Image Processing Reference
In-Depth Information
In a WDM transmission with large dispersion, pulses in different channels move through each
other very rapidly. To resolve the collisions (Sinkin et al., 2003) between pulses in different
channels the step-size in the walk-off method is chosen, so that in a single step two pulses in
the two edge channels shift with respect to each other by a time that is a specified fraction of
the pulse width. Mathematically it is depicted as in Eq. 19.
C
υ g
=
h
(19)
υ g is
Whereas, C is a error bounding constant that can vary from system to system,
the largest group velocity difference between the channels.
In any transmission model
υ g =
λ i , j is the wavelength difference between channels i and j . fthe
transmission link consists of same kind of fiber, step-size selection due to walk-off method
is considered as constant (Sinkin et al., 2003).
|
D
| Δ λ i , j .Where
3.3.3 Local error method
Local error method adaptively adjusts the step-size for required accuracy.
In this method
step-size is selected by calculating the relative local error
δ L of non-linear phase shift in
each single step (Sinkin et al., 2003), taking into account the error estimation and linear
extrapolation. The local error method provides higher accuracy than constant step-size SSFM
method, since it is method of third order. On the other hand, the local error method needs
additional 50% computational effort (Jaworski, 2008) comparing with the constant step-size
SSFM. Simulations are carried out in parallel with coarse step-size (2 h )andfine( h )steps.
In each step the relative local error is being calculated:
δ =
u f
u c
/
u c
.Whereas,
=
|
(
) |
2 dt .
u f determines fine solution, u c is the coarse solution and
u
u
t
The step size
is chosen by keeping in each single step the relative local error
δ
within a specified range
(1/2
δ G ,
δ G ), where
δ G is the global local error.
The main advantage of this algorithm is
adaptively controlled step size (Jaworski, 2008) .
4. Recent developments in DBP
4.1 Correlated backward Propagation (CBP)
Recently a promising method to implement DBP is introduced by (Li et al., 2011; Rafique et
al., 2011c) which is correlated backward propagation (CBP). The basic theme of implementing
this scheme is to take into account the effect of neighbouring symbols in the calculation of
non-linear phase shift
φ NL at a certain instant. The physical theory behind CBP is that the SPM
imprinted on one symbol is not only related to the power of that symbol but also related to the
powers of its neighbouring symbols because of the pulse broadening due to linear distortions.
The schematic diagram of the CBP is as given in Fig. 7.
The correlation between neighbouring symbols is taken into account by applying a
time-domain filter (Rafique et al., 2011c) corresponding to the weighted sum of neighbouring
symbols. Non-linear phase shift on a given symbol by using CBP can be given as in Eq. 20
and 21.
exp
c k a
E i x t
b
E i y t
+(
N
1
)
/2
2
2
k T s
2
k T s
2
E out
x
E i x ·
=
j
·
+
(20)
k
= (
N
1
)
/2
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