ZTE Communications

Compensating for Nonlinear
Effects in Coherent-Detection
Optical Transmission Systems
Fan Fan Zhang Zhang
(State Key Laboratory of Advanced Optical Communication Systems & Networks, Peking University, Beijing 100871, P.R.China)
Abstract
Fiber nonlinearity is one of the most important limiters of capacity in coherent optical communications. In this paper, we review two nonlinear
compensation methods: digital backward propagation (BP) and nonlinear electrical equalizer (NLEE) based on the time-domain Volterra
series. These compensation algorithms are implemented in a single-channel 50 Gb/s coherent optical single-carrier frequency-division
multiplexed (CO-SCFDM) system transmitting over 10 × 80 km of standard single-mode fiber (SSMF).
Keywords
coherent optical communication; fiber nonlinearity; digital signal processing
T1 Introduction
he demands of high-capacity optical
transmission systems have led to the rapid
development of coherent optical systems. A
coherent receiver with optical hybrid allows the
electrical field in the two fiber polarizations to be
recovered. High spectral efficiency can thus be implemented
using advanced modulation-format encoding information in
all the available degrees of freedom. Digital signal processing
(DSP) simplifies coherent detection and gives it greater
flexibility and hardware transparency as well as the potential
to adaptively compensate for channel impairments in the
electrical domain [1], [2]. In coherent optical communications,
linear impairments, such as fiber chromatic dispersion (CD)
and polarization mode dispersion (PMD) (all orders), can be
compensated for in principle. Fiber capacity is limited by
nonlinearity and amplified spontaneous emission (ASE) in
optical amplifiers. ASE is white noise and cannot be
eliminated. The maximum transfer rate for a given noise level
is called the Shannon limit. Fiber nonlinearity is caused by the
optical Kerr effect during signal propagation, and evolution of
the optical pulse is governed by the nonlinear Schrödinger
equation (NLSE). Therefore, nonlinear distortions are
determinate and can be partially compensated for by DSP in
the coherent receiver.
Backward propagation (BP) is proposed as a universal
method of inverting nonlinear systems. In direct-detection
S pecial Topic
Compensating for Nonlinear Effects in Coherent-Detection Optical Transmission Systems
Fan Zhang
systems, electrical predistortion (EPD) can be used to
equalize intrachannel nonlinearities by modeling channel
inversion for nonlinear effects and predistorting transmitted
waveform accordingly [3], [4]. Digital BP is incorporated into
coherent optical receivers by using a split-step Fourier (SSF)
method [5]-[7] based on a hybrid time and
frequency-domain approach. BP can also be implemented
using a split-step finite-impulse response filter (SS-FIR) [8]
that operates entirely in the time domain. Coherent detection
is usually combined with polarization-division multiplexing
(PDM) to increase spectral efficiency. Fiber nonlinearity in
PDM coherent systems can be compensated for by BP in the
Manakov frame [9], [10], which takes the average effect of
fast polarization rotations into account.
BP is an iterative numerical method. Because it is
non-recursive, a nonlinear electrical equalizer based on the
time-domain Volterra series has been proposed for coherent
optical systems [11]. If a sufficient number of delay taps are
used, the accuracy of BP is comparable to that of an SSF
method with one step per span.
Coherent optical orthogonal frequency-division
multiplexing (CO-OFDM) has intrinsic advantages, such as
flexibility in dividing spectrum, high spectral efficiency (SE),
and outstanding tolerance of CD and PMD [12]. Nonlinearity
compensation has previously been performed in CO-OFDM
systems using back propagation [10]-[13] and the Volterra
series [14], [15].
Although CO-OFDM has some impressive advantages, its
March 2012 Vol.10 No.1 ZTE COMMUNICATIONS 45