Error probability of M-ary DPSK in fast Rician fading and lognormalshadowing

A new expression for the symbol error probability (SER) of M-ary DPSK in fast Rician fading, lognormal shadowing and Gaussian noise is derived. New SER curves are computed and the effects of K factor, fading bandwidth and shadowing spread on the error probability are analysed and discussed     

Error Rate Bounds for Differential PSK

Differential phase-shift keying (DPSK) and coherent phase-shift keying (CPSK) are two of the techniques widely used in digital communications over channels such as satellite, terrestrial radio, and voiceband telephone. Because of the linear nature of the demodulation process in CPSK, the error performance of CPSK with various sources of impairments has been exhaustively treated, but even with additive Gaussian noise, only asymptotic approximations are available to determine the detection performance ofM-ary DPSK,M> 2. In this note, the error performance of nonbinary DPSK in additive Gaussian noise channels has been bounded in terms of tabulated functions and various approximations are then derived.     

An Error Probability Formula for M-ary DPSK in Fast Rician Fading and Gaussian Noise

A formula for the symbol error probability is derived which applies to differential detection ofM-ary phase-shift keying (MDPSK) in fast Rician fading and white Gaussiau noise. This formula is an extension of a result already known for MDPSK in Gaussian noise interference.     

Double Symbol Error Rates of M-ary DPSK in a Satellite-Aircraft Multipath Channel

Double symbol error rates ofM-ary differentially coherent phase shift keying (DPSK) systems in a satellite-aircraft multipath channel are evaluated. A joint probability density function (pdf) of two consecutive differential phase errors in the DPSK outputs is newly derived. Numerically calculated results are shown in figures for binary, quaternary, and octonary DPSK systems. It is further shown that the analytical values agree well with the data observed by ATS-5 experimental tests.     

On M-ary DPSK Transmission Over Terrestrial and Satellite Channels

The error rate performance ofM-ary DPSK systems is investigated in the presence of phase change offset, noise correlation, and power imbalance. Both the terrestrial channel and the hard-limiting satellite repeater channel are considered. In the satellite repeater case, the noise correlations and power imbalances are assumed to be present on both the up- and downlinks. The emphasis is on exact results, or asymptotic approximations obtained therefrom, as opposed to error rate bounds. Most of the results are given in terms of integrals readily evaluated by quadrature. Performance curves showing the effects of the various impairments are presented. Some specific conclusions which follow from the results are that 1) the phase change offset is relatively unimportant forM geq 4, 2) theM-ary case is less sensitive to imbalance than is the binary case, and 3) the satellite link performance depends strongly upon the quality of the uplink.     

Error Rate Lower Bounds for Digital Communication with Multiple Interferences

This paper presents simple and general lower bounds for error rates in digital communication systems. The information bearing signal is taken to be impaired by additive interference and carrier phase jitter. The former is taken to be composed of two components; one component is peak-limited while the other is not. Intersymbol and cochannel interference are examples of peak-limited interference while additive thermal noise is an example of a nonpeak-limited interference. The novelty of the paper is in the generality of the results and in obtaining a simple error bound for transmission in the presence of cochannel interference and carrier phase jitter.     

On Differential Detection of M-ary DPSK with Intersymbol Interference and Noise Correlation

In this paper we study differential detection ofM-ary differential phase-shift-keyed (DPSK) signals with intersymbol interference and noise correlation. With these impairments there can be a wide variation in the error rate of the individual symbols, with this variation increasing withM. However, by adding a phase shift offset and adjusting the decision boundaries in the detector, this variation can be reduced and the average symbol error rate can be decreased. For example, for quaternary DPSK with a signal to adjacent (from the previous and next symbols) intersymbol interference power ratio of 17 dB, these methods can reduce the variation in symbol error rates by more than two orders of magnitude and decrease the required signal-to-thermal noise ratio for a 10^-6symbol error rate by more than 2 dB.     

Bit error rate analysis of M-ary DPSK in frequency selective Ricianfading

A simple, exact expression for the probability distribution of differential phase noise is derived for calculating the average bit error rate (BER) of M-ary DPSK in frequency selective Rician fading. The irreducible BER due to multipath delay spread is evaluated for M=2-16 assuming a double-spike delay profile of the Rayleigh faded diffused component and a spectrally raised cosine Nyquist filter response     

Error Rate Bounds for Digital PAM Transmission with Phase Jitter and Intersymbol or Cochannel Interference

A simple method is presented for computing upper and lower bounds for binary PAM signaling over channels with phase jitter. Other impairments to reliable communication are taken to be additive thermal noise and intersymbol or cochannel interference. The important cases of binary and quadrature phase shift keying are cases for which the analysis presented is valid. The method consists of finding upper and lower bounds conditioned on the phase jitter, φ, in a form in which the auguments of theQ-functions involved are linear incos phiandsin phi. When these functions are represented by a piecewise linear approximation, the average of these bounds can be given in closed form. In most cases 5 piecewise linear segments provides an error rate estimate that is accurate to at least 1 dB in system signal-to-noise ratio (SNR).     

广义多径信道MDPSK相位比较解调性能

本文提出了一种适合于广义多径信道多进制差分相移键控信号相位比较解调的性能分析方法，推导出符合平均错误率积分表达式。该表达式考虑了信号幅度衰落，时间选择性衰落和高斯白噪声对体制性能的影响。并针对几种形式的衰落功率谱分别对二进制，四进制和八进制的符号平均错误率进行了数值计算，讨论了衰落功率谱的形式对ＭＤＰＳＫ信号性能的影响，并给出了ＭＤＰＳＫ信号的“不可克服符号错误率”与衰落功率谱归一化带宽的关系曲线     

A closed-form expression for the symbol-error rate of M-ary DPSK in fast Rayleigh fading

The error performance of M-ary differential phase-shift keying on Rayleigh fading channels is widely analyzed in the framework originated by Pawula, and the results usually take the form of an integral. In this letter, we formulate the same problem in a different framework, and solve it by using a linear prediction-based technique resulting in a simple solution in closed form.     

The Effect of Phase Error on DPSK Error Probability

Expressions are found for the effect of an error in the delay of the preceding signal, which provides the reference phase for the decoding of the present signal in differential phase-shift-keying reception. The signal-to-noise ratio is allowed to be different for the two signals that are compared by the receiver's phase detector. The results are applicable to both binary and quaternary DPSK. In addition, an approximation is obtained for the error probability when the two Signal-to-noise ratios are equal to the same large value.     

Symbol Error Probabilities for M-ary CPFSK: Coherent and Noncoherent Detection

Continuous-phase frequency shift keying (CPFSK) is discussed and theoretical predictions for symbol error probabilities are derived, where the memory inherent in the phase continuity is used to improve performance. Previously known results concluded that binary CPFSK can outperform coherently detected PSK at high SNR. New results presented here show thatM-ary CPFSK outperforms more tranditionally usedM-ary modulation systems. Specifically, coherently detected quaternary CPFSK with a five-symbol interval decision can outperform coherent QPSK by 3.5 dB, and octal coherent CPFSK with a three- symbol decision can outperform octal orthogonal signaling by 2.6 dB at high SNR. Results for coherently detected and noncoherently detected CPFSK are derived. These performance improvements are estimates derived from symbol error probability upper bounds. Monte Carlo simulation was performed which then verified the results.     

Computation of the Bit Error Rate of Coherent M-ary PSK with Gray Code Bit Mapping

Efficient computation of the bit error rate (BER) for the coherentM-ary PSK signals with Gray code bit mapping is considered. A closed-form expression for the exact BER of 8-ary PSK is presented. Tight upper and lower bounds on BER are also obtained forM-ary PSK with largerM.     

Switched Dual Diversity Reception of M-ary DPSK Signals on Nakagami Fading Channels

The paper deals with dual diversity reception of M-ary differential phase-shift keying modulated signals in the presence of additive white Gaussian noise and Nakagami-distributed slow and nonselective fading. The performance of a switched diversity system is analysed and compared to that of the predetection selection diversity combining scheme. The general case of correlated diversity branches is considered, without restrictions on the fading severity parameter. Average symbol error rate formulas are analytically derived in terms of integral expressions that can be easily computed via numerical integration routines. Moreover, the numerical evaluation of the optimum switching threshold is carried out and the influence of the fading severity parameter, the branch correlation, and the cardinality of the symbol alphabet is analysed. Finally, three fixed switching threshold strategies that allow to obtain a satisfactory diversity gain are considered.     

Bit error rate analysis of reduced-state Viterbi differentialdetection of M-ary DPSK signals

A tight upper bound or bit error rate (BER) is derived for approximate maximum likelihood differential detection (DD) implemented by the reduced state Viterbi algorithm (VA) known as RSVDD. The BER performance of RSVDD is compared with Viterbi DD (VDD) for M-ary DPSK in additive white Gaussian noise (AWGN) channels     

Error rates for M-ary noncoherent FSK in impulsive reverberation noise

It is shown that reverberation noise for primary acoustic scattering in the ocean has an integral representation and that a canonical model for its analysis can be found. Exact values of error rates for M-ary noncoherent FSK for correlation receivers in such noise are given. Comparison with the well known Gaussian case is also made.     

Error probabilities of two-dimensional M-ary signaling in fading

A new exact method for computing the average symbol error probability of two-dimensional M-ary signaling in slow fading is presented. The method is generally applicable to polygonal decision regions. The exact average symbol error rate of coherent 16-star-QAM is obtained and compared to that of 16-rectangular-QAM. New results for optimum ring ratios of 16-star-QAM in additive white Gaussian noise (AWGN) and in slow fading are also given     

瑞利衰落信道MDPSK相位比较解调性能

本文提出一种适合于瑞利衰落信道多进制差分相移键控系统相位比较解调的性能分析方法，推导出符号错误率解析表示式，考虑了瑞利衰落、时间选择性衰落和高斯白噪声对体制性能的影响，并针对衰落功率谱为高斯型和矩形分别对二进制、四进制和八进制情形进行了数值计算。