Investigation of Nonlinear DPSK Fading Due to Cross-Polarization Modulation Marcus Winter Klaus...
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Investigation of Nonlinear DPSK Fading Due to Cross-Polarization Modulation
Marcus WinterKlaus Petermann
Hochfrequenztechnik-Photonik
TECHNISCHEUNIVERSITÄTBERLIN
Dario Setti
http://www.marcuswinter.de/publications/ofc2009
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Fachgebiet Hochfrequenztechnik
what are we talking about?
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a typical system
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selective upgrade of an existing 10 Gbps NRZ infrastructure with DPSK channels (10 / 40 Gbps)
worst case for interchannel nonlinearities
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cross-polarization modulation(XPolM)
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XPolM is very similar to XPM
nonlinear variation of the
birefringence refractive index
proportional to sum of interfering channel
Stokes vectors powers
results in the modulation of signal
polarization phase
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nonlinear polarization effects only
XPolM demonstration / quantification setup
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polarization states (SOPs) of the CW probe at the transmitter
500 × 256 bits
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polarization states (SOPs) of the CW probe at a receiver
500 × 256 bits
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DPSK fading
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the balanced detector output current depends on the relative polarization between the interfering bits
I cos(Δθ/2)
(Δθ is the angle between Stokes vectors of the two symbols)
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exemplary SOP evolution over 100 bits @ 10 Gbps
adjacent bits are not completely uncorrelated
the angle Δθ remains relatively small
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how can we quantify fading?
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the autocorrelation function (ACF) of thetime series of SOPs
ACF(T) = E[Ŝ(t) · Ŝ(t-T)] = E[cos Δθ(T)]
is an average function of the angle Δθ between SOPs with time interval T
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every iteration of a fixed system (with random initial parameters) will yield a different set of output SOPs
these result in individual sample ACF(T)
the ensemble of all possible initial parametersis described by ACF(T)
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average signal fading: ~1.5%
BUT: probability for 15% fading is approximately 10-4
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systems with high symbol rates are less affectedthan low-rate systems
• T is smaller • ACF(T) is monotonously decreasing
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systems with residual dispersion per span (RDPS)have higher ACFs than those without (at equal DOP)
• RDPS correlates the distortions in neighboring bits
typical 10G systems have significant RDPSto suppress XPM
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SOP evolution over 100 bits @ 10 Gbps (systems with equal average DOP)
no RDPS 25% RDPS
there is less “motion” with RDPS
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what is the (relative) impact on systems?
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CW probe + 10 × 10 Gbps NRZ interferers
determine the ROSNR of the CW probe as if it were a10 Gbps DPSK signal (all zeros)
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by using an all-zero DPSK data sequence, we minimize any influence of GVD, PMD, SPM on the result
by correlating the sample ACF(T) and the sample ROSNR penalty for each iteration, we can extrapolate the contribution of XPolM to the interchannel penalty
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ROSNR penalty (dispersion map 1)
25% RDPS, 0.5 ps/km1/2, Pch = 4 mW
no statistical correlation penalty (distribution) is XPM-related
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NLT for XPM penalty ~ 1dB is only 1 mWalso no statistical correlation
ROSNR penalty (dispersion map 2)
no RDPS, 0.1 ps/km1/2, Pch = 1 mW
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XPolM should not be ignored completely
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ROSNR penalty in a PolDM subchannel
Winter et al., LEOS Annual Meeting 2008, WH3
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summary
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XPolM induces polarization changesbetween adjacent bits
such polarization misalignment leads to fadingof the detected DPSK signal
the effect is very small compared to XPM distortions
scalar simulations are sufficient(regarding nonlinear DPSK fading)