Non-linear equalizer in a coherent optical receiver
View Patent ↗A method of recovering a most likely value of each symbol transmitted through an optical communications network using a high speed optical signal. A stream of multi-bit digital samples of the optical signal is processed to generate a respective multi-bit estimate X′(n) of each transmitted symbol. A first function is applied to each symbol estimate X′(n) to generate a corresponding soft decision value {tilde over (X)}(n). Each soft decision value {tilde over (X)}(n) is processed to generate a corresponding hard decision value. {circumflex over (X)}(n) having an ideal amplitude and phase. A plurality of successive soft decision values and hard decision values are processed to determine a second function, which is applied to each soft decision value {tilde over (X)}(n) to generate a most likely symbol value {circumflex over ({circumflex over (X)}(n).
1. A method of recovering a most likely value of each symbol transmitted through an optical communications network using a high speed optical signal, the method comprising, in a receiver of the network, steps of:
a data path of the receiver processing a stream of multi-bit digital samples of the optical signal using a first compensation function to generate a respective soft decision value {tilde over (X)}(n) of each transmitted symbol; and
a non-linear compensator applying a second compensation function to each soft decision value {tilde over (X)}(n) to generate a most likely symbol value {circumflex over ({circumflex over (X)}(n);
wherein processing the stream of multi-bit digital samples of the optical signal comprises:
processing the multi-bit digital samples to generate multi-bit symbol estimates X′(n) of transmitted symbols; and
rotating a respective phase of each symbol estimate X′(n) to compensate a frequency mismatch between a local oscillator and a carrier of the optical signal.
2. A method as claimed in claim 1 , wherein the first compensation function comprises a linear equalization function for at least partially compensating any one or more of linear dispersion, linear polarization distortions and carrier phase error.
3. A method as claimed in claim 2 , wherein the first compensation function further comprises a non-linear equalization function for compensating either one or both of non-linear dispersion and non-linear polarization effects.
4. A method as claimed in claim 2 , wherein the step of processing the stream of multi-bit digital samples to generate multi-bit symbol estimates X′(n) of transmitted symbols comprises steps of:
processing the multi-bit digital samples to generate a dispersion compensated symbol stream; and
deconvolving a transmitted polarization from the dispersion compensated symbol stream to generate a respective stream of multi-bit symbol estimates X′(n).
5. A method as claimed in claim 1 , wherein the second compensation function comprises a non-linear equalization function for at least partially compensating a residual Inter-Symbol Interference (ISI) of the multi-bit symbol estimates.
6. A method as claimed in claim 4 , wherein the step of applying a second compensation function to each soft decision value {tilde over (X)}(n) comprises steps of:
processing each soft decision value {tilde over (X)}(n) to generate a corresponding hard decision value {circumflex over (X)}(n) having an ideal amplitude and phase;
processing a plurality of successive soft decision values and hard decision values to accumulate an ISI compensation value for each possible value A of the soft decision value {tilde over (X)}(n);
determining a mapping between each possible value A of the soft decision value {tilde over (X)}(n) and a respective most likely symbol value {circumflex over ({circumflex over (X)}(n); and
applying the mapping to each soft decision value {tilde over (X)}(n).
7. A method of recovering a most likely value of each symbol transmitted through an optical communications network using a high speed optical signal, the method comprising, in a receiver of the network, steps of:
a data path of the receiver processing a stream of multi-bit digital samples of the optical signal to generate a respective multi-bit estimate X′(n) of each transmitted symbol;
a carrier recovery block of the receiver applying a first function to each symbol estimate X′(n) to generate a corresponding soft decision value {tilde over (X)}(n), wherein applying the first function comprises rotating a respective phase of each symbol estimate X′(n) to compensate a frequency mismatch between a local oscillator and a carrier of the optical signal;
the carrier recovery block further processing each soft decision value {tilde over (X)}(n) to generate a corresponding hard decision value {circumflex over (X)}(n) having an ideal amplitude and phase;
a parameter calculator processing a plurality of successive soft decision values and hard decision values to determine a second function; and
a non-linear compensator applying the second function to each soft decision value {tilde over (X)}(n) to generate a most likely symbol value {circumflex over ({circumflex over (X)}(n).
8. A method as claimed in claim 7 , wherein the step of processing a stream of multi-bit digital samples of the optical signal comprises steps of:
processing the multi-bit digital samples to generate a dispersion compensated symbol stream; and
deconvolving a transmitted polarization from the dispersion compensated symbol stream to generate a respective stream of multi-bit symbol estimates.
9. A method as claimed in claim 8 , wherein the step of deconvolving a transmitted polarization from the dispersion compensated symbol stream comprises a step of compensating a polarization angle difference between the transmitted polarization and the received optical signal.
10. A method as claimed in claim 7 , wherein each multi-bit symbol estimate comprises a respective multi-bit estimate of amplitude and a phase components of a corresponding transmitted symbol.
11. A method as claimed in claim 7 , wherein the stream of multi-bit digital samples comprises a block of contiguous samples encompassing at least one SYNC burst and a plurality of data symbols, each SYNC burst having a predetermined symbol sequence.
12. A method as claimed in claim 7 , wherein the step of processing each soft decision value {tilde over (X)}(n) to generate a corresponding hard decision value {circumflex over (X)}(n) comprises a step of mapping two most significant bits (MSBs) of the soft decision value {tilde over (X)}(n) to a corresponding hard decision value {circumflex over (X)}(n) having an ideal amplitude and phase for a quadrant in which the soft decision value {tilde over (X)}(n) lies.
13. A method as claimed in claim 7 , wherein the step of processing a plurality of successive soft decision values and hard decision values to determine a second function comprises steps of:
accumulating, for each combination of three consecutive hard decision values {circumflex over (X)}(n), {circumflex over (X)}(n−1) and {circumflex over (X)}(n−2), an ISI compensation value ℑ n [Addr] based on a corresponding soft decision value {tilde over (X)}(n−1) where Addr is an index value determined by the consecutive hard decision values {circumflex over (X)}(n), {circumflex over (X)}(n−1) and {circumflex over (X)}(n−2); and
for each possible value A of the soft decision value {tilde over (X)}(n):
using the accumulated ISI compensation values ℑ n [Addr] to compute an array of distance metrics M(m,j), where m=0 . . . 3, j=0 . . . 15 for either one of QPSK and 4ASK encoded symbols, and m=0 . . . 1, j=0 . . . 3 for BPSK encoded symbols;
processing the array of distance metrics M(m,j) to obtain a parameter value P(m); and
mapping the parameter value P(m) to a most likely symbol value {circumflex over ({circumflex over (X)}(n) corresponding to the soft decision value {tilde over (X)}(n)=A.
14. A method as claimed in claim 13 , wherein the ISI compensation value ℑ n [Addr] is calculated in accordance with ℑ n [Addr]=ℑ n-1 [Addr]+μ NC └α*{tilde over (X)}(n−1)−ℑ n-1 [Addr]┘, where α is a scaling factor used to adjust a number of bits resolution of {tilde over (X)}(n−1) to equal that of ℑ n [Addr]; and μNC is a training step size.
15. A method as claimed in claim 14 , wherein μ NC has a value of between 2 −5 and 2 −0 .
16. A method as claimed in claim 13 , wherein the distance metrics M(m,j) are calculated in accordance with one of:
M
(
m
,
j
)
=
α
*
A
-
[
16
m
+
j
]
2
N
0
for either one of QPSK and 4ASK encoded symbols, where m=0 . . . 3, j=0 . . . 15, and N 0 represents an expected noise floor; and
M
(
m
,
j
)
=
α
*
A
-
[
4
m
+
j
]
2
N
0
for BPSK encoded symbols, where m=0 . . . 1, j=0 . . . 3; wherein N 0 represents an expected noise floor.
17. A method as claimed in claim 16 , wherein the step of processing the array of distance metrics M(m,j) to obtain a parameter value P(m) comprises steps of:
initializing P(m)=M(m,0)*α; and
recursively calculating:
P
(
m
)
=
-
min
{
M
(
m
,
k
)
,
P
(
m
)
}
+
floor
[
α
*
log
(
1
+
e
-
M
(
m
,
k
)
-
P
(
m
)
α
)
+
0.5
]
,
where k=1 . . . 3 for BPSK encoded symbols and k=1 . . . 15 for QPSK and 4ASK encoded symbols.
18. A method as claimed in claim 17 , wherein the step of mapping the parameter value P(m) to a most likely symbol value {circumflex over ({circumflex over (X)}(n) comprises steps of:
selecting a value m=m 0 which corresponds to max[P(m)]; and
mapping m 0 to the most likely symbol value {circumflex over ({circumflex over (X)}(n).
19. A method as claimed in claim 13 , wherein the transmitted symbols are either one of QPSK and 4ASK encoded symbols, and wherein the distance metrics M(m,j) are calculated in accordance with either one of:
M(m,j)=|α*A−ℑ[16m+j]| 2 for either one of QPSK and 4ASK encoded symbols, where m=0 . . . 3, j=0 . . . 15, and N 0 represents an expected noise floor; and
M(m,j)=|α*A−ℑ[4m+j]| 2 for BPSK encoded symbols; where m=0 . . . 1, j=0 . . . 3.
20. A method as claimed in claim 19 , wherein the step of processing the array of distance metrics M(m,j) to obtain a parameter value P(m) comprises steps of:
initializing P(m)=M(m,0)*α; and
recursively calculating:
P
(
m
)
=
∑
j
α
*
A
-
[
16
m
+
j
]
2
,
where k=1 . . . 3 for BPSK encoded symbols and k=1 . . . 15 for QPSK and 4ASK encoded symbols.
21. A method as claimed in claim 20 , wherein the step of mapping the parameter value P(m) to a most likely symbol value {circumflex over ({circumflex over (X)}(n) comprises steps of:
selecting a value m=m 0 which corresponds to min[P(m)]; and
mapping m 0 to the most likely symbol value {circumflex over ({circumflex over (X)}(n).
22. A method as claimed in claim 13 , wherein the step of applying the second function to each soft decision value {tilde over (X)}(n) comprises a step of storing the respective most likely symbol value {circumflex over ({circumflex over (X)}(n) corresponding to each possible soft decision value {tilde over (X)}(n)=A in a look-up table.