Blind Polarization Demultiplexing Research Articles

Blind Polarization Demultiplexing of Shaped QAM Signals Assisted by Temporal Correlations.

While probabilistic constellation shaping (PCS) enables rate and reach adaption with finer granularity [1], it imposes signal processing challenges at the receiver. Since the distribution of PCS-quadrature amplitude modulation (QAM) signals tends to be Gaussian, conventional blind polarization demultiplexing algorithms are not suitable for them [2]. It is known that independently and identically distributed (iid) Gaussian signals, when mixed, cannot be recovered/separated from their mixture. For PCS-QAM signals, there are algorithms such as [3], [4] which are designed by extending conventional blind algorithms used for uniform QAM signals. In these algorithms, an initialization point is obtained by processing only a part of the mixed signal, which have non-Gaussian statistics. In this paper, we propose an alternative method wherein we add temporal correlations at the transmitter, which are subsequently exploited at the receiver in order to separate the polarizations. We will refer to the proposed method as frequency domain (FD) joint diagonalization (JD) probability aware-multi modulus algorithm (pr-MMA), and it is suited to channels with moderate polarization mode dispersion (PMD) effects. Furthermore, we extend our previously proposed JD-MMA [5] by replacing the standard MMA with a pr-MMA, improving its performance. Both FDJD-pr-MMA and JD-pr-MMA are evaluated for a diverse range of PCS (entropy ) over a first-order PMD channel that is simulated in a proof-of-concept setup. A MMA initialized with a memoryless constant modulus algorithm (CMA) is used as a benchmark. We show that at a differential group delay (DGD) of 10% of symbol period and 18 dB SNR/pol., JD-pr-MMA successfully demultiplexes the PCS signals, while CMA-MMA fails drastically. Furthermore, we demonstrate that the newly proposed FDJD-pr-MMA is robust against moderate PMD effects by evaluating it over a DGD of up to 40% of . Our results show that the proposed FDJD-pr-MMA successfully equalizes PMD channels with a DGD up to 20% of .

Simplified radius-directed linear Kalman filter algorithm for lightning-induced state of polarization compensation in optical ground wire

Lightning strokes can cause an ultrafast rotation of the state of polarization (RSOP) in an optical ground wire cable, which leads to communication interruptions. To address this, a simplified radius-directed linear Kalman filter (S-RD-LKF) for blind polarization demultiplexing was developed. The ultrafast RSOP under thunderstorm weather conditions was simulated based on the Heidler model, and the simulation results indicated that the proposed S-RD-LKF algorithm effectively compensated for the RSOP impairment caused by the first and subsequent lightning strokes. Moreover, the RD-LKF algorithm and the proposed S-RD-LKF algorithm exhibited a similar performance; however, the computation complexity of the proposed algorithm was lower.

Probability-Aware Stokes Space Blind Polarization Demultiplexing for Probabilistically Shaped Signals

A probability-aware blind polarization demultiplexing (PolDemux) algorithm using symbols of different radii in the Stokes space is proposed for polarization division multiplexed (PDM) coherent optical communication systems with probabilistically shaped (PS) signals. By leveraging the larger radius symbols which correspond to a non-trivial proportion of the PS signal, a more accurate estimation of the normal vector is obtained for PolDemux by least squares plane fitting with these higher signal-to-noise ratio (SNR) symbols. To properly discriminate symbols of different radii, the optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${s_0}$</tex-math></inline-formula> boundaries are derived using the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> criterion. Monte-Carlo simulation of a PDM PS-64QAM system with the Maxwell-Boltzmann distribution under various constellation entropies (H) is conducted to evaluate the performance of three PolDemux methods based on the smallest, the second smallest, and the third smallest radius symbols, namely Pt <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , Pt <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and Pt <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , respectively. The numerical results verify that the method with larger radius symbols outperforms the one with smaller radius symbols in terms of both the normal vector estimation accuracy and the required optical SNR at a targeted normalized generalized mutual information (NGMI), which is more significant for larger entropies as the proportion differences among Pt <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> /Pt <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Pt <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> symbols increase. Higher tolerance to polarization mode dispersion and polarization dependent loss is also achieved by the PolDemux method with larger radius symbols. The fiber transmission results show that, compared with Pt <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , the achievable transmission distances at the NGMI of 0.9 are extended by 115--206 km and 62--151 km with Pt <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> and Pt <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> in systems with H of 4.33--5.17, respectively.

Low-complexity blind polarization demultiplexing and frequency domain equalization for coherent passive optical network systems

Algorithmic and architectural options and trade-offs between performance and complexity/power dissipation are necessary to consider in the transfer of coherent technology from long-haul transmission to short-reach application. An adaptive equalization algorithm cascading polarization demultiplexing and frequency domain equalization is proposed to target passive optical network applications that feature extremely low computational complexity. Three coordinate rotation digital computer-based vector rotators are introduced to realize polarization demultiplexing without performing multiplications. A simplified gradient descent algorithm is proposed to search and trace the state of polarization. A nonbutterfly adaptive equalizer in the frequency domain for each polarization is designed to handle link chromatic dispersion and the imperfection of the transceiver frequency response. The performance of the proposed equalization scheme is experimentally verified by a 32-GBaud dual-polarization Nyquist quadrature phase-shift keying system over 20-km standard single-mode fiber transmission. With the proposed method, the number of hardened multipliers for field-programmable gate array realization is reduced by ∼85 % compared with a conventional 2 × 2 multiple-input multiple-output finite impulse response filter with the same receiver sensitivity.

Tracking channel alignment in blind polarization de-multiplexing

Blind de-multiplexing methods such as the constant modulus algorithm (CMA) or independent component analysis (ICA) are an effective means of de-multiplexing dual polarization modulated optical signals mixed by the evolution of the polarization state on propagation through the transmission medium. However, the recovery matrix estimated by these methods has an inherent permutation ambiguity in the assignment of polarization channels to ports. As a consequence, frequent instances of channel alignment permutation can occur resulting in loss of data during system recovery. This paper describes a method of maintaining the initial alignment by setting the diversity combiner weight matrix to a member of the equivalence class of the estimated recovery matrix that is the nearest to the previous weight matrix. The method is verified by computer simulation of de-multiplexing by ICA of dual polarization differential quadrature phase shift keyed coherent optical transmission subject to aggressive changes in polarization state as well as experimental investigation of de-multiplexed QPSK modulation by CMA. Perfect maintenance of channel alignment and accurate recovery of the constellations is achieved.

Modulation format independent blind polarization demultiplexing algorithms for elastic optical networks

We demonstrate a novel modulation format independent algorithm for adaptive blind polarization demultiplexing for elastic optical networks (EONs). We compare the proposed algorithm with traditional constant modulus algorithm (CMA) and radius-directed algorithm (RDA), in terms of performance in PM-QPSK, PM-16QAM and PM-64QAM coherent system, by simulating in back-to-back (BTB) and transmission sceneries. The simulation result shows that the modulation format independent algorithm can achieve universal adaptive blind polarization demultiplexing for PM-mQAM signals and gain slightly better performance in condition of lower optical signal noise ratio (OSNR). Furthermore, we also carry out experiments to investigate the performance of the proposed algorithm in BTB and 800 km transmission scenarios for 16 GBaud PM-QPSK and PM-16QAM. The experimental results demonstrate the conclusion of the numerical simulations.

Polarization Demultiplexing for Stokes Vector Direct Detection

The conventional intensity modulation with direct detection faces the capacity bottleneck beyond 100-Gb/s per wavelength, due to its 1-dimension (1-D) modulation and detection. To increase the spectral efficiency, there emerge a variety of direct detection subsystems based on the Stokes vector receiver (SV-R). The Stokes space contains the intensity information of three independent polarizations. Therefore, the SV-R enlarges the detection dimensions at receiver to 3. The SV-R can recover any 2-D or 3-D signal modulated in Stokes space. One of the most significant features of SV-R is the DSP-enabled polarization demultiplexing. Instead of a 2 × 2 Jones matrix, in Stokes space, a 3 × 3 rotation matrix (RM) characterizes the polarization variation during fiber transmission. Previously, we have demonstrated a training-assisted polarization demultiplexing algorithm, which uses three basis vectors in Stokes space to estimate the RM. In this paper, we propose a blind polarization demultiplexing using the signal distribution in Stokes space. Combined with the blind adaptive algorithm, the new method converts the two-stage polarization demultiplexing (RM estimation and channel equalization) to a single-stage blind 3 × 2 real-value multiple-input multiple-output equalization, which significantly simplify the DSP procedures. We experimentally demonstrate the SV-R based on either training or blind demultiplexing algorithms, and compare the performance between them.

Blind polarization demultiplexing by constructing a cost function for coherent optical PDM-OFDM.

We propose a training symbols-free polarization demultiplexing method by constructing a cost function (CCF-PDM) for coherent optical PDM-OFDM. This method is applicable for high-speed, wide-bandwidth OFDM signals, different subcarrier modulation formats and long-haul transmission. It shows comparable performance with that of conventional method but without overhead and converges fast. Since the neighboring subcarriers experience similar polarization effects, we set the initial matrix parameters by the neighboring subcarrier to reduce the number of iteration for the gradient algorithm and prevent swapping the data of the two orthogonal polarizations. We verify this method in experiment by transmitting 66.6-Gb/s PDM-OFDM signal with 4QAM subcarrier modulation over 5440 km SSMF and 133.3-Gb/s PDM-OFDM signal with 16QAM subcarrier modulation over 960 km SSMF respectively. We compare its performance with that of training symbols. We also analyze the convergence speed of this method.

Blind polarization demultiplexing for quadrature amplitude modulation coherent optical communication systems using low-complexity and fast-converging independent component analysis

A kind of blind polarization demultiplexing algorithm based on low-complexity and fast-converging independent component analysis (ICA) for quadrature amplitude modulation (QAM) coherent optical communications systems is proposed. The polarization demultiplexing is achieved by maximizing the signal’s non-Gaussianity measured by the information theoretic quantity of negentropy. We demonstrate that some approximate nonlinear functions can be substituted for the negentropy and this greatly reduces the computational complexity. An adaptive gradient optimization algorithm and a fast-converging quasi-Newton algorithm are employed to maximize the negentropy. The numerical simulation and experimental results for polarization division multiplexing quadrature phase shift keying/16QAM without neglecting polarization mode dispersion reveal that the proposed ICA demultiplexing algorithms are feasible and effective for coherent optical receivers.

Blind Polarization Demultiplexing With Low Computational Complexity

A blind polarization demultiplexing technique is proposed and experimentally validated. Our algorithm is transparent to modulation format, pulse-shape, and sampling phase. Without resorting to Stokes parameters, it combines the versatility of the polarization alignment in Stokes space with the computational simplicity of the constant modulus algorithm.

Multi-Modulus Blind Equalizations for Coherent Quadrature Duobinary Spectrum Shaped PM-QPSK Digital Signal Processing

A novel digital signal processing (DSP) scheme for quadrature duobinary (QDB) spectrum shaped polarization multiplexed quadrature phase shift keying (PM-QPSK) based on multi-modulus blind equalizations (MMBE) is proposed and demonstrated with both simulation and experimental results. The key algorithms for this novel digital signal processing scheme include the cascaded multi-modulus algorithm (CMMA) for blind polarization de-multiplexing, multi-modulus QPSK partitioning frequency offset estimation (FOE) and two stage carrier phase recovery (CPR) with maximum likelihood phase estimation. The final signal is detected by maximum-likelihood sequence detection (MLSD) for data BER measurement. It shows that CMMA have better frequency response performance compared with CMA for noise compression. The performances of FOE and CPR are also investigated with different spectrum shaping bandwidth, group size and laser linewidth. Finally, the feasibility of the proposed digital signal processing scheme is demonstrated by the experiment of 112 Gb/s QDB spectrum shaped PM-QPSK signal with a 25 GHz bandwidth waveshaper for Nyquist WDM channels.

Convergence Comparison of the CMA and ICA for Blind Polarization Demultiplexing

An algorithm based on independent component analysis for blind polarization demultiplexing in a coherent transmission system is presented. A comparison with the constant modulus algorithm in terms of the convergence properties is performed, and it is found that the suggested algorithm has a significantly faster convergence rate and does not have any singularity problems. We also demonstrate that the algorithm convergence is strongly dependent on the choice of starting condition and show how this can be exploited to increase the convergence rate.

A Novel Blind Polarization Demultiplexing Algorithm Based on Correlation Analysis

We propose a novel correlation-based blind polarization demultiplexing technique for coherent optical communication systems. The basic procedure involves the blind estimation of various channel parameters through correlation analysis, and resolving ambiguities using pilot symbols. In a 56 Gb/s/polarizaton multiplexing transmission system employing quadrature phase-shift keying, for both symbol-rate sampling and double symbol-rate sampling, the proposed algorithm achieves the same performance as that of the receiver with known channel parameters and significantly outperforms the constant modulus algorithm.

Transmission of 32-Tb/s Capacity Over 580 km Using RZ-Shaped PDM-8QAM Modulation Format and Cascaded Multimodulus Blind Equalization Algorithm

In this paper, we propose a novel synthesizing method for high-speed 8-ary quadratic-amplitude modulation (QAM) optical signal generation using commercial optical modulators with binary electrical driving signals. Using this method, we successfully generated 114-Gb/s pulse-duration modulation (PDM)-8QAM optical signals. Intradyne detection of PDM-8QAM optical signals with robust blind polarization demultiplexing has been demonstrated by using a new cascaded multimodulus equalization algorithm. With return-to-zero-shaped PDM-8QAM modulation and the proposed blind polarization demultiplexing algorithm, we demonstrate transmission of a record 32-Tb/s fiber capacity (320 × 114 Gb/s) over 580 km of ultralow-loss single-mode fiber-28 fiber by utilizing C+L-band erbium-doped fiber-amplifier-only optical amplification and single-ended coherent detection technique at an information spectral efficiency of 4.0 bit/s·Hz.

DSP for Coherent Single-Carrier Receivers

In this paper, we outline the design of signal processing (DSP) algorithms with blind estimation for 100-G coherent optical polarization-diversity receivers in single-carrier systems. As main degrading optical propagation effects, we considered chromatic dispersion (CD), polarization-mode dispersion (PMD), polarization-dependent loss (PDL), and cross-phase modulation (XPM). In the context of this work, we developed algorithms to increase the robustness of the single DSP receiver modules against the aforesaid propagation effects. In particular, we first present a new and fast algorithm to perform blind adaptive CD compensation through frequency-domain equalization. This low complexity equalizer component inherits a highly precise estimation of residual dispersion independent from previous or subsequent blocks. Next, we introduce an original dispersion-tolerant timing recovery and illustrate the derivation of blind polarization demultiplexing, capable to operate also in condition of high PDL. At last, we propose an XPM-mitigating carrier phase recovery as an extension of the standard Viterbi-Viterbi algorithm.