Translucent Photonic Network Dimensioning - OSA Publishing

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1) Fujitsu R&D Center, 13/F, Tower A, Ocean International Center, No. 56 Dong Si Huan Zhong Rd, Chaoyang District Beijing, 100025, China. 2) Fujitsu ...
© 2009 OSA/OFC/NFOEC 2009 a1696_1.pdf OMT2.pdf OMT2.pdf

Initial Tap Setup of Constant Modulus Algorithm for Polarization De-multiplexing in Optical Coherent Receivers Ling Liu1), Zhenning Tao1), Weizhen Yan1), Shoichiro Oda2), Takeshi Hoshida3), Jens C. Rasmussen3) 1) Fujitsu R&D Center, 13/F, Tower A, Ocean International Center, No. 56 Dong Si Huan Zhong Rd, Chaoyang District Beijing, 100025, China 2) Fujitsu Laboratories Ltd., 3) Fujitsu Limited, 1-1 Kamikodanaka 4-chome, Nakahara-ku, Kawasaki 211-8588, Japan [email protected]

Abstract: We demonstrate a modified constant modulus algorithm (CMA) for polarization de-multiplexing and equalization. By designing the initial tap values for CMA, degeneration of the two polarization tributaries can be avoided. ©2009 Optical Society of America OCIS codes: (060.1660) Coherent communications; (060.2360) Fiber optics links and subsystems

1. Introduction Dual-polarization (DP) system with coherent detection is a promising candidate for high bit-rate transmission systems such as 100Gb/s because it doubles the information rate and enables flexible electrical equalization. Adaptive polarization de-multiplexing and equalization can be realized by the butterfly-structured finite-impulse response (FIR) filters associated with some adaptive algorithms in digital domain [1-3]. The constant modulus algorithm (CMA) is often used in either real time experiment [1] or offline processing [3], because of its simplicity and immunity to phase noise. However, it suffers from the singularity problem which means the two polarization tributaries tend to converge to the same source [4,5], because CMA adjusts the FIR filters in both tributaries independently. This problem can be solved by setting the FIR filter tap values of one polarization tributary according to the other tributary [4], but this is limited to the 1-tap FIR cases. Other algorithms such as independent component analysis method [5] have been proposed, but they tend to suffer increased computational complexity. In this paper, we investigate the singularity problem for CMA in detail and reveal that the choice of initial tap values plays an important role for CMA convergence. We propose a way to set the initial FIR tap values to solve the singularity problem under various waveform distortions. 2. Singularity problem for CMA Fig. 1 shows a basic dual-polarization transmission system with polarization diversity coherent receiver. The multiplexing matrix is give by Jones matrix of the fiber link ⎛ cos α e − jφ sin α ⎞ , (1) ⎟ T = ⎜⎜ jφ ⎟ − e sin α cos α ⎝ ⎠ which hereafter is referred to as “basic system” since there is no distortion. The butterfly-structured FIR driven by CMA is used for polarization de-multiplexing.

Fig. 1 Basic dual-polarization system with polarization diversity coherent receiver. Tx: transmitter; PBC: polarization beam combiner; PBS: polarization beam splitter; LO: local oscillator; PD: photodetector; AD: analog to digital converter; CMA: constant modulus algorithm.

The butterfly structured FIR is symmetric in the sense that the filtering process for tributary x and tributary y are exactly the same except for the choice of initial FIR tap values. If α = 45o , for the input dual-polarization signal of ETin = (Ein , x Ein , y ) , the received signal is given by ⎛ Er , x ⎞ ⎛ E ⎞ ⎛ ( E ) 2 2 + ( Ein , y e − jφ ) 2 2 ⎞ . ⎟ ⎜ ⎟ = T⎜ in , x ⎟ = ⎜ in , x jφ + jπ ⎜E ⎟ ⎜ E ⎟ ⎜ (E e ) 2 2 + ( Ein , y ) 2 2 ⎟⎠ ⎝ r,y ⎠ ⎝ in , y ⎠ ⎝ in , x

(2)

© 2009 OSA/OFC/NFOEC 2009 a1696_1.pdf OMT2.pdf OMT2.pdf

Because CMA is not sensitive to the phase of the complex field, Ein ,* and Ein ,*e jφ cannot be distinguished by the algorithm and thus there is no stochastic difference expected between Er,x and Er,y. Therefore, if we take the most trivial initial tap setting of Hxx=(… 0 1 0 ...), Hyx=(… 0 0 0 ...), Hxy=(… 0 0 0 ...), Hyy=(… 0 1 0 ...), the two tributaries are equivalent for Ein , x and Ein , y , and the butterfly-structured FIR may converge to a situation where the two output the same tributary data. 3. Experimental result

Fig. 2 Experimental setup and offline processing

The experimental set up is shown in Fig. 2. A 112Gb/s dual-polarization NRZ-QPSK signal was generated from a single NRZ-QPSK signal in a split-delay-combine manner. Polarization dependent loss (PDL) was emulated by attenuating one polarization signal before multiplexing. Differential group delay (DGD) and chromatic dispersion (CD) were added after multiplexing. The received signal with OSNR=18dB was fed to a polarization diversity coherent optical front-end to produce horizontal and vertical baseband electrical signals. Next, the electrical signals were sampled at 50GSa/s and stored for offline processing. In the offline processing, the digital signals were re-sampled to 56GSa/s (2 Sa/Symbol), and were aligned to input state of polarization (SOP) by multiplying the inverse Jones matrix of the channel. The polarization control (PC) was emulated in the offline processing with the transfer matrix shown in Fig. 2. The rotation angle α was swept from 0° to 90° , and the phase angle φ was swept from − 180° to 180° , so that the emulated PC should cover the whole Poincaré sphere. Four 7-tap FIR filters were used here, whose initial tap values were set to Hxx=(0 0 0 1 0 0 0), Hyx=(0 0 0 0 0 0 0), Hxy=(0 0 0 0 0 0 0), Hyy=(0 0 0 1 0 0 0). The 2-dimensional sweep results are shown in Fig. 3. The PC states that lead to singularity are marked with dark color while the white areas indicate successful separation. Fig. 3(a) shows that when α ≈ 45° , the two tributaries converge to the same source. This is consistent with our analysis in Section 2. If there is PDL in the channel, the singular region will be larger (Fig. 3(b) and Fig. 3(c)).

(a) PDL=0dB, DGD=0, CD=0 (b) PDL=1dB, DGD=0, CD=0 (c) PDL=3dB, DGD=0, CD=0 Fig. 3 Polarization de-multiplexing results with CMA. PC states that lead to singularity are marked with dark color.

3. Modified CMA to solve the singularity problem Generally speaking, the result of convergence strongly depends on the choice of initial FIR tap values. By choosing proper initial tap values for the two tributaries, we may avoid the singularity problem for CMA. When DGD is the only source of distortion, the channel transfer matrix of the fiber is given by a unitary matrix in frequency domain v( f ) ⎞ . ⎛ u( f ) (3) ⎟ TDGD = ⎜⎜ * * v f u − ( ) ( f ) ⎟⎠ ⎝

© 2009 OSA/OFC/NFOEC 2009 a1696_1.pdf OMT2.pdf OMT2.pdf

* * The inverse of the channel is also a unitary matrix in frequency domain, with H yy ( f ) = H xx ( f ) , H xy ( f ) = − H yx (f) whose time domain representation is * * (4) hyy (t ) = hxx (−t ) , hxy (t ) = − hyx ( −t ) .

This special relationship can be used to determine one tributary FIR filter tap values according to the other, so that the singularity problem can be solved. Although the relationship no longer holds if there are other sources of channel distortion such as CD and PDL, the above relationship can be used to determine initial tap values so that the two tributaries should not degenerate. The proposed "modified CMA" method is as follows. 1) Set the initial tap values for tributary x as single spike, i.e. Hxx=(… 0 1 0 ...), Hyx=(… 0 0 0 ...) 2) Run CMA for tributary x until it is considered to have reached a convergence, 3) Set the initial tap value for tributary y according to Eq. (4) with the tap values for tributary x, 4) Continue with CMA update for the two tributaries independently. Fig. 4 shows the experimental results for the modified CMA. Compared with Fig. 3, it is evident that the proposed method has solved the singularity problem and de-multiplexed the two channels successfully for all the PC states.

(a) PDL=0dB, DGD=0, CD=0 (b) PDL=1dB, DGD=0, CD=0 (c) PDL=3dB, DGD=0, CD=0 Fig. 4 Polarization de-multiplexing results with modified CMA. Singularity problem is solved for all PC states.

Fig. 5 shows the experimental results under the distortions of PDL=3dB, DGD=18ps, and CD=200ps/nm, with simple CMA (left) and modified CMA (right). The results confirmed that the modified CMA operates robustly under mixed channel distortions due to CD, DGD and PDL.

Fig. 5 Polarization de-multiplexing results with simple CMA (left) and modified CMA (right). PDL=3dB, DGD=18ps, CD=200ps/nm

4. Summary We have proposed a modified constant modulus algorithm for polarization de-multiplexing and equalization that solves the output degeneration problem by designing the initial tap values for CMA update. The algorithm showed robust operation under various waveform distortions. 5. Acknowledgement This work was partly supported by the National Institute of Information and Communications Technology (NICT), Japan. 6. References [1] A. Leven et al, OFC2008, OTUO2. [2] T. Pfau et al., ECOC2007, 8.3.3. [3] S. J. Savory et al., ECOC2006, 2.5.5. [4] K. Kikuchi, IEEE LEOS Summer Topical Meetings 2008, MC2.2. [5] H. Zhang et al, ECOC2008, Mo.3.D.5.