Simple carrier-phase estimator for high-speed RSOA-based coherent WDM PON

It has been recently reported that reflective semiconductor optical amplifiers (RSOAs) can be used as phase modulators for the cost-effective implementation of the high-speed wavelength-division-multiplexed passive optical networks (WDM PONs). For the detection of the phase-shift-keying (PSK) signal generated by using an RSOA, we should be able to estimate its carrier phase accurately at the digital coherent receiver. However, when the baud rate of this PSK signal is set to be much higher than the RSOA’s modulation bandwidth, the conventional M-th power algorithm cannot estimate its carrier phase accurately. To solve this problem, we develop a simple carrier-phase estimation technique for the high-speed (>10 Gb/s) PSK signals generated by using bandwidth-limited RSOAs. This technique estimates the carrier phase of the PSK signal by measuring the angular direction of the opening occurred in the trajectory of the phasor diagram. By using the proposed technique, we demonstrate the upstream transmission of the 25.78-Gb/s quadrature phase-shift-keying (QPSK) signal generated by using an RSOA (3-dB bandwidth: 3.2 GHz) in a 60-km reach coherent WDM PON. ©2014 Optical Society of America OCIS codes: (060.1660) Coherent communications; (060.2360) Fiber optics links and


Introduction
There have been numerous efforts to realize a cost-effective wavelength-division-multiplexed passive optical network (WDM PON) by using reflective semiconductor optical amplifiers (RSOAs) as colorless optical transmitters [1,2].In such an RSOA-based WDM PON, the wavelength-specific seed light is sent to the RSOA placed at each optical network unit (ONU) from the central office (CO).Thus, it is possible to utilize the identical RSOA at every ONU and overcome the inventory problem inherent in WDM PONs.However, it is challenging to realize high-speed (>10 Gb/s) WDM PONs by using RSOAs due to their limited modulation bandwidth, which is typically in the range of only 1~3 GHz.Previously, it has been reported that the per-wavelength operating speed of the RSOA-based WDM PON can be increased to >10 Gb/s by utilizing the post-detection electrical equalization [3], optical offset filtering [4], delay interferometer [5], four-level pulse-amplitude modulation (4-PAM) format [6], and orthogonal frequency-division multiplexing [7,8].All these techniques have utilized RSOAs as intensity modulators.However, we have recently demonstrated that an RSOA can also be used as a phase modulator due to its large frequency chirp [9].It is well known that phasemodulated signals outperform intensity-modulated signals in terms of the receiver sensitivity [10].Thus, we can significantly improve the system's performance by utilizing RSOAs as phase modulators instead of intensity modulators.For example, we have demonstrated 10-Gb/s, 80-km-reach WDM PON by utilizing the quadrature-phase-shift-keying (QPSK) signals generated by directly modulating RSOAs [11].In this experiment, the self-homodyne coherent receivers together with various digital signal processing (DSP) techniques are used for the detection of these QPSK signals.In particular, we have utilized the conventional M-th power algorithm for the carrier-phase estimation (CPE).However, the performance of this algorithm deteriorates rapidly when the operating speed of RSOA is increased to be much faster than 10 Gb/s due to its limited modulation bandwidth [12].In this paper, we propose and demonstrate a simple CPE technique for the use in the high-speed (>10 Gb/s) WDM PONs implemented by using bandwidth-limited RSOAs.When we generate the QPSK signal by directly modulating an RSOA using an equally-spaced 4-level electrical signal, a ~90° opening occurs naturally in the trajectory of its phasor diagram.Thus, we can estimate the carrier phase of the QPSK signal simply by measuring the angular direction of this opening.By using this simple CPE technique, we successfully demonstrate the upstream transmission of 25.78-Gb/s QPSK signal generated by directly modulating an RSOA (bandwidth: 3.2 GHz) in a 60-km-reach coherent WDM PON.

Operating principle of the proposed CPE technique
When the high-speed QPSK signal is generated by using a bandwidth-limited RSOA, the conventional M-th power algorithm cannot estimate its carrier phase properly.This is mainly because the information-bearing optical phases of the detected signal cannot be easily stripped off due to the distortion in the optical phases (caused by the limited bandwidth of RSOA).To solve this problem, we propose a novel CPE technique independent of this distortion.We assume that the RSOA is directly modulated by using an equally-spaced 4-level electrical signal to achieve the maximum Euclidean distance between adjacent symbols in the generated QPSK signal.As a result, the phase of the generated QPSK signal varies by ~270°.In other words, there is a ~90° opening in the trajectory of its phasor diagram even though the QPSK signal is distorted by the band-limitation of the RSOA.We estimate the carrier phase of the QPSK signal simply by identifying the angular direction of this opening.Figure 1(a) shows the operating principle of the proposed CPE technique.We first construct an angular histogram from L received data samples, r k , where k is the sample index, and then search for the opening (i.e., between the angles of θ a and θ b ) where there is no sample in the angular histogram.The angular direction of the opening can be obtained by calculating the arithmetic mean of these two angles, θ a and θ b .Figure 1(b) shows an exemplary phasor diagram of the QPSK signal generated by directly modulating an RSOA.The phase of this signal varies from −20° to 270° and an opening is observed in the trajectory of this phasor diagram in the 4th quadrant.The angular direction of this opening can be readily identified by using an angular histogram, as shown in Fig. 1(c).It clearly shows that no sample is received between 270° and 340° (as depicted by the red lines in Fig. 1(c)).Thus, the angular direction of the opening is calculated to be (270 + 340)/2 = 305°.The M-th power algorithm is the most common technique used for the CPE of the QPSK signal.For received data samples, r k , the carrier phase estimated by the M-th power algorithm can be expressed as  where N is the block length.However, when we generate a high-speed (>>10 Gb/s) QPSK signal by directly modulating an RSOA (which typically has a modulation bandwidth of only 1~3 GHz), the conventional M-th power algorithm cannot estimate its carrier phase accurately [12].To describe this problem, we evaluate the performance of the M-th power algorithm used in the RSOA-based QPSK transmission system by numerical simulations.When we modulate the injection current of the RSOA, both the phase and intensity of its output signal are modulated.Thus, we model the RSOA as a phase modulator followed by an intensity modulator.In addition, we install low-pass filters (3-dB bandwidth: 3.2 GHz, roll-off slope: −20 dB/decade) at the electrical inputs of these modulators for the emulation of the bandwidth-limited RSOA.The amplitude of the 4-level electrical signal applied to the phase modulator is adjusted to achieve the phase shift of 270° in the phasor diagram.The modulation depth of the intensity modulator (i.e., the ratio between the highest and lowest intensity levels) is set to be 1.5.All these parameters are identical to the measured values of the RSOA used in this work.We detect the generated QPSK signal by using a coherent receiver and utilize the M-th power algorithm for the estimation of its carrier phase.Since we assume that the laser linewidth is zero in the simulations, the carrier must have a constant phase.Thus, we can evaluate the performance of the M-th power algorithm by measuring the phase error (which is defined as the phase difference between the CPE result and the constant phase).Figure 2 shows the standard deviation of the phase errors estimated as a function of the data rate of the QPSK signal.The block length of the M-th power algorithm is set to be 14 [13].This figure shows that the M-th power algorithm works well up until 12 Gb/s, but the phase errors increase exponentially when the data rate exceeds this value.This is because, when the bandwidth of the modulator is extremely limited in comparison to the desired data rate, the M-th power operation fails to strip off the modulation.Thus, as the data rate increases, the received symbols deviate from their original points (i.e., 90° × i where i = 0, 1, 2, and 3 for the QPSK signal) and become to be scattered along a circle in the constellation diagram.Then, the M-th power operation cannot bring the symbols together on a single point, of which the phase indicates the carrier phase of the QPSK signal [13].Consequently, the Mth power algorithm fails to extract the carrier phase information accurately due to the scattered symbols.For example, Figs. 2(b)-2(d) show that the phase error increases drastically as the data rate is increased to be much faster than the modulator's bandwidth.For comparison, we also plot the standard deviation of the phase errors obtained by using the proposed CPE technique in Fig. 2(a).The sample size of the histogram, L, is selected to be 350 (which will be described in details in Section 3).Although the performance of the proposed CPE technique was slightly worse that the conventional M-th power algorithm until 12 Gb/s, it has a shallower slope against the data rate.As a result, by using the proposed CPE technique, we can achieve the phase error of only 7° even when the data rate is increased to 25 Gb/s.The power penalty (@ BER = 10 −4 ) caused by this phase error is expected to be less than 1.5 dB [14].

Experiment and results
Figure 3 shows the experimental setup to demonstrate the effectiveness of the proposed CPE technique.For this demonstration, we evaluated the transmission performance of the 25.78-Gb/s QPSK upstream signal generated by using a directly modulated RSOA in the WDM PON implemented in loopback configuration.A tunable laser (linewidth: 150 kHz) operating at 1549.87 nm was used as the seed light.We sent this seed light to the RSOA placed at the ONU and generated 25.78-Gb/s QPSK signal by modulating it using an RSOA with a 4-level electrical signal.The modulation bandwidth of this butterfly-packaged RSOA was measured to be 3.2 GHz when we set its bias current to be 80 mA.At the CO, the upstream signal was detected by using a self-homodyne receiver.In this receiver, we utilized a portion of the seed light as a local oscillator (LO) and a 3 × 3 coupler as a 120° optical hybrid.The optical power of the LO incident on the coupler was 3 dBm.Since we placed a Faraday rotator in front of the RSOA at the ONU, there was no need to utilize the polarization-diversity receiver [15].The output signals from the 3 × 3 coupler were detected by using three PIN photodiodes, and then sampled at 40 GSample/s by using a digital sampling oscilloscope.For the offline DSP, we first obtained the I-and Q-components of the QPSK signal by using the coordinate transformation.A high-pass filter was used to filter out the low-frequency interference components caused by Rayleigh backscattering.The effect of the chromatic dispersion was compensated in the frequency domain by applying the inverse fiber-dispersion function [16].
We then applied the proposed CPE technique to estimate the carrier phase of the 25.78-Gb/s QPSK signal.Finally, an electronic equalizer, consisted of a half-symbol-spaced 16-tap feedforward equalizer and a 10-tap decision-feedback equalizer, was used for the compensation of the limited modulation bandwidth of the RSOA.The tap coefðcients of these equalizers were determined by using the minimum mean-square error criteria [17].It should be noted that we applied this electronic equalization technique only to the phase portion of the received signal [11].For this purpose, we extracted the phase information from the detected symbols and discarded the intensity information by taking arg(r k ).The real-number sampled data (containing phase information of the signal) are then sent to the equalizer for compensation.We first optimized the sample size of the angular histogram used in the proposed CPE technique.Figure 4 shows the receiver sensitivities of the 25.78-Gb/s QPSK signal (@ BER = 10 −3 ) measured after the transmission over 20-km long standard single-mode fiber (SSMF) as a function of the sample size.Although it would be helpful to utilize a large sample size for averaging out the additive Gaussian noises, it could make the proposed CPE technique insensitive to the fast fluctuations of the carrier phase.As a result, the optimum performance of the proposed CPE technique was obtained when we set the sample size to be 350.The proposed CPE technique utilizes the opening observed in the phase trajectory of the QPSK signal for the identification of its carrier phase.Thus, for the use of the proposed CPE technique, the amplitude of the modulation current applied to the RSOA should be limited so that this opening could remain open.On the other hand, to achieve the optimum receiver sensitivity, the modulation current should be large enough to rotate the phase of the QPSK signal by up to 270°.It should also be noted that, when the operating speed of the RSOA was set to be much faster than its modulation bandwidth, the received signal could suffer from a serious pattern dependency.This was because the data patterns containing high-frequency components could not be rotated sufficiently for the generation of the QPSK signal (as the high-frequency components were filtered out by the bandwidth-limited RSOA).Thus, it would be necessary to optimize the amplitude of the modulation current applied to the RSOA.For this purpose, we measured the receiver sensitivities of the 25.78-Gb/s QPSK signal in the back-to-back condition while varying the amplitude of the modulation current.The results in Fig. 5(a) show that we could improve the receiver sensitivity from −24.5 dBm to −30.0 dBm by increasing the modulation current from 48 mA p-p to 65 mA p-p , respectively.This was because we could not obtain the sufficient phase rotation required for the generation of an ideal QPSK signal when the modulation current was small, as shown in Figs.5(b)-5(e).However, when we set the modulation current to be larger than 65 mA p-p , the proposed CPE technique did not work properly since the phase rotation of the QPSK signal became to exceed 360° and, as a result, the opening in the phase trajectory was completely closed.We also attempted to measure the BER curves of the 25.78-Gb/s QPSK signal generated by directly modulating an RSOA using the conventional M-th power algorithm under the same conditions.However, in this case, we could not obtain the BER better than 10 −2 regardless of the amplitudes of modulation current.We measured the BER curves of the 25.78-Gb/s QPSK signal at various transmission distances by using the proposed CPE technique.In this experiment, we utilized the optimized sample size and RSOA's modulation current of 350 and 65 mA p-p , respectively.The results are shown in Fig. 6.When we set the transmission distance to be 20 km, the power penalty with respect to the back-to-back operation was measured to be 0.7 dB.This penalty was caused by the Rayleigh backscattered upstream signal (which was modulated again by the RSOA and interfered with the original upstream signal) [18].However, when we increased the transmission distance to 60 km, this power penalty was slightly increased to 0.9 dB due to the reduced optical signal-to-noise ratio caused by the reduced optical power incident on the RSOA.The inset of Fig. 6 shows the constellation diagram of the 25.78-Gb/s QPSK signal measured after the 60-km long SSMF transmission.Thus, we concluded that, by using the proposed CPE technique, it would be possible to achieve the error-free transmission of the 25.78-Gb/s QPSK signal generated by using a bandwidth-limited RSOA (modulation bandwidth: 3.2 GHz) even in the 60-km reach WDM PON environment.

Summary
We have proposed and demonstrated a simple technique to estimate the carrier phase of the high-speed (>10 Gb/s) QPSK signal generated by using a bandwidth-limited RSOA.The proposed technique can estimate the carrier phase of the QPSK signal simply by identifying the angular direction of the opening naturally occurred in the trajectory of the phasor diagram.We showed by numerical simulations that, when the QPSK signal was generated by using a bandwidth-limited RSOA, the conventional M-th power algorithm failed to estimate its carrier phase accurately as the operating speed of the signal was increased to be much faster than the modulation bandwidth of RSOA.We also confirmed this experimentally.For example, when we generated the 25.78-Gb/s QPSK signal by using an RSOA having a modulation bandwidth of 3.2 GHz, it was not possible to achieve the BER better than 10 −2 by using the M-th power algorithm.However, when the proposed CPE technique was used, we could obtain a decent receiver sensitivity of −30 dBm (@ BER = 10 −3 ) for this 25.78-Gb/sQPSK signal.By using this CPE technique, we also demonstrated the transmission of the 25.78-Gb/s upstream QPSK signal in a 60-km reach RSOA-based WDM PON.Since the performance of the proposed CPE technique is not dependent on the number of the modulation levels, we believe that this technique can also be used for the estimation of the carrier phase of M-ary (M>4) PSK signals generated by using a bandwidth-limited RSOA as long as we have an opening in the trajectory of the phasor diagram.

Fig. 1 .
Fig. 1.(a) Operating principle of the proposed CPE technique, (b) phasor diagram of the QPSK signal generated by directly modulating an RSOA, and (c) angular histogram obtained from the phasor trajectory in (b).

Fig. 2 .
Fig. 2. (a) Standard deviations of the phase errors plotted as a function of the data rate of the QSPK signal generated by using the bandwidth-limited modulator (3-dB bandwidth: 3.2 GHz).The black and red curves represent the standard deviations of the phase errors achievable by using the conventional M-th power algorithm and the proposed CPE technique, respectively.Exemplary phase errors obtained by using the M-th power algorithm for the (b) 2-Gb/s QPSK signal, (c) 10-Gb/s QPSK signal, and (d) 14-Gb/s QPSK signal.

Fig. 5 .
Fig. 5. (a) Measured BER curves of the QPSK signal in back-to-back operation with different modulation amplitudes.Also shown are the phasor diagrams of the signal when the peak-topeak modulation currents are (b) 48 mA, (c) 55 mA, (d) 60 mA, and (e) 65 mA.

Fig. 6 .
Fig. 6.Measured BER curves at various transmission distances.The inset is the constellation diagram of the 25.78-Gb/s QPSK signal measured after the transmission over 60 km of SSMF.