Presence Of Nonlinear Phase Noise Research Articles

Performance analysis of mode division multiplexing system in presence of nonlinear phase noise

Abstract The potential for higher spectral efficiency has increased interest in mode division multiplexing (MDM) systems. However, the sensitivity of MDM to fiber nonlinearity and mode coupling, which induces nonlinear phase noise (NLPN), forms the main penalty. In this work, we developed an analytical model that describes the effects of fiber nonlinearity on the performance of m-array quadrature amplitude modulation (mQAM) MDM system based few-mode fiber (FMF). The random NLPN is mainly induced when Kerr nonlinearities such as self-phase modulation (SPM), cross-phase modulation (XPM) and four-wave mixing (FWM) as well as their interaction with optical amplifiers noise occur over an optical fiber link. FMF is proposed and designed to carry six spatial modes. The parameters of proposed FMF are used with the analytical model for evaluating the NLPN versus power and distance. To verify the analytical results, an MDM system, that uses proposed FMF without any nonlinear compensation, is demonstrated by numerical simulation. Each spatial mode is modulated by a 4QAM format with a symbol rate of 20 Gsymbol/s. The results are obtained for single-, two- and six–mode propagations to show the influence of fiber nonlinearity on the system performance. The results reveal that the XPM phase noise is the dominant effect that degrades the system performance, specifically when two degenerate spatial modes or modes within the same mode group are co-propagated. In addition, for six-mode transmission, FWM insignificantly induces the NLPN. Finally, the results confirm that the numerical and analytical results in good agreement.

K-Nearest Neighbor Detector for Enhancing Performance of Optical Phase Conjugation System in the Presence of Nonlinear Phase Noise

Nonlinear phase noise (known as Gordon–Mollenauer phase noise) results from power fluctuations arising from amplified spontaneous-emission noise of the inline amplifier which is converted into phase fluctuations due to the self-phase modulation effect. It may severely impair the phase of optical signal, and would further degrade the performance of the long-haul optical transmission systems. The case can be compensated partially by mid-span optical phase conjugation(OPC). In this paper, an effective k-nearest neighbor (KNN) detector have been introduced to further improve the performance of OPC system by mitigating non-Gaussian impairments caused by nonlinear phase noise. The effectiveness is investigated in a 112-Gb/s 16QAM optical phase conjugation system with 800-km dispersion-managed link and 1280-km dispersion-shifted-fiber link. The results show that the effective and optimal KNN detector can enhance the overall performance of OPC system, even the asymmetric system.

Performance analysis of an all-optical OFDM system in presence of non-linear phase noise.

The potential for higher spectral efficiency has increased the interest in all-optical orthogonal frequency division multiplexing (OFDM) systems. However, the sensitivity of all-optical OFDM to fiber non-linearity, which causes nonlinear phase noise, is still a major concern. In this paper, an analytical model for estimating the phase noise due to self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) in an all-optical OFDM system is presented. The phase noise versus power, distance, and number of subcarriers is evaluated by implementing the mathematical model using Matlab. In order to verify the results, an all-optical OFDM system, that uses coupler-based inverse fast Fourier transform/fast Fourier transform without any nonlinear compensation, is demonstrated by numerical simulation. The system employs 29 subcarriers; each subcarrier is modulated by a 4-QAM or 16-QAM format with a symbol rate of 25 Gsymbol/s. The results indicate that the phase variance due to FWM is dominant over those induced by either SPM or XPM. It is also shown that the minimum phase noise occurs at -3 dBm and -1 dBm for 4-QAM and 16-QAM, respectively. Finally, the error vector magnitude (EVM) versus subcarrier power and symbol rate is quantified using both simulation and the analytical model. It turns out that both EVM results are in good agreement with each other.

Optimal signal constellation design for ultra-high-speed optical transport in the presence of nonlinear phase noise

In this paper, we first describe an optimal signal constellation design algorithm suitable for the coherent optical channels dominated by the linear phase noise. Then, we modify this algorithm to be suitable for the nonlinear phase noise dominated channels. In optimization procedure, the proposed algorithm uses the cumulative log-likelihood function instead of the Euclidian distance. Further, an LDPC coded modulation scheme is proposed to be used in combination with signal constellations obtained by proposed algorithm. Monte Carlo simulations indicate that the LDPC-coded modulation schemes employing the new constellation sets, obtained by our new signal constellation design algorithm, outperform corresponding QAM constellations significantly in terms of transmission distance and have better nonlinearity tolerance.

Multi-Level Coded Modulation for 16-ary Constellations in Presence of Phase Noise

Application of multi-level coded modulation (MLCM) for 16-ary constellations in coherent systems is studied. An MLCM system with Reed-Solomon component codes and multi-stage decoder is considered. A systematic numerical method for finding set-partitioning and optimal code rates is presented. The method only requires the probability density function of received samples and can be applied to any constellation regardless of irregularity or lack of symmetry. Performance of the designed MLCM system is verified in presence of nonlinear phase noise and normal phase noise. For nonlinear phase noise limited system, it is shown that the block error rate (BLER) of the system can be improved using our approach for set-partitioning. For phase noise limited system, both BLER and bit error rate (BER) are studied for a phase noise optimized and square 16-quadrature amplitude modulation (16QAM). Post forward-error correction (FEC) BER performance of the optimized constellation over square 16QAM is studied for different levels of phase noise. It is shown that the optimized constellation along with MLCM system decreases the required signal-to-noise ratio by several dB at high phase noise regime and low post FEC BER.

Nonlinear phase noise in optical communication systems using eigenfunction expansion method

We report on a generalization of the eigenfunction expansion method to model the performance of multichannel optical-fiber communications systems in the presence of nonlinear phase noise. Our method is fast, accurate, and easy to implement for numerical simulations in multichannel wavelength-division multiplexed (WDM) systems. We also account for the dispersion to all orders for increased accuracy in multichannel systems.

Modeling nonlinear phase noise in differentially phase-modulated optical communication systems

Using an alternative approach for evaluating the Bit-Error Rate (BER), we present a numerical and experimental investigation of the performance of phase-modulated optical communication systems in the presence of nonlinear phase noise and dispersion. The numerical method is based on the well known Karhunen-Lo;eve expansion combined with a linearization technique of the Nonlinear Schr odinger Equation (NLSE) to account for the nonlinear interaction between signal and noise. Our numerical results show a good agreement with experiments.

Signal Design and Detection in Presence of Nonlinear Phase Noise

In optical fiber transmission systems using inline amplifiers, the interaction of a signal and amplifier noise through the Kerr effect leads to nonlinear phase noise that can impair the detection of phase-modulated signals. We present analytical expressions for the maximum-likelihood (ML) decision boundaries and symbol-error rate (SER) for phase-shift keying and differential phase-shift keying systems with coherent and differentially coherent detection, respectively. The ML decision boundaries are in the form thetas(r) = c2r2 + c1r + c0, where thetas and r are the phase and the amplitude of the received signal, respectively. Using the expressions for the SER, we show that the impact of phase error from carrier synchronization is small, particularly for transoceanic links. For modulation formats such as 16-quadrature amplitude modulation, we propose various transmitter and receiver phase rotation strategies such that the ML detection is well approximated by using straight-line decision boundaries. The problem of signal constellation design for optimal SER performance is also studied for a system with four signal points.

Power Profile Optimization in Phase-Modulated Systems in Presence of Nonlinear Phase Noise

In optical fiber transmission systems using inline amplifiers, the interaction of signal and amplifier noise through the Kerr effect leads to nonlinear (NL) phase noise that impairs detection of phase-modulated signals. We study the minimization of the total phase noise variance (linear, NL, and receiver) by using a power profile along the link that is linear (on a decibel scale) with distance. For DPSK systems with direct detection, a total variance reduction of 65% can be achieved by designing the transmitted power to be about 8 dB higher than the received power in typical terrestrial links. In addition, for a given transmitted power and received power, the optimal power profile along the link is numerically determined