Rapid calculation of nonlinear optical transmission impairments
A method of estimating nonlinear transmission impairments of an Optical Channel (OCh) trail in an optical communications network. A per-span nonlinear field variance is calculated for each span of the trail. The per-span nonlinear field variance represents nonlinearly induced noise due to the transmission impairments of that span. The nonlinearly induced noise being imparted to a signal transmitted through the trail and detected by the receiver. A respective covariance between the nonlinear fields contributed by each span pair of the OCh trail is computed. The covariance represents the correlation of the nonlinearly induced noise imparted to the signal within the first span of a span pair with the nonlinearly induced noise imparted to the signal within the second span of the pair. A covariance matrix is populated using the computed per-span variance values and covariance values. A total nonlinear field variance is computed by summing over the covariance matrix elements.
1. A method of estimating impairments of an Optical Channel (OCh) trail between a transmitter and a receiver in an optical communications network, the method comprising:
computing a respective per-span nonlinear field variance for each span of the OCh trail, the per-span nonlinear field variance representing nonlinearly induced noise due to the transmission impairments of the respective span, the nonlinearly induced noise being imparted to a signal transmitted through the OCh trail and detected by the receiver;
computing a respective covariance between the nonlinear fields contributed by each span pair of the OCh trail, the covariance representing the correlation of the nonlinearly induced noise imparted to the signal within the first span of a span pair with the nonlinearly induced noise imparted to the signal within the second span of the pair;
populating a covariance matrix using the computed per-span variance values and covariance values; and
computing a total nonlinear field variance by summing over the covariance matrix elements.
2. The method as claimed in claim 1 , wherein the steps of computing respective per-span variances and covariances, and populating a covariance matrix are repeated for each type of transmission impairment, and wherein the step of computing a total nonlinear field variance comprises computing a sum over all respective elements of the relevant covariance matrices.
3. The method as claimed in claim 2 , wherein the type of nonlinear impairment comprises any one or more of: self-phase modulation (SPM); cross-phase modulation (XPM); cross-polarization modulation (XPolM); and four wave mixing (FWM).
4. The method as claimed in claim 3 , wherein the known properties of the signal comprise any one or more of:
an accumulated chromatic dispersion of a waveform of the signal;
a modulation format of the waveform; and
a symbol rate of the signal.
5. The method as claimed in claim 3 , wherein the known properties of the involved span comprise any one or more of:
an effective core area of the fiber comprising each span;
a respective chromatic dispersion of each span;
a respective chromatic dispersion slope of each span; and
respective accumulated relative group delays of the signal and any interfering signals between each span pair.
6. The method as claimed in claim 1 , wherein the respective per-span nonlinear field variance for each span of the OCh trail is computed based on known properties of the signal and the involved span.
7. The method as claimed in claim 1 , wherein computing the respective covariance for each span pair comprises computing a respective correlation ratio for each span pair, each correlation ratio defining a proportionality between the respective covariance of the span pair and the respective per-span variances of the involved spans.
8. The method as claimed in claim 7 , wherein the respective correlation ratio for each span pair is derived based on known properties of the signal, each of the involved spans, and a type of transmission impairment.
9. The method as claimed in claim 8 , wherein the type of impairment comprises any one or more of: self-phase modulation (SPM); cross phase modulation (XPM); cross polarization modulation (XPolM); and four wave mixing (FWM).