Decision-aided Maximum Likelihood Research Articles

Characteristics of Attention Bias in Patients With Depression Disorder, and the Influence of High Frequency Transcranial Magnetic Stimulation Therapy on the Attention Bias

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 0.18 dB, 0.46 dB and 0.65 dB, respectively, when in-line residual dispersion is 0 ps/nm.

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.

Performance of ADC resolution-limited optical coherent receivers with DA-ML carrier phase estimation

We investigate the performance of decision-aided maximum likelihood (DA-ML) carrier phase estimation (CPE) algorithm in analog-to-digital converter (ADC) resolution-limited optical coherent receivers. The signal model of ADC resolution-limited receiver is established, and its bit error rate with DA-ML CPE in M-ary phase-shift keying (MPSK) system is analyzed. Simulation results show that $$N+2$$N+2 (N bits per symbol)-bit resolution is acceptable and $$N+3$$N+3 bit is sufficient for DA-ML receiver in MPSK $$(M=4, 8, 16)$$(M=4,8,16) system, and for 16-ary quadrature amplitude modulation system, 6-bit resolution is reasonable. Simulation and theoretical analyses both indicate that the optimal ADC quantization range equals to the average amplitude of received symbols which carry the information symbols with the highest energy on the constellation.

A Low-Complexity, Low-Cycle-Slip-Probability, Format-Independent Carrier Estimator with Adaptive Filter Length

We present a low-complexity carrier estimator with an effective filter length that automatically adapts according to the signal-to-noise ratio, laser-linewidth-symbol-duration product, nonlinear phase noise, and modulation format. Laser-linewidth and frequency-offset tolerances are studied. The filter length of a carrier estimator is shown to affect the cycle slip probability besides the bit-error rate (BER) performance. Considering that forward-error-correction codes are not robust to burst errors and phase slips, we demonstrate that filter-length optimization is necessary to avoid spectral-efficiency reduction in pilot assisted systems and potential system failures in differential encoding systems. Our estimator achieves a lower cycle slip probability and a greater nonlinear phase noise tolerance than DiffFE-MPE, DiffFE-BPS, and complex-weighted decision-aided maximum-likelihood (CW-DA-ML) estimator. DiffFE-MPE and DiffFE-BPS refer to the differential frequency estimator (DiffFE) followed by block Mth power phase estimator (MPE) and blind phase search (BPS), respectively. For a 4100 km quaternary phase-shift keying transmission at a BER of 2.5 ×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">- 2</sup> , our estimator achieves a cycle slip probability of 2.9 ×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">- 7</sup> compared to 5.6 ×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">- 6</sup> , 5.3 ×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">- 6</sup> , and 3.2 ×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">- 7</sup> for DiffFE-MPE, DiffFE-BPS, and CW-DA-ML, respectively.

On Decision Aided Carrier Phase and Frequency Offset Estimation in Coherent Optical Receivers

We investigate carrier estimation (CE) for coherent optical receivers where the received signal is impaired by additive white Gaussian noise, laser phase noise, and frequency offset. Best practical 4-, 8-, and 16-point constellations are identified. A generalized differential encoding rule for signal constellations is presented. Performance of our complex-weighted decision-aided maximum-likelihood (CW-DA-ML) phase noise and frequency offset estimator is analyzed at low signal-to-noise ratio (SNR) and the optimal filter lengths are found. CW-DA-ML CE is put in perspective with respect to two fundamental estimators in the literature: (i) differential frequency estimator followed by block <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th power phase estimator (DiffFE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE), and (ii) fast Fourier transform based frequency estimator followed by block <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th power phase estimator (FFTbE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE), in terms of laser linewidth tolerance, frequency estimation range and speed, SNR threshold, and cycle slip probability. CW-DA-ML CE is 2.5 and 10.5 times faster than DiffFE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE in 4 phase-shift keying and 16 quadrature amplitude modulation signals, respectively, at a 1-dB system penalty for a bit-error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . Our CE has lower cycle slip probability and transmission overhead than DiffFE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th and FFTbE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE. Hence, our CE is shown to be favourable in pilot-assisted (PA) systems. A PA CW-DA-ML CE is introduced and shown to be robust against time-varying frequency offset with minimal training overhead. Analog-to-digital convertor quantization error on our CE performance is also addressed.

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.

Decision-Aided Carrier Phase Estimation for Coherent Optical Communications

We analytically studied the block length effect (BLE) of decision-aided maximum likelihood (DA ML) carrier phase estimation in coherent optical phase-modulated systems. The results agree well with the trends found using extensive Monte Carlo simulations. In order to eliminate the BLE and accurately recover the carrier phase, an adaptive decision-aided (DA) receiver is proposed that does not require knowledge of the statistical characteristics of the carrier phase, or any parameter to be preset. The simulation results show that using the adaptive DA receiver, the maximum tolerance ratio of the linewidth per laser to symbol rate (?vT) at a bit error rate (BER) = 10-4 has been increased to 2.5 × 10-4, 4.1 × 10-5, and 9.5 × 10-6, respectively, for quadrature-, 8- and 16-phase-shift keying formats. The ratio (?vT) of the adaptive DA receiver in 16 quadrature amplitude modulation (QAM) is decreased to 2 × 10-5 due to the constellation penalty from 2.5 × 10-5 by using DA ML with optimum memory length, though it consistently performs well without optimizing any parameters as in DA ML. The phase error variance of the adaptive DA receiver is also analytically investigated. In addition, an analog-to-digital converter with bit resolution higher than 4 bits is shown to be sufficient to implement our adaptive DA receiver.

Bit-Error Rate Performance of Coherent Optical M-ary PSK/QAM using Decision-Aided Maximum Likelihood Phase Estimation

The bit-error rate (BER) expressions of 16- phase-shift keying (PSK) and 16- quadrature amplitude modulation (QAM) are analytically obtained in the presence of a phase error. By averaging over the statistics of the phase error, the performance penalty can be analytically examined as a function of the phase error variance. The phase error variances leading to a 1-dB signal-to-noise ratio per bit penalty at BER=10(-4) have been found to be 8.7 x 10(-2) rad(2), 1.2 x 10(-2) rad(2), 2.4 x 10(-3) rad(2), 6.0 x 10(-4) rad(2) and 2.3 x 10(-3) rad(2) for binary, quadrature, 8-, and 16-PSK and 16QAM, respectively. With the knowledge of the allowable phase error variance, the corresponding laser linewidth tolerance can be predicted. We extend the phase error variance analysis of decision-aided maximum likelihood carrier phase estimation in M-ary PSK to 16QAM, and successfully predict the laser linewidth tolerance in different modulation formats, which agrees well with the Monte Carlo simulations. Finally, approximate BER expressions for different modulation formats are introduced to allow a quick estimation of the BER performance as a function of the phase error variance. Further, the BER approximations give a lower bound on the laser linewidth requirements in M-ary PSK and 16QAM. It is shown that as far as laser linewidth tolerance is concerned, 16QAM outperforms 16PSK which has the same spectral efficiency (SE), and has nearly the same performance as 8PSK which has lower SE. Thus, 16-QAM is a promising modulation format for high SE coherent optical communications.

Pilot-Assisted Decision-Aided Maximum-Likelihood Phase Estimation in Coherent Optical Phase-Modulated Systems With Nonlinear Phase Noise

We proposed pilot-assisted (PA) decision-aided maximum-likelihood (DA ML) phase estimation for coherent optical M-ary phase-shift-keying systems. In a nonlinear-phase-noise channel with laser phase noise, the required launched power at bit-error-rate (BER) =10-4 using the proposed PA DA ML algorithm without differential encoding (DE) can be reduced by about 0.7 dB in quadrature phase-shift keying and eight-phase-shift keying systems, and about 0.4 dB in 16-quadrature amplitude modulation format, compared to their DE counterparts using DA ML.

Parallel Implementation of Decision-Aided Maximum-Likelihood Phase Estimation in Coherent $M$-ary Phase-Shift Keying Systems

To make decision-aided (DA) maximum-likelihood (ML) phase estimation suitable for real-time processing, a parallel implementation is proposed. The variance of the phase error using the parallel DA ML is analytically examined. The bit-error-rate performance is also analytically investigated in different M-ary phase-shift keying (PSK) systems. The results show that parallel DA ML can outperform block Mth-power in binary PSK format, while suffering performance penalty originating from parallelism and pipelining in high-order PSK formats.

Laser Linewidth Tolerance of Decision-Aided Maximum Likelihood Phase Estimation in Coherent Optical $M$-ary PSK and QAM Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This letter extends the decision-aided (DA) maximum likelihood (ML) phase estimation in an <formula formulatype="inline"><tex Notation="TeX">$M$</tex> </formula>-ary phase-shift keying (PSK) system to quadrature amplitude modulation (QAM) signals. The block length effect is simulated for both <formula formulatype="inline"> <tex Notation="TeX">$M$</tex></formula>-ary PSK and QAM systems, and also investigated in <formula formulatype="inline"><tex Notation="TeX">$M$</tex> </formula>-ary PSK systems through analysis. Our results show that the tolerance of DA ML to laser linewidth for square 16-QAM can be increased by <formula formulatype="inline"><tex Notation="TeX">$&gt;$</tex></formula>10 times compared to the block <formula formulatype="inline"><tex Notation="TeX">$M$</tex></formula>th power scheme. </para>

Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system

A novel decision-aided maximum likelihood (DA ML) technique is proposed to estimate the carrier phase in coherent optical phase-shift-keying system. The DA ML scheme is a totally linear computational algorithm which is feasible for on-line processing in the real systems. The simulation results show that the DA ML receiver can outperform the conventional Mth power scheme, especially when the nonlinear phase noise is dominant.

Low-complexity frequency-offset insensitive detection for orthogonal modulation

A low-complexity, frequency-offset insensitive detection for ortho-gonal modulation, using decision-aided maximum likelihood detection is derived. The proposed detection method significantly improves the performance with extremely low receiver complexity. In particular, the performance of the noncoherent maximum likelihood detection is approached, to within 1 dB, by the proposed low-complexity detection. The trade-off between receiver complexity and performance is provided for orthogonal modulation.