Nelson Costa

Novel Approach for BER Evaluation of DQPSK Systems Using Differential Phase Q

A novel approach for BER evaluation of differential quadrature phase-shift keying systems using differential phase Q and taking into account the electrical filtering influence is proposed. Good agreement with results from direct error counting is achieved.

Single-Sideband Differential Phase-Shift Keying Asynchronous Carrier-Suppressed Return-to-Zero – A Novel Signaling Format Optimized for Long-Haul UDWDM Systems

In this paper, a novel single-sideband differential phase-shift keying asynchronous carrier-suppressed return-to-zero (SSB-DPSK-ACS-RZ) format is proposed for long-haul ultradense wavelength-division multiplexing (UDWDM) systems with 43 Gbit/s/channel and 50 GHz of channel spacing. The time delay between the DPSK and clock signals is optimized to achieve higher eye-opening and improved group velocity dispersion tolerance. Furthermore, the tight SSB filtering performed by the multiplexer is used to convert the DPSK-ACS-RZ signal from phase- to amplitude-shift keying, allowing using a lower-cost direct-detection receiver and improving its spectral efficiency. The single-channel and UDWDM transmission performance of the novel format is numerically investigated and compared to the SSB duobinary carrier-suppressed RZ, bandwidth-limited duobinary, phase-modulated duobinary transmission, and bandwidth-limited DPSK formats. The SSB-DPSK-ACS-RZ format shows similar Q-factor and tolerances to pre- and in-line dispersion compensations and fiber nonlinearity to the ones of other investigated direct-detection formats. Significant total residual dispersion tolerance improvement is achieved by the SSB-DPSK-ACS-RZ format relative to the other formats due to the signal chirp. Moreover, the SSB-DPSK-ACS-RZ format shows higher Q-factor than the one of the bandwidth-limited DPSK for long-haul UDWDM transmission systems. In ultra-long-haul UDWDM transmission systems, SSB-DPSK-ACS-RZ and bandwidth-limited DPSK formats show similar performance.

Novel Semi-Analytical Method for BER Evaluation in Simulated Optical DQPSK Systems

A novel semi-analytical method for optical differential quadrature phase-shift keying systems performance evaluation based on the equivalent differential phase (EDP) is proposed. The proposed method is computationally much faster than Monte-Carlo (MC) simulation and methods based on the combination of MC simulation with the EDP. Discrepancies not exceeding 0.2 dB on the required optical signal-to-noise ratio are obtained between MC simulation and the proposed method.

Analysis of DQPSK signals performance in upgrading metropolitan area networks to 40 Gbit/s per channel

The always increasing traffic demand requires the upgrade of current 10 Gbit/s per channel metropolitan area networks (MANs) to higher bit rate per channel. Differential quadrature phase shift keying (DQPSK) appears as one of the most promising modulation formats for this upgrade. In this paper, 40 Gbit/s per channel DQPSK signals performance is assessed through numerical simulation in presence of the main limitations of deployed 10 Gbit/s MANs. It is shown that DQPSK signals have high tolerance to the limited available bandwidth and better robustness to nonlinear impairments than optical single sideband (OSSB) signals, another very promising modulation format for the MANs upgrade. However, OSSB signals show higher tolerance to residual dispersion (when electrical dispersion compensation is used) and better performance when transmitted together with 10 Gbit/s intensity modulated signals.

Influence of the Channel Number on the Optimal Dispersion Map Due to XPM in WDM Links

The influence of the channel number on the optimal dispersion map (ODM) due to cross-phase modulation (XPM) in wavelength division multiplexed links is assessed using an analytical method. The analytical method is validated by comparison with numerical simulation using two different methods: the pump-probe method and a realistic method in which all channels are digitally modulated carriers. It is shown that there are usually, at least, two local ODMs due to XPM: one characterized by negative residual dispersion per span (RDPS) and another characterized by positive RDPS. These two local ODMs due to XPM lead to similar XPM-induced degradation. However, the local ODM with negative RDPS shows always much higher tolerance to the dispersion map (DM) variation. Furthermore, as the ODM due to the combined effect of self-phase modulation and group-velocity dispersion is characterized by negative RDPS when reduced and moderate power levels are used, the use of the local ODM due to XPM with negative RDPS is recommended. This local ODM due to XPM remains approximately the same as long as, at least, 8 channels are transmitted when 100 or 50 GHz channel spacings are used and 12 channels are transmitted when 25 GHz channel spacing is used. However, the high XPM tolerance to the DM variation for 25 GHz channel spacing leads to the conclusion that the ODM for 8 channels is the recommended DM in case of an arbitrary number of channels, independently of the channel spacing. These outcomes are independent of the power level, number and length of spans and transmission fiber type.

Influence of Dispersion Compensation Granularity on the XPM-Induced Degradation in NRZ-IM-DD WDM Links at 10 Gbit/s per Channel with 50 GHz of Channel Spacing

The influence of the dispersion compensation granularity on the cross-phase modulation (XPM) induced degradation in non-return-to-zero intensity modulated with direct detection wavelength division multiplexed links at 10 Gbit/s per channel with 50 GHz of channel spacing is assessed analytically for different power levels and four dispersion maps. The dispersion compensation granularity may lead to an increase of the power penalty due to XPM exceeding 1.5 dB for the locally optimal dispersion map (from the XPM degradation viewpoint) with high positive residual dispersion per span. The increase of the XPM normalized variance due to the dispersion compensation granularity is higher for links showing noticeable XPM degradation in the absence of dispersion compensation granularity. Lower XPM degradation tolerance to the dispersion map variation and higher power level leads to higher XPM degradation due to the dispersion compensation granularity.

Dependence of XPM Degradation on the Dispersion Map for 10 Gbit/s WDM Links over Standard-Fibre Employing Duobinary Format

The dependence of cross-phase modulation (XPM) -induced degradation on the dispersion map for wavelength division multiplexing (WDM) systems at 10 Gbit/s per channel with 50 GHz of channel spacing and standard single-mode fibre employing duobinary format is investigated through numerical simulation. It is shown that, for low optical power levels at the input of each span and reduced number of spans, the optimum residual dispersion per span is about 150 ps/nm whereas, for higher optical power levels and number of spans, it is about -150 ps/nm. The results suggest that the optimum amount of residual dispersion per span and post-compensation dispersion are almost independent of the pre-compensation dispersion amount. Moreover, the amount of pre-compensation dispersion has a small influence on the XPM-induced degradation.

Optical DQPSK System Performance Evaluation Using Equivalent Differential Phase in Presence of Receiver Imperfections

The performance evaluation of optical differential quadrature phase-shift keying (DQPSK) systems through numerical simulation using a Gaussian approach (GA) for the equivalent differential phase (EDP) statistics is analyzed. It is shown that the GA describes quite accurately the probability density function (PDF) of EDP for a large range of DQPSK receiver (RX) imperfections. A semi-analytical simulation method (SASM) for bit error probability (BEP) evaluation based on the GA for the EDP is derived, proving to be quite accurate in presence of RX imperfections. The SASM takes into account the signal-noise beat variance dependence on signal waveform distortion and arbitrary optical and electrical filtering frequency responses. Closed-form expressions for the mean and standard deviation of EDP are derived which allows evaluating the DQPSK system performance in a quite time-efficient manner. Discrepancies not exceeding 0.1 dB on the optical SNR penalty estimated by the SASM for a BEP of 10-4 when compared with Monte Carlo simulation are observed for the majority of the acceptable RX imperfections. Only the time-misalignment of the signals at the balanced detector input leads to higher discrepancies but not exceeding 0.3 dB even for considerable time-misalignment.

Impact of inter-symbol interference on optical DQPSK systems performance evaluation using equivalent differential phase

The statistics of “equivalent” differential phase (EDP) of differential quadrature phase-shift keying (DQPSK) systems is assessed numerically. It is shown that the EDP statistics is approximately Gaussian for a large range of system parameters. Thus, performance evaluation methods based on a Gaussian approximation for the EDP may be used. However, both the mean and variance of the Gaussian distribution associated with each symbol depend on the transmitted symbol sequence, showing that the impact of inter-symbol interference (ISI) on the bit error ratio should not be neglected. Indeed, ISI may lead to an inaccuracy exceeding 1 dB on the required OSNR when not accurately taken into account.

Influence of local oscillator-to-signal power ratio on the gaussianity of CP-QPSK signal statistics

The statistics of quadrature phase-shift keying with coherent-detection and polarization multiplexing (CP-QPSK) signal at the decision circuit input is assessed by numerical simulation for different local oscillator-to-signal (LO/S) power ratios. It is shown that the signal statistics at the decision circuit input is approximately Gaussian distributed for high LO/S power ratios. However, the mean and variance of the Gaussian distribution that approximates the statistics of each symbol depend on the transmitted symbol sequence, especially for low LO/S power ratios, demonstrating the impact of the waveform on the statistics of the detected signal. Moreover, the signal statistics starts to deviate from Gaussian for LO/S power ratios below 17 dB. A semi-analytical simulation method (SASM) based on the Gaussian approximation for the signal statistics at the decision circuit input is used for performance evaluation of CP-QPSK system. The accuracy of the SASM is assessed for different LO/S power ratios by comparison with Monte-Carlo (MC) simulation results. The SASM shows good agreement with MC simulation results for LO/S power ratios between 6 and 30 dB.