD and strong ICI from neighboring OFDM subchannels. We further show that CD up to 16,000 ps/nm can be compensated using the hybrid method needing 15 taps per subchannel. We note that we do not employ a time-gating optical modulator to suppress ICI and we only require devices having electronic bandwidth less than 16 GHz, which contribute to additional energy savings.

## 2. Experimental procedure

In Fig. 1
, we show the experimental set up for CO-OFDM transmission. We generate 5-GHz spaced optical frequency comb by sinusoidally modulating DFB laser output (λ = 1554.02 nm) using a lithium-niobate (LN) Mach-Zehnder modulator (MZM) followed by a LN phase modulator [10]. The spectrum of the optical comb is shown in Fig. 2(a)
, wherein we use the central 13 spectral lines (Ch. −6 …Ch. 0 (λ = 1554.02 nm) … Ch. 6) whose spectral flatness is 6.3 dB. The optical comb is split into two sets (even and odd) using a delay line interferometer with 10-GHz free spectral range. The extinction ratio of the delay line interferometer is 17.5 dB (21 dB) for the even (odd)-subcarrier output port. Using lithium niobate nested Mach-Zehnder modulators, each set is modulated by 5-Gbaud NRZ-QPSK data (2^{11}-1 PRBS) that are decorrelated with each other by electrical and optical delays. After optical amplification to compensate for the optical losses in the modulators, the two data streams are polarization- and time-aligned before being combined by a PM coupler to generate an OFDM superchannel.

The optical spectra of the even, odd, and combined subchannels are shown in Fig. 2(b). To generate polarization-multiplexed (pol-mux) signal, the OFDM signal is split into two, one of which is delayed and combined with the other after its polarization is rotated 90 degrees. The polarization-multiplexed signal is then propagated through standard single mode fiber spans. After transmission through the spans, the delivered OFDM signal is amplified by a two-stage EDFA before being sent into the all-optical DFT circuit for channel selection.

The optical DFT device we use for demultiplexing the OFDM signal is shown in Fig. 3
. It is well known that DFT can be all-optically performed using such a passive optical device. This can be understood from the equation for DFT in the context of demultiplexing an OFDM signal$E(t)$into subchannel *E _{n}* [11]:

*τ*(

*=*symbol period

*/N*) is the temporal delay. Thus, all-optical DFT can be implemented using essentially passive components comprising optical delay lines with incremental temporal delay of

*τ*and optical phase shifters for adjusting the optical phases of the delay lines. The simplest example of all-optical DFT was implemented using an asymmetric Mach-Zehnder interferometer (AMZI) for N = 2 [2, 3]. Cascaded AMZIs can be used to demultiplex subchannels when N = 2

^{M}for a positive integer M [5, 12, 13]. Alternatively, optical DFT can be implemented by a lightwave circuit consisting of 1xN input splitter followed by N delay lines, which are then combined by an NxN or Nx1 coupler. For this type of device, the phase relationships connecting the input optical fields into the optical couplers with the output fields need to be carefully considered to realize the DFT Eq. (1). Devices based on star couplers were proposed [14, 15] and experimentally demonstrated [4] recently. The device for our experiment instead consists of multi-mode coupler (MMI)-based couplers for splitting (combining) optical signals. It is further composed of 8 optical delay lines with an incremental delay of 25 ps, thermo-optic phase shifters for each delay arms, and variable optical attenuators (VOAs). We show in Fig. 3 the optical transmission spectrum of the optical DFT filter when the phase shifters are tuned to receive subchannel 0. We previously used the circuit as an optical Fourier transform correlator for optical bit pattern recognition [16], wherein more details of the device can be found. We select each subchannel one at a time by tuning the optical DFT circuit thermally since an 8x1 MMI is used as the combiner. However, simultaneous demultiplexing of all subchannels can be achieved by replacing the 8x1 MMI by an 8x8 MMI as we have shown recently [6].

The DFT circuit is polarization sensitive owing to the different group index of the TE and TM modes of the planar lightwave circuit. The ideal solution to overcome the polarization dependence is to design and fabricate devices with much reduced polarization-dependent group index. Alternatively, we can use a polarization-diversity scheme employing two DFT circuits that are substantially identical to each other, wherein incoming polarization-multiplexed OFDM signal is split into two orthogonal components first using a polarization beam splitter (PBS) and each polarization component is demultiplexed using one of the two identical DFT circuits. In our experiment, we sequentially receive one polarization at a time from the pol-mux OFDM signal by first aligning one polarization to the transmitting principal axis of the PBS in Fig. 1 using a polarization controller 3 (PC3), receive that polarization component, and then rotate the incoming signal polarization by 90 degrees using PC3 and receive the perpendicular polarization component.

Each polarization of each subchannel is analyzed using a coherent receiver consisting of a polarization-diversity 90-degree hybrid, followed by four balanced detectors, or using direct detection. The photodetector signal is digitized using a real-time sampling scope running at 50 Gsamples/s with input digital band-pass filters having 16-GHz analog bandwidth, acquiring 0.5-million samples per run. We typically take 10 data acquisition runs (5M samples) and minimum 5 runs (2.5M samples) per polarization. The digitized data are re-sampled at 16.7 Gsamples/s (3 samples/symbol). As mentioned previously, we do not use FFT-based CD compensation that is typically used in coherent-optical signal processing for compensating CD. Instead, transmitted symbols are directly recovered in the presence of large CD and ICI via blind equalization using the classic constant modulus algorithm (CMA) employing a FIR digital filter having fractionally-spaced (T/3) taps [17]. It takes less than approximately 2,000 initial data points for the CMA to converge for obtaining initial tap coefficients. We find that stable convergence is achieved when more than 3 points are sampled per symbol. After the initial convergence, the tap coefficients continue to get updated by moving averages. The phase estimation (PE) block size is set to either 3 or 5 symbols. After processing the entire sampled data points, we count the number of errors and estimate the Q-factor from the BER for each polarization. The final BER reported is the average of the BERs of both polarizations.

## 3. Transmission results

We first show the eye diagrams of the subcarrier Ch. 1 of the single-polarization OFDM signal measured using *direct* detection for back-to-back transmission (Fig. 4(a)
) and for 400-km transmission (Fig. 4(b)). With these direct-detected eye diagrams, the impact of ICI is easy to visualize: the b-t-b eye diagram clearly shows the temporal windows of inter-(sub)carrier interference (ICI)-free zone amidst strong ICI elsewhere. However, such an ICI-free zone is not found for the case of 400-km transmission. There are two causes for the degradation of the eye diagram: first, the disappearance of the ICI-suppressed temporal windows is in large part caused by the bit-misalignment of the subchannels due to the group velocity dispersion of the fiber. Note that the temporal bit alignment is the necessary condition for satisfying the orthogonality among the subcarrier channels in OFDM signal reception [11]. In addition, temporal broadening and chirp induced by CD further degrades the signal quality by inter-symbol interference (ISI).

However, even with this simultaneous presence of uncompensated ICI and CD, information can be successfully recovered by applying coherent detection with time-domain electronic digital equalization to the optically-channelized OFDM signal. We show the constellations obtained using coherent detection and signal processing in the insets to the eye diagrams in Fig. 4, wherein BER for Ch. 1 after transmission over 400-km SSMF is 3.4x10^{−4} after signal processing using 7-tap equalization. Our implementation is distinguished from the previous all-optical OFDM demonstrations in two aspects: first, we do not employ optical dispersion compensation. Precise control of CD/PMD compensation introduces increasing complexity as the modulation speed of the subcarriers is increased. As a result, the complexity, optical loss, and extra power consumption associated with tunable CD/PMD compensation is avoided. Second, no optical gating is necessary. In fact, it would be extremely challenging to implement time-gating to isolate the ICI-free region without precise dispersion compensation as is evident from the eye diagram in Fig. 4(b). Hence, the complications arising from having to use a time-gating modulator per each subchannel, such as clock recovery per subchannel, optical loss, energy consumption for driving the temporal modulators, can be entirely bypassed.

We believe the CMA algorithm semi-deterministically compensates the interference from the neighboring subchannels. The ICI may vary over time owing to the environmental changes including mechanical vibration having the typical time scale of ~1 ms and thermal drifts occurring over the time scale of 1s or longer. We find that the convergence and adaptation of the CMA algorithm is fast and stable enough to track these changes. The fastest significant ICI comes from the beating between the nearest neighbor subcarriers and as a result we would expect that we need at least 2 samples per symbol and probably more to mitigate the effects of ICI. Indeed, we determine that the algorithm is unstable with 2 samples/symbol but is stabilized when 3 samples/symbol. We do not observe material improvement with 4 samples/symbol, confirming that the interference from the subchannels further away than the nearest ones is not significant.

In Fig. 5
, we show the BER of all 13-subchannels of the pol-mux OFDM signal (0.26 Tb/s over 65-GHz) after 400-km transmission. All channels, when measured using 7-tap equalization, show BER much lower than the threshold of 7%-overhead FEC (4x10^{−3}). We observe that the BERs for the even channels are in general better than those of the neighboring odd channels. The trend is attributed to the asymmetry of the extinction ratios of the delay line interferometer (DLI) that was mentioned in Section 2. The imperfect extinction of the DLI leads to interference between the subcarrier channel of interest and spurious signal from the complementary port of the DLI having the same wavelength. We plot in Fig. 4 the extinction ratio as defined as the ratio between the relevant subcarrier power and the power of the spurious subcarrier from the complementary DLI port. The BER and the extinction ratio are well correlated, showing the penalty arising from the interference. We note that the number of taps can be throttled depending on the condition of the system. As shown in Fig. 4, 5 taps are sufficient to achieve BER smaller than the FEC threshold for several channels.

In Fig. 6 , we show in more detail how BER scales with the number of taps N for Ch. 0 after 400-km transmission. We observe similar trends for the other channels as well, showing asymptotic saturation of BER and Q for N>7. The required number of taps for different transmission distance is plotted in Fig. 6(b), where we show N for achieving BER less than the FEC threshold for transmission distance up to 960 km. The data for distance up to 400-km are measured in a straight transmission line consisting of 80-km SSMF spans using Erbium-doped fiber amplifiers (EDFAs) for compensating the span loss. The data for 640-km and 960-km transmission are obtained by using a re-circulating loop consisting of four 80-km SSMF spans using EDFAs. We observe that at least 3 taps are required to compensate for ICI even for back-to-back transmission and then the required number of taps increases more or less linearly for accumulated dispersion larger than ~4000 ps/nm. We note that the impact of ICI would saturate after the temporal walk-off of the neighboring subchannels exceeds the symbol period (CD~5000ps/nm), while ISI due to CD would continue to worsen with the increasing CD. It has been shown [18] that arbitrary amount of impairments due to CD and PMD can be mitigated using the tap-and-delay FIR for single-carrier coherent transmission when the optical nonlinearity is neglected. Although our case is different because of the ICI and potential nonlinear penalties, the trend is promising in that longer distance transmission is feasible with reasonable amount of taps; for example, N~15 for up to 1000-km.

Detailed quantitative comparison of the complexity and energy consumption between our hybrid optical-electronic signal processing and an all-electronic scheme is beyond the scope of this paper as it would depend on many variables including specific algorithm, subcarrier channel plan, and DSP technologies. Nonetheless, we can list potential advantages the hybrid scheme can offer. First, the speed of electronics needed is substantially reduced. For instance, our sampling rate is 16.7 Gsamples/s (~3x oversampling) while an analog-to-digital converter (ADC) of ~100 Gsamples/s (1.5x oversampling) is necessary at least if an optical signal having comparable optical bandwidth (~65 GHz) is to be all-electronically processed with a *single* polarization-diversity coherent receiver. Second, the number of taps required for CD/PMD compensation is much reduced. If we consider transmission of signal with 65-GHz spectral content over 1,000-km SSMF, all-electronic signal processing would require at least ~1,000 taps for frequency domain equalization for fixed CD alone with additional signal processing for dynamic equalization of PMD and time-varying residual CD [1]. In comparison, ~200 (13x15) taps at 3 x symbol rate would be sufficient for the hybrid case. The gain is likely to be greater if we include the computational complexity of FFT, IFFT, and complex multiplication, and the electronic de-serialization to lower rates that are necessary for the electronic FDE. Finally, the signal processing can be done entirely in the time domain with the benefit of reduced latency for transmission over up to ~1,000 km although frequency-domain implementation may provide more simplified architecture for transmission over much longer distances, depending on the number of taps required [1].

The complexity in the optical receiver is clearly greater for the hybrid case and the trend of simplification in the electronic processing needs to be considered against the concomitant increase of the complexity of the hardware that would be required to implement multi-comb generation, multi-channel modulation, and demodulation. Also, the optical DFT will be far more susceptible to the drift of the signal and local-oscillator wavelengths as the number of subcarriers are increased and the channel spacing is reduced. However, the level of complexity required for integrating multiple coherent receivers with suitable optical DFT circuits for the case of 5-10 subchannels having 5-10 GHz channel spacing is within the capability of the state-of-the-art PIC technology [19] and it can be mitigated considering the reduced electronic bandwidth requirement in the hybrid approach. This reduced bandwidth requirement is appealing for silicon photonic integration, where fabrication of high-speed photodetectors and modulators is relatively more challenging in comparison to III-V photonic integration. Additional energy savings can be achieved with full integration of the silicon-photonic OFDM receivers with the electronic signal processing. Implementation of silicon-photonic OFDM receivers is a topic future study.

## 4. Summary

To summarize, we have proposed and demonstrated a novel coherent-optical OFDM transmission scheme based on the combined use of AO-DFT and electronic equalization, capable of supporting long-haul transmission having large accumulated dispersion with significantly reduced complexity and energy consumption in comparison to all-electronic solutions. The use of low-speed subcarrier channels for large dispersion tolerance and all-optical DFT for channelization enabled the simplification of the electronic signal processing, leading to reduced DSP complexity and relaxed electronic bandwidth requirement. We expect this hybrid optical-electronic signal processing approach to be an attractive candidate solution for future high-data-rate transmission systems where energy efficiency is of a major concern.

## Acknowledgments

The authors would like to thank Robert Tkach, Andrew Charplyvy, and Randy Giles for support. This work is partially supported by the city government of Seoul, Republic of Korea, under Seoul R&BD Program WR080951.

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