Performance analysis of an asymptotically quantum-limited opticalDPSK receiver

An optical, direct-detection differential phase-shift keying (DPSK) receiver whose error probability is quantum-limited as the transmitting laser linewidth vanishes is analyzed. The receiver design is based on a binary equiprobable hypothesis test with doubly stochastic point process observations, the conditional random rates of which depend on the transmitting laser phase noise, which is modeled as a Brownian motion. The receiver structure consists of a simple delay-and-sum optical preprocessor followed by a photoelectric converter and an integrate-and-dump circuit. Upper and lower bounds on the receiver bit error rate are derived by developing bounds on the conditional rates of the point process, and it is shown that the error probability bounds converge to the true value as the transmitting laser linewidth decreases. Bounds on the power penalty are computed for parameters corresponding to existing semiconductor injection lasers, and are seen to be less than the limiting power penalty for the balanced DPSK receiver     

Error probabilities in binary angle modulation

It is shown that many signal-detection problems involving binary phase and frequency modulation can be solved by considering the problem as the convolution of two independent phase distributions. When the two distributions are similar and each represents the probability density function of the phase of a sinusoid in noise, the probability of error is described in terms of modified Bessel functions by the expression obtained recently by Jain and Blachman. The probability of error can also be expressed in terms of Rice'sIefunction. By appropriate definition of the signal-to-noise ratios, this general expression can be used to determine the error probability in a number of cases of practical interest, such as detection of a hard-limited phase-shift keyed (PSK) signal, PSK detection with noisy reference, DPSK detection, frequency-shift keying (FSK) detection, binary FM with discriminator detection, and binary pulse-position modulation (PPM).     

Probability distribution of DPSK in tone interference andapplications to SFH/DPSK

The probability distribution of the received DPSK (differential phase-shift keying) signal under tone jamming is studied. The results should facilitate the analysis of the SFH/DPSK (slow frequency-hopped DPSK) system. The results given are more general than those previously published, in several aspects. First, the differential phase of the transmitted DPSK signal can assume any value. Second, probability distributions are derived instead of a set of probabilities calculated over certain symmetrical regions. This allows analyzing performance for arbitrary selected decision regions as well as determining optimum decision regions for demodulating the DPSK signal. Third, the joint probability distribution of both the magnitude and differential phase of the jammed DPSK signal is given. This can be used in the analysis where both tone jamming and Gaussian noise are considered. These results are used to analyze the error probability performance of a general uncoded SFH/DPSK signal under worst-case tone jamming and Gaussian noise     

Influence of the nonlinear phase and ASE noise on DPSK balanced optical receiver in optical fiber communication system

The analytical expression of bit error probability in a balanced differential phase-shift keying(DPSK) optical receiver considering nonlinear phase noise and EDFA ASE noise is given,which is very useful to estimate the performance of DPSK balanced and unbalanced receiver in optical communication system.Through analysis,if only nonlinear phase noise is considered,both the balance and unbalanced receivers have the same performances.But if adding the ASE noise of EDFA,the balanced receiver is better.     

基于光纤四波混频DPSK系统相位噪声提取检测和抑制

差分相移键控(DPSK）在长距离光纤通信系统中有高接收机灵敏度、高频谱效率以及抗非线性效应方面的优势,最近受到广泛关注。在DPSK通信系统中,线性相位噪声和非线性相位噪声是影响系统性能的主要因素。研究了如何利用光纤四波混频（FWM）效应来监测和抑制相位噪声,降低相位噪声对DPSK通信系统的影响。结果表明利用光纤FWM效应产物可以检测相位噪声值,并且基于光纤饱和FWM效应全光限幅器可以有效地降低非线性相位噪声,提高了DPSK系统性能。该结果对研究高速全光通信有重要意义。     

Error rates of DPSK systems with MIMO EGC diversity reception over Rayleigh fading channels

This paper analyzes the average bit error probability (BEP) of the differential binary and quaternary phase-shift keying (DBPSK and DQPSK respectively) with multiple-input multiple-output (MIMO) systems employing postdetection equal gain combining (MIMO EGC) diversity reception over Rayleigh fading channels. Finite closed-form expressions for the average BEP of DBPSK and DQPSK are presented. Two approaches are introduced to analyze the error rate of DQPSK. The proposed structure for the differential phase-shift keying (DPSK) with MIMO EGC provides a reduced-complexity and low-cost receiver for MIMO systems compared to the coherent phase-shift keying system (PSK) with MIMO employing maximal ratio combining (MIMO MRC) diversity reception. Finally, a useful procedure for computing the associated Legendre functions of the second kind with half-odd-integer order and arbitrarily degree is presented.     

Performance analysis of equalized OFDM systems in Rayleigh fading

Channel estimation is usually needed to compensate for the amplitude and phase distortions associated with a received orthogonal frequency-division multiplexing (OFDM) waveform. This paper presents a systematic approach for analyzing the bit-error probability (BEP) of equalized OFDM signals in Rayleigh fading. Closed-form expressions for BEP performance of various signal constellations [phase-shift keying (PSK), differential phase-shift keying (DPSK), quaternary phase-shift keying (QPSK)] are provided for receivers that use a linear pilot-assisted channel estimate. We also derive the optimal linear channel estimates that yield the minimum BEP and show that some previous known results are special cases of our general formulae. The results obtained here can be applied to evaluate the performance of equalized single-carrier narrowband systems as well.     

The Distribution of Error Probability for Rayleigh Fading and Gaussian Noise

The distribution function of the probability of error in the presence of Rayleigh fading and Gaussian noise is determined for the basic binary modulation schemes of coherent frequencyshift keying (CFSK), noncoherent frequency-shift keying (NCFSK), differential phase-shift keying (DPSK), and coherent phase-shift keying (CPSK). General expressions for the distribution function of error probability are also derived when linear maximal-ratio diversity combining is employed. Results are given for various values of average error probability and various orders of diversity.     

Theoretical investigation of optical wavelength conversion techniques for DPSK Modulation formats using FWM in SOAs and frequency comb in 10 gb/s transmission systems

We have investigated the wavelength conversion techniques for differential phase-shift keying (DPSK) modulation formats in 10 Gb/s transmission systems, compared with the non-return-to-zero (NRZ) modulation format. For the wavelength conversion of DPSK modulation formats, we employed the wavelength converters based on the four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) and the frequency comb generated by phase modulation. The power penalty at 10/sup -9/ bit error rate was used as a measure of the system performance degraded by the wavelength conversion. Our simulation results show that the DPSK modulation formats have a smaller power penalty than the NRZ modulation format for the wavelength conversion using the FWM effect in an SOA due to a much lower pattern effect. However, as the wavelength conversion uses the frequency comb generated by phase modulation, it has a similar power penalty compared with the NRZ modulation format. It is also shown that the DPSK modulation formats are possible to obtain the power penalty less than 0.4 dB for both wavelength conversion techniques.     

A comparative study of DPSK and OOK WDM transmission over transoceanic distances and their performance degradations due to nonlinear phase noise

We have compared experimentally the transmission performance of return-to-zero differential phase-shift keying (RZ-DPSK) with RZ-ON-OFF keying (OOK), nonreturn-to-zero differential phase-shift keying (NRZ-DPSK), and NRZ-OOK for 100/spl times/10-Gb/s transmission with a spectral efficiency of 0.22 b/s/Hz over transoceanic distances. The Q degradation of the RZ-DPSK after transmission over 9180 km was 3 dB greater than that of RZ-OOK. The experimental results clearly showed the major cause of degradation for DPSK is not cross-phase modulation but self-phase modulation. The calculated nonlinear phase noise, i.e., the Gordon-Mollenauer effect, agreed with the experimental results. A distributed-Raman-amplifier assisted erbium-doped-fiber-amplified transmission line acted well in reducing the nonlinear phase noise.     

Asymptotical analysis and comparison of two coded modulationschemes using PSK signaling .I

An asymptotical analysis and comparison of two coded modulation systems using phase-shift keying (PSK) signaling with the transmission taking place over the additive white Gaussian noise (AWGN) channel is provided. In this paper, bounds for the decoding error probability of conventional coded modulation are derived. Both block and trellis coding are considered. The state-complexity error exponent is introduced     

Effects of chromatic dispersion on optical coherent-detection systems

Chromatic dispersion induces to a phase-modulated optical signal a constand phase rotation that was never included in most previous studies. When the constant phase shift is removed by a phase-locked loop, the dispersion tolerance of a coherent-detection system is increased. The dispersion tolerance of phase-shift keying (PSK) signal is compared with differential PSK (DPSK) signals by numerical simulation and experimental measurement. Contrary to conventional belief, PSK signal has larger dispersion tolerance than DPSK signal.     

Digital transmission through a land mobile satellite channel

An analytical derivation of the probability of bit error noncoherent frequency-shift keying (FSK) and coherent phase-shift keying (PSK) signals transmitted through a land-mobile satellite channel is described. The channel characteristics used in the analysis are based on a recently developed model which includes the combined effects of fading and shadowing. Analytical expressions for the probability of bit error of FSK and coherent phase-shift keying (CPSK) signals are obtained. The results show that large amounts of signal-to-noise ratio (SNR) are required to compensate for the combined effect of fading and shadowing. An analytical expression for the irreducible probability of bit error of a CPSK signal due to phase variations caused by fading and shadowing is derived. The results described should be useful in the design of land mobile satellite communication systems     

Error probability of DPSK signals with intrachannel four-wave mixing in highly dispersive transmission systems

A semianalytical method evaluates the error probability of differential phase-shift keying signals with intrachannel four-wave mixing in a highly dispersive fiber link with strong pulse overlap. Depending on initial pulsewidth, the mean nonlinear phase shift of the system can be from 1 to 2 rad for signal-to-noise ratio penalty less than 1 dB. An approximated empirical formula, valid for penalty less than 2 dB, uses the variance of the differential phase of the ghost pulses to estimate the penalty.     

Sensitivity penalty in multichannel coherent optical communications

The error rates and sensitivity penalties for multichannel coherent optical communications systems are evaluated for amplitude-shift keying (ASK), phase-shift keying (PSK), and frequency-shift keying (FSK) modulation, taking into account adjacent channel interference. Both time-domain and frequency-domain analysis are used, the latter being based on a Gaussian approximation. Both techniques yield similar results for sensitivity penalties below 1 dB. For FSK systems, larger values of the modulation index Δ do not necessarily lead to larger channel spacings. ASK and PSK systems both require larger channel spacings than FSK systems with Δ=1. The study was conducted for sources with linewidths narrow enough so that phase noise does not degrade the performance of receivers with matched filter demodulators     

Weak-Signal DPSK Detection in Narrow-Band Impulsive Noise

The weak-signal receiver for binary differential phase-shift keying (DPSK) in additive noise is derived, and its performance in terms of the error probability in the most general narrow-band impulsive (nonGaussian) noise model, Middleton's class A noise, is analyzed.     

Hard-limited versus linear combining for frequency-hopping multiple-access systems in a Rayleigh fading environment

In comparing two proposed frequency-hopping mobile radio systems for digitized speech, Goodman et al. have observed that the system employing multiple frequency-shift keying (MFSK) can accommodate many more users than the one with differential phase-shift keying (DPSK). Besides the difference in modulation methods, the MFSK system uses hard-limited combining while the DPSK one uses linear combining. Upper bounds are obtained on the probability of error for DPSK systems with hard-limited combining and linear combining. These bounds suggest that the DPSK system with hard limiters can support about twice as many users as the original one.     

On the Statistics of Intrachannel Four-Wave Mixing in Phase-Modulated Optical Communication Systems

We have analytically derived the correlation functions of intrachannel four-wave mixing (IFWM)-induced phase and amplitude noises in phase-modulated optical communication systems. The phase and amplitude noises are correlated with each other for binary phase-shift keying (PSK) systems but uncorrelated for $M$-ary PSK systems with $M>2$. We have also derived analytical approximations to the probability distribution of IFWM-induced phase noise for PSK and differential PSK systems. Furthermore, we have studied the performance of an optimal linear phase-noise predictor derived from the IFWM-induced phase-noise autocorrelation function. This yields a performance improvement of 1.8 dB when IFWM-induced phase noise is the dominant impairment, and an improvement of 0.8 to 1.2 dB in the presence of amplified spontaneous emission noise and nonlinear phase noise in typical terrestrial links.      

Compensation improvement of DPSK signal with nonlinear phase noise

When nonlinear phase noise is compensated by the received intensity, simple formulas are derived for the error probability of differential phase-shift keying signals. Simulation is conducted to verify the error probability. The tolerance of nonlinear phase noise is doubled by the compensator, allowing doubling of the transmission distance if nonlinear phase noise is the dominant impairment.