Carrier phase estimator for non-linear impairment monitoring and mitigation in coherent optical systems
The present document relates to a method and apparatus in optical transmission systems for the estimation of the carrier phase and the degree of non-linear distortions incurred in an optical transmission channel. A plurality of signal samples are provided at succeeding time instances such that the plurality of signal samples: is associated with a modulation scheme and a carrier phase; has been transmitted over the optical transmission channel; comprises a plurality of signal phases, respectively; comprises a plurality of data phases and a plurality of residual phases, respectively; and the plurality of residual phases is associated with the carrier phase. The method comprises further canceling the plurality of data phases from the plurality of signal phases by taking into account the modulation scheme; thereby yielding the plurality of residual phases; and determining a set of autocorrelation values of the plurality of residual phases for a set of lag values, respectively.
1. A method for measuring a non-linearity of an optical transmission channel of an optical fiber, the method comprising:
providing, at a receiver, a plurality of signal samples at succeeding time instances; wherein the plurality of signal samples is associated with a modulation scheme, which allows a number of possible data phase values, and a carrier phase;
at a corresponding transmitter, the plurality of signal samples has been encoded using the modulation scheme, modulated onto an optical carrier signal having the carrier phase and transmitted over the optical transmission channel;
the plurality of signal samples comprises a plurality of signal amplitudes and signal phases, respectively;
the plurality of signal phases comprises a plurality of data phases and a plurality of residual phases, respectively;
the plurality of residual phases is associated with the carrier phase;
canceling the plurality of data phases from the plurality of signal phases by taking into account the modulation scheme, thereby yielding the plurality of residual phases; and determining a set of autocorrelation values of the plurality of residual phases for a set of lag values, respectively, thereby yielding a measure for the non-linearity of the optical transmission channel.
2. The method of claim 1 , wherein the plurality of residual phases comprises a plurality of non-linear induced phase noise values and a plurality of laser phase noise values, respectively, the method further comprising:
determining an autocorrelation value of the plurality of residual phases for a first lag value, thereby yielding an autocorrelation value of the laser phase noise; and
determining a set of autocorrelation values of the non-linear induced phase noise by subtracting the autocorrelation value of the laser phase noise from the set of autocorrelation values of the plurality of residual phases.
3. The method of claim 2 , further comprising:
determining an autocorrelation value of the non-linear induced phase noise at a lag value of zero, by interpolating a plurality of autocorrelation values of the set of autocorrelation values of the non-linear induced phase noise for lag values different from zero.
4. The method of claim 2 , further comprising
determining a second lag value for which a value of the set of autocorrelation values of the non-linear induced phase noise is at half of a maximum value of the set of autocorrelation values of the non-linear induced phase noise, wherein the second lag value is a measure for the non-linearity of the optical transmission channel.
5. The method of claim 4 , wherein the first lag value is greater than the second lag value.
6. The method of claim 1 , wherein
the modulation scheme corresponds to M-PSK and the canceling step comprises raising the plurality of signal phases to the power of M; or
the modulation scheme corresponds to x-QAM and the canceling step comprises raising the plurality of signal phases to a power which is associated with the number of possible data phase values of the modulation scheme.
7. The method of claim 1 , wherein the determining the set of autocorrelation values of the plurality of residual phases for the set of the lag values comprises:
multiplying a residual phase of the plurality of residual phases at a first time instance by a residual phase of the plurality of residual phases at a second time instance, wherein the lag value corresponds to a difference between the second time instance and the first time instance.
8. The method of claim 1 , further comprising:
determining an autocorrelation value of the plurality of residual phases for a lag value of zero; and
normalizing the set of autocorrelation values of the plurality of residual phases for the set of lag values by the autocorrelation value of the plurality of residual phases for the lag value of zero.
9. A method for determining a plurality of estimates of a carrier phase of a signal transmitted over an optical transmission channel of an optical fiber, the method comprising:
receiving, at a receiver, a plurality of samples of the signal at succeeding time instances; wherein
the plurality of signal samples is associated with a modulation scheme, which allows a number of possible data phase values, and the carrier phase;
at a corresponding transmitter, the plurality of signal samples has been encoded using the modulation scheme, modulated onto an optical carrier signal having the carrier phase and transmitted over the optical transmission channel;
the plurality of signal samples comprises a plurality of signal amplitudes and signal phases, respectively;
the plurality of signal phases comprises a plurality of data phases and a plurality of residual phases, respectively;
the plurality of residual phases is associated with the carrier phase;
canceling the plurality of data phases from the plurality of signal phases by taking into account the modulation scheme, thereby yielding the plurality of residual phases;
determining a second lag value; and
filtering the plurality of residual phases with a filter comprising a number of filter taps corresponding to two times the second lag value, thereby yielding a plurality of filtered residual phases, associated with the plurality of estimates of the carrier phase at the succeeding time instances.
10. The method of claim 9 , wherein weights of the filter taps are equal.
11. The method of claim 9 , wherein a filtered residual phase value of a first time instance is determined from residual phase values from the plurality of residual phases at time instances before and after the first time instance.
12. The method of claim 9 , further comprising:
dividing the plurality of filtered residual phases by a factor associated with the modulation scheme; and
unwrapping the plurality of divided filtered residual phases, thereby yielding the plurality of estimates of the carrier phase at the succeeding time instances.
13. A system configured to provide a measure of a non-linearity of an optical transmission channel of an optical fiber, the system comprising:
a reception unit configured to provide a plurality of signal samples at succeeding time instances; wherein the plurality of signal samples is associated with a modulation scheme, which allows a number of possible data phase values, and a carrier phase;
at a corresponding transmitter, the plurality of signal samples has been encoded using the modulation scheme, modulated onto an optical carrier signal having the carrier phase and transmitted over the optical transmission channel;
the plurality of signal samples comprises a plurality of signal 14 amplitudes and signal phases, respectively;
the plurality of signal phases comprises a plurality of data phases and a plurality of residual phases, respectively;
the plurality of residual phases is associated with the carrier phase;
a data phase cancellation unit configured to cancel the plurality of data phases from the plurality of signal phases by taking into account the modulation scheme, thereby yielding the plurality of residual phases; and a carrier phase statistics determination unit configured to determine a set of autocorrelation values of the plurality of residual phases for a set of lag values,
respectively, thereby yielding the measure for the non-linearity of the optical transmission channel.
14. A carrier phase estimation unit configured to provide a plurality of estimates of a carrier phase at succeeding time instances, the unit comprising:
a reception unit configured to provide a plurality of signal samples at the succeeding time instances; wherein
the plurality of signal samples is associated with a modulation scheme, which allows a number of possible data phase values, and the carrier phase;
the plurality of signal samples has been encoded using the modulation scheme, modulated onto an optical carrier signal having the carrier phase and transmitted over an optical transmission channel;
the plurality of signal samples comprises a plurality of signal amplitudes and signal phases, respectively;
the plurality of signal phases comprises a plurality of data phases and a plurality of residual phases, respectively;
the plurality of residual phases is associated with the carrier phase;
a data phase cancellation unit configured to cancel the plurality of data phases from the plurality of signal phases by taking into account the modulation scheme, thereby yielding the plurality of residual phases;
a carrier phase statistics determination unit configured to determine a second lag value; and
a filtering unit configured to filter the plurality of residual phases with a filter comprising a number of filter taps corresponding to two times the second lag value, thereby yielding a plurality of filtered residual phases, associated with the plurality of estimates of the carrier phase at the succeeding time instances.