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Abstract
With the requirement for large capacity communication systems, the technology to close the gap between the achievable information rate and the Shannon capacity limit attracts more and more attention. In this paper, we present a novel scheme of trellis coded modulation combined with probabilistic shaping (PS-TCM) in the intensity-modulation/direct detection (IM/DD) system, using generalized frequency division multiplexing (GFDM). The principle of PS-TCM is analyzed with mutual information. We experimentally demonstrate the proposed scheme in the optical GFDM system. The results show that 4 Gb/s PS-TCM-32QAM signal achieves ∼2dB gain over the regular 16QAM signal in the back to back case. After 20 km transmission, the scheme of PS-TCM-32QAM provides 1.8 dB performance gain over that of the regular 16QAM signal. The bandwidth effect of optical filter on the performance of PS-TCM-32QAM signal is analyzed. The proposed scheme has significant gain, flexible spectrum efficiency, and approached Shannon limit, which brings a better trade-off between effectiveness and reliability performance for the multi-carrier optical system.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As the next generation mobile communication system, the fifth-generation (5G) mobile communication is capable of satisfying the exponentially increasing internet traffic all over the world. In order to meet the ever-increasing demand of bandwidth by the end users, nowadays the technology to improve the capacity of optical transmission system has become a highly endeavored research area. High-order modulation assisted with high speed digital signal processing (DSP) has been successfully demonstrated to be able to enhance the capacity of optical fiber communication in the laboratory [1–2]. However, higher order modulation formats, such as 64-ary quadrature amplitude modulation (64QAM) and 128QAM, require higher optical signal to noise ratio (OSNR) to achieve a certain bit error rate (BER) threshold, and they are more susceptible to transmission impairments from the channel and other components in optical network [3–4]. Therefore, the technology of concatenated coded modulation can be employed to improve the performance by providing extra gain [5]. Trellis coded modulation (TCM) is one of the technologies by combining coding and modulation together to achieve significant coding gain without sacrificing the effective spectrum and power efficiency [6–7], and it has been proved to be a promising technology to enhance the capacity of optical systems [8]. TCM was first proposed by G. Ungerboeck in 1982 [9], and then it was investigated by other groups [10–12]. However, the traditional TCM is commonly reviewed under the assumption of uniform channel input. In practice, the optimal channel distribution with the constraint power in Gaussian channel is a Gaussian distribution. There is a gap between the achievable information rate and the Shannon capacity limit for the coded QAM w/o shaping in the additive white Gaussian noise (AWGN) channel.
Probabilistic shaping (PS) technology has been widely used in optical fiber communication systems to narrow the gap to achieve high transmission capacity with lower computation complexity, which can also overcome power limits caused by nonlinearity [13–20]. The principle of PS technology is to optimize the probability distribution of symbols according to the Gaussian channel, which means different points in the constellation carry various amount of information. The large signal-to-noise ratio (SNR) gain of 1.53 dB can be achieved by PS [14–16]. Recently, a PS scheme with 16QAM signal for optical WDM systems was proposed with simulation results only [17]. The rate adaptation and reach increase was experimentally demonstrated by probabilistically shaped 64QAM, which showed that the probabilistically shaped 64QAM signals outperform the regular 64QAM signals by more than 40% in the transmission reach [18]. To improve the performance of the multiple-input multiple-output (MIMO) radio-over-fiber (RoF) system by PS, F. Buchali et.al experimentally demonstrated a reliable 8 Gbaud polarization multiplexed PS 16QAM signal transmitted in a MIMO RoF system with 20 km single-mode fiber-28 (SMF-28) and 2.5 m wireless link at 60 GHz [19]. As recently demonstrated PS can be integrated into the coded modulation scheme with powerful forward error correction (FEC) codes, thus increasing transmission distance and approaching the high data rate demand which is required by the optical fiber systems [20–24]. Until now, no research can be found in the literatures for probabilistic shaped TCM, theoretically or experimentally. It is a promising issue to optimize the probabilistic shaped TCM to fill the gap of Shannon capacity for the optical communication system.
In addition, the generalized frequency division multiplexing (GFDM) based on multicarrier filter bank is a promising modulation technique for the 5G standard, since it has low out of band power leakage and is insensitive to frequency offset and phase noise [25–28]. The GFDM technology with high spectral efficiency enables the optical system to support a huge number of optical network units [29]. The main scenarios for the 5G networks are machine type communication (MTC), tactile internet and wireless area network, which can meet the requirements of vehicular adhoc networking, intelligent transportation, high-definition video, and virtual reality.
In this paper, we propose a novel scheme that combines probabilistic shaping with TCM to achieve near-Shannon performance. The achievable information rate can be optimized by using general mutual information (GMI) numerically. The designed system achieves high OSNR gain and flexible spectrum efficiency. The proposed novel coded modulation scheme is experimentally demonstrated and validated in the data center optical networks.
2. Principle of channel model
The schematic configuration of channel model is shown in Fig. 1, which includes probabilistic shaped-trellis coded modulation (PS-TCM) encoder and GFDM modulation at the transmitter, as well as GFDM demodulation and PS-TCM decoder at the receiver. Each part is described in detail in the following subsections.
2.1 Probabilistic shaped trellis coded modulation
The principle of PS-TCM is shown in Fig. 2. The original bits are divided into four branches by serial-parallel conversion. Then the four branch signals are divided into two groups. One group is variable and denoted by ${x_{i,1}}$, ${x_{i,2}}$, which is responsible for PS with the mapping of different length of bits. The other group is constant with a fixed length and denoted by ${x_{i,3}}$, ${x_{i,4}}$, which is used for convolution coding of TCM. Here, one bit of redundancy check is added to design the TCM coding with a code rate of R = 4/5 [29]. PS encoder is realized by adding redundancy bits according to the symbol prefix [30]. The unequal constellation distribution is achieved with higher proportion of low-energy symbols and lower proportion of high-energy symbols, as shown in Fig. 2(a) and Fig. 2(b). The mapping rule is shown in Table 1, which adds bits with the source code as prefix. It can be seen that the probability of 0 and 1 before shaping is 50% and 50%, the probability of 0 after mapping in Table 1 is 66.7%. After PS encoder and TCM coding, the five bits are mapped into one symbol. Therefore, the expected probability distribution of the constellation points can be met by adjusting the mapping rule for the Gaussian channel, as shown in Fig. 2(c). Moreover, the proposed scheme can also be integrated with FEC shown in Fig. 2 with the dotted boxes.
Table 1. Construction of PS encoder.
The main idea behind PS-TCM is set partitioning, which takes PS and TCM into consideration together to maximize the Euclidean distance between the points of the same subset, and it can improve the error correction ability by transmitting small bits with large constellation, without reducing the bandwidth and power utilization. PS technology is applied to optimize the probability distribution of symbols to increase the spectral efficiency (SE) and reduce the average transmitted energy. Both PS and TCM can be well compatible together. The set partitioning process for PS-TCM32QAM is shown in Fig. 3. Different shapes are used to present various probability distributions. That is, the probability of 4 constellation points in the innermost circle (represented by a triangle) is P1, the probability of the middle 12 constellation points (denoted by a circle) is P2, and the probability of 16 constellation points (represented by a square) in the outermost circle is P3. Here, 4×P1+12×P2+16×P3=1. The constellation is divided into subsets in half and half, and each subset has an increasing distance step by step. After 3 steps the constellation will be finally divided into 8 subsets which are differentiated with different colors. From Fig. 3, it can be seen that considering PS with the constellation, the point in each subset is related to the probability distribution. When calculating the metrics with minimum Euclidean distance, the function will be multiplied by the probability coefficient and modified to be $L\textrm{ = }{\sum\limits_{k = 1}^{{N_c}} {|{{\gamma_k} - \rho {b_k}} |} ^2}$, where Nc is length of the coded sequence, γk is the received signal, bk is the most likely transmitted sequence, andρis the probability coefficient. Therefore, probabilistic shaping and trellis coding are compatible together to improve the performance.
At the receiver side, Viterbi algorithm is used for TCM decoding, which brings complexity as well as gain. The complexity of the algorithm is proportional to the length of transmitted symbols and the number of trellis states [31–32]. In practice, in order to make Viterbi decoding be more suitable for optical network, some researchers have focused on the methods to reduce the complexity of Viterbi algorithm by reducing the number of states [33–34]. However, the complexity reduction is achieved using the M-algorithm, which will introduce the performance damage [34–35]. Therefore, considering both the sensitivity gain and complexity of convolutional encoder, 16-state encoder architecture is selected in the system. In practical application, the complexity can be reduced by reducing the number of states under the condition of the practical demand.
GMI is regarded as an effective approach to represent the capacity of the communication system [36–38]. As a function of SNR, the achieved GMI for different modulation formats including 16QAM, TCM-32QAM, PS-16QAM and PS-TCM-32QAM is shown in Fig. 4. It can be seen that when SNR < 13 dB, the GMI of 16QAM is better than that of TCM-32QAM because the code gain of TCM is small in low SNR region. While the SNR increases to be larger than 13 dB, GMI of TCM-32QAM will converge towards 5bits/symbol, and that of 16QAM will towards 4bit/ symbol, that’s because TCM-32QAM contains one bit of redundancy check. Similarly, When SNR > 12.5 dB, the GMI of PS-TCM-32QAM with entropy of 4.62 is better than that of PS-16QAM because trellis code brings coding gain. It is observed that the GMI is improved significantly with shaping and coding gain below a certain SNR after employing PS and TCM.
The data rate of the proposed scheme can be calculated by R = H (ρ)-m (1-r) [36,38], where H (ρ) is the entropy of the PS-TCM-32QAM, m is the number of bits per symbol and r is the coding rate. In our proposed scheme, the code rate r of TCM is 4/5. Figure 4 shows that the GMI curve is different with the various values of H (ρ) for PS-TCM-32QAM, and therefore we can adjust the H (ρ) to change the GMI of the system. The flexible spectrum efficiency and data-rate transmission can be achieved by adjusting the entropy of the system.
Based on the previous theoretical analysis, the formula of GMI is expressed by [36–37].
For PS-TCM32QAM signal, the required SNR can be written as [39]
Where ρ is the coefficient related to probability distribution, γ represents the gain factor introduced by trellis coding. From Eqs. (1) and (3), we find that the GMI is closely related to SNR and the parameter ν. Figure 5 presents the 3-D diagram of the GMI for PS-TCM-32QAM, which shows that the GMI is directly proportional to the SNR, and inversely proportional to ν.2.2 Principle of GFDM modulation
The principle of GFDM modulation is shown in Fig. 6, which is a multi-carrier modulation scheme using non-rectangular pulse shaping filter. The input signal is upsampled by a factor of N, and the lowpass pulse shaping filter (LPF), tail biting are applied to shape the signal to reduce band radiation. After subcarrier up-conversion and digital-to-analog conversion, the output samples can be expressed as [26–28]
Where x(n,k) is the transmitted symbol on the nth carrier and kth time slot, g(k) is the pulse shaping filter and fn indicates different carriers’ frequency.At the receiver, the GFDM signal is converted to digital baseband signal, and then demodulated by matched filter (MF) receiver with frequency domain equalization [27].
The scheme of PS-TCM based on GFDM provides significant performance gain, thus increasing transmission distance and approaching the high data rate demand that the optical fiber system requires, which enables the system to support a huge number of optical network units. There is no research reported about PS-TCM based on GFDM for data center optical network until now. It is a promising candidate to optimize the PS-TCM in GFDM system, which brings a better trade-off between effectiveness and reliability performance for the optical fiber communication system.
3. Experimental setup
Figure 7 shows the experimental setup for PS-TCM-32QAM optical system. At the transmitter, the lightwave is generated from an external cavity laser (ECL) with the line-width of 100 kHz. The central wavelength of the ECL is 1549.480 nm and its output power can be adjusted from 7.5 dBm to 15 dBm. The Mach-Zehnder modulator (MZM) with 40 GHz bandwidth is adopted to modulate the electrical signal onto the lightwave. The Arbitrary Waveform Generator (AWG) at 25GSa/s with 3 dB bandwidth of 14 GHz is used to produce the electrical signal (PS-TCM-32QAM GFDM) with a bit rate of 4 Gbit/s, which is then sent into the radio-frequency (RF) port of the MZM biased at 5.4 V. Then the optical signal is amplified by a commercial Erbium-doped fiber amplifier (EDFA) before it is launched into 20 km standard single mode fiber (SSMF) with a total loss of 4.5 dB. The variable optical attenuator (VOA) is applied to change the received power of the photodetector (PD). The optical filter is used to suppress the noise out of band. Finally the signal is sampled by an analog to digital converter (ADC) with 50 GSa/s for the subsequent offline DSP. The received signal corresponding to the time domain and frequency domain is shown in Fig. 7(a) and Fig. 7(b), respectively. The offline DSP includes resampling, synchronization, down-conversion, low-pass filtering, down-sampling, MF algorithm, and decoding algorithm. The MF algorithm is used for GFDM demodulation, and the Viterbi algorithm is used for TCM decoding.
Fig. 7. Experimental setup. (a) The detected electrical signal in time domain. (b) The electrical spectrum of the detected signal. DAC: digital-to-analog converter; MZM: Mach-Zehnder modulator; EDFA: Erbium-doped fiber amplifier; VOA: variable optical attenuator; PD: photodetector; ADC: analog-to-digital converter.
4. Experimental results
In the experiment, we have measured the bit error ratio (BER) performance for the 16QAM, TCM-32QAM, and PS-TCM-32QAM signals in GFDM system at the same bit rate of 4 Gb/s. Figure 8 illustrates the BER curve versus different received power. It can be seen that the PS combined with TCM brings the performance gain of about ∼2 dB compared to 16QAM at BER of 1 × 10−3, whereas the PS brings a gain of about 0.7 dB for TCM-32QAM signal.
Figure 9 presents the BER performance for PS-TCM-32QAM with bit rates of 4Gb/s, 6Gb/s, and 8Gb/s, respectively. When the rate is increased by 2Gb/s, ∼1 dB power penalty will be introduced for the system at the BER of 1 × 10−3. It can be considered that when the data rate is higher, the more noise components in the received signal and the BER performance of the signal is worse with the same received optical power.
Figure 10 shows the BER performance versus the received power at different distance for the 16QAM and PS-TCM-32QAM signals, respectively. The bit rate is fixed at 4 Gb/s. It can be seen that 20 km fiber transmission causes ∼0.3 dB power penalty (which is caused from the nonlinearity of the transmission link or devices) for both the PS-TCM-32QAM and 16QAM signal. The PS-TCM-32QAM signal provides a performance improvement of 1.8 dB compared to the 16QAM signal after 20 km transmission.
Figure 11 shows the optical spectrum for PS-TCM-32QAM signal, the central wavelength is 1549.480 nm and the effective bandwidth is less than 0.2 nm. The signal passes through the optical filter before sending to the PD, the bandwidth narrowing will affect the signal performance [40], so the bandwidth effect will be discussed in the following.
The optical Gaussian filter and Bandpass filter is applied separately in the system with the bit rate of 4 Gb/s. Figure 12 represents the performance comparision for PS-TCM-32QAM signal by employing different types of optical filters, which shows the signal distortion with Bandpass filter is worst than Gaussian filter within 0.15 nm bandwidth. While continuing to increase filter bandwidth larger than 0.15 nm, the deployment of the Bandpass filter is much better than gussian filter for PS-TCM32QAM signal. That’s because the amplitude characteristic of the transition zone is steeper for Bandpass filter than that of Gussian filter, when the bandwidth is smaller than 0.15 nm, the performance of Bandpass filter is worse because more signal components are filtered out which will cause distortions for the signal. When the bandwidth is larger than 0.15 nm, more noise will be introduced into the signal for Gaussian filter, so the best option is bandpass filter with 0.2 nm bandwidth.
5. Conclusion
In this paper, we have proposed a novel scheme of PS-TCM based on GFDM for the data center optical system. The achievable benefits of PS-TCM-32QAM are discussed by comparing it with the regular 16QAM and TCM-32QAM both theoretically and experimentally. The experiment demonstrates that the PS-TCM-32QAM signal has a ∼2 dB gain improvement compared to the 16QAM signal in a 4 Gb/s GFDM system for the back-to-back case. After 20 km transmission, the PS-TCM-32QAM signal provides 1.8 dB performance gains over the 16QAM signal. Furthermore, the effect of bandwidth narrowing from different optical filters to the signal is also investigated. The joint method achieved flexible spectrum efficiency, and ∼2 dB significant gains closed to the Shannon capacity limit. The theoretical and experimental results show that the proposed scheme would be a prospective solution for the future data center optical network.
Funding
Fund of State Key Laboratory of Information Photonics and Optical Communications of BUPT (IPOC2018ZT02); National Key R&D program of China (2018YFB1801001); National Natural Science Foundation of China (61425022, 61605013, 61727817, 61875248); Basic Science Research Fund in BUPT (2019RC04).
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