## Abstract

Fiber chromatic dispersion (CD) in optical OFDM transmission degrades carrier orthogonality, resulting in a system penalty. Such penalty can be mitigated by per-carrier delay precompensation and spectrum filtering. We present a theoretical model to investigate the CD impairment in all-optical OFDM system, and demonstrate experimentally that both methods restore performance without overhead or guard interval.

©2013 Optical Society of America

## 1. Introduction

All-optical orthogonal frequency division multiplexing (AO-OFDM) is a recently developed novel technique where OFDM symbols at single channel rates beyond 100 Gbps are generated by all optical circuitry. In the past years, many research groups have reported related theories and proof-of-concept demonstrations [1–7], and are now advancing with novel component and system technologies that can achieve data rates up to 26 Tbps [8]. Such high transmission rates can be achieved by substituting the electrical processors of transceivers such as discrete Fourier transform (DFT) with optical parallel circuits. Previous works suggested manufacturing of an optical DFT circuit using time delays, phase shifters, and couplers [5,9], delay interferometers [8,10], or arrayed waveguide gratings (AWG) utilizing slab-star couplers [4,11,12]. Yet the key mechanisms of carrier orthogonality in AO-OFDM have not been fully investigated. One of the major concerns rises how fiber transmission impairment affects the carrier orthogonality. This paper introduces a mathematical model to investigate chromatic dispersion (CD) penalty in the AO-OFDM transmission [5–8], and proposes a novel system solution to restore carrier orthogonality, which eliminates requirement of guard band [5,8] or OFDM cyclic prefix [6]. In this paper, we propose two zero-guard-band CD penalty mitigation techniques based on theoretical understandings and demonstrate their benefits experimentally. The first technique is per-carrier time-delay precompensation at a transmitter, and the second is per-carrier optical bandpass filtering. We demonstrate for the first time that the adjacent carrier interference due to CD can be mitigated by delay adjustment and carrier bandwidth limit at the transmitter in an AO-OFDM system.

## 2. Theoretical model for all optical OFDM

The penalty of dispersion consists of two parts. The first problem is symbol waveform deformation that causes inter-symbol interference (ISI), and the other is inter-carrier interference (ICI). In order to investigate the impact of CD impairment in an AO-OFDM transmission system, let us consider an AO-OFDM demultiplexer model of Fig. 1 [5,13], which consists of delay ${T}_{m}\left(\omega \right)={e}^{-j(N-1-m)\tau \omega}$(*m* = 0..*N*-1) and DFT phase-shift ${\varphi}_{mn}={e}^{-j\text{\hspace{0.17em}}{\scriptscriptstyle \frac{2\pi}{N}}mn}$ waveguide arrays for the *n*-th demultiplexer output port. Here, *N* and * ^{τ}* denote the number of OFDM carriers and the period of OFDM sampling, respectively, and hence the OFDM symbol period is

*T*

_{o}=

*Nτ*, and the carrier spacing is

*B*= 1/

*T*

_{o}. Neglecting a constant time delay factor of ${T}_{m}\left(\omega \right)$, and using $\Delta =2\pi B$, the overall transfer function for the

*n*-th output port of the demultiplexer is then:

An ideal OFDM symbol at carrier *i* in the time domain is represented as ${s}_{i}(t)={a}_{i}\Pi (t,T){e}^{-j\text{\hspace{0.17em}}\Delta it}$, where *a _{i}* is the symbol value of on-off keying (OOK), phase shift keying (PSK), or quadrature amplitude modulation (QAM), and rectangle function $\Pi (t,w)=1$for $\left|t\right|\le w/2$; 0, otherwise. The corresponding frequency-domain representation of ${s}_{i}(t)$ is ${S}_{i}(\omega )={a}_{i}\mathrm{sin}c\left((\omega -\Delta i)T\right)$. The CD impairment of the fiber can be modeled as, $C\left(\omega \right)={e}^{j\beta \omega \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, where $\beta =DL{\lambda}^{2}/2\pi c$, and $D$, $L$, $\lambda $, and

*c*, are the fiber CD coefficient, fiber length, wavelength, and speed of light, respectively. Finally, the optical output waveform of the

*i*-th carrier at the

*n*-th AO-OFDM demultiplexer port that has propagated through an amplified fiber transmission system with an uncompensated fiber length of

*L*can be found by numerical inverse Fourier transform of the following expression:

An example application of Eq. (2) to investigate the impact of CD in an AO-OFDM transmission system model is achieved in an *N* = 4 carrier AO-OFDM system model as shown in Fig. 2. In this model, carriers 0, 1, and 2 are amplitude modulated as shown in Fig. 2(a). The carriers are separated by 10 GHz, and centered at a wavelength of 1550 nm. In a fiber transmission system with no CD, ICI is inherently canceled by DFT at designated temporal sampling positions of 50, 150, … 450 ps in Fig. 2(b). Notice that all the ICIs are confined within *T*_{o} = 100 ps. As CD is introduced by 20 km of an SMF-28 fiber, the ICIs spread broader than 100 ps, and shift in time (Fig. 2(c)) according to the group delay difference between different carriers. As a result, carrier-carrier orthogonality is degraded as depicted in Fig. 3(b) due to ICIs from adjacent and far carriers, which affect ICI-free time positions, compared with that of the transmitter AO-OFDM symbol as shown in Fig. 3(a). More careful speculations of the ICI position shift suggests a surprising observation; even though a spectral side lobe of a transmitted carrier experiences the same group delay as the interfering carrier at the same frequency, the ICI-free position shifts in time. Another observation is that ICI waveform broadening produces residual power at ICI-free positions resulting in interference even after orthogonal positions are aligned in the time domain.

As the first zero guard band (ZGB) solution, we propose to adjust the carrier arrival time at an AO-OFDM demultiplexer, as depicted in Fig. 3(c). In this scheme, ICIs are aligned to each other so as to preserve ICI-free intervals at the centers of symbol periods. The proposed scheme can be realized by addition of per-carrier tunable delay lines at the transmitter side as shown in Fig. 4. Even though this AO-OFDM multiplexer design utilizes tunable optical delay at every carrier to ease the understanding of the idea, actual system implementation of delayadjustment can be achieved simply by adjusting modulator reference clock phase electrically instead of the optical delay adjustment.

Another ZGB technique is narrow-band filtering on all carriers at a transmitter so that side-lobe frequency components into far carriers are removed completely. There are two-fold benefits of carrier filtering, which are ICI and ISI reductions. Carrier filtering is an effective alternative to precompensation since complete elimination of interference from far carriers is better than null point alignment. However, filtering only is not fully effective on adjacent carrier ICIs because of the spectrum overlap.

Other dispersion penalty mitigation in AO-OFDM was reported in the literature [5–8,11]. However, most proposals considered the addition of guard band interval, using cyclic prefix, or sub-rate data modulation of carriers. Such methods can avoid dispersion penalty by ICI-free interval broader than spread of ICIs as can be inspired from Fig. 3(d), but sacrifice a large portion of the spectral efficiency and reduce the feasible data rates. The use of dispersion compensation fiber (DCF) is another method to avoid the dispersion penalty but is not a flexible solution especially under dynamic networking environment since wavelength selective switching in WDM networks introduce channel-wise random residual CDs.

## 3. Experimental results

The experimental setup to investigate our proposed scheme is shown in Fig. 5. A comb consisting of 15 tones is generated using mode-locked laser diode (MLLD) and a filter at a repetition rate of 10.7 GHz. The comb is fed into an AO-OFDM 1x16 AWG device [4] (custom made by NEL, Tokyo) to generate 15 continuous-wave carriers separated exactly by 10.7 GHz. The rightmost inset of Fig. 5 shows a measured typical transfer function taken from the port for carrier 8 of the AWG sample, overlapped on ideal transfer functions of all 15 carriers. This transfer function is not ideal so it introduces ICI even in the back-to-back system setup. Hence, we have to utilize partial polarization interleaving among even and oddcarriers. However, this arrangement does not alter the principle of ICI management by precompensation. The inset of Fig. 5 shows the spectrum-sliced carrier spectrum after the first AWG exhibiting only a 20-dB adjacent carrier suppression, which limits the system performance in our experiment.

The outputs of the first AWG are separated into 5 groups in order to apply $data$ and $\overline{data}$ modulations from a pseudorandom bit sequence (PRBS) with a word length of 2^{31}-1 to carriers alternatively to decorrelate adjacent carriers. We applied polarization interleaving on carriers to adjust adjacent carrier crosstalk to get reasonable ICIs for this proof of concept experiment. Hence, we can control the precompensation alignment of only 4 adjacent neighbors at a time since adjacent neighbors impose higher interference than far carriers. In each group, 3 carriers with the same power and polarization have a frequency separation of 5x10.7GHz. These 3 carriers are modulated, polarization controlled, and delay-adjusted for pre-compensation together. In our experimental setup, we characterized performance of carrier 8 for application of both delay precompensation and carrier narrow-band filtering. The filtering is applied on adjacent carriers 7 and 9. The 5-carrier groups are coupled together to form an OFDM symbol centered at a wavelength of 1549.8nm whose spectrum is shown in the inset of Fig. 5. The OFDM symbols are then transmitted through a 150-km dispersion managed fiber transmission system followed by additional fiber options of lengths of 0km, 54km, 75km, and 83km, consisting of single-mode fibers (SMF-28) with a CD coefficient of 16 ps/nm/km. At the receiver side, symbols are demultiplexed using another 1x16 AWG. We measure the BER of carriers from the AWG output with an O/E converter, clock data recovery, and bit-error detector.

We first investigate the effect of delay precompensation with fiber lengths of 0km, 54km, 75km, and 83km. The corresponding group delays between adjacent carriers are measured to be approximately 0ps, 55ps, 80ps, and 90ps, respectively. These group delays cause a significant degradation of the eye pattern (Fig. 6(a)) and the corresponding increase of BERs (Fig. 6(c)) due to orthogonality degradation. After applying delay pre-compensation with the same aforementioned group delay values and hence restoring the ICI-free position alignment, the eye pattern is improved as shown in Fig. 6(b), and the BER is reduced by approximately an order of magnitude in the case of 83 km of uncompensated fiber, as shown in Fig. 6(c), which corresponds to power penalty reduction from 3.7 dB to 2.1 dB. Considering dispersion coefficient of 16 ps/nm∙km and carrier modulation at 10.7 GHz, the compensation by this method seems to be limited to 83km of residual uncompensated fiber, which corresponds to a 102-ps group delay that is comparable to *T*_{0}. When group delay becomes larger than *T*_{0}, ISIpenalty becomes not negligible although ICI can be mitigated by precompensation.

Filtering can be implemented in parallel with delay precompensation for additional improvement. Our observation from the experiment shows that lowering the ICI effect of adjacent carriers is more important than removing interference from far carriers in the spectrum. We installed the band pass filters with a full width of approximately 30 GHz at half maximum on carriers 7 and 9 for our proof-of-concept test. The bandwidth limit on OFDM symbols may degrade orthogonality in the back-to-back performance but it mitigates the penalty from CD impairment. Figure 7 compares the results of filtering only and filtering with delay precompensation. The experimental results clearly show that filtering successfully reduces a large portion of the BER. As delay precompensation added, the majority of the dispersion penalty is mitigated. Both techniques do not require any overhead or waste of the spectrum usage. In our experiment, 128.4 Gbps is transmitted over 149.8 GHz. Considering 7% FEC overhead for a 120-Gbps transmission, the achieved spectral efficiency is approximately 0.81 bps/Hz.

## 4. Conclusion and discussions

We investigated an AO-OFDM transmission with two dispersion mitigation techniques: delay precompensation and carrier filtering. Experimental results show that applying both techniques can reduce a large portion of the system BER penalty of chromatic dispersion with no additional overhead. A total of 120 Gbps IM/DD transmission with FEC is successfully achieved with 0.81 bps/Hz spectral efficiency with an 83-km fiber dispersion tolerance in an SMF-28 transmission system. In addition, we introduced the corresponding mathematical system model to study CD penalty in AO-OFDM transmission systems. The application of dispersion precompensation is limited in maximum bit rate and achievable distance due to ISI penalty caused by chromatic dispersion. In general, the number of carriers in not limited, but the symbol modulation rate of carriers has to be the same in order to avoid interferences in the time domain.

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