## Abstract

We demonstrate, for the first time, the generation and transmission of polarization-switched QPSK (PS-QPSK) signals at 42.9 Gb/s. Long-haul transmission of PS-QPSK is experimentally investigated in a recirculating loop and compared with transmission of dual-polarization QPSK (DP-QPSK) at 42.9 Gb/s per channel. A reduction in the required OSNR of 0.7 dB was found at a BER of 3.8x10^{−3}, resulting in an increase in maximum reach of more than 30% for a WDM system operating on a 50 GHz frequency grid. The maximum reach of 13640 km for WDM PS-QPSK is, to the best of our knowledge, the longest distance reported for 40 Gb/s WDM transmission, over an uncompensated link, with standard fiber and amplification.

©2011 Optical Society of America

## 1. Introduction

Coherent detection, combined with digital signal processing (DSP), has led to recent increases in capacity [1], reach [2] and spectral efficiency [3]. While much research has been devoted to generating, processing and transmitting spectrally-efficient modulation formats such as high-level quadrature amplitude modulation (QAM) [4], these modulation formats rely on a regular 4-dimensional lattice constellation design. However, it has been recently shown that these modulation formats are not optimal for the optical channel in terms of the *asymptotic power efficiency* [5], and some work has been undertaken to determine the optimal modulation format for a 4-dimensional additive Gaussian noise channel [5,6].

This research has led to a variety of new modulation formats being proposed, with various degrees of complexity and difficulty of realization. A format which has attracted interest is polarization-switched quadrature phase shift keying (PS-QPSK) [5–8]. This format transmits a symbol, on one of two orthogonal polarizations, with one of four equally spaced phase levels from a QPSK constellation, such that the resulting symbol carries 3 bits of information. This is illustrated with a pair of experimentally obtained constellations below in Fig. 1
. Whilst this modulation format has a lower available spectral efficiency than DP-QPSK, the gain in noise tolerance is as much as 1.76 dB [5] at equal bit rates and asymptotically high optical signal to noise ratio (OSNR). For the bit-error-rate (BER) values combined with modern forward error correction (FEC) codes, improvements of 1 dB at a BER of 10^{−3} and of 0.55 dB at a BER of 10^{−2} are theoretically achievable. Due to the significant benefit in noise tolerance over DP-QPSK which has become the standard modulation format for 100 GbE technology [9], there has been some interest recently in the transmission properties of PS-QPSK [7,8].

In this paper we use an easily realizable technique to experimentally generate PS-QPSK, without the use of either a four-dimensional modulator or custom-made photonic integrated circuits. Section 2 describes our transmitter, and the experimental setup used for characterization of PS-QPSK transmission. Section 3 describes the DSP used for blind equalization of the signals and recovery of the carrier phase. Section 4 describes the results obtained for receiver sensitivity for both single channel and wavelength division multiplexed (WDM) systems, and a comparison of nonlinear WDM transmission performance between PS-QPSK and DP-QPSK at equal bit rates. Section 5 provides a summary and discussion of results.

## 2. PS-QPSK generation and the experimental setup

To evaluate the achievable benefits of employing the PS-QPSK modulation format over DP-QPSK, we first measured the OSNR tolerance and maximum reach of both modulation formats. The experiments were conducted at the constant bit rate of 42.9 Gb/s, corresponding to 14.3 Gbaud for PS-QPSK and 10.725 Gbaud for DP-QPSK. In WDM transmission, both formats were transmitted over a 50 GHz frequency grid, with spectral efficiency of 0.8 b/s/Hz in both cases.

The PS-QPSK format was generated as follows (Fig. 2(b)
). First a triple Mach-Zehnder modulator (MZM) was used to modulate continuous-wave (CW) light from an external cavity laser (ECL) at 1554 nm to generate a single polarization QPSK sequence. The applied data pattern was a pseudo-random bit sequence (PRBS) of length 2^{15}-1, where the PRBS was decorrelated by half of the pattern length between the in-phase and quadrature signal components. Polarization switching was then applied to the signal by passively 50:50 splitting the QPSK signal and intensity modulating each arm, symbol-synchronously, with two MZMs. The two intensity modulators were driven by $\text{DATA}$ and $\overline{\text{DATA}}$ respectively from the pattern generator. The effect of this configuration being that only one intensity modulator was transmitting during each symbol period. The two arms were then tuned to be orthogonally polarized using polarization controllers, before entering a polarization beam splitter (PBS) to combine the two signals. Any residual symbol timing difference, due to different path lengths in the polarization switching stage, was compensated with a variable optical delay line in one arm.

DP-QPSK was generated using a similar method except that, after the 50:50 splitter, the QPSK signal was polarization-multiplexed by decorrelating the signal polarizations in each arm of a passive delay-line stage (Fig. 2(a)). The effective delay between the QPSK signals in each polarization was 24 symbols.

In order to generate a 7-channel WDM comb, two alterations to the above configuration were introduced. Firstly, a 50 GHz WDM comb was created by combining CW light from six temperature- and current-controlled DFB lasers. An ECL with a linewidth of 100 kHz was used for the central channel. The comb was bulk modulated, and an interleaver with a channel spacing of 50 GHz was used to separate alternate channels, which were then decorrelated by 10 ns before being recombined with a 3-dB fiber coupler, as described in [10].

To investigate the transmission performance, a single-span recirculating fiber loop was used. An EDFA followed by a variable optical attenuator (VOA) was used to set the launch power to an acousto-optic modulator controlled recirculating fiber loop (Fig. 2(c)), as described in [11]. The loop span consisted of 80.24 km of standard single-mode fiber (SMF), with a loss of 15.4 dB and total chromatic dispersion of 1347 ps/nm at 1554 nm. Wavelength-dependant gain of the loop EDFAs was equalized using gain flattening filters.

After the desired number of recirculations, the signal was detected with a phase and polarization diverse coherent receiver. The frequency offset between the signal and LO lasers typically measured as being less than 1 GHz, while the LO linewidth was measured as 100 kHz. Digitization was then performed using a real-time digital sampling oscilloscope (DSO) with 8 physical bits of resolution and 50 GSa/s. The captured waveforms were subsequently processed offline using Matlab. When processing DP-QPSK, we used the linear processing methods, described in detail in [12].

## 3. Digital signal processing for PS-QPSK

The captured digital signal was first de-skewed, normalized to unit power per polarization and re-sampled to 2 Samples/symbol. If required, chromatic dispersion was compensated with a complex valued FIR filter [13]. Equalization was then performed using a polarization-switched constant modulus algorithm (PS-CMA) equalizer with least-mean squares (LMS) updating, described in detail in [14]. The equalizer utilizes a decision on the relative power in each output polarization, with the error terms described by the pseudo-code in Eq. (1):

*and * denote the Hermite and complex conjugates respectively. This equalizer has an attractive practical advantage over that which is used for dual-polarization QPSK. The PS-CMA equalizer when used with PS-QPSK modulation does not suffer from degenerate mal-convergence when initialized as described in [14].*

^{H}To estimate the intradyne frequency offset, the PS-QPSK symbol sequence was reduced to a QPSK symbol sequence at the output of the receiver. This was done by making relative decisions on the energy in each symbol, the polarization with higher energy in each symbol was determined to contain the QPSK phase information, and was extracted. The resultant QPSK sequence was raised to the 4th power to remove the modulation. The offset was then determined by finding the peak power in the FFT of the signal.

Carrier phase estimation was performed after removing the polarization modulation. This was done by selecting one sample per symbol based on which polarization has more energy. Carrier phase was then recovered for our reduced QPSK sequence using the Viterbi & Viterbi algorithm.

The transmitted symbol sequence was determined by correlating the received symbol sequence with the PRBS data, and calculating the delays and phase rotations in the transmitter and channel. The transmitted and received symbol sequences were then transformed into three bit sequences each using the bit-mapping described in [5], which were then compared to calculate the BER.

## 4. Transmission results at 42.9 Gb/s

First, the receiver noise sensitivity was measured for DP- and PS-QPSK using additional noise loading at the receiver. The results of this back-to-back measurement are shown in Fig. 3 , together with the theoretical SNR limit as derived in [6].

From Fig. 3 we note at a BER of 3.8x10^{−3} that for WDM operation there is no significant difference in the implementation penalty of the two formats, with PS-QPSK having an implementation penalty of 1.0 dB, compared with 0.9 dB for DP-QPSK. At a BER of 3.8x10^{−3} this results in a required OSNR for WDM operation of 8.1 dB for PS-QPSK, compared to 8.8 dB for DP-QPSK.

The transmission performance was then experimentally measured for a 7-channel WDM system using the recirculating loop. The launch power per channel was varied between −13 and 3 dBm, to determine the variation in maximum reach with launch power at the BER limit of 3.8x10^{−3}. The resulting comparison between PS-QPSK and DP-QPSK at 42.9 Gb/s is presented in Fig. 4
, with a polynomial fit for each curve as described in [15].

It can be seen from Fig. 4 that in the low power, linear transmission regime (less than −7 dBm per channel), for a given reach a reduction in launch power of approximately 1dB per channel is possible for PS-QPSK, agreeing with the back-to-back receiver sensitivity results in Fig. 3. For both modulation formats, the optimum launch power was found to be approximately −3.5 dBm per channel. The maximum reach of PS-QPSK was found to be 170 recirculations, corresponding to 13640 km; this may be compared to a maximum reach of 129 recirculations for DP-QPSK, corresponding to 10350 km. This result represents an increase of more than 18% on the previous record reach for 40 Gb/s WDM transmission [16] which in contrast to this work utilized large effective area fiber.

The use of PS-QPSK rather than DP-QPSK modulation therefore enabled an increase in maximum reach of more than 30%. In the high power, highly nonlinear transmission region (launch power greater than 0 dBm per channel), we note that the improvement in performance available from PS-QPSK is reduced in comparison to the linear regime. This reduction in improvement was due to high levels of nonlinear phase noise present.

## 6. Summary

We have presented the first experimental measurements of the transmission performance of PS-QPSK at 42.9 Gb/s using a simple and easily realizable generation technique. The implementation penalty for PS-QPSK modulation was found be less than 1 dB at a BER of 3.8x10^{−3}. This transmitter was then used to perform a characterization of transmission performance for PS-QPSK, comparing PS-QPSK and DP-QPSK at 42.9 Gb/s over a 50 GHz frequency grid. An improvement in launch power margin (the range of launch powers for which the FEC limit may be maintained) of greater than 1 dB was found in all cases. The optimum launch power for both modulation formats was found to be −3.5 dBm per channel, while maximum reach was increased by more than 30% from 10350 km to 13640 km. To the best of our knowledge this is the longest distance 40 Gb/s WDM transmission achieved over an uncompensated link, with standard fiber and amplification.

## Acknowledgments

The work described in this paper was carried out with the support of UK Engineering and Physical Sciences Research Council (EPSRC), Oclaro, Huawei, Yokogawa, and the Royal Society.

## References and links

**1. **A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguci, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432 x 171-Gb/s) C – and extended L-band transmission over 240km using PDM-16-QAM modulation and digital coherent detection,” Proc. OFC/NFOEC 2010, San Diego, CA, Mar. 21–25, 2009, PDPB7.

**2. **J.-X. Cai, Y. Cai, Y. Sun, C. R. Davidson, D. G. Foursa, A. Lucero, O. Sinkin, W. Patterson, A. Pilipetskii, G. Mohs, and N. S. Bergano, “112x112 Gb/s transmission over 9,360 km with channel spacing set to the baud rate (360% spectral efficiency),” Proc. ECOC 2010, Paper PD2.1, Sept. 2010.

**3. **A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100 x 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” Proc. ECOC 2010, Paper PD2.4, Sept. 2010.

**4. **P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol. **28**(4), 547–556 (2010). [CrossRef]

**5. **M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express **17**(13), 10814–10819 (2009). [CrossRef] [PubMed]

**6. **E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol. **27**(22), 5115–5126 (2009). [CrossRef]

**7. **P. Poggiolini, G. Bosco, A. Carena, V. Curri, and F. Forghieri, “Performance evaluation of coherent WDM PS-QPSK (HEXA) accounting for non-linear fiber propagation effects,” Opt. Express **18**(11), 11360–11371 (2010). [CrossRef] [PubMed]

**8. **P. Serena, A. Vannucci, and A. Bononi, “The performance of polarization switched-QPSK (PS-QPSK) in dispersion managed WDM transmissions,” Proc. ECOC 2010, Th.10.E.2, Sept. 2010.

**9. **Optical Internetworking Forum, “Implementation agreement for integrated dual polarization intradyne coherent receivers” (2010, April 16) [Online]. Available: www.oiforum.com/public/documents/OIF_DPC_RX-01.0.pdf

**10. **A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “10 × 224-Gb/s WDM transmission of 28-Gbaud PDM 16-QAM on a 50-GHz grid over 1,200 km of fiber,” Proc. OFC/NFOEC 2010, Paper PDPB8, Mar. 2010.

**11. **E. Torrengo, S. Makovejs, D. S. Millar, I. Fatadin, R. I. Killey, S. J. Savory, and P. Bayvel, “Influence of pulse shapes in 112-Gb/s WDM PDM-QPSK transmission,” IEEE Photon. Technol. Lett. **22**(23), 1714–1716 (2010). [CrossRef]

**12. **D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1217–1226 (2010). [CrossRef]

**13. **S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1164–1179 (2010). [CrossRef]

**14. **D. S. Millar and S. J. Savory, “Blind adaptive equalization of polarization-switched QPSK modulation,” Opt. Express **19**(9), 8533–8538 (2011). [CrossRef] [PubMed]

**15. **S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. **22**(10), 673–675 (2010). [CrossRef]

**16. **G. Charlet, M. Salsi, H. Mardoyan, P. Tran, J. Renaudier, and S. Bigo, M. A*s*tr**uc**, P. Sillard, L. Provost and F. Cérou, “Transmission of 81 channels at 40Gbit/s over a transpacific-distance erbium-only link, using PDM-BPSK modulation, coherent detection, and a new large effective area fibre,” Proc. ECOC 2008, Paper Th.3.E.3, Sept. 2008.