Carrier Recovery in Coherent Optical Communication Systems

In this paper, we present a carrier phase recovery (CPR) algorithm using a modified superscalar parallelization based phase locked loop (M-SSP-PLL) combined with a maximum-likelihood (ML) phase estimation. Compared to the original SSP-PLL, M-SSP-PLL + ML reduces the required buffer size using a novel superscalar structure. In addition, by removing the differential coding/decoding and employing ML phase recovery it also improves the performance. In simulation, we show that the laser linewidth tolerance of M-SSP-PLL + ML is comparable to blind phase search (BPS) algorithm, which is known to be one of the best CPR algorithms in terms of performance for arbitrary QAM formats. In 28 Gbaud QPSK (112 Gb/s) and 16-QAM (224 Gb/s), and 7 Gbaud 64-QAM (84 Gb/s) experiments, it is also demonstrated that M-SSP-PLL + ML can increase the transmission distance by at least 12% compared to BPS for each of them. Finally, the computational complexity is discussed and a significant reduction is shown for our algorithm with respect to BPS.

We propose a polarity decision carrier recovery algorithm that is useful for carrier acquisition in high order-QAM (quadrature amplitude modulation). The PD (phase detector) output and its variance characteristics are mathematically derived and the simulation results are presented. We design a carrier recovery loop with this polarity decision PD and ATC (automatic transfer-mode controller), which is proposed to detect a proper time for mode change and to yield fine phase tracking error in the steady state. While the conventional DD (decision directed) algorithm can only acquire frequency offsets of less than /spl plusmn/10 kHz, the proposed carrier recovery algorithm can acquire up to /spl plusmn/200 kHz without AFC (automatic frequency control). We show the RMS (root mean square) phase error performance using the proposed carrier recovery PLL (phase locked loop).

An optimized principal component-based phase estimation (OPCPE) algorithm is proposed for probabilistically shaped (PS) square-quadrature amplitude modulation (QAM) systems. The optimization method is based on mirroring and partially scaling the received constellation. Numerical simulation validation shows that the proposed phase recovery algorithm outperforms the well-known blind phase search (BPS) algorithm at low signal-to-noise ratio (SNR) and solves the incompatibility between principal component-based phase estimation (PCPE) and PS at high SNR. It's worth mentioning that the proposed algorithm retains the advantages of low cycle slip rate (CSR) and low computational complexity of PCPE. Furthermore, the performance of a hybrid implementation combining the proposed algorithm and BPS is also investigated. When the shaping parameter for a PS-64QAM system is 0.03, by using the proposed simple and hybrid methods, the SNR required to reach the 0.8 normalized generalized mutual information (NGMI) threshold can be reduced by about 0.74 dB and 0.98 dB, respectively, benchmarking the widely used two-stage BPS (2S-BPS) algorithm. To the best of our knowledge, this is the first time to robustly apply PCPE algorithm to PS systems, and the proposed design has stable GMI performance, strong cycle slip tolerance and low computational complexity, which makes it a suitable candidate for practical probabilistically-shaped transmissions.

One typical use of sensor networks is monitoring targets. The sensor networks classify, detect, locate, and track targets. The ML (Maximum likelihood) algorithm is one of the estimation algorithms of target location and has high accuracy to estimate target location. However, the calculation amount of the ML estimation algorithm is large. Energy-Ratios Source Localization Nonlinear Least Square (ER-NLS) is proposed to realize the ML algorithm. ER-NLS is the algorithm of estimating source location by using the ratio of sensors' receiving energies. However, ER-NLS has to search all the areas, so that the calculation amount of ER-NLS is large. In this paper we propose a method of reducing search area for localization. The proposed method uses the ratio of sensors' receiving energies. It can be used with the ML algorithm. We show that the proposed method with the ML algorithm can reduce the search areas to estimate the target location and thus reduce the complexity, while achieving the RMSE (root mean square error) close to that of the ML algorithm.

We present a simple and robust symbol timing recovery algorithm for OFDM systems, such as IEEE 802.11a/g. The algorithm is derived according to a maximum likelihood (ML) algorithm utilizing the cyclic extension or cyclic prefix (CP), which is appended in front of each OFDM symbol. Simulation results show that the performance of the proposed algorithm is better than the conventional ML algorithm in the additive white Gaussian noise (AWGN) channel and approaches to the ML algorithm in the Rayleigh fading channel. Furthermore, the implementation complexity is lower than that of the ML algorithm.

After decades of research in Direction of Arrival (DoA) estimation, today Maximum Likelihood (ML) algorithms still provide the best performance in terms of resolution capabilities. At the cost of a multidimensional search, ML algorithms achieve a significant reduction of the outlier production mechanism in the threshold region, where the number of snapshots per antenna and/or the signal to noise ratio (SNR) are low. The objective of this paper is to characterize the resolution capabilities of ML algorithms in the threshold region. Both conditional and unconditional versions of the ML algorithms are investigated in the asymptotic regime where both the number of antennas and the number of snapshots are large but comparable in magnitude. By using random matrix theory techniques, the finite dimensional distributions of both cost functions are shown to be Gaussian distributed in this asymptotic regime, and a closed form expression of the corresponding asymptotic covariance matrices is provided. These results allow to characterize the asymptotic behavior of the resolution probability, which is defined as the probability that the cost function evaluated at the true DoAs is smaller than the values that it takes at the positions of the other asymptotic local minima.

A refined phase estimation based parallel carrier recovery algorithm for high speed wireless communication systems is proposed in this paper. This parallel algorithm is based on a serial DPLL (digital phase locked loop) carrier recovery feedback architecture and a novel refined phase estimation module. To archive high speed communication, parallelization of serial DPLL carrier recovery algorithm is presented; to guarantee high accuracy, a refined phase estimation design is proposed. A 32 parallel baseband simulation model of 16QAM modulation is performed on MATLAB platform to validate the proposed algorithm. Simulation results demonstrate that the performance loss of EVM (Error Vector Magnitude) introduced by the proposed algorithm is less than 0.3%, which is only half of the traditional coarse compensation algorithm.

This paper presents an all digital DS-CDMA upstream transmitter arid a head-end baseband receiver for upstream cable/HFC networks. The upstream transmitter supports frequency agility of the carrier, QPSK and QAM constellations up to 64QAM, variable symbol rates from 160kchip/s to 5.12Mchip/s increasing by power of two, and direct-digital up-conversion to achieve accurate amplitude and phase of modulation. The transmitter consists of pulse shaping filter, half-band filter, cascaded integrator-comb (CIC) filter, and inverse SINC filter. The all digital head-end baseband receiver supports programmable quadrature amplitude modulation up to 64QAM. Fast timing and carrier recovery algorithms are adopted for burst mode transmission. Code acquisition can be achieved within 2 symbols, and the carrier acquisition can be achieved within 31 symbols. All digital timing recovery is designed with /spl plusmn/200ppm symbol timing offset tolerance and the carrier recovery can compensate /spl plusmn/100ppm of carrier frequency offset.

For high-speed optical communication systems, laser phase noise (LPN) stands as a pivotal factor influencing the quality of the received signal. Therefore, the employment of a highly accurate carrier phase recovery (CPR) algorithm at the receiving end is indispensable to ensure the reliability of transmission. While a CPR algorithm called principal component-based phase estimation (PCPE) has been proven to be capable of achieving low-complexity and high-performance phase recovery for even-bit quadrature amplitude modulation (QAM) (i.e., square QAM) signals, it is not compatible with traditional cross-shaped odd-bit QAM signals. To circumvent this problem, a signal constellation design scheme based on geometric shaping (GS) is proposed. The pair-wise optimization (PO) algorithm is used to optimize the constellation structure of 32QAM and 128QAM signals in order to obtain results that are compatible with the PCPE algorithm. Monte Carlo simulation results reveal that for odd-bit QAM signals utilizing PCPE for phase recovery, the proposed GS constellations enhance the mutual information (MI) performance across the entire measured signal-to-noise (SNR) range. Moreover, compared with regular 32QAM and 128QAM constellations using the well-known blind phase search (BPS) algorithm, the proposed GS and PCPE scheme can achieve SNR gains of 1.10 dB and 2.59 dB, respectively, when considering the 20% soft-decision forward error correction (SD-FEC) overhead. Verification through commercial simulation software corroborates these findings, demonstrating that the proposed GS constellations are particularly suitable for the PCPE algorithm, especially under conditions of high optical signal-to-noise ratio (OSNR). To the best of our knowledge, this is the first time that the incompatibility between the PCPE algorithm and odd-bit QAM signals has been investigated, and the proposed GS scheme has broadened the application scope of the low-complexity CPR algorithm.

Frequency offset estimation is one of the crucial stages for frequency synchronization in OFDM based systems such as MB-OFDM UWB systems. A frequency offset estimation scheme is proposed for coarse frequency offset estimate. Variance of the proposed frequency offset estimated scheme is compared with the Cramer Rao lower bound (CRLB). BER performance of the proposed scheme is also reported

The reverberation power spectral density (PSD) is often required for dereverberation and noise reduction algorithms. In this work, we compare two maximum likelihood (ML) estimators of the reverberation PSD in a noisy environment. In the first estimator, the direct path is first blocked. Then, the ML criterion for estimating the reverberation PSD is stated according to the probability density function of the blocking matrix (BM) outputs. In the second estimator, the speech component is not blocked. Instead, the ML criterion for estimating the speech and reverberation PSD is stated according to the probability density function of the microphone signals. To compare the expected mean square error (MSE) between the two ML estimators of the reverberation PSD, the Cramer–Rao Bounds (CRBs) for the two ML estimators are derived. We show that the CRB for the joint reverberation and speech PSD estimator is lower than the CRB for estimating the reverberation PSD from the BM outputs. Experimental results show that the MSE of the two estimators indeed obeys the CRB curves. Experimental results of multimicrophone dereverberation and noise reduction algorithm show the benefits of using the ML estimators in comparison with another baseline estimators.

A novel OWDM system with blind identification based on the maximum likelihood (ML) algorithm is studied for the multipath fading channel. New OWDM structures based on the ML algorithm and blind identification and H̃ matrix based on the ZF (zero forcing) algorithm are the two novel aspects of this system. The performance of the system under the multipath fading channel is analysed.

Multipath fading as encountered in the portable radio communications environment produces rapid and large carrier phase changes coincident with rapid fades. Any phase-locked loop (PLL) used for carrier recovery must accurately track these phase changes. This experiment studies the effects of PLL parameters on carrier recovery performance in the presence of noise-free multipath fading by use of a hardware fading simulator and a typical analog carrier recovery circuit. The Doppler spread, PLL damping factor, and PLL 3dB loop bandwidth were individually and jointly varied to determine their relationships to loop phase error performance. The key parameter affecting the loop phase error behavior is the ratio of the 3dB loop bandwidth to the Doppler spread, not their individual values. Important relationships between this ratio and performance measures of the carrier recovery loop were also found.

Maximum-likelihood (ML) estimation is an established paradigm for the assessment of imaging system performance in nonlinear quantitation tasks. At high signal-to-noise ratio (SNR), ML estimates are asymptotically Gaussian-distributed, unbiased and efficient, thereby attaining the Cramer–Rao bound (CRB). Therefore, at high SNR the CRB is useful as a predictor of the variance of ML estimates and, consequently, as a basis for measures of estimation performance. At low SNR, however, the achievable parameter variances are often substantially larger than the CRB and the estimates are no longer Gaussian-distributed. These departures imply that inference about the estimates that is based on the CRB and the assumption of a normal distribution will not be valid. We have found previously that for some tasks these effects arise at noise levels considered clinically acceptable. We have derived the mathematical relationship between a new measure, χ2pdf-ML, and the expected probability density of the ML estimates, and have justified the use of χ2pdf-ML-isocontours in parameter space to describe the ML estimates. We validated this approach by simulation experiments using spherical objects imaged with a Gaussian point spread function. The parameters, activity concentration and size, were estimated simultaneously by ML, and variances and covariances calculated over 1000 replications per condition from 3D image volumes and from 2D tomographic projections of the same object. At low SNR, where the CRB is no longer achievable, χ2pdf-ML-isocontours provide a robust prediction of the distribution of the ML estimates. At high SNR, the χ2pdf-ML-isocontours asymptotically approach the analogous χ2pdf-F-contours derived from the Fisher information matrix. The χ2pdf-ML model appears to be suitable for characterization of the influence of the noise level and characteristics, the task, and the object on the shape of the probability density of the ML estimates at low SNR. Furthermore, it provides unique insights into the causes of the variability of estimation performance.

Different carrier recovery algorithms and strategies are presented and compared in terms of performance and hardware complexity, along with insights into the real-time implementation of such algorithms.