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We find that an adaptive equalizer and a phase-locked loop operating with decision-directed mode exhibit degraded performances when they are used in a digital coherent receiver to demodulate a 16QAM signal with intrinsically distorted constellation, and that the degradation is more significant for the dual-polarization case. We then propose a scheme to correctly demodulate such a distorted 16QAM signal, where the reference constellation and the threshold for the decision are adaptively adjusted such that they fit to the distorted ones. We experimentally confirm the improved performance of the proposed scheme over the conventional one for single-and dual-polarization 16QAM signals with distortion. We also investigate the applicable range of the proposed scheme for the degree of distortion of the signal.
© 2013 Optical Society of America
1. Introduction
Dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM) is an attractive modulation format due to its twice higher spectral efficiency than DP-QPSK, and it is a promising candidate as a format for next-generation optical transport systems. To demodulate a DP-16QAM signal in the receiver, digital signal processing (DSP) is used after coherent detection. For example, the carrier-phase recovery to track the frequency offset between the signal and the local oscillator (LO) and to recover the original phase is implemented in the digital domain [1–5], and an adaptive equalizer (AEQ) performs linear impairments compensation [1] and polarization demultiplexing [2]. To improve the quality of the demodulated signal, an AEQ should operate with decision-directed (DD) mode, where a decision is made for an incoming symbol and the error information is used to control the tap coefficients. So far, some implementations of AEQ having blind start-up function and combined with decision-directed phase-locked loop (DD-PLL) for carrier-phase recovery have been developed [4, 5] and proven to work well for DP-16QAM signals with an ideal constellation of square QAM signal.
At the transmitter side, on the other hand, technical progresses on photonic integrated circuits (PICs) are driving research and development of monolithically integrated optical transmitters based on InP [6], silicon [7], and GaAs [8] for simultaneous generation of multiple channels of an optical signal in a single chip. An integrated multi-channel DP-16QAM transmitter will also be realized in near future. However, such waveguide devices might have unexpected large loss and phase error in a waveguide, originating from an imperfect waveguide structure or the frequency chirp due to their carrier relaxation mechanisms. Furthermore, a driver amplifier also integrated in a chip might have a nonlinear gain. As a result, generated optical 16QAM signals would tend to have distortion such as amplitude imbalance, phase error, or their combinations, which results in an inherent distortion of the signal constellation [9]. We note that a high-speed and high-resolution digital-to-analogue converter (DAC) would realize pre-emphasis of an electric signal to equalize the distortion, but such a DAC is still under development and a conventional 2-bit DAC will be employed in production for the moment. Therefore, if a digital coherent receiver can handle 16QAM signals having “intrinsically distorted constellations” originating from imperfect modulation, it would greatly help to keep a high yield for PIC-based multi-channel 16QAM transmitters, or it would improve the interoperability of optical transmitters in dynamic optical-path networks where optical paths are changed according to demands from users [10].
In this paper, we experimentally generate single- and dual-polarization 16QAM signals with intrinsically distorted constellation and examine the performance of a conventional demodulation scheme based on coherent detection with DSP. We find that an AEQ combined with PLL both operating with DD mode exhibit degraded performances for the distorted 16QAM signals, and that the degradation is more significant for the dual-polarization case. We then propose a new scheme to successfully demodulate such a distorted 16QAM signal, where the reference constellation used in the decision process for the AEQ and the PLL is adaptively adjusted such that it fits well with that of the distorted 16QAM signal. We verify in experiment that the proposed scheme successfully demodulate the distorted 16QAM signals for both single-and dual-polarization conditions. We also quantitatively evaluate the applicable range of the proposed scheme for the degree of distortion of the signal.
2. Experiment with conventional demodulation scheme
We generate 16QAM signals having an ideal and an artificially distorted constellations, and compare the signal qualities obtained by a conventional demodulation scheme. Here we define the ideal constellation of 16QAM signal such that all of the complex amplitudes therein consist of an equidistant rectangular lattice in the complex plane.
Figure 1(a) depicts the experimental setup. The transmitter consisted of a laser diode (LD), a nested Mach-Zehnder IQ modulator (IQM), and an arbitrary waveform generator (AWG), and it generated a 12-Gbaud 16QAM signal encoded from a pseudo random bit sequence (PRBS) with the length of 215 – 1 by the Gray code. To give an intrinsic distortion to a 16QAM signal, we adjusted the AWG to reduce the voltage swing of the electric signal for the quadrature component by 20 % compared with the in-phase one, and we also adjusted the bias voltage of the IQM so that the IQ components of the 16QAM signal had the quadrature phase error of 20 degrees. The generated 16QAM signals were evaluated in single- or dual-polarization conditions, and we used a polarization multiplexing emulator with a fixed delay of 10.8 ns for the latter case. A variable optical attenuator (VOA) and an optical amplifier were used to adjust the optical signal-to-noise ratio (OSNR) of the signal. An OSNR was defined with 0.1-nm noise bandwidth, and it was measured by an optical spectrum analyzer (OSA). We used a band-pass filter (BPF) with the 4.5-nm passband to reduce the excess optical power of the out-band noise. The signal was detected by a coherent receiver followed by a real-time oscilloscope (OSC) which was used as analog-to-digital converters and data storage. Note here that the sampling rate of the converters was 80 and 40 GSa/s for the cases of single-polarization (SP-) and DP-16QAM, respectively. The stored signal data was then analyzed by an offline DSP.
In the offline DSP, the received signal was resampled at 24 GSa/s, corresponding to the over sampling rate of 2, and it was then fed into an AEQ combined with DD-PLL. Figure 1(b) represents a schematic diagram of the AEQ and the DD-PLL to perform adaptive equalization including polarization demultiplexing and carrier-phase recovery [4, 5]. The AEQ consisted of four finite-impulse response (FIR) filters with butterfly structure, each of which was a T/2-spaced nine-tap filter, and the tap coefficients were updated according to least-mean square (LMS) algorithm with the calculated error signal based on constant-modulus algorithm (CMA) for pre-convergence in the blind start-up process and DD mode for regular operation. The PLL was a digitally implemented second-order one [11], and it utilized the difference of the signal phases before and after the decision. Therefore, correct decisions are required for the stable operation of the PLL. The PLL was initially turned off and was turned on after the AEQ operating with CMA converged. At this moment, only the PLL used the decision result and the AEQ was still unconcerned about the result. We employed a conventional decision process such that a complex value closest to an incoming symbol was chosen from a reference constellation of 16QAM signal. This means that the decision threshold is given by the boundaries of the Voronoi region [12] of the symbols in the reference constellation. We here used the ideal 16QAM constellation as the reference. Finally, the AEQ also moved to the operation with the DD mode, and both the AEQ and the PLL converged to steady-state operations under the DD mode utilizing the common decision result. The bit-error rate (BER) and the error-vector magnitude (EVM) [13] of the symbols output from the AEQ were then evaluated. Typical numbers of the evaluated symbols were 68000 and 210000 for the cases of the SP- and DP-16QAM signals, respectively. We employed the following definition for the root-mean square (rms) value of the EVM,
where rm is one of the M points in the reference constellation of an M-QAM signal, xn is the n-th signal in the total N incoming signals, and r(xn) is the reference point chosen from (r1, ··· ,rM) according to the decision result for xn. In evaluating the BER and the EVM of the obtained symbols, we did not employ the decision results used to drive the AEQ and the PLL, but we applied an optimum detecting scheme based on the maximum a posteriori probability (MAP) rule for decision [12]. This means that the correct reference constellation was already known at the receiver even if the signal had an intrinsically distorted constellation, and it was used for the decision so that the BER and the EVM could get the best values regardless of the shape of the constellation. Consequently, we can focus on the performances of the AEQ and the PLL operating for a signal having a distorted constellation. We note that such a decision rule could not be applied to the AEQ and the PLL in the blind start-up stage, because any of prior information on the received signal were not available, so we had to use the ideal constellation as the reference for the AEQ and the PLL in the demodulation process.Figures 2(a) and 2(b) represent the measured BER and EVM, respectively, for SP- and DP-16QAM signals having the ideal and the distorted constellations. In Fig. 2(a), significant OSNR penalty and error floor can be seen for the distorted 16QAM signals, which is worse than expected from the measured EVM results shown in Fig. 2(b). Furthermore, the DP-16QAM has larger penalty than the SP-16QAM. Those degradations for the distorted 16QAM signals are the results of disturbed operations of the AEQ and/or the PLL operating with DD mode. Figures 2(c) and 2(d) describe the constellations of the ideal and the distorted SP-16QAM signals with the OSNR of 30 dB, respectively. Comparing these constellations, one can observe that the outer symbols in the distorted 16QAM are significantly scattered due to the phase noise. This phase noise was caused by unstable operation of the DD-PLL. In fact, the standard deviation of the oscillating frequency of the numerically-controlled oscillator in the PLL was 12 MHz for the distorted 16QAM signal, while it was 4 MHz for the ideal one. Thus, much of decision error made the DD-PLL unstable and gave the phase error to the signal with distorted constellation. On the other hand, Fig. 2(e) shows the constellation of one of the polarizations of the distorted DP-16QAM signal with the OSNR of 33 dB. We note that similar result was observed for the other polarization of the signal. One can see from Fig. 2(e) that all the symbols have large noise-like components, in addition to the phase noise only for the outer symbols. Since the intensity of the optical noise is small as shown in Figs. 2(c) and 2(d), we attribute the origin of the noise-like components to the polarization demultiplexing function of the AEQ degraded by the decision error. To conclude, the AEQ and/or the PLL operating with DD mode for the distorted 16QAM signals were disturbed by much of decision error when the ideal 16QAM constellation was used as the reference for decision, and accordingly a large OSNR penalty and the floor for the BER appeared, even though we applied an optimum MAP detector to the signal after the AEQ and the PLL.
Fig. 2 Measured BER (a) and EVM (b) for SP- and DP-16QAM signals with ideal and distorted constellations, demodulated by the conventional scheme. Constellations of the ideal SP-16QAM (c) and distorted SP-16QAM (d) with OSNR of 30 dB, and distorted DP-16QAM (e) with OSNR of 33 dB. Dotted lines in (c)–(e) represent the decision threshold.
3. Improved demodulation scheme for distorted 16QAM signal
We develop a new scheme to successfully demodulate the distorted 16QAM signals, where we propose a method to adaptively adjust the reference constellation used for decision in the AEQ and the PLL, so that it fits well to the distorted one of the incoming signal. We note that some techniques to address signals with distorted constellations in a receiver have been proposed [14, 15]. These techniques utilize the previously demodulated symbols to compensate the hardware skew of a coherent receiver or to reduce the BER of the signal which was distorted during the transmission. On the other hand, we apply the proposed scheme to the symbols before demodulation in order for the AEQ and the PLL to work correctly. Combining the previously and currently proposed techniques to address the signals having distorted constellations, we expect to further improve the performance of a digital coherent receiver.
Figure 3(a) shows the constellations of the ideal and a distorted 16QAM signals in the complex plane. At the initial stage of the decision process, the ideal constellation is used as the reference. The key feature of our proposal is to adjust each point of the reference constellation to fit with that of the distorted signal by an iterative process during the operations of the AEQ and the PLL. Figure 3(b) depicts a schematic of the adjusting process, where one of the points in the constellation is focused on. Let rn and xn be the vectors to indicate in the complex plane the positions of the reference and the received signal at the n-th iteration of the process for the point, respectively. Note that rn has been chosen from the reference points after a decision for xn. We then update the reference vector as
where μ is a small positive constant like the step-size parameter used in an AEQ, and we employ μ = 0.005 in the experiment. In deriving Eq. (2), we defined the cost function J as so that we minimize the mean decision error. We also applied the steepest descent algorithm as where Jn = ||rn−xn||2 and ∂Jn/∂rn = 2(rn − xn). Repeating the procedure as shown in Eq. (2), the reference point approaches the mean position of the received signals, E[xn]. We have found that it is effective to use this adjusting process from the moment after the PLL is locked until the AEQ is converged under the operation with DD mode. Particularly in our offline DSP, we applied the above procedure to 16000 symbols at the very last stage of the blind start-up process after the PLL was locked, and to another 10000 symbols after switching to the DD-mode operation. These numbers of the symbols were enough for the procedure to be converged for constellations having a variety of the distortion.Fig. 3 (a) Constellation diagrams for ideal (crosses) and distorted (points) 16QAM signals. (b) Schematic of adaptive adjustment process for a point in the reference constellation.
Applying the above proposed scheme, we demodulated the same stored data of the 16QAM signals with those used to obtain the results of Fig. 2. The calculated BER, EVM, and constellations are presented in Fig. 4, where one can see that the qualities of the distorted 16QAM signals were drastically improved for both the SP and DP conditions compared with the case of the conventional demodulation scheme, and no error floor was observed for the distorted signals. In Fig. 4(a), the distorted signals still exhibit the OSNR penalty of approximately 1 dB from the ideal ones, despite the EVMs of the both signals are indistinguishable. This penalty is an inherent one originating from the fact that the distorted signal has the 20-% reduced amplitude for the quadrature component compared with the in-phase one. Under the condition of the same average power, the 20-% reduction of the quadrature amplitude while keeping the in-phase amplitude means the 12-% reduction of the symbol spacing along to the quadrature axis. Therefore, 1.29 times (+1.1 dB) larger power is required to recover the BER of the signal with the ideal constellation. We note that the quadrature phase error of 20 degrees given to the distorted signals has less contribution to the OSNR penalty.
Fig. 4 Measured BER (a) and EVM (b) for SP- and DP-16QAM signals with ideal and distorted constellations, demodulated by the proposed scheme. Constellations of the ideal SP-16QAM (c) and distorted SP-16QAM (d) at OSNR with 30 dB, and distorted DP-16QAM (e) with OSNR of 33 dB. Dotted lines in (c)–(e) represent the decision threshold.
Understanding the applicable range of the above proposed scheme for the degree of distortion of the signal is an important issue. Qualitatively, it can operate as long as a certain number of correct decision is achieved. In other words, too large distortions will lead to wrong decision results in the proposed scheme following to Eq. (2). To investigate the applicable range quantitatively, we varied the degree of artificial distortion of a DP-16QAM signal at the transmitter side, and we received and demodulated the signal with and without the proposed scheme. Figure 5 plots the measured EVM of DP-16QAM signals with the OSNR of 35 dB versus the ratio of the reduced amplitude of the quadrature component to the in-phase one from 0 to 45%, for various quadrature phase errors from 0 to 25 degrees. Comparing Figs. 5(a) and 5(b), one can see that the proposed scheme was successful in the demodulation over a wide range of the distortion and kept the EVM almost constant in every case. The proposed scheme had practical limits of the amplitude’s reduction ratio and the quadrature phase error to be 40 % and 20 degrees, respectively, while they were 20 % and 15 degrees for the case without the proposed scheme.
Fig. 5 Measured EVM of DP-16QAM signals with different degree of distortion, demodulated with (a) and without (b) the proposed scheme.
The proposed scheme can provide the reference constellation of a received signal, with which the amplitude skew and the quadrature phase difference between the in-phase and the quadrature components can be estimated. Figure 6(a) shows the reference constellations of a distorted 16QAM signal and their average points P1, P2, P3, and P4 for the quadrants in the complex plane. We then obtain the quadrature phase difference between the in-phase and the quadrature components, θIQ, and the ratio of the amplitudes of the quadrature components to the in-phase one, RIQ, as
In fact, we had used θIQ given by Eq. (5) to precisely control the quadrature phase error in the experiments shown above. On the other hand, we confirmed that the RIQ given by the reference constellation of the received signals was consistent with the voltage setting of the AWG for the amplitude of the quadrature component. Figure 6(b) depicts RIQ calculated from the measured results shown in Fig. 5(a), against the voltage setting of the AWG for the quadrature component relative to the in-phase one. The obtained RIQ is in good agreement with the AWG setting. It would be effective if the information on θIQ and RIQ obtained from the reference constellation given by the proposed scheme is fed back to the transmitter to compensate the distortions.Fig. 6 (a) Reference constellations of a distorted 16QAM signal (open circles) and their average position (closed) for each quadrant. (b) Relationship between RIQ obtained from the reference constellations and the voltage setting of AWG for the quadrature component.
Throughout the above discussion, we assumed to use PLL for the carrier-phase recovery in a receiver. However, the use of PLL in a practical DSP is not feasible, because a DSP must operate with parallelized processing structure under the clock rate which is much slower than the symbol rate of the signal, and the symbol-by-symbol feedback required for the PLL to operate is then impossible. On the other hand, the adaptive adjustment scheme of the reference constellation proposed above is also applicable to a receiver that employs other types of decision-directed carrier-phase recovery schemes. When some functions of a DSP such as an AEQ or a carrier-phase recovery are parallelized by P streams, Eq. (2) should be modified as
where is the signal in the k-th tributary of the parallel streams in n-th iteration of the process. For example, a practical feedforward carrier-phase recovery scheme for M-QAM signals [3] can cooperate with the proposed scheme based on Eq. (7).4. Conclusion
We experimentally examined a conventional demodulation scheme for SP- and DP-16QAM signals with an intrinsically distorted constellation originating from imperfect modulation, and found that the operations of the AEQ and the PLL with the conventional DD mode were disturbed by much of decision error and resulted in the degraded qualities of the demodulated signals. Furthermore, the degradation was more significant for the DP-16QAM signal. We then proposed a new demodulation scheme, where the reference constellation used in the decision process for the AEQ and the PLL was updated adaptively so that it fitted well with that of the received signal. Applying the proposed demodulation scheme, we experimentally confirmed that in both single- and dual-polarization cases the distorted 16QAM signals were successfully demodulated without penalty except for an intrinsic one. We also quantitatively evaluated the applicable range of the proposed scheme to the degree of distortion of DP-16QAM signals. Although we examined only 16QAM signals in this work, we expect that the proposed scheme is also effective to demodulating 64- or higher order QAM signals. Furthermore, we used the digital PLL for carrier-phase recovery in this work, but other schemes of decision-directed carrier-phase recovery can also be used with the proposed demodulation scheme.
Acknowledgments
This work was supported in part by Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
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