On the probability distribution of differential phase perturbed bytone interference and Gaussian noise

This paper presents a novel method for determination of the general probability distribution of a received differential phase corrupted by both continuous tone jamming and Gaussian noise. An alternative and yet simple expression is derived for this general probability distribution. As an example of its application, we analyze the error performance of a general uncoded SFH/DPSK system under partial-band multitone jamming     

Time diversity in DPSK noisy phase channels

Differential phase shift keying (DPSK) in the presence of both additive white Gaussian noise and a phase impairment, modeled by a Brownian motion is considered. A time-diversity scheme is used for mitigating the effects of phase noise. This scheme renders a repetition coding approach where the transmitter sends multiple replicas of each data bit. An upper bound on the bit error probability, relying on a bivariate moment-generating function admitted by certain real functionals of the phase sample-path, is derived. The approach taken yields a trackable analysis, which rigorously adheres the phase noise effects. The impact of an incomplete statistical characterization on the tightness of the resultant bound is addressed. The theory, which is applicable to assess the design and performance of general heterodyned lightwave systems using (delay) differential demodulation (as DPSK and CP-FSK, or continuous phase frequency-shift keying), is exemplified and explicit results for the considered time-diversity DPSK scheme are provided. The optimum design of the diversity level is discussed and it is concluded that power efficient transmission is feasible even at bit rates comparable with the signal linewidth     

Differential detection with IIR filter for improving DPSK detectionperformance

This paper presents a method for improving the performance of differential detection of differentially encoded phase shift keying (DPSK). The structure of the proposed detection scheme consists of a conventional differential detection circuit equipped with an infinite impulse response (IIR) filter combined with decision feedback. The results of theoretical analysis and computer simulation show that performance of the proposed detection method can approach that of coherent detection of DPSK under additive white Gaussian noise (AWGN) conditions without any increase in architectural complexity. Furthermore, a parameter of the proposed detector can be varied to optimize performance for static or fading conditions. An adaptive scheme suitable for time varying Rician-fading channel conditions is presented, and performance results obtained by computer simulation are given     

Postdetection diversity using differential phase detection forM-ary DPSK

Postdetection diversity that uses L differential phase detector outputs for data decision is described for M-ary differential phase shift keying (M-ary DPSK. Data decision is based on minimising the weighted sum of the errors of L DPD detector outputs. The squared geometric mean of the two consecutively received signal envelope samples is used as the branch weight. The simulation results on average bit error rate (BER) performances due to additive white Gaussian noise (AWGN), multipath Doppler spread, and delay spread of π/4-shift 4DPSK are reported     

Offset DPSK and a Comparison of Conventional and Symmetric DPSK with Noise Correlation and Power Imbalance

The bit error rate performance of binary DPSK with an arbitrary offset of the phase change vector is derived in the presence of noise correlation and power imbalance, and the special cases of conventional DPSK (0 phase change offset) and symmetric DPSK (pi/2phase change offset) are compared. Precise conditions are given for optimum offsets, and it is shown that, from a practical standpoint, conventional DPSK gives the optimum performance of any offset scheme, and outperforms symmetric DPSK by an order of magnitude and more in error rate when the noise correlation becomes significant. It is also found that performance improvement over conventional DPSK can be realized, provided the noise correlation is known, by making the bit decision regions in phase space unequal, thereby demonstrating that the MAP estimator for DPSK without correlation is no longer optimum when the noise is correlated.     

BER for optical heterodyne DPSK receivers using delay demodulationand integration detection

Previous work on the bit error rate (BER) performance of differential phase-shift keying (DPSK) including the effects of additive white Gaussian noise (AWGN) and phase noise has concentrated on the delay demodulator with narrow-band intermediate frequency (IF) bandpass filtering (BPF) and sampling detection. No similar analysis has yet been performed for the delay demodulator with wideband IF bandpass filtering and integration detection. Phase noise is an important consideration in coherent optical communication systems and the most widely accepted model is a Brownian motion process. A closed-form BER expression along with detailed Monte Carlo simulation results are presented for the DPSK delay demodulator with wideband IF bandpass filtering and integration detection filtering including phase noise effects using the Brownian motion model. Analytic expressions are also obtained for the moments of the phase noise component of the decision variable. Using these moments, estimates of the phase noise BER floor are produced. It is found that this receiver has noise performance comparable to receivers with narrowband IF bandpass filtering and sampling detectors for signal-to-noise ratio (SNR) and phase noise in the range of practical interest, but with potentially less degradation due to intersymbol interference (ISI)     

基于判决反馈的TurboDPSK

本文针对衰落信道中DPSK(differential phase-shift keying)信号的特点,提出了一种基于判决反馈的Turbo DPSK解调/译码算法,它利用判决反馈进行衰落信道的估计并计算信息比特的似然比.与基于BCJR(Bahl-Cocke-Jelinek-Raviv)的Turbo DPSK解调/译码算法相比,它可以大大降低运算复杂度,减少迭代译码过程中所需的存储空间.仿真结果表明,采用这种新的迭代解调/译码算法可以获得和基于BCJR的迭代解调/译码算法几乎一样的性能.     

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.     

Analysis methods for optical heterodyne DPSK receivers corrupted bylaser phase noise

Two methods are presented for analyzing the effects of phase noise on the performance of an optical heterodyne binary differential-(DPSK) system. The first method utilizes a perturbation solution for filtered phase noise. By comparing the results of this analysis with simulated results, it is shown that the perturbation solution is accurate for laser linewidths up to at least 10% of the bit rate. Using this analysis, the accuracy of the widely used approximation, whereby the effects of filtering on the magnitude of the phase-noise corrupted signal are neglected, is verified. The author's second method is based on moments of random variables. As the level of phase noise in a practical DPSK system must be small, an improved formulation for the moments of the filtered phase noise is derived. It removes the major cause of this numerical instability. A maximum-entropy probability density function estimation technique is applied to the problem of analyzing the performance of a DPSK receiver. By comparing results with those obtained using the perturbation analysis, it is found that the moment-based method is effectively limited to relatively large error probabilities     

Error probability of 2DPSK with phase noise

A simple tight upper bound on the BEP of 2DPSK over the AWGN channel with phase noise in the received signal is obtained. The phase is modeled as a Gaussian random process which is slowly varying compared to the bit rate so that a piecewise-constant approximation can be made. The bound is verified by computer simulations, and it provides good estimates of the error probability. It shows that for high SNR the error probability decreases as the reciprocal of the square-root of the SNR. The results are applicable in particular to heterodyne optical communications     

Simple error probability derivation for binary DPSK over fast Rician channels with diversity

Bit error probability (BEP) performance of binary differential phase shift keying (DPSK) with differential detection over the nonselective, fast Rician fading channels with combining diversity reception is analysed. The analytical approach that exists in previously published literature for computing the BEP relied on a special case of the derivation given by Proakis that was concerned with the probability that a general quadratic form in complex Gaussian random variables is less than zero. However, evaluating the various coefficients required in the derivation leads to a computationally intensive solution. A simple derivation is presented which leads to a new, alternative BEP expression.     

Error performance of differentially coherent detection of binary DPSK data transmission on the hard-limiting satellite channel

The error performance of differentially coherent detection of a binary differential phase-shift keying (DPSK) system operating over a hard-limiting satellite channel is derived. The main objective is to show the extent of error rate degradation of a DPSK system when a power imbalance exists between the two symbol pulses that are used in a bit decision interval. Consideration is also given to the DPSK error rate performance for the special case of {em uncorrelated} uplink and {em correlated} downlink noises at the sampling instants in adjacent time slots. Error probabilities are given as functions of uplink signal-to-noise ratio (SNR) and downlink SNR with different levels of SNR imbalance and different downlink SNR and uplink SNR as parameters, respectively. Our numerical results show that 1) as long as the symbols are equiprobable, the error probability is not dependent upon the downlink noise correlation, regardless of whether there is a power imbalance; 2) error performance is definitely affected by the power imbalance for all cases of symbol distributions; and 3) the error probability does depend upon downlink noise correlation for all levels of power imbalance if the symbol probabilities are not equal.     

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.     

Offset DPSK with differential phase detector in satellite mobilechannel with narrow-band receiver filter

An expression is derived for the error probability of M-ary offset differential phase-shift keying (DPSK) with the differential phase detector and narrowband receiver filter in the satellite mobile (Rician) channel, which includes as special cases the Gaussian and land mobile (Rayleigh) channels. The error probability is computed as a function of various system parameters for M=2, 4, and 8 symbols and third-order Butterworth receiver filter. Both symmetric and conventional DPSK systems are considered. The optimal normalized bandwidth is close to 1.0. Symmetric and conventional DPSK differ significantly in error probability only for M=2 and in the lower range filter bandwidth. In most cases, symmetric DPSK outperforms conventional DPSK. This was particularly noted when the time delay between the specular and diffused signal components was taken into account     

The performance of trellis coded multilevel DPSK on a fading mobilesatellite channel

The performance of a trellis-coded multilevel differential phase-shift keying (DPSK) modulation over a mobile satellite channel characterized by additive white Gaussian noise (AWGN) and slow Rician fading is presented. Both the optimum and Gaussian (suboptimum) decoding metrics are considered, with performance results given only for the latter. Analytical results (upper bounds on bit error rate) are obtained wherever possible and illustrated by several numerical examples. Also given are simulation results which are more indicative of the exact system performance. Comparisons with results previously obtained for coherent detection of the same coded modulations are presented     

Probability of error of M-ary PSK and DPSK on a Rayleighfading channel

M-ary phase-shift keying and differential phase-shift keying (DPSK) on a slow fading Rayleigh channel without diversity is investigated. Expressions for the distribution of the phase angle between a vector with Rayleigh amplitude distribution and a noiseless reference, and between two vectors both with Rayleigh amplitude distribution perturbed by Gaussian noise are obtained     

Antijam Performance of Fast Frequency-Hopped M-ary NCFSK--An Overview

The antijam performance ofM-ary noncoherent FSK with fast frequency hopping (one or more hops per symbol) is studied. A summary of terminology, definitions, and an overview of the literature is given. A general analysis method based upon circularly symmetric signal theory is presented. It provides a means for exact analysis of performance forM-ary operation with any combination of signal tone distribution (frequency bins contiguously or noncontiguously spaced), jamming distribution, jamming form (partial-band noise or multitone), and receiver system noise. Some previous results are derived as subcases of the general theory. A simple robust diversity combining technique of transmitting a symbol onLhops followed by a majority vote decision is found to provide significant performance improvements. This improvement is comparable to that obtained by most error-correction coding methods. Illustrative calculations of performance were chosen to indicate trends rather than to be exhaustive. Performance is usually presented as probability of bit error versus fraction of the band jammed to emphasize worst-case operation.     

Nearly Shot-Noise-Limited Performance of Dual-Channel Linear Optical Sampling for Ultrafast DPSK Signals

This paper describes a newly developed dual-channel linear optical sampling technique for observing ultrafast optical differential phase-shift keying (DPSK) signals. As the proposed measurement scheme offsets two parallel interferometers by a relative delay corresponding to 1-symbol length of the DPSK signal, the measured phase distribution reflects the signal quality which is determined by the phase difference between adjacent symbols. This technique, based on interferometric optical gating by local short-pulses, also offers ultrafast measurement at symbol rates of greater than 100 Gsymbol/s. Moreover, its detection sensitivity can reach the shot noise limit. The waveform degradation caused by the coherence of the light source and the pattern effect of the phase modulator is successfully observed in continuous waves and 10-Gsymbol/s nonreturn-to-zero DPSK signals, and the constellation measurement is demonstrated for a 160-Gsymbol/s return-to-zero DPSK signal. Measurement system noise is also discussed for characterizing the detection sensitivity, and the nearly shot-noise-limited performance is experimentally verified.      

Differential phase noise distribution of Rayleigh faded DPSK signal with selection diversity

Closed-form expressions for the distribution of differential phase noise due to additive white Gaussian noise (AWGN) are derived for predetection selection diversity with independent, equal power very slow Rayleigh fading signals. Also investigated are the effects of fading correlation and unequal powers between diversity antennas on practical two-branch diversity reception. The derived phase distribution is used to calculate the average symbol error rate of 8 DPSK as an example.<>     

Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise

This paper presents a novel method based on a parametric gain (PG) approach to study the impact of nonlinear phase noise in single-channel dispersion-managed differentially phase-modulated systems. This paper first shows through Monte Carlo simulations that the received amplified spontaneous emission (ASE) noise statistics, before photodetection, can be reasonably assumed to be Gaussian, provided a sufficiently large chromatic dispersion is present in the transmission fiber. This paper then evaluates in a closed form the ASE power spectral density by linearizing the interaction between a signal and a noise in the limit of a distributed system. Even if the received ASE is nonstationary in time due to pulse shape and modulation, this paper shows that it can be approximated by an equivalent stationary process, as if the signal were continuous wave (CW). This paper then applies the CW-equivalent ASE model to bit-error-rate evaluation by using an extension of a known Karhunen-Loe/spl acute/ve method for quadratic detectors in colored Gaussian noise. Such a method avoids calculation of the nonlinear phase statistics and accounts for intersymbol interference due to a nonlinear waveform distortion and optical and electrical postdetection filtering. This paper compares binary and quaternary schemes with both nonreturn- and return-to-zero (RZ) pulses for various values of nonlinear phases and bit rates. The results confirm that PG deeply affects the system performance, especially with RZ pulses and with quaternary schemes. This paper also compares ON-OFF keying (OOK) differential phase-shifted keying (DPSK) systems, showing that the initial 3-dB advantage of DPSK is lost for increasing nonlinear phases because DPSK is less robust to PG than OOK.