Abstract

We investigate feedforward carrier recovery (FFCR) in coherent polarization diversity receivers where the signal to noise ratio (SNR) of polarization demultiplexed signals can be unequal, such as in polarization-dependent loss impaired systems. A joint-polarization FFCR mechanism for estimating the carrier phase noise based on samples from both polarizations is proposed and compared with three other plausible alternatives. We evaluated each architecture using Monte Carlo simulations and observed that the joint-polarization FFCR yields a 1.1 dB SNR penalty for a given laser linewidth × baud rate product, while the other three architectures offer 1.8 dB, 2.0 dB and 3.9 dB, for QPSK at BER = 10-3 and 3 dB SNR imbalance.

©2009 Optical Society of America

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References

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  1. E. Ip and J. M. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightwave Technol. 25, 2033–2043 (2007).
    [Crossref]
  2. T. Duthel, C.R.S. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent POLMUX-NRZ-DQPSK,” Optical Fiber Communications conference, Paper OThU5, OFC San Diego (2008).
  3. E. Ip and J.M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. 25, 2675–2692 (2007).
    [Crossref]
  4. L. G. Kazovsky, G. Kalogerakis, and W.-T. Shaw, “Homodyne phase-shift-keying systems: past challenges and future opportunities,” J. Lightwave Technol. 24, 4876–4884 (2006).
    [Crossref]
  5. R. Noé, “Phase noise-tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery,” J. Lightwave Technol. 23, 802–808 (2005).
    [Crossref]
  6. E. Ip, A. P. T. Lau, D. J. F. Barros, and J.M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16, 753–791 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-2-753.
    [Crossref] [PubMed]
  7. M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.
  8. M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
    [Crossref]
  9. G. Goldfarb and G. Li, “BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing,” Opt. Express 14, 8043–8053 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8043.
    [Crossref] [PubMed]
  10. A. J. Viterbi and A. M. Viterbi, “Nonlinear Estimation of PSK-Modulated Carrier Phase with Application to Burst Digital Transmission,” IEEE Trans. Inf. Theory 29, 543–551 (1983).
    [Crossref]
  11. E. Alpman, “Estimation of oscillator phase noise for MPSK-based communication systems over AWGN channels,” theses for degree of master of science (2004), http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.8940.

2008 (3)

E. Ip, A. P. T. Lau, D. J. F. Barros, and J.M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16, 753–791 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-2-753.
[Crossref] [PubMed]

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
[Crossref]

2007 (2)

2006 (2)

2005 (1)

1983 (1)

A. J. Viterbi and A. M. Viterbi, “Nonlinear Estimation of PSK-Modulated Carrier Phase with Application to Burst Digital Transmission,” IEEE Trans. Inf. Theory 29, 543–551 (1983).
[Crossref]

Adamczyk, O.

M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
[Crossref]

Alpman, E.

E. Alpman, “Estimation of oscillator phase noise for MPSK-based communication systems over AWGN channels,” theses for degree of master of science (2004), http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.8940.

Barros, D. J. F.

Duthel, T.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

T. Duthel, C.R.S. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent POLMUX-NRZ-DQPSK,” Optical Fiber Communications conference, Paper OThU5, OFC San Diego (2008).

El-Darawy, M.

M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
[Crossref]

Fludger, C.R.S.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

T. Duthel, C.R.S. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent POLMUX-NRZ-DQPSK,” Optical Fiber Communications conference, Paper OThU5, OFC San Diego (2008).

Geyer, J.

T. Duthel, C.R.S. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent POLMUX-NRZ-DQPSK,” Optical Fiber Communications conference, Paper OThU5, OFC San Diego (2008).

Geyer, J.C.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

Goldfarb, G.

Hauske, F.N.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

Hoffmann, S.

M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
[Crossref]

Ip, E.

Kahn, J. M.

Kahn, J.M.

Kalogerakis, G.

Kazovsky, L. G.

Koch, B.

M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
[Crossref]

Kuschnerov, M.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

Lankl, B.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

Lau, A. P. T.

Li, G.

Noé, R.

M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
[Crossref]

R. Noé, “Phase noise-tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery,” J. Lightwave Technol. 23, 802–808 (2005).
[Crossref]

Peveling, R.

M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
[Crossref]

Pfau, T.

M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
[Crossref]

Piyawanno, K.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

Porrmann, M.

M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
[Crossref]

Schmidt, E.-D.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

Schulien, C.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

T. Duthel, C.R.S. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent POLMUX-NRZ-DQPSK,” Optical Fiber Communications conference, Paper OThU5, OFC San Diego (2008).

Shaw, W.-T.

Spinnler, B.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

van den Borne, D.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

Viterbi, A. J.

A. J. Viterbi and A. M. Viterbi, “Nonlinear Estimation of PSK-Modulated Carrier Phase with Application to Burst Digital Transmission,” IEEE Trans. Inf. Theory 29, 543–551 (1983).
[Crossref]

Viterbi, A. M.

A. J. Viterbi and A. M. Viterbi, “Nonlinear Estimation of PSK-Modulated Carrier Phase with Application to Burst Digital Transmission,” IEEE Trans. Inf. Theory 29, 543–551 (1983).
[Crossref]

Wrdehoff, C.

M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
[Crossref]

Wuth, T.

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

IEEE Photon. Technol. Lett. (1)

M. El-Darawy, T. Pfau, S. Hoffmann, R. Peveling, C. Wrdehoff, B. Koch, M. Porrmann, O. Adamczyk, and R. Noé, “Fast adaptive polarization and PDL tracking in a realtime FPGA based coherent PolDM-QPSK receiver,” IEEE Photon. Technol. Lett. 20, 1796–1798 (2008).
[Crossref]

IEEE Trans. Inf. Theory (1)

A. J. Viterbi and A. M. Viterbi, “Nonlinear Estimation of PSK-Modulated Carrier Phase with Application to Burst Digital Transmission,” IEEE Trans. Inf. Theory 29, 543–551 (1983).
[Crossref]

J. Lightwave Technol. (4)

Opt. Express (2)

Other (3)

T. Duthel, C.R.S. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent POLMUX-NRZ-DQPSK,” Optical Fiber Communications conference, Paper OThU5, OFC San Diego (2008).

M. Kuschnerov, D. van den Borne, K. Piyawanno, F.N. Hauske, C.R.S. Fludger, T. Duthel, T. Wuth, J.C. Geyer, C. Schulien, B. Spinnler, E.-D. Schmidt, and B. Lankl, “Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors,” ECOC 2008, Mo.4.D.2.

E. Alpman, “Estimation of oscillator phase noise for MPSK-based communication systems over AWGN channels,” theses for degree of master of science (2004), http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.8940.

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Figures (11)

Fig. 1.
Fig. 1. (a) Polarization multiplexed system employing a homodyne coherent receiver. (b) PDL model.
Fig. 2.
Fig. 2. Ideal homodyne coherent receiver with a DSP feedforward carrier recovery unit.
Fig. 3.
Fig. 3. Single polarization feedforward carrier recovery.
Fig. 4.
Fig. 4. Individual feedforward carrier recovery for dual polarization.
Fig. 5.
Fig. 5. Mean of unwrapped angles. This architecture would lead to catastrophic failures.
Fig. 6.
Fig. 6. Mean feedforward carrier recovery for dual polarization.
Fig. 7.
Fig. 7. Flat filter feedforward carrier recovery for dual polarization.
Fig. 8.
Fig. 8. Joint feedforward carrier recovery for dual polarization.
Fig. 9.
Fig. 9. Normalized filter weigths for polarizations V and H when SNRV = 7 dB (curves on the left) and SNRH = 4 dB (curves on the right). Dashed line: individual estimation. Solid line: joint estimation. The difference between adjacent phase noise samples is a Gaussian process with zero mean and variance σ2 Δ = 2πΔv Ts = 2π10-4. The filter length N = 10.
Fig. 10.
Fig. 10. Modulation constellation for 5,000 received QPSK symbols corrupted by AWGN and Wiener Noise with ΔvTs = 10-3. The figures on the left show constellations before carrier recovery, and those on the right after carrier recovery using the individual method. In the upper curves the SNR is 3 dB higher (7 dB) than for those on the bottom (4 dB).
Fig. 11.
Fig. 11. SNR penalty versus laser linewidth×baud rate product for the four feedforward carrier recovery estimation methods (@ QPSK, 3 dB SNR imbalance, worst case polarization and BER = 10-3).

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

Sk=[skVskH],
rk=Hsk exp (jθk) +nk,
H=[cosαsinαsinαcosα] [1γ001+γ] [cosβsinβsinβcosβ],
yk=Wrk=W[Hskexp(jθk)+nk]=WHskexp(jθk)+Wnk
sk exp (jθk)+wk,
ykV/H=skV/Hexp(jθk)+wkV/H .
yk=skexp(jθk) + wk ,
PU(·)=(·)+(12+θ̂k1(·)2π/M) 2πM .
θk=θk1+Δk;
θk1= θk+m=0i1λm;
θk+1= θk+m=0i1μm,
ykiM={sk1exp[j(θk+m=0i1λm)]+wki}M;
skiMexp[jM(θk+m=0i1λm)]+zki,
ykiM EsM/2exp(jMθk)(1+jMm=0i1λm)+zki.
yk+iM EsM/2exp(jMθk)(1+jMm=0i1μm)+zk+i.
fr|θk(rθk)=1(2π)L/2(detC)1/2exp[12(rmr)HC1(rmr)] ,
C=EsMM2K σΔ2 +EsM1M2Kn,
K=[N21000022100001110000000000000001110000122000012N].
Λln=ln (1(2π)L/2(detC)1/2) 12 (rmr)HC1(rmr),
θk=1M arctan {1TC1·r}{1TC1·r} .
θ̂k=PU{1Marg(1TC1·r)} .
θ̂kV=PU{1Marg[1T(CV)1·rV]} ,
θ̂kH=PU{1Marg[1T(CH)1·rH]} .
θ̂k=PU{1Marg[1T(CV)1·rV+1T(CH)1·rH2]} .
θ̂k=PU{1Marg[i=NN(yk+iV)M+i=NN(yk+iH)M2]} ,
r’=[(rkNV)M,,(rkV)M,,(rk+NV)M,(rkNV)M,,(rkH)M,,(rk+NH)M]T.
C’=EsMM2KσΔ2+EsM1M2K’n,
K’=[KKKK];
K’n=[ILxLσwnV200ILxLσwnH2].
θ̂k=PU{1Marg[1TC’1·r’]} .
BER(SNR=EbN0)2Q[sin(πM)4EbN0].

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