Abstract

We propose a novel configuration of the finite-impulse-response (FIR) filter adapted by the phase-dependent decision-directed least-mean-square (DD-LMS) algorithm in digital coherent optical receivers. Since fast carrier-phase fluctuations are removed from the error signal which updates tap coefficients of the FIR filter, we can achieve stable adaptation of filter-tap coefficients for higher-order quadrature-amplitude modulation (QAM) signals. Computer simulations show that our proposed scheme is much more tolerant to the phase noise and the frequency offset than the conventional DD-LMS scheme. Such theoretical predictions are also validated experimentally by using a 10-Gsymbol/s dual-polarization 16-QAM signal.

© 2012 OSA

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References

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  1. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express16(2), 804–817 (2008).
    [CrossRef] [PubMed]
  2. K. Kikuchi, “Clock recovering characteristics of adaptive finite-impulse-response filters in digital coherent optical receivers,” Opt. Express19(6), 5611–5619 (2011).
    [CrossRef] [PubMed]
  3. D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun.28(11), 1867–1875 (1980).
    [CrossRef]
  4. H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in Technical Digest of European Conference on Optical Communication (ECOC 2008), Tu.1.E.6.
  5. P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol.28(4), 547–556 (2010).
    [CrossRef]
  6. K. Kikuchi, “Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers,” Opt. Express19(10), 9868–9880 (2011).
    [CrossRef] [PubMed]
  7. S. U. H. Qureshi, “Adaptive equalization,” Proc. IEEE73(9), 1349–1387 (1985).
    [CrossRef]
  8. S. Haykin, Adaptive Filter Theory (Prentice Hall, 2001).
  9. Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express17(3), 1435–1441 (2009).
    [CrossRef] [PubMed]
  10. T. Tsukamoto, Y. Ishikawa, and K. Kikuchi, “Optical homodyne receiver comprising phase and polarization diversities with digital signal processing,” in Technical Digest of European Conference on Optical Communication (ECOC 2006), Th3.5.2.
  11. C. R. S. Fludger, D. Nuss, and T. Kupfer, “Cycle-slips in 100G DP-QPSK transmission systems,” in 2012 OSA Technical Digest of Optical Fiber Communication Conference (Optical Society of America, 2012), OTu2G.1.

2011 (2)

2010 (1)

2009 (1)

2008 (1)

1985 (1)

S. U. H. Qureshi, “Adaptive equalization,” Proc. IEEE73(9), 1349–1387 (1985).
[CrossRef]

1980 (1)

D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun.28(11), 1867–1875 (1980).
[CrossRef]

Buhl, L. L.

Doerr, C. R.

Gnauck, A. H.

Godard, D. N.

D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun.28(11), 1867–1875 (1980).
[CrossRef]

Igarashi, K.

Katoh, K.

Kikuchi, K.

Magarini, M.

Mori, Y.

Qureshi, S. U. H.

S. U. H. Qureshi, “Adaptive equalization,” Proc. IEEE73(9), 1349–1387 (1985).
[CrossRef]

Savory, S. J.

Winzer, P. J.

Zhang, C.

IEEE Trans. Commun. (1)

D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun.28(11), 1867–1875 (1980).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (4)

Proc. IEEE (1)

S. U. H. Qureshi, “Adaptive equalization,” Proc. IEEE73(9), 1349–1387 (1985).
[CrossRef]

Other (4)

S. Haykin, Adaptive Filter Theory (Prentice Hall, 2001).

H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” in Technical Digest of European Conference on Optical Communication (ECOC 2008), Tu.1.E.6.

T. Tsukamoto, Y. Ishikawa, and K. Kikuchi, “Optical homodyne receiver comprising phase and polarization diversities with digital signal processing,” in Technical Digest of European Conference on Optical Communication (ECOC 2006), Th3.5.2.

C. R. S. Fludger, D. Nuss, and T. Kupfer, “Cycle-slips in 100G DP-QPSK transmission systems,” in 2012 OSA Technical Digest of Optical Fiber Communication Conference (Optical Society of America, 2012), OTu2G.1.

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Figures (12)

Fig. 1
Fig. 1

Configurations of the FIR filter adapted by (a) CMA/MMA and (b) the phase-independent DD-LMS algorithm, both of which are followed by phase estimators. Figures (c) and (d) are those adapted by the standard phase-dependent DD-LMS algorithm. Figure (c) does not include a phase estimator, whereas in Fig. (d), the phase estimator follows the FIR filter.

Fig. 2
Fig. 2

Proposed configuration of the FIR filter followed by the phase estimator. Filter-tap coefficients are adapted by the phase-dependent DD-LMS algorithm. |⋅|/(⋅) denotes |f|/f.

Fig. 3
Fig. 3

Unwrapped phases tracked by the proposed configuration. Upper figures (a), (b), and (c) are calculated when the laser linewidth equals to 100 kHz and the offset frequency is 0 Hz. Lower figures (d), (e), and (f) are calculated when the laser linewidth is 0 Hz and the offset frequency is 10 MHz. μpf = 1 and M + 1 = 1 in left figures (a) and (d), μpf = 1 and M + 1 = 4 in middle figures (b) and (e), and μpf = 1/4 and M + 1 = 1 in right figures (c) and (f). Red curves: unwrapped phase φp(n) defined as the phase difference of the signal between the output and input ports of the FIR filter. Blue broken curves: unwrapped phase φf(n) defined as the phase difference of the signal between the output and input ports of the phase estimator. Green broken curves: total phases φp(n) + φf(n). Black curves: sign-inverted values of the actual phase fluctuation -φn(n).

Fig. 4
Fig. 4

Phase-separation ratio α as a function of the number of FIR-filter taps. Figure (a) is calculated when the laser linewidth equals to 100 kHz and the offset frequency is 0 Hz. Figure (b) is calculated when the laser linewidth is 0 Hz and the offset frequency is 10 MHz. Squares, dots, and plus marks correspond to μpf = 1, 1/4, and 1/16, respectively. Solid curves show the relation given by Eq. (15).

Fig. 5
Fig. 5

FIR-filter configuration adapted by the DD-LMS algorithm, which employ the dual-stage decision-directed phase estimator. |⋅|/(⋅) denotes either |f|/f or |s|/s.

Fig. 6
Fig. 6

Butterfly-structured FIR filters combined with dual-stage decision-directed phase estimators, which are adapted by the phase-dependent DD-LMS algorithm. |⋅|/(⋅) denotes either |fx,y|/fx,y or |sx,y|/sx,y.

Fig. 7
Fig. 7

BER characteristics of 10-Gsymbol/s 16-QAM signals calculated as a function of Eb/N0 (a) with the proposed scheme. Figures (b) and (c) are those with the conventional DD-LMS algorithm. Figure (b) corresponds to the scheme shown in Fig. 1(c), and Fig. (c) to that shown in Fig. 1(d). δf and Δf denote the linewidth of the laser and the frequency offset, respectively. We calculate BERs for δf = 0 Hz and 100 kHz and Δf = 0 Hz and 100 MHz. Filter orders M are 4, 16, and 64.

Fig. 8
Fig. 8

Phase-noise tolerance of the proposed scheme in 4-QAM, 16-QAM, and 64-QAM systems. Solid curves are calculated by using the phase correlation between the two polarization tributaries, whereas broken curves are calculated without using such correlation.

Fig. 9
Fig. 9

Frequency-offset tolerance of the proposed scheme in 4-QAM, 16-QAM, and 64-QAM systems. Solid curves are calculated by using the phase correlation between the two polarization tributaries, whereas broken curves are calculated without using such correlation.

Fig. 10
Fig. 10

Experimental setup for measuring the performance of the proposed FIR-filtering configuration.

Fig. 11
Fig. 11

BER characteristics of 10-Gsymbol/s dual-polarization 16-QAM signals measured as a function of the received power (a) with the proposed scheme. Figures (b) and (c) are obtained with the conventional DD-LMS schemes, Fig. 1(c) and Fig. 1(d), respectively. δf and Δf denote the individual laser linewidth and the frequency offset, respectively. We measure BERs when Δf = 0 Hz and 100 MHz, whereas δf is about 100 kHz. Filter orders M are 4, 16, and 64.

Fig. 12
Fig. 12

Constellation maps of a tributary of the 10-Gsymbol/s dual-polarization signals (a) before the butterfly-structured FIR filters, (b) after the butterfly-structured FIR filters, (c) after the first-stage phase estimator, and (d) after the second-stage phase estimator. The received power was −30 dBm, the frequency offset 100 MHz, and the filter order 64. The horizontal axis and the vertical axis of each figure denote the real axis and the imaginary axis of the complex plane, respectively.

Tables (2)

Tables Icon

Table 1 Laser linewidth that ensures the power penalty at BER = 10−3 less than 1 dB in 10-Gsymbol/s QAM systems.

Tables Icon

Table 2 Frequency offset that ensures the power penalty at BER = 10−3 less than 1 dB in 10-Gsymbol/s QAM systems.

Equations (28)

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E( n )= [ E( n ),E( n1 ),,E( nM ) ] T ,
p( n )= [ p( n ),p( n1 ),,p( nM ) ] T .
E ( n )= p ( n ) T E( n ) .
p( n+1 )=p( n )+ μ p e p ( n )E ( n ) ,
e CMA ( n )= E ( n ){ r 2 | E ( n ) | 2 } ,
e MMA ( n )= E ( n ){ r ( n ) 2 | E ( n ) | 2 } ,
e PILMS ( n )= E ( n ){ | d( n ) | 2 | E ( n ) | 2 } ,
e PDLMS ( n )= d( n ) E ( n ) .
e p ( n )=d( n ) { f(n)/| f(n) | } 1 E ( n ) ,
f( n+1 )=f( n )+ μ f | E ( n ) | 2 +ε e f ( n ) E ( n ) * ,
e f ( n )=d( n )f( n ) E ( n ) ,
p( n+1 )=( 1 μ p )p( n )+ μ p d( n ) E( n ) | f( n ) | f( n ) ,
f( n+1 )=( 1 μ f )f( n )+ μ f d( n ) p( n )E( n ) ,
α= 1 N n=1 N ϕ p ( n+1 ) ϕ p ( n ) ϕ f ( n+1 ) ϕ f ( n ) ,
α μ p μ f 1 M+1 .
s( n+1 )=s( n )+ μ s | f( n ) E ( n ) | 2 +ε e s ( n ) { f( n ) E ( n ) } ,
e s ( n )=d( n )s( n )f( n ) E ( n ),
e p ( n )=d( n ) { f( n )/| f( n ) | } 1 { s( n )/| s( n ) | } 1 E ( n ).
E x,y ( n )= [ E x,y ( n ), E x,y ( n1 ),, E x,y ( nM ) ] T
p k,l ( n )= [ p k,l ( n ), p k,l ( n1 ),, p k,l ( nM ) ] T .
p xx ( n+1 )= p xx ( n )+ μ p e px ( n ) E x ( n ) * , p xy ( n+1 )= p xy ( n )+ μ p e px ( n ) E y ( n ) * , p yx ( n+1 )= p yx ( n )+ μ p e py ( n ) E x ( n ) * , p yy ( n+1 )= p yy ( n )+ μ p e py ( n ) E y ( n ) * ,
e px ( n )= d x ( n ) { f x (n)/| f x (n) | } 1 { s x (n)/| s x (n) | } 1 E x ( n ) , e py ( n )= d y ( n ) { f y (n)/| f y (n) | } 1 { s y (n)/| s y (n) | } 1 E y ( n ) ,
E x ( n )= p xx ( n ) T E x ( n )+ p xy ( n ) T E y ( n ) , E y ( n )= p yx ( n ) T E x ( n )+ p yy ( n ) T E y ( n ) .
f x,y ( n+1 )= f x,y ( n )+ μ f | E x,y ( n ) | 2 +ε e fx,y ( n ) E x,y ( n ) ,
e fx,y ( n )= d x,y ( n ) f x,y ( n ) E x,y ( n ) ,
s x,y ( n+1 )= s x,y ( n )+ μ s | f x,y ( n ) E x,y ( n ) | 2 +ε e sx,y ( n ) { f x,y ( n ) E x,y ( n ) } ,
e sx,y ( n )= d x,y ( n ) s x,y ( n ) f x,y ( n ) E x,y ( n ) ,
f ave ( n )= f x ( n )+ f y ( n ) 2 .

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