Method and arrangement for blind demultiplexing a polarisation diversity multiplex signal

1. A method of blind demultiplexing a polarization diversity multiplex signal in a coherent receiver, deriving x-polarization samples r X (n) and orthogonal y-polarization samples r Y (n) of the received polarization diversity multiplex signal, calculating complex filter functions of a multidimensional equalizer between the x-polarization samples r X (n), y-polarization samples r y (n) and output x-signal samples z x (n), y-signal samples z y (n) representing optical signals received as the polarization diversity multiplex signal,

the method comprising:

calculating at least one error correction factor derived from the x-signal samples and y-signal samples z x (n), z y (n) output from the equalizer by deriving averaged correlation factors according to:

ρ xy (n) [k ]=(1−ε)·ρ xy (n−1) [k]+ε·z x [n]z y *[n−k]; k= 0 , . . . , k max

ρ yx (n) [k ]=(1−ε)·ρ yx (n−1) [k]+ε·z y [n]z x *[n−k]; k= 0 , . . . , k max,

with k=0, . . . , k max being a corrlation delay time variable; and

deriving error correction factors according to:

η x (n) =−ρ xy (n) [k x ]·z y [n−k x ] for k x =argmax{ρ xy ( k )}; k= 0 , . . . , k max ,

η y (n) =−ρ yx (n) [k y ]·z x [n−k y ] for k y =argmax{ρ yx ( k )}; k= 0 , . . . , k max ,

calculating correction values from the at least one error correction factor multiplied by an update factor and by an x-polarization sample or a y-polarization sample;

calculating corrected filter coefficients by adding the correction values to filter coefficients of the complex filter functions; and

wherein n is a time instant, ρ is a correlation factor, k=0, 1, . . . , k max is a correlation delay time variable and ε is a forgetting factor.

2. The method according to claim 1 , which comprises calculating a common error correction factor corresponding to a maximum absolute correlation factor of the x-polarization and the y-polarizations.

3. The method according to claim 1 , which comprises calculating filter transfer functions according to:

h xx (n) [k]=h xx (n−1) [k]+μ·η y (n) ·r y [n−k]+e CMA,LMS (n)

h yx (n) [k]=h yx (n−1) [k]+μ·η x (n) ·r y [n−k]+e CMA,LMS (n)

h xy (n) [k]=h xy (n−1) [k]+μ·η y (n) ·r x [n−k]+e CMA,LMS (n)

h yy (n) [k]=h yy (n−1) [k]+μ·η x (n) ·r x [n−k]+e CMA,LMS (n) ,

or according to:

h xx (n) [k]=h xx (n−1) [k]+e CMA,LMS (n)

h yx (n) [k]=h yx (n−1) [k]+μ·η x (n) ·r y [n−k]+e CMA,LMS (n)

h xy (n) [k]=h xy (n−1) [k]+μ·η y (n) ·r x [n−k]+e CMA,LMS (n)

h yy (n) [k]=h yy (n−1) [k]+e CMA,LMS (n) ,

wherein h is a filter coefficient, k=0, . . . , (N−1) is a filter tap variable, μ is an update factor; r x and r y are complex filter input samples with x-polarization and y-polarization, respectively, and e CMA,LMS is a correction signal derived by a standard algorithm.

4. The method according to claim 3 , which comprises changing the transfer functions only if an absolute value of one of the correlation factors (ρ xy (n) [k], ρ yx (n) [k]) exceeds a predetermined threshold value.

5. An arrangement for blind demultiplexing a polarization diversity multiplex signal in a coherent receiver, comprising:

a multidimensional filter receiving x-polarization samples and y-polarization samples of the polarization diversity multiplex signal received at an input;

a control unit configured for determining complex transfer functions by a standard equalization algorithm of said multidimensional filter and outputting x-signal samples and y-signal samples representing optical signals of the polarization diversity multiplex signal received at the input;

an error calculating circuit including:

a first storage device storing the signal x-samples and a second storage device storing the signal y-samples;

a plurality of calculation branches calculating correlation factors from actual and stored signal x-samples and signal y-samples;

a maximum detector selecting a maximum absolute correlation factor; and

selection circuits and a further multiplier connected to said maximum detector for calculating at least one error correction factor of the maximum correlation factor and the x-signal sample and y-signal sample respectively; and

said control unit being configured for:

calculating at least one error correction value by multiplying the error correction factor by an update factor and by an x-polarization sample or a y-polarization sample; and

calculating corrected filter coefficients by adding the correction values to filter coefficients of the complex transfer functions;

wherein:

the correlation factors are calculated accorrding to:

ρ xy (n) [k ]=(1−ε)·ρ xy (n−1) [k]+ε·z x [n]z y *[n−k]; k= 0 , . . . , k max

ρ yx (n) [k ]=(1−ε)·ρ yx (n−1) [k]+ε·z y [n]z x *[n−k]; k= 0 , . . . , k max ; and

error correction signals are calculated according to:

η

x

(

n

)

=

-

∑

k

=

0

k

max

⁢

ρ

xy

(

n

)

⁡

[

k

]

·

z

y

⁡

[

n

-

k

]

,

⁢

η

y

(

n

)

=

-

∑

k

=

0

k

max

⁢

ρ

yx

(

n

)

⁡

[

k

]

·

z

x

⁡

[

n

-

k

]

;

where z x and z y are x-signal samples and y-signal samples, respectively, at equalizer outputs, n is a time instant, k is a correlation delay time variable and ε is a forgetting factor.

6. An arrangement for blind demultiplexing a polarization diversity multiplex signal in a coherent receiver, comprising:

a multidimensional filter receiving x-polarization samples and y-polarization samples of the polarization diversity multiplex signal received at an input;

a control unit configured for determining complex transfer functions by a standard equalization algorithm of said multidimensional filter and outputting x-signal samples and y-signal samples representing optical signals of the polarization diversity multiplex signal received at the input;

an error calculating circuit including:

a first storage device storing the signal x-samples and a second storage device storing the signal y-samples;

a plurality of calculation branches calculating correlation factors from actual and stored signal x-samples and signal y-samples;

a maximum detector selecting a maximum absolute correlation factor;

selection circuits and a further multiplier connected to said maximum detector for calculating at least one error correction factor of the maximum correlation factor and the x-signal sample and y-signal sample respectively; and

said control unit being configured for:

calculating at least one error correction value by multiplying the error correction factor by an update factor and by an associated x-or y-polarization sample; and

calculating corrected filter coefficients by adding the correction values to filter coefficients of the complex transfer functions;

wherein:

the correlation factors are calculated according to:

ρ xy (n) [k ]=(1−ε)·ρ xy (n−1) [k]+ε·z x [n]z y *[n−k]; k= 0 , . . . , k max

ρ yx (n) [k ]=(1−ε)·ρ yx (n−1) [k]+ε·z y [n]z x *[n−k]; k= 0 , . . . , k max,

and

the error signals are derived according to:

η x (n) =−ρ xy (n) [k x ]·z y [n−k x ] for k x =argmax{ρ xy ( k )}; k= 0 , . . . , k max ,

η y (n) =−ρ yx (n) [k y ]·z x [n−k y ] for k y =argmax{ρ yx ( k )}; k= 0 , . . . , k max ; and

where n is a time instant, ρ is a correlation signal, k is a correlation delay time variable, z x and z y are x-signal samples and y-signal samples, respectively, at equalizer outputs and ε is a forgetting factor.

7. The arrangement according to claim 5 , wherein:

said control unit is configured to calculate the filter coefficients according to:

h xx (n) [k]=h xx (n−1) [k]+μ·η y (n) ·r y [n−k]+e CMA,LMS (n)

h yx (n) [k]=h yx (n−1) [k]+μ·η x (n) ·r y [n−k]+e CMA,LMS (n)

h xy (n) [k]=h xy (n−1) [k]+μ·η y (n) ·r x [n−k]+e CMA,LMS (n)

h yy (n) [k]=h yy (n−1) [k]+μ·η x (n) ·r x [n−k]+e CMA,LMS (n) ;

or according to

h xx (n) [k]=h xx (n−1) [k]+e CMA,LMS (n)

h yx (n) [k]=h yx (n−1) [k]+μ·η x (n) ·r y [n−k]+e CMA,LMS (n)

h xy (n) [k]=h xy (n−1) [k]+μ·η y (n) ·r x [n−k]+e CMA,LMS (n)

h yy (n) [k]=h yy (n−1) [k]+e CMA,LMS (n) ;

where h is a filter function, k=0, . . . , (N−1) is a filter tap variable, μ is an update factor; r x and r y (at the equalizer input) are complex x-polarization samples and y-polarization samples, respectively; and e CMA,LMS is a standard correction signal derived by a standard algorithm.

8. A method of blind demultiplexing a polarization diversity multiplex signal in a coherent receiver, deriving x-polarization samples r x (n) and orthogonal y-polarization samples r y (n) of the received polarization diversity multiplex signal, calculating complex filter functions of a multidimensional equalizer between the x-polarization samples r x (n), y-polarization samples r y (n) and output x-signal samples z x (n), y-signal samples z y (n) representing optical signals received as the polarization diversity multiplex signal,

the method comprising:

calculating at least one error correction factor derived from the x-signal samples and y-signal samples z x (n), z y (n) output from the equalizer by deriving averaged correlation factors according to:

ρ xy (n) [k ]=(1−ε)·ρ xy (n−1) [k]+ε·z x [n]z y *[n−k]; k= 0 , . . . , k max

ρ yx (n) [k ]=(1−ε)·ρ yx (n−1) [k]+ε·z y [n]z x *[n−k]; k= 0 , . . . , k max

and deriving error correction factors according to:

η

x

(

n

)

=

-

∑

k

=

0

k

max

⁢

ρ

xy

(

n

)

⁡

[

k

]

·

z

y

⁡

[

n

-

k

]

,

⁢

η

y

(

n

)

=

-

∑

k

=

0

k

max

⁢

ρ

yx

(

n

)

⁡

[

k

]

·

z

x

⁡

[

n

-

k

]

,

calculating correction values from the at least one error correction factor multiplied by an update factor and by an x-polarization sample or a y-polarization sample;

calculating corrected filter coefficients by adding the correction values to filter coefficients of the complex filter functions; and

wherein ρ is a correlation factor, n is a time instant, k is a correlation delay time index, and ε is a forgetting factor.

9. The arrangement according to claim 6 , wherein only a common error signal η(n) is selected according to a maximum absolute value of the correlation factors (|ρ xy (n) [k]|, |ρ yx (n) [k]|).

10. The arrangement according to claim 6 , wherein:

said control unit is configured to calculate the filter coefficients according to:

h xx (n) [k]=h xx (n−1) [k]+μ·η y (n) ·r y [n−k]+e CMA,LMS (n)

h yx (n) [k]=h yx (n−1) [k]+μ·η x (n) ·r y [n−k]+e CMA,LMS (n)

h xy (n) [k]=h xy (n−1) [k]+μ·η y (n) ·r x [n−k]+e CMA,LMS (n)

h yy (n) [k]=h yy (n−1) [k]+μ·η x (n) ·r x [n−k]+e CMA,LMS (n) ,

or according to:

h xx (n) [k]=h xx (n−1) [k]+e CMA,LMS (n)

h yx (n) [k]=h yx (n−1) [k]+μ·η x (n) ·r y [n−k]+e CMA,LMS (n)

h xy (n) [k]=h xy (n−1) [k]+μ·η y (n) ·r x [n−k]+e CMA,LMS (n)

h yy (n) [k]=h yy (n−1) [k]+e CMA,LMS (n) ,

where h is a filter function, k=0, . . . , (N−1) is a filter tap variable, μ is an update factor; r x and r y (at the equalizer input) are complex x-polarization samples and y-polarization samples, respectively; and e CMA,LMS is a standard correction signal derived by a standard algorithm.

11. An arrangement for blind demultiplexing a polarization diversity multiplex signal in a coherent receiver, comprising:

a multidimensional filter receiving x-polarization samples and y-polarization samples of the polarization diversity multiplex signal received at an input;

a control unit configured for determining complex transfer functions by a standard equalization algorithm of said multidimensional filter and outputting x-signal samples and y-signal samples representing optical signals of the polarization diversity multiplex signal received at the input;

an error calculating circuit including:

a first storage device storing the signal x-samples and a second storage device storing the signal y-samples;

a plurality of calculation branches calculating correlation factors from actual and stored signal x-samples and signal y-samples;

a maximum detector selecting a maximum absolute correlation factor; and

selection circuits and a further multiplier connected to said maximum detector for calculating at least one error correction factor of the maximum correlation factor and the x-signal sample and y-signal sample respectively; and

said control unit being configured for:

calculating at least one error correction value by multiplying the error correction factor by an update factor and by an associated x-or y-polarization sample; and

calculating corrected filter coefficients by adding the correction values to filter coefficients of the complex transfer functions;

wherein said control unit is configured to modify the filter functions only if an absolute value of one of the correlation factors exceeds a predetermined threshold value.