Decision-aided Maximum Likelihood Phase Estimation Research Articles

Cold-start of coherent optical receivers with decision-aided maximum likelihood phase estimation scheme

Abstract In coherent optical communication systems adopting decision-aided maximum likelihood (DA-ML) phase estimation, receiver initialization requires transmission of a training sequence followed by data symbols. However, such a start-up scheme is infeasible under the scenarios like burst-mode transmission and multi-receiver scheme. We propose a novel cold-start concept for DA-ML receiver without using a training sequence. By adopting the M th-power scheme, initial data symbols are estimated and further utilized to start up the DA-ML receiver effectively. Extensive numerical simulations are conducted under different situations for comparison. Results verify the feasibility of the proposed cold-start scheme. Based on conventional DA-ML, adopting cold-start can effectively start up the DA-ML receiver as well as achieve comparative bit error rate (BER) performance under burst-mode transmission and multi-receiver scenarios, with good robustness and nearly the same system complexity.

Flexible DAML phase estimation algorithm in coherent optical M-PSK systems

Decision-aided maximum likelihood (DAML) phase estimation has been applied in coherent optical communication systems due to its high computational efficiency. However, conventional DAML algorithm only considers constant laser phase noise over the entire block length, thus causing block length effect. Given time-varying laser phase noise, a flexible DAML phase estimation algorithm is proposed in coherent optical M-PSK systems, which can eliminate the block length effect of conventional DAML. Weighted coefficients are introduced to estimate carrier phase more accurately than the conventional algorithm. Meanwhile, the phase estimation error is derived and simulations justify its validity. Simulation results also show that the flexible DAML algorithm can eliminate the block length effect of conventional DAML and relax the requirement of laser linewidth in coherent optical M-PSK systems.

Flexible decision-aided maximum likelihood phase estimation in coherent optical phase-shift-keying systems

Decision-aided maximum likelihood (DA-ML) phase estimation has been applied in coherent optical communication systems due to its high computational efficiency. However, conventional DA-ML scheme only assumes constant phase noise within each observation block, thus causing block length effect (BLE) which degrades system performance. In this paper, we take into account the time-varying laser phase noise and propose a flexible DA-ML phase estimation method for carrier phase recovery in coherent optical phase-shift-keying systems so as to eliminate BLE. Weighted coefficients based on ML criterion are introduced to strengthen the estimation accuracy. The statistical property of phase estimation error is derived, and the bit error rate (BER) performance is also evaluated. Numerical simulation results show that our flexible DA-ML scheme is very robust against time-varying phase noise. Compared with conventional DA-ML receiver, it can significantly reduce the phase estimation variance, improve the BER performance and increase the laser linewidth tolerance. By adopting the flexible DA-ML method with a relatively larger block length, BLE can be effectively eliminated. Thus, the BER performance can be significantly improved without carefully finding out the optimum block length or the optimum forgotten factor.

A flexible decision-aided maximum likelihood phase estimation in hybrid QPSK/OOK coherent optical WDM systems

Although decision-aided (DA) maximum likelihood (ML) phase estimation (PE) algorithm has been investigated intensively, block length effect impacts system performance and leads to the increasing of hardware complexity. In this paper, a flexible DA-ML algorithm is proposed in hybrid QPSK/OOK coherent optical wavelength division multiplexed (WDM) systems. We present a general cross phase modulation (XPM) model based on Volterra series transfer function (VSTF) method to describe XPM effects induced by OOK channels at the end of dispersion management (DM) fiber links. Based on our model, the weighted factors obtained from maximum likelihood method are introduced to eliminate the block length effect. We derive the analytical expression of phase error variance for the performance prediction of coherent receiver with the flexible DA-ML algorithm. Bit error ratio (BER) performance is evaluated and compared through both theoretical derivation and Monte Carlo (MC) simulation. The results show that our flexible DA-ML algorithm has significant improvement in performance compared with the conventional DA-ML algorithm as block length is a fixed value. Compared with the conventional DA-ML with optimum block length, our flexible DA-ML can obtain better system performance. It means our flexible DA-ML algorithm is more effective for mitigating phase noise than conventional DA-ML algorithm.

Decision-aided maximum likelihood phase estimation with optimum block length in hybrid QPSK/16QAM coherent optical WDM systems

We propose a general model to entirely describe XPM effects induced by 16QAM channels in hybrid QPSK/16QAM wavelength division multiplexed (WDM) systems. A power spectral density (PSD) formula is presented to predict the statistical properties of XPM effects at the end of dispersion management (DM) fiber links. We derive the analytical expression of phase error variance for optimizing block length of QPSK channel coherent receiver with decision-aided (DA) maximum-likelihood (ML) phase estimation (PE). With our theoretical analysis, the optimum block length can be employed to improve the performance of coherent receiver. Bit error rate (BER) performance in QPSK channel is evaluated and compared through both theoretical derivation and Monte Carlo simulation. The results show that by using the DA-ML with optimum block length, bit signal-to-noise ratio (SNR) improvement over DA-ML with fixed block length of 10, 20 and 40 at BER of 10−3 is 0.18dB, 0.46dB and 0.65dB, respectively, when in-line residual dispersion is 0ps/nm.

Relative Phase Noise-Induced Phase Error and System Impairment in Pump Depletion/Nondepletion Regime

Although the pump relative intensity noise transfer phenomenon in traditional Raman amplified amplitude-shift keying fiber communication systems has been investigated intensively, the stochastic intensity fluctuation of Raman pump laser will interplay with fiber nonlinearity and leads to additional phase noise of signal in the multilevel modulated coherent optical communication system. Such phase noise is defined as relative phase noise (RPN). In this paper, we present comprehensive analysis regarding the characteristics and impairments of RPN through both theoretical derivation and Monte Carlo simulation. We derive the analytical expressions of phase error variance for M-ary PSK and 16QAM modulation formats in consideration of RPN using decision-aided maximum-likelihood phase estimation algorithm. The analysis can be used to predict RPN induced impairment theoretically. Bit error rate (BER) performance is evaluated and compared for QPSK, 8PSK, 16PSK, and 16QAM modulation formats, and the result shows that in the context of RPN 16QAM signal outperforms 16PSK which has the same spectral efficiency. Finally, we extend the analytical result obtained in pump nondepletion regime to depletion regime via numerical analysis. It is observed by comparison that Q-factor penalty will increase in depletion regime.

Experiment on Coherent Optical RZ 8-Star QAM Systems Using Decision-Aided Maximum Likelihood Phase Estimation

In this letter, a return-to-zero 8-star quadrature amplitude modulation (QAM) signal is generated for the first time by using a parallel I/Q modulator followed by an amplitude modulator with binary drive signals. Our experimental results verify the theoretically derived approximate bit-error rate and ring ratio optimization algorithm of the 8-star QAM. Decision-aided maximum likelihood phase estimation (PE) shows comparable performance with V&V Mth-power PE, but with much less computational complexity.

Performance analysis of coherent optical 8-star QAM systems using decision-aided maximum likelihood phase estimation

An approximate bit-error rate (BER) expression of 8-star quadrature amplitude modulation (QAM) in the presence of a phase estimation error is derived. The accuracy of the approximate BER is verified via numerical integration of the conditional BER and the Monte-Carlo (MC) simulations. This approximation allows quick estimation of the BER performance and prediction of laser linewidth tolerance, and also facilitates optimization of the ring ratio.