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Hartmut Hafermann

Publications and source records attributed to Hartmut Hafermann.

At least 19 recordsLinked to original sources
arXiv2025

Wideband Gaussian Noise Model of Nonlinear Distortions From Semiconductor Optical Amplifiers

A wideband Gaussian Noise Model of the nonlinear noise power spectral density is developed for a single semiconductor optical amplifier as described by the Agrawal model. A simple, interpretable closed-form expression is obtained for the nonlinear noise-to-signal ratio of broadband wavelength-division multiplexed signals as a function of the Agrawal model parameters, the amplifier output power and the transmission bandwidth. The accuracy of the closed-form expression and its region of validity are assessed in numerical simulations. The error is smaller than 0.1 dB when the product of bandwidth and gain recovery time $B\times\tau_c$ exceeds 100. A complete treatment of gain compression is shown to enhance nonlinear noise by a factor $1+P_\text{out}/P_\text{sat}$ compared to the first-order perturbation theory result.

physics.optics↗
arXiv2023

Sequence Selection with Dispersion-Aware Metric for Long-Haul Transmission Systems

We introduce a novel sign-dependent metric: the energy dispersion index (EDI) of sequences that endured chromatic dispersion, denoted as D-EDI, which exhibits a more accurate opposite variations with the transmission performance compared to the standard EDI metric. Then, by applying D-EDI and EDI to the sequence selection (SS) process, %with enumerative sphere shaping (ESS) for $M$-QAM signaling, we present two signaling approaches denoted as D-SS and E-SS respectively. These approaches are designed to minimize rate loss and enhance transmission performance in nonlinear optical fiber transmission systems, catering to both short-distance and long-haul scenarios. With enumerative sphere shaping (ESS) as distribution matcher (DM), our simulation results reveal significant performance gains over ESS without sequence selection (SS), with improvements up to $0.4$~bits/4D-symbol. These improvements were observed over a $205$-km single-span standard single mode fiber link in WDM transmission, with five dual-polarization channels, each operating at a net rate of $400$~Gbit/s. Furthermore, we demonstrate that D-SS surpasses ESS without SS by $0.03$~bits/4D-symbol in achievable information rate over a $30\times80$~km link in a single-wavelength, with 8 discrete multi-band (DMB) transmission, and an $880$~Gbit/s net rate. Notably, our proposed D-SS scheme achieves similar performance to a sequence selection based on a full split-step Fourier method (SSFM) simulation and it consistently delivers throughput enhancements across various block lengths and selected sequence lengths.

eess.SP↗
arXiv2020

Analysis and Experimental Demonstration of Orthant-Symmetric Four-dimensional 7 bit/4D-sym Modulation for Optical Fiber Communication

We propose a new four-dimensional orthant-symmetric 128-ary modulation format (4D-OS128) with a spectral efficiency of 7bit/4D-sym. The proposed format fills the gap between polarization-multiplexed 8- and 16-ary quadrature-amplitude modulation (PM-8QAM and PM-16QAM).Numerical simulations show that 4D-OS128 outperforms two well-studied 4D geometrically-shaped modulation formats: 128SP-16QAM and 7b4D-2A8PSK by up to 0.65dB for bit-interleaved coded modulation at the same spectral efficiency. These gains are experimentally demonstrated in a 11$\times$233Gbit/s wavelength division multiplexing (WDM) transmission system operating at 5.95 bit/4D-sym over 6000km and 9000km for both EDFA-only and hybrid amplification scenarios, respectively. A reach increase of 15% is achieved with respect to 128-ary set-partitioning 16QAM. Furthermore, the proposed 4D-OS128 is also compared to $\boldsymbol{D}_4$ lattice-based constellation and probabilistically-shaped 16QAM with finite blocklength via simulation.

eess.SP↗
arXiv2019

Data Transmission based on Exact Inverse Periodic Nonlinear Fourier Transform, Part I: Theory

The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission scheme inherently compatible with the nonlinear fiber is obtained. Despite potential advantages, the periodic NFT (PNFT) has been studied less compared to its counterpart based on vanishing boundary conditions, due to the mathematical complexity of the inverse transform. In this paper we extract the theory of the algebrogeometric integration method underlying the inverse PNFT from the literature, and tailor it to the communication problem. We provide a complete algorithm to compute the inverse PNFT. As an application, we employ the algorithm to design a novel modulation scheme called nonlinear frequency amplitude modulation, where four different nonlinear frequencies are modulated independently. Finally we provide two further modulation schemes that may be considered in future research. The algorithm is further applied in Part II of this paper to the design of a PNFT-based communication experiment.

eess.SP↗
arXiv2019

Data Transmission based on Exact Inverse Periodic Nonlinear Fourier Transform, Part II: Waveform Design and Experiment

The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear Fourier transform (PNFT) has been much less investigated compared to its counterpart based on vanishing boundary conditions. In this paper, we design a first experiment based on the PNFT in which information is encoded in the invariant nonlinear main spectrum. To this end, we propose a method to construct a set of periodic waveforms each having the same fixed period, by employing the exact inverse PNFT algorithm developed in Part I. We demonstrate feasibility of the transmission scheme in experiment in good agreement with simulations and obtain a bit-error ratio of $10^{-3}$ over a distance of 2000 km. It is shown that the transmission reach is significantly longer than expected from a naive estimate based on group velocity dispersion and cyclic prefix length, which is explained through a dominating solitonic component in the transmitted waveform. Our constellation design can be generalized to an arbitrary number of nonlinear degrees of freedom.

eess.SP↗
arXiv2019

Experimental realization of Fermi-Pasta-Ulam-Tsingou recurrence in a long-haul optical fiber transmission system

The integrable nonlinear Schr\"odinger equation (NLSE) is a fundamental model of nonlinear science which also has important consequences in engineering. The powerful framework of the periodic inverse scattering transform (IST) provides a description of the nonlinear phenomena modulational instability and Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in terms of exact solutions. It associates the complex nonlinear dynamics with invariant nonlinear spectral degrees of freedom that may be used to encode information. While optical fiber is an ideal testing ground of its predictions, maintaining integrability over sufficiently long distances to observe recurrence, as well as synthesizing and measuring the field in both amplitude and phase on the picosecond timescales of typical experiments is challenging. Here we report on the experimental realization of FPUT recurrence in terms of an exact space-time-periodic solution of the integrable NLSE in a testbed for optical communication experiments. The complex-valued initial condition is constructed by means of the finite-gap integration method, modulated onto the optical carrier driven by an arbitrary waveform generator and launched into a recirculating fiber loop with periodic amplification. The measurement with an intradyne coherent receiver after a predetermined number of revolutions provides a non-invasive full-field characterization of the space-time dynamics. The recurrent space-time evolution is in close agreement with theoretical predictions over a distance of 9000 km. Nonlinear spectral analysis reveals an invariant nonlinear spectrum. The space-time scale exceeds that of previous experiments on FPUT recurrence in fiber by three orders of magnitude.

eess.SP↗
arXiv2019

Practical Product Code Construction of Polar Codes

In this paper, we study the connection between polar codes and product codes. Our analysis shows that the product of two polar codes is again a polar code, and we provide guidelines to compute its frozen set on the basis of the frozen sets of the component polar codes. Moreover, we show how polar codes can be described as irregular product codes. We propose a two-step decoder for long polar codes taking advantage of this dual nature to heavily reduce decoding latency. Finally, we show that the proposed decoding technique outperforms both standard polar codes and state-of-the-art codes for optical communications under latency constraints.

cs.IT↗
arXiv2019

Partially Ordered Statistics Demapping for Multi-Dimensional Modulation Formats

We propose a very low-complexity and high-performance algorithm for soft-demapping of multi-dimensional modulation formats. We assess its performance over the linear channel for four 8D formats, generated using binary arithmetics. This solution outperforms current algorithms in terms of complexity without loss in performances.

cs.IT↗
arXiv2019

Eight-dimensional Polarization-ring-switching Modulation Formats

We propose two 8-dimensional (8D) modulation formats (8D-2048PRS-T1 and 8D-2048PRS-T2) with a spectral efficiency of 5.5 bit/4D-sym, where the 8 dimensions are obtained from two time slots and two polarizations. Both formats provide a higher tolerance to nonlinearity by selecting symbols with nonidentical states of polarization (SOPs) in two time slots. The performance of these novel 8D modulation formats is assessed in terms of the effective signal-to-noise ratio (SNR) and normalized generalized mutual information. 8D-2048PRS-T1 is more suitable for high SNRs, while 8D-2048PRS-T2 is shown to be more tolerant to nonlinearities. A sensitivity improvement of at least 0.25 dB is demonstrated by maximizing normalized generalized mutual information (NGMI). For a long-haul nonlinear optical fiber transmission system, the benefit of mitigating the nonlinearity is demonstrated and a reach increase of 6.7% (560 km) over time-domain hybrid four-dimensional two-amplitude eight-phase shift keying (TDH-4D-2A8PSK) is observed.

eess.SP↗
arXiv2019

Polarization-ring-switching for nonlinearity-tolerant geometrically-shaped four-dimensional formats maximizing generalized mutual information

In this paper, a new four-dimensional 64-ary polarization ring switching (4D-64PRS) modulation format with a spectral efficiency of 6 bit/4D-sym is introduced. The format is designed by maximizing the generalized mutual information (GMI) and by imposing a constant-modulus on the 4D structure. The proposed format yields an improved performance with respect to state-of-the-art geometrically shaped modulation formats for bit-interleaved coded modulation systems at the same spectral efficiency. Unlike previously published results, the coordinates of the constellation points and the binary labeling of the constellation are jointly optimized. When compared with polarization-multiplexed 8-ary quadrature-amplitude modulation (PM-8QAM), gains of up to 0.7 dB in signal-to-noise ratio are observed in the additive white Gaussian noise (AWGN) channel. For a long-haul nonlinear optical fiber system of 8,000 km, gains of up to 0.27 bit/4D-sym (5.5% data capacity increase) are observed. These gains translate into a reach increase of approximately 16% (1,100 km). The proposed modulation format is also shown to be more tolerant to nonlinearities than PM-8QAM. Results with LDPC codes are also presented, which confirm the gains predicted by the GMI.

eess.SP↗
arXiv2018

Fermion-boson vertex within Dynamical Mean-Field Theory

In the study of strongly interacting systems, correlations on the two-particle level are receiving more and more attention. In this work, we study a particular two-particle correlation function: the fermion-boson vertex. It describes the response of the Green's function when an external field is applied and is an important ingredient of diagrammatic extensions of Dynamical Mean-Field Theory. We provide several perspectives on this object, using Ward identities, sum rules, perturbative analysis and asymptotic relations. We then use these tools to study the vertex across the doping-driven metal-insulator transition and find a divergence in the imaginary part.

cond-mat.str-el↗
arXiv2018

Second-order dual fermion approach to the Mott transition in the two-dimensional Hubbard model

We apply the dual fermion approach with a second-order approximation to the self-energy to the Mott transition in the two-dimensional Hubbard model. The approximation captures nonlocal dynamical short-range correlations as well as several features observed in studies using cluster dynamical mean-field theory. This includes a strong reduction of the critical interaction and inversion of the slope of the transition lines with respect to single-site dynamical mean-field theory. We show that these effects coincide with a much smaller momentum differentiation compared to cluster methods. We further discuss the role of the self-consistency condition and show that the approximation behaves as an asymptotic series at low temperature.

cond-mat.str-el↗
arXiv2018

Intersite electron correlations on inhomogeneous lattices: a real-space dual fermion approach

We develop a real-space extension of the dual fermion approach. This method is formulated in terms of real-space Green's functions and local vertex functions, which enables us to discuss local and nonlocal correlations in inhomogeneous systems with an arbitrary geometric structure. We first demonstrate that the approach gives us reasonable results for a homogenous periodic system by taking into account onsite and nearest-neighbor intersite correlations. Moreover, we study the half-filled Hubbard model on the quasiperiodic Penrose lattice and clarify the role of intersite correlations for the Mott transition. The intersite correlations lead to a rich structure in local observables which is inherited from the quasiperiodic structure of the lattice.

cond-mat.str-el↗