Effective Mitigation of Non-linearities Using Extended Kalman Filtering for Dispersion Managed Links - Pakala, Lalitha; Schmauß, Bernhard (ITG Fachtagung Photonische Netze, 2016)
We investigate our proposed carrier phase and amplitude noise estimation (CPANE) algorithm using extended Kalman filter (EKF) for mitigation of non-linearities as well as ASE induced phase and amplitude distortions, in fully compensated periodic dispersion managed (DM) links employing standard single mode fiber (SSMF) and dispersion compensating fiber (DCF). Numerical simulations were carried out on a 224 Gb/s polarization multiplexed (PM) 16-quadrature amplitude modulation (QAM) coherent transmission system for DM links with varying launch power and transmission distance, in this study. The non-linear mitigation performance of EKF-CPANE is compared to that of conventional single step non-linear (SSNL) compensation. Numerical results show that EKF-CPANE exhibits slightly improved performance compared to SSNL compensation method. We further investigate the combined performance of these two methods by employing EKF-CPANE after SSNL compensation for the mitigation of residual non-linear distortions. As a result, an enhanced tolerance towards non-linearities of up to 2 dB can be obtained. Moreover, the combination of SSNL compensation and EKF-CPANE is quite feasible for real-time implementations since each method requires only few complex multiplications to recover one symbol.
lhft_intern.bib::Pakala2016a

Enhanced Transmission Performance Using Digital Back Propagation and Extended Kalman Filtering for Dispersion Unmanaged Links - Pakala, Lalitha; Schmauß, Bernhard (Signal Processing in Photonics and Communications, 2016)
The transmission performance of extended Kalman filtering (EKF) significantly outperforms one-step-per-span optimized digital back propagation (DBP). At the expense of few DBP steps deployed prior to EKF yields further enhanced non-linear tolerance.
lhft_intern.bib::Pakala2016d

Evaluation of correlated digital back propagation and extended Kalman filtering for non-linear mitigation in PM-16-QAM WDM systems - Pakala, Lalitha; Schmauß, Bernhard (SPIE Photonics West OPTO, 2017)
We investigate the individual and combined performance of correlated digital back propagation (CDBP) and extended Kalman filtering (EKF) in mitigating inter and intra-channel non-linearities in wavelength division multiplexed (WDM) systems. The afore-mentioned algorithms are verified through numerical simulations on 28 Gbaud polarization multiplexed (PM) 16-quadrature amplitude modulation (16-QAM) 9-channel WDM system with 50 GHz spacing. A single channel CDBP with one-step-per-span based on asymmetric split step Fourier method (A-SSFM) with optimized non-linear coefficient has been employed. We also study an amplitude dependent optimization (AO) of the non-linear coefficient for CDBP which shows an improvement of ≈ 0.8 dB compared to the conventional optimized CDBP, in the non-linear regime. Moreover, our proposed carrier phase and amplitude noise estimation (CPANE) algorithm based on EKF outperforms AO-CDBP in both linear and non-linear regimes with an enhanced performance besides significantly reduced complexity. We further investigate the combined performance of AO-CDBP and EKF which results in an enhanced non-linear tolerance at the expense of increased computational cost trading off to the number of required CDBP steps per span. Furthermore, we also analyze the impact of cross phase modulation (XPM) on the combined performance of AO-CDBP and EKF by varying the number of WDM channels. Numerical results show that the obtained gain from employing AO-CDBP prior to EKF reduces with increasing effects of XPM. Additionally, we also discuss the computational complexity of the aforementioned algorithms. © (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
lhft_intern.bib::Pakala2017d

Extended Kalman filtering for joint mitigation of phase and amplitude noise in coherent QAM systems - Pakala, Lalitha; Schmauß, Bernhard (Optics Express, 2016)
We numerically investigate our proposed carrier phase and amplitude noise estimation (CPANE) algorithm using extend Kalman filter (EKF) for joint mitigation of linear and non-linear phase noise as well as amplitude noise on 4, 16 and 64 polarization multiplexed (PM) quadrature amplitude modulation (QAM) 224 Gb/s systems. The results are compared to decision directed (DD) carrier phase estimation (CPE), DD phase locked loop (PLL) and universal CPE (U-CPE) algorithms. Besides eliminating the necessity of phase unwrapping function, EKF-CPANE shows improved performance for both back-to-back (BTB) and transmission scenarios compared to the aforementioned algorithms. We further propose a weighted innovation approach (WIA) of the EKF-CPANE which gives an improvement of 0.3 dB in the Q-factor, compared to the original algorithm. © 2016 Optical Society of America
lhft_intern.bib::Pakala2016c

Extended Kalman filtering for simultaneous phase and amplitude noise mitigation in WDM systems - Pakala, Lalitha; Schmauß, Bernhard (International Conference on Transparent Optical Networks (ICTON), 2015)
The proposed carrier phase and amplitude noise estimation (CPANE) algorithm using extended Kalman filter (EKF) has been employed for joint mitigation of linear and non-linear phase noise and amplified spontaneous emission (ASE) noise in wavelength division multiplexing (WDM) systems. Numerical investigations on polarization multiplexed (PM) 16-quadrature amplitude modulation (16-QAM) 28 Gbaud/s WDM systems show that the proposed EKF technique outperforms the other considered carrier phase estimation (CPE) methods in mitigating inter and intra-channel non-linearities, laser phase noise and ASE noise.
lhft_intern.bib::Pakala2015b

Improved decision directed carrier phase estimation for nonlinearity mitigation in 16-QAM systems - Pakala, Lalitha; Schmauß, Bernhard (International Conference on Transparent Optical Networks (ICTON), 2014)
We propose and numerically investigate an improved decision directed (IDD) carrier phase estimation (CPE) to mitigate fiber nonlinearity in 16 quadrature amplitude modulation (QAM) coherent transmission systems. The proposed IDD-CPE algorithm is derived based on a two stage approach and compared with other CPE algorithms namely, the pre-decision directed (PDD) CPE and the decision directed (DD) phase locked loop (PLL). By exploiting the symbol position information in the I-Q plane and a euclidean distance measure, the proposed IDD-CPE algorithm outperforms the PDD-CPE and DD-PLL methods, exhibiting an optimal performance at signal launch power of 0 dBm and at optical signal to noise ratios (OSNRs) greater than 28dB, where no bit errors are detected.
lhft_intern.bib::Pakala2014b

Joint Compensation of Frequency Offset, Phase and Amplitude Noise Using Two Stage Extended Kalman Filtering - Pakala, Lalitha; Schmauß, Bernhard (18. ITG-Fachtagung Photonische Netze, 2017)

Joint compensation of phase and amplitude noise using extended Kalman filter in coherent QAM systems - Pakala, Lalitha; Schmauß, Bernhard (40th European Conference on Optical Communication (ECOC), 2014)
We propose and numerically investigate an optimal carrier phase and amplitude noise estimation (CPANE) algorithm using extended Kalman filter (EKF) for effective mitigation of linear and nonlinear phase noise with simultaneous suppression of amplified spontaneous emission (ASE) noise.
lhft_intern.bib::Pakala2014a

Joint Tracking of Polarization State and Phase Noise Using Adaptive Cascaded Kalman Filtering - Pakala, Lalitha; Schmauß, Bernhard (IEEE Photonics Technology Letters, 2017)
We propose a cascaded Kalman filtering (CKF) technique, a series of extended Kalman filter (EKF), and a linear Kalman filter, for joint tracking of phase and amplitude noise as well as polarization state. We further propose an adaptive CKF (A-CKF), in which the process noise covariance has been estimated adaptively, using covariance matching method. Numerical results on back-to-back and transmission scenarios on 28-Gbd polarization-multiplexed 16-quadrature amplitude modulation system justify that our proposed CKF as well as A-CKF outperforms the earlier proposed EKF and the unscented Kalman filter (UKF) with an improved tolerance toward polarization rotations and phase noise besides less computational effor
lhft_intern.bib::Pakala2017f

Kalman Filters - Theory for Advanced Applications - Pakala, Lalitha; Schmauß, Bernhard (Kalman Filters - Theory for Advanced Applications, 2018)
lhft_intern.bib::Pakala2018a

Nonlinearity and Phase Noise Mitigation Using Feed-forward Carrier Phase Estimation and Digital Backward Propagation in Coherent QAM Transmission - Pakala, Lalitha; Schmauß, Bernhard (Physics Procedia, Proceedings of the 8th International Conference on Laser Assisted Net Shape Engineering (LANE 2014), 2014)
We numerically investigate the performance of Viterbi-Viterbi (VV) carrier phase estimation (CPE) and feed-forward decision directed (DD) CPE along with digital backward propagation (DBP) to mitigate laser phase noise, linear and nonlinear fiber impair- ments for polarization multiplexed (PM) 4 and 16-ary quadrature amplitude modulation (QAM) coherent systems. For 16-QAM, DD-CPE is compared with quadrature phase shift keying (QPSK) partitioning method that is based on the modification of VV-CPE. When the laser phase noise is negligible, both CPE methods exhibit a similar performance when employed after DBP. However, in the presence of phase noise, non-decision directed VV-CPE (for 4-QAM) and QPSK partitioning (for 16-QAM) methods outper- form DD-CPE with greater phase noise tolerance and reduced complexity.
lhft_intern.bib::Pakala2014c

Non-linear Mitigation Using Carrier Phase Estimation and K-Means Clustering - Pakala, Lalitha; Schmauß, Bernhard (ITG Fachtagung Photonische Netze, 2015)
We investigate the non-linear mitigation performance of modulation format independent or universal carrier phase estimation (U-CPE) along with K-Means clustering (KMC) algorithm for a 28 Gbaud/s polarization multiplexed (PM) 16 quadrature amplitude modulation (16-QAM) coherent transmission system. Numerical simulations on transmission performance prove that the U-CPE outperforms decision directed carrier phase estimation (DD-CPE) with a gain of 1 dB and non-linear tolerance of approximately 2 dB. Furthermore, it has been verified that a gain of 0.3 dB in both linear and non-linear regimes can be obtained by employing KMC after U-CPE. In addition, the benefit acquired from the combined use of the afore-mentioned algorithms has been also investigated in the presence of laser linewidth effects in addition to fiber non-linearity as well as increasing the feedback delay of U-CPE up to 50 symbol periods to realize the feasibility for real-time implementations. Besides single channel systems, the algorithms have also been employed for wavelength division multiplexing (WDM) systems with 50 GHz channel spacing to see the impact of cross phase modulation (XPM) on their performance. Numerical investigations show that the gain obtained from K-Means algorithm starts vanishing as the XPM effect becomes stronger with an increase in the number of WDM channels.
lhft_intern.bib::Pakala2015a

Performance evaluation of modulation format independent carrier phase estimation and decision directed carrier phase estimation for fiber non-linearity mitigation - Pakala, Lalitha; Schmauß, Bernhard (International Conference on Application of Photonic Technology, Photonics North, 2014)
We numerically investigate and compare the performance of modulation format independent carrier phase esti- mation (CPE) (or universal CPE (U-CPE)) and decision directed CPE (DD-CPE) along with digital backward propagation (DBP) to compensate fiber non-linearity, for polarization multiplexed (PM) 4 and 16-ary quadrature amplitude modulation (QAM) coherent systems. We analyze the impact of each of the CPE methods in reducing the complexity of DBP, in terms of required DBP steps, as well as the influence of the laser line width effects on their performance. By optimizing the step size, the U-CPE method, in spite of its low complexity, exhibits a similar performance as the DD-CPE method in non-linearity mitigation. However, at high signal launch powers, and in the presence of laser phase noise, the performance of DD-CPE method is significantly impaired owing to increased erroneous pre-decisions, whereas, the U-CPE method is still capable of mitigating both non-linearity and phase noise, equivalently good as the ideal DD-CPE case. Moreover, also without DBP for non-linear compensation, U-CPE method outperforms the DD-CPE method allowing high signal launch powers and with greater tolerance towards phase noise. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
lhft_intern.bib::Pakala2014d

Propagation Parameter Tracking using Extended Kalman Filter - Pakala, Lalitha (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2011)

Two Stage Extended Kalman Filtering for Joint Compensation of Frequency Offset, Linear and Nonlinear Phase Noise and Amplitude Noise in Coherent QAM Systems - Pakala, Lalitha; Schmauß, Bernhard (ICTON 2017, 19th International Conference on Transparent Optical Networks, 2017)