A Spectrally Efficient Digitized Radio-over-fiber System with K-means

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A Spectrally Efficient Digitized Radio-over-fiber System with K-means Clustering based Multidimensional Quantization LU ZHANG,1,3 XIAODAN PANG,2,3 OSKARS OZOLINS,2 ALEKSEJS UDALCOVS,2 SERGEI POPOV,3 SHILIN XIAO,1 WEISHENG HU,1 AND JIAJIA CHEN3,4* 1State

Key Laboratory of Advanced Optical Communication System and Networks, Shanghai Jiao Tong University, Shanghai 200240, China and Transmission Laboratory, RISE Acreo AB, Kista 16425, Sweden 3KTH Royal Institute of Technology, Kista 16440, Sweden 4MOE International Laboratory for Optical Information Technologies, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, China. *Corresponding author: [email protected] 2Networking

Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX

We propose a spectrally efficient digitized radio-overfiber (D-RoF) system by grouping highly-correlated neighboring samples of the analog signals into multidimensional vectors, where the k-means clustering algorithm is adopted for adaptive quantization. A 30Gbit/s D-RoF system is experimentally demonstrated to validate the proposed scheme, reporting carrier aggregation of up to 40 100-MHz orthogonal frequency division multiplexing (OFDM) channels with quadrate amplitude modulation (QAM) order of 4 and aggregation of 10 100-MHz OFDM channels with QAM order of 16384. The equivalent common public radio interface rates from 37-Gbit/s to 150-Gbit/s are supported. Besides, the error vector magnitude (EVM) of 8% is achieved with the number of quantization bits of 4, and the EVM can be further reduced to 1% by increasing the number of quantization bits to 7. Compared with conventional pulse coding modulation based D-RoF systems, the proposed DRoF system improves the signal-noise-ratio up to ~9-dB and greatly reduces the EVM given the same number of quantization bits. © 2018 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.4080) Modulation; (060.5625) Radio frequency photonics. http://dx.doi.org/10.1364/OL.99.099999

Driven by emerging Internet based services, such as virtual reality, high-definition videos for terrestrial televisions, the traffic demand is growing rapidly [1,2]. Fiber-optics is considered as a promising way to transmit signals thanks to its inherent merits of large capacity. Radio-over-fiber (RoF) system is an attractive technique because of its centralized processing ability, leading to high cost

and energy efficiency of network management [1]. Nowadays, the implementations of RoF systems are mainly focusing on the analog transceivers and the signal processing behind them. Although the analog RoF (A-RoF) systems provide a lean solution for signal transmission, it always requires photonics and electrical devices with high linearity to avoid nonlinear distortions to the analog signals [3]. Besides, since analog signals (e.g. orthogonal frequency division multiplexing, OFDM) typically have a high peak-toaverage power ratio (PAPR), complex digital signal processing (DSP) algorithms and system configurations [4,5] are needed, which further increases the system cost. Compared to A-RoF systems, digitized RoF (D-RoF) systems transmit the digitized samples of analog signals that provides strong robustness against the system nonlinear impairments [3]. However, the conventional D-RoF systems use uniform quantization of analog signals requiring a large number of quantization bits and hence resulting in low spectral efficiency. For instance, common public radio interface (CPRI) in mobile fronthaul uses 15 quantization bits based non-companding pulse coding modulation (PCM), which requires ~100-Gbit/s data rate to support only 21 100MHz OFDM channels [3]. To solve the capacity crunch in D-RoF systems, several approaches have been proposed [6-11]. However, the function splitting proposed in [6] needs complicated network configurations and the centralized processing gain of D-RoF systems is influenced. The delta-sigma modulation adopted in [7,8] needs high sampling rate, and the statistical estimation and companding algorithms in [9,10] yield a limited reduction of quantization bits. Since continuous samples of the analog OFDM signals typically do not vary sharply, exhibiting strong sample-to-sample correlations, [11] proposes linear predictor to quantize the differential samples of OFDM signals to decrease the required quantization bits. Nevertheless, it needs online training to configure the predictor coefficients.

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Fig. 1. Experimental setup for the proposed D-RoF system, (a) electrical spectrum of one OFDM symbol before quantization, (b) equalized PAM-4 eye diagram.

In this Letter, we propose a novel method that groups highlycorrelated neighboring samples of the analog signals (e.g. OFDM) into multidimensional vectors, and adopts the k-means clustering algorithm for adaptive quantization. We significantly extend the previous work [12] by 1) introducing theoretical derivations on how to group multidimensional vectors by using k-means clustering algorithm, 2) optimizing training processing to improve the system performance and 3) carrying out extensive proof-ofconcept experiments to verify the proposed quantization scheme. Figure. 1 shows the experimental setup for the proposed D-RoF system. A 30-Gbit/s D-RoF system is carried out over 20-km standard single mode fiber (SSMF). The evaluated analog signal is OFDM with 2048-inverse fast Fourier transfer (IFFT) points. The sampling rate per OFDM symbol is 122.88-MSa/s and the bandwidth is 100-MHz. The spectrum of the OFDM signal is shown in Fig. 1(a). The digitized signals are mapped to 4-level pulse amplitude modulation (PAM-4) with the baud rate of 15-Gbaud. The amplified signals are downloaded to the arbitrary waveform generator (AWG, 50-GSa/s). A Mach-Zehnder modulator (MZM) is used for modulation with an external cavity laser (ECL) (16-dBm, 1550-nm). The optical signal is transmitted over 20-km SSMF. At the receiver, a variable optical attenuator (VOA) is used to set the received optical power for the error vector magnitude (EVM) measurements. The signal is detected by an 8-GHz PIN photodiode. Then, the signal is captured by digital storage oscilloscope (DSO, 80-GSa/s) and processed offline. A decisionfeedback equalizer (DFE) with 41 feed-forward taps and 7 feedback taps is used for the PAM-4 signal recovery. The equalized error-free eye diagram after SSMF transmission is shown in Fig. 1(b). As shown in Fig. 1, the digitization of OFDM signal at the transmitter is composed of 3 steps, namely, 1) vector construction, 2) k-means clustering and 3) multidimensional quantization. In the first step, the discrete time domain in-phase (I) and quadrate (Q) OFDM signals si with length L {real(si), imag(si)|i∈[1,L]} are converted into vectors by grouping N samples into N-dimensional (N-D) vectors (e.g. xi={real(si), imag(sj), real(sk) | i,j,k∈[1,L] } forms a 3D vector). There are mainly two options for vector grouping: Option-1 is realized by grouping consecutive I-way samples and consecutive Q-way samples (e.g., xi={real(si), real(si+1)|i∈[1,L-1]})

Normalized OFDM Samples (Dimension-2)

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Fig. 2. 2D clustering and quantization.

independently, while Option-2 groups I-way and Q-way samples at the same time instant (e.g., xi={real(si), imag(si)|i∈[1,L]}). Option-1 is chosen in the implementations, since there are no correlations between orthogonal I-way and Q-way samples at the same time instant in Option-2. The second step is the k-means clustering for the N-dimensional vectors. The M centroids {c1,…,cM} of clusters are generated randomly in the initial stage. Then the k-means algorithm partitions the vector space by associating each vector xi to a single cluster using nearest neighbor search [13]. Therefore, given an input vector xi, it belongs to cluster V (cj) if: (1) d ( xi , c j )  d ( xi , cq ), q  j , where d (xi, cj) is the Euclidean square distance between vector xi and cj. The nearest neighbor search can be further associated to the pertinence function εj (xi): 1, if c j  nearest neighbor of xi . (2)  j ( xi )   0, otherwise  The distortion obtained by representing the vector xi by its corresponding quantized version cj (nearest neighbor) is: M

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Eq. (1) and Eq. (4) are related to the partitioning of the signal vectors and the update of codebook (i.e. the group of codewords). δ is denoted as the distortion threshold of stop criterion, and the update ends at k-th iteration if: D(k  1)  D(k )  ， k  1 . D(k )

(5)

The k-means clustering produces M clusters, which correspond to M quantization levels and log2(M) quantization bits, and the number of quantization bits per sample is log2(M)/N. Fig. 2 shows an example of 2D clustering for samples of the OFDM signals. For each vector, it falls into one cluster with a typical codeword, and then it is quantized as the corresponding codeword. The cluster edge (i.e. decision threshold) is determined by partitioning the signal space by Voronoi boundaries [14]. The clusters are not evenly distributed due to high PAPR of the OFDM signals, which

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Fig. 3. (left) 1D clustering and quantization, (right) probability distribution of OFDM samples.

demonstrates that the proposed scheme can be adaptively adjusted to the statistical properties of OFDM signals. Fig.3 shows an example of 1D clustering of samples of the OFDM signals and the probability distribution of OFDM samples. It can be seen that the distribution of OFDM samples [9] fits Gaussian distribution S ~ N (μ, σ2) with mean value μ = 0. Besides, 1D quantization can also adapt to the high PAPR signals with uneven quantization levels. Comparing 1D and 2D quantization schemes, it can be seen the vectors are more centralized along positive proportion distribution (e.g. y = x for 2D space). It is because of the high correlations of neighboring OFDM samples without sharp changes. This indicates that more redundant information space can be removed with the increase of quantization dimension. Finally, in the quantization step, each vector is firstly mapped to the index of its corresponding codeword, then transferred to binary data. The quantized data of different analog symbols, which corresponds to different carriers or users, is multiplexed in time domain and sent to the transmitter. In other words, the carrier aggregation in our proposed D-RoF system is done in time domain. There are two ways to perform the clustering and get the codebooks in the proposed D-RoF system, namely supervised and unsupervised clustering. The difference between the supervised and unsupervised clustering is whether to use or not to use the training symbols for the clustering. For the supervised clustering, the k-means clustering is trained offline and the quantization of the untrained vectors use the codebook generated by the training symbols, so the signals do not need to pass the clustering module in every quantization implementation. On the other hand, the

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Fig. 4. EVM versus the number of training symbols, (a-c) recovered constellations with 1D, 2D, 3D quantization.

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Fig. 5. EVM performance versus the number of quantization bits.

unsupervised clustering updates the codebook in every quantization implementation. The computational complexity of the unsupervised clustering based quantization in operation is k*M*L+M*L/N and the computational complexity of the supervised clustering based quantization in operation is M*L/N. Besides, the storage complexity of the unsupervised quantization in operation corresponds to (M+L/N)*N and the storage complexity of the supervised one in operation is M. The complexity of the supervised scheme is lower than the unsupervised one, but the performance might be affected by inaccurate estimation of the signal distributions due to a limited set of training symbols. Thus, the supervised scheme often needs a large number of offline training symbols to get satisfied performance. On the other hand, the unsupervised scheme has very high complexity so that might be not practical for real implementations. Nevertheless, the unsupervised scheme can be used as the benchmark to understand the performance upper limit. In our experiment, the quantization performance is firstly evaluated with error-free PAM-4 20-km SSMF transmissions. The EVM performances versus the training symbols with 1D, 2D and 3D quantization are shown in Fig. 4. The unsupervised clustering is shown as benchmark for comparison. The constellation graphs of unsupervised quantization are shown in Fig. 4(a-c). The number of quantization bits per sample is set to be 5, the aggregated 100MHz OFDM channels are 24 here, and the length per symbol is 1.2288×106 points. δ= 0.01% in Eq. (5) is set as the stop criterion for iterations, and the iteration number k is in the order of ~100 times. The results show that the 1D quantization requires much less number of training symbols to get an optimized performance, and the performance penalty is negligible. Comparatively, the 2D quantization requires more training symbols, and there is ~ 0.5% EVM penalty for 2D supervised quantization. Moreover, it is observed that the 3D quantization requires a larger number of training symbols and 900 training symbols are not long enough to approach the optimal convergence. There is more than 1% EVM penalty for the 3D supervised quantization with 900 training symbols. Although increasing the quantization dimension requires more training symbols to get stable performance, the EVM is considerably reduced when a higher dimensional quantization is adopted. Besides, since the training is processed offline and the offline training is not much affected by dynamic channel factors, it does not need to be repeated for every transmission, and its influence on the operational complexity is minor.

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Fig. 6. (a) SNR versus the subcarrier index, (b) EVM versus the received optical power.

The EVM performance in terms of quantization bits per OFDM sample is shown in Fig. 5. The EVM thresholds are given according to 3GPP release 12 [15] and DOCSIS3.1 [9]. The EVM performance is improved by increasing the number of quantization bits. With the unsupervised clustering, 1D/ 2D/ 3D quantization schemes can realize EVM smaller than 1% and are able to approach ~ 0.1% with a large number of quantization bits, which can support errorfree transmissions up to 16384-QAM. For the 3D quantization, EVM of 8% is achieved with the number of quantization bits of 4 and 1% EVM is achieved with the number of quantization bits of 7. Besides, with the number of training symbols up to 900, the supervised quantization can also support error-free OFDM signal transmissions with QAM orders up to 4096. The average signal-noise-ratio (SNR) of aggregated OFDM channels versus the subcarrier index is shown in Fig. 6(a). PCM is also presented for comparison. The number of quantization bits per sample is set to be 5 for all the considered cases. It can be seen that the quantization noise is uniformly distributed for all subcarriers. With the increase of quantization dimensions, the average SNR is greatly improved. Compared with the PCM based quantization, the 1D, 2D and 3D quantization increase the average SNR with ~ 1-dB, ~ 5-dB, and ~ 9-dB, respectively. The EVM performances as a function of the received optical power (RoP) after 20-km SSMF transmission are shown in Fig. 6(b). It demonstrates the system sensitivity and the robustness of quantization scheme against transmission distortions from fiber Table. 1. System equivalent CPRI rate and aggregated channels

QAM 4 16 64 256 1024 4096 16384 QAM 4 16 64 256 1024 4096 16384

Equivalent CPRI rate (Gbit/s) (Overhead Excluded) Supervised Unsupervised 1D 2D 3D 1D 2D 3D 112 150 150 112 150 150 90 112 112 90 112 112 90 112 112 90 112 112 75 75 75 75 75 90 64 64 64 64 64 75 50 50 50 50 56 64 37 41 50 50 Aggregated 100MHz channels 30 40 40 30 40 40 24 30 30 24 30 30 24 24 24 24 24 30 20 20 20 20 20 24 17 17 17 17 17 20 13 13 13 13 15 17 10 11 13 13

links. With the RoP varying from -15dBm to -12dBm, the EVM is almost unchanged and starts to increase when the RoP is less than -16dBm, where fiber transmission bit error rate is larger than 1e-3. The performance of the proposed scheme is significantly improved compared with the PCM with 5-bit quantization, since it has optimized quantization levels when it adopts the same number of quantization bits as the PCM. When the quantization dimension increases, the EVM is greatly reduced. While the PCM with 5-bits quantization can only meet the transmission requirements of 16QAM, the proposed schemes can realize 64-QAM with 1D and 2D quantization and achieves 256-QAM with 3D quantization. To conclude, by grouping highly-correlated neighboring samples into multi-dimensional vectors and adopt k-means clustering for quantization in D-RoF systems, we have experimentally demonstrated spectrally-efficient D-RoF transmissions. The aggregated 100-MHz OFDM channels and the equivalent CPRI rates (30-Gbit/s╳15bits/quantization-bits) are shown in Table. 1. The 30-Gbit/s RoF transmissions have been experimentally demonstrated for up to 40 100MHz OFDM channels over 20-km fiber. The equivalent CPRI rates from 37Gbit/s to 150-Gbit/s are supported. Funding. The Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), Göran Gustafsson Foundation, the Swedish ICT-TNG, VINNOVA project C2015/3-5 SENDATE-FICUS, National Natural Science Foundation of China (#61775137, 61671212, and 61550110240).

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Full References 1. K. Tanaka and A. Agata, “Next-generation optical access networks for CRAN,” in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2015), Tu2E.1. https://doi.org/10.1364/OFC.2015.Tu2E.1 2. R. Shiina, T. Fujiwara, and T. Sugawa, “Optical Video Transmission System of Terrestrial Broadcasting by Digitized-RoF Technology with Rate Reduction Method,” in European Conference on Optical Communication (IEEE, 2017), M.1.B.5. 3. T. Pfeiffer, "Next generation mobile fronthaul architectures," in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2015), M2J.7. https://doi.org/10.1364/OFC.2015.M2J.7 4. M. Sung, C. Han, S. H. Cho, H. S. Chung and J. H. Lee, “Improvement of the transmission performance in multi-IF-over-fiber mobile fronthaul by using tone-reservation technique,” Opt. Express 23(23), 29615-29624 (2015). https://doi.org/10.1364/OE.23.029615 5. J. Wang, C. Liu, J. Zhang, M. Zhu, M. Xu, F. Lu, L. Cheng and G.-K. Chang, “Nonlinear inter-band subcarrier intermodulations of multi-RAT OFDM wireless services in 5G heterogeneous mobile fronthaul networks.” J. Lightwave Technol. 34(17), 4089–4103 (2016). http://dx.doi.org/10.1109/JLT.2016.2584621 6. eCPRI Specification, V1.0, “eCPRI 1.0 specification,” (2017). www.cpri.info 7. J. Wang, Z. Yu, K. Ying, J. Zhang, F. Lu, M. Xu, L. Cheng, X. Ma and G. K. Chang, "Digital Mobile Fronthaul Based on Delta–Sigma Modulation for 32 LTE Carrier Aggregation and FBMC Signals," J. Optical Communications and Networking 9(2), A233-A244 (2017). http://dx.doi.org/10.1364/JOCN.9.00A233 8. L. Breyne, G. Torfs, X. Yin, P. Demeester, and J. Bauwelinck, “Comparison Between Analog Radio-Over-Fiber and Sigma Delta Modulated RadioOver-Fiber. ” IEEE Photonics Tech. Letters, 29(21), 1808-1811 (2017). http://dx.doi.org/10.1109/LPT.2017.2752284 9. M. Xu, F. Lu, J. Wang, L. Cheng, D. Guidotti, and G.-K. Chang, "Key technologies for next generation digital RoF mobile fronthaul with statistical data compression and multiband modulation", J. Lightwave Technol. 35(17), 3671-3679 (2017). http://dx.doi.org/10.1109/JLT.2017.2715003 10. S.-H. Park, O. Simeone, O. Sahin and S. Shamai (Shitz), “Fronthaul compression for cloud radio access networks: Signal processing advances inspired by network information theory.” IEEE Signal Process. Mag. 31(6), 69–79 (2014). http://dx.doi.org/10.1109/MSP.2014.2330031 11. L. Zhang, X. Pang, O. Ozolins, A. Udalcovs, R. Schatz, U. Westergren, G. Jacobsen, S. Popov, L. Wosinska, W. Hu, S. Xiao, and J. Chen, “Digital mobile fronthaul employing differential pulse code modulation with suppressed quantization noise,” Opt. Express 25(25), (2017). http://dx.doi.org/10.1364/OE.25.031921 12. L. Zhang, X. Pang, O. Ozolins, A. Udalcovs, S. Popov, S. Xiao, and J. Chen, “K-means Clustering based Multi-Dimensional Quantization Scheme for Digital Mobile Fronthaul ,” in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2018). 13. M. David, “An Example Inference Task: Clustering,” in Information Theory, Inference and Learning Algorithms, (Cambridge University Press), Chap. 20, pp. 284–292 (2003). www.inference.org.uk/mackay/itprnn/ps/284.292.pdf 14. F. Aurenhammer "Voronoi Diagrams – A Survey of a Fundamental Geometric Data Structure," ACM Computing Surveys. 23 (3), 345–405 (1991). http://dx.doi.org/10.1145/116873.116880 15. 3GPP TS 36.104 V12.6.0 (2014-12). www.3gpp.org/dynareport/36104.html