Machine learning for optical fiber communication systems: An introduction and overview

Optical networks generate a vast amount of diagnostic, control and performance monitoring data. When information is extracted from this data, reconfigurable network elements and reconfigurable transceivers allow the network to adapt both to changes in the physical infrastructure but also changing traffic conditions. Machine learning is emerging as a disruptive technology for extracting useful information from this raw data to enable enhanced planning, monitoring and dynamic control. We provide a survey of the recent literature and highlight numerous promising avenues for machine learning applied to optical networks, including explainable machine learning, digital twins and approaches in which we embed our knowledge into the machine learning such as physics-informed machine learning for the physical layer and graph-based machine learning for the networking layer

Optical Performance Monitoring in Digital Coherent Receivers

Optical performance monitoring (OPM) is an important issue for proper operation of next-generation optical networks. Among various monitored parameters, the optical signal-to-noise ratio (OSNR) and fiber transmission impairments such as chromatic dispersion (CD), polarization mode dispersion (PMD), and polarization dependent loss (PDL) are paid special attention, because they serve information of the channel quality, which helps to manage the network. Several methods have been proposed for monitoring tasks, which are based on pilot tones, RF tones, asynchronous histogram, and fiber nonlinear effects. Most of them need costly devices, tap optical power from the channel, and introduce transmission overhead. On the other hand, in this research, we investigate OPM based on digital coherent receivers, which overcomes such difficulties and ensures cost-efficient, robust and reliable monitoring. Linear channel impairments such as CD, PMD, and PDL are monitored from the transfer functions of adaptive filters. A digital coherent receiver allows polarization demultiplexing and equalization of all these impairments by using four finite-impulse-response (FIR) filters structured in a two-by-two butterfly configuration. After the filters are adapted by a suitable algorithm, we can construct a frequency-dependent two-by-two matrix with four elements, which are transfer functions of the adapted four FIR filters. The inverse of this matrix is called the monitoring matrix and can be approximated as the transfer matrix of the channel, and contains combined effects of CD, PMD and PDL. A precise algorithm is required to separate out the impairments from this matrix. We propose a simple and unified algorithm to separate out CD, differential group delay (DGD), PDL, and second-order PMD from the monitoring matrix. The components of second-order PMD, polarization-dependent chromatic dispersion (PCD) and depolarization (DEP) of principal states of polarization are obtained separately. This algorithm has an advantage that individual impairment can be estimated directly from the monitoring matrix without any matrix decomposition; thus it enables accurate estimation of the impairments, even when the transmitted signal suffers from distortion stemming from various origins. Also, no additional hardware is required for our proposed algorithm. For filter adaptation, we use the constant-modulus algorithm (CMA), as it enables long-tap-filter adaptation efficiently even in the presence of large laser phase noise unlike the commonly used decision-directed least-mean-square (DD-LMS) algorithm. However, CMA can suffer from the singularity problem which means both the output ports of butterfly configuration converge to the same polarization tributary. Consequently, we avoid the singularity problem by introducing the training mode in CMA. In the training mode, the LMS algorithm is used to determine in which output port of the butterfly configuration each polarization tributary appears, and after such initial training the algorithm is switched to the blind CMA to enable high-order-filter adaptation. The multi-impairment monitoring algorithm and the singularity-free operation of CMA with the training mode, which we have proposed in this thesis, are verified by dual-polarization quadrature phase-shift keying (QPSK) transmission experiments. For such an impairment-monitoring method, the delay tap length of filters should be long enough to compensate for all the impairments. However, the computational complexity of FIR filters increases with the number of taps. The frequency-domain approach can reduce this computational cost by block-by-block processing and fast implementation of discrete Fourier transform (DFT). However, the adaptive frequency-domain equalizer (FDE) has hardly been investigated for optical communication systems. We have proposed a novel adaptive FDE based on CMA, which maintains all the advantages of the adaptive TDE based on FIR filters. Even in the block processing mode of FDE, it can work on the twofold-oversampled input sequence by introducing even and odd sub-equalizers. Therefore, when we configure this filter in the butterfly structure, we can achieve adaptive equalization together with polarization demultiplexing and adjustment of the arbitrary initial sampling phase of analog-to-digital converters (ADCs) so that the best symbol-spaced sequence is produced. The equalization performance of the proposed adaptive FDE as well as multi-impairment monitoring from the equalizer is verified by dual-polarization QPSK transmission experiments. We have proposed a novel OSNR monitoring method. This is based on the analysis of higher-order statistical moments of adaptive-equalizer output in digital coherent receivers. After equalization and clock recovery by an adaptive equalizer, symbol-spaced signal samples and noise samples have well-defined but dissimilar statistical properties. In our proposed algorithm, we measure the second- and fourth-order moments of the adaptive-equalizer output. Then, by using the known statistics of the phase-modulated signal in the QPSK format and amplified spontaneous emission (ASE) noise, we estimate the OSNR. The proposed method is simple and accurate. We also experimentally verify this monitoring algorithm with 10-Gsymbol/s QPSK transmission experiments.光パフォーマンスモニタリングは次世代光ネットワークを構築するための重要な技術である. 適切にネットワークを運用するためには, 受信信号の光信号対雑音比(OSNR)や伝送路の波長分散(CD), 偏波モード分散(PMD), 偏波依存損失(PDL)などを観測する必要がある. これまで, パイロットトーン, RFトーン, 非同期ヒストグラム, ファイバ非線形効果などに基づく観測手法が提案されている. しかし, これらの多くは高価で煩雑なシステムとなってしまうという欠点があった. 一方, 我々はディジタルコヒーレント受信器を用いたモニタリング技術を提案し, 低コストかつ信頼できるモニタリングを可能とした. CD, PMD, そしてPDLのような線形な伝送路障害は適応フィルタの伝達関数から求めることができる. ディジタルコヒーレント受信器では, 検波後にバタフライ構成のFIRフィルタを用いることで, 偏波多重分離及び等化が可能である. フィルタを適切なアルゴリズムにより適応させることで, FIRフィルタの伝達関数を示す周波数依存の2×2の行列を構築できる. この逆伝達関数はモニタリング行列と呼ばれ, これからCD, PMD, PDLの情報を含む伝送路の伝達関数を推定することができる. 我々はCD, DGD, PDL, そして2次PMDを分離する簡易なアルゴリズムを提案した. 2次PMDの構成要素である偏波依存波長分散および主偏波状態の偏波解消を独立に得ることができる. このアルゴリズムは行列分解することなくモニタリング行列から個別の伝送路障害を求めることができる. 様々な伝送路障害が同時に存在していようとも, 正しい推定を簡易なアルゴリズムで行うことができる. フィルタの適応アルゴリズムとして, 我々はCMAを用いた. これはDD-LMSアルゴリズムと比較して, 位相雑音が存在しても安定に動作するためである. しかし, CMAはバタフライ構成の出力が同じ偏波に収束するという特異点問題を持つ. したがって, 我々はCMAにトレーニングモードを導入することによってこの特異点問題を解決した. トレーニングモードでは, LMSアルゴリズムを用いることで各偏波チャネルがどのポートから出力されるかを決定する. その後, 位相無依存であるブラインドCMAに切り替えることで, 高次フィルタを用いることができる. 本稿で提案するモニタリングアルゴリズムの有効性はQPSK信号の伝送実験を行うことで確認した. 伝送路障害モニタリングを正しく行うためには, フィルタタップ長は十分長くなければならない. しかし, FIRフィルタの計算コストはタップ数とともに増加する. 一方で, 周波数領域での処理は. ブロック処理およびDFTの高速実装によって計算コストを減少させることができる. しかし, これまで周波数領域における適応等化器は光通信分野ではほとんど研究されていなかった. このような状況下で, 我々はCMAに基づく新たな適応FDEを提案した. 本提案手法は, 偶数次及び奇数次のサブ等化器を用いている. 本手法を用いることで, 偏波多重分離及びADCのサンプリング位相の調整を行うことができる. 偏波多重QPSK信号の伝送実験を行うことで, 我々が提案する適応FDEの性能を評価した. 我々は新しいOSNRモニタリング技術を提案した. これは適応等化器出力の高次の統計学的モーメントを解析することで行われる. 適応等化器の等化及びクロック再生後信号及び雑音は異なる統計的性質を持つ. 我々のアルゴリズムでは2次および4次のモーメントを測定する. その後, 位相変調信号およびASEの統計的性質を用いることでOSNRを推定する. 我々は本方式の有効性を10Gsymbol/s QPSKの伝送実験で確認した.報告番号: 甲27498 ; 学位授与年月日: 2011-09-27 ; 学位の種別: 課程博士 ; 学位の種類: 博士(工学) ; 学位記番号: 博工第7584号 ; 研究科・専攻: 工学系研究科電気系工学専

ディジタルコヒーレント受信器を用いた光パフォーマンスモニタリング

Optical performance monitoring (OPM) is an important issue for proper operation of next-generation optical networks. Among various monitored parameters, the optical signal-to-noise ratio (OSNR) and fiber transmission impairments such as chromatic dispersion (CD), polarization mode dispersion (PMD), and polarization dependent loss (PDL) are paid special attention, because they serve information of the channel quality, which helps to manage the network. Several methods have been proposed for monitoring tasks, which are based on pilot tones, RF tones, asynchronous histogram, and fiber nonlinear effects. Most of them need costly devices, tap optical power from the channel, and introduce transmission overhead. On the other hand, in this research, we investigate OPM based on digital coherent receivers, which overcomes such difficulties and ensures cost-efficient, robust and reliable monitoring. Linear channel impairments such as CD, PMD, and PDL are monitored from the transfer functions of adaptive filters. A digital coherent receiver allows polarization demultiplexing and equalization of all these impairments by using four finite-impulse-response (FIR) filters structured in a two-by-two butterfly configuration. After the filters are adapted by a suitable algorithm, we can construct a frequency-dependent two-by-two matrix with four elements, which are transfer functions of the adapted four FIR filters. The inverse of this matrix is called the monitoring matrix and can be approximated as the transfer matrix of the channel, and contains combined effects of CD, PMD and PDL. A precise algorithm is required to separate out the impairments from this matrix. We propose a simple and unified algorithm to separate out CD, differential group delay (DGD), PDL, and second-order PMD from the monitoring matrix. The components of second-order PMD, polarization-dependent chromatic dispersion (PCD) and depolarization (DEP) of principal states of polarization are obtained separately. This algorithm has an advantage that individual impairment can be estimated directly from the monitoring matrix without any matrix decomposition; thus it enables accurate estimation of the impairments, even when the transmitted signal suffers from distortion stemming from various origins. Also, no additional hardware is required for our proposed algorithm. For filter adaptation, we use the constant-modulus algorithm (CMA), as it enables long-tap-filter adaptation efficiently even in the presence of large laser phase noise unlike the commonly used decision-directed least-mean-square (DD-LMS) algorithm. However, CMA can suffer from the singularity problem which means both the output ports of butterfly configuration converge to the same polarization tributary. Consequently, we avoid the singularity problem by introducing the training mode in CMA. In the training mode, the LMS algorithm is used to determine in which output port of the butterfly configuration each polarization tributary appears, and after such initial training the algorithm is switched to the blind CMA to enable high-order-filter adaptation. The multi-impairment monitoring algorithm and the singularity-free operation of CMA with the training mode, which we have proposed in this thesis, are verified by dual-polarization quadrature phase-shift keying (QPSK) transmission experiments. For such an impairment-monitoring method, the delay tap length of filters should be long enough to compensate for all the impairments. However, the computational complexity of FIR filters increases with the number of taps. The frequency-domain approach can reduce this computational cost by block-by-block processing and fast implementation of discrete Fourier transform (DFT). However, the adaptive frequency-domain equalizer (FDE) has hardly been investigated for optical communication systems. We have proposed a novel adaptive FDE based on CMA, which maintains all the advantages of the adaptive TDE based on FIR filters. Even in the block processing mode of FDE, it can work on the twofold-oversampled input sequence by introducing even and odd sub-equalizers. Therefore, when we configure this filter in the butterfly structure, we can achieve adaptive equalization together with polarization demultiplexing and adjustment of the arbitrary initial sampling phase of analog-to-digital converters (ADCs) so that the best symbol-spaced sequence is produced. The equalization performance of the proposed adaptive FDE as well as multi-impairment monitoring from the equalizer is verified by dual-polarization QPSK transmission experiments. We have proposed a novel OSNR monitoring method. This is based on the analysis of higher-order statistical moments of adaptive-equalizer output in digital coherent receivers. After equalization and clock recovery by an adaptive equalizer, symbol-spaced signal samples and noise samples have well-defined but dissimilar statistical properties. In our proposed algorithm, we measure the second- and fourth-order moments of the adaptive-equalizer output. Then, by using the known statistics of the phase-modulated signal in the QPSK format and amplified spontaneous emission (ASE) noise, we estimate the OSNR. The proposed method is simple and accurate. We also experimentally verify this monitoring algorithm with 10-Gsymbol/s QPSK transmission experiments.光パフォーマンスモニタリングは次世代光ネットワークを構築するための重要な技術である. 適切にネットワークを運用するためには, 受信信号の光信号対雑音比(OSNR)や伝送路の波長分散(CD), 偏波モード分散(PMD), 偏波依存損失(PDL)などを観測する必要がある. これまで, パイロットトーン, RFトーン, 非同期ヒストグラム, ファイバ非線形効果などに基づく観測手法が提案されている. しかし, これらの多くは高価で煩雑なシステムとなってしまうという欠点があった. 一方, 我々はディジタルコヒーレント受信器を用いたモニタリング技術を提案し, 低コストかつ信頼できるモニタリングを可能とした. CD, PMD, そしてPDLのような線形な伝送路障害は適応フィルタの伝達関数から求めることができる. ディジタルコヒーレント受信器では, 検波後にバタフライ構成のFIRフィルタを用いることで, 偏波多重分離及び等化が可能である. フィルタを適切なアルゴリズムにより適応させることで, FIRフィルタの伝達関数を示す周波数依存の2×2の行列を構築できる. この逆伝達関数はモニタリング行列と呼ばれ, これからCD, PMD, PDLの情報を含む伝送路の伝達関数を推定することができる. 我々はCD, DGD, PDL, そして2次PMDを分離する簡易なアルゴリズムを提案した. 2次PMDの構成要素である偏波依存波長分散および主偏波状態の偏波解消を独立に得ることができる. このアルゴリズムは行列分解することなくモニタリング行列から個別の伝送路障害を求めることができる. 様々な伝送路障害が同時に存在していようとも, 正しい推定を簡易なアルゴリズムで行うことができる. フィルタの適応アルゴリズムとして, 我々はCMAを用いた. これはDD-LMSアルゴリズムと比較して, 位相雑音が存在しても安定に動作するためである. しかし, CMAはバタフライ構成の出力が同じ偏波に収束するという特異点問題を持つ. したがって, 我々はCMAにトレーニングモードを導入することによってこの特異点問題を解決した. トレーニングモードでは, LMSアルゴリズムを用いることで各偏波チャネルがどのポートから出力されるかを決定する. その後, 位相無依存であるブラインドCMAに切り替えることで, 高次フィルタを用いることができる. 本稿で提案するモニタリングアルゴリズムの有効性はQPSK信号の伝送実験を行うことで確認した. 伝送路障害モニタリングを正しく行うためには, フィルタタップ長は十分長くなければならない. しかし, FIRフィルタの計算コストはタップ数とともに増加する. 一方で, 周波数領域での処理は. ブロック処理およびDFTの高速実装によって計算コストを減少させることができる. しかし, これまで周波数領域における適応等化器は光通信分野ではほとんど研究されていなかった. このような状況下で, 我々はCMAに基づく新たな適応FDEを提案した. 本提案手法は, 偶数次及び奇数次のサブ等化器を用いている. 本手法を用いることで, 偏波多重分離及びADCのサンプリング位相の調整を行うことができる. 偏波多重QPSK信号の伝送実験を行うことで, 我々が提案する適応FDEの性能を評価した. 我々は新しいOSNRモニタリング技術を提案した. これは適応等化器出力の高次の統計学的モーメントを解析することで行われる. 適応等化器の等化及びクロック再生後信号及び雑音は異なる統計的性質を持つ. 我々のアルゴリズムでは2次および4次のモーメントを測定する. その後, 位相変調信号およびASEの統計的性質を用いることでOSNRを推定する. 我々は本方式の有効性を10Gsymbol/s QPSKの伝送実験で確認した.University of Tokyo (東京大学

Research data supporting "200 Gb/s/λ Upstream PON Using Polarization Multiplexed PAM4 with Coherent Detection"

The processed data was obtained by analising captured oscilloscope traces using offline digital signal processing (DSP) in Matlab. The DSP contains carrier frequency recovery, an adaptive equalizer based on least-mean squares, and a maximum likelihood sequence estimator. The sensitivity is taken at BER = 10^-2. Power budget is a combination of sensitivity and launch power, taken at the SOA output. The SOA characteristics were measured using a commercial optical power meter."This work was funded by Engineering and Physical Sciences Research Council grant [EP/S022139/1, EP/R035342/1

Research Data Supporting "A Minimal Coherent Receiver for 200 Gb/s/λ PON Downstream with Measured 29 dB Power Budget"

The processed data was obtained by analising captured oscilloscope traces using offline digital signal processing (DSP) in Matlab. The DSP contains carrier frequency recovery and adaptive equalizer based on least-mean squares. The sensitivity is taken at BER = 10^-2. Power budget is a combination of sensitivity and launch power, taken at the EDFA output. Optical Spectrum analyser power measurement raw data. Text file contains power measurement for each frequenc

A Minimal Coherent Receiver for 200 Gb/s/λ PON Downstream with Measured 29 dB Power Budget

We experimentally demonstrate 200 Gb/s/λ downstream transmission for a passive optical network (PON) with a minimal coherent receiver at optical network unit (ONU). The low complexity receiver required at the cost-sensitive ONU employs heterodyne detection and requires a single photodiode, a 3-dB optical coupler and a local oscillator, and is the simplest coherent receiver. At the optical line terminal (OLT), digital pre-emphasis and Alamouti-coding is applied to the 50 GBaud signal. A power budget of 29 dB is experimentally demonstrated, increasing to 34.5 dB if a balanced receiver is utilized

Dataset supporting publication "200 Gb/s/λ Upstream PON using Polarization Multiplexed PAM4 with Coherent Detection"

The processed data was obtained by analysing captured oscilloscope traces using offline digital signal processing (DSP) in Matlab. The DSP contains carrier frequency recovery, an adaptive equalizer based on least-mean squares, and a maximum likelihood sequence estimator. The sensitivity is taken at BER = 10^-2. Power budget is a combination of sensitivity and launch power, taken at the SOA output. The SOA characteristics were measured using a commercial optical power meter. The MLSE trellis size scales 4^x, where x is the memory depth. In the nonlinear equalisers plot optimum MLSE lenght was used. Volterra equalizer is of 3rd order

Data supporting publication "Symmetric Bidirectional 200 Gb/s/λ PON Solution Demonstrated over Field Installed Fiber"

This data supports the publication for OFC 2024. The data was obtained by analising the oscilloscope traces using the digital signal processing algorithms descibed in the conference submission. The data contains Sensitivity and Power Budget numbers for a PON system in line with International Telecommunication Union Telecommunication Standardization Sector (ITU-T) standard requirements. For power budget the bit error rate threshold is taken at pre-FEC error rate of 10^-2. Only processed data is included due to the large size of the oscilloscope trace collectio