Image Processing Reference
In-Depth Information
(, ,)
(
,
,
)
111
2
2
2
E
(z,t)
E
(z,t)
E (z,t)
in
E
(z,t)
FP
DBP
FP
-N - 1 1
Digital Backward Propagation (DBP)
N + 1 1
Forward Propagation (FP)
Fig. 2. Block diagram of forward propagation (FP) and digital backward propagation (DBP).
operator is below a certain value. It has been reported (Sinkin et al., 2003) that when
φ max is
below 0.05 rad , the split-step Fourier method gives a good result for simulation of most optical
communication systems. The simulation time of Eq.11 will greatly depend on the step-size of
h . The block diagram of SSFM method is shown in Fig. 4.
3.2 Digital backward propagation (DBP)
The non-linear Schrödinger equation can be solved inversely to calculate the undistorted
transmitted signal from the distorted received signal. The received signal at the receiver after
transmission i.e. forward propagation (FP), is processed through a numerical model by using
the negative sign with the propagation parameters i.e.
dispersion D , non-linear coefficient
γ
. The method is termed as digital backward propagation (DBP) and is illustrated in Fig. 2.
Mathematically inverse non-linear Schrödinger equation can be given as in Eq. 12;
z =
D E
E
N
(12)
Whereas; the D and N are the linear and non-linear operators respectively.
The performance of DBP algorithm mainly depends on the estimation of propagating
parameters of NLSE. To numerically solve NLSE with high accuracy, split-step Fourier
method (SSFM) is used as discussed in the previous section. Both the operators i.e. linear
D and non-linear N are solved separately and also that linear D part is solved in frequency
domain whereas non-linear N is solved in time domain. This DBP model can be implemented
both on the transmitter side as well as on the receiver side. When the signal is numerically
distorted at the transmitter by DBP algorithm and then this pre-distorted signal is transmitted
through fiber link it is termed as transmitter side DBP (Ip et al., 2008). While in majority
of the cases DBP is implemented along with the coherent receiver, it is termed as receiver
side DBP (Ip et al., 2008), and as an example QPSK receiver is illustrated as in Fig. 3. In
the absence of noise in the transmission link both the schemes of DBP are equivalent. As the
backward propagation operates on the complex-envelope of E
, this algorithm in principle
is applicable with any modulation format of the transmission. It should be noted that the
performance of DBP is limited by the amplified spontaneous emission (ASE) noise as it is
a non-deterministic noise source and cannot be back propagated (Ip et al., 2008). DBP can
only take into account the deterministic impairments. In terms of step-size h ,DBPcanbe
categorized in 3 types: (a) sub-span step size in which multiple calculation steps are processed
over a single span of fiber; (b) per-span step size which is one calculation step per fiber span
and (c) multi-span step size in which one calculation step is processed over several spans of
(
z , t
)
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