arXiv subjects
Publications and source records attributed to Henning Buelow.
A receiver with shared complexity between optical and digital domains is experimentally demonstrated. Reservoir computing is used to equalize up to 4 directly-detected optically filtered spectral slices of a 32 GBd OOK signal over up to 80 km of SMF.
Optical nonlinear Fourier transform-based communication systems require an accurate estimation of a signal's nonlinear spectrum, computed usually by piecewise approximation methods on the signal samples. We propose an algorithm, named successive eigenvalue removal, to improve the spectrum estimation of a multi-soliton pulse. It exploits a property of the Darboux transform that allows removing eigenvalues from the nonlinear spectrum. This results in a smaller pulse duration and smaller bandwidth. The spectral coefficients are estimated successively after removing the eigenvalues of a signal. As a beneficial application, we show that the algorithm decreases the computational complexity by iteratively reducing the pulse duration.
There has been much interest in the non-linear frequency-division multiplexing (NFDM) transmission scheme in the optical fibre communication system. Up to date, most of the demonstrated NFDM schemes have employed only single polarisation for data transmission. Employing both polarisations can potentially double the data rate of NFDM systems. We investigate in simulation a dual-polarisation NFDM transmission with data modulation on the $b$-coefficient. First, a transformation that facilitates the dual-polarisation $b$-modulation was built upon an existing transformation. Second, the $q_c$- and $b$-modulation for dual-polarisation were compared in terms of Q-factor, spectral efficiency (SE), and correlation of sub-carriers. The correlation is quantified via information theoretic metrics, joint and individual entropy. The polarisation-multiplexed $b$-modulation system shows 1 dB Q-factor improvement over $q_c$-modulation system due to a weaker correlation of sub-carriers and less effective noise. Finally, the $b$-modulation system was optimised for high data rate, achieving a record net data rate of 400 Gbps (SE of 7.2 bit/s/Hz) over $12\times 80$ km of standard single-mode fibre (SSMF) with erbium-doped fibre amplifiers (EDFAs). Based on the above simulation results, we further point out the drawbacks of our current system and quantify the error introduced by the transceiver algorithms and non-integrability of the channel.
Spectral amplitude modulation for dual-polarization multi-soliton transmission is considered. We show, that spectral amplitudes become highly correlated during propagation along a noisy fiber link. Thus, joint equalization is generally needed at the receiver. We propose a simple precoding scheme to almost remove these correlations. It significantly improves the detection performance even without any complex equalization. The spectral amplitudes are transformed into pairs of common and differential information part. We show, that the differential part is almost preserved along the link, even in the presence of noise. Thus, it can be detected directly from the received spectral amplitudes with high reliability. Using the precoding, disjoint detection of the common and the differential part causes only a small performance loss. We analyze our precoding and verify its performance gain in Split-Step-Fourier simulations by comparing it to the conventional independent modulation of spectral amplitudes for first and second order solitons.
Multi-soliton pulses are potential candidates for fiber optical transmission where the information is modulated and recovered in the so-called nonlinear Fourier domain. While this is an elegant technique to account for the channel nonlinearity, the obtained spectral efficiency, so far, is not competitive with classic Nyquist-based schemes. This is especially due to the observation that soliton pulses generally exhibit a large time-bandwidth product. We consider the phase modulation of spectral amplitudes of higher order solitons, taking into account their varying spectral and temporal behavior when propagating along the fiber. For second and third order solitons, we numerically optimize the pulse shapes to minimize the time-bandwidth product. We study the behavior of multi-soliton pulse duration and bandwidth and generally observe two corner cases where we approximate them analytically. We use these results to give an estimate on the minimal achievable time-bandwidth product per eigenvalue.
We present an efficient, fast and robust Nonlinear Fourier Transform (NFT) algorithm to detect eigenvalues of the discrete spectrum. It outperforms other known NFT algorithms as it detects the eigenvalues from the continuous spectrum, the numerically more robust part of the nonlinear spectrum.
We consider dual-polarized optical multi-soliton pulse transmission. Modulating the nonlinear spectrum, it becomes highly correlated in noisy fiber links. We propose a simple precoding to significantly reduce the correlation, allowing disjoint detection of spectral amplitudes.
We demonstrate, for the first time, a b-modulated dual-polarisation NFDM transmission in simulation, achieving a record net data rate of 400 Gbps (SE of 7.2 bit/s/Hz) over 960 km. The proposed scheme shows 1 dB Q-factor improvement over qc-modulation scheme.
We show a non-negligible cross-talk between nonlinear modes in Nonlinear Frequency-Division Multiplexed system when data is modulated over the nonlinear Fourier spectrum, both the continuous spectrum and the discrete spectrum, and transmitted over a lumped amplified fiber link. We evaluate the performance loss if the cross-talks are neglected.
Record-high data rate of 125 Gb/s and SE over 2 bits/s/Hz in burst-mode single-polarization NFDM transmissions were achieved over 976 km of SSMF with EDFA-only amplification by transmitting and processing 222 32 QAM-modulated nonlinear subcarriers simultaneously
Multi-soliton pulses are potential candidates for fiber optical transmission where the information is modulated and recovered in the so-called nonlinear Fourier domain. While this is an elegant technique to account for the channel nonlinearity, the obtained spectral efficiency, so far, is not competitive with the classic Nyquist-based schemes. In this paper, we study the evolution of the time-bandwidth product of multi-solitons as they propagate along the optical fiber. For second and third order soliton pulses, we numerically optimize the pulse shapes to achieve the smallest time-bandwidth product when the phase of the spectral amplitudes is used for modulation. Moreover, we analytically estimate the pulse-duration and bandwidth of multi-solitons in some practically important cases. Those estimations enable us to approximate the time-bandwidth product for higher order solitons.
We explain how to optimize the nonlinear spectrum of multi-soliton pulses by considering the practical constraints of transmitter, receiver, and lumped-amplified link. The optimization is applied for the experimental transmission of 2ns soliton pulses with independent on-off keying of 10 eigenvalues over 2000 km of NZ-DSF fiber spans.
We report a 3 dB increase in the nonlinear threshold of a 64*0.5Gbaud 16-QAM continuous-nonlinear-spectrum modulated signal by nonlinear multiplexing with QPSK modulated multi-solitons, showing the first ever fully nonlinear-spectrum modulated system in the highly nonlinear regime.
2-ns waveforms with 7 eigenvalues and their QPSK-modulated spectral amplitudes were optimized by taking constraints of link, transmitter, and receiver into account. In experiment these signals were transmitted with a BER of 3.2E-3 over 1440-km of NZ-DSF fiber spans.
We experimentally demonstrate an NFDM optical system with modulation over nonlinear discrete spectrum. Particularly, each symbol carries 4-bits from multiplexing two eigenvalues modulated by QPSK constellation. We show a low error performance using NFT detection with 4Gbps rate over 640km.