Maximum likelihood sequence detection in laser phase noise-impaired coherent optical systems

The performances of the proposed decision-aided maximum likelihood (DA ML) and maximum likelihood sequence detection (MLSD) algorithms are investigated in this paper. It is shown that MLSD significantly improves laser linewidth tolerance. 100 Gb/s DP-QPSK experiments are carried out to verify our results.

We report the use of implicit training-aided channel estimation (ITA-CE) for polarization-division-multiplexed (PDM) single-carrier coherent optical systems. With the concept of ITA-CE, where the training sequence (TS) is arithmetically added onto the information symbols rather than appearing in separate time slots, overhead-free transmission can be achieved with minor optical signal to noise ratio (OSNR) penalty. ITA-CE system enables simple digital pilot-tone based frequency-offset compensation, and inherits the benefits from typical training-aided channel acquisition and data recovery. Furthermore, we address the issue of self-interference to channel estimation (CE) of ITA-CE system in this paper. The data-induced interference can be eliminated by removing the cyclic mean of the transmitted signal, which can accelerate the convergence of the CE and allows smaller power to be allocated to the TS, leading to enhanced system performance. Numerical simulations and experiments for both PDM-QPSK and PDM-16-QAM systems have been conducted to verify the proposed scheme. Comparable performance to the conventional blind equalization system can be achieved when employing the transmitter side pre-distortion approach to the ITA-CE system.

This study evaluates the performance of binary- and M-ary-PSK coherent optical systems using cascaded optical amplifiers in the presence of noise originating from the detector, receiver, optical amplifiers, and the laser phase fluctuations. Our results on the analysis of these systems indicate that at an amplifier input power of −20 dBm and a system length of 10,000 km, the power penalties incurred due to the laser phase noise at a bit error rate of 10−9 correspond to 0.57, 0.99, and 3.38 dB at linewidths of 770.31, 101.86, and 6.37 kHz for binary-PSK, four-PSK, and eight-PSK systems, respectively. ©1996 John Wiley & Sons, Inc.

Nowadays, the coherent optical communication system plays an important role in communication field because of large capability and bandwidth. A coherent optical communication, based on high-order modulation and digital signal processing technologies, consists of optical transmitters, optical fiber lines, optical amplifiers and optical receivers. In the high-speed coherent optical communication system, the phase noise from the transmitter laser and the local oscillator laser can significantly degrade the performance of the signal transmission and detection, especially for the systems using high-order modulation format, such as m-ary phase shift keying (mPSK) and m-ary quadrature amplitude modulation (m-QAM). Therefore, investigations on laser phase noise compensation algorithm based on digital signal processing technologies has become more and more significant. In this work, a multi-ring carrier phase recovery algorithm is developed for compensating the laser phase noise in optical fiber communication systems using high-order modulation formats. Degradations on the performance of communication systems due to the laser phase noise have been investigated. The system performance using the proposed algorithm and the conventional Viterbi-Viterbi algorithm were also evaluated in 9-channel and 15- channel, 32-Gbaud, Nyquist-spaced QPSK, 16-QAM, 64-QAM and 256-QAM coherent transmission systems with considering the impact of the laser phase noise. It is found that the phase noise leads to stricter constraints on the linewidths of transmitter-side and receiver-side lasers, and it can greatly degrade the achievable information rates in communication systems. Besides, compared to the conventional Viterbi-Viterbi algorithm, which is usually applied in the QPSK system, our proposed algorithm can also well mitigate the laser phase noise in 16-QAM, 64-QAM and 256-QAM optical communication systems.
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The frequency separation between the two channels of a dual-filter heterodyne FSK optical system is a very important parameter to evaluate in the presence of laser phase noise. In this work the impairment due to the corsstalk interference between the two transmitted tones of a weakly coherent FSK optical system is investigated. In order to make accurate computations, the method of moments seems to be the most suitable: to this aim, in this work an algorithm for the moments evaluation is proposed. The numerical results are then compared with a Monte Carlo simulation appraoch

Theory of Optical Communications. Fiber Devices for Optical Communication Systems. Integrated Devices for Optical Communication Systems. Direct Detection Optical Communication Systems. Coherent Systems: Structure and Ideal Performance. Performance Degradation Sources in Coherent Optical Systems. Multilevel Coherent Optical Systems. Multichannel Optical Systems. Present--Day Systems Implementations. Appendices. Index.

An efficient trellis-based phase noise mitigation algorithm is proposed to highly improve the performance of coherent transmission systems, especially in high order modulation formats. The proposed method targets the coherent optical systems where the performance is limited by various sources of phase noise including laser line-width, fiber non-linearity, and phase noise induced by phase-locked loop. Considering hardware limitations of ultra-high data rate processing in optical systems, a hardware-efficient parallelized and pipelined architecture is utilized. Experimental results in 200 Gb/s DP-16QAM co-propagated with 10-G channels demonstrate significant performance improvement over other existing methods.

Several authors have recently investigated phase noise in semiconductor lasers and the related problems that arise when such lasers are employed in coherent optical communication systems. We report accurate measurements of high-frequency phase noise in single-mode injection lasers that show the presence of a peak in the phase-noise spectrum at the same frequency as that of the amplitude-noise peak. This peculiar phenomenon must be taken into account when one studies the characteristics of coherent optical communication systems.

The magnetic recording channel at high-density exhibits significant nonlinear intersymbol interference, which degrades the performance of linear equalization techniques. The RAM-DFE has been proposed as a solution to the problem, in which a digital RAM is used in the feedback path of a decision feedback equalizer (DFE). It is capable of canceling the nonlinear post-cursor intersymbol interference. Maximum-likelihood sequence detection (MLSD) offers the best performance attainable on these binary-input finite-memory channels; however, the complexity grows exponentially with the memory length. It was found that about 6 dB of detection signal-to-noise ratio is lost to nonlinear effects, and the RAM-DFE can retrieve about 1.5 dB. A gap of about 6 dB remains between the RAM-DFE performance and the MLSD bound, which suggests the possibility of improved receivers for nonlinear channels. >

Polarization dependent loss (PDL) causes imbalanced optical signal to noise ratio (OSNR) of the two polarizations, thus remains one of the major bottlenecks for next-generation polarization-division-multiplexed (PDM) coherent optical transmission systems. In this paper, we investigate Pairwise Coding for adaptive PDL mitigation in PDM coherent optical systems. By pre-coding across two polarizations, the PDL-induced performance degradation can be largely mitigated without any coding overhead. We present details of the coding and de-coding design, and also derive the analytical symbol/bit error rate of the Polarization Pairwise Coding scheme, which can be used to predict the performance gain as well as for optimal rotation angle calculation. Simulation results verify that Pairwise Coding achieves substantial system performance gains over a wide range of PDL values. Compared with other digital coding techniques, Polarization Pairwise Coding shows improved performance than Walsh-Hadamard transform since it maximizes the coordinate diversity; and also Pairwise Coding is computationally much simpler to decode compared with the Golden and Silver Codes, therefore is practical for current 100-Gb/s and future 400-Gb/s and 1-Tb/s digital coherent transceivers.

The presence of laser phase noise (or frequency jitter) limits the resolution of a variety of interferometric sensors ranging from fiber optic acoustic sensors to gravitational wave detectors. At low frequencies, 0 to 100 kHz, the laser phase noise in semiconductor and diode pumped solid-state lasers is dominated by 1/f noise, the source of which is not well understood. We report on phase noise measurements for external cavity semiconductor lasers (ECSLs) utilizing a fiber Bragg grating in a compact butterfly package design produced by K2 Optronics. The results show that the phase noise is dominated by 1/f noise for low frequencies (10 to 100 kHz) transitioning to a white noise due to spontaneous emission for f > 100 kHz. We observed a factor of 40 improvement in the magnitude of the 1/f phase noise as compared to previously published results for a Hitachi HLP 1400 830 nm diode laser. The magnitude of the low frequency phase noise ranges from 100 to 10 microradians per meter per root Hz for frequencies ranging from 10 Hz to 2 kHz. These results are within a factor of 10 for phase noise measurements of the more expensive Lightwave Electronics Nd:YAG laser and a variety of Er-doped fiber lasers in this frequency range. For nominally similar ECSLs, experimental results indicate that the phase noise increases for lasers with larger leakage currents. Linewidth measurement results showed a Schawlow-Townes inverse power dependence for output powers up to 33 mWatts with the observed onset of a linewidth floor of 30 kHz. The RIN of the ECSLs varied from -120 to -155 dB Vrms per root Hz for frequencies ranging from 10 to 500 kHz. These RIN results are roughly equal to those observed for the Nd:YAG laser for frequencies less that 100 kHz. In summary, such low phase noise and RIN results make such ECSLs suitable for all but the most sensitive fiber optic sensing applications where the frequency range of interest is below 1 MHz.

We investigate the force measurement sensitivity in a squeezed dissipative optomechanics within the free-mass regime under the influence of shot noise (SN) from the photon number fluctuations, laser phase noise from the pump laser, thermal noise from the environment, and optical losses from outcoupling and detection inefficiencies. Generally, squeezed light could generate a reduced SN on the squeezed quadrature and an enlarged quantum backaction noise (QBA) due to the antisqueezed conjugate quadrature. With an appropriate choice of phase angle in homodyne detection, QBA is cancellable, leading to an exponentially improved measurement sensitivity for the SN-dominated regime. By now, the effects of laser phase noise that is proportional to laser power emerge. The balance between squeezed SN and phase noise can lead to an sub-SQL sensitivity at an exponentially lower input power. However, the improvement by squeezing is limited by optical losses because high sensitivity is delicate and easily destroyed by optical losses.

A pilot-aided channel equalizer (PACE) is proposed to mitigate the impairments caused by the polarization mode dispersion and laser phase noise simultaneously in reduced-guard-interval polarization-division-multiplexing coherent-optical orthogonal-frequency-division-multiplexing (RGI-PDM-CO-OFDM) transmission systems. Since PACE updates the channel state information symbol-by-symbol, it enables us to track the drifts in the optical channel. Adaptive PACE (APACE) and boosted PACE (BPACE) are then proposed to further improve the performance of PACE. Numerical simulations are carried out to compare the performance of APACE and BPACE with a conventional training symbols aided channel equalizer (TSACE) and adaptive decision-direct channel equalizer for a 108-Gb/s (56-GS/s) RGI-PDM-CO-OFDM system. It is revealed that both APACE and BPACE offer superior performances over the other two equalizers in the presence of laser phase noise, and they can tolerate lasers with a line width around <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\beta=2000~{\rm k}$</tex></formula> ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$2\pi\beta T_{s}=2.24\times 10$</tex></formula> when it is normalized to the symbol rate <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$1/T_{s}$</tex></formula> ). We also show that only small additional computation efforts are required for APACE and BPACE when compared with TSACE.

In this paper, an optical FSK system with TFS (two-filter structure) also known as dual-filter FSK is observed in the presence of laser phase noise. Sensitivity of the receiver is shown as a function of IF bandwidth and a bandwidth of the low-pass postdetection filter. It is shown that there is an optimal pair of bandwidths witch minimizes required receiver sensitivity: a few figures for different amounts of phase noise are given. The results in this paper are based on truncated Taylor expansion method.

In this research, the effect of laser phase noise fixing is investigated for different optical channel parameters such as dispersion, attenuation and link distance for Coherent Optical Orthogonal Frequency Division Multiplexing (CO-OFDM) systems. The effect of laser phase noise is examined at different data rates and link distances utilizing only one RF and optical carrier. In this research Phase Shift Keying (PSK) is used as a digital modulation format to maintain the maximum data rate with the acceptable BER value. By fixing the laser phase noise 1.7 Tb/s (111∗16 Gb/s) can be obtained from 191.4 to 185.9 THz at 50 GHz spacing over 1000 km link distance using only one optical cable in C and L bands according to the Telecommunication Standardization Sector (ITU-T). In that case high level modulation formats (N-PSK) should be performed with DWDM technique.