System and method for polarization de-multiplexing in a coherent optical receiver

1. An optical receiver system comprising:

a coherent receiver for receiving a polarization multiplexed optical signal and providing a first plurality of outputs in response to a first polarization of said optical signal and a second plurality of outputs in response to a second polarization of said optical signal; and

a digital signal processor (DSP) configured to apply a modified constant modulus algorithm (CMA) to a first digital signal established in response to said first plurality of outputs and a second digital signal established in response to said second plurality of outputs to provide first and second digital outputs representative of a first polarization state of said optical signal at which data is modulated and a second polarization state of said optical signal at which data is modulated,

said modified CMA comprising a plurality of sub-equalizer filters, each of said sub-equalizer filters comprising a plurality of delays for producing successively delayed versions of said input signal and a plurality of multipliers, each of said multipliers multiplying said input signal or an associated one of said delayed versions of said input signal with an associated filter coefficient to produce an associated tap weight product, said tap weight products being summed to provide an output for said equalizer,

said plurality of sub-equalizers comprising a first sub-equalizer and a second sub-equalizer, each of said filter coefficients for said first sub-equalizer being determined by said modified CMA as the sum of a first component and a second component,

said first component being determined using a previous filter coefficient for said first-sub-equalizer and an update gradient for said first sub-equalizer modified by a function of a coupling coefficient,

said second component being determined using a filter coefficient of said second sub-equalizer and an update gradient of said second sub-equalizer modified by a function of said coupling coefficient.

2. An optical receiver system according to claim 1 , wherein said coupling coefficient has a value greater than zero and less than one.

3. An optical receiver system according to claim 1 , wherein said coupling coefficient is 10 −2 or less.

4. An optical receiver system according to claim 1 , wherein said coupling coefficient is adjusted in response to the value of a determinant of a CMA matrix.

5. An optical receiver system according to claim 4 , wherein said coupling coefficient is increased when said value of said determinant decreases below a threshold.

6. An optical receiver system according to claim 5 , wherein said coupling coefficient is increased to a value of 10 −2 or less.

7. An optical receiver system according to claim 5 , wherein said determinant is normalized such that said value is between 0 and 1, and wherein said threshold is between 0.5 and 1.0.

8. An optical receiver system according to claim 1 , wherein said filter coefficients for said first sub-equalizer are calculated according to the following equation:

h xx ( n,k+ 1)=(1−μ)( h xx ( n,k )+Δ h xx ( n,k ))+μ( h yy ( M+ 1 −n,k )+Δ h yy ( M+ 1 −n,k ))*

for n=1 to M, where M is the number of said multipliers in each of said sub-equalizers, k is a current update cycle, k+1 is a next update cycle, μ is the coupling coefficient, the superscript * means complex conjugation, Δh xx designates said updated gradient for said first sub-equalizer, h yy designates said filter coefficient of said second sub-equalizer and Δh yy designates said update gradient of said second sub-equalizer.

9. An optical receiver system according to claim 8 , wherein said update gradient of said first and second sub-equalizers are calculated according to the following equation:

Δ h xx ( k )=ε(1 −|u ( k )| 2 ) u ( k ) x *( k )

Δ h yy ( k )=ε(1 −|v ( k )| 2 ) v ( k ) y *( k )

where u(k) is said first digital output, v(k) is said second digital output, and ε is a step size.

10. An optical communication system comprising:

a transmitting terminal for transmitting a plurality of optical signals, each at a different associated wavelength, on an optical information path, at least one of the optical signals being a polarization multiplexed phase shift keying (PSK) signal having data modulated thereon according to a phase shift keying modulation format; and

an optical receiver system coupled to the optical information path for receiving said at least one of the plurality of optical signals, said optical receiver system comprising:

a coherent receiver for receiving said at least one of the plurality of optical signals and providing a first plurality of outputs in response to a first polarization of said at least one of the plurality of optical signals and a second plurality of outputs in response to a second polarization of said at least one of the plurality of optical signals, and

a digital signal processor (DSP) configured to apply a modified constant modulus algorithm (CMA) to a first digital signal established in response said first plurality of outputs and a second digital signal established in response to said second plurality of outputs to provide first and second digital outputs representative of a first polarization state of said at least one of the plurality of optical signals on which said data is modulated and a second polarization state of said at least one of the plurality of optical signals on which said data is modulated,

said modified CMA comprising a plurality of sub-equalizer filters, each of said sub-equalizer filters comprising a plurality of delays for producing successively delayed versions of said input signal and a plurality of multipliers, each of said multipliers multiplying said input signal or an associated one of said delayed versions of said input signal with an associated filter coefficient to produce an associated tap weight product, said tap weight products being summed to provide an output for said equalizer,

said plurality of sub-equalizers comprising a first sub-equalizer and a second sub-equalizer, each of said filter coefficients for said first sub-equalizer being determined by said modified CMA as the sum of a first component and a second component,

said first component being determined using a previous filter coefficient for said first-sub-equalizer and an update gradient for said first sub-equalizer modified by a function of a coupling coefficient,

said second component being determined using a filter coefficient of said second sub-equalizer and an update gradient of said second sub-equalizer modified by a function of said coupling coefficient, wherein said coupling coefficient has a value greater than zero and less than one.

11. An optical communication system according to claim 10 , wherein said coupling coefficient is 10 −2 or less.

12. A method of demodulating a polarization multiplexed optical signal using a constant modulus algorithm (CMA) without convergence of the outputs of the CMA, said method comprising:

coupling a first digital signal established in response to a first polarization of said optical signal and a second digital signal established in response to a second polarization of said optical signal to a digital signal processor (DSP) for processing by a plurality of sub-equalizers of the CMA; and

determining filter coefficients for a first sub-equalizer of the CMA as the sum of a first component and a second component,

said first component being determined using a previous filter coefficient for said first-sub-equalizer and an update gradient for said first sub-equalizer modified by a function of a coupling coefficient,

said second component being determined using a filter coefficient of a second sub-equalizer of the CMA and an update gradient of said second sub-equalizer modified by a function of said coupling coefficient.

13. A method according to claim 12 , wherein said coupling coefficient has a value greater than zero and less than one.

14. A method according to claim 12 , wherein said coupling coefficient is 10 −2 or less.

15. A method according to claim 12 , said method further comprising adjusting said coupling coefficient in response to the value of a determinant of a CMA matrix.

16. A method according to claim 15 , wherein said adjusting said coupling coefficient comprises increasing said coupling coefficient when said value of said determinant decreases below a threshold.

17. A method according to claim 16 , wherein coupling coefficient is increased to a value of 10 −2 or less.

18. A method according to claim 16 , wherein said determinant is normalized such that said value is between 0 and 1, and wherein said threshold is between 0.5 and 1.0.

19. A method according to claim 12 , wherein said determining said filter coefficients comprises calculating said filter coefficients according to the following equation:

h xx ( n,k+ 1)=(1−μ)( h xx ( n,k )+Δ h xx ( n,k ))+μ( h yy ( M+ 1 −n,k )+Δ h yy ( M+ 1 −n,k ))*

for n=1 to M, where M is the number of said multipliers in each of said sub-equalizers, k is a current update cycle, k+1 is a next update cycle, μ is the coupling coefficient, the superscript * means complex conjugation, Δh xx designates said updated gradient for said first sub-equalizer, h yy , designates said filter coefficient of said second sub-equalizer and Δh yy designates said update gradient of said second sub-equalizer.

20. A method according to claim 19 , wherein said update gradient of said first and second sub-equalizers are calculated according to the following equation:

Δ h xx ( k )=ε(1 −|u ( k )| 2 ) u ( k ) x *( k )

Δ h yy ( k )=ε(1 −|v ( k )| 2 ) v ( k ) y *( k )

where u(k) is said first digital output, v(k) is said second digital output, and ε is a step size.