PHASE SKEW COMPENSATION AT A COHERENT OPTICAL RECEIVER
It is disclosed a coherent optical receiver configured to receive a modulated optical signal and to generate an in-phase component and a quadrature component. The optical coherent receiver comprises a phase skew compensator in turn comprising a first digital circuit and a second digital circuit retroactively connected between an output and a control input of the first digital circuit. The first digital circuit provides a compensated in-phase component as a sum of the in-phase component multiplied by a first gain and the quadrature component multiplied by a second gain, and a compensated quadrature component as a sum of the in-phase component multiplied by a third gain and the quadrature component multiplied by a fourth gain. The second digital circuit computes the first, second, third and fourth gain as functions of an estimated cross-correlation between the compensated in-phase component and the compensated quadrature component.
1 . A coherent optical receiver for an optical communication network, said coherent optical receiver being configured to receive a modulated optical signal and to process said modulated optical signal to generate an in-phase component and a quadrature component, said optical coherent receiver comprising a phase skew compensator comprising:
a first digital circuit configured to provide:
a phase skew compensated in-phase component as a sum of said in-phase component multiplied by a first gain and said quadrature component multiplied by a second gain; and
a phase skew compensated quadrature component as a sum of said in-phase component multiplied by a third gain and said quadrature component multiplied by a fourth gain; and
a second digital circuit retroactively connected between an output and a control input of said first digital circuit and configured to compute said first gain, said second gain, said third gain and said fourth gain as functions of an estimated cross-correlation between said phase skew compensated in-phase component and said phase skew compensated quadrature component.
2 . The coherent optical receiver according to claim 1 , wherein said second digital circuit is configured to compute said first gain and said fourth gain as a function of said estimated cross-correlation according to the following equation:
G
11
=
G
22
=
cos
(
asin
(
R
[
m
]
)
/
2
)
2
cos
2
(
asin
(
R
[
m
]
)
/
2
)
-
1
,
G 11 being said first gain, G 22 being said fourth gain and R[m] being said estimated cross-correlation.
3 . The coherent optical receiver according to claim 1 , wherein said second digital circuit is configured to compute said second gain and said third gain as a function of said estimated cross-correlation according to the following equation:
G
12
=
G
21
=
-
sin
(
asin
(
R
[
m
]
)
/
2
)
2
cos
2
(
asin
(
R
[
m
]
)
/
2
)
-
1
,
G 12 being said second gain, G 21 being said third gain and R[m] being said estimated cross-correlation.
4 . The coherent optical receiver according to claim 1 , wherein said second digital circuit comprises a multiply-and-add module and an accumulator connected at the output of said first digital circuit wherein:
said multiply-and-add module is configured to receive N samples of said phase skew compensated in-phase component and N samples of said phase skew compensated quadrature component from said first digital circuit, N being an integer equal to or higher than 1, and to calculate a sum according to the following equation:
S
=
∑
k
=
1
N
I
k
*
·
Q
k
*
,
S being said sum, I k * being said N samples of the phase skew compensated in-phase component and Q k * being said N samples of said phase skew compensated quadrature component; and
said accumulator is configured to update its content by adding said sum to it, to obtain said estimated cross-correlation.
5 . The coherent optical receiver according to claim 4 , wherein said second digital circuit further comprises a multiplier interposed between said multiply-and-add module and said accumulator, said multiplier being configured to multiply said sum by an adaptation factor before forwarding it to said accumulator.
6 . The coherent optical receiver according to claim 4 , wherein said multiply-and-add module is configured to select a subset of said N samples of said phase skew compensated in-phase component and said N samples of said phase skew compensated quadrature component, and to calculate said sum according to said selected subset.
7 . The coherent optical receiver according to claim 1 , wherein said second digital circuit further comprises a first lookup table and a second lookup table, wherein:
said first lookup table stores a number of possible cross-correlation values and a same number of corresponding possible values of said first gain calculated according to the following equation:
G
11
i
=
cos
(
asin
(
R
i
)
/
2
)
2
cos
2
(
asin
(
R
i
)
/
2
)
-
1
,
R, being said number of possible cross-correlation values and G 11 i being said same number of corresponding possible values of said first gain; and
said second lookup table stores said number of possible cross-correlation values and said same number of corresponding possible values of said second gain calculated according to the following equation:
G
12
i
=
-
sin
(
asin
(
R
i
)
/
2
)
2
cos
2
(
asin
(
R
i
)
/
2
)
-
1
,
R i being said number of possible cross-correlation values and G 12 i being said same number of corresponding possible values of said second gain.
8 . The coherent optical receiver according to claim 7 , wherein:
said first lookup table is configured to receive said estimated cross-correlation, to determine, among said number of possible cross-correlation values, the possible cross-correlation value closest to said estimated cross-correlation, and to set said first gain and said fourth gain equal to the one of said same number of corresponding possible values of said first gain that corresponds to said closest possible cross-correlation value;
said second lookup table is configured to receive said estimated cross-correlation, to determine, among said number of possible cross-correlation values, the possible cross-correlation value closest to said estimated cross-correlation, and to set said second gain and said third gain equal to the one of said same number of corresponding possible values of said second gain that corresponds to said closest possible cross-correlation value.
9 . The coherent optical receiver according to claim 1 , wherein said second digital circuit further comprises a lookup table and a computation module, wherein:
said computation module is configured to receive said estimated cross-correlation and to compute said second gain and said third gain according to the following equation:
G
12
=
G
21
=
-
sin
(
asin
(
R
[
m
]
)
/
2
)
2
cos
2
(
asin
(
R
[
m
]
)
/
2
)
-
1
,
G 12 being said second gain, G 21 being said third gain and R[m] being said estimated cross-correlation; and
said lookup table stores a number of possible values of said second gain and a same number of corresponding possible values of said first gain calculated according to the following equation:
G
11
i
=
1
+
3
2
G
12
i
2
,
G 12 i being said number of possible values of said second gain and G 11 i being said same number of corresponding possible values of said first gain.
10 . The coherent optical receiver according to claim 9 , wherein said lookup table is configured to receive said computed second gain from said computation module, to determine, among said number of possible values of said second gain, the possible second gain value closest to said computed second gain and to set said first gain and said fourth gain equal to the one of said same number of corresponding possible values of said first gain that corresponds to said closest possible second gain value.
11 . The coherent optical receiver according to claim 1 , wherein said phase skew compensator is an ASIC module or an FPGA module.
12 . A node for an optical communication network, said node comprising a coherent optical receiver according to claim 1 .
13 . An optical communication network comprising a node according to claim 12 .
14 . A method for compensating a phase skew between an in-phase component and a quadrature component of a modulated optical signal received at a coherent optical receiver for an optical communication network, said method comprising:
adding said in-phase component multiplied by a first gain and said quadrature component multiplied by a second gain, to provide a phase skew compensated in-phase component;
adding said in-phase component multiplied by a third gain and said quadrature component multiplied by a fourth gain, to provide a phase skew compensated quadrature component;
estimating a cross-correlation between said phase skew compensated in-phase component and said phase skew compensated quadrature component; and
retroactively computing said first gain, said second gain, said third gain and said fourth gain as functions of said estimated cross-correlation.