Carrier Phase Estimation Research Articles

A novel two-stage phase noise estimation algorithm for coherent optical OFDM systems

In coherent optical orthogonal frequency-division-multiplexing (CO-OFDM) receivers, the phase noise caused by the instabilities of the local oscillator is a potentially serious problem. In order to deal with the common phase error (CPE) caused by the phase noise in actual CO-OFDM receiver, a novel two-stage Least Mean Square (LMS) phase noise adaptive estimation algorithm is proposed. In the proposed estimation algorithm, an initial coarse estimation of the optical carrier phase to exploit the knowledge of pilot symbols is followed by a fine LMS adaptive estimation. The main advantage of the proposed method is that the phase-ambiguity problem is avoided after a cycle slip and the Bit Error Rate (BER) performance is improved. Furthermore, the phase noise effect induced by the transmitter laser and receiver Local Oscillator (LO) is analyzed. A simple CO-OFDM transmission system with QPSK to apply the proposed adaptive estimation algorithm is simulated, the simulation analysis shows that the proposed adaptive estimation algorithm has a more excellent performance.

Single DPLL Joint Carrier Phase Compensation for Few-Mode Fiber Transmission

A carrier phase estimation and compensation algorithm using a digital phase locked loop is proposed which exploits the common-mode impairment from the shared local oscillator at the receiver side in a few-mode fiber transmission system. We verify that the proposed algorithm is more tolerant to phasemismatches than earlier work. The carrier phase estimation (CPE) scheme is evaluated for a 3 × 112 Gbit/s dual polarization quadrature phase shift keying mode division multiplexed transmission over 80 km including an in-line multimode erbium doped fiber amplifier. The digital signal processing computational complexity is reduced in comparison to a traditional CPE stage. In addition, the proposed scheme is shown to perform similarly with respect to the 3.8 × 10-3forward error correcting limit optical signal to noise ratio tolerance of the traditional CPE scheme.

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.

An improved multiplier-free feed-forward carrier phase estimation for dual-polarization QPSK modulation format

An improved multiplier-free feed-forward carrier phase estimation algorithm is proposed for dual-polarization quadrature-phase-shift-keying (DP-QPSK) with coherent detection. The bit error rate (BER) performance, block length effect and linewidth tolerance of the proposed algorithm are evaluated for a 112 Gbit/s DP-QPSK system. A linewidth symbol duration product of 2.9×10−4 is demonstrated for 1 dB optical signal-to-noise-ratio (OSNR) penalty at BER of 10−3 for the proposed algorithm. The hardware complexity of the proposed multiplier-free algorithm is demonstrated to be much lower than that of the 4th power algorithm.

Modulation-Format-Independent Carrier Phase Estimation for Square M-QAM Systems

A modulation-format-independent or universal carrier phase estimation (U-CPE) technique is proposed for square 4-, 16-, and 64-ary quadrature amplitude modulation transmission systems for future elastic optical networks. The proposed U-CPE is based on a feedback architecture and eliminates the need to know the signal modulation format (MF) by using a cost function in the phase estimation update that is common to all square-shaped constellations. Compared with standard decision directed phase lock loop (S-DD-PLL) that requires the knowledge of the MF, the U-CPE method maintains close OSNR performance and linewidth tolerance. When MF is agnostic, the proposed U-CPE outperforms a modulation format oblivious (MFO)-DD-PLL in which QPSK decision rules are always used irrespective of actual MF of the signal.

GPS Carrier Phase Spectrum Estimation for Ionospheric Scintillation Studies

GPS signal carrier phase spectrum is an important measure of ionospheric scintillations. The conventional means of obtaining the carrier phase spectrum is by performing an FFT of the detrended carrier phase estimation generated by the carrier phase lock loop (PLL). The PLL is a feedback system whose outputs are influenced by the system parameters and are not true representations of the input phase. In this paper, we use simulated GPS scintillation signals to demonstrate the distortion of the input carrier phase spectrum by the PLL and receiver noise. An inverse filter and mean high frequency power subtraction operation are cascaded following the PLL to restore the original input carrier phase spectrum. The carrier phase spectrum restoration method performance is evaluated using both simulated and real scintillation signals and its limitation is also addressed. Copyright © 2013 Institute of Navigation.

Quasi-unambiguous state discrimination for coherent states with phase fluctuation

This paper describes unambiguous state discrimination (USD) for a sequence of coherent states with fluctuating phase, while considering eavesdropping against differential-phase-shift quantum key distribution systems. A measurement system extracts a fraction of the incoming signal of coherent states, estimates the carrier phase from that fraction, and then conducts a USD measurement on the main signal based on the estimated carrier phase. In such a system, the estimated carrier phase can be different from a true value because of the phase fluctuation, and an error can occur in the USD measurement because of the error in the estimated phase. The USD performance in such a situation is formalized and simulated.

Iterative carrier phase and channel estimation algorithm in BICM-ID

This paper proposed an iterative carrier phase and channel estimation algorithm for 16APSK in Bit-Interleaved Coded Modulation with Iterative Decoding(BICM-ID).The algorithm was based on Maximum Likelihood(ML) estimation,which made use of the decision information provided by the decoder and exchanged information between phase,channel estimation and decoder through iteration,so as to combine phase,channel estimation with decoder.The simulation results show the algorithm can get the performance only 0.5 dB lower than the ideal one,and can effectively estimate the phase difference from-20 degree to 20 degree.

Heterodyne coherent detection of WDM PDM-QPSK signals with spectral efficiency of 4b/s/Hz

We experimentally demonstrate heterodyne coherent detection of 8 × 112-Gb/s ultra-density wavelength-division-multiplexing (WDM) polarization-division-multiplexing quadrature-phase-shift-keying (PDM-QPSK) signal after 1120-km single-mode fiber-28 (SMF-28) transmission. The spectral efficiency (SE) is 4b/s/Hz. It is the first time to realize WDM signal transmission with high SE by adopting heterodyne coherent detection. At the heterodyne coherent receiver, intermediate frequency (IF) down conversion is realized in digital frequency domain after analog-to-digital conversion. A digital post filter and 1-bit maximum likelihood sequence estimation (MLSE) adopted after carrier phase estimation (CPE) in the conventional digital-signal-processing (DSP) process is used to suppress the enhanced noise and crosstalk as well as overcome the filtering effects. The bit-error ratio (BER) for all channels is under the forward-error-correction (FEC) limit of 3.8 × 10(-3) after 1120-km SMF-28 transmission.

Carrier Phase and Amplitude Estimation for Phase Shift Keying Using Pilots and Data

We consider least squares estimators of carrier phase and amplitude from a noisy communications signal that contains both pilot signals, known to the receiver, and data signals, unknown to the receiver. We focus on signaling constellations that have symbols evenly distributed on the complex unit circle, i.e., M-ary phase shift keying. We show, under reasonably mild conditions on the distribution of the noise, that the least squares estimator of carrier phase is strongly consistent and asymptotically normally distributed. However, the amplitude estimator is asymptotically biased and converges to a positive real number that is a function of the true carrier amplitude, the noise distribution and the size of the constellation. This appears to be the first time that the statistical properties of a non-data-aided estimator for carrier amplitude have been analyzed theoretically. The results of Monte Carlo simulations are provided and these agree with the theoretical results.

Linewidth-Tolerant and Low-Complexity Two-Stage Carrier Phase Estimation Based on Modified QPSK Partitioning for Dual-Polarization 16-QAM Systems

Three novel linewidth-tolerant, low-complexity, two-stage feed-forward carrier phase estimation algorithms are introduced for dual-polarization 16-ary quadrature amplitude modulation (DP 16-QAM) with coherent detection. The first stage employs either the quadrature phase-shift keying (QPSK) partitioning algorithm, simplified QPSK partitioning algorithm, or blind phase search (BPS) algorithm. The second stage employs a novel modified QPSK partitioning algorithm. Based on experimental data, all three algorithms achieve comparable performance for DP 16-QAM back to back and transmission systems. The linewidth tolerance for the three algorithms is numerically studied. A linewidth symbol duration product of 1.3×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> is demonstrated for a 1 dB optical signal-to-noise-ratio penalty at a bit error ratio 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> of for all the proposed algorithms, which is comparable to the single-stage BPS algorithm with a large number of test phases. Reductions in the hardware complexity by factors of about 1.7-5.3 are achieved in comparison to the single-stage BPS algorithm.

Carrier phase estimation methods in coherent transmission systems influenced by equalization enhanced phase noise

We present a comparative study on three carrier phase estimation algorithms, including a one-tap normalized least mean square (NLMS) method, a block-average method, and a Viterbi–Viterbi method in the n-level phase shift keying coherent transmission systems considering the equalization enhanced phase noise (EEPN). In these carrier phase estimation methods, the theoretical bit-error-rate floors based on traditional leading-order Taylor expansion are compared to the practical simulation results, and the tolerable total effective linewidths (involving the transmitter, the local oscillator lasers and the EEPN) for a fixed bit-error-rate floor are evaluated with different block sizes, when the fiber nonlinearities are neglected. The complexity of the three carrier phase estimation methods is also discussed. We find that the carrier phase estimation methods in practical systems should be analyzed based on the simulation results rather than the traditional theoretical predictions, when large EEPN is involved. The one-tap NLMS method can always show an acceptable behavior, while the step size is complicated to optimize. The block-average method is efficient to implement, but it behaves unsatisfactorily when using a large block size. The Viterbi–Viterbi method can show a small improvement compared to the block-average method, while it requires more computational complexity.

Linewidth-Tolerant and Low-Complexity Two-Stage Carrier Phase Estimation for Dual-Polarization 16-QAM Coherent Optical Fiber Communications

Two novel linewidth-tolerant, low-complexity feedforward carrier phase estimation algorithms are described for dual-polarization 16-ary quadrature-amplitude-modulation with coherent detection. For both algorithms, the carrier phase is estimated in two stages. The first stage employs either a simplified quadrature-phase-shift-keying (QPSK) partitioning algorithm or the blind phase search (BPS) algorithm. The second stage employs a novel QPSK constellation transformation algorithm. The performance and linewidth tolerance of both algorithms are evaluated using experimental and simulation data, and the hardware complexity is assessed. For both proposed two-stage algorithms, the linewidth symbol duration product is 1.3 × 10-4 for a 1 dB penalty in optical signal-to-noise ratio at a bit error ratio of 10-3. This performance is comparable to a single-stage BPS algorithm with a large number of test phases, but with a reduction of the hardware complexity by factors of about 2.5-11.

Nonlinear mitigation using carrier phase estimation and digital backward propagation in coherent QAM transmission

We investigate the performance of carrier phase estimation (CPE) and digital backward propagation (DBP) in compensating fiber nonlinearity for 224 Gbps polarization-multiplexed quadrature-amplitude-modulation coherent systems with level of 4 and 16 (PM-4-QAM and PM-16-QAM) over standard single-mode fiber (SSMF) uncompensated link. The results from numerical simulation show the individual performance of CPE and DBP as well as their mutual influence. With DBP compensation, required CPE tap number for optimal performance can be reduced by 50% for 4-QAM signal and 67% for 16-QAM signal compared to linear compensation. On the other hand, employing CPE compensation after DBP also allows to reduce DBP steps. In the mentioned PM-16-QAM system, 60% reduction in the required number of DBP steps to achieve BER=10(-3) is possible, with a step-size of 200 km, which reveals great potential to reduce the complexity for future real time implementation.

Performance analysis of code-aided iterative carrier phase recovery in turbo receivers

Code-aided (CA) iterative carrier phase synchroniser can greatly improve the accuracy of phase estimation in turbo receivers. However, because of the iteration involved between phase recovery and decoding, most existing studies depend on extensive simulations rather than on theoretical analysis to evaluate the performance improvement of phase recovery by exploiting the coding constraints. In this study, the authors propose analytical methods to fill this void. The first step is to approximate the cross-talks caused by phase offset as Gaussian noise at low signal-to-noise ratios. Then, a semi-analytical method is proposed to express the distribution of extrinsic information from channel decoder as a function of phase offset. Building on this model, both the open-loop and closed-loop performances of CA iterative phase synchronisers are derived in closed-form. The analytical results explicitly reveal how extrinsic information contributes to the performance of carrier phase estimation. Monte Carlo simulation results corroborate that the proposed methods are able to accurately characterise the performance of CA iterative carrier phase recovery for systems with different channel codes.

Performance of carrier phase recovery for electronically dispersion compensated coherent systems

An analytical approach taking into account carrier phase estimation (CPE) is presented to predict performance of quadrature phase shift-keying (QPSK) systems using coherent detection. Using this approach, system performance is found as a function of symbol rate, local oscillator (LO) linewidth, chromatic dispersion (CD) and signal-to-noise ratio (SNR). A new expression is derived for the covariance matrix of the conditional probability density function (pdf) of the decision statistic. This pdf is used to find bit error rate (BER) semi-analytically. Our analytical derivation assumes perfect removal of data modulation which corresponds to an ideal decision feedback (DF) carrier recovery. The validity of the analytical pdf for predicting BER is verified for a wide range of system parameters of interest in long haul systems. In addition, our semi-analytical BER provides a lower bound for the Viterbi-Viterbi (VV) BER, while showing the analytical BER previously proposed in the literature shows an overly pessimistic prediction of VV BER performance. We show that inaccuracy in previous analysis stems from overly simple model for the CPE when compensating large accumulated dispersion electronically. Finally, we study extension of our results to quadrature amplitude modulation (QAM). Preliminary simulation results are promising but the accuracy of our semi-analytical approach for predicting BER should be investigated further.

Joint-Polarization and Joint-Subchannel Carrier Phase Estimation for 16-QAM Optical Systems

Carrier phase estimation using information from multiple subchannels and orthogonal polarization channels is proposed and experimentally verified. The concept is evaluated with a 112 Gb/s dual-channel DP-16-QAM system, but may find applications in next generation Terabit systems utilizing superchannels and containing densely packed subchannels originating from the same laser. The new technique requires an accurate carrier frequency estimation algorithm, implemented in the paper using a decision-directed method. The algorithms are tested with a narrow (100 kHz) and a broad (2 MHz) linewidth laser in the coherent receiver.

Multi-stage feed-forward optical carrier phase estimation based on QPSK partitioning for 64-QAM signals

We numerically investigate two multi-stage feed-forward optical carrier phase estimation (CPE) methods for coherent optical 64-QAM signals, which are QPSK partitioning with maximum likelihood (ML) method and QPSK partitioning with blind phase search (BPS) method. Both methods are proved to be possible solutions for CPE of 64-QAM signals, with good laser phase noise tolerance and simple complexity. For QPSK partitioning with ML method, we creatively introduce cascaded multi-stage ML following QPSK partitioning, which leads to further improved laser phase noise tolerance compared to 1-stage ML condition. For QPSK partitioning with BPS method, BPS with 8 or 12 test phases and test phase range of π/4 is found to be suitable for practical application, because it can achieve good laser phase noise tolerance while keeping low complexity, and the use of BPS with more test phases in this method has limited advantage over single stage BPS with the same test phases.

Cramér–Rao lower bound for non-data-aided carrier phase estimation from general M-ary phase-shift keying modulation signals over flat Rayleigh fading channel

The authors derive the true Cramér–Rao lower bound (CRLB) for a non-data-aided (NDA) carrier phase estimation from general M-ary phase-shift keying (M-PSK) modulation signal over flat Rayleigh fading channels (FRFC). The numerical Monte Carlo method is used to compute the true CRLB from general M-PSK modulation signals over FRFC with complex additive white Gaussian noise. The efficiency of the proposed method is made obvious through the assessment of the true CRLBs from both symmetric and asymmetric 8-PSK modulation signals for various observation window sizes. The simulation results show that optimal NDA carrier phase recovery is harder to acquire from symmetric modulation signals for signal-to-noise ratio (SNR) range up to 5 dB, but depends on the constellation density, only for SNR range superior to 5 dB. For both constellations the CRLB decreases as long as the observation window size increases. The derived bound provides an efficient standard for evaluating the performance of any unbiased NDA carrier phase estimator from general M-PSK modulation signals over FRFC. The method presented here stands useful for general M-ary quadrature amplitude modulation signals as well.

A complex-weighted, decision-aided, maximum-likelihood carrier phase and frequency-offset estimation algorithm for coherent optical detection

We present a symbol-by-symbol coherent optical receiver, which employs a novel, complex-weighted, decision-aided, maximum-likelihood (CW-DA-ML) carrier phase and frequency offset estimator. The CW-DA-ML carrier estimator uses a CW transversal filter to generate a carrier reference phasor, and the filter weights are automatically adapted on-line by linear regression on the observed signals. A complete modulo-R reduced frequency offset estimation (FOE) range of ± R/2 is achieved, independent of modulation format, where R is the symbol rate. Carrier phase and frequency tracking is achieved rapidly. The acquisition speed of frequency offset in quaternary phase-shift keying (4-PSK) signals is more than 5 times faster than that of differential FOE. A constant penalty of approximately 1 dB at bit-error rate of 10(-4) is demonstrated for all frequency offsets in 4-PSK signals with laser-linewidth-symbol-duration product of 8 × 10(-5).