Methods and systems for reduced complexity nonlinear compensation

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 Cmn{right arrow over (A)}H(tj+m+n){right arrow over (A)}(tj+n), where Cmn 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;
• tj 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(ωk+m+n){right arrow over (A)}(ωk+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;
• ωk denotes the frequency of the first sample;
• and {right arrow over (A)}H(ω) denotes the Hermitian conjugate of {right arrow over (A)}(ω).

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 Cmn{right arrow over (A)}H(tj+m+n){right arrow over (A)}(tj+n), where Cmn 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;
• tj 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(ωk+m+n){right arrow over (A)}(ωk+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;
• ωk denotes the frequency of the first sample;
• and {right arrow over (A)}H(ω) denotes the Hermitian conjugate of {right arrow over (A)}(ω).

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 Cmn{right arrow over (A)}H(tj+m+n){right arrow over (A)}(tj+n), where Cmn 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;
• tj 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(ωk+m+n){right arrow over (A)}(ωk+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;
• ωk denotes the frequency of the first sample;
• and {right arrow over (A)}H(ω) denotes the Hermitian conjugate of {right arrow over (A)}(ω).