arXiv subjects
Publications and source records attributed to Gunnar Jacobsen.
We experimentally demonstrate the impact of inter-core crosstalk in multicore fibers on 56Gbaud PAM-4 signal quality after 2.5-km transmission over a weakly-coupled and uncoupled sevencore fibers, revealing the crosstalk dependence on carrier central wavelength in range of 1540-1560 nm.
This paper reports the demonstration of high-speed PAM-4 transmission using a 1.5-μm single-mode vertical cavity surface emitting laser (SM-VCSEL) over multicore fiber with 7 cores over different distances. We have successfully generated up to 70 Gbaud 4-level pulse amplitude modulation (PAM-4) signals with a VCSEL in optical back-to-back, and transmitted 50 Gbaud PAM-4 signals over both 1-km dispersion-uncompensated and 10-km dispersion-compensated in each core, enabling a total data throughput of 700 Gbps over the 7-core fiber. Moreover, 56 Gbaud PAM-4 over 1-km has also been shown, whereby unfortunately not all cores provide the required 3.8 $\times$ 10 $^{-3}$ bit error rate (BER) for the 7% overhead-hard decision forward error correction (7% OH HDFEC). The limited bandwidth of the VCSEL and the adverse chromatic dispersion of the fiber are suppressed with pre-equalization based on accurate end-to-end channel characterizations. With a digital post-equalization, BER performance below the 7% OH-HDFEC limit is achieved over all cores. The demonstrated results show a great potential to realize high-capacity and compact short-reach optical interconnects for data centers.
We experimentally demonstrate a net-rate 503.61-Gbit/s discrete multitone (DMT) transmission over 10-km 7-core fiber with 1.5-μm single mode VCSEL, where low-complexity kernelrecursive-least-squares algorithm is employed for nonlinear channel equalization.
We experimentally demonstrate a 28-Gbaud 16-QAM self-homodyne digital radio-over- 33.6km-7-core-fiber system with entropy coding for mobile fronthaul, achieving error-free carrier aggregation of 330 100-MHz 4096-QAM 5G-new-radio channels and 921 100-MHz QPSK 5G-new-radio channels with CPRI-equivalent data rate up to 3.73-Tbit/s.
Kernel adaptive filtering (KAF) is proposed for nonlinearity-tolerant optical direct detection. For 7x128Gbit/s PAM4 transmission over 33.6km 7-core-fiber, KAF only needs 10 equalizer taps to reach KP4-FEC limit (BER@2.2e-4), whereas decision-feedback-equalizer needs 43 equalizer taps to reach HD-FEC limit (BER@3.8e-3).
In optical transport networks, signal lightpaths between two terminal nodes can be different due to current network conditions. Thus the transmission distance and accumulated dispersion in the lightpath cannot be predicted. Therefore, the adaptive compensation of dynamic dispersion is necessary in such networks to enable flexible routing and switching. In this paper, we present a detailed analysis on the adaptive dispersion compensation using the least-mean-square (LMS) algorithm in coherent optical communication networks. It is found that the variable-step-size LMS equalizer can achieve the same performance with a lower complexity, compared to the traditional LMS algorithm.
The study on carrier phase estimation (CPE) approaches, involving a one-tap normalized least-mean-square (NLMS) algorithm, a block-wise average algorithm, and a Viterbi-Viterbi algorithm has been carried out in the long-haul high-capacity dispersion-unmanaged coherent optical systems. The close-form expressions and analytical predictions for bit-error-rate behaviors in these CPE methods have been analyzed by considering both the laser phase noise and the equalization enhanced phase noise. It is found that the Viterbi-Viterbi algorithm outperforms the one-tap NLMS and the block-wise average algorithms for a small phase noise variance (or effective phase noise variance), while the three CPE methods converge to a similar performance for a large phase noise variance (or effective phase noise variance). In addition, the differences between the three CPE approaches become smaller for higher-level modulation formats.
The performance of long-haul coherent optical fiber transmission system is significantly affected by the equalization enhanced phase noise (EEPN), due to the interaction between the electronic dispersion compensation (EDC) and the laser phase noise. In this paper, we present a comprehensive study on different chromatic dispersion (CD) compensation and carrier phase recovery (CPR) approaches, in the n-level phase shift keying (n-PSK) and the n-level quadrature amplitude modulation (n-QAM) coherent optical transmission systems, considering the impacts of EEPN. Four CD compensation methods are considered: the time-domain equalization (TDE), the frequency-domain equalization (FDE), the least mean square (LMS) adaptive equalization are applied for EDC, and the dispersion compensating fiber (DCF) is employed for optical dispersion compensation (ODC). Meanwhile, three carrier phase recovery methods are also involved: a one-tap normalized least mean square (NLMS) algorithm, a block-wise average (BWA) algorithm, and a Viterbi-Viterbi (VV) algorithm. Numerical simulations have been carried out in a 28-Gbaud dual-polarization quadrature phase shift keying (DP-QPSK) coherent transmission system, and the results indicate that the origin of EEPN depends on the choice of chromatic dispersion compensation methods, and the effects of EEPN also behave moderately different in accordance to different carrier phase recovery scenarios.
The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of which is a key to unlocking the fiber optic systems specifications required in high resolution spectroscopy, metrology, biomedicine and telecommunications. Here, by using direct stochastic modeling, the mapping of interplay of the Raman scattering-based nonlinearity, the random birefringence of a fiber, and the pump-to-signal intensity noise transfer has been done in terms of the fiber Raman amplifier parameters, namely polarization mode dispersion, the relative intensity noise of the pump laser, fiber length, and the signal power. The obtained results reveal conditions for emergence of the random birefringence-induced resonance-like enhancement of the gain fluctuations (stochastic anti-resonance) accompanied by pulse broadening and rare events in the form of low power output signals having probability heavily deviated from the Gaussian distribution.
The performance of long-haul high speed coherent optical fiber communication systems is significantly degraded by the laser phase noise and the equalization enhanced phase noise (EEPN). In this paper, the analysis of the one-tap normalized least-mean-square (LMS) carrier phase recovery (CPR) is carried out and the close-form expression is investigated for quadrature phase shift keying (QPSK) coherent optical fiber communication systems, in compensating both laser phase noise and equalization enhanced phase noise. Numerical simulations have also been implemented to verify the theoretical analysis. It is found that the one-tap normalized least-mean-square algorithm gives the same analytical expression for predicting CPR bit-error-rate (BER) floors as the traditional differential carrier phase recovery, when both the laser phase noise and the equalization enhanced phase noise are taken into account.
Using coherent optical detection and digital signal processing, laser phase noise and equalization enhanced phase noise can be effectively mitigated using the feed-forward and feed-back carrier phase recovery approaches. In this paper, theoretical analyses of feed-back and feed-forward carrier phase recovery methods have been carried out in the long-haul high-speed n-level phase shift keying (n-PSK) optical fiber communication systems, involving a one-tap normalized least-mean-square (LMS) algorithm, a block-wise average algorithm, and a Viterbi-Viterbi algorithm. The analytical expressions for evaluating the estimated carrier phase and for predicting the bit-error-rate (BER) performance (such as the BER floors) have been presented and discussed in the n-PSK coherent optical transmission systems by considering both the laser phase noise and the equalization enhanced phase noise. The results indicate that the Viterbi-Viterbi carrier phase recovery algorithm outperforms the one-tap normalized LMS and the block-wise average algorithms for small phase noise variance (or effective phase noise variance), while the one-tap normalized LMS algorithm shows a better performance than the other two algorithms for large phase noise variance (or effective phase noise variance). In addition, the one-tap normalized LMS algorithm is more sensitive to the level of modulation formats.
An analytical model is presented for assessing the performance of the bit-error-rate (BER) in the differential m-level phase shift keying (m-PSK) transmission systems, where the influence of equalization enhanced phase noise (EEPN) has been considered. Theoretical analysis has been carried out in differential quadrature phase shift keying (DQPSK), differential 8-PSK (D8PSK), and differential 16-PSK (D16PSK) coherent optical transmission systems. The influence of EEPN on the BER performance, in term of signal-to-noise ratio (SNR), are investigated for different fiber dispersion, LO laser linewidths, symbol rates, and modulation formats. Our analytical model achieves a good agreement with previously reported EEPN induced BER floors, and can give an accurate prediction for the DQPSK system, and a leading-order approximation for the D8PSK and the D16PSK systems.
We present a study of the influence of dispersion induced phase noise for CO-OFDM systems using FFT multiplexing/IFFT demultiplexing techniques (software based). The software based system provides a method for a rigorous evaluation of the phase noise variance caused by Common Phase Error (CPE) and Inter-Carrier Interference (ICI) including - for the first time to our knowledge - in explicit form the effect of equalization enhanced phase noise (EEPN). This, in turns, leads to an analytic BER specification. Numerical results focus on a CO-OFDM system with 10-25 GS/s QPSK channel modulation. A worst case constellation configuration is identified for the phase noise influence and the resulting BER is compared to the BER of a conventional single channel QPSK system with the same capacity as the CO-OFDM implementation. Results are evaluated as a function of transmission distance. For both types of systems, the phase noise variance increases significantly with increasing transmission distance. For a total capacity of 400 (1000) Gbit/s, the transmission distance to have the BER < 10^-2 for the worst case CO-OFDM design is less than 800 and 460 km, respectively, whereas for a single channel QPSK system it is less than 1400 and 560 km.
The analysis of adaptive carrier phase estimation is investigated in long-haul high speed n-level phase shift keying (n-PSK) optical fiber communication systems based on the one-tap normalized least-mean-square (LMS) algorithm. The close-form expressions for the estimated carrier phase and the bit-error-rate floor have been derived in the n-PSK coherent optical transmission systems. The results show that the one-tap normalized LMS algorithm performs pretty well in the carrier phase estimation, but will be less effective with the increment of modulation levels, in the compensation of both intrinsic laser phase noise and equalization enhanced phase noise.
We present a comparative study of the influence of dispersion induced phase noise for CO-OFDM systems using Tx channel multiplexing and Rx matched filter (analogue hardware based); and FFT multiplexing/IFFT demultiplexing techniques (software based). An RF carrier pilot tone is used to mitigate the phase noise influence. From the analysis, it appears that the phase noise influence for the two OFDM implementations is very similar. The software based system provides a method for a rigorous evaluation of the phase noise variance caused by Common Phase Error (CPE) and Inter-Carrier Interference (ICI) and this, in turns, leads to a BER specification. Numerical results focus on a CO-OFDM system with 1GS/s QPSK channel modulation. Worst case BER results are evaluated and compared to the BER of a QPSK system with the same capacity as the OFDM implementation. Results are evaluated as a function of transmission distance, and for the QPSK system the influence of equalization enhanced phase noise (EEPN) is included. For both types of systems, the phase noise variance increases significantly with increasing transmission distance. An important and novel observation is that the two types of systems have very closely the same BER as a function of transmission distance for the same capacity. For the high capacity QPSK implementation, the increase in BER is due to EEPN, whereas for the OFDM approach it is due to the dispersion caused walk-off of the RF pilot tone relative to the OFDM signal channels. For a total capacity of 400 Gb/s, the transmission distance to have the BER < 10-4 is less than 277 km.
In this paper we present a comparative study in order to specify the influence of equalization enhanced phase noise (EEPN) for pre- and post-compensation of chromatic dispersion in high capacity and high constellation systems. This is - to our knowledge - the first detailed study in this area for pre-compensation systems. Our main results show that the local oscillator phase noise determines the EEPN influence in post-compensation implementations whereas the transmitter laser determines the EEPN in pre-compensation implementations. As a result of significance for the implementation of practical longer-range systems it is to be emphasized that the use of chromatic dispersion equalization in the optical domain - e.g. by the use of dispersion compensation fibers - eliminates the EEPN entirely. Thus, this seems a good option for such systems operating at high constellations in the future.
For coherent and direct-detection Orthogonal Frequency Division Multiplexed (OFDM) systems employing radio frequency (RF) pilot tone phase noise cancellation the influence of laser phase noise is evaluated. Novel analytical results for the common phase error and for the (modulation dependent) inter carrier interference are evaluated based upon Gaussian statistics for the laser phase noise. In the evaluation it is accounted for that the laser phase noise is filtered in the correlation signal detection. Numerical results are presented for OFDM systems with 4 and 16 PSK modulation, 200 OFDM bins and baud rate of 1 GS/s. It is found that about 225 km transmission is feasible for the coherent 4PSK-OFDM system over normal (G.652) fiber.
The frequency domain equalizers (FDEs) employing two types of overlap-add zero-padding (OLA-ZP) methods are applied to compensate the chromatic dispersion in a 112-Gbit/s non-return-to-zero polarization division multiplexed quadrature phase shift keying (NRZ-PDM-QPSK) coherent optical transmission system. Simulation results demonstrate that the OLA-ZP methods can achieve the same acceptable performance as the overlap-save method. The required minimum overlap (or zero-padding) in the FDE is derived, and the optimum fast Fourier transform length to minimize the computational complexity is also analyzed.