Investigation of Nonlinear DPSK Fading Due to Cross-Polarization Modulation

Marcus WinterKlaus Petermann

Hochfrequenztechnik-Photonik

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Dario Setti

http://www.marcuswinter.de/publications/ofc2009

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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)