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Abstract
An effective bit-based support vector machine (SVM) is proposed as a non-parameter nonlinear mitigation approach in the millimeter-wave radio-over-fiber (RoF) mobile fronthaul (MFH) system for various modulation formats. First, we analyze the impairments originated from nonlinearities in the millimeter-wave RoF system. Then we introduce the operation principle of the bit-based SVM detector. As a classifier, the SVM can create nonlinear decision boundaries by kernel function to mitigate the distortions caused by both linear and nonlinear noise. In our design, SVM can learn and capture the link characteristics from only a few training data without requiring the prior estimation of the system link. The bit-based SVM only needs log2M SVMs to detect the signal of M-order modulation format. Experimental results have been obtained to verify the feasibility of the proposed method. The sensitivities are improved by 1.2-dB for 16-QAM, 1.3-dB for 64-QAM, 1.8-dB for 16-APSK and 1.3-dB for 32-APSK at BER = 1E-3 with SVM detector, respectively. The proposed bit-based SVM gains a large improvement in the nonlinear system tolerance and outperforms the system employing k-means algorithm.
© 2017 Optical Society of America
1. Introduction
In 5G heterogeneous mobile fronthaul (MFH) network [1, 2], the drastic growth of data traffic generated by video-intensive services for smart mobile terminals is requiring higher bandwidth and data rate in wireless access networks [3]. Radio-over-fiber (RoF) technology which provides high-level centralization and minimizes complexity of data distribution system is considered as a promising platform next generation integrated optical and wireless access network due to its large bandwidth, low transmission loss over optical fibers while maintaining the mobility of wireless services [4, 5]. However, the traditional microwave band below 10-GHz which has been widely used will be exhausted soon. Therefore, higher frequency spectrum attracts much more attentions recently in order to further increase the bandwidth. Thus the large bandwidth available in 30-300 GHz millimeter-wave (mm-wave) band is a promising candidate for both indoor and outdoor small-cell coverage in the 5th generation communications [6]. The unlicensed 60-GHz band provides a 7-GHz bandwidth in the United Stated for mobile applications and is supported by IEEE 802.11ad [7]. Hence, mm-wave RoF based MFH is a tremendous candidate in 5G mobile communication network as shown in Fig. 1.
In mm-wave RoF-based MFH systems, both linear and nonlinear impairments occur inevitably. System impairments caused by fiber nonlinearity, phase noise, chromatic dispersion, the nonlinear response of optical modulators and IQ imbalance in down conversion all have the potential to contribute to transmission impairments [5, 8]. The nonlinearities in RoF transmission system play a dominant role in performance degradation when the analog RoF and wireless links are cascaded together [9–11]. In mm-wave RoF systems, optical Mach-Zehnder modulators (MZMs) can be employed in the baseband unit (BBU) to generate optical millimeter wave signals by optical carrier suppression (OCS) modulation and carry data modulation [12]. The MZM has a nonlinear cosine transfer function, which leads to a distinct nonlinear mechanism that is data-dependent cross-modulation (XM) especially for vector signals (such as 16-QAM and 64-QAM) [5]. The signals transmitted over fiber suffer from the Kerr effects, the most common nonlinear effects are self-phase modulation (SPM) and four-wave mixing (FWM) [13]. In addition, amplified spontaneous emission (ASE) noise caused by optical amplifiers like EDFA and phase noise introduced by wide laser linewidth also degrade the system performance [14]. In addition to optical impairments, electrical signals can be degraded by IQ imbalance, electrical-amplifier nonlinearity and inherent nonlinearity of optical to electrical conversion [15].
Various techniques have been proposed to mitigate the impairments in mm-wave RoF systems. Among them, digital signal processing (DSP) based algorithms are commonly applied for signal detection and channel impairment compensation because of its flexibility and low-cost. In [16], linear impairments have been compensated effectively by means of linear signal processing algorithms. DSP-assisted optical coherent detection with a two-tone local light has been utilized to reduce the laser phase fluctuation [17]. The joint effects of the three impairments (phase noise, IQ imbalance and amplifier nonlinearity) were analyzed theoretically [18]. A digital receiver has been designed to eliminate IQ imbalance [19]. Nonlinearities caused by intensity MZMs in RoF system have been investigated by both simulations [20] and experiments [21]. Based on structuring the likelihood function, a close-form maximum likelihood-based data detection algorithm [22] and a maximum posteriori detector based on the Bayesian framework of factor graphs were proposed [23]. The k-means algorithm, widely used clustering algorithm in nonlinear signal processing was also utilized in compensating nonlinear noise [24, 25]. However, most of the aforementioned methods remain highly dependent on computational complexity and the parameters of the transmission link. It is impractical to master all parameters of a dynamic optical-wireless integrated network. In addition, there are almost no previous methods designing for high-order modulation signals such as 32QAM or 64-QAM. And nearly every approach focuses on compensating single type of impairments, but any existed system is impossible to suffer from only one single impairment during transmission. Furthermore, majority of previous schemes were mostly verified in simulation model instead of experimental verification. Therefore, efficient and flexible DSP algorithms for multi-impairments compensation in mm-wave RoF system are urgently needed for research.
Machine learning, considered as a powerful and promising non-parameter tool, has been widely applied in various areas [26]. Recently, machine learning techniques have been introduced in optical communication systems [27,28], in which area, we also proposed several schemes of linear and nonlinear impairments mitigation by applying machine learning algorithms such as artificial neural network (ANN), distance weighted-k-nearest neighbors (DW-KNN) and convolutional neural network (CNN) [29–33]. To our best knowledge, there are very few schemes for mm-wave RoF system utilizing machine learning methods. In [34], an ANN nonlinear equalizer was used in mm-wave RoF system in order to mitigate nonlinearities. However, it also suffered from computational complexity and a large number of training data leading to time-consuming. In addition, there are only few schemes considering high-order modulation signals in mm-wave RoF system. The support vector machine (SVM) as one of powerful, intelligent and widely used machine learning algorithms [35], which requires a small number of training data, has been successfully implemented in multiple scenarios with relative lower complexity [36–39] and is suitable for mm-wave RoF system especially for high-order modulation formats.
In this paper, we propose a novel bit-based SVM nonlinear detector for impairments mitigation in mm-wave RoF mobile fronthaul, which is capable compensating both linear and nonlinear degradations. SVM as a non-parameter method is applied for a single carrier (SC) transmission system with lower peak-to-average power (PAPR) compared to orthogonal frequency division multiple access (OFDMA) and it is appropriate for mm-wave RoF system due to its abundant bandwidth and low-cost components. SVM can learn and capture the link properties from only a few training data and then generate the optimum nonlinear decision boundary which classifies the data precisely to avoid the errors introduced by amplitude and phase noise. With the help of bit-based SVM detector, the impairments of single-carrier 16-QAM and 64-QAM mm-wave RoF systems are mitigated effectively without any prior information or heuristic assumptions. In addition, the additional theoretical analysis of SVM is provided in detail and further extend it to the 16 amplitude phase shift keying (16-APSK) and 32-APSK mm-wave RoF systems, which have received considerable attentions because of the better nonlinear tolerance and lower PAPR. A mm-wave RoF-based MFH experimental test-bed with various high-order modulation format signals is used to verify the feasibility of the bit-based SVM nonlinear detector. The bit-based SVM with relatively low computation and complexity plays an essential role in mitigating multi-impairments in single-carrier mm-wave RoF transmission.
2. Principle of bit-based SVM detector for mm-wave RoF system
Multi-impairments mitigation for multilevel modulation signals in mm-wave RoF based mobile fronthaul by means of bit-based SVM is achieved via numbers of parallel binary SVMs on the basis of each bit of high-order modulation signals. Each binary SVM splits the clusters of data into two groups using the optimum binary classification hyperplane, which is achieved by learning system’s properties from only a few training data in the training step. Then under the established classification strategies, SVM conducts classification in the testing step according to the hyperplane. Therefore, it is not essential to capture any prior characteristics of the transmission system. In the two-class separable case, the hyperplane f(x) has the following form:
where the vector w and the scalar b are the parameters of the hyperplane. The hyperplane function f(x) is learned from training vectors with the corresponding labels l, where l ∈ {− 1, + 1}, and the test data are classified according to the sign of f(x) as Eq. (2).Figure 2 shows the example of separable data from two groups in two dimensions. The two clusters represent “0” bit and “1” bit of multilevel modulation signals, respectively. The nonlinear boundary, that is hyperplane, can be obtained by utilizing the kernel function which helps to solve the nonlinear separable situation. In our scheme, the Gaussian radial basis function (RBF) is chosen as the kernel function [34]:
So the two clusters are separated by the nonlinear hyperplane effectively. The detailed mathematic principle of the SVM and derivation for classification using kernel function are discussed accurately in [35].Based on the theory of binary SVM classifier, a bit-based SVM detector is proposed for high-order modulation signals in mm-wave RoF mobile fronthaul. If different constellation points are regarded as different clusters of data, it is inevitable to build multiclass classifiers by using many binary SVMs to separate them precisely. One of the most commonly used multiple classifier schemes is the “one-against-all” approach [24], in which the number of binary SVM required is the same as the number of clusters. Therefore, M-QAM signal requires M binary SVM classifiers. For instance, 16-QAM signal needs 16 binary SVMs. However, this method is time-consuming and needs more training data due to the large number of binary SVM classifiers. In this paper, the bit-based SVM scheme we propose only requires log2M two-class SVM for M-QAM signal. In our method, each signal's category is labeled in binary format with each bit modeled by a conventional two-class SVM. Each SVM conducts binary classification with nonlinear boundary under a learned classification strategy for the received signal. There are two process in the whole classification procedure, namely, training step and testing step. The purpose of training process is to obtain the nonlinear hyperplane from a few training data, then classification will be completed according to the previous hyperplane namely the sign of f(x) in the testing process:
Figure 3(a) illustrates the classification strategy for 16-QAM. It can be seen that all the constellations points of 16-QAM can be detected correctly by only 4 binary SVMs. With the help of the kernel function, nonlinear compression and distortion of constellations can be detected precisely because of the nonlinear hyperplane. As we know, for higher order modulation signals, the tolerance of nonlinearity is relatively lower than low-order modulation signals. What’s more, the detection process for higher order modulation signals is more complicated and inflexible. The bit-based SVM detector can be utilized in 64-QAM signals as well. Figure 3(b) shows the detection strategy of 64-QAM, only 6 two-class SVMs are required to detect the signal correctly by utilizing the bit-based SVM method. The gray-coded constellations are applied for both 16-QAM and 64-QAM signal.In addition to the conventional modulation format, APSK which has higher tolerance of nonlinearities than QAM is also considered in this paper. APSK signals are characterized by a smaller number of amplitude levels than QAM which leads to lower PAPR, and lower PAPR can increase energy efficiency and allow minimizing many effects of nonlinear distortions [40]. Hence, APSK is beneficial specially in highly nonlinearly distorted scenarios. Choosing a suitable mapping scheme is crucial for APSK construction. Some distributions of APSK constellation are not applied to Gray mapping, which may lead to high demapping loss [41]. In our scheme, the (88)-APSK is chosen for test since it shows a better nonlinearity tolerance than other constructed constellations [42] as shown in Fig. 4(a). What’s more, the detection of APSK signals are relatively more complex than QAM, especially for higher-order modulation format signals. Bit-based SVM detector we propose is also suitable for APSK, which has the same complexity as QAM and can mitigate both nonlinear and linear impairments effectively. Figures 4(a) and 4(b) show the classification strategy of 16-APSK and 32-APSK by bit-based SVM, respectively. According to the above classification scheme, 16-APSK needs 4 binary SVMs and 32-APSK needs 5 binary SVMs.
3. Experiment setup
In this section, we demonstrate an end-to-end RoF system for 56.2-GHz single-carrier mm-wave to verify the feasibility of the proposed bit-based SVM detector. The experimental setup is shown in Fig. 5 consisting of a baseband unit (BBU), a remote radio head (RRH) and a user equipment (UE).
Fig. 5 Experimental setup of the mm-wave RoF system. BBU: baseband unit. RRH: remote radio head. DFB: distributed feedback laser. MZM: Mach-Zehnder modulator. AWG: arbitrary waveform generator. EDFA: Erbium doped fiber amplifier. SMF: single-mode fiber. PD: photo-detector. EA: electrical amplifier. DSO: digital oscilloscope.
In the experiments, intermediate frequency MQAM (IF-MQAM) and MAPSK (IF-MAPSK) modulation formats are utilized to transmit the multilevel symbols. After up-sampled, the signals are converted to IF which is at 600-MHz. The baud rate of this system is 0.4-GBaud/s, so the bit rates of 16-QAM, 64-QAM, 16-APSK and 32-APSK are 1.6-Gbps, 2.4-Gbps, 1.6-Gbps and 2.0-Gbps, respectively. The samples are converted to analog waves by an arbitrary waveform generator (AWG) running at 4-GS/s. A continuous wave (CW) distributed feedback laser at 1554.17-nm with linewidth of 10-MHz is used in the BBU as a light source. The double-side-band optical-carrier- suppression (OCS) modulation method is applied by the first Mach-Zehnder modulator (MZM) and 28.1-GHz sinusoidal electrical signal source. The OCS optical spectrum is shown in Fig. 6. Then the signals are modulated by the second MZM and then amplified by an erbium-doped fiber amplifier (EDFA) before transmission of 15-km single mode fiber. At the RRH, the two first-order sidebands beat in the photo-detector (PD) with a bandwidth of 60-GHz, and up-convert the down-link (DL) data to mm-wave frequency at 56.2-GHz. Amplified by a 60-GHz power amplifier (PA), the DL signal is transmitted through the RRH antenna with a gain of 20-dBi. The 56.2-GHz mm-wave wireless signal is delivered over a distance of 1-m to the receiving antenna. At the UE, after the receiving antenna, an envelope detector is utilized for down-conversion from radio frequency to IF, which helps to overcome the phase noise produced by the laser. A real-time oscilloscope samples the waveform at 10-GS/s. Then the received signal is processed offline by means of Matlab including the steps of synchronization, down-conversion to baseband and normalization. After that, the signal is detected by the proposed bit-based SVM detector.
4. Experimental Results
In this section, experimental measurements are carried out to validate the proposed scheme. To assess the nonlinear mitigation performance of the bit-based SVM for mm-wave RoF system, the Gaussian radial basis function is applied as kernel function for each SVM. In order to determine the performance of the bit-based SVM, we compare the scheme with regular maximum likelihood (RML) detector and k-means algorithm [24, 25] which is another widely used clustering algorithm in nonlinear signal processing. The regular maximum likelihood algorithm conducts detection by computing the Euclidean distance between received signal and original constellation points and then finding the minimum distance. The k-means algorithm computes the means of the clusters and then updates the centroids of each cluster, at last the signals are detected by the final centroids. In our experiments, 16-QAM, 64-QAM, 16-APSK (88) and 32-APSK modulation format signals are used to test and signal impairments are evaluated in terms of bit error rate (BER).
Figure 7(a) shows the BER performance of 16-QAM signal as a function of amplitude Vin of input signals of the amplifier before the second MZM (as shown in Fig. 5) with bit-based SVM, k-means and RML. Vin is an essential factor for system performance, the higher value of Vin is able to increase the power of signals leading to higher signal noise ratio (SNR) of system. It can be seen that the nonlinear distortion of the signal becomes more serious with the increase of Vin. From the three constellations with the three different Vin on the right side of Fig. 7(a), the nonlinear compression is induced by nonlinear XM, phase rotation is caused by phase noise due to laser linewidth and diamond-like distortion is caused by IQ imbalance in the process of down-conversion. The compressions of constellation points are from outside to inside regions and the outer points are more obvious particularly. Firstly, BER decrease and reaches the optimal value with the increase of Vin because of the improvement of SNR. Then BER begins to increase with the constantly increasing Vin due to the influence of nonlinearity. The proposed SVM detector has a 47-mV improvement of Vin compared with k-means at BER = 1E-3. Figure 7(b) shows the BER as a function of received optical power (ROP) for Vin = 350-mV. The bit-based SVM detector has the absolutely advantage than the other two methods at high ROP. The benefits diminish as the decreasing of ROP because of the decrease of SNR. A detection example using the bit-based SVM for 16-QAM with 380-mV Vin shown in Fig. 8. In each subplot, the red points represent bit “1” and bit “0” marked by the blue points, separated by the green line, namely hyperplane.
Fig. 7 (a) Measured BER as a function of the Vin for 16-QAM; (b) Measured BER as a function of received optical power for 16-QAM.
Figure 9(a) illustrates the BER performance of the 64-QAM signal as a function of Vin. The trend of the BER is the generally same as the BER of 16-QAM as a function of Vin expect for a slight difference that the Vin value at the optimal BER value for 64-QAM signal is much lower than the Vin for 16-QAM signal. As we expected, 64-QAM signals are more vulnerable to nonlinearity than 16-QAM signals. When the Vin value is 170-mV, the benefits of the bit-based SVM method are limited as the random noise of the signals dominates the BER performances which leads to low SNR. The BER decreases and then reaches its optimal value along with the increasing of Vin due to the larger SNR. With further increment Vin, the nonlinear compression effects become more serious which results in the blended constellation points. In this case, even the bit-based SVM is unable to detect the data precisely as shown in the c point of Fig. 9(a). Figure 9(b) gives the BER performance of 64-QAM signal as a function of the received optical power under Vin = 250-mV. A 1.3-dB sensitivity improvement is achieved by using the bit-based SVM compared with k-means. Figure 10 shows the detection example using the bit-based SVM for 64-QAM at 240-mV Vin which consists of six SVMs. In each subplot, every bit is separated by the green nonlinear hyperplane.
Fig. 9 (a) Measured BER as a function of the Vin for 64-QAM; (b) Measured BER as a function of received optical power of 64-QAM.
In our experiments, APSK signals are also tested to verify the feasibility and flexibility of the proposed bit-based SVM detector in addition to QAM signals. APSK signals are specially beneficial in highly nonlinearly distorted scenarios because they are characterized by a smaller number of amplitude levels than QAM which leads to lower PAPR, and lower PAPR can increase energy efficiency and allows minimizing many effects of nonlinear distortions. Figure 11 illustrates the results of BERs for 16-APSK and 16-QAM signals as functions of Vin. The (88)-APSK constructed constellations are used in this experiment. It can be observed that the 16-QAM outperforms 16-APSK constellations in the low Vin less than 390-mV, while the 16-APSK signals show a significant performance improvement in the high voltage values. The Vin value at the optimal BER for 16-APSK is 50-mV higher than 16-QAM. As expected, 16-APSK signals have better tolerance of nonlinearity than 16-QAM signals.
The BER results of (88)-16-APSK as a function of Vin is depicted in Fig. 12(a). The tendency of the BER for 16-APSK is similar to the BER for 16-QAM except that the Vin value at the optimal BER value is higher than 16-QAM. The reason of the BER tendency is the same as mentioned above. The proposed SVM detector has a 30-mV improvement of Vin compared with k-means at BER = 1E-3. Figure 12(b) shows the BER performances of the 16-APSK signal as a function of the received optical power under Vin = 450-mV. It can be seen that the proposed method can improve the sensitivity from −16.8-dBm to −18.6-dBm. The classification of (88)-16-APSK signal based on the proposed method under Vin = 420-mV is shown in Fig. 13. Four binary SVMs are applied to detect the 16-APSK signal according to each bit. The nonlinear boundaries are marked as green lines.
Fig. 12 (a) Measured BER as a function of the Vin for 16-APSK; (b) Measured BER as a function of received optical power of 16-APSK.
At last, the 32-APSK signal, which is a widely used high-order modulation format, is utilized in our experimental test. Figure 14(a) shows the measured BER performance of 32-APSK signal as a function of Vin. As the BER of 16-APSK, the BER of 32-APSK also experiences decrease and increase successively with the growing of Vin. It can be seen that the proposed SVM scheme improves the value of Vin from 290-mV to 312-mV at BER = 1E-3 compared with k-means detector. Figure 14(b) gives the BER results of 32-APSK signal as functions of the received optical power under Vin = 300-mV. A 1.3-dB sensitivity improvement is obtained by means of the bit-based SVM compared with k-means. It can be observed that 32-APSK is more susceptible to nonlinear impairments than 16-APSK. A detection example using the bit-based SVM for 32-APSK with 290-mV Vin is shown in Fig. 15.
Fig. 14 (a) Measured BER as a function of the Vin for 32-APSK; (b) Measured BER as a function of received optical power of 32-APSK.
From the results described above, it can be validated that the proposed bit-based SVM detector is feasible to mitigate both linear and nonlinear impairments in the mm-wave RoF system. It is suitable for both QAM and APSK signals, especially for high-order modulation signals. What’s more, the bit-based SVM has better performance for QAM signals than APSK signals on mitigating nonlinear impairments since APSK signals have more relative complicated hyperplanes than QAM signals. And the proposed detector is more effective for 16QAM and 16APSK signals rather than higher-order modulation signals because higher-modulation signals are more sensitive for nonlinear effects and they have more complex hyperplanes. In addition, the computational complexity of SVM is mainly determined by the number of SVMs and the number of support vectors (SVs) for each SVM. In this scheme, the proposed bit-based SVM only requires log2M binary SVMs for M-QAM and M-APSK signals. The complexity of the bit-based SVM testing procedure scales approximately as Ο(nlog2M) in which n is the number of testing data. Only few training data is needed to create the hyperplanes in test stage implying that bit-based SVM has a potential advantage of low complexity. However, the complexity of k-means algorithm is Ο (Mnt) in which M is the number of M-order modulation, n and t represent the number of testing data and iterations respectively. When the number of testing data is very large, k-means will suffer from much higher complexity. So the bit-based SVM not only achieves better performance but has relatively lower complexity compared with k-means in terms of mitigating nonlinear impairments in mm-wave RoF system.
5. Conclusion
In this paper, for the first time as we know, we proposed a bit-based SVM detector for the single-carrier 16-QAM, 64-QAM, 16-APSK and 32APSK signals transmissions in mm-wave RoF based mobile fronthaul. Both theoretical analysis and experimental measurements were carried out, and consistent results were obtained to verify the feasibility of the proposed method. We first analyzed various transmission impairments including both linear and nonlinear impairments in single-carrier mm-wave RoF system. It was observed that QAM and APSK signals were both suffered from linear and nonlinear distortions during the transmission in the mm-wave RoF system, and higher-order modulation formats were more susceptible to nonlinear effects. The proposed bit-based SVM scheme can improve the system performance without considering the specific characteristics of channel link, the experimental results showed that the bit-based SVM allowed higher value of Vin which affects the system performance in terms of the SNR significantly. Compared with the k-means algorithm, the bit-based SVM achieved lower BER values for a fixed Vin, and increases the value of Vin by 47-mV for 16-QAM, 41-mV for 64-QAM, 30-mV for 16-APSK and 22-mV for 32-APSK at BER = 1E-3. Meanwhile, the sensitivities were improved with the proposed method for all four modulation formats, the received sensitivity improvements were 1.2-dB for 16-QAM, 1.3-dB for 64-QAM, 1.8-dB for 16-APSK and 1.3-dB for 32-APSK at BER = 1E-3. Therefore, the proposed bit-based SVM is a powerful and promising tool for mitigating nonlinear impairments in future 5G mobile fronthaul.
Funding
National Natural Science Foundation of China (NSFC) Project No.61372119.
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