Comparison of Intra-Channel Nonlinearity Tolerance
between Reduced-Guard-Interval CO-OFDM Systems and
Nyquist Single Carrier Systems
Qunbi Zhuge, Benoît Châtelain, and David V. Plant
Dept. of Electrical and Computer Engineering
McGill University, Montreal, QC, Canada H3A 2A7
[email protected]
Abstract: Attributed to the higher intra-channel nonlinearity tolerance, reduced-guard-interval
CO-OFDM systems achieve approximately 25% longer maximum reach than Nyquist single
carrier systems for 56 Gbaud QPSK modulations.
OCIS codes: (060.1660) Coherent communications; (060.2330) Fiber optics communications; (060.4080) Modulation.
1. Introduction
As the available bandwidth of a fiber is limited, it is crucial to improve the spectral efficiency in order to increase
the total capacity of optical transmission systems and to satisfy the growing bandwidth demand [1]. For a given
modulation format, because of their compact spectrums, both Nyquist single carrier (SC) and orthogonal frequency
division multiplexing (OFDM) signals facilitate a reduction in channel spacing. The increased spectral efficiency
provided by these modulation formats [2, 3] is achieved without inducing significant inter-channel crosstalk.
Recently, Nyquist 32-QAM SC signals were used to realize a 450 Gb/s transmission with a spectral efficiency of
8.37 b/s/Hz [2]. Also, a 16-QAM reduced-guard-interval (RGI) CO-OFDM system with a data rate of 448 Gb/s and
a spectral efficiency of 5 b/s/Hz was experimentally demonstrated [3]. Moving forward as the speed of digital-toanalog converters (DACs) is continuously increasing, e.g. 56 GSamp/s DACs in [4], the generation of both Nyquist
SC and RGI CO-OFDM signals above 50 Gbaud becomes feasible.
In this paper, we compare the tolerance to the intra-channel nonlinearities between RGI CO-OFDM systems and
Nyquist SC systems. We first show that the two systems have similar equalization complexity and narrow filtering
tolerance. Then by simulation we show that the number of subcarriers Ns affects intra-channel nonlinearities
tolerance of RGI CO-OFDM and the optimal Ns varies as the transmission distance changes. With the optimal Ns,
RGI CO-OFDM achieves >1.4 dB higher Q-factor at various distances than SC with a roll-off factor α=0.1 for
single channel 56 Gbaud QPSK transmissions. As a metric to assess the nonlinearities tolerance, we also show that
RGI CO-OFDM with Ns=64 achieves 25% longer maximum distance than SC systems with α=0.1 given a target bit
error rate (BER) of 3.8×10-3.
2. Comparison of equalization complexity and narrow filtering tolerance
FFT
H CD
FDE
IFFT
FFT
A
C
FFT
IFFT
IFFT
c
IFFT
d
H CD
FFT
OFDE
Optical Channel
FFT
FFT
IFFT
Filter
Filter
Optical Channel
H CD
(b )
B
H CD
TDE
a
b
Filter
Filter
OFDE
IFFT
(a )
D
Fig. 1. Block diagram of (a) Nyquist SC systems and (b) RGI CO-OFDM systems with two-stage equalization.
The complexity of systems is an important design issue, since in practical systems hardware resources for high
speed digital signal processing are very limited. The simplified block diagrams of Nyquist SC systems and RGI COOFDM systems with two-stage equalization are shown in Fig. 1. Nyquist SC systems require a pulse-shaping filter
at the transmitter to obtain the desired compact spectrum, and a matched filter at the receiver to maximize the signalto-noise ratio. Both SC and RGI CO-OFDM systems employ an overlapped frequency domain equalizer (OFDE) as
a cost-effective approach to compensate the static chromatic dispersion (CD) as the length of CD is normally quite
large in dispersion-unmanaged transmissions [6]. Then an adaptive TDE for SC or FDE for RGI CO-OFDM is
employed to compensate for the residual inter-symbol interference and time-varying linear effects such as
polarization mode dispersion (PMD). Because the second stage TDE of SC and FDE of OFDM have similar
complexity, it can be seen from Fig. 1 that the two systems have comparable hardware requirements for linear
equalization as discussed in [6]. The complexity of other processing blocks such as carrier synchronization depends
on the specific algorithms employed, but the differences are expected to be small.
We also compare the narrow filtering tolerance between Nyquist SC and RGI CO-OFDM systems. The
spectrums of SC signals with root raised cosine (RRC) pulse shape (α=0.1) and OFDM signals (Ns=128) are shown
in Fig. 2 (a) and (b), respectively. It can be seen that more energy of OFDM signals are confined within f < 0.5R than
SC signals, where f denotes the frequency and R denotes the baud rate. However, the side lobes of OFDM signals
are much more severe than SC signals as the energy of the OFDM spectrum decreases much more slowly for
f > 0.5R. Fig. 2 (c) shows the OSNR penalty versus the normalized 3 dB filter bandwidth fB/R for various signals.
Back-to-back transmissions were simulated with 4th order Gaussian filters applied at both the transmitter and
receiver, and amplified spontaneous emission (ASE) noise added in-between. Other impairments such as laser phase
noise were not considered. It is observed that all systems have similar filtering tolerance. Using 128 and 64
subcarriers for OFDM yields in slightly better results than using OFDM with 32 subcarriers or SC (α=0.1). It is also
seen that the penalty at the filter bandwidth equal to half the baud rate (fB/R=0.5) is equal to or less than 0.5 dB.
Therefore, both systems are eligible for high spectral efficiency transmissions with small guard band between WDM
channels.
(c )
(a )
(b )
Fig. 2. The spectrum of (a) Nyquist SC signals and (b) RGI CO-OFDM signals. (c) OSNR penalty versus the normalized filter bandwidth.
3. Comparison of intra-channel nonlinearities tolerance
Multi-carrier modulations, e.g. OFDM using multiple frequencies [3] and superchannel (or multiband) using
multiple wavelength carriers [7, 8], are conventionally considered to be more vulnerable to nonlinearities than SC
due to their high peak-to-average power ratios (PAPRs). However, it has been recently demonstrated that in
superchannel scenarios, despite of the higher PAPR of signals generated at the transmitter, using multiple carriers is
beneficial for fiber nonlinearities tolerance compared to SC systems attributed to the effect of CD [7, 8]. However,
those superchannel techniques require additional modulators and filters at both ends and thus increase the system
complexity. Moreover, the orthogonality between carriers should be ensured. Otherwise, the induced crosstalk will
degrade the performance [9]. We will show that with the availability of high speed DACs/ADCs RGI CO-OFDM
with a small number of subcarriers can achieve similar nonlinearities improvements compared to SC systems, and
meanwhile reduce the system requirements of additional hardware complexities and the orthogonality between
carriers.
Before Transmission
After Transmission
SC Pulses
Before Transmission
After Transmission
OFDM subcarriers
Fig. 3. Illustration of the CD effect on the SC pulses and OFDM subcarriers in the time domain.
The nonlinearity tolerance improvement using multi-carrier modulations has been explained by the theory of
four-wave mixing efficiency in [7] and intensity fluctuation difference in [8]. Here we propose another explanation.
Fig. 3 illustrates the evolution of SC pulses and OFDM subcarriers in the time domain. Note that OFDM subcarriers
within each symbol are overlapped in the time domain but for clarity they are vertically separated in Fig. 3. It is
known that CD broadens SC pulses, leading to overlaps between them. But because the relative position between
pulses is unchanged, SC pulses are highly correlated during the transmission. For OFDM, the duration of subcarriers
remains almost the same in transmission, due to the much narrower bandwidth of each subcarrier. Instead, CD
induces a walk-off between subcarriers as shown in Fig. 3 and thus decorrelates them during transmission. Such a
decorrelation will result in an averaging effect on their nonlinearity interactions and thus reduce the net phase
modulation, i.e. fiber nonlinearity distortions.
Single channel 56 Gbaud QPSK dual-polarization (224 Gb/s) transmissions of both SC and OFDM systems were
simulated in Optisystem 9.0 to investigate the intra-channel nonlinearity tolerance. RRC pulse with α=0.1 was used
for SC systems, while OFDM signals with various Ns were assessed. The fiber was simulated with a dispersion
parameter of 17 ps/(nm·km), an attenuation factor of 0.2 dB/km, an effective area of 80 μm2, and a nonlinearity
refractive index of 2.6×10-26 m2/W. EDFAs with a gain of 16 dB were used to compensate the loss of each span with
a length of 80 km, and the noise figure was 5 dB. Laser linewidths were set to zero and PMD was neglected. CD
was assumed to be completely compensated by the OFDE at the receiver for both systems.
It has been shown in [8] that the optimal number of carriers that maximize the nonlinearity tolerance is
dependent of the transmission distance. For RGI CO-OFDM, we observe a consistent trend as shown in Fig. 4. In
particular, the optimal Ns increases as the transmission distance becomes longer. We also plot the Q-factor versus
the transmission distance, where the Q-factor is calculated from the variance of the constellation spread. The RGI
CO-OFDM with Ns=64 achieves 1.6 dB higher Q-factor than SC at L = 4800 km, but the improvement becomes
smaller while the distance decreases. However, with the optimized Ns RGI CO-OFDM achieves > 1.4 dB Q-factor
improvement compared to SC for all distances in Fig. 4. It is also worth noting that in Fig. 4 for L larger than
3000 km the Q-factor difference between the system with the optimal Ns which is around 40 and the system with
Ns = 64 is small (<0.3 dB). Although the intra-channel nonlinearity tolerance is improved, using such small number
of subcarriers (e.g. 32) might affect the other aspects of OFDM systems, including the increased cyclic prefix
overhead which can be handled using the equalization scheme proposed in [10], the increased dispersion-enhanced
phase noise [11], and the reduced narrow filtering tolerance as already discussed in section II. .
Fig. 4. Q-factor versus the distance and the optimization of Ns.
Fig. 5. Launch power versus the reach distance at BER = 3.8×10-3.
In Fig. 5, we use the maximum reach as a metric to investigate the intra-channel nonlinearity tolerance. The ASE
noise is loaded before the coherent detection in order to obtain a reasonable maximum reach close to the
experimental demonstrations of QPSK transmission [12]. The reach distance is obtained when the BER reaches
3.8×10-3. First, for low launch powers (<-2 dBm) where the linear impairment dominates, all systems achieve
identical reach distances. But as the launch power increases, OFDM systems begin to outperform the SC system as
the reach distance becomes larger attributed to the improved nonlinearity tolerance. At the maximum SC (α=0.1)
reaches a distance of 4604 km, OFDM (Ns=128) reaches 5328 km and OFDM (Ns=64) reaches 5753 km. Therefore,
the maximum reach is increased by 15.7% and 25% for OFDM (Ns=128) and OFDM (Ns=64), respectively,
compared to SC (α=0.1).
4. Conclusions
With the similar linear equalization complexity and narrow filtering tolerance, reduced-guard-interval (RGI) COOFDM systems are superior to Nyquist single carrier (SC) systems in terms of intra-channel fiber nonlinearity
tolerance. We show by simulation that RGI CO-OFDM increases the maximum transmission distance by
approximately 25% compared to Nyquist SC for 56 Gbaud QPSK transmissions.
Reference
[1] P. J. Winzer, Communications Magazine, vol. 48, pp. 26-30, 2010.
[2] X. Zhou, et al., OFC’11, PDPB3.
[3] X. Liu, et al., JLT, vol. 29, pp. 483-490, 2011.
[4] Y. M. Greshishchev, et al., ISSCC’11, 10.8.
[5] Q. Zhuge, et al., ECOC'11, Th.11.B.5.
[6] B. Spinnler, JSTQE, vol. 16, pp. 1180-1192, 2010.
[7] W. Shieh, et al., Photonics Journal, vol. 2, pp. 276-283, 2010.
[8] L. B. Du, et al., OE, vol. 19, pp. 8079-8084, 2011.
[9] J. Zhao, et al., OE, vol. 19, pp. 14617-14631, 2011.
[10] C. Chen, et al., OE, vol. 19, pp. 7451-7467, 2011.
[11] Q. Zhuge, et al., OE, vol. 19, pp. 4472-4484, 2011.
[12] E. Torrengo, et al., PTL, vol. 22, pp. 1714-1716, 2010.