Image Processing Reference
In-Depth Information
Alternatively, infinite impulse response (IIR) filters can used (Goldfarb et al., 2007) to reduce
the complexity of the DSP circuit.
However, with the use of higher order modulation formats, i.e QPSK and QAM, to meet the
capacity requirements, it becomes vital to compensate non-linearities along with the fiber
dispersion. Due to this non-linear threshold point (NLT) of the transmission system can be
improved and more signal power can be injected in the system to have longer transmission
distances. In (Geyer et al., 2010) a low complexity non-linear compensator scheme
with automatic control loop is introduced. The proposed simple non-linear compensator
requires considerably lower implementation complexity and can blindly adapt the required
coefficients. In uncompensated links, the simple scheme is not able to improve performance,
as the non-linear distortions are distributed over different amounts of CD-impairment.
Nevertheless the scheme might still be useful to compensate possible non-linear distortions of
the transmitter. In transmission links with full in-line compensation the compensator provides
1dB additional noise tolerance. This makes it useful in 10Gbit/s upgrade scenarios where
optical CD compensation is still present. Another promising electronic method, investigated
in higher bit-rate transmissions and for diverse dispersion mapping, is the digital backward
propagation (DBP), which can jointly mitigate dispersion and non-linearities. The DBP
algorithm can be implemented numerically by solving the inverse non-linear Schrödinger
equation (NLSE) using split-step Fourier method (SSFM) (Ip et al., 2008). This technique is
an off-line signal processing method. The limitation so far for its real-time implementation
is the complexity of the algorithm (Yamazaki et al., 2011). The performance of the algorithm
is dependent on the calculation steps (
h
), to estimate the transmission link parameters with
accuracy, and on the knowledge of transmission link design.
In this chapter we give a detailed overview on the advancements in DBP algorithm based on
different types of mathematical models. We discuss the importance of optimized step-size
selection for simplified and computationally efficient algorithm of DBP.
2. State of the art
Pioneering concepts on backward propagation have been reported in articles of (Pare et al.,
1996; Tsang et al., 2003). In (Tsang et al., 2003) backward propagation is demonstrated as a
numerical technique for reversing femtosecond pulse propagation in an optical fiber, such
that given any output pulse it is possible to obtain the input pulse shape by numerically
undoing all dispersion and non-linear effects. Whereas, in (Pare et al., 1996) a dispersive
medium with a negative non-linear refractive-index coefficient is demonstrated to compensate
the dispersion and the non-linearities. Based on the fact that signal propagation can be
interpreted by the non-linear Schrödinger equation (NLSE) (Agrawal, 2001). The inverse
solution i.e. backward propagation, of this equation can numerically be solved by using
split-step Fourier method (SSFM). So backward propagation can be implemented digitally at
the receiver (see section 3.2 of this chapter). In digital domain, first important investigations
(Ip et al., 2008; Li et al., 2008) are reported on compensation of transmission impairments
by DBP with modern-age optical communication systems and coherent receivers. Coherent
detection plays a vital role for DBP algorithm as it provides necessary information about the
signal phase. In (Ip et al., 2008) 21.4Gbit/s RZ-QPSK transmission model over 2000km single
mode fiber (SMF) is used to investigate the role of dispersion mapping, sampling ratio and
multi-channel transmission. DBP is implemented by using a asymmetric split-step Fourier
method (A-SSFM). In A-SSFM method each calculation step is solved by linear operator (
D
)