Methods and systems for reduced complexity nonlinear compensation
Aspects of the present invention provide techniques for compensating nonlinear impairments of a signal traversing an optical communications system. A parallel array of linear convolutional filters are configured to process a selected set of samples of the signal to generate an estimate of a nonlinear interference field. The predetermined set of samples comprises a first sample and a plurality of second samples. A processor applies the estimated nonlinear interference field to the first sample to least partially compensate the nonlinear impairment.
1. An apparatus for compensating a nonlinear impairment of a signal traversing an optical communications system, the apparatus comprising:
a parallel array of linear convolutional filters configured to process a selected set of samples of the signal to calculate an estimate of a nonlinear interference field, the selected set of samples comprising a first sample and a plurality of second samples; and
a processor configured to apply the estimated nonlinear interference field to the first sample so as to at least partially compensate the nonlinear impairment;
wherein either:
the selected set of samples of the signal are time-domain samples and each linear convolutional filter comprises a set of taps, each tap being configured to compute a product C mn {right arrow over (A)} H (t j+m+n ){right arrow over (A)}(t j+n ), where C mn is a complex number representing an efficiency of nonlinear interaction; m and n are index values that range between −M≦m≦M and −N≦n≦N; {right arrow over (A)}(t) is a vector representing the modulated time domain transmit signal; t j denotes the time of the first sample; and {right arrow over (A)} H (t) denotes the Hermitian conjugate of {right arrow over (A)}(t); or
the selected set of samples of the signal are frequency-domain samples and each linear convolutional filter comprises a set of taps, each tap being configured to compute a product {tilde over (C)} mn {right arrow over (A)} H (ω k+m+n ){right arrow over (A)}(ω k+n ), where {tilde over (C)} mn is a complex number representing an efficiency of nonlinear interaction; m and n are index values that range between −M≦m≦M and −N≦n≦N; {right arrow over (A)}(ω) is a vector representing the Fourier transform of the modulated transmit signal; ω k denotes the frequency of the first sample; and {right arrow over (A)} H (ω) denotes the Hermitian conjugate of {right arrow over (A)}(ω).
2. The apparatus as claimed in claim 1 , wherein the processor is configured to apply the estimated nonlinear interference field to the first sample at either one or both of an optical transmitter and an optical receiver of the optical communications system.
3. The apparatus as claimed in claim 1 wherein a span of the selected set of time domain samples is less than or equal to a channel memory of the optical communications system.
4. The apparatus as claimed in claim 1 wherein the time-domain sample rate is equal to the transmitter symbol rate.
5. The apparatus as claimed in claim 1 , wherein C mn is quantized to a predetermined number of levels, and wherein the number of complex multiplication operations used to evaluate the output of each linear convolutional filter is less than the number of filter taps.
6. The apparatus as claimed in claim 1 , wherein either electronic or optical dispersion pre-compensation is applied at the optical transmitter.
7. The apparatus as claimed in claim 1 , wherein a span of the selected set of frequency domain samples is less than a modulation bandwidth of the optical communications system.
8. The apparatus as claimed in claim 1 , wherein the span of the selected set of frequency domain samples corresponds with a nonlinear bandwidth of the optical communications system.
9. The apparatus as claimed in claim 1 , wherein the plurality of second samples are frequency samples disposed about the first frequency sample.
10. The apparatus as claimed in claim 1 , wherein the first sample comprises a sample of one frequency sub-band and the plurality of second samples comprises samples of one or more frequency sub-bands.
11. The apparatus as claimed in claim 10 , wherein the frequency sub-bands are modulated subcarriers.
12. A transmitter configured to transmit a signal through an optical communications system, the transmitter comprising:
a parallel array of linear convolutional filters configured to process a selected set of samples of the signal to calculate an estimate of a nonlinear interference field indicative of a non-linear impairment of the signal traversing the optical communications system, the selected set of samples comprising a first sample and a plurality of second samples; and
a processor configured to apply the estimated nonlinear interference field to the first sample so as to at least partially compensate the nonlinear impairment;
wherein either:
the selected set of samples of the signal are time-domain samples and each linear convolutional filter comprises a set of taps, each tap being configured to compute a product C mn {right arrow over (A)} H (t j+m+n ){right arrow over (A)}(t j+n ), where C mn is a complex number representing an efficiency of nonlinear interaction; m and n are index values that range between −M≦m≦M and −N≦n≦N; {right arrow over (A)}(t) is a vector representing the modulated time domain transmit signal; t j denotes the time of the first sample; and {right arrow over (A)} H (t) denotes the Hermitian conjugate of {right arrow over (A)}(t); or
the selected set of samples of the signal are frequency-domain samples and each linear convolutional filter comprises a set of taps, each tap being configured to compute a product {tilde over (C)} mn {right arrow over (A)} H (ω k+m+n ){right arrow over (A)}(ω k+n ), where {tilde over (C)} mn is a complex number representing an efficiency of nonlinear interaction; m and n are index values that range between −M≦m≦M and −N≦n≦N; {right arrow over (A)}(ω) is a vector representing the Fourier transform of the modulated transmit signal; ω k denotes the frequency of the first sample; and {right arrow over (A)} H (ω) denotes the Hermitian conjugate of {right arrow over (A)}(ω).
13. A receiver configured to receive a signal through an optical communications system, the receiver comprising:
a parallel array of linear convolutional filters configured to process a selected set of samples of the signal to calculate an estimate of a nonlinear interference field indicative of a non-linear impairment of the signal traversing the optical communications system, the selected set of samples comprising a first sample and a plurality of second samples; and
a processor configured to apply the estimated nonlinear interference field to the first sample so as to at least partially compensate the nonlinear impairment;
wherein either:
the selected set of samples of the signal are time-domain samples and each linear convolutional filter comprises a set of taps, each tap being configured to compute a product C mn {right arrow over (A)} H (t j+m+n ){right arrow over (A)}(t j+n ), where C mn is a complex number representing an efficiency of nonlinear interaction; m and n are index values that range between −M≦m≦M and −N≦n≦N; {right arrow over (A)}(t) is a vector representing the modulated time domain transmit signal; t j denotes the time of the first sample; and {right arrow over (A)} H (t) denotes the Hermitian conjugate of {right arrow over (A)}(t); or
the selected set of samples of the signal are frequency-domain samples and each linear convolutional filter comprises a set of taps, each tap being configured to compute a product {tilde over (C)} mn {right arrow over (A)} H (ω k+m+n ){right arrow over (A)}(ω k+n ), where {tilde over (C)} mn is a complex number representing an efficiency of nonlinear interaction; m and n are index values that range between −M≦m≦M and −N≦n≦N; {right arrow over (A)}(ω) is a vector representing the Fourier transform of the modulated transmit signal; ω k denotes the frequency of the first sample; and {right arrow over (A)} H (ω) denotes the Hermitian conjugate of {right arrow over (A)}(ω).
14. A method of compensating a nonlinear impairment of a signal traversing an optical communications system, the method comprising:
processing, by a parallel array of linear convolutional filters, a selected set of samples of the signal to calculate an estimate of a nonlinear interference field, the selected set of samples comprising a first sample and a plurality of second samples; and
applying, by a processor, the estimated nonlinear interference field to the first sample so as to at least partially compensate the nonlinear impairment;
wherein either:
the selected set of samples of the signal are time-domain samples and each linear convolutional filter comprises a set of taps, each tap being configured to compute a product C mn {right arrow over (A)} H (t j+m+n ){right arrow over (A)}(t j+n ), where C mn is a complex number representing an efficiency of nonlinear interaction; m and n are index values that range between −M≦m≦M and −N≦n≦N; {right arrow over (A)}(t) is a vector representing the modulated time domain transmit signal; t j denotes the time of the first sample; and {right arrow over (A)} H (t) denotes the Hermitian conjugate of {right arrow over (A)}(t); or
the selected set of samples of the signal are frequency-domain samples and each linear convolutional filter comprises a set of taps, each tap being configured to compute a product {tilde over (C)} mn {right arrow over (A)} H (ω k+m+n ){right arrow over (A)}(ω k+n ), where {tilde over (C)} mn is a complex number representing an efficiency of nonlinear interaction; m and n are index values that range between −M≦m≦M and −N≦n≦N; {right arrow over (A)}(ω) is a vector representing the Fourier transform of the modulated transmit signal; ω k denotes the frequency of the first sample; and {right arrow over (A)} H (ω) denotes the Hermitian conjugate of {right arrow over (A)}(ω).
15. The method as claimed in claim 14 , wherein the estimated nonlinear interference field is applied to the first sample at either one or both of an optical transmitter and an optical receiver of the optical communications system.
16. The method as claimed in claim 14 wherein a span of the selected set of time domain samples is less than or equal to a channel memory of the optical communications system.
17. The method as claimed in claim 14 wherein the time-domain sample rate is equal to the transmitter symbol rate.
18. The method as claimed in claim 14 , wherein C mn is quantized to a predetermined number of levels, and wherein the number of complex multiplication operations used to evaluate the output of each linear convolutional filter is less than the number of filter taps.
19. The method as claimed in claim 14 , wherein the first sample comprises a sample of one frequency sub-band and the plurality of second samples comprise samples of one or more other frequency sub-bands.