Reduced complexity constrained frequency-domain block LMS adaptive equalization for coherent optical receivers
A method and structure for equalization in coherent optical receivers. Block-based LMS (BLMS) algorithm is one of the many efficient adaptive equalization algorithms used to (i) increase convergence speed and (ii) reduce implementation complexity. Since the computation of the equalizer output and the gradient of the error are obtained using a linear convolution, BLMS can be efficiently implemented in the frequency domain with the constrained frequency-domain BLMS (FBLMS) adaptive algorithm. The present invention introduces a novel reduced complexity constrained FBLMS algorithm. This new approach replaces the two discrete Fourier transform (DFT) stages required to evaluate the DFT of the gradient error, by a simple frequency domain filtering. Implementation complexity can be drastically reduced in comparison to the standard constrained FBLMS. Furthermore, the new approach achieves better performance than that obtained with the unconstrained FBLMS in ultra-high speed coherent optical receivers.
1. A coherent optical receiver device comprising
a constrained frequency-domain block least means square (CFBLMS) circuit module configured to receive a discrete Fourier transform (DFT) of an input signal, a DFT of an error of the input signal, and a DFT of a Chromatic Dispersion (CD) output signal,
wherein the CFBLMS circuit module is configured to filter the input signal according to a CFBLMS algorithm that determines a difference between the DFT of the CD output signal and a circular convolution term, the circular convolution term being derived from the DFT of the input signal, the DFT of the error of the input signal, and a frequency domain window.
2. The device of claim 1 , wherein the input signal is a dual-polarization input with an x-type polarization input and a y-type polarization input.
3. The device of claim 1 , wherein the CFBLMS circuit module is configured to filter the input signal according to the following equation:
C (( n+ 1) N )= C ( nN )−β U ( nN )
where N refers to an N-dimensional vector of time-domain (TD) equalizer taps,
where C(nN) is the DFT of the CD output signal,
where β is a step-size,
where U(nN) is equal to first 2N elements of the circular convolution of W and [R*(nN)E(nN)],
where W is a frequency domain window,
where R*(nN) is the DFT of the input signal, and
where E(nN) is the DFT of the error of the input signal.
4. The device of claim 1 , wherein the CFBLMS circuit module is configured to filter the input signal according to the following equation:
C (( n+ 1) N )= C ( nN )−β/4 W X se ( nN )
where N refers to an N-dimensional vector of time-domain (TD) equalizer taps,
where C(nN) is the DFT of the CD output signal,
where β is a step-size,
where W is the frequency domain window,
where W is a 2N×2N circular convolution matrix,
where X se (nN)=R*(nN)E(nN),
where R*(nN) is the DFT of the input signal, and
where E(nN) is the DFT of the error of the input signal.
5. The device of claim 4 , wherein the CFBLMS circuit module is configured such that the 2N×2N circular convolution matrix W is defined by
[
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.
6. The device of claim 4 , wherein the CFBLMS circuit module is configured to subsample the frequency-domain (FD) correlation vector X se (nN).
7. The device of claim 1 , wherein the CFBLMS circuit module is configured such that the frequency domain window W=½[1, −j0.5, 0, 0, 0, . . . , 0, j0.5] T , this vector being 2N long.
8. The device of claim 1 , wherein the CFBLMS circuit module is configured such that the frequency domain window W=¼[1, −j0.75, −0.5, j0.25, 0, 0, . . . , 0, −j0.25, −0.5, j0.75]T, this vector being 2N long.
9. A method of operating a coherent optical receiver device, the method comprising:
receiving, by a constrained frequency block least means square (CFBLMS) circuit module, a discrete Fourier transform (DFT) of an input signal;
receiving, by the CFBLMS circuit module, a DFT of an error of the input signal;
receiving, by the CFBLMS circuit module, a DFT of a Chromatic Dispersion (CD) output signal; and
filtering, by the CFBLMS circuit module, the input signal according to a CFBLMS algorithm that determines a difference between the DFT of the CD output signal and a circular convolution term, the circular convolution term being derived from the DFT of the input signal, the DFT of the error of the input signal, and a frequency domain window.
10. The method of claim 9 , wherein the input signal is a dual-polarization input with an x-type polarization input and a y-type polarization input.
11. The method of claim 9 , wherein the filtering of the input signal by the CFBLMS circuit module is according to the following equation:
C (( n+ 1) N )= C ( nN )−β U ( nN )
where N refers to an N-dimensional vector of time-domain (TD) equalizer taps,
where C(nN) is the DFT of the CD output signal,
where β is a step-size,
where U(nN) is equal to first 2N elements of the circular convolution of W and [R*(nN)E(nN)],
where W is the frequency domain window,
where R*(nN) is the DFT of the input signal, and
where E(nN) is the DFT of the error of the input signal.
12. The method of claim 9 , wherein the filtering of the input signal by the CFBLMS circuit module is according to the following equation:
C
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N
)
=
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-
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4
W
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X
se
(
nN
)
where N refers to an N-dimensional vector of time-domain (TD) equalizer taps,
where C(nN) is the DFT of the CD output signal,
where β is a step-size,
where W is the frequency domain window,
where W is a 2N×2N circular convolution matrix,
where X se (nN)=R*(nN)E(nN),
where R*(nN) is the DFT of the input signal, and
where E(nN) is the DFT of the error of the input signal.
13. The method of claim 12 , wherein filtering by the CFBLMS circuit module is such that the 2N×2N circular convolution matrix W is defined by
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.
14. The method of claim 12 , wherein filtering by the CFBLMS circuit module includes subsampling the frequency-domain (FD) correlation vector X se (nN).
15. The method of claim 9 , wherein the CFBLMS circuit module is configured such that the frequency domain window W=½[1, −j0.5, 0, 0, 0, . . . , 0, j0.5] T , this vector being 2N long.
16. The method of claim 9 , wherein the CFBLMS circuit module is configured such that the frequency domain window W=¼[1, −j0.75, −0.5, j0.25, 0, 0, . . . , 0, −j0.25, −0.5, j0.75] T , this vector being 2N long.
17. A method for adaptive signal equalization in a coherent digital signal processor using a constrained frequency-domain block least means square (CFBLMS) circuit module, the method comprising:
receiving, by a constrained frequency block least means square (CFBLMS) circuit module, a discrete Fourier transform (DFT) of an input signal;
receiving, by the CFBLMS circuit module, a DFT of an error of the input signal;
receiving, by the CFBLMS circuit module, a DFT of an equalizer output signal; and
filtering, by the CFBLMS circuit module, the input signal according to a CFBLMS algorithm that determines a difference between the DFT of the equalizer output signal and a circular convolution term, the circular convolution term being derived from the DFT of the input signal, the DFT of the error of the input signal, and a frequency domain window.
18. The method of claim 17 , wherein the filtering of the input signal by the CFBLMS circuit module is according to the following equation:
C (( n+ 1) N )= C ( nN )−β U ( nN )
where N refers to an N-dimensional vector of time-domain (TD) equalizer taps,
where C(nN) is the DFT of the equalizer output signal,
where β is a step-size,
where U(nN) is equal to first 2N elements of the circular convolution of W and [R*(nN)E(nN)],
where W is the frequency domain window,
where R*(nN) is the DFT of the input signal, and
where E(nN) is the DFT of the error of the input signal.
19. The method of claim 17 , wherein the filtering of the input signal by the CFBLMS circuit module is according to the following equation:
C
(
(
n
+
1
)
N
)
=
C
(
nN
)
-
β
4
W
_
X
se
(
nN
)
where N refers to an N-dimensional vector of time-domain (TD) equalizer taps,
where C(nN) is the DFT of the equalizer output signal,
where β is a step-size,
where W is the frequency domain window,
where W is a 2N×2N circular convolution matrix;
where X se (nN)=R*(nN)E(nN),
where R*(nN) is the DFT of the input signal, and
where E(nN) is the DFT of the error of the input signal.
20. The method of claim 17 , wherein filtering by the CFBLMS circuit module is such that the 2N×2N circular convolution matrix W is defined by
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.