arXiv subjects
Publications and source records attributed to Jochen Schröder.
We propose a novel frequency-domain blind equalization scheme for coherent optical communications. The method is shown to achieve similar performance to its recently proposed time-domain counterpart with lower computational complexity, while outperforming the commonly used CMA-based equalizers.
We monitor a 524km live network link using an FPGA-based sensing-capable coherent transceiver prototype during a human-caused cable break. Post-analysis of polarization data reveals minute-level potential warning precursors and baseline-exceeding changes directly preceding the break.
Lithium niobate (LN) is a promising material for future complex photonic-electronic circuits, with wide applications in fields like communications, sensing, quantum optics, and computation. LN took a great stride toward compact photonic integrated circuits (PICs) with the development of partially-etched LN on insulator (LNOI) waveguides. However, integration density is still limited for future high-compact PICs due to the partial edge nature of their waveguides. Here, we demonstrate a fully-etched LN PIC platform which, for the first time, simultaneously achieves ultra-low propagation loss and compact circuit size. The tightly-confined fully-etched LN waveguides with smooth sidewalls allow us to bring the bending radius down to 20 $μ$m (corresponds to 1 THz FSR). We have achieved compact high-$Q$ microring resonators with $Q/V$ of 7.1 $\times$ 10$^{4}$ $μ$m$^{-3}$, almost one order of magnitude larger than previous demonstrations. The statistical mean propagation losses of our LN waveguides is 8.5 dB/m (corresponds to mean $Q$-factor of 4.9 $\times$ 10$^{6}$) even with a small bending radius of 40 $μ$m. Our compact and ultra-low-loss LN platform shows great potential in future miniaturized multifunctional integration systems. As complementary evidence to show the utility of our platform, we demonstrate soliton microcombs with an ultra-high repetition rate of 500 GHz in LN.
State-of-the-art high-spectral-efficiency communication systems employ high-order modulation formats coupled with high symbol rates to accommodate the ever-growing demand for data rate-hungry applications. However, such systems are more vulnerable to linear and nonlinear transmission impairments, and it is important to mitigate the performance loss via digital signal processing. In this paper, we propose a novel machine learning approach for blind channel equalization and estimation using the vector quantized (VQ) \ac{VAE} framework. The proposed approach generalizes the applicability of the conventional \ac{VAE}-based equalizer to nonlinear systems employing high-order modulation formats by introducing a codebook component and an associated novel loss function. We evaluate the performance of the proposed method over a linear additive white Gaussian noise channel with intersymbol interference and two nonlinear scenarios. Simulation results show that the proposed method can achieve similar performance as a data aided equalizer using the \acf{MMSE} criterion, and outperforms the blind\ac{CMA} and the \ac{VAE}-based channel equalizer. Furthermore, we show that for the linear channel, the proposed scheme exhibits better convergence properties than the \ac{MMSE}-based, the \ac{CMA}-based, and the \ac{VAE}-based equalizers in terms of both convergence speed and robustness to variations in training batch size and learning rate.
Optical interconnects (OIs) based on vertical-cavity surface-emitting lasers (VCSELs) are the main workhorse within data centers, supercomputers, and even vehicles, providing low-cost, high-rate connectivity. VCSELs must operate under extremely harsh and time-varying conditions, thus requiring adaptive and flexible designs of the communication chain. Such designs can be built based on mathematical models (model-based design) or learned from data (machine learning (ML) based design). Various ML techniques have recently come to the forefront, replacing individual components in the transmitters and receivers with deep neural networks. Beyond such component-wise learning, end-to-end (E2E) autoencoder approaches can reach the ultimate performance through co-optimizing entire parameterized transmitters and receivers. This tutorial paper aims to provide an overview of ML for VCSEL-based OIs, with a focus on E2E approaches, dealing specifically with the unique challenges facing VCSELs, such as the wide temperature variations and complex models.
End-to-end autoencoder (AE) learning has the potential of exceeding the performance of human-engineered transceivers and encoding schemes, without a priori knowledge of communication-theoretic principles. In this work, we aim to understand to what extent and for which scenarios this claim holds true when comparing with fair benchmarks. Our particular focus is on memoryless multiple-input multiple-output (MIMO) and multi-user (MU) systems. Four case studies are considered: two point-to-point (closed-loop and open-loop MIMO) and two MU scenarios (MIMO broadcast and interference channels). For the point-to-point scenarios, we explain some of the performance gains observed in prior work through the selection of improved baseline schemes that include geometric shaping as well as bit and power allocation. For the MIMO broadcast channel, we demonstrate the feasibility of a novel AE method with centralized learning and decentralized execution. Interestingly, the learned scheme performs close to nonlinear vector-perturbation precoding and significantly outperforms conventional zero-forcing. Lastly, we highlight potential pitfalls when interpreting learned communication schemes. In particular, we show that the AE for the considered interference channel learns to avoid interference, albeit in a rotated reference frame. After de-rotating the learned signal constellation of each user, the resulting scheme corresponds to conventional time sharing with geometric shaping.
Laser frequency combs are enabling some of the most exciting scientific endeavours in the 21st century, ranging from the development of optical clocks to the calibration of the astronomical spectrographs used for searching Earth-like exoplanets. Today, dissipative Kerr solitons generated in microresonators offer the prospect of attaining frequency combs in miniaturized systems by capitalizing on advances in photonic integration. Most of the applications based on soliton microcombs rely on tuning a continuous-wave laser into a longitudinal mode of a microresonator whose dimensions are engineered to display anomalous dispersion at the pump laser frequency. In this configuration, however, nonlinear physics precludes from attaining dissipative Kerr solitons with high power conversion efficiency, with typical comb powers amounting to ~1% of the available laser power. Here, we demonstrate that this fundamental limitation can be overcome by inducing a controllable frequency shift to a selected cavity resonance. Experimentally, we realize this shift using two linearly coupled anomalous-dispersion microresonators (a photonic molecule), resulting in a coherent dissipative Kerr soliton with a conversion efficiency exceeding 50% and excellent line spacing stability. We describe the physical soliton dynamics in this configuration, and discover the system displays unusual characteristics, such as the possibility to backwards initiate solitons and stable operation with a blue detuned pump laser. By optimizing the microcomb power available on chip, these results facilitate the practical implementation of a scalable integrated photonic architecture for energy-efficient applications.
We propose an AE-based transceiver for a WDM system impaired by hardware imperfections. We design our AE following the architecture of conventional communication systems. This enables to initialize the AE-based transceiver to have similar performance to its conventional counterpart prior to training and improves the training convergence rate. We first train the AE in a single-channel system, and show that it achieves performance improvements by putting energy outside the desired bandwidth, and therefore cannot be used for a WDM system. We then train the AE in a WDM setup. Simulation results show that the proposed AE significantly outperforms the conventional approach. More specifically, it increases the spectral efficiency of the considered system by reducing the guard band by 37\% and 50\% for a root-raised-cosine filter-based matched filter with 10\% and 1\% roll-off, respectively. An ablation study indicates that the performance gain can be ascribed to the optimization of the symbol mapper, the pulse-shaping filter, and the symbol demapper. Finally, we use reinforcement learning to learn the pulse-shaping filter under the assumption that the channel model is unknown. Simulation results show that the reinforcement-learning-based algorithm achieves similar performance to the standard supervised end-to-end learning approach assuming perfect channel knowledge.
We demonstrate, for the first time, experimental over-the-fiber training of transmitter neural networks (NNs) using reinforcement learning. Optical back-to-back training of a novel NN-based digital predistorter outperforms arcsine-based predistortion with up to 60\% bit-error-rate reduction.
Receiver sensitivity is a particularly important metric in optical communication links operating at low signal-to-noise ratios (SNRs), for example in deep-space communication, since it directly limits the maximum achievable reach and data rate. Pulse position modulation (PPM) with direct detection photon-counting detectors are the most power-efficient solution known, however, the sensitivity gain comes at the expense of reduced spectral efficiency. We show that quadrature phase-shift keying (QPSK) modulation with a phase-sensitive ultralow noise pre-amplified coherent receiver outperforms other well-known power-efficient multi-dimensional coherent modulation formats, while simultaneously having higher spectral efficiency. It also results in better sensitivity than PPM for orders up to 64 with ideal direct detection using photon-counting receivers. This is because of the bit error rate characteristics favoring the QPSK format when forward error correction with a large overhead is considered.
We propose an end-to-end learning-based approach for superchannel systems impaired by non-ideal hardware component. Our system achieves up to 60% SER reduction and up to 50% guard band reduction compared with the considered baseline scheme.
Many physical systems display quantized energy states. In optics, interacting resonant cavities show a transmission spectrum with split eigenfrequencies, similar to the split energy levels that result from interacting states in bonded multi-atomic, i.e. molecular, systems. Here, we study the nonlinear dynamics of photonic diatomic molecules in linearly coupled microresonators and demonstrate that the system supports the formation of self-enforcing solitary waves when a laser is tuned across a split energy level. The output corresponds to a frequency comb (microcomb) whose characteristics in terms of power spectral distribution are unattainable in single-mode (atomic) systems. Photonic molecule microcombs are coherent, reproducible, and reach high conversion efficiency and spectral flatness whilst operated with a laser power of a few milliwatts. These properties can favor the heterogeneous integration of microcombs with semiconductor laser technology and facilitate applications in optical communications, spectroscopy and astronomy.
End-to-end data-driven machine learning (ML) of multiple-input multiple-output (MIMO) systems has been shown to have the potential of exceeding the performance of engineered MIMO transceivers, without any a priori knowledge of communication-theoretic principles. In this work, we aim to understand to what extent and for which scenarios this claim holds true when comparing with fair benchmarks. We study closed-loop MIMO, open-loop MIMO, and multi-user MIMO and show that the gains of ML-based communication in the former two cases can be to a large extent ascribed to implicitly learned geometric shaping and bit and power allocation, not to learning new spatial encoders. For MU-MIMO, we demonstrate the feasibility of a novel method with centralized learning and decentralized executing, outperforming conventional zero-forcing. For each scenario, we provide explicit descriptions as well as open-source implementations of the selected neural-network architectures.
Noise fundamentally limits the capacity and reach in all communication links. In optical space communications, noise primarily originates from the detection process and limits the signal fidelity. . Therefore, the receiver sensitivity plays a key role, dictating the minimum power needed to recover the information transmitted. The widely explored approach of using the pulse-position modulation format trades-off sensitivity against receiver bandwidth and thus data-rate. Here we report on a novel, spectrally efficient, approach based on a coherent receiver with a near-noiseless phase-sensitive pre-amplifier operating at room temperature and demonstrate a sensitivity of one photon-per-bit of incident power at a data rate of 10 Gb/s. The results provide a path to future high-capacity inter-satellite and deep space, and other free-space communication links
Performance monitoring is an essential function for margin measurements in live systems. Historically, system budgets have been described by the Q-factor converted from the bit error rate (BER) under binary modulation and direct detection. The introduction of hard-decision forward error correction (FEC) did not change this. In recent years technologies have changed significantly to comprise coherent detection, multilevel modulation and soft FEC. In such advanced systems, different metrics such as (nomalized) generalized mutual information (GMI/NGMI) and asymmetric information (ASI) are regarded as being more reliable. On the other hand, Q budgets are still useful because pre-FEC BER monitoring is established in industry for live system monitoring. The pre-FEC BER is easily estimated from available information of the number of flipped bits in the FEC decoding, which does not require knowledge of the transmitted bits that are unknown in live systems. Therefore, the use of metrics like GMI/NGMI/ASI for performance monitoring has not been possible in live systems. However, in this work we propose a blind soft-performance estimation method. Based on a histogram of log-likelihood-values without the knowledge of the transmitted bits, we show how the ASI can be estimated. We examined the proposed method experimentally for 16 and 64-ary quadrature amplitude modulation (QAM) and probabilistically shaped 16, 64, and 256-QAM in recirculating loop experiments. We see a relative error of 3.6%, which corresponds to around 0.5 dB signal-to-noise ratio difference for binary modulation, in the regime where the ASI is larger than the assumed FEC threshold. For this proposed method, the digital signal processing circuitry requires only a minimal additional function of storing the L-value histograms before the soft-decision FEC decoder.
We investigated a suitable auxiliary channel setting and the gap between Q-factors with hard and soft demapping. The system margin definition should be reconsidered for systems employing complex coded modulation with soft forward error correction.
Temporal waveform manipulation is a fundamental functionality in optics and crucial for applications like optical communications, microwave photonics and quantum optics. Traditional IQ- or phase-amplitude modulators shape light by carving energy from the input lightwave and are thus fundamentally lossy, and cannot apply independent modulation to multiple input wavelengths simultaneously. Taking inspiration from the space-time duality, we produce arbitrary unitary spectro-temporal transformations on multiple temporal input vectors with a modulation structure comprising of only lossless phase modulation and dispersive allpass filtering. The bandwidth of the output waveforms is not restricted by the driving electronics and independent transformations can be performed simultaneously on multiple orthogonal inputs such as spectrally separated frequency tones. This overcomes the main limitations of traditional electro-optic modulators and offers fundamental new insight into temporal wave manipulation.
Modern optical communication systems transmit multiple frequency channels, each operating very close to its theoretical limit. The total bandwidth can reach 10THz limited by the optical amplifiers. Maximizing spectral efficiency, the throughput per bandwidth is thus crucial. Replacing independent lasers with an optical frequency comb can enable very dense packing by overcoming relative drifts. However, to date, interference from non-ideal spectral shaping prevents exploiting the full potential of frequency combs. Here, we demonstrate comb-enabled multi-channel digital signal processing, which overcomes these limitations. Each channel is detected using an independent coherent receiver and processed at two samples-per-symbol. By accounting for the unique comb stability and exploiting aliasing in the design of the dynamic equalizer, we show that the optimal spectral shape changes, resulting in a higher signal to noise ratio that pushes the optimal symbol rate towards and even \emph{above} the channel spacing, resulting in the first example of frequency-domain super-Nyquist transmission with multi-channel detection for optical systems. The scheme is verified both in back-to-back configuration and in single span transmission of a 21 channel superchannel originating from a 25GHz-spaced frequency comb. By jointly processing 3 wavelength channels at a time, we achieve spectral efficiency beyond what is possible with independent channels. At the same time, one significantly relaxes the hardware requirements on digital-to-analog resolution and bandwidth, and well as filter tap numbers. Our results show that comb-enabled multi-channel processing can overcome the limitations of classical dense wavelength division multiplexing systems by enabling tighter spacing to reach the ultimate spectral efficiency in optical communications.