Data transport using pairwise optimized multi-dimensional constellation with clustering
Systems and methods for data transport in an optical communications system, including generating a pairwise optimized (PO) multi-dimensional signal constellation in a single stage. The PO multi-dimensional signal constellation is generated by selecting a pair of symbols from a received constellation with M symbols, defining and minimizing an objective function with one or more constraints to optimize the selected pair of symbols, and iteratively selecting and optimizing one or more different pairs of symbols from the received constellation until a threshold condition is reached. Neighbor symbols from the generated PO multi-dimensional signal constellation in each polarization are clustered to formulate a clustered PO multi-dimensional signal constellation, and data is modulated and transmitted in accordance with the clustered PO multi-dimensional signal constellation.
1. A method for data transport in an optical communications system, comprising:
generating a pairwise optimized (PO) multi-dimensional signal constellation in a single-stage, the generating comprising:
selecting a pair of symbols from a received constellation with M symbols;
defining and minimizing an objective function with one or more constraints to optimize the selected pair of symbols; the objective function and constraints are defined by the following objective function:
∑
i
=
1
M
∑
j
=
i
+
1
M
h
(
β
i
,
β
j
)
·
Q
(
s
i
-
s
j
4
N
0
/
N
)
subject to the following constraints
∑
i
=
1
M
s
i
=
0
;
and
∑
i
=
1
M
s
i
2
=
M
;
and iteratively selecting and optimizing one or more different pairs of symbols from the received constellation until a threshold condition is reached;
clustering neighbor symbols from the generated PO multi-dimensional signal constellation in each polarization to formulate a clustered PO multi-dimensional signal constellation; and
modulating and transmitting data in accordance with the clustered PO multi-dimensional signal constellation.
2. The method as recited in claim 1 , further comprising normalizing the selected pairs of symbols into unit power, and specifying a level of signal-to-noise ratio (SNR) to calculate an initial bit-error-rate (BER).
3. The method as recited in claim 1 , wherein the one or more constraints include zero mean and unit power constraints.
4. The method as recited in claim 1 , wherein the pairwise optimized (PO) multi-dimensional signal constellation is a 4-dimensional-8-quadrature-amplitude modulation (4D-8QAM) signal constellation.
5. The method as recited in claim 1 , wherein the neighbor symbols are K-nearest neighbors in a selected polarization, and coordinates of a selected symbol and its neighbors in the selected polarization are replaced with a centroid of the symbols.
6. The method as recited in claim 5 , further comprising determining an optimum K for the selected symbol in the selected polarization such that a penalty of an estimated bit-error-rate (BER) from the objective function is lower than a specified threshold value.
7. A system for data transport in an optical communications system, comprising:
a transmitter, including a processor, the processor being configured for generating a pairwise optimized (PO) multi-dimensional signal constellation in a single-stage, the generating comprising:
selecting a pair of symbols from a received constellation with M symbols;
defining and minimizing an objective function with one or more constraints to optimize the selected pair of symbols; the objective function and constraints are defined by the following objective function:
∑
i
=
1
M
∑
j
=
i
+
1
M
h
(
β
i
,
β
j
)
·
Q
(
s
i
-
s
j
4
N
0
/
N
)
subject to the following constraints
∑
i
=
1
M
s
i
=
0
;
and
∑
i
=
1
M
s
i
2
=
M
;
and iteratively selecting and optimizing one or more different pairs of symbols from the received constellation until a threshold condition is reached;
clustering neighbor symbols from the generated PO multi-dimensional signal constellation in each polarization to formulate a clustered PO multi-dimensional signal constellation; and
modulating and transmitting data in accordance with the clustered PO multi-dimensional signal constellation.
8. The system as recited in claim 7 , wherein the one or more constraints include zero mean and unit power constraints.
9. The system as recited in claim 7 , wherein the pairwise optimized (PO) multi-dimensional signal constellation is a 4-dimensional-8-quadrature-amplitude modulation (4D-8QAM) signal constellation.
10. The system as recited in claim 7 , wherein the neighbor symbols are K-nearest neighbors in a selected polarization, and coordinates of a selected symbol and its neighbors in the selected polarization are replaced with a centroid of the symbols.
11. A system for data transport in an optical communications system, comprising:
a receiver, including a processor, the processor being configured for decoding a received data stream in accordance with a clustered single stage pairwise optimized (PO) multi-dimensional signal constellation, the clustered PO multi-dimensional signal constellation being generated by:
selecting a pair of symbols from a received constellation with M symbols;
defining and minimizing an objective function with one or more constraints to optimize the selected pair of symbols; the objective function and constraints are defined by the following objective function:
∑
i
=
1
M
∑
j
=
i
+
1
M
h
(
β
i
,
β
j
)
·
Q
(
s
i
-
s
j
4
N
0
/
N
)
subject to the following constraints
∑
i
=
1
M
s
i
=
0
;
and
∑
i
=
1
M
s
i
2
=
M
;
and iteratively selecting and optimizing one or more different pairs of symbols from the received constellation until a threshold condition is reached; and
clustering neighbor symbols from the generated PO multi-dimensional signal constellation in each polarization to formulate a clustered PO multi-dimensional signal constellation.
12. The system as recited in claim 11 , wherein the one or more constraints include zero mean and unit power constraints.
13. The system as recited in claim 11 , wherein the pairwise optimized (PO) multi-dimensional signal constellation is a 4-dimensional-8-quadrature-amplitude modulation (4D-8QAM) signal constellation.
14. The system as recited in claim 11 , wherein the neighbor symbols are K-nearest neighbors in a selected polarization, and coordinates of a selected symbol and its neighbors in the selected polarization are replaced with a centroid of the symbols.