Carrier Phase Recovery Algorithm Research Articles

Equalization Enhanced Phase Noise in Coherent Receivers: DSP-Aware Analysis and Shaped Constellations

We revisit the analysis of equalization-enhanced phase noise (EEPN) arising in coherent receivers from the interaction between the chromatic dispersion compensation by an electronic equalizer and the phase noise of the local oscillator. Through numerical simulations we highlight EEPN characteristics and investigate its impact on the behavior of the carrier phase recovery algorithm. We show that the blind phase search, which is usually used in practice to recover the carrier phase, partially mitigates the EEPN. We detail a numerical approach to predict the system performance including the phase recovery algorithm, and show that taking into account EEPN characteristics relaxes the constraint on the system laser phase noise given by previous pessimistic analytical models. We present experimental validations of our claims, and address future advanced transoceanic systems using 98 GBd probabilistically shaped QAM formats.

Low-complexity carrier phase recovery based on principal component analysis for square-QAM modulation formats.

We propose, numerically analyze and experimentally demonstrate a low-complexity, modulation-order independent, non-data-aided (NDA), feed-forward carrier phase recovery (CPR) algorithm. The proposed algorithm enables synchronous decoding of arbitrary square-quadrature amplitude modulation (QAM) constellations and it is suitable for a realistic hardware implementation based on block-wise parallel processing. The proposed method is based on principal component analysis (PCA) and it outperforms the well-known and widely used blind phase search (BPS) algorithm at low signal-to-noise ratio (SNR) values, showing much lower cycle slip rate (CSR) both numerically and experimentally. For operation at higher SNR values, a hybrid two-stage implementation combining the proposed method and BPS is also proposed and their performance are investigated benchmarking them against the two-stage BPS (2S-BPS). The complexity of the proposed simple and hybrid methods are evaluated against 2S-BPS and computational complexity savings of 92% and 40% are expected for the simple and hybrid methods, respectively.

Low-Complexity Blind Carrier Phase Recovery for C-mQAM Coherent Systems

A novel carrier phase recovery algorithm is proposed for coherent optical systems with circular multilevel quadrature amplitude modulation (C-mQAM). After amplitude segmentation and phase rotation, the particular distribution of the constellation points in a C-mQAM signal is exploited to construct a special cost function to provide a rough estimate of phase noise. The cost function can be replaced with a simple cosine function, and only two or three test phases are required for the calculation of its parameters. The performances of different cost functions are compared and simulation results show that the cost function can be chosen with the high phase noise tolerance and low computational complexity. Maximum-likelihood phase noise estimation algorithm is combined with the proposed algorithm to mitigate residual phase noise. Compared to the single-stage blind phase search and n-phase-shift keying partitioning algorithms, the numerical results demonstrate that the proposed two-stage algorithm shares similar phase noise tolerance and offers a lower computational complexity for a 28-GBaud back-to-back coherent optical QAM transmission system.

一种高精度的四次方载波相位恢复算法

一种高精度的四次方载波相位恢复算法

基于简化扩展卡尔曼滤波的双偏振载波相位恢复算法

基于简化扩展卡尔曼滤波的双偏振载波相位恢复算法

180° rotationally invariant polar code

Non-data-aided (NDA) carrier phase recovery (CPR) is one of simple CPR algorithms which simply rotates received symbols to the nearest constellation point. Unfortunately, when the NDA CPR is used with M-ary phase shift keying, it suffers inherent M-fold phase ambiguity and thus the phase ambiguity must be resolved. On the other hand, the generator matrix of polar code G can be obtained with the Kronecker product of a 2 × 2 lower triangular matrix. Hence, the Hamming weights of all columns of G are given by non-negative integer powers of 2. Based on this observation, an 180 ° rotationally invariant polar code suitable for digital communication systems employing binary phase shift keying and NDA CPR is proposed. The proposed polar code offers virtually identical performance under both 0 ° and 180 ° carrier phase offsets to that of conventional polar code with perfect CPR with identical encoding and decoding complexities.

Numerical Investigation of the Equalization Enhanced Phase Noise Penalty for M-Quadrature Amplitude Modulation Formats in Short-Haul Few-Mode Fiber Transmission Systems with Time-Domain Equalization

The equalization enhanced phase noise (EEPN), caused by the interaction of the chromatic dispersion (CD) with the phase noise of the local oscillator (LO), has been extensively studied for single-mode optical communication systems. Few-mode fiber (FMF) transmission systems introduce a new channel impairment, the differential mode delay (DMD), which also creates EEPN and hence limits the maximum transmission distance of those systems. In this work, we numerically investigate the optical signal to noise ratio (OSNR) penalties caused by the EEPN in a 3-mode FMF transmission system at 25 GBd for quadrature phase-shift keying (QPSK), 16-quadrature amplitude modulation (QAM), 32-QAM and 64-QAM modulation formats when using the blind phase search (BPS) carrier phase recovery (CPR) algorithm, which has been demonstrated to be both robust and suitable for optical communication systems. Our numerical study assumes a short-span of FMF, modeled in the weakly-coupled regime, and includes two cases; the use of ideal mode-selective de/multiplexers at both ends of the FMF span (model A), and the use of ideal non-mode-selective de/multiplexers (model B). The results show that the EEPN has almost no effect in model A. However, EEPN produces a severe penalty in model B with the onset of the OSNR degradation starting for a DMD spread of the impulse response of about 100 symbols for all modulation formats investigated. The distribution ratio of the amount of phase noise between the transmitter and receiver lasers is also assessed for model B and we confirm that the degradation is mainly due to the phase noise of the LO.

基于线型卡尔曼滤波器的双偏振并行载波相位恢复算法

基于线型卡尔曼滤波器的双偏振并行载波相位恢复算法

Calibration of Estimated BER from Error Vector Magnitude with Carrier Phase Recovery

This paper presents the estimation of bit error ratio (BER) from error vector magnitude (EVM) for the quadrature phase shift keying (QPSK) modulation format with the Viterbi & Viterbi algorithm and differential decoding to compensate for laser phase noise. It is demonstrated analytically and through simulation that a calibration is necessary when using the established relationship between EVM and BER to take into account the implementation penalty associated with the carrier phase recovery algorithm. Simulation results using the proposed calibration technique are presented for different combined linewidth symbol duration product in a QPSK coherent system. The impact on the number of symbols used to estimate the BER from EVM analysis is also investigated and compared to error counting. An estimation with lower uncertainty is demonstrated to be achievable with EVM analysis compared to error counting for different number of symbols. Finally, the estimation of BER for a 16-ary quadrature amplitude modulation (16- QAM) optical coherent system is investigated using the blind phase search algorithm for carrier phase recovery.

Laser Phase Noise Effects and Joint Carrier Phase Recovery in Coherent Optical Transmissions With Digital Subcarrier Multiplexing

In this paper, we numerically and experimentally investigate the impairments related to laser phase noise in coherent digital subcarrier multiplexing (SCM) systems. Based on the evaluation in both back-to-back and transmission scenarios and the performance comparison between single carrier (SC) and SCM systems, we show that even though SCM systems suffer from degraded performance of carrier phase recovery (CPR) algorithms, they can potentially achieve an improved laser linewidth tolerance compared with SC systems after long-haul transmission attributed to the mitigation of equalization-enhanced phase noise. In addition, the effect of dispersion-enhanced phase noise is discussed in digital SCM systems, and a joint CPR (J-CPR) algorithm is proposed for cycle slip detection and correction. The effectiveness of the proposed J-CPR algorithm is then demonstrated in a 16-quadrature amplitude modulation (QAM) digital SCM system by both simulations and experiments.

Optimized Carrier Frequency and Phase Recovery Based on Blind <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math> </inline-formula>th Power Schemes

We report an optimized hardware scheme for carrier frequency and phase recovery algorithms based on Mth-order power schemes for flexible intradyne coherent receivers. The phase recovery is based on the traditional Viterbi & Viterbi algorithm with a feedforward architecture, which requires an Mth-order power nonlinear operation. The output of such operation is also used in the differential phase-based approach for frequency offset estimation by means of a feedback loop. Hence, by using a single Mth-order operation, the reported architecture saves approximately half of the hardware resources for quadrature phase shift keying (QPSK) in the frequency recovery stage compared with fully independent phase and frequency algorithms. The evaluation of the accuracy of the proposed method is performed with digital signal processing in real-time using a field-programmable gate array (FPGA) for differential QPSK and 8PSK modulation formats. No significant performance penalty is observed when compared with an implementation featuring independent algorithms.

Analytical Investigations on Carrier Phase Recovery in Dispersion-Unmanaged n-PSK Coherent Optical Communication Systems

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.

Carrier Phase Recovery Algorithms for Coherent Optical Circular mQAM Systems

The phase noise tolerance of circular multilevel quadrature amplitude modulation (C-mQAM) constellations employing different carrier phase recovery (CPR) algorithms is studied. A differential decoding scheme and a bit mapping for this type of constellations are proposed. A novel CPR scheme for C-mQAM constellations is also presented. The particular distribution of the constellation points in a C-mQAM signal is exploited to reduce the required Nth power for the removal of the modulation component by a factor of two. Hence, the computational complexity of the proposed algorithm is drastically reduced. The combined linewidth symbol duration product $(\Delta \nu T_{s})$ tolerance of different CPR algorithms for C-mQAM constellations is studied and compared with the proposed CPR scheme. The results are analyzed at 3.8e-3 and 1e-2 bit error rate forward error correction limits. The proposed CPR scheme achieves similar $\Delta \nu T_{s}$ tolerance compared to single stage BPS algorithm while its computational complexity is reduced by group factors of 27.2 | 32.3, and 30.5 | 32.6 (in the form of multipliers | adders ) for C-16QAM and C-64QAM, respectively.

Optimized Superscalar Parallelization-Based Carrier Phase Recovery for Agile Metro Optical Networks

In this paper, we present a format-transparent carrier phase recovery algorithm for the agile metropolitan optical networks based on an optimized superscalar parallelization structure. The pilot overhead and the buffer size in the superscalar parallelization can be minimized by optimizing the parallelization structure depending on the required laser linewidth tolerance of the system. The trade-off between the laser linewidth tolerance and the reduction of buffer size in the proposed superscalar parallelization is revealed in simulations for 16-QAM, 32-QAM, and 64-QAM, respectively. The results indicate that the buffer size in the superscalar parallelization can be reduced significantly when commercially available external cavity lasers (ECL) are employed for coherent detection in metro links beyond 100 Gb/s. Experiments are further conducted in a single-channel system with ECLs as the transmitter and local oscillator lasers to demonstrate the reduction of the pilot overhead and buffer size using the proposed superscalar parallelization compared with the previous superscalar structures.

Improved eighth-order statistics blind phase recovery algorithm for coherent receivers with 16-QAM modulation format

An improved eighth-order statistics (EOS) blind phase recovery method is proposed for high-order coherent modulation formats. The method uses a multistage feed-forward carrier phase recovery algorithm by combining an EOS blind phase estimate with a maximum-likelihood carrier phase estimate. Experimental results show that the proposed new algorithm can reduce the required computational effort by more than a factor of 3 for a 16-QAM system.

Advanced DSP for 400 Gb/s and Beyond Optical Networks

This paper presents a systematic review of several digital signal processing (DSP)-enabled technologies recently proposed and demonstrated for high spectral efficiency (SE) 400 Gb/s-class and beyond optical networks. These include 1) a newly proposed SE-adaptable optical modulation technology-time-domain hybrid quadrature amplitude modulation (QAM), 2) two advanced transmitter side digital spectral shaping technologies-Nyquist signaling (for spectrally-efficient multiplexing) and digital pre-equalization (for improving tolerance toward channel narrowing effects), and 3) a newly proposed training-assisted two-stage carrier phase recovery algorithm that is designed to address the detrimental cyclic phase slipping problem with minimal training overhead. Additionally, this paper presents a novel DSP-based method for mitigation of equalizer-enhanced phase noise impairments. It is shown that performance degradation caused by the interaction between the long-memory chromatic dispersion compensating filter/equalizer and local oscillator laser phase noise can be effectively mitigated by replacing the commonly used fast single-tap phase-rotation-based equalizer (for typical carrier phase recovery) with a fast multi-tap linear equalizer. Finally, brief reviews of two high-SE 400 Gb/s-class WDM transmission experiments employing these advanced DSP algorithms are presented.

Frequency Offset Compensation and Carrier Phase Recovery for Differentially Encoded 16-QAM Vector Signal in a 60-GHz RoF System

Differentially encoding and frequency offset compensating for a 16-quadrature amplitude modulation (16-QAM) vector signal in 60-GHz millimeter-wave radio-over-fiber (RoF) systems are experimentally investigated. The fourfold phase ambiguity issue in a non-data-aided signal communication transmission system with conventional square 16-QAM constellations is successfully tackled based on the differentially encoding scheme. Experimental results show that frequency offset compensation and carrier phase recovery are simultaneously achieved by utilizing the decision-directed carrier phase recovery algorithm. Up to ~ ±1.3 ×10-3 frequency offset times symbol rate product Δf ·Ts is well compensated at the given bit-error-ratio (BER) value of ~ 10-3.

Differential carrier phase recovery for QPSK optical coherent systems with integrated tunable lasers

The performance of a differential carrier phase recovery algorithm is investigated for the quadrature phase shift keying (QPSK) modulation format with an integrated tunable laser. The phase noise of the widely-tunable laser measured using a digital coherent receiver is shown to exhibit significant drift compared to a standard distributed feedback (DFB) laser due to enhanced low frequency noise component. The simulated performance of the differential algorithm is compared to the Viterbi-Viterbi phase estimation at different baud rates using the measured phase noise for the integrated tunable laser.

High Spectral Efficiency 400 Gb/s Transmission Using PDM Time-Domain Hybrid 32–64 QAM and Training-Assisted Carrier Recovery

We report the successful transmission of ten 494.85 Gbit/s DWDM signals on the standard 50 GHz ITU-T grid over 32 × 100 km of ultra-large-area (ULA) fiber. A net spectral efficiency (SE) of 8.25 b/s/Hz was achieved, after excluding the 20% soft-decision forward-error-correction (FEC) overhead. Such a result was accomplished by the use of a recently proposed polarization-division-multiplexed (PDM) time-domain hybrid 32-64 quadrature-amplitude-modulation (QAM) format, along with improved carrier frequency and phase recovery algorithms. It is shown that time-domain hybrid QAM provides a new degree of design freedom to optimize the transmission performance by fine tuning the SE of the modulation format for a specific channel bandwidth and FEC redundancy requirement. In terms of carrier recovery, we demonstrate that 1) hardware efficient estimation and tracking of the frequency offset between the signal and local-oscillator (LO) can be achieved by using a new feedback-based method, and 2) a training-assisted two-stage phase estimation algorithm effectively mitigates cyclic phase slipping problems. This new phase recovery algorithm not only improves the receiver sensitivity by eliminating the need for differential coding and decoding, but also enables an additional equalization stage following the phase recovery. We have shown that the introduction of this additional equalization stage (with larger number of taps) helps reduce the implementation penalty. This paper also presents the first experimental study of the impact of inphase (I) and quadrature (Q) correlation for a high-order QAM. It is shown that an adaptive equalizer could exploit the correlation between I and Q signal components to artificially boost the performance by up to 0.7 dB for a PDM time-domain hybrid 32-64 QAM signal when the equalizer length is significantly longer than I/Q de-correlation delay.

Simple and efficient frequency offset tracking and carrier phase recovery algorithms in single carrier transmission systems

In this paper, we propose a low-complexity and efficient carrier recovery algorithm for single carrier transmission systems that is capable of tracking frequency offset (FO) variations. Working as a FO tracking estimator, the algorithm demonstrates good accuracy in simulation and a FO drift of up to 200 MHz/μs can be compensated with minimal degradation in a QPSK system. In 112 Gb/s dual polarization (DP) QPSK experiments, the algorithm recovers a data sequence having >80 MHz of FO drift within 250 μs, providing better performance than a one-time estimator. In a regime that utilizes parallel processing of the data, we further demonstrate FO tracking and carrier phase recovery (CPR) using only one of the streams in a parallelized configuration, and we apply the carrier information to recover neighbouring streams directly. Consequently, the complexity of both the FO tracking and the CPR is further reduced.