Image Processing Reference
In-Depth Information
Asymmetric SSFM (A SSFM)
h
step-size.
☺
r
non-linear operator
calculation point.
smaller step-size gives
higher accuracy.
increases computation
cost.
ˆ
ˆ
e
h
e
h
Symmetric SSFM (S SSFM)
ˆ
ˆ
ˆ
(
h
/
2
D
h
(
h
/
2
D
e
e
e
h
z
0
Modified SSFM (M SSFM)
ˆ
ˆ
ˆ
h
rh
D
e
(
r
)
h
e
e
Ezt
(,)
Ez ht
(
, )
Fig. 4. Comparison of the split-step Fourier methods (SSFM).
(Du et al., 2010). Also that non-linearities behave differently for diverse input parameters of
transmission i.e. input power and modulation formats. So we have to modify
Nlpt
(0
≤
r
≤
0.5)
along with the optimization of dispersion
D
and non-linear coefficient
,usedintheDBP,to
get the optimum system performance. It is also well known in the SSFM literature that the
linear section
D
of the two subsequent steps can be combined to reduce the number of Fourier
transforms. This modified split-step Fourier method (M-SSFM) can mathematically be given
as in Eq. 15.
γ
exp
h D
exp
h N
exp
h D
E
z
,
t
(
+
)=
(
−
)
(
)
·
E
z
h
,
t
1
r
r
(15)
3.2.3 Filtered split-step Fourier method (F-SSFM)
In (Du et al., 2010), the concept of filtered DBP (F-DBP) is introduced along with the
optimization of non-linear operator calculation point. It is observed that during each DBP
step intensity of the out-of-band distortion becomes higher. The distortion is produced
by high-frequency intensity fluctuations modulating the outer sub-carriers in the non-linear
sections of DBP. This limits the performance of DBP in the form of noise. To overcome this
problem a low pass filter (LPF), as shown in Fig.5, is introduced in each DBP step. The
digital LPF limits the bandwidth of the compensating waveform so we can optimize the
compensation for the low frequency intensity fluctuations without overcompensating for the
high-frequency intensity fluctuations. This filtering also reduces the required oversampling
factor. The bandwidth of the LPF has to be optimized according to the DBP stages used to
compensate fiber transmission impairments i.e bandwidth is very narrow when very few BP
steps are used and bandwidth increases accordingly when more DBP stages are used. By
using F-SSFM (Du et al., 2010), the results depict that with four backward propagation steps,
the Q at the optimal launch power was improved by 2 dB and 1.6 dB for single wavelength
CO-OFDM and CO-QPSK systems, respectively, in a 3200 km (40x80km) single-mode fiber
link, with no optical dispersion compensation.
3.2.4 Logarithmic split-step Fourier method (L-SSFM)
As studies from (Asif et al., 2011) introduces the concept of logarithmic step-size based DBP
(L-DBP) using split-step Fourier method. 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 as shown in Fig 6. First SSFM methods were based