## Abstract

The performance of a differential carrier phase recovery algorithm is investigated for the quadrature phase shift keying (QPSK) modulation format with an integrated tunable laser. The phase noise of the widely-tunable laser measured using a digital coherent receiver is shown to exhibit significant drift compared to a standard distributed feedback (DFB) laser due to enhanced low frequency noise component. The simulated performance of the differential algorithm is compared to the Viterbi-Viterbi phase estimation at different baud rates using the measured phase noise for the integrated tunable laser.

© 2013 Optical Society of America

## 1. Introduction

Advanced modulation formats in combination with digital coherent receivers are currently receiving significant attention for the next-generation of optical communication systems. In particular, the quadrature phase shift keying (QPSK) modulation format has attracted a lot of research interest to increase data capacity due to its robustness to linear impairments and optical signal-to-noise ratio requirements [1, 2]. With coherent detection, it becomes possible to compensate for various impairments in the digital domain including phase noise contributions from the transmitter laser and the local oscillator (LO). Laser phase noise is known to have a limiting effect on the performance of optical coherent systems by increasing the bit error ratio (BER) and causing cycle slips. Therefore, reliable digital carrier phase estimation is indispensable for QPSK coherent receivers with a free-running LO without an optical phase locked loop.

Several carrier phase estimation algorithms have been proposed in the literature [3–9] for the QSPK modulation format. The Viterbi and Viterbi phase estimation (VVPE) [10] is the most commonly employed technique which raises the QPSK symbols to the power of four to remove the phase encoded data modulation. The VVPE has been demonstrated to be an effective algorithm for coherent systems employing commercially available distributed feedback (DFB) lasers. To add network configurability such as the flexibility to switch between different channels, widely-tunable lasers are also of interest in coherent optical communication systems with robust carrier phase recovery algorithms [11]. However, it is noted that the requirements for rapid channel switching may conflict with design approaches that minimize linewidth and FM noise associated with integrated tunable lasers.

In this paper, we first characterize the phase noise of an integrated tunable laser and a standard DFB laser using a digital coherent receiver. The low frequency noise components for the two lasers are extracted from the frequency modulation (FM) noise spectra. The performance of a differential carrier phase recovery algorithm is then investigated and compared to the VVPE to compensate for the laser phase noise associated with the integrated tunable laser at different baud rates for a QPSK coherent system in the back-to-back configuration. We show that for transmission speeds less than 5 Gbaud, the differential algorithm can give comparable performance to the VVPE with lower implementation complexity.

## 2. Laser phase noise characterization

The coherent detection technique is a promising approach to fully characterize the laser phase noise in terms of the field spectrum, FM-noise spectrum, and the phase-error variance [12–14]. The experimental setup used to measure the phase noise characteristics of the lasers under test is shown in Fig. 1. An optical 90° hybrid was used to beat the lasers under test with a 5 kHz linewidth reference laser. The phase noise of the reference laser was significantly lower than the lasers under test and therefore has negligible effect on the measurements. The in-phase, *E _{I}*(

*t*), and quadrature,

*E*(

_{Q}*t*), components of the optical field were detected with two single-ended photodiodes and captured with a 20 GSa/s real-time oscilloscope. The frequency offset between the lasers was first determined in the frequency domain and removed from the measured data prior to extracting the laser phase noise. The time-variant phase,

*ψ*(

*t*), was obtained using

*ν*(

*t*), given as The power spectral density of the FM-noise can then be computed using (2) and the Fourier transformation. The single-sided spectral density of the FM-noise with the low-frequency noise contributions can be expressed as where

*s*

_{2}is the random walk frequency noise component,

*s*

_{1}is the 1/

*f*-noise component, and

*s*

_{0}is the white frequency noise component related to the intrinsic Lorentzian linewidth,

*δf*, of the laser [12].

The phase noise characteristics of a widely-tunable laser and a standard DFB laser were measured using the experimental setup shown in Fig. 1. The integrated tunable laser was based on a digital supermode-distributed Bragg reflector (DS-DBR) laser which uses current injection in multiple sections for wavelength tuning and the laser module under test was intended for 10 Gbit/s direct-detection application where optical phase noise is not a critical parameter. Figures 2(a) and 2(b) show the measured phase noise fluctuations for the integrated tunable laser and the DFB laser, respectively, using the digital coherent receiver. As it can be seen, the integrated tunable laser exhibits significant drift compared to the DFB laser. The large phase noise fluctuation associated with the integrated tunable laser can be explained from the FM-noise spectra shown in Fig. 3 where the low frequency noise was significantly higher compared to the DFB laser. The tunable laser module exhibited significant low frequency FM noise due to electrical noise on the tuning sections, and hence provided a stringent test of the differential phase estimation algorithm presented in this paper. Driving circuitry with a low-noise current source to bias an electrically tunable laser is therefore important to mitigate the contribution of the low-frequency noise. Table 1 shows the extracted parameters of the lasers by fitting the analytical expression (3) to the FM noise spectra. The intrinsic Lorentzian linewidths of the integrated tunable laser and the DFB laser, estimated from the white frequency noise component, were found to be 911 kHz and 286 kHz, respectively. However, as it can be seen from the phase noise fluctuation in Fig. 2(a), the Lorentzian linewidth is not necessarily the only parameter required to reliably predict the performance of a coherent system. A full characterization of the laser including an analysis of the low frequency noise contribution [15] with a digital coherent receiver can thus be invaluable. The next section presents the simulation results for a QPSK coherent system at different baud rates using the above measured phase noise data for the integrated tunable laser.

## 3. Simulation results

The compensation of the phase noise fluctuation associated with the integrated tunable laser is discussed below for a QPSK coherent system. The performance of the VVPE is compared to the differential algorithm at different baud rates by re-sampling the measured phase noise. The estimated phase, *θ _{est}*, which is common to all the samples in the block, was obtained using [6]

*N*is the averaging block size for the VVPE algorithm. The recovered QPSK constellation was then differentially decoded to solve the four-fold phase ambiguity.

Differential carrier phase recovery is an alternative algorithm to the VVPE that can be used to recover the transmitted bits from the phase difference between consecutive QPSK symbols. The differential algorithm can thus be achieved using

followed by the mod(Δ*θ*, 2

*π*) operation. Equation (5) is a direct differential decoding on the optical field measured by a coherent receiver and, in contrast to the VVPE, the algorithm does not require the power of four operation to remove the data modulation, averaging or phase unwrapping for carrier phase recovery. For hardware implementation on FPGAs, for example, the arg(.) operation can effectively be implemented using look-up tables.

The VVPE was found to consistently outperform the differential algorithm at different baud rates for a QPSK coherent system with the measured phase noise of the DFB laser shown in Fig. 2(b). However, the performance of the VVPE was significantly different for the integrated tunable laser depending on the baud rate and the chosen value of *N* as seen in Fig. 4. The BER floor at 5 Gbaud was close to a BER of 10^{−3} with *N* = 4. For lower baud rates, a smaller block size was required by the VVPE to successfully track the large phase noise fluctuation associated with the integrated tunable laser.

Figure 5 shows the SNR required to achieve a target BER of 10^{−2} and 10^{−3} assuming hard decision forward error correction with coding overhead of 20% and 7%, respectively [16]. For transmission speeds higher than 10 Gbaud, the VVPE was found to outperform the differential algorithm by at least 0.7 dB for the results shown in Fig. 5. However, for transmission speeds lower than 5 Gbaud, the performance of the differential algorithm can be seen to be comparable with the VVPE. Carrier phase recovery can thus be achieved effectively using the differential algorithm with widely-tunable and fast-switching DS-DBR lasers currently of interest in coherent-enabled 10 Gbit/s passive optical networks [11].

## 4. Conclusions

A digital coherent receiver has been used to extract the phase noise characteristics of an integrated tunable laser. The performance of the differential carrier phase recovery algorithm has been investigated and compared to the VVPE at different baud rates. The differential algorithm is shown to give comparable performance to the VVPE for transmission speeds less than 5 Gbaud with lower implementation complexity.

## Acknowledgments

This work was supported by the Department for Business Innovation and Skills at NPL and the Piano+ CRITICAL project. The authors would like to thank Dr. R. Griffin at Oclaro for measurement support on the phase noise characterization of the lasers.

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