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.     

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.     

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.     

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.     

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.     

Semiconductor optical amplifier used as regenerator for degraded differential phase-shift keying signals

Phase and amplitude regeneration are necessary for degraded differential phase-shift keying communication systems.This paper proposes a regenerator based on semiconductor optical amplifier for differential phase-shift keying signals.The key regeneration mechanism is theoretically analysed.The effectiveness of semiconductor optical amplifier based regenerator is demonstrated by comparing the bit error rate and eye diagrams before and after regeneration for 40-Gbit/s differential phase-shift keying 1080-km transmission systems.The results show that regeneration effects are very well.Bit error rate is less than 10 12 with the regenerator.     

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.     

Noise suppression properties of an interferometer-based regenerator for differential phase-shift keying data

We studied the amplitude and phase noise suppression properties of an all-optical regenerator for differential phase-shift keying data. A detailed analytical investigation is performed and compared with numerical simulations for different working points. The results show that both amplitude and phase can be regenerated. However, simultaneous amplitude and phase noise suppression is possible only if the phase degradation is stronger than the amplitude degradation, for instance, due to nonlinear phase noise.     

Numerical analysis for four-wave mixing based wavelength conversion of differential phase-shift keying signals

We numerically investigate the main constrains for high efficiency wavelength conversion of differential phase-shift keying （DPSK） signals based on four-wave mixing （FWM） in highly nonlinear fiber （HNLF）. Using multi-tone pump phase modulation techniques, high efficiency wavelength conversion of DPSK signals is achieved with the stimulated BriIlouin scattering （SBS） effects effectively suppressed. Our analysis shows that there is a compromise between conversion efficiency and converted idler degradation. By optimizing the pump phase modulation configuration, the converted DPSK idler＇s degradation can be dramatically decreased through balancing SBS suppression and pump phase modulation degradation. Our simulation results also show that these multi-tone pump phase modulation techniques are more appropriate for the future high bit rate systems.     

All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification

All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification is described. Nearly ideal phase regeneration can be achieved in the undepleted-pump regime, and simultaneous amplitude and phase regeneration can be realized in the depleted-pump regime.     

Generation and detection of 80-Gbit/s return-to-zero differential phase-shift keying signals

Nonlinear polarization rotation between a pump and a probe signal in a highly nonlinear fiber is used as a modulation process to generate 80-Gbit/s return-to-zero differential phase-shift keying signals. Its performance is analyzed and compared with a conventional on-off keying modulated signal.     

Hedged maximum likelihood quantum state estimation

This Letter proposes and analyzes a new method for quantum state estimation, called hedged maximum likelihood (HMLE). HMLE is a quantum version of Lidstone's law, also known as the "add β" rule. A straightforward modification of maximum likelihood estimation (MLE), it can be used as a plug-in replacement for MLE. The HMLE estimate is a strictly positive density matrix, slightly less likely than the ML estimate, but with much better behavior for predictive tasks. Single-qubit numerics indicate that HMLE beats MLE, according to several metrics, for nearly all "true" states. For nearly pure states, MLE does slightly better, but neither method is optimal.     

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.     

Monolithic modulator and demodulator of differential quadrature phase-shift keying signals based on silicon microrings

Silicon microring resonators are proposed to achieve ultrasmall differential quadrature phase-shift keying modulators and demodulators operated at 20 Gb/s, which may require a dramatically reduced chip size. The modulators are characterized in terms of the carrier transit time and misalignment of the driving signals, while the demodulation performance is analyzed in terms of the bandwidth and frequency detuning of the demodulator. A bit-error rate of <10(-9) is achieved using all microring-based devices in the back-to-back case.     

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.     

Noise statistics in optically preamplified differential phase-shift keying receivers with Mach-Zehnder interferometer demodulation

We report an analysis of the noise statistics for an optically preamplified differential phase-shift keying (DPSK) receiver with balanced and single-port detections. It is found that identical signal-amplified spontaneous emission beating noise exists for bits 1 and 0 in DPSK balanced detection. It is also revealed that the bit error ratio (BER) of a DPSK receiver with balanced detection has no direct relation to the conventional Q factor. Moreover, an analytic BER expression for the DPSK balanced detection receiver is presented.     

Parameter estimation for power-law distributions by maximum likelihood methods

Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the exponent are a mathematically sound alternative to graphical methods.     

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.