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We compare the performance of sub-symbol-rate sampling for polarization-division-multiplexed quadrature-phase-shift-keying (PDM-QPSK) signals in super-Nyquist wavelength division multiplexing (WDM) system by using quadrature duo-binary (QDB) and quadrature four-level poly-binary (4PB) shaping together with maximum likelihood sequence estimation (MLSE). PDM-16QAM is adopted in the simulation to be compared with PDM-QPSK. The numerical simulations show that, for a software defined communication system, the level number of quadrature poly-binary modulation should be adjusted to achieve the optimal performance according to channel spacing, required OSNR and sampling rate restrictions of optics. In the experiment, we demonstrate 3-channel 12-Gbaud PDM-QPSK transmission with 10-GHz channel spacing and only 8.4-GSa/s ADC sampling rate at lowest. By using QDB or 4PB shaping with 3tap-MLSE, the sampling rate can be reduced to the signal baud rate (1 samples per symbol) without penalty.
© 2016 Optical Society of America
1. Introduction
In recent years, the fast growth of mobile and cloud services has a strong demand of higher bit rate and lower cost optical communication. In order to satisfy this demand, the bandwidth and sampling rate requirement for the optoelectronic devices increase correspondingly. The straight forward method for tackling this challenge is to increase the devices’ bandwidth directly [1]. However, the cost of optics has an exponential growth with the increase of the devices’ bandwidth.
Therefore, combining the advanced DSPs and lower-bandwidth optics together is always a technological path to achieve the broadband communication, especially in the cost-sensitive and vast metropolitan-area networks (MAN) and data centers [2–4]. Partial response shaping has attracted great attention to increase the spectral efficiency (SE) in both coherent systems and intensity modulation and direct detection (IM/DD) systems, which achieves higher bit rate with limited optics’ bandwidth [5–11]. At receiver, analog-to-digital converter (ADC) also face challenges with increasing bit rate, especially the sampling rate. Traditionally, a number of samples per symbol (NSPS) value of 2 is necessary to reconstruct the original continuous-time signals from the sampled discrete-time signals in case of spectral aliasing, according to the Nyquist sampling theorem. However, as the transmission bandwidth increases, the demands of sampling rate already exceed the capabilities of current state of the art ADC. Li Jianqiang et al. released the sampling rate to a NSPS value of 1 by using quadrature duo-binary (QDB) shaping detection at receiver [12]. Guan Gui et al. proposed sub-symbol-rate sampling based sparse channel estimation in wireless communication system [13]. In our previous work [14], we realize a NSPS value of 0.8 at receiver for super-Nyquist wavelength division multiplexing (WDM) signals without introducing additional OSNR penalty compared with a NSPS value of 2 by using quadrature 4-level poly-binary (4PB) shaping and 9-tap maximum likelihood sequence estimation (MLSE).
In this paper, simulations are conducted to compare the performance of two poly-binary shaping schemes in a sub-symbol-rate sampling super-Nyquist WDM polarization-division-multiplexed quadrature-phase-shift-keying (PDM-QPSK) system. The receiver side DSP is as following: a partial response shaping filter + a multi-tap mutli-modulus algorithm (MMA) equalizer + a MLSE detector [15]. The performance of a 112-Gb/s PDM-QPSK signal using the two detection schemes is investigated with different MLSE tap numbers, WDM channel spacing and sampling rates of ADC. At the same time, the performance of three-channel 112Gbit/s PDM-16QAM is added in the simulation as a reference. Finally, the performance of partial-response shaping schemes is examined experimentally, where a three channel 12-Gbaud PDM-QPSK WDM signal multiplexed at different channel spacing is detected by an ADC with different sampling rate.
2. Receiver design for sub-symbol-rate sampling
Known as a class of partial response, poly-binary shaping is realized by a finite impulse response (FIR) filter with equal weight taps, as shown in. Figure 1(a) [2,5,6]. For generating QDB and 4PB signals, a duo-binary (n = 3) filter and a tri-binary (n = 4) filter are needed respectively. The constellation conversions with duo-binary shaping and tri-binary shaping are shown in the insets of Fig. 1(a). The process of poly-binary shaping can be also achieved with a Bessel filter [16]. By adjusting the order and bandwidth of the Bessel filter, different levels poly-binary shaping can be obtained. By introducing the correlation among two and more adjacent symbols, the level number n is increased and the bandwidth is reduced to half or less of original bandwidth correspondingly, which can be described by the power-spectral density of poly-binary signals [17,18]
Fig. 1 (a) The FIR filter used to generate n level poly-binary signal and the constellation conversion of QDB and 4PB; (b) the spectrum of QPSK, QDB and 4PB signals
Where A and T are the amplitude and symbol period of input non-return-to-zero (NRZ) pulses. Regardless of the correlation of several symbols and increased level numbers, each poly-binary symbol still carries one-bit information [15,16]. As shown in Fig. 1(b), the spectrum of QPSK, QDB and 4PB are respectively depicted in red, green and blue, from which we can find that the 3-dB bandwidth of poly-binary shaped signals is obviously reduced. The two side-located arches of 4PB signals (blue) are side lobes which can be filtered without penalty. The sampling schematic spectral diagrams are shown in Fig. 2. The QPSK signal generally occupies a large amount of spectrum outside the Nyquist band which means when the sampling rate is lower than the requirement of Nyquist sampling theorem, the sampled signals will be subjected to significant spectral aliasing [12]. However, the poly-binary shaping re-locate the dominant power of signals within a much narrower band than Nyquist band which leads to a much lower requirement of sampling rate.
Fig. 2 Schematic spectral diagrams at sub-symbol-rate sampling for (a) full-response signals and (b) poly-binary signals.
MLSE is adopted to mitigate the serious inter-symbol interference (ISI) introduced by super-Nyquist WDM system and further reducing the sampling rate [19,20]. The principle of MLSE is to maximize the probability of p(y|x) (x = 0,1), where and are the transmitted and received information, respectively. Since the prior probability p(x) is assumed to be equal, Bayes’ Law can be used to search the maximum likelihood probability. If the probability density function (PDF) p(x|y) is available, the most probable value of x can be chosen simply [21]. When there is ISI in the channel, multiple adjacent symbols can be used together to make decisions on a sequence of bits. Instead of deciding a single bit, a most likely sequence is selected by a given set of received samples. The probability function can be described as [21]
We assume that the noise is independent, even though the adjacent symbols are correlated. In this way, the total probability can be given by the product of the individual probabilities [21]:
where is the time index of received sample sequence. Then, the Viterbi algorithm (VA) is employed to solve the Eq. (3).
By combining the poly-binary shaping and MLSE, the receiver design is shown in Fig. 3 [6,15]. QDB and 4PB, as two kinds of poly-binary signals, are chosen to investigate and compare the performance of sub-symbol-rate sampling under different conditions. The sub-symbol-rate sampled signal is up-resampled to a NSPS value of 2 after being filtered to mitigate the inter-channel crosstalk. Then, the QPSK signal is shaped into QDB or 4PB signal with an FIR filter which has been described in Fig. 1 (a). Multi-tap MMA is implemented to conduct the channel equalization followed by carrier recovery. A multi-tap MLSE is used to mitigate the residual ISI.
The cascade of poly-binary shaping and MMA is an enhanced-MMA for the super-Nyquist condition. MMA is an algorithm aiming to erase the ISI distortion completely. However, the introduced poly-binary shaping before MMA changes the length of impulse response (including transmitter, channel, coherent receiver, poly-binary shaping and MMA) from 1 to 2 (duo-binary) or 3 (tri-binary). Since the ISI distortion is too serious to be mitigated at one time by using MMA, some ISI is intentionally left to be equalized with MLSE.
3. Simulations of QDB and 4PB shaping
The performance of a super-Nyquist WDM system is affected by ISI and inter-channel crosstalk, and both of them depends on spectrum, which can be shaped with either optical filters or DSP and digital-to-analog converters (DACs). To simplify transmitters, no DSP and DACs are adopted here and different channels are combined together with a WDM multiplexer.
Although both sub-symbol-rate sampling and super-Nyquist WDM system can introduce long channel memories for full response signals, poly-binary shaping has the impact of shortening the channel memory into symbols in theory ( is the level number of poly-binary signals) [15,22]. We first investigate the influence of MLSE tap numbers on QDB and 4PB signals.
Simulations are conducted on a three channel 112-Gb/s PDM-QPSK system with a 20-GHz channel spacing and a NSPS value of 0.9 at receiver. The WDM multiplexer is modeled as a 5th-order super-Gaussian filter with a 3-dB bandwidth of 18.2-GHz. The receiver has a low pass 5th-order super-Gaussian filter with 19-GHz bandwidth (3-dB). Each channel is modulated with 215-1 pseudo-random bit sequence (PRBS) with delay decorrelation among channels. Both transmitter and local oscillator lasers have 100-KHz linewidth and frequency offset between two lasers is 200-MHz. The OSNR is set at 17-dB.
QDB and 4PB are both investigated with different MLSE tap numbers, as shown in Fig. 4. With the tap numbers increasing, the performance does not have obvious changes for both QDB and 4PB shaping. Since the QDB and 4PB respectively introduce the correlation of 2 and 3 adjacent symbols, 2-tap and 3-tap MLSE is enough to equalize the QDB and 4PB signal respectively [15]. For a fair comparison, 3-tap is chosen for both QDB and 4PB signals in the following investigations to reduce the computation complexity of MLSE that increases exponentially with tap number.
Fig. 4 BER vs. MLSE tap number for a 112-Gb/s PDM-QPSK signal with 20-GHz channel spacing and a NSPS value of 0.9 at an OSNR of 17-dB
In order to compare the limits of QDB and 4PB shaping, a three channel 112-Gb/s PDM-QPSK system with different channel spacing and sampling rates is studied. The WDM multiplexer filter uses a 5th-order super-Gaussian filter with bandwidth optimized according to different channel spacing. The channel spacing ranges from 16-GHz to 28-GHz. The other simulation parameters keep the same as those in the previous sessions. In comparison, the performance of 112-Gb/s PDM-16QAM with a NSPS value of 2 is studied as well. The 16QAM employing the same MMA and PLL is detected with symbol-by-symbol (SbS) detection, as shown in Fig. 5.
Fig. 5 Required OSNR at BER of 3.8x10−3 vs. channel spacing for the 3-channel 112-Gb/s PDM-16QAM signal, the 3-channel 112-Gb/s PDM-QPSK signal with different DSP schemes
The required OSNR at bit-error rate (BER) of 3.8x10−3 for 16QAM and QPSK signal with different DSP schemes is shown in Fig. 5. A NSPS value of 2 is used for all signals. For the incremental inter-channel crosstalk and ISI, the required OSNR increases for all detection schemes. For the QPSK signals, the traditional QPSK detection scheme is better than poly-binary shaping schemes at the Nyquist spacing (28-GHz). When the signals are narrow-bandwidth filtered at the start (19-27GHz), QDB shaping has big advantage than the other two scheme. With the spacing decreasing further (<19-GHz), the advantage of 4PB shaping becomes obvious gradually. In order to achieve the optimal performance, the shaping scheme should be adjusted with different channel spacing requirements. Compared with 16QAM, QPSK with 4PB shaping has similar performance during the spacing from 17 to 20-GHz. When the spacing decreases to 16-GHz, 4PB shaping needs a higher OSNR. However, QPSK signals with 4PB shaping scheme do not need a DAC at the transmitter.
Then, the performance of sub-symbol-rate sampling for both QDB and 4PB shaping in super-Nyquist WDM system is investigated with numerical simulations. All the parameters keep the same as above, except the sampling rate. Figure 6 shows the performance of QDB and 4PB shaping with different sampling rates and different channel spacing. For QDB shaping, a NSPS value of 1 can be achieved without penalty. The lowest achievable NSPS value is 0.9 with about 1-dB OSNR penalty. For 4PB shaping, a NSPS value of 1 without OSNR penalty is still available. And the lowest achievable NSPS value is 0.7 with also about 1-dB OSNR penalty.
Fig. 6 Required OSNR at BER of 3.8x10−3 vs. channel spacing for the 3-channel 112-Gb/s PDM-QPSK signal with different poly-binary shaping and sampling rate.
At the larger spacing region (>19-GHz), QDB and 4PB shaping schemes both have their own advantages, compared with each other. When the sampling rate is highly restricted by low-cost optics, 4PB shaping can be chosen to relieve the hard requirements at the cost of OSNR. If the sampling rate is not restricted too much, QDB shaping is an attractive candidate that has a lower OSNR requirement. When the spacing becomes narrower (<19-GHz), 4PB shaping is the better scheme for either sampling rate or OSNR restriction.
4. Experimental results
The experimental setup is shown in Fig. 7. The sub-symbol-rate sampling of a 12-Gbaud WDM PDM-QPSK signal is experimentally investigated. At the transmitter, three external cavity lasers (ECLs) with ~100-kHz linewidth and different channel spacing are used. The ECLs used for channel 1 and 3 are combined together with a 3-dB polarization maintaining coupler and sent into the same nested Mach-Zehnder modulator (MZM). The left one used for the middle channel is sent into another MZM. The Tektronix (7122C) arbitrary waveform generator (AWG) supplies the 12-Gbaud binary electrical signal for both in-phase and quadrature arms of modulators. The signal supplied for both MZMs is de-correlated 215-1 PRBSes. No electrical pulse shaping is used for the signals. The modulated signals from two modulators are multiplexed together with a wavelength selective switch (WSS) at different channel spacing. The spectra of WDM signals and the eye diagrams of both driving signals and optical signal are shown in the insets of Fig. 7. Then, the signals are polarization multiplexed with 400ns delay between the two polarization tributaries. The polarization controllers (PC) in the channel branches are used to align the signal polarization with the polarization multiplexer (PolMux). In the B2B measurements, the variable optical attenuator (VOA) and two Erbium Doped Fiber Amplifiers (EDFAs) are deployed to adjust the OSNR of the signal.
Fig. 7 Experiment setup. The insets are eye diagrams of the electrical driving signal and optical signal after the WSS, and the spectra of the WDM signal at 10-GHz channel spacing
At the receiver, the signal is mixed with a free running ECL local oscillator (LO) in a polarization and phase diversity coherent receiver. Then the detected signal is captured by a Tektronix (DPO73304D) 50GSa/s real-time oscilloscope with 20-GHz bandwidth. Since the sampling rate of oscilloscope used in the experiment cannot be tuned arbitrarily. The signal with desired sampling rate is obtained by DSP offline. Then, the digitized signal is resampled to a NSPS value of 2, after filtered by a 5th-order super Gaussian filter to mitigate the inter-channel crosstalk from neighboring channels.
After being shaped into QDB or 4PB signals, a 19-tap MMA is adopted for polarization de-multiplexing and ISI mitigation. The laser frequency offset is corrected by a phase-increment estimation algorithm and carrier phase is estimated by a 2nd-order phase locked loop (PLL). A 3-tap MLSE detector is implemented to mitigate the residual ISI, and calculate the BER.
As shown in Fig. 8, the performance of different NSPS values using QDB and 4PB shaping are compared in the three channel 12-Gbaud PDM-QPSK B2B measurement at different channel spacing. A 3-tap MLSE is implemented in all experiments. As shown in Fig. 8(a), 4PB shaping can achieve the lowest NSPS value (i.e. 0.7) with about 3~4-dB OSNR penalty and 0.8 with about 1-dB OSNR penalty. QDB shaping can only lower the NSPS value to 0.9 at cost of about 3.5-dB penalty. When the NSPS value is reduced from 2 to 1, both QDB and 4PB do not have any penalty. However, QDB shaping have a lower required OSNR compared with 4PB shaping. With the increase of OSNR, the performance of QDB shaping with a NSPS value of 0.9 and 4PB shaping with a NSPS value of 0.8 at the spacing of 10GHz and 11GHz is also shown in Fig. 8(b). For the NSPS value of 0.8 using 4PB, the required OSNR is close to the NSPS value of 0.9 using QDB. When the spacing varies from 12-GHz to 10-GHz, the trend does not have any change, as shown in Fig. 8(c). For a software defined optical transmission, poly-binary level, sampling rate, MLSE algorithm and channel spacing can be flexibly adjusted to achieve the optimal performance according to the OSNR and other performance requirements.
Fig. 8 (a) Required OSNR vs. Samples per symbol; (b) Required OSNR vs. channel spacing; (c)The performance of QDB shaping with a NSPS value of 0.9 and 4PB shaping with a NSPS value of 0.8 at the spacing of 10GHz and 11GHz
5. Summary
We compare the performance of QDB and 4PB shaping detection schemes for sub-symbol-rate sampled QPSK signals in super-Nyquist WDM systems. Both detection schemes with 3-tap MLSE have similar performance as that with more MLSE taps. A NSPS value of 2 is first investigated with simulations as a reference. At super-Nyquist channel spacing, poly-binary shaping detection scheme shows better performance than traditional QPSK detection scheme. With the spacing narrowed further, the performance of higher level poly-binary (4PB) shaping detection shows its advantage gradually.
At the relatively higher super-Nyquist channel spacing (QDB shaping is better than 4PB with a NSPS value of 2), 4PB shaping can achieve a lower NSPS value than QDB at the cost of OSNR. At narrower spacing, 4PB shows a better performance with any NSPS value. The experimental results on a 12-Gbaud WDM PDM-QPSK super-Nyquist system show that the QDB and 4PB shaping can achieve a NSPS value of 0.9 and 0.7 at lowest respectively. For a software defined transmission system, the channel spacing, shaping schemes and sampling rate can be flexibly adjusted according to the OSNR, performance requirements and other restrictions of optics. Compared with 16QAM, poly-binary shaped QPSK signal is more flexible and has lower demand for hardware (no DAC). Meanwhile, duo-binary shaped QPSK signals is more resistant to noise for a less number of level.
Funding
National High-tech R&D Program (863 program) (2015AA015503); National Natural Science Foundation of China (NSFC) (61302085, 62171189); Fundamental Research Funds for the Central Universities (2016RC25); Fund of State Key Laboratory of Information Photonics and Optical Communications (2015ZT03).
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