## Electronic polarization-division demultiplexing based on digital signal processing in intensity-modulation direct-detection optical communication systems |

Optics Express, Vol. 22, Issue 2, pp. 1971-1980 (2014)

http://dx.doi.org/10.1364/OE.22.001971

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### Abstract

We propose a novel configuration of optical receivers for intensity-modulation direct-detection (IM·DD) systems, which can cope with dual-polarization (DP) optical signals electrically. Using a Stokes analyzer and a newly-developed digital signal-processing (DSP) algorithm, we can achieve polarization tracking and demultiplexing in the digital domain after direct detection. Simulation results show that the power penalty stemming from digital polarization manipulations is negligibly small.

© 2014 Optical Society of America

## 1. Introduction

1. E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP, ” Opt. Express **19**, 13139–13184 (2011). [CrossRef]

2. K. Kikuchi, “Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers,” Opt. Express **19**, 9868–9880 (2011). [CrossRef] [PubMed]

3. K. Kikuchi, “Digital coherent optical communication systems: Fundamentals and future prospects,” IEICE Electron. Express **8**, 1642–1662 (2011). [CrossRef]

1. E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP, ” Opt. Express **19**, 13139–13184 (2011). [CrossRef]

## 2. SOP of the DP signal

*λ*/2) and a polarization beam combiner (PBC). The tributary 1 has the linear

*x*polarization at the transmitter, whereas the tributary 2 does the linear

*y*polarization. The intensity of the lasers is modulated in a binary manner. In a low logic level, the intensity of each tributary is zero. In the following analysis, we assume that the intensity of each tributary in a high logic level is two so that the average intensity is normalized to unity when both logic levels occur at the same probability of 1/2.

## 3. Receiver configuration

*I*. Inserting a polarizer (0° Pol), whose transmission axis is the

_{t}*x*axis, we measure the intensity of the

*x*-polarization component

*I*in the second branch. Using a polarizer (45° Pol), whose transmission-axis is rotated by 45° with respect to the positive

_{x}*x*axis, we detect the intensity of the 45° linearly-polarized component

*I*

_{45°}in the third branch. With a quarter-wave plate (

*λ*/4), whose fast axis is aligned to the

*x*axis, and a 45°-rotated polarizer (45° Pol), we measure

*I*, which is the intensity of the right-circularly-polarized component, in the fourth branch. This configuration is known as the Stokes analyzer, which determines Stokes parameters from

_{R}*I*,

_{t}*I*,

_{x}*I*

_{45°}, and

*I*[4] as

_{R}## 4. DSP circuit

*S*

_{0}(

*n*) with the threshold

*S*, where

_{th}*n*denotes the number of samples. When

*S*

_{0}(

*n*) ≤

*S*, both of the tributaries are decided to be in the low level.

_{th}**v**(

*n*) be a noise-free unit vector expressing the SOP of the tributary 1 at the receiver (See Fig. 2). Note that the SOP for the tributary 2 is given as −

**v**(

*n*) in such a case. Provided that

**v**(

*n*) is known, we can calculate the inner product between the received normalized Stokes vector

**S**(

*n*)/

*S*

_{0}(

*n*) and the reference Stokes vector

**v**(

*n*) as which means the normalized Stokes-vector amplitude along the direction of the reference Stokes vector. Then, Fig. 2 shows that we can separate the three cases (II)(a), (II)(b), and (III), discriminating the distribution of

*u*(

*n*) into three regions. Let discrimination thresholds for

*u*(

*n*) be

*u*(> 0) and −

_{th}*u*. When

_{th}*u*(

*n*) ≥

*u*, we decide that the measured sample belongs to the tributary 1. In such a case, the tributary 1 is in the high level, whereas the tributary 2 is in the low level. The reference Stokes vector is then updated as where

_{th}*μ*is the step-size parameter. Equation (6) shows that the reference vector

**v**(

*n*) is modified by using the error signal

*ε*=

**S**(

*n*)/

*S*

_{0}(

*n*) −

**v**(

*n*) and tracks the SOP of the tributary 1 even when it fluctuates on the Poincaré sphere due to the random change in fiber birefringence. A smaller value of

*μ*improves the signal-to-noise ratio of

**v**(

*n*) but reduces the SOP tracking speed; therefore, we need to choose an optimum value of

*μ*, depending on the SOP fluctuation speed.

*u*(

*n*) ≤ −

*u*, we decide that the measured sample belongs to the tributary 2. In such a case, the tributary 1 is in the low level, whereas the tributary 2 is in the high level. Reversing the sign of the normalized Stokes vector in Eq. (6), we have the update formula for

_{th}**v**(

*n*) given as where the error signal

*ε*= −

**S**(

*n*)/

*S*

_{0}(

*n*) −

**v**(

*n*) controls the reference Stokes vector.

*u*(

*n*)| <

*u*, both of the tributaries are in the high level. We do not update the reference Stokes vector, because the SOP is not fixed in such a case. It should be noted that in cases (I) and (III), we do not update the reference Stokes vector and keep that defined in the nearest preceding case of (II); however, since the fluctuation speed of the reference Stokes vector is much slower than the bit rate, such thinned-out operation of the update process never degrades the BER performance as shown in 5.3.

_{th}**v**(

*n*) is known, the update process using Eqs. (6) and (7) can start from an arbitrary reference vector in the blind mode. However, depending on the initial choice of the reference Stokes vector, the tributaries 1 and 2 may be exchanged. After a sufficient number of iteration with the proper choice of

*μ*, the initial tracking process is converged and we can find an accurate estimate for

**v**(

*n*) even under very fast SOP fluctuations. Thus, we can discriminate the four cases (I), (II)(a), (II)(b), and (III). Finally, we complete the demodulation process, aligning bit sequences of the tributaries.

## 5. Simulation results

### 5.1. Simulation model

*N*= 2

^{20}. The Jones vector of the DP signal at the transmitter is written as Complex amplitudes of electric fields

*E*(

_{in, x}*n*) and

*E*(

_{in, y}*n*) are given as In these equations,

*s*(

_{x}*n*) and

*s*(

_{y}*n*) are signal amplitudes, which are either

*n*(

_{x}*n*) and

*n*(

_{y}*n*) are complex-valued Gaussian noises. The variance of the real part of

*n*(

_{x, y}*n*) and that of the imaginary part of

*n*(

_{x, y}*n*) are represented as

*ϕ*(

_{x}*n*) and

*ϕ*(

_{y}*n*) are phase noises of the lasers LD 1 and LD 2, respectively. We express them as Parameters Δ

*ϕ*(

_{x}*n*) and Δ

*ϕ*(

_{y}*n*) are real-valued Gaussian noises and their variance

6. K. Kikuchi, “Characterization of semiconductor-laser phase noise and estimation of bit-error rate performance with low-speed offline digital coherent receivers,” Opt. Express **20**, 5291–5302 (2012). [CrossRef] [PubMed]

*δf*is the 3-dB spectral width of the lasers and

*T*the bit duration.

**J**(

*n*) is the Jones matrix of the fiber for transmission. From

**E**

*(*

_{out}*n*), Stokes parameters of the received signal is obtained [4] as where

*δ*(

*n*) = arg[

*E*(

_{out, y}*n*)/

*E*(

_{out, x}*n*)]. Equations (16)–(19) are equivalent to Eqs. (1)–(4).

*ϕ*(

_{r}*n*) and

*θ*(

_{r}*n*). Parameters

*ϕ*(

_{r}*n*) and

*θ*(

_{r}*n*) including fluctuations obey the following equations: where Δ

*ϕ*(

_{r}*n*) and Δ

*θ*(

_{r}*n*) are real-valued Gaussian noises having the variance given as The parameter

*A*with the dimension of

*s*

^{−1}is a constant under a specific condition of the fiber for transmission.

### 5.2. Determination of discrimination thresholds

*S*for discriminating

_{th}*S*

_{0}(

*n*) and

*u*for discriminating

_{th}*u*(

*n*) through computer simulations. Ignoring the laser phase noise, we assume that

*δf*= 0 in Eq. (14). The fluctuation of the received SOP is also neglected throughout 5.2; then, we assume that

**J**=

**1**in Eq. (15).

*S*

_{0}(

*n*) when CNR/pol=10, 12, and 14 dB. The cases (I) and (II) are clearly separated, and we can decide that both logic levels of the tributaries are low, when the measured intensity

*S*

_{0}is smaller than the threshold

*S*= 0.6 shown by the sold line. On the other hand, the discrimination ability between (II) and (III) is so poor that the intensity discrimination shown by the broken line cannot be applied to separate (II) and (III).

_{th}### 5.3. BER performance

*A*in Eq. (23) is 10

^{5}[

*s*

^{−1}]. The variance

*σ*(

_{f}*N*)

^{2}of

*ϕ*(

_{r}*n*) and

*θ*(

_{r}*n*) at the

*N*-th bit is written as Therefore, if we assume the 25-Gbit/s/pol system (

*T*= 40 [ps]), the standard deviation is 2 rad in a 40-

*μ*s time span for

*N*= 2

^{20}bits. This value is much larger than SOP fluctuations observed in real systems [7]. The step-size parameter

*μ*is set at 1/2

^{7}to track the SOP fluctuation most accurately. We also include the effect of the laser linewidth

*δf*, assuming that

*δf ·T*= 1×10

^{−3}, which means

*δf*= 25 MHz at the bit rate of 25 Gbit/s/pol.

*ε*|| controlling the reference Stokes vector, where we use the moving average with the span of 21 samples. Within 1,000-sample periods, the SOP tracking process is stabilized; then bit errors are counted after the convergence of the error magnitude.

*β*

_{2}

*L/T*

^{2}= 0.125, where

*β*

_{2}denotes the dispersion parameter and

*L*the fiber length. This value corresponds to a 10-km-long standard single-mode fiber (SMF) at the bit rate of 25 Gbit/s/pol and at the wavelength of 1.55

*μ*m. Red curves in Fig. 9 show BER characteristics of the proposed DP-IM scheme with and without chromatic dispersion, whereas black curves show those of the SP-IM signal. We find that the dispersion effect is severer in the proposed DP-IM scheme than in the conventional SP-IM scheme; however, the difference in the receiver-sensitivity degradation due to chromatic dispersion is not so significant between the two cases.

## 6. Conclusions

## Acknowledgments

## References and links

1. | E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP, ” Opt. Express |

2. | K. Kikuchi, “Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers,” Opt. Express |

3. | K. Kikuchi, “Digital coherent optical communication systems: Fundamentals and future prospects,” IEICE Electron. Express |

4. | C. Brosseau, |

5. | T. Okoshi and K. Kikuchi, |

6. | K. Kikuchi, “Characterization of semiconductor-laser phase noise and estimation of bit-error rate performance with low-speed offline digital coherent receivers,” Opt. Express |

7. | P. M. Krummrich and K. Kotten, “Extremly fast (microsecond timescale) polarization changes in high speed long haul WDM transmission systems,” in 2004 OSA Technical Digest of |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.4080) Fiber optics and optical communications : Modulation

**ToC Category:**

Optical Communications

**History**

Original Manuscript: November 29, 2013

Revised Manuscript: January 11, 2014

Manuscript Accepted: January 13, 2014

Published: January 23, 2014

**Citation**

Kazuro Kikuchi, "Electronic polarization-division demultiplexing based on digital signal processing in intensity-modulation direct-detection optical communication systems," Opt. Express **22**, 1971-1980 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-1971

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### References

- E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP, ” Opt. Express 19, 13139–13184 (2011). [CrossRef]
- K. Kikuchi, “Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers,” Opt. Express 19, 9868–9880 (2011). [CrossRef] [PubMed]
- K. Kikuchi, “Digital coherent optical communication systems: Fundamentals and future prospects,” IEICE Electron. Express 8, 1642–1662 (2011). [CrossRef]
- C. Brosseau, Fundamentals of Polarized Light (John Wiley & Sons, Inc. 1998).
- T. Okoshi, K. Kikuchi, Coherent Optical Communication Systems (KTK/Kluwer, 1988), Chap. 6.
- K. Kikuchi, “Characterization of semiconductor-laser phase noise and estimation of bit-error rate performance with low-speed offline digital coherent receivers,” Opt. Express 20, 5291–5302 (2012). [CrossRef] [PubMed]
- P. M. Krummrich, K. Kotten, “Extremly fast (microsecond timescale) polarization changes in high speed long haul WDM transmission systems,” in 2004 OSA Technical Digest of Optical Fiber Communication Conference (Optical Society of America, 2004), FI3.

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