Image Processing Reference
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stage. In (Li et al., 2011) the investigations depict the results in 100GHz channel spaced
DP-QPSK transmission and multi-span DBP shows a reduction of DBP stages upto 75%.
While in (Rafique et al., 2011c) the algorithm is investigated for single channel DP-QPSK
transmission. In this article upto 80% reduction in required back-propagation stages is
shown to perform non-linear compensation in comparison to the standard back-propagation
algorithm.
In the aforementioned investigations there is a trade-off relationship between achievable
improvement and algorithm complexity in the DBP. Therefore DBP algorithms with higher
improvement in system performance as compared to conventional methods are very
attractive. Due to this fact simplification of the DBP model to efficiently describe fiber
transmission especially for POLMUX signals and an estimation method to precisely optimize
parameters are the keys for its future cost-effective implementation. By keeping in mind that
existing DBP techniques are implemented with constant step-size SSFM methods.
The use
of these methods, however, need the optimization of D ,
and r for efficient mitigation of
CD and NL. In (Asif et al., 2011) numerical investigation for the first time on logarithmic
step-size distribution to explore the simplified and efficient implementation of DBP using
SSFM is done (see section 3.2.4 of this chapter). The basic motivation of implementing
logarithmic step-size relates to the fact of exponential decay of signal power and thus NL
phase shift in the beginning sections of each fiber span. The algorithm is investigated in
N-channel 112Gbit/s/ch DP-QPSK transmission (a total transmission capacity of 1.12Tbit/s)
over 2000km SMF with no in-line optical dispersion compensation. The results depict
enhanced system performance of DP-QPSK transmission, i.e. efficient mitigation of fiber
transmission impairments, especially at higher baud rates. The benefit of the logarithmic
step-size is the reduced complexity as the same forward propagation parameters can be used
in DBP without optimization and computational time which is less than conventional M-SSFM
based DBP.
The advancements in DBP algorithm till date are summarized in Appendix A. The detailed
theory of split-step methods and the effect of step-size selection is explained in the following
sections.
γ
3. Non-linear Schrödinger equation (NLSE)
The propagation of optical signals in the single mode fiber (SMF) can be interpreted by the
Maxwell's equations. It can mathematically be given as in the form of a wave equation as in
Eq. 1 (Agrawal, 2001).
2 E
2 P
c 2
1
2 t μ 0
(
E
)
2 E
=
(1)
2 t
Whereas, E is the electric field,
μ 0 is the vacuum permeability, c is the speed of light and P
is the polarization field. At very weak optical powers, the induced polarization has a linear
relationship with E such that;
x ( 1 ) (
t
r , t
dt
P L (
)= ε 0
) ·
(
)
r , t
t
E
(2)
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