Optical communication apparatus and method
View Patent ↗An apparatus for optical communication and optical communication method are provided, the method comprising the steps of generating an optical signal for transmitting the sequence of information data, transmitting the sequence of information data as a sequence of transmit matrices, S(k) being the k-th transmit matrix and k being a positive integer, and wherein the sequence of transmit matrices is transmitted through an optical channel characterized by a unitary channel matrix H, receiving a sequence of receive matrices, the k-th receive matrix R(k) being expressed as: R(k)=H·S(k)+N(k) wherein k is a positive integer and N(k) is a complex matrix of noise samples and providing a sequence of decision matrices, the k-th decision matrix D(k) being expressed as: D(k)=R H (k−1)R(k).
1. An optical communication method, comprising
generating an optical signal for transmitting a sequence of information data;
mapping the sequence of information data into a sequence of information matrices selected from an alphabet ={Q 1 , Q 2 , . . . , Q N } of N complex 2×2 unitary matrices, a k-th one of the information matrices, Q(k), being a unitary matrix, and k being a positive integer;
encoding the sequence of information matrices in a sequence of transmit matrices, wherein a k-th one of the transmit matrices, S(k), is expressed as:
S ( k )= S ( k− 1) Q ( k )
transmitting the transmit matrices through an optical channel characterized by a unitary channel matrix H;
receiving a sequence of receive matrices, a k-th one of the receive matrices, R(k), being expressed as:
R ( k )= H·S ( k )+ N ( k )
wherein N(k) is a complex matrix of noise samples;
characterized by;
providing a sequence of decision matrices, a k-th one of the decision matrices, D(k), being expressed as:
D ( k )= R H ( k− 1) R ( k );
and
estimating the k-th information matrix by selecting from the alphabet the information matrix having the smallest distance measure to the k-th decision matrix D(k).
2. A method according to claim 1 , the k-th transmit matrix S(k) being expressed as:
S
(
k
)
=
[
s
11
(
k
)
s
12
(
k
)
s
21
(
k
)
s
22
(
k
)
]
wherein k is a positive integer, s 11 (k) is a symbol that is transmitted through a first polarization (X) and within a first time interval (2k), s 21 (k) is a symbol that is transmitted through a second polarization (Y) and within the first time interval (2k), s 12 (k) is a symbol that is transmitted through the first polarization (X) and within a second time interval (2k+1), and s 22 (k) is a symbol that is transmitted through the second polarization (Y) and within the second time interval (2k+1);
the first (X) and the second (Y) polarizations being orthogonal with respect to each other; the first (2k) and the second (2k+1) time intervals being subsequent time intervals;
the k-th transmit matrix S(k) being a unitary matrix;
the symbols s 11 (k), s 21 (k), s 12 (k) and s 22 (k) being complex scalar values.
3. A method according to claim 2 , further comprising:
arranging the sequence of transmit matrices into a first and a second sequence of complex scalar values.
4. A method according to claim 3 , wherein with respect to the k-th transmit matrix S(k), the first sequence of complex scalar values includes the symbols s 11 (k) and, s 12 (k) and the second sequence of complex scalar values includes the symbols s 21 (k) and s 22 (k).
5. A method according to claim 4 , further comprising:
extracting a first sequence of in-phase components (Re{s 11 (k)}, Re{s 12 (k)}) and a first sequence of quadrature components (Im{s 11 (k)}, Im{s 12 (k)}) from the first sequence of complex scalar values; and
extracting a second sequence of in-phase components (Re{s 21 (k)}, Re{s 22 (k)}) and a second sequence of quadrature components (Im{s 21 (k)}, Im{s 22 (k)}) from the second sequence of complex scalar values.
6. A method according to claim 1 , further comprising:
estimating the sequence of information matrices, the k-th estimated matrix {circumflex over (Q)}(k) being expressed as
Q
^
(
k
)
=
arg
D
(
k
)
-
Q
2
=
arg
tr
{
D
H
(
k
)
·
Q
+
Q
H
D
(
k
)
}
.
7. A method according to claim 6 , further comprising:
providing a sequence of first error matrices, the k-th first error matrix E(k) being expressed as:
E ( k )≡{circumflex over ( Q )}( k )− D ( k );
providing a sequence of second error matrices, the k-th s error matrix E B (k) being expressed as:
E B ( k )= R ( k− 1) E ( k );
providing polarization mode dispersion compensation by means of a polarization mode compensator including a plurality of coefficients;
determining the plurality of coefficients by means of the sequence of second error matrices.
8. A method according to claim 1 , further comprising:
estimating a sequence of enhanced information matrices, the k-th enhanced estimated matrix {circumflex over (Q)} E (k) being expressed as:
Q
^
E
(
k
)
=
arg
D
E
(
k
)
-
Q
2
=
arg
tr
{
D
H
(
k
)
·
Q
+
Q
H
D
E
(
k
)
}
D E (k) being a k-th enhanced decision matrix belonging to a sequence of enhanced decision matrices, D E (k) being expressed as:
D E ( k )=(1−α)· U H ( k− 1)· R ( k )
U(k) being a k-th reference matrix belonging to a sequence of reference matrices, U(k) being expressed as:
U ( k )= R ( k )+α U ( k− 1)· {circumflex over (Q)} E ( k )
wherein α is a real positive scalar belonging to an interval [0; 1].
9. A method according to claim 8 , further comprising:
providing a sequence of first enhanced error matrices, the k-th first enhanced error matrix E E (k) being expressed as:
E E ( k )≡ {circumflex over (Q)} E ( k )− D E ( k );
providing a sequence of enhanced second error matrices, the k-th enhanced second error matrix E B (k) being expressed as:
E B E ( k )=(1−α) U ( k− 1) E E ( k )
providing polarization mode dispersion compensation by means of a polarization mode compensator including a plurality of coefficients;
determining the plurality of coefficients by means of the sequence of enhanced second error matrices.
10. A method according to claim 8 , further comprising:
determining an optimal value of the scalar α according to conditions of an optical channel.
11. A method according to claim 1 , wherein N(k) is a complex 2×2 matrix of noise samples expressed as
N
(
k
)
=
[
n
11
(
k
)
n
12
(
k
)
n
21
(
k
)
n
22
(
k
)
]
and k is a positive integer.
12. An apparatus for optical communication, comprising
a receiver configured to receive a sequence of receive matrices via an optical channel characterized by an unitary channel matrix H, a k-th of the receive matrices, R(k), being expressed as:
R ( k )= H·S ( k )+ N ( k )
wherein k is a positive integer, N(k) is a complex 2×2 matrix of noise samples, S(k) is a transmit matrix where S(k)=S(k−1)Q(k) and Q(k) is a k-th information matrix selected from an alphabet ≡{Q 1 , Q 2 , . . . , Q N } of unitary 2×2 matrices into which information data has been mapped for transmission;
characterized in that:
the apparatus includes means for providing a sequence of decision matrices, a k-th one of the decision matrices D(k), being expressed as:
D ( k )= R H ( k− 1) R ( k ); and
means for estimating the k-th information matrix by selecting from the alphabet the information matrix which has the smallest distance measure to the k-th decision matrix D(k).
13. An optical communication method, comprising
receiving a sequence of receive matrices via an optical channel characterized by a unitary matrix H, where R(k) is a k-th one of the receive matrices and k is a positive integer,
wherein the sequence of transmit matrices into which is mapped a sequence of information and which is provided to an optical channel result from differential encoding with unitary matrices Q(k) selected from an alphabet of complex 2×2 unitary matrices;
providing a sequence of decision matrices, a k-th of the decision matrices being expressed as:
D ( k )= R H ( k− 1) R ( k ); and
estimating the k-th information matrix by selecting from the alphabet the information matrix having the smallest distance measure to the k-th decision matrix D(k).