Abstract

We propose a stochastic bit error ratio estimation approach based on a statistical analysis of the retrieved signal phase for coherent optical QPSK systems with digital carrier phase recovery. A family of the generalized exponential function is applied to fit the probability density function of the signal samples. The method provides reasonable performance estimation in presence of both linear and nonlinear transmission impairments while reduces the computational intensity greatly compared to Monte Carlo simulation.

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References

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  1. C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, G.-D. Khoe, and H. de Waardt, “Coherent Equalization and POLMUX-RZ-DQPSK for Robust 100-GE Transmission,” J. Lightwave Technol. 26(1), 64–72 (2008).
    [CrossRef]
  2. T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, and R. Noé, “Coherent optical communication: towards realtime systems at 40 Gbit/s and beyond,” Opt. Express 16(2), 866–872 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-2-866 .
    [CrossRef] [PubMed]
  3. G. Goldfarb and G. Li, “BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing,” Opt. Express 14(18), 8043–8053 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-18-8043 .
    [CrossRef] [PubMed]
  4. K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (2006).
    [CrossRef]
  5. J. G. Proakis, Digital Communications, (New York: McGraw-Hill, Ed.4, 2001).
  6. E. Ciaramella, “Effective Approach to Estimate Optical System Performance from Numerical Simulations,” IEEE Photon. Technol. Lett. 20(20), 1703–1705 (2008).
    [CrossRef]
  7. M. Jeruchim, “Techniques for Estimating the Bit Error Rate in the Simulation of Digital Communication Systems,” IEEE J. Sel. Areas Comm. 2(1), 153–170 (1984).
    [CrossRef]

2008

2006

G. Goldfarb and G. Li, “BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing,” Opt. Express 14(18), 8043–8053 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-18-8043 .
[CrossRef] [PubMed]

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (2006).
[CrossRef]

1984

M. Jeruchim, “Techniques for Estimating the Bit Error Rate in the Simulation of Digital Communication Systems,” IEEE J. Sel. Areas Comm. 2(1), 153–170 (1984).
[CrossRef]

Adamczyk, O.

Ciaramella, E.

E. Ciaramella, “Effective Approach to Estimate Optical System Performance from Numerical Simulations,” IEEE Photon. Technol. Lett. 20(20), 1703–1705 (2008).
[CrossRef]

De Man, E.

de Waardt, H.

Duthel, T.

Fludger, C. R. S.

Geyer, J.

Goldfarb, G.

Herath, V.

Hoffmann, S.

Jeruchim, M.

M. Jeruchim, “Techniques for Estimating the Bit Error Rate in the Simulation of Digital Communication Systems,” IEEE J. Sel. Areas Comm. 2(1), 153–170 (1984).
[CrossRef]

Khoe, G.-D.

Kikuchi, K.

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (2006).
[CrossRef]

Li, G.

Noé, R.

Peveling, R.

Pfau, T.

Porrmann, M.

Schmidt, E.-D.

Schulien, C.

van den Borne, D.

Wuth, T.

IEEE J. Sel. Areas Comm.

M. Jeruchim, “Techniques for Estimating the Bit Error Rate in the Simulation of Digital Communication Systems,” IEEE J. Sel. Areas Comm. 2(1), 153–170 (1984).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (2006).
[CrossRef]

IEEE Photon. Technol. Lett.

E. Ciaramella, “Effective Approach to Estimate Optical System Performance from Numerical Simulations,” IEEE Photon. Technol. Lett. 20(20), 1703–1705 (2008).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Other

J. G. Proakis, Digital Communications, (New York: McGraw-Hill, Ed.4, 2001).

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Figures (7)

Fig. 1
Fig. 1

QPSK constellation diagram

Fig. 2
Fig. 2

QPSK constellations. (a) linear transmission; (b) nonlinear transmission. OSNR = 10dB.

Fig. 3
Fig. 3

PDF fitting of the PN after phase estimation for the four symbols 0, 1, 2 and 3 after (a) linear transmission (b) nonlinear transmission. OSNR = 10dB.

Fig. 4
Fig. 4

BER estimation results as a function of OSNR after (a) linear transmission (b) nonlinear transmission.

Fig. 5
Fig. 5

QPSK constellations. (a) linear transmission; (b) nonlinear transmission without nonlinear phase noise; (c) nonlinear transmission with nonlinear phase noise. OSNR = 9.1dB. With MC simulation, the BERs are calculated as (a) 1.8e-4, (b) 7.4e-4 and (c) 1.1e-3. By GEF-ISI fitting, the BERs are calculated as (a) 1.3e-4, (b) 6.6e-4 and (c) 9.4e-4, respectively.

Fig. 6
Fig. 6

PDF fitting of the PN after phase estimation for the four symbols 0, 1, 2 and 3 with nonlinear phase noise. OSNR = 9.1dB.

Fig. 7
Fig. 7

BER estimation via the launch power. GEF-ISI is performed with different sequence lengths.

Equations (11)

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P E = S f ( x ) d x .
X = exp [ i ( n t + 1 / 2 ) π / 2 ] , n t { 0 , 1 , 2 , 3 } .
n d , k = ( n d , k 1 + n t , k ) mod ( max { n t } + 1 ) .
ϕ k = ϕ l a s e r + ϕ A S E + ϕ N L .
ϕ ^ e s t = 1 m arg [ k = 1 N X k m ] .
n ^ d , k = Δ θ k m 2 π + 1 2 .
n ^ t , k = ( n ^ d , k n ^ d , k 1 ) mod ( max { n t } + 1 ) .
P S E R = S f ( Δ θ k , Δ θ k 1 ) d ( Δ θ k ) d ( Δ θ k 1 ) = S f ( Δ θ k ) f ( Δ θ k 1 ) d ( Δ θ k ) d ( Δ θ k 1 ) .
P B E R = 1 2 S 1 f ( Δ θ k ) f ( Δ θ k 1 ) d ( Δ θ k ) d ( Δ θ k 1 ) + S 2 f ( Δ θ k ) f ( Δ θ k 1 ) d ( Δ θ k ) d ( Δ θ k 1 )
f 0 ( x ) = 1 64 i , k f i 0 k ( x ) , f 1 ( x ) = 1 64 i , k f i 1 k ( x ) , f 2 ( x ) = 1 64 i , k f i 2 k ( x ) , f 3 ( x ) = 1 64 i , k f i 3 k ( x ) .
f v ( x ) = v 2 2 σ Γ ( 1 / v ) exp ( | x μ 2 σ | v ) , x R .

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