Abstract:
A received optical signal is coherently demodulated and converted into orthogonal x-polarization samples, and y-polarization samples. These samples are converted into signal x-samples and signal y-samples by an FIR butterfly filter. Correction values are calculated in an error calculating circuit of a control unit and added to filter transfer functions derived by a standard algorithm to determine corrected filter coefficients. Degenerate convergences calculating the transfer functions are avoided.

Description:
FIELD OF THE INVENTION 
     The invention refers to a method and an arrangement for blind demultiplexing of polarisation diversity signals for a coherent receiver. 
     BACKGROUND OF THE INVENTION 
     In order to meet the growing demand for internet bandwidth with traffic growth rates around 40-50% per year, telecommunication component providers face the task of increasing the spectral efficiency of fiber utilization. After 10 Gbit/s systems (G−Giga) became successful in the 1990&#39;s, solutions for 40 Gbit/s became available in the last years. Standardization and research are now focused on the development of 100 Gbit/s systems with coherent polarisation multiplexed (CP) QPSK being the most likely modulation format for next generation systems. Since polarisation multiplexing utilizes both light polarisations, it is possible to send the signal at a rate of ˜25-28 Gsymbols per second, thus fitting nicely into the standard 50 GHz grid for DWDM (Dense Wavelength Diversity Multiplex) optical systems. 
     In some applications, like point-to-point radio systems, where polarisation multiplexing is employed, a visual line of sight is given, so that transmitter and receiver polarisations can be aligned during installation, and usually only small variations of the polarisation occurs. 
     Manually aligning the transmitter and receiver polarisations is not possible for fiber links with time-varying polarisation changes. Other solutions have been proposed for optical fiber systems like polarisation controllers. In fiber optic systems, polarisation changes arbitrarily with time and an adaptive optical polarisation controller is complicated and expensive. Moreover, PDL (polarisation depending loss) leads to a polarisation-dependent attenuation, thereby causing different SNR-levels (signal-to-noise ratio) for the two polarisations. 
     Since coherent reception also enables the separation of orthogonally polarized signals in the electrical domain, the use of a similar polarisation controller is not needed nor economically viable. 
     Current fiber network standards do not incorporate training sequences, so that in the receiver the channel has to be estimated blindly without any further knowledge. 
     E. g. Seb J. Savory, “Digital filters for coherent optical receivers”, Optics Express 16, No. 2, pp. 804-817, 9. January 2008 describes the principles of digital coherent receivers. Savory describes especially blind polarisation demultiplexing by multidimensional digital filtering and compensation of polarisation independent impairments by dispersion compensators and of polarisation dependent impairments by a multidimensional filter referred to as a butterfly filter. 
     Two algorithms are applied, the LMS (Least Mean Square) algorithm is employed after the carrier phase has been acquired, and the received symbols are compared with ideal symbols in order to derive errors for channel tracking, and the CMA (constant modulus algorithm) that is used for initial acquisition without requiring carrier phase compensation, where the goal is to achieve symbols of equal power. Applying these equalisation algorithms can lead to degenerative solutions, where one polarized signal is demultiplexed to both output polarisations and half of the information lost. 
     OBJECTS AND SUMMARY OF THE INVENTION 
     It is an object of the invention to provide a method and an arrangement for blind polarisation demultiplexing. 
     The object is achieved by the features recited in a claimed method and arrangement. 
     The present invention provides a method for blind demultiplexing of a polarisation diversity multiplex signal in a coherent receiver deriving x-polarisation samples and orthogonal y-polarisation samples of the received polarisation diversity multiplex signal, calculating complex functions of a multidimensional filter between said x-polarisation samples, y-polarisation samples and output signal x-samples, output signal y-samples representing optical signals received as polarisation diversity multiplex signal the method comprising the steps of
         calculating at least one error correction factor of both output signal samples,   calculating correction values from the at least one error correction factor multiplied by an update factor and by a x-polarisation sample or y-polarisation sample, and   calculating corrected filter coefficients by adding the correction values to the filter coefficients determining corrected transfer functions.       

     The present invention further provides an arrangement for blind demultiplexing of a polarisation diversity multiplex signal in a coherent receiver with a multidimensional filter receiving x-polarisation samples and y-polarisation samples of the received polarisation diversity multiplex signal and with a control unit determining complex filter functions by a standard equalisation algorithm of the multidimensional filter and outputting signal x-samples and signal y-samples representing optical signals (S H  and S V ) of the received polarisation diversity multiplex signal 
     the arrangement comprising an error calculating circuit including 
     
         
         
           
             a first storage storing the signal x-samples and a second storage storing the signal y-samples, 
             a plurality of calculation branches calculating correlation factors from the actual and stored signal x-samples and signal y-samples, 
             a maximum detector selecting a maximum correlation value, and 
             selection circuits and a further multiplier calculating an error correction factor of the maximum correlation function and the associated signal x-sample or signal y-sample, and 
             the control unit calculating error correction values by multiplying the error correction factor by an update factor and by an associated x- or y-polarisation sample, and calculating corrected filter coefficients by adding the correction values to the filter coefficients determining corrected transfer functions. 
           
         
       
    
     Advantageous features are described in the pending claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Examples of the invention including a presently preferred embodiment are described below with reference to accompanying drawings, where 
         FIG. 1  is a schematic block diagram of a coherent receiver with polarisation demultiplexing, 
         FIG. 2  shows a schematic block diagram of a butterfly equalizer, 
         FIG. 3  is a schematic block diagram of an error calculation circuit, and 
         FIG. 4  shows a performance diagram. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     An embodiment of the invention will be described as a part of a coherent polarisation diversity multiplex (polmux) receiver. This system transmits two optical signals S H  and S V  with the same carrier wavelength but orthogonal polarisations in two subchannels of a single-carrier transmission channel. 
       FIG. 1  shows a schematic block diagram of a today&#39;s polarisation multiplex receiver. The received polmux (polarisation diversity multiplex) signal S H , S V  is split by a polarisation beam splitter  1  into an x-component signal S X  with x-polarisation and an orthogonal y-component signal S Y  with y-polarisation. A local oscillator  2  generates a constant wave signal, which is split into two orthogonally polarized constant wave signals and fed together with the orthogonal component signals Sx and Sy to two 90° hybrids  3  and  4 , where each x- and y-component signal is split into two orthogonal components x I , x Q  and y I , y Q  respectively (in-phase component I, quadrature component Q or real and imaginary component). These components are converted by converter units  51 - 54  into digital complex x-samples X I (n)+jX Q (n) and y-samples Y I (n)+jY Q (n) in the electrical domain (n−time instant). 
     These complex samples X I  (n)+jX Q (n) and Y I (n)+jY Q (n) still carry all the information of the optical component signals Sx and Sy (which usually are not the transmitted signals). 
     These samples are often dispersion compensated by separate dispersion compensation units  61  and  62  (CDC−chromatic dispersion compensation). Subsequently the timing phase and frequency offsets are corrected in an interpolator and clock recovery unit  7  known to those skilled in the art in order to enable fast equalizer convergence. Then these corrected filter input samples r x (n)=r XI (n)+jr XQ (n) and r y (n)=r YI (n)+jr YQ (n),—also referred to as “x-polarisation samples” and “y-polarisation samples”—are fed to a FIR (finite impulse response) butterfly equalizer  8  (implemented as filter or as digital processor with the same functionality), which reconstructs the received optical signals S H , S V  in a sample format as x-signal samples z x (n)=z XI (n)+jz XQ (n) and y-signal samples z y (n)=z YI (n)+jz YQ (n) (the r and z in-phase and quadrature samples are only shown in  FIG. 1 ). The x-signal samples and y-signal samples are fed to a carrier recovery unit  9  and a error calculation circuit, which is a part of an equalizer control unit  11 . A symbol estimation  10  unit outputs retrieved signals S HOUT  and S VOUT  derived from the x-signal samples and y-signal samples respectively. 
       FIG. 2   a  shows a more detailed block diagram of the multidimensional butterfly equalizer and  FIG. 2   b  shows an embodiment of an FIR filter with N=3 taps. The complex x-polarisation samples r X (n) and y-polarisation samples r Y (n) are fed to inputs of the FIR butterfly equalizer  8 . The butterfly equaliter  8  includes four FIR filters  81 - 84  with time domain filter functions h XX , h YX , h XY , h YY  and two adders AD 1  and AD 2  (index xy means from x to y). These filter functions are adapted to the changing polarisation of the received polmux signal. The output signals of the filters  81  and  82  are combined by the adder AD 1  and the output signals of the filters  83  and  84  are combined by the adder AD  2 . The combined equalizer output x-signal samples z x (n) and y-signal samples z y (n) represent the transmitted optical signals S H , S V . A control unit  11  calculates the filter functions, more precisely the filter coefficients by standard equalisation algorithms as LMS and CMA and adds correction values derived according to the present invention. 
     The FIR filter with N=3 taps illustrated in  FIG. 2   b  comprises two storage stages SF 1  and SF 2 . The filter taps for k=1, 2, 3 are connected via multipliers M implementing the filter coefficients h xx   (n) [ 0 ], h xx   (n) [ 1 ] and h xx   (n) [ 2 ]. The output samples are combined by an adder AD determining the filter function h XX . 
     The proposed invention consists of an adaptation algorithm for the FIR butterfly filters that can be used on top of the standard equalisation algorithms in order to separate the two polarisations. While blind algorithms like CMA equalize for the linear channel distortion, the proposed blind source separation (BSS) approach evaluates the correlation between the two equalized signals corresponding to two polarisations and calculates error correction values to update the equalizer taps and decorrelate the two signals. The time averaged correlation between equalized x-signal samples z x [n] and y-signal samples z y [n] at time instant n is given by
 
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   (1)
 
where ρ-correlation factor, ε is a forgetting factor ca. 0.01-0.1. z x =x-signal sample, z y =y-signal sample, z x *, z y *—conjugate complex signal values, k—correlation delay time variable, which corresponds to the time delay between the equalizer output x/y-signal samples/symbols.
 
     Here, each polarisation is correlated with post cursors, thus effectively giving correlation for both precursors and post cursors. The number of correlation coefficients, which must be taken into account, depends on the number N of filter taps and a maximum timing offset between the two signals that shall be detected and removed. If it is guaranteed that there is no timing offset between the two signals at the output of the equalizer one tap would be sufficient. 
     The error correction factors η x  and η y  are given by 
                       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     ]               ,           (   2   )               
wherein k=0, . . . , k max ; k=correlation delay time variable;
     k max ≧(N−1) for a T-spaced equalizer filter with N taps;   k max ≧(N−1)/2 for a T/2-spaced equalizer filter with N taps;   1/T=symbol rate.   

     The equalizer is updated similarly to algorithms like LMS and CMA, which are still needed for equalisation purposes. The filter coefficients h xx   (n) [k], h yx   (n) [k], h xy   (n) [k], h yy   (n) [k] at time instant n are given by
 
 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) ,  (3)
 
where e CMA,LMS  are the updates from LMS and CMA, r x , r y =equalizer filter input sample values; μ=update factor ca. 0.0001-0.01; index xy means from x to y; and
     k=0, 1, . . . , N−1—filter tap variable (depending on the filter implementation, the signal delay between filter taps indicated by k might be different from the delay of the correlation time variable used in equations (1) and (2));   (μ·η·[n−k])—correction values. While equation (3) shows the update of the filter coefficients using four complex equations, the update can as well be done using 16 equivalent real update equations as is usually done in hardware implementations.   

     The filter functions derived by a standard algorithm are corrected by adding correction values from the second terms of these equations. It is sufficient that the two equalizer filters h yx  and h xy  are updated according to the invention while the other two filters are only updated according to a common algorithm. 
     For an implementation, the presented equations can be simplified. It is only necessary to compute the error values η x , η Y  from the maximum of both correlation factors ρ xy , ρ yx  and the associated filter output samples z x (n), z y (n) reducing the complexity of the update algorithm and therefore the circuit complexity of a calculation circuit.
 
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 ,  (4)
 
     The complexity is further reduced if only one error value η(n) is derived for both polarisations in an error calculation circuit  13  as shown in  FIG. 3 . 
     A first storage SX 1  receives and stores signal x-signal samples z X (n) and outputs time delayed x-signal samples z X (n−1) with the symbol rate 1/T. A second storage SY 2  receives samples z y (n) and outputs delayed y-signal samples z y (n−1), also with the symbol rate 1/T. The number of storage stages (e.g. of a shift register) depends on the necessary correlation length and depends therefore of the number N of filter taps and filter clock rate; only one storage stage for each polarisation and k=0, 1 (N=2) is shown for reasons of clarity in this embodiment. 
     The correlation factors ρ xy   (n) [k], ρ yx   (n) [k] are derived according to the equations (4). Conjugate complex sample values z X *(n) are derived from actual signal y-samples z y (n) and from time shifted signal samples z y (n−1), z x (n−1) by calculation circuits CC. The conjugate complex signal samples z y *(n), z y*(n− 1) are then multiplied by an actual signal x-signal sample z x (n) by multipliers M 1  and M 2 . The time shifted signal x-signal sample z x (n−1) is converted into a conjugate complex x-signal sample z x *(n−1) and multiplied by the actual y-signal sample z y (n) by a multiplier M 3 . The result is multiplied by a forgetting factor ε (ca. 0.001-0.1) and added to the already stored sums in storages ST 1 -ST 3 . The sum is reduced by (1−ε) for each new sample by calculation circuits comprising storages ST 1 -ST 3 , multipliers (1−ε) and adders A 1 -A 3 . Only three calculation paths are needed for the calculation of η x  and η y  because ρ xy (k=0)=ρ* yx (k=0). Multiplications by the forgetting factor ε (and by the update factor μ in the control unit  11 ) can be simplified and replaced by bit shifting (equivalent to the division by a power of 2 for binary numbers). Of course, other stores and calculation units may be applied. 
     The derived correlation factors ρ yx   (n) [0], ρ yx   (n) [1], and ρ xy   (n) [ 1 ] are fed to a maximum detector  13 , which selects a maximum absolute correlation value and controls a second multiplexer MUX 2  and a first multiplexer MUX 1 . Different error values η x , η Y  may be calculated with a time multiplex arrangement or with an additional multiplexer. But also the calculation of a common error values η(n) is sufficient. The correlation factor with a maximum absolute value (e.g. ρ yx [ 1 ]) is fed via the multiplexer MUX 2  to a multiplier M 4  and the associated sample value (e.g. z Y [n−1]) is fed via the first multiplexer MUX 1  to the multiplier M 4 . The selected correlation factor is then multiplied by the associated signal sample value according to equations (2). The negative product is a simplified common error correction factor η(n), which is used instead of η x , η Y  in the equations (2) or (3) for calculating the filter coefficients. Moreover, correlation factors below a certain threshold are discarded, in order to avoid noise enhancement. 
       FIG. 4  shows that the performance is in fact optimal up to worst case distortions of 10 dB for both worst case and best case PDL (polarisation depending loss). 45° alignment means that the transmission element is aligned at an angle of 45° in respect to the signal polarisations. In this example the chromatic dispersion is 1000 ps/nm, the mean DGD (Differential Group Delay) is 30 ps, and QPSK (Quadrature Phase Shift Keying) with 112 Gbit/s is used. Misconvergences were not observed. 
     The performance can be evaluated in presence of PDL (Polarisation-Dependent Loss) against theoretical boundaries given by the attenuation inflicted by PDL. Only if the equalizer performance is on these boundaries, the equalisation can be considered optimal.  FIG. 4  shows that the performance is in fact optimal up to worst case distortions of 10 dB for both worst case and best case PDL. 
     The present invention is not limited to the details of the above described principles. The scope of the invention is defined by the appended claims and all changes and modifications falling within the equivalents of the scope of the claims are therefore to be embraced by the invention. 
     REFERENCE SIGNS 
     
         
           1  polarisation beam splitter 
           2  local oscillator 
           3  first 90° hybrid 
           4  second 90° hybrid 
           5  optical-electrical converters 
           61 ,  62  dispersion compensation units 
           7  clock recovery unit 
           8  butterfly equalizer 
           81 - 84  FIR filter 
           9  carrier recovery unit 
           10  symbol estimation unit 
           11  equalizer control unit 
           12  error calculation circuit 
           13  maximum detector 
         S H , S V  received polmux signal 
         S X  x-component signal 
         S Y  y-component signal 
         x I  x in-phase component 
         x Q  x quadrature component 
         y I  y in-phase component 
         Y Q  y quadrature component 
         X I , X Q  x-samples 
         Y I , Y Q  y-samples 
         r x  x-polarisation samples (CD compensated) 
         r y  y-polarisation samples (CD compensated) 
         h xx  filter function in the time domain 
         z x  x-signal sample 
         z y  y-signal sample 
         η error correction factor 
         ρ correlation factor 
         S HOUT , S VOUT  retrieved signals 
         h transfer function 
         AD 1  first adder 
         AD 2  second adder 
         SF 1  first filter storage stage 
         SF 2  second filter storage stage 
         M multiplier 
         AD adder 
         SX 1  z X -sample storage 
         SY 1  z Y -sample storage 
         M 1 , M 2 , . . . multiplier 
         A 1 , A 2 , . . . adder 
         ε forgetting factor 
         η error factor 
         μ update factor 
         ρ correlation factor 
         ST 1 , ST 2 , . . . storage 
         MUX 1  first multiplexer 
         MUX 2  second multiplexer