Method, device and communication system for reducing optical transmission impairments

1. A method for reducing optical transmission impairments, particularly nonlinear effects, of at least one link, comprising the following steps:

a) receiving an optical signal via the at least one link;

b) converting the optical signal into a digital electrical representation;

c) extracting a phase information of the optical signal from the digital electrical representation,

d) determining with a processor a nonlinear coefficient, associated with the at least one link, based on the phase information,

e) applying with the processor a control mechanism to the digital electrical representation using the nonlinear coefficient to compensate for impairments of the optical signal,

wherein the phase information is extracted after a carrier recovery of the optical signal,

wherein

a cost function is derived based on the extracted phase information, and

an optimization algorithm is applied in connection with the cost function to determine the nonlinear coefficient, and

wherein the optimization algorithm is based on a steepest descent algorithm defined as

γ( i+ 1)=γ( i )+μΔγ( i ), wherein

i is an index of a discrete time

γ(i+1) is representing a value of the nonlinear coefficient at iteration (i+1)

γ(i) is representing a value of the nonlinear coefficient at the preceding iteration step (i)

μ is representing a convergence factor, comprising an effective fiber length L eff and a channel power P, and

Δγ(i)=∂CF (γ)/∂γ, wherein CF denotes the cost function.

2. The method according to claim 1 ,

repeating the steps c) to e) until a value of the nonlinear coefficient reaches or exceeds a given value.

3. The method according to claim 1 , wherein

the extracted phase information comprises a spreading of received symbols being part of the optical signal, and

the determination of the nonlinear coefficient is such that a reduced spreading of the received symbols is achieved.

4. The method according to claim 3 , wherein a respective spreading of the received symbols comprises respective phase differences between the received symbols and respective transmitted symbols which are derived either with or without a training sequence.

5. The method according to claim 4 , wherein

the optical signal is a coherent signal based on a 16 QAM modulation,

4 th power is applied to the optical signal,

the respective phase differences are derived from a 4 th power signal,

a cost function (CF), based on those derived phase differences, is defined as

CF=[δ θ1 +δ θ3 ]*(1/ R 2 )+δ θ2 *(1/ R 1 +1/ R 3 )

wherein

δ θ1 , δ θ2 , and δ θ3 are representing a standard deviation for each of the respective phase differences, and

R1, R2 and R3 are representing radii of a 16 QAM constellation.

6. The method according to claim 1 , wherein

the optimization algorithm starts by calculating two values of the cost function corresponding to two different values of the nonlinear coefficient, and

a first starting value of the nonlinear coefficient is represented by a selected initial value.

7. The method according to claim 1 , wherein

the nonlinear coefficient is refined as a n-dimensional nonlinear coefficient, representing n single links, and

the n-dimensional nonlinear coefficient is determined by a n-dimensional calculation.

8. A device comprising

a converter for converting an optical signal received via at least one link into a digital electrical representation; and

a processor unit configured for:

a) extracting phase information of the optical signal from the digital electrical representation,

b) determining a nonlinear coefficient, associated with the at least one link, based on the phase information,

c) applying a control mechanism to the digital electrical representation using the nonlinear coefficient to reduce optical transmission impairments of the optical signal, including non-linear effects of the at least one link,

wherein the phase information is extracted after a carrier recovery of the optical signal,

wherein

a cost function is derived based on the extracted phase information, and

an optimization algorithm is applied in connection with the cost function to determine the nonlinear coefficient, and

wherein the optimization algorithm is based on a steepest descent algorithm defined as

γ( i+ 1)=γ( i )+μΔγ( i ), wherein

i is an index of a discrete time

γ(i+1) is representing a value of the nonlinear coefficient at iteration (i+1)

γ(i) is representing a value of the nonlinear coefficient at the preceding iteration step (i)

μ is representing a convergence factor, comprising an effective fiber length L eff and a channel power P, and

Δγ(i)=∂CF (γ)/θγ, wherein CF denotes the cost function.

9. The device according to claim 8 , wherein the processor unit is arranged so as to repeat the steps a) to c) until a value of the nonlinear coefficient reaches or exceeds a value.

10. The device according to claim 8 , wherein said device is a communication device that is or is associated with a receiver for optical signals.

11. A communication system comprising the device according to claim 8 .