A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. k-means clustering <s> A k-means algorithm for phase recovery of three, 50 Mbaud, 8PSK subcarrier multiplexed signals at 5 GHz for optical phase-modulated radio-over-fiber is proposed and experimentally demonstrated after 40 km of single mode fiber transmission. <s> BIB001 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. k-means clustering <s> Highest reported bit rate of 2.5 Gb/s for optically phase-modulated radio-over-fiber (RoF) link, employing digital coherent detection, is demonstrated. Demodulation of 3×2.5 Gb/s quadrature phase-shift-keying modulated wavelength-division-multiplexed RoF channels is achieved after 79 km of transmission through deployed fiber. Error-free performance (bit-error rate corresponding to 10-4) is achieved using a digital coherent receiver in combination with a K-means algorithm for radio-frequency phase recovery. <s> BIB002 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. k-means clustering <s> Abstract We propose a machine learning-based nonsymmetrical demodulation technique relying on clustering to mitigate time-varying distortions derived from several impairments such as IQ imbalance, bias drift, phase noise and interchannel interference. Experimental results show that those impairments cause centroid movements in the received constellations seen in time-windows of 10k symbols in controlled scenarios. In our demodulation technique, the k-means algorithm iteratively identifies the cluster centroids in the constellation of the received symbols in short time windows by means of the optimization of decision thresholds for a minimum BER. We experimentally verified the effectiveness of this computationally efficient technique in multicarrier 16QAM Nyquist-WDM systems over 270 km links. Our nonsymmetrical demodulation technique outperforms the conventional QAM demodulation technique, reducing the OSNR requirement up to ∼0.8 dB at a BER of 1 × 10−2 for signals affected by interchannel interference. <s> BIB003 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. k-means clustering <s> In this work, we proposed two k-means-clustering-based algorithms to mitigate the fiber nonlinearity for 64-quadrature amplitude modulation (64-QAM) signal, the training-sequence assisted k-means algorithm and the blind k-means algorithm. We experimentally demonstrated the proposed k-means-clustering-based fiber nonlinearity mitigation techniques in 75-Gb/s 64-QAM coherent optical communication system. The proposed algorithms have reduced clustering complexity and low data redundancy and they are able to quickly find appropriate initial centroids and select correctly the centroids of the clusters to obtain the global optimal solutions for large k value. We measured the bit-error-ratio (BER) performance of 64-QAM signal with different launched powers into the 50-km single mode fiber and the proposed techniques can greatly mitigate the signal impairments caused by the amplified spontaneous emission noise and the fiber Kerr nonlinearity and improve the BER performance. <s> BIB004 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. k-means clustering <s> We propose a spectrally efficient digitized radio-over-fiber (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 30 Gbit/s D-RoF system is experimentally demonstrated to validate the proposed scheme, reporting a carrier aggregation of up to 40 100 MHz orthogonal frequency division multiplexing (OFDM) channels with quadrate amplitude modulation (QAM) order of 4 and an aggregation of 10 100 MHz OFDM channels with a QAM order of 16384. The equivalent common public radio interface rates from 37 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 D-RoF system improves the signal-to-noise-ratio up to ∼9 dB and greatly reduces the EVM, given the same number of quantization bits. <s> BIB005 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. k-means clustering <s> Coherent optical multi-carrier communications have recently dominated metro-regional and long-haul optical communications. However, the major obstacle of networks involving coherent multi-carrier signals such as coherent optical orthogonal frequency-division multiplexing (CO-OFDM) is the fiber-induced nonlinearity and the parametric noise amplification from cascaded optical amplifiers which results in significant nonlinear distortion among subcarriers. Here, we present the first nonlinear equalizer in optical communications using the traditional Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm and a novel modified version of DBSCAN which combines K-means clustering on the noisy un-clustered symbols. For a 24.72 Gbit/sec differential quaternary phase-shift keying (DQPSK) CO-OFDM system, the modified DBSCAN can increase the signal quality-factor by up to 2.158 dB compared to linear equalization at 500 km of transmission. The modified DBSCAN slightly outperforms the traditional DBSCAN, fuzzy-logic C-means, hierarchical and conventional K-means clustering at high launched optical powers. <s> BIB006 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. k-means clustering <s> We investigate the performance of a machine learning classification technique, called the Parzen window, to mitigate the fiber nonlinearity in the context of dispersion managed and dispersion unmanaged systems. The technique is applied for detection at the receiver side and deals with the non-Gaussian nonlinear effects by designing improved decision boundaries. We also propose a two-stage mitigation technique using digital back propagation and Parzen window for dispersion unmanaged systems. In this case, digital back propagation compensates for the deterministic nonlinearity and the Parzen window deals with the stochastic nonlinear signal–noise interactions, which are not taken into account by digital back propagation. A performance improvement up to 0.4 dB in terms of Q factor is observed. <s> BIB007
Definition: The k-means partitions data into k clusters, and assigns each data point to the nearest mean cluster. This problem has high computations; however, heuristic algorithms converging to local optimum can be used. The "k" refers to the number of clusters, which should be identified among observations, such that the sum of the squared error of data points be minimized. At first this algorithm takes randomly K center cluster positions. Then each data point is assigned to the cluster with the nearest center, then based on the defined clusters, a new cluster center is defined (the summation of the cluster points). The same procedure is repeated until convergence. Fiber OC: Time-varying distortions, derived from I/Q imbalance, NLPN, and inter-channel interference, result in centroid deviation of received symbols. Employing short time windows for detection enables inline tracking of signal variations based on centroids and cluster deviations. These issue could be solved by blending the time windowing phenomena and k-means detection BIB003 . To reduce the complexity and redundancy, and to improve speed and accuracy of the standard k-means other k-means algorithms such as training sequence assisted k-means, as well as blind k-means are proposed. In BIB006 a traditional Density-Based Spatial Clustering of Applications with Noise (DBSCAN) (Fig.18.b) NLE is presented. Furthermore, this algorithm is combined by k-means clustering and implemented on the noisy "unclustered" symbols. In BIB007 a Parzen window classifier (Fig.18.c) based detector is used to mitigate the fiber non-Gaussian nonlinear effects in dispersion managed and unmanaged fibers, by designing improved decision boundaries. Parzen window algorithm is a non-parametric method of estimating the class-conditional densities (likelihoods) in a supervised pattern classification problem from training data. The proposed k-means algorithms proved to be proper for mitigating nonlinearity effects BIB004 BIB005 , and parametric noise of cascaded EDFA BIB001 . Few RoF systems are investigated in ML for OC applications; however, they mostly used k-means based detector to mitigate fiber effects BIB005 BIB001 BIB002 . The k-means is simple and a good choice for RF phase recovery (for phase modulation) BIB001 , and it is a good RF carrier phase method for higher order modulation formats BIB002 . By grouping highly correlated neighboring samples into multi-dimensional vectors and adopting k-means clustering for quantization in digitized RoF systems, BIB005 demonstrated spectrally efficient digitized RoF transmissions. This technique has better performance than PCM based RoF system. 