Constellation optimization based on generalized mutual information over a nonlinear optical channel
Aspects of the present disclosure describe methods of generating an optimized set of constellation symbols for an optical transmission network wherein the optimized constellation is based on GMI cost and considers both fiber nonlinearity and linear transmission noise.
1. A computer implemented method of generating an optimized constellation for an optical fiber network including one or more optical channels, the method comprising: by the computer:
receiving by the computer for one of the one or more optical channels, a target constellation X with assigned bit mapping and geometric shape, wherein X is taken from an N-dim signal constellation {X 1 ,X 2 , - - - ,X M } at a specified probability mass function (PMF) given by p(Xi), i∈{1,2, - - - ,M};
receiving by the computer for the one of the one or more optical channels, channel parameters for the one channel including fiber dispersion, nonlinearity coefficients, span length, noise figures, channel spacing and symbol baudrate;
determining by the computer for the one of the one or more optical channels using the target constellation and the channel parameters, a received nonlinear signal-to-noise ratio (SNR) including both linear amplifier noise and modulation-dependent nonlinear noise;
iteratively determining for the received nonlinear SNR, a generalized mutual information (GMI) cost function by generating random symbols from the target constellation X following a given PMF p(xi), the GMI determined according to the following relationship:
R
GMI
=
H
(
X
)
+
∑
i
=
1
l
o
g
2
M
〈
log
2
[
b
i
(
j
)
·
L
1
(
j
)
+
(
1
-
b
i
(
j
)
)
·
L
0
(
j
)
p
y
(
j
)
]
〉
,
where bi(j)ε{0,1} denotes transmitted bits for jth symbol at ith bit and Py(j) is a probability of a received jth symbol Y(j), and operator <⋅> represents an arithmetic average over all a simulated symbol index j;
L 0 and L 1 represent a bit likelihood (L) for the received jth symbol Y(j), which is determined according to the following relationship:
L
b
,
=
0
,
1
j
∑
x
b
i
=
0
,
1
p
(
y
(
j
)
|
x
b
i
=
0
,
1
)
p
(
x
b
i
=
0
,
1
)
=
∑
x
b
i
=
0
,
1
(
2
π
σ
2
)
-
n
/
2
exp
(
-
y
(
j
)
-
x
b
i
=
0
,
1
2
2
σ
2
)
p
(
x
b
i
-
0
,
1
)
,
Where σ 2 ≙σ n 2 /N is a noise variance in each dimension; and
continuing with the iteratively determining until an increment of GMI cost function is less than a target range.