Electrical domain compensation of non-linear effects in an optical communications system
Nonlinearity-induced signal distortions are compensated by processing an input communications signal, in the electrical domain prior to Electrical-to-optical conversion and transmission through an optical link of a communications system. According to the invention, a compensation operator is determined that substantially mitigates the nonlinearity-induced signal distortions imparted to an optical signal traversing the communications system. The input communications signal is then input to the compensation operator to generate a predistorted electrical signal. This predistorted electrical signal is then used to modulate an optical source to generate a corresponding predistorted optical signal for transmission through the optical communications system. With this arrangement, arbitrary nonlinearity-induced signal distortions imparted by the optical link can be compensated in such a manner that a comparatively undistorted optical signal is obtained at the receiving end of the optical link.
1. A method of compensating optical signal distortions due to nonlinear and cross channel effects of an optical communications system, the method comprising steps of:
determining a compensation operator C[(E(t)] that is the inverse of a link complex non-linear operator T[E(t)] representing one or more signal distortions due to nonlinear and cross channel effects imparted to a Wavelength Division Multiplexed communications signal E(t) as it traverses the optical communications system;
digitally processing an electrical input signal X(t) comprising at least two parallel channel input signals x(t,ω i ) using the compensation operator C[(E(t)] to generate a predistorted electrical signal X 1 (t) comprising a respective predistorted channel input signal x 1 (t,ω i ) corresponding to each channel input signal x(t,ωi); and
modulating an optical source using the predistorted channel input signals x 1 (t,ω i ) to generate corresponding predistorted optical channel signals E(t,ωi) for transmission through the optical communications system;
wherein the step of digitally processing the electrical input signal X(t) comprises steps of:
calculating successive numerical values of the predistorted electrical signal, X 1 (t), based on the electrical input signal X(t) and the compensation operator C[E(t)]; and
converting each successive numerical value into corresponding analog values of each predistorted channel input signal x 1 (t,ω i ) of the predistorted electrical signal X 1 (t);
wherein each channel input signal x(t,ω i ) of the electrical input signal X(t) comprises a substantially undistorted binary signal, and wherein the step of calculating successive numerical values of the predistorted electrical signal X 1 (t) comprises steps of:
calculating a respective numerical value of the predistorted electrical signal X 1 (t) corresponding to each one of a set of predetermined N-bit sequences;
storing each calculated numerical value in a look-up table; and
extracting a plurality of successive numerical values of the predistorted electrical signal X 1 (t) from the look-up table using the electrical input signal X(t).
2. A method as claimed in claim 1 , wherein the step of determining a compensation operator comprises steps of:
measuring a performance parameter related to the signal distortions due to nonlinear and cross channel effects; and
calculating respective values of one or more parameters of the compensation operator that optimizes the measured performance parameter.
3. A method as claimed in claim 2 , wherein the step of measuring the performance parameter comprises a step of measuring any one or more of:
cross-phase modulation;
self phase modulation;
modulation instability; and
cross-talk.
4. A method as claimed in claim 1 , wherein each predistorted channel input signal x 1 (t,ω i ) of the predistorted electrical signal E 1 (t) is represented by a pair of orthogonal components, and the step of calculating successive numerical values of the predistorted electrical signal E 1 (t) comprises a step of calculating successive corresponding values of each component.
5. A method as claimed in claim 1 , wherein the set of predetermined N-bit sequences encompasses all possible sequences of N-bits.
6. A method as claimed in claim 1 , wherein the step of extracting a plurality of successive numerical values of the predistorted electrical signal X 1 (t) comprises steps of:
converting the electrical input signal X(t) into a series of N-bit words;
using each N-bit word as an index value to access a respective register of the look-up table.
7. A method as claimed in claim 6 , wherein the step of extracting a plurality of successive numerical values of the predistorted electrical signal X 1 (t) comprises a step of extracting at least one numerical value of each predistorted channel input signal x 1 (t,ω i ) of the predistorted electrical signal X 1 (t) for each N-bit word.
8. A method as claimed in claim 1 , wherein the number (N) of bits within each sequence is based on any one or more of:
an expected maximum dispersion of the optical communications system; and
an expected response time of the look-up table.
9. A method as claimed in claim 1 , wherein the steps of calculating respective numerical values of the predistorted electrical signal X 1 (t) and storing the calculated numerical values in a look-up table are repeated at predetermined intervals.
10. A compensation system for compensating optical signal distortions due to nonlinear and cross channel effects of an optical communications system, the compensation system comprising:
a processor for determining a compensation operator C[E(t)] that is the inverse of a link complex non-linear operator T[E(t)] representing one or more signal distortions due to non-linear and cross channel effects imparted to a Wavelength Division Multiplexed communications signal E(t) as it traverses the optical communications system;
a compensation processor for digitally processing an electrical input signal X(t) comprising at least two parallel channel input signals x(t,ω i ) using the compensation operator C[(E(t)] to generate a predistorted electrical signal X 1 (t) comprising a respective predistorted channel input signal x 1 (t,ω i ) corresponding to each channel input signal x(t,ω i ); and
an optical modulator for modulating an optical source using the predistorted channel input signals x 1 (t,ω i ) to generate a corresponding predistorted optical channel signals E(t,ω i ) for transmission through the optical communications system;
wherein the compensation processor comprises:
a digital filter for filtering the electrical input signal X(t) using the compensation operator C[E(t)] to generate a series of successive numerical values of the predistorted electrical signal X 1 (t); and
a digital-to-analog converter for converting each successive numerical value into corresponding analog values of each predistorted channel input signal x 1 (t,ω i ) of the predistorted electrical signal X 1 (t);
wherein the digital filter comprises a Look-up table comprising:
a serial to parallel converter (SPC) for converting the electrical input signal X(t) into a series of successive N-bit words; and
a Random Access Memory (RAM) coupled to receive each N-bit word from the SPC, the RAM being adapted to store a plurality of numerical values of the predistorted electrical signal X 1 (t), and output a selected one numerical value based on the N-bit word from the SPC.
11. A system as claimed in claim 10 , wherein the processor is implemented remote from the compensation processor.
12. A system as claimed in claim 10 , wherein the processor comprises:
a detector for measuring a performance parameter related to the signal distortions due to nonlinear and cross channel effects; and
a calculation engine for calculating respective values of one or more parameters of the compensation operator that optimizes the measured performance parameter.
13. A system as claimed in claim 12 , wherein the detector is adapted to measure any one or more of:
cross-phase modulation;
self phase modulation;
modulation instability; and
cross-talk.
14. A system as claimed in claim 10 , wherein the RAM comprises:
a plurality of parallel RAMs; and
a digital ADDER for digitally summing the output of each RAM to generate each successive numerical values of the predistorted electrical signal X 1 (t).
15. A system as claimed in claim 10 , wherein the Random Access Memory (RAM) is coupled to receive a center portion of each N-bit word from the SPC, the RAM being adapted to output a selected one numerical value based on the received center portion of the N-bit word, and wherein the look-up table further comprises:
a respective linear adder tree for digitally summing each end portion of the N-bit word from the SPC;
a first digital ADDER for digitally summing the output of each linear adder tree; and
a second digital ADDER for digitally summing the output of the first digital ADDER and the RAM to generate each successive numerical value of the predistorted electrical signal X 1 (t).
16. A system as claimed in claim 10 , wherein each predistorted channel input signal x 1 (t,ω i ) is represented by a pair of orthogonal components, and the look-up-table comprises a respective look-up-table for generating each component.
17. A system as claimed in claim 10 , wherein at least one numerical value of the predistorted signal is extracted from the look-up-table for each N-bit word.
18. A system as claimed in claim 10 , wherein the number (N) of bits within each N-bit word is based on any one or more of:
an expected maximum dispersion of the optical communications system; and
an expected response time of the look-up-table.
19. A distortion compensator for compensating optical signal distortions due to nonlinear and cross channel effects of an optical communications system, the distortion compensator comprising:
a compensation processor for digitally processing an electrical input signal X(t) comprising at least two parallel channel input signals x(t,ω i ) using a predetermined complex compensation operator C[(E(t)] to generate a predistorted electrical signal X 1 (t) comprising a respective predistorted channel input signal x 1 (t,ω i ) corresponding to each channel input signal x(t,ω i ), the compensation operator C[E(t)] being the inverse of a link complex non-linear operator T[E(t)] representing one or more signal distortions due to nonlinear and cross channel effects imparted to a Wavelength Division Multiplexed communications signal E(t) as it traverses an optical link of the optical communications system, such that modulation of an optical source using the predistorted channel input signals x 1 (t,ω i ) generates a corresponding predistorted optical channel signals E(t,ω i ) for transmission through the optical link;
wherein the compensation processor comprises:
a digital filter for filtering the electrical input signal X(t) using the compensation operator C[E(t)] to generate a series of successive numerical values of the predistorted electrical signal X 1 (t); and
a digital-to-analog converter for converting each successive numerical value into corresponding analog values of each predistorted channel input signal x 1 (t,ω i ) of the predistorted electrical signal X 1 (t);
wherein the digital filter comprises a look-up table comprising:
a serial to parallel converter (SPC) for converting the electrical input signal X(t) into a series of successive N-bit words; and
a Random Access Memory (RAM) coupled to receive each N-bit word from the SPC, the RAM being adapted to store a plurality of numerical values of the predistorted electrical signal X 1 (t), and output a selected one numerical value based on the N-bit word from the SPC.
20. A distortion compensator as claimed in claim 19 , wherein the RAM comprises:
a plurality of parallel RAMs; and
a digital ADDER for digitally summing the output of each RAM to generate each successive numerical values of the predistorted electrical signal X 1 (t).
21. A distortion compensator as claimed in claim 19 , wherein the Random Access Memory (RAM) is coupled to receive a center portion of each N-bit word from the SPC, the RAM being adapted to store a plurality of numerical values of the predistorted electrical signal X 1 (t), and output a selected one numerical value based on the received center portion of the N-bit word, and wherein the look-up table further comprises:
a respective linear adder tree for digitally summing each end portion of the N-bit word from the SPC;
a first digital ADDER for digitally summing the output of each linear adder tree; and
a second digital ADDER for digitally summing the output of the first digital ADDER and the RAM to generate each successive numerical value of the predistorted electrical signal X 1 (t).
22. A distortion compensator as claimed in claim 19 , wherein each predistorted channel input signal x 1 (t,ω i ) is represented by a pair of orthogonal components, and the look-up-table comprises a respective look-up-table for generating each component.
23. A distortion compensator as claimed in claim 19 , wherein at least one numerical value of the predistorted signal is extracted from the look-up-table for each N-bit word.
24. A distortion compensator as claimed in claim 19 , wherein the number (N) of bits within each N-bit word is based on any one or more of:
an expected maximum dispersion of the optical communications system; and
an expected response time of the look-up-table.