Analysis of intrachannel impairments in differential phase-shift keying transmission systems

The evolution of the phase in a return-to-zero differential phase-shift keying system is studied by the generalized momentum method. The results show that phase fluctuation in the case of dispersion-managed solitons is much smaller than that in quasi-linear systems for a given launch power.     

A fiber-optic transmission system based on differential polarization-shift keying

A differential polarization-shift keying (DPolSK) scheme in which information is encoded as a differential polarization state with respect to the previous symbol is considered. A novel DPolSK demodulator consisting of optical delay interferometer and a pair of birefringence plates that do polarization rotation are proposed. Numerical simulations of the long haul fiber-optic systems based on differential phase-shift keying (DPSK) and DPolSK are carried out and it is found that DPolSK has a higher nonlinear tolerance than DPSK. This is because the ghost pulse generation due to intra-channel four-wave mixing (IFWM) is less efficient for DPolSK signals as compared to DPSK.     

Interchannel nonlinear transmission penalties in polarization-multiplexed 2 x 10 Gbit/s differential phase-shift keying transmission

We discuss the performance of a multichannel 2 x 10 Gbit/s polarization-multiplexed differential phase-shift keying transmission system. Through simulations and transmission experiments we find that, despite the constant power envelope of non-return-to-zero phase-shift keying modulation formats, polarization multiplexing strongly reduces the nonlinear tolerance and transmission performance at a 2 x 10 Gbit/s line rate with multichannel transmission. This results in a 10 dB power penalty when comparing single- and nine-channel transmission. Additionally, multichannel impairments in differential phase-shift keying and on-off keying are compared for 2 x 10 Gbit/s polarization-multiplexed transmission.     

Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems

Self-phase modulation and intrachannel cross-phase-modulation- (IXPM) induced nonlinear phase noise is investigated by the variational method. IXPM can cause a considerable increase of phase noise. We show, however, that IXPM leads to a partial correlation between the phase noises of adjacent pulses, which tends to reduce the influence of nonlinear phase noise in return-to-zero differential phase-shift keying transmission. In highly dispersive transmission systems, intrachannel four-wave mixing-induced differential phase fluctuations are typically larger than differential nonlinear phase noise. The analysis is validated by Monte Carlo simulation.     

All-optical amplitude-shift keying and differential phase-shift keying to differential phase amplitude-shift keying format combination in highly nonlinear fiber

We propose an all-optical modulation formats combination scheme that merges an amplitude-shift keying （ASK） signal and a differential phase-shift keying （DPSK） signal into a single differential phase amplitude- shift keying （DPASK） signal based on parametric amplification in a highly nonlinear fiber. By optimizing the power of the ASK channel, formats combination of ASK and DPSK to DPASK signal is successfully demonstrated by computational simulation. The demodulation process of the generated DPASK pulses is investigated and the relationship between optical signal-to-noise ratio （OSNR） penalty and the input ASK power is presented. The proposed scheme may be used for increasing spectral efficiency and all-optical logic device.     

Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion

Intrachannel four-wave mixing (IFWM) in highly dispersed differential phase-shift keying (DPSK) transmission systems is studied with a simple analytical model and numerical simulation. It is found that the IFWM effect in DPSK systems is smaller and less dependent on the bit pattern than in on-off-keying systems with the same average power. The reduced pulse energy in DPSK and correlation between the nonlinear phase shifts of two adjacent pulses contribute to the robustness of DPSK versus IFWM.     

Convergence of phase fluctuation induced by intrachannel four-wave mixing in differential phase-shift keying transmission systems via phase fluctuation averaging

This work investigates the effect of phase fluctuation averaging on phase fluctuation induced by intrachannel four-wave mixing (IFWM) in highly dispersed differential phase-shift keying transmission systems. Through repeatedly averaging the phase fluctuations of adjacent pulses, a simple analytical model and numerical simulation revealed that the IFWM-induced differential phase fluctuation is suppressed and convergent, even after an ultralong transmission. The influence of averaging the phase fluctuations on the bit error rate is also evaluated by the semianalytical method.     

Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission

A novel scheme for postnonlinearity compensation is proposed to reduce the phase jitter in phase-shift keying transmission. A phase modulator is used to modulate the phase of the data pulses in front of the receiver. The magnitude of the phase modulation is proportional to the detected pulse intensity, and the sign is opposite to that of the nonlinear phase shift caused by self-phase modulation. Thus, the nonlinear phase noise induced by amplitude fluctuation and self-phase modulation is partially compensated for. We show by numerical simulations that a differential phase-shift keying dispersion-managed soliton system at 10Gbits/s with such postnonlinearity compensation can provide greater than 3dB of improvement in ultralong-haul dense wavelength-division multiplexing transmissions.     

Simultaneous demodulation and slow light of differential phase-shift keying signals using stimulated-Brillouin-scattering-based optical filtering in fiber

For the first time to our knowledge, we demonstrate simultaneous demodulation and slow-light delay of differential phase-shift keying (DPSK) signals at flexible bit rates using the stimulated-Brillouin-scattering-based optical filtering effect in optical fiber. Both 10 and 2.5 Gbit/s DPSK signals have been demodulated and delayed with excellent performances. In the case of the 10 Gbit/s DPSK signal, after demodulation the tunable delay range with error-free operation is about 50 ps, which we believe is the best result obtained for 10 Gbit/s slow-light demonstrations. For the 2.5 Gbit/s DPSK signal, the optimal sensitivity after demodulation is -36.5 dBm, which is comparable with the back-to-back sensitivity of a 2.5 Gbit/s nonreturn-to-zero signal.     

Nonlinear polarization effects and mitigation in polarization-division-multiplexed coherent transmission systems

Using numerical simulations, the nonlinear transmission performance of polarization-division-multiplexed quadrature-phase-shift-keying （PDM-QPSK） coherent systems is studied. It is found that inter-channel cross-polarization modulation （XPolM） induced nonlinear polarization scattering can significantly degrade the transmission performance of PDM-QPSK coherent systems and change the perspective of dispersion management in optical coherent transmission systems. Some techniques to mitigate nonlinear polarization scattering in dispersion-managed PDM coherent transmission systems are discussed, including the use of time-interleaved return-to-zero （RZ） PDM formats, the use of periodic-group-delay PGD dispersion compensators, and the judicious addition of some polarization-mode-dispersion （PMD） in the transmission link. It is shown that if nonlinear polarization scattering can be well mitigated, a polarization multiplexed optical coherent transmission system with dispersion management could perform better than that without it.     

High speed optical transmission utilizing constant envelope modulation based on frequency shift keying and minimum-shift keying

A novel 40-Gb/s constant envelope optical frequency shift keying （FSK） transmitter and the transmission characteristics are investigated both by simulation and experiment. Meanwhile, to increase the spectrum efficiency of FSK, we propose a novel optical minimum-shift keying （MSK） scheme and analyze its per-formance compared with other MSK schemes and other traditional modulation formats. Simulation and experimental results show that the novel FSK scheme could be a potential candidate for the future high speed transmission and label switching systems. And the novel MSK scheme deserves future deep research for its potential excellent performance.     

Tolerance of laser frequency offset in optical minimum-shift keying transmission systems

A mismatch between laser frequency and delay interferometer (DI) phase is found to be the most critical impairment for the receiver performance in a practical phase-modulated (PM) system. This paper investigates the receiver performance degradation caused by frequency offset between optical signal and DI in a 10 Gb/s minimum-shift keying (MSK) system, and compares it with the conventional PM formats, optical differential-phase-shift keying (DPSK) and differential-quadrature-phase-shift keying (DQPSK), which are nonreturn-to-zero (NRZ) and 50% duty cycle return-to-zero (RZ). Results show that the MSK system is about double times and six times more robust to frequency offset than the DPSK and DQPSK systems operating at the same bit rate, respectively.     

Ultrafast all-optical three-input Boolean XOR operation for differential phase-shift keying signals using periodically poled lithium niobate

We propose and demonstrate that periodically poled lithium niobate (PPLN) can act as an ultrafast three-input XOR gate for differential phase-shift keying (DPSK) signals based on cascaded sum- and difference-frequency generation. PPLN-based all-optical three-input Boolean XOR operations for 20 Gbits/s return-to-zero DPSK (RZ-DPSK), 40 Gbits/s RZ-DPSK, and 20 Gbits/s non-return-to-zero DPSK signals are all successfully verified in the experiment.     

Balanced differential phase-shift keying detector performance: an analytical study

A simple explanation of the observed approximately 3 dB advantage of differential phase-shift keying (DPSK) balanced detection over the intensity-modulated directly detected (IM-DD) type detection that can be easily used for system engineering purposes is presented. A Gaussian approximation is used to describe the tails of the detected noisy random signals leading to an analytical explanation of the observed approximately 3 dB advantage of DPSK balanced detection over the IM-DD type detection.     

Effect of phase noise on optical minimum-shift keying transmission systems

Phase-modulated (PM) signals have recently been used in long-haul lightwave communication systems to reach record distances. Added directly to the signal phase, linear and nonlinear phase noise cause performance degradation in PM systems. Minimum-shift keying (MSK), as a special format of PM signals, presents some different features of phase noise tolerance. This paper investigates the effect of phase noise on the performance degradation in the 10 Gb/s optical MSK systems and analyzes the contribution of phase noise to the bit error rate (BER), compared with the conventional PM format, 50% duty cycle optical return-to-zero differential phase-shift keying (RZ-DPSK) signals, in several typical local fiber dispersion transmission systems. The effect of intensity noise on the performance degradation in the corresponding transmission systems is also investigated.     

Polyspectral analysis and optimization of the frequency-domain differential phase-shift keying

Using the mathematical tool of high-order spectra (polyspectra), we consider the synthesis of optimal variants of high-order differential phase-shift keying in the frequency domain. The proposed approach allows all possible variants of the second-order differential phase-shift keying to be reduced to phase modulation of a special form of the fourth-order spectrum (trispectrum) — triphase modulation. The optimal triphase shift keying variants which have the best spectral efficiency and outperform the known variants of the second-order differential phase-shift keying in noise immunity are devised. It is shown that the noise immunity of proposed modulation is higher than that of the first-order differential phase-shift keying in the channels with simultaneous time and frequency offsets.     

Exact analysis of a balanced receiver for differential phase-shift keying signals

The performance of differential phase-shift keying signals with a balanced receiver is exactly analyzed by using a closed-form expression without approximation. The numerical results are well matched with previous results based on the saddle-point approximation. The error probability is calculated exactly using the well-known Marcum Q function.