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Abstract
High peak-to-average power ratio (PAPR) is an inherent defect in intensity modulation and direct detection (IM/DD) discrete-multitone (DMT) system, which will cause serious signal nonlinear distortion over fiber transmission. Single carrier-DMT (SC-DMT), which also refers to the discrete-Fourier-transform spread DMT (DFT-spread DMT), is a promising technology for DMT signal PAPR reduction, but higher computational complexity is required due to the additional DFT/IDFT operations in transceiver. In this paper, we experimentally compare the performance of SC-DMT and conventional DMT (CDMT) signal when the computational complexity of SC-DMT transceiver is lower than CDMT by reducing the FFT size in SC-DMT. The results show that the receiver sensitivity of 20 GHz 1024-point FFT based SC-DMT improves by 0.7 dB than 8192-point FFT based CDMT for both 120 Gb/s 64QAM-DMT and 140 Gb/s 128QAM-DMT signal transmission over 2-km single mode fiber (SMF) at the BER of 3.8 × 10−3 and 2.0 × 10−2, respectively. It is the first time to find that the SC-DMT with lower transceiver computational complexity outperforms CDMT. In addition, fast-Hartley-transform (FHT) technique is employed to replace FFT for further transceiver computational complexity reduction. The results give out that FHT-based SC-DMT shows the same BER performance with FFT-based SC-DMT, while the computational complexity of the transceiver can be reduced by half.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The ever-increasing emerging applications such as Internet of Things (IoT), 5G mobile front haul, Augmented/Virtual Reality and etc., are requiring high data rate transmission in data center and access network [1]. Beyond 100 Gb/s per wavelength data transmission is urgently needed in short reach applications in which the intensity modulation and direct detection (IM/DD) system will be more attractive due to its lower cost and lower system complexity [1–12]. One straightforward solution to increase the system capacity is using wider bandwidth for signal transmission, but the manufacturing technology for communication devices in transceiver will undergo a great challenge. Another way to enhance the capacity is employing high spectral efficiency advanced modulation formats such as discrete multi-tone (DMT) [2–8], pulse amplitude modulation (PAM) [2–5,9–11] and carrier-less amplitude/phase modulation (CAP) [2–5,12]. Among them, DMT is a multi-carrier scheme which can be used in IM/DD systems to create real value orthogonal frequency division multiplexing (OFDM) signal. It inherits all merits of OFDM such as high spectral efficiency, strong robustness against chromatic dispersion (CD), and great flexible with independent modulation formats in each subcarrier. However, as a normal multi-carrier technique, an inherent disadvantage of DMT signal is the high peak-to-average power ratio (PAPR) which will induce serious nonlinear signal distortion over fiber transmission. Thus, the PAPR of DMT signal should be reduced to enhance system performance.
Several methods have been proposed to reduce the PAPR in optical communication systems. Among them, the most widely used scheme is directly clipping technique in which the peak envelope of signal is clipped into a determined value [13]. However, the clipping induced signal distortion will degrade the system bit-error-ratio (BER) performance. Alternatively, a digital pre-distortion technique based on commanding transform is applied to reduce the signal PAPR in coherent OFDM system [14]. It outperforms the clipping scheme but increases the signal average power. Another well-known PAPR reduction scheme is selective mapping (SLM) [15,16] which can reduce the PAPR effectively without any signal distortion. Unfortunately, SLM suffers from very high computation complexity due to the multiple IFFT processing needed in transmitter for each OFDM symbol.
Compared with above mentioned PAPR reduction schemes, the single-carrier OFDM(SC-OFDM), which also refers to DFT-spread OFDM in the uplink of long-term evolution (LTE) networks, is considered as a more attractive solution which cannot only reduce the PAPR, but also effectively eliminate the bandwidth limitation induced inter-symbol interference (ISI) as reported in [17,18]. The computational complexity of FFT-based single-carrier DMT (SC-DMT) is lower than SLM DMT due to only one additional DFT block is needed in transmitter, while it is still higher than conventional DMT (CDMT). DSP computational complexity is an important issue in short reach applications, which determines its practicability. Many works regarding the realization of DSP computational complexity analysis on multi-carrier or single-carrier optical communication systems [19–23], i.e., J. Wei et al experimentally compared the complexity between multi-band CAP and DMT for practical high-speed data center interconnects [19]. Fast-Hartley-transform (FHT) technique is discussed widely to replace FFT scheme for DMT signal modulation, which can effectively reduce the computational complexity by half by using real value rather than complex value multiplication and addition [24,25] in signal modulation/demodulation. However, whether SC-DMT can outperform CDMT remains to be verified when its computational complexity is the same as or even lower than CDMT.
In this paper, we experimentally compare the performance of SC-DMT and CDMT in an IM/DD system when the transceiver computational complexity of SC-DMT is lower than CDMT by reducing the FFT/FHT size. The results show that the receiver sensitivity of 1024-point FFT based SC-DMT has 0.7 dB improvement compared to 8192-point FFT based CDMT at BER of Hard-decision Forward Error Correction (HD-FEC) threshold (3.8 × 10−3) over 2-km single mode fiber (SMF) transmission with 120 Gb/s data rate. When the data rate increases to 140 Gb/s, the required received optical power (ROP) of 1024-point FFT based SC-DMT and 8192-point FFT based CDMT at BER of Soft-decision Forward Error Correction (SD-FEC) threshold (2 × 10−2) over 2-km SMF transmission are −6.2 dBm and −5.5 dBm, respectively. It is the first time to find that the SC-DMT outperforms CDMT while its transceiver computational complexity is still lower than the latter one. What’s more, the FHT technique is discussed to further reduce the computational complexity of SC-DMT transceiver, and the results show that FHT-based SC-DMT shows the same BER performance as FFT-based SC-DMT while its transceiver computational complexity can be reduced by half.
2. Principle
2.1 Complexity computation
In this section, the computational complexity of DMT transmitter is discussed in detail in terms of complex multiplication and addition. To generate a CDMT symbol with 2N-subcarriers, 2N-point IFFT is needed in transmitter, which includes Nlog2(2N) complex multiplications and 2Nlog2(2N) complex additions. For FFT-based SC-DMT, additional n-point DFT is required. In this paper, the DAC sampling rate and signal bandwidth are 86-GSa/s and 20GHz, respectively. The relationship between n and 2N is described as n = 20/86·2N which is not exactly 2k. Actually, n should be regarded as n1 = 2k during calculating the computational complexity of FFT. For example, when 2N = 1024, n = 309, and n should be regarded as n1 = 512 when we calculate the computational complexity. The computational complexity of FFT-based SC-DMT transmitter involves Nlog2(2N) + n1/2log2(n1) complex multiplications and 2Nlog2(2N) + n1log2(n1) complex additions. Table 1 presents the detail number of complex multiplications and additions of the CDMT and FFT-based SC-DMT with different FFT size. It can be seen that the required additional computational complexity of FFT-based SC-DMT is enhanced with the increase of FFT size. In order to realize the fact that the transceiver computational complexity of FFT-based SC-DMT can be lower than CDMT, the FFT size of the former one is chosen as 1024 and the latter one is discussed from 1024 to 8192. Figure 1 shows the computational complexity differences beteween1024-point FFT based SC-DMT and different FFT size (1024 to 8192) based CDMT, in which computational complexity comparison is taken with the same signal time period for SC-DMT and CDMT. The results show that the computational complexity of 1024-point FFT based SC-DMT is higher than 1024 and 2048-point FFT based CDMT, and the same as 4096-point FFT based CDMT. In addition, the computational complexity of 1024-point FFT based SC-DMT is reduced by 7.69% compared with 8192-point FFT based CDMT. The 7.69% complexity reduction is calculated by
In following experiments, we focus on comparing the performance of 1024-point FFT based SC-DMT and 4096/8192-point FFT based CDMT.
Table 1. The computational complexity of CDMT and FFT-based SC-DMT signal with different FFT size.
Fig. 1 Computational complexity of 1024-point FFT based SC-DMT and 1024 to 8192-point FFT based CDMT in terms of same signal length.
2.2 FHT
The FHT technique has attracted a lot of interest as an alternative solution to the FFT due to its lower computation complexity [24,25]. Compared to FFT which is obtained from DFT
The FHT is obtained from DHT as shown below: Where . Note that the DHT is a real trigonometric transform with a self-inverse property.In the DMT modulation, the Hermitian symmetry combined with IFFT are the most widely used scheme. Alternatively, we also can employ the complex to real(C2R) combined with FHT scheme to realize the real value DMT signal modulation with same spectra efficiency as IFFT scheme. The C2R processing can be expressed as
Where x(n) is the modulated QAM symbol, the h(n) and h(2N-n) are the real value data after C2R, and 2N is number of total subcarriers. Then we can get the real value DMT signal according to the (3). In the receiver, we can recovery the x(n) byCompared with FFT, the computational complexity of FHT can be reduced by half by using real value rather than complex value multiplication and addition.3. Experimental setup
Figure 2(a) depicts the offline DSP block and the experimental setup for 20GHz bandwidth DMT signal transmission and reception in IM/DD system. In the transmitter, pseudorandom binary sequence (PRBS) is firstly generated in MATLAB and mapped into M-QAM signal for transmission. The optional n-point DFT or 2n-point DHT is added to reduce the signal PAPR. Figure 2(b) gives out the complementary cumulative distribution function (CCDF) of PAPR for FFT-based SC-DMT and CDMT signals. It is obvious that the DFT-spread technique effectively reduces the PAPR of DMT signal by 2.5 dB at a probability of 1 × 10−3. Then, 5-DMT symbols with QPSK modulation format are inserted in the front of payload symbols as training sequences (TSs) for receiver synchronization and channel equalization. It is worth noting that the TSs are the CDMT signal, as the TSs without DFT-spread processing show better post equalization performance [17]. Next, Zero-Forcing (ZF) based digital pre-equalization is performed to compensate the system bandwidth limitation induced ISI. It is noteworthy that RF signal power should be increased to compensate the pre-equalization induced power loss over bandwidth limited system transmission. After complex conjugation or complex to real conversion (C2R), the signal transformation from frequency to time domain is realized by 2N-point IFFT/FHT. In order to reduce the computational complexity of SC-DMT, the value of N in SC-DMT is lower than CDMT. After that, a cyclic prefix (CP) with 32-point is added to alleviate the ISI induced by chromatic dispersion. The generated real-value signal is uploaded into an 86-GSa/s sampling rate Fujitsu DAC with 16.7 GHz 3-dB bandwidth and 8-bit resolution. A 30 GHz driver with 20-dB gain is employed to amplify the signal from DAC, and a bias-tee is used to create non-negative value signal and reduce the modulation nonlinearity. An optical carrier generated from a 40 GHz 3-dB bandwidth Opnext electro-absorption modulated laser (EML) is directly modulated by the DC coupled signal from bias-tee, then the optical signal is fed into 2-km signal mode fiber (SMF). The optical spectra of CDMT signal with and without pre-equalization are shown in Fig. 2(c). It is quite clear that the system high frequency power fading is compensated by digital pre-equalization. At the receiver, a variable optical attenuator (VOA) is employed to adjust the received optical power. A Discovery Semiconductor photodiode (PD) (DSC-R410 HG) with 20 GHz 3-dB bandwidth is applied to realize signal optical-to-electrical transformation. The detected signal is sampled by a Lecroy 80-GSa/s real time oscilloscope (OSC) and processed off-line in MATLAB. The off-line DSPs including synchronization, CP removing, 2N-point FFT/FHT, optional n-point IDFT/2n-point DHT, Zero-Forcing based post equalization, M-QAM signal de-mapping and BER calculation.
Fig. 2 (a) The offline DSP block and experimental setup diagram (b) CCDF versus PAPR of FFT-based SC-DMT and CDMT signal (c) optical spectra of CDMT signal with and without pre-equalization.
4. Results and discussion
The BER performance of 20 GHz 64-QAM and 128-QAM CDMT signal versus different FFT size are experimentally discussed in optical back-to-back (OBTB) and shown in Fig. 3(a). Obviously, the BER performance is improved with the increase of FFT size in the DMT modulation. Figures 3(b) and 3(c) give out the constellations of received 8192-point FFT based 128-QAM CDMT signal with and without pre-equalization in OBTB transmission, respectively, and Figs. 3(d) and 3(e) are the similarly results of 64-QAM CDMT signal. It can be seen that the digital pre-equalization can effectively enhance the system BER performance. Figures 4(a) and 4(b) give out the error symbol number of each subcarrier with 21 8192-point FFT based 64-QAM CDMT samples without and with pre-equalization, respectively. Obviously, error in CDMT signal without pre-equalization is mainly distributed in high frequency. After pre-equalization, error shows a more even distribution.
Fig. 3 (a) BER performance of M-QAM CDMT signal with different FFT size. Constellation of 8192-point FFT based (b) 128-QAM CDMT signal with pre-equalization and (c) without pre-equalization (d) 64-QAM CDMT signal with pre-equalization and (e) without pre-equalization.
Fig. 4 Error symbol number of each subcarrier with 21 8192-point FFT based 64-QAM CDMT samples (a) without (b) with pre-equalization.
Figure 5(a) shows the pre-equalization coefficients of different FFT size based 20 GHz CDMT signal, which are acquired by the TSs based channel estimation in the calibration stage. We can find that the frequency resolution of 4096-point FFT based CDMT signal is much higher than 256-point FFT based CDMT. With the higher frequency resolution, we can obtain the more accurate channel estimation results, and the channel equalization performance will be enhanced. This is the reason why the system BER performance will be better with the increase of FFT size in the DMT modulation as shown in Fig. 3(a). The electrical spectrums of CDMT signal without and with pre-equalization are given in Figs. 5(b) and 5(c), respectively. It is obvious that the system bandwidth limitation induced high frequency power fading is compensated by digital pre-equalization.
Fig. 5 (a) Pre-equalization coefficients of the 20GHz CDMT signal with different FFT size (b) electrical spectra of CDMT signal without pre-equalization and (c) with pre-equalization.
Figures. 6(a) and 6(b) give out the measured BER performance versus ROP of 120 Gb/s and 140 Gb/s DMT signal, respectively. The FFT size of CDMT is discussed at 4096 and 8192, in which the computational complexity of CDMT is the same as and higher than 1024-point FFT based SC-DMT, respectively. As shown in Fig. 6(a), the receiver sensitivity of 120 Gb/s 1024-point FFT based SC-DMT is improved by 0.7 dB than 8192-point FFT based CDMT at BER of 3.8 × 10−3 over 2-km SMF transmission. When the data rate is enhanced to 140 Gb/s by using 128-QAM modulation formats, the required ROP of 1024-point FFT based SC-DMT and 8192-point FFT based CDMT at BER of 2 × 10−2 over 2-km SMF transmission are −6.2 dBm and −5.5 dBm, respectively. It is the first time to find that the SC-DMT outperforms CDMT while its computational complexity is still lower than the latter one. Furthermore, the performance of FHT-based SC-DMT and FFT-based SC-DMT are experimentally discussed, and the results give out in Fig. 7. It is clearly that the 120 Gb/s 1024-point FFT/FHT based SC-DMT show almost the same BER performance, while the transceiver computation complexity of FHT-based SC-DMT can be reduced by half due to real value rather than complex value multiplication and addition employed for calculation.
Fig. 6 Measured BER versus ROP of (a) 64-QAM DMT signal with 120Gb/s data rate and (b) 128-QAM DMT signal with 140 Gb/s data rate.
5. Conclusion
We experimentally compared the performance of SC-DMT and CDMT signal when the FFT size of FFT-based SC-DMT is reduced to realize the fact that its transceiver computational complexity can be equal or lower than CDMT. The results show that the receiver sensitively of 1024-point FFT based SC-DMT has 0.7 dB improvement than 8192-point FFT based CDMT, both for 120 Gb/s and 140 Gb/s data rate transmission over 2-km SMF. It is the first time to find that SC-DMT with 7.69% lower transceiver computational complexity shows better BER performs compared to CDMT. Furthermore, FHT technique is applied to further reduce the computational complexity, and the results reveal that the FHT-based SC-DMT shows the same BER performance as FFT-based SC-DMT while the transceiver computational complexity can be reduced by half.
Funding
National Natural Science Foundation of China (NSFC) (61601199, 61435006, 61525502); Local Innovation and Research Teams Project of Guangdong Pearl River Talents Program (2017BT01X121, 2018B010114002); The Science and Technology Planning Project of Guangdong Province (2017B010123005).
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