Abstract

The noise statistics of optically demodulated signal of the recently proposed modulation format, namely differential polarization-phase-shift keying, are analyzed. It is found that, in the linear regime, the Gaussian approximation is reasonably accurate in estimating the BER. In the nonlinear regime, the noise of the demodulated signal is dominated by the effect of nonlinear phase noise and obeys chi-squared statistics with a degree of freedom of one. Gaussian approximation underestimates the BER in the nonlinear regime. A two-step BER estimation method accounting for both linear beat noise and nonlinear phase noise is proposed. The effectiveness of this two-step BER estimation method at all power levels has been established by comparison with direct error counting.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

IEEE Photon. Technol. Lett. (2)

P. J. Winzer, S. Chandrasekhar, and H. Kim, �??Impact of filtering on RZ-DPSK reception,�?? IEEE Photon. Technol. Lett. 15, 840-842 (2003).
[CrossRef]

X. Wei, X. Liu, and C. Xu, �??Numerical simulation of the SPM penalty in a 10-Gb/s RZ-DPSK system,�?? IEEE Photon. Technol. Lett. 15, 1636-1638 (2003).
[CrossRef]

IEEE Trans. Commu. (1)

S. Benedetto, and P. Poggiolini, �??Theory of polarization shift keying modulation,�?? IEEE Trans. Commu. 40, 708-721 (1992).
[CrossRef]

J. Lightwave Technol. (3)

S. Walklin, and J. Conradi, �??Multilevel signaling for increasing the reach of 10 Gb/s lightwave systems,�?? J. Lightwave Technol. 17, 2235-2248 (1999).
[CrossRef]

D. Marcuse, �??Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers,�?? J. Lightwave Technol. 8, 1816-1823 (1990).
[CrossRef]

P. A. Humblet, and M. Azizoglu, �??On the bit error rate of lightwave systems with optical amplifiers,�?? J. Lightwave Technol. 9, 1576-1582 (1991)
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (1)

G. Jacobsen, Noise in digital optical transmission systems, (Artech House, Boston, MA, 1994).

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Figures (3)

Fig. 1.
Fig. 1.

(a) schematic of DPolPSK transmitter and receiver; (b) mathematical model of DPolPSK optical demodulator and receiver with optical preamplification. The inset is a typical eye diagram after transmission comprising four distinct levels.

Fig. 2.
Fig. 2.

SER of (a) the middle eye (b) the upper (lower) eye calculated by using the exact chi-squared statistics (solid line) and Gaussian approximation (dashed line)

Fig. 3.
Fig. 3.

BER estimation of DPolPSK using different method: Gaussian approximation, chi-squared approximation, direct error counting and the proposed two-step method.

Equations (7)

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ν = ν Γ ν Λ = ( 8 n p 3 · Γ + n + n 2 2 + 4 n p 3 · Γ + n + n 2 2 )
( 8 n p 3 · Λ + n n 2 2 + 4 n p 3 · Λ + n n 2 2 )
p d f ( x | n , σ 2 , m c 2 ) = 1 2 σ 2 ( x m c 2 ) n 4 1 2 exp ( x + m c 2 2 σ 2 ) × I n 2 1 ( m c 2 x σ 2 )
S E R = 0 [ 0 x p d f Γ ( y ) d y ] p d f Λ ( x ) d x
S E R = 1 2 0 [ x + thre p d f Γ ( y ) d y ] p d f Λ ( x ) d x + 1 2 0 [ 0 x + thre p d f Γ ( y ) d y ] p d f Λ ( x ) d x
i ( t ) = ( R 3 ) I A I B cos [ θ 1 ( t ) + Δ θ D ] + ( 2 R 3 ) I A I B cos [ θ 2 ( t ) + Δ θ D ]
Δ i ( t ) = i ( t ) Δ θ D = 0 [ 1 cos Δ θ D ] i ( t ) Δ θ D = 0 Δ θ D 2 2

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