Image Processing Reference
In-Depth Information
(1 -Stage)
st
(N -Stage)
th
A/D
LO
Data
out
A/D
A/D
A/D
Coherent Receiver and Digital Processing Module
Fig. 3. Block diagram of coherent receiver with digital signal processing module of DBP
(LC=linear compensation and NLC=non-linear compensation).
fiber. The SSFM methods which are used to implement the DBP algorithm are discussed in
next sections.
3.2.1 Asymmetric and Symmetric SSFM (A-SSFM and S-SSFM)
SSFM can be implemented by using two conventional methods: asymmetric SSFM (A-SSFM)
method where the linear operator (
D
) is followed by a non-linear operator (
N
) and symmetric
SSFM (S-SSFM) method where the linear operator (
D
) is split into two halves and is evaluated
on both sides of non-linear operator (
N
), as shown in Fig. 4. Mathematically S-SSFM can be
given as in Eq. 13 and A-SSFM in Eq. 14.
exp
hD
2
exp
h N
exp
hD
E
z
,
t
E
(
z
+
h
,
t
)=
·
(13)
2
exp
h D
exp
h N
·
E
z
,
t
(
+
)=
E
z
h
,
t
(14)
Two methods are adapted for computing parameters in S-SSFM (Asif et al., 2010; Ip et al.,
2008).
N
N
(
+
)
(
)
The method in which
z
h
is calculated by initially assuming it as
z
then
,whichenablesanewvalueof
N
new
(
+
)
(
+
)
estimating
E
z
h
,
t
z
h
and subsequently estimating
E
new
(
is termed as iterative symmetric SSFM (IS-SSFM). The other method, which is
less time consuming and has fewer computations, is based on the calculation of
z
+
h
,
t
)
N
at
the middle of propagation
h
is termed as non-iterative symmetric SSFM (NIS-SSFM). However
computational efficiency of NIS-SSFM is better then IS-SSFM method (Asif et al., 2010).
(
z
+
h
)
3.2.2 Modified split-step Fourier method (M-SSFM)
For the modification of conventional SSFM method, (
?
) introduces a coefficient
r
which defines
the position of non-linear operator calculation point (
Nlpt
), as illustrated in Fig. 4. Typically,
r
=0 for A-SSFM and
r
=0.5 for S-SSFM. Which means that with per-span DBP compensation
A-SSFM models all the fiber non-linearities as a single lumped non-linearity calculation point
which is at
r
=0 (at the end of DBP fiber span) and S-SSFM models all the fiber non-linearities
as a single lumped non-linearity calculation point which is at
r
=0.5. This approximation
becomes less accurate particularly in case of sub-span DBP or multi-span DBP due to
inter-span non-linear phase shift estimation
φ
NL
, which may result in the over-compensation
or under-compensation of the fiber non-linearity, reducing the mitigation of fiber impairments