ZTE Communications

S pecial Topic
Exploiting the Faster-Than-Nyquist Concept in Wavelength-Division Multiplexing Systems Using Duobinary Shaping
Jianqiang Li, Ekawit Tipsuwannakul, Magnus Karlsson, and Peter A. Andrekson
near-symbol-rate channel spacing. Ideally, inter-symbol
interference (ISI) is absent. However, filtering or spectral
shaping often requires special treatment so that this Nyquist
ISI-free criterion is met. It is also difficult to approach the
Nyquist limit in practice; the channel spacing has to be
slightly larger than the symbol rate because of inter-channel
linear crosstalk [12]-[15]. Nyquist WDM assumes that the
overall channel has no ISI or a small amount of linear ISI
(excluding chromatic dispersion and polarization-mode
dispersion, which are all-pass effects). Thus, optimum
performance can be approached by combining a linear
equalizer and a hard-decision-based detector, which is
widely used in conventional WDM systems with coherent
detection. In Nyquist WDM, the lower bound of the channel
spacing is the symbol rate because the Nyquist ISI-free
criterion dictates that the symbol rate cannot exceed the
Nyquist rate of 2W over an ISI-free band-limited channel with
single-sided cut-off bandwidth W [16].
To exceed the Nyquist limit, faster-than-Nyquist has been
proposed [16]-[19]. The fundamental idea behind this new
concept is to increase the symbol rate above Nyquist rate by
accepting a certain amount of ISI left to the detectors. The
optimum detectors are those based on maximum a-posteriori
probability (MAP) and maximum-likelihood (ML) criteria, not
hard-decision criteria. Relaxing the ISI-free criterion greatly
reduces bandwidth requirements on the transceiver and
eases the difficulty of Nyquist filtering or shaping in practice.
These benefits encourage the application of
faster-than-Nyquist in realistic WDM systems. Our intention
is to use faster-than-Nyquist without forcing the symbol rate
beyond the Nyquist rate (even though it can be done).
Although faster-than-Nyquist is relatively new in optical
communications, it has already been leveraged in the
systems described in [20]-[25]. In these systems, ISI was
introduced by commercial electrical or optical analog filters
(without any specific designs), and some ISI was left to the
final MAP or ML detectors. A problem with an optimal MAP or
ML receiver is that computations and storage grow
exponentially with channel memory [26]. The channel memory
induced by ISI in constrained-bandwidth systems (such as
those in [20]-[22]) often spans a large number of symbols,
and this results in unacceptably complex detectors.
Moreover, the ISI pattern in these systems is unknown and
unconditioned, and additional channel estimators are needed.
Therefore, the success of faster-than-Nyquist depends on
innovations that address all these problems.
3 A Practical Suboptimal Receiver
In [27], a finite impulse response (FIR) equalizer is used to
shape the channel response into an intermediate truncated
channel response with a short memory. The FIR equalizer then
feeds the equalized output to a simplified
maximum-likelihood sequence detector (MLSD) (Fig. 1). This
equalizer is a partial-response equalizer because its shaping
goal is one channel with a specified truncated ISI pattern. By
using a partial-response equalizer, the overall memory or
24
ZTE COMMUNICATIONS
March 2012 Vol.10 No.1
Tx Channel Rx
Partial-Response
Equalizer
Original Channel Response with
Long and Unknow Memory
MLSD: maximum-likelihood sequence detector
▲Figure1. The typical system structure suggested in [27].
MLSD
Intermediate Response with
Short and Unknow Memory
accounted-for ISI can be arbitrarily shared between the
partial-response equalizer and the MLSD. This allows a
trade-off between complexity and performance, and the
solution has been the basis of numerous receiver structures
[28]-[30]. In these receivers, the least-mean-square (LMS)
algorithm is commonly used so that the equalizer is adaptive.
The adaptive equalizer can operate in a decision-directed
[28], [29] or decision-feedback manner [30]. Regardless of
which structure is used, the performance advantage of the
MLSD is retained by carefully selecting the intermediate
truncated channel so that the amplitude response is similar to
that of the original channel. The reason for this guideline is
that the shaping process by the partial-response equalizer
would alter the spectral characteristic and power of the noise,
which would ultimately influence the effective signal-to-noise
ratio (SNR) and MLSD performance.
Linear equalizers in fiber-optic systems are essential and
have been widely applied [31]. Adaptive equalizers can
conveniently perform polarization demultiplexing and
compensate for almost all static and time-varying linear
impairments. In optical coherent receivers, adaptive
equalizers using constant modulus algorithm (CMA) and
decision-directed LMS (DD-LMS) algorithm are used to
mitigate ISI in the channel. However, noise may be strong if ISI
is strong [26]. The shaping goal of an adaptive equalizer is an
ISI-free channel, and an adaptive equalizer cannot be used
for partial-response shaping. Moreover, it might also be
inadvisable to modify the equalizer in an optical coherent
receiver referring to [28]-[30] because this would not only
complicate the equalizer itself but also significantly change
the carrier recovery algorithms. For example, the equalizer
structure proposed in [22] is similar to that in [29] for optical
coherent receivers whereas the frequency offset was
assumed to be known and had to be compensated for before
the equalizer. Therefore, it is desirable to innovate on receiver
structures without altering the existing mature coherent
receiver algorithms.
Another concern is how to determine the intermediate
channel response in spectrally-efficient optical WDM systems
by using the previously mentioned guideline. For general
time-varying channels, an algorithm has been developed to
adaptively optimize the intermediate channel response by
minimizing the mean-square error [28]. In real optical
networks, the memory or ISI in one channel (excluding the ISI
induced by dispersion) is commonly introduced by
bandwidth-limiting components such as the optical
modulators, WDM components, reconfigurable optical