Bit error rate for 4-DPSK in fast Rician fading and Gaussian noise

A closed-form expression for the bit error rate of 4-DPSK in fast Rician fading and white Gaussian noise is presented. This expression is a supplement to an already known formula for the symbol error rate of MDPSK, which can be evaluated only by numerical integration     

A new formula for MDPSK symbol error probability

This article presents an extremely compact new formula for the symbol error probability in M-ary differential phase shift keying (MDPSK) that is extraordinarily similar to its counterpart for M-ary phase shift keying (MPSK). This result follows from a new form for a generic error probability associated with the phase angle between two vectors perturbed by Gaussian noise. The new form also leads to a new expression for the Marcum Q-function. As special cases, the generic error probability is noted to also contain MPSK, CPFSK, and digital FM. Finally, it is pointed out that the generic error probability simplifies the error probability expressions in other situations such as nonorthogonal signaling, maximum-likelihood differential detection of DPSK with block-by-block detection, and Gray coding of MDPSK     

带有相位噪声的MPSK和MDPSK性能统一分析

本文研究了相位噪声场对MPSK、MDPSK性能的影响.首先在统一框架下,推导了AWGN、Nakagami-m衰落和莱斯衰落信道中带有相位噪声时MPSK相干解调和MDPSK差分解调的误符号率;然后运用计算机仿真和数值方法,对误符号率和相位噪声的关系进行了验证;最后通过应用示例,展示了本文工作在系统设计和性能评估中的重要作用.     

Generic error probabilities

This paper presents new forms for an error probability associated, with the phase angle between two vectors perturbed by Gaussian noise. An interesting consequence of the underlying generic form is a new expression for the symbol error rate in MDPSK that is very similar to its counterpart for MPSK. The generic error probability is further shown to contain as special cases MPSK, MDPSK, CPFSK, and digital FM; and to give a new expression for the Marcum Q-function. The generic error probability also simplifies the error probability expressions in other situations such as nonorthogonal signaling, maximum likelihood differential detection of DPSK with block-by-block detection, and Gray coding of MDPSK     

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。     

A general SER formula for an OFDM system with MDPSK in frequency domain over Rayleigh fading channels

A closed-form formula for symbol-error rate (SER) of an orthogonal frequency-division multiplexing (OFDM) system with M-ary differential phase-shift keying (MDPSK) in frequency domain over Rayleigh fading channels is obtained. It is found that, by MDPSK in frequency domain, identical SERs can be achieved on all subcarriers. However, both time and frequency dispersion in the channel will introduce error floors. A comparison between OFDM-MDPSK in frequency domain and that in time domain reveals that the former system offers superior SER performance in a fast fading environment, while the latter performs better if the channel is mainly frequency selective. Moreover, the former system has lower implementation complexity.     

Particle filtering for demodulation in fading channels withnon-Gaussian additive noise

An efficient particle filtering algorithm is developed to solve the problem of demodulation of M-ary modulated signals under conditions of fading channels in the presence of non-Gaussian additive noise. Simulations for MDPSK signals are presented. The results show that the algorithm outperforms the current methods     

Error Probabilities for MRC Diversity Reception of MDPSK in Slow Nakagami Fading

New closed form error probability expressions for M-arydifferential-phase-shift-keying (MDPSK) with maximal ratio combining (MRC)diversity reception in Nakagami fading, are derived. These expressions involveeasily computable Legendre polynomials and Associated Legendre functions. Bysetting the fading severity parameter m to unity, the new general errorprobability formula reduces to the known results for MDPSK systems in slowRayleigh fading. For binary DPSK, the bit error rate (BER) performance withMRC is compared with known results for selection diversity combining (SDC).It is shown that MRC is more effective than SDC in improving BER performancefor the Nakagami channels, as expected. We also discuss the ranges of thefading severity parameter and diversity order, within which the errorprobability expressions can be computed efficiently.     

New exponential bounds and approximations for the computation of error probability in fading channels

We present new exponential bounds for the Gaussian Q function (one- and two-dimensional) and its inverse, and for M-ary phase-shift-keying (MPSK), M-ary differential phase-shift-keying (MDPSK) error probabilities over additive white Gaussian noise channels. More precisely, the new bounds are in the form of the sum of exponential functions that, in the limit, approach the exact value. Then, a quite accurate and simple approximate expression given by the sum of two exponential functions is reported. The results are applied to the general problem of evaluating the average error probability in fading channels. Some examples of applications are also presented for the computation of the pairwise error probability of space-time codes and the average error probability of MPSK and MDPSK in fading channels.     

Performance limits of coded multilevel DPSK in cellular mobileradio

Performance limits of coded multilevel differential PSK (MDPSK) in multipath Rayleigh fading channels are described. The simple Gaussian metric is assumed for reasons for practicality even though it is not the maximum likelihood. The channel cutoff rate, R₀ of MDPSK is analyzed based on the metric. Account is taken of additive white Gaussian noise (AWGN), cochannel interference, and multipath channel delay spread. For the analysis of the spectrum efficiency of a cellular mobile radio system employing coded MDPSK, its service area is defined as the area in which, with a bit rate of R information bit/symbol (R⩽R₀), reliable communications are possible. Three optimal information bit rates are determined from the channel cutoff rate to minimize the required average signal energy per information bit-to-noise power spectral density ratio (E_b/N₀) to maximize the tolerable r.m.s. delay spread τ_r.m.s. and to maximize the spectrum efficiency     

New performance results for MDPSK with noncoherent diversity in fast Rayleigh fading

The error performance for M-ary differential phase-shift keying (MDPSK) with non-coherent diversity in fast fading was recently tackled, ending up with a very general formula applicable to various operational environments. The only drawback of this formula is its expression with a double integral which, alongside a singularity existing in the integrand, poses considerable burdens in numerical calculation. In this correspondence, by restricting to the case of independent fast Rayleigh fading channels with equal power, we show how to obtain a much simpler solution with only one integral.     

移动卫星信道中的TC-MDPSK特性界

本文基于Ｒｉｃｒ－Ｌｏｇｎｏｒｍａｌ联合分布的两种信道模型,定性地分析了移动卫星信道中的ＴＣ－ＭＤＰＳＫ特性界,推导出了适合这两种信道模型的一种新的特性表达式,讨论了８Ｕ－ＴＣ－ＭＤＰＳＫ方案的误比特率,计算机模拟显示出,本文推导的方法不仅简便,而且得到的特性界比已有的界紧,能够较好地反应这类信道的ＴＣ－ＭＤＰＳ特性。     

Reduced state Viterbi differential phase detection of MDPSK signals

An improved differential phase detection scheme that uses a reduced state Viterbi algorithm (RSVDPD) is proposed for the reception of M-ary differential phase shift keying (MDPSK) signals. The transmitted sequence is estimated from the received signal phases only. The number of trellis states equals that of the signal constellation points M. The branch metric is computed by tracing back the surviving path connected to each state. The bit error rate (BER) performance with RSVDPD is evaluated using computer simulation for 4DPSK transmission in additive white Gaussian noise (AWGN) channels     

BER performance of OFDM-MDPSK system in frequency-selective Ricianfading with diversity reception

A closed form formula is derived for the bit error rate (BER) of orthogonal-frequency-division-multiplexing (OFDM) with M-ary differential-phase-shift-keying (MDPSK) systems in frequency-selective Rayleigh and Rician fading channels with diversity reception. New BER curves are obtained as a function of the rms delay spread of the diffused component for three different types of delay profiles: (1) one-sided exponential, (2) uniform and (3) double spike profiles. Both slow and fast fading conditions are considered. It is shown that the existence of a strong line-of-sight (LOS) component and the use of reception diversity can effectively improve transmission performance     

Reduced state transition Viterbi differential detection of M-aryDPSK signals

A reduced state transition Viterbi differential detection (RST VDD) consisting of conventional one symbol DD (1DD) and 3^L-1 state VDD is proposed for the reception of M-ary differential phase shift keying (MDPSK) signals, where L+1 is the observation time length in symbols. The proposed RST VDD has a significantly lower degree of computational complexity compared with the M^L-1 state VDD. The bit error rate (BER) performance of 8DPSK in additive white Gaussian noise (AWGN) channels is evaluated by computer simulation     

Linear diversity analyses for M-PSK in Rician fading channels

Symbol and bit error rates of M-ary differentially encoded/differentially decoded phase-shift keying (MDPSK) and coherent M-ary phase-shift keying (M-PSK) over slow, flat, Rician fading channels are derived when linear diversity combining is applied to combat degradation due to fading. These closed-form solutions are general enough to cover several cases of nondiversity, additive white Gaussian noise (the nonfading mode), Rayleigh fading, mixtures of Rayleigh and Rician fading (the mixed mode), and Rician fading. The results presented here can also be applied to predict the error-rate performance when recent transmit diversity techniques are employed. The solutions for the nonuniform fading profile are included as well. Error probabilities are graphically displayed for both modulation schemes.     

Distribution of the Phase Angle Between Two Vectors Perturbed by Gaussian Noise

The probability distribution of the phase angle between two vectors perturbed by correlated Gaussian noises is studied in detail. Definite integral expressions are derived for the distribution function, and its asymptotic behavior for large signal-to-noise is found for "small," "nearpi/2," and "large" angles. The results are applied to obtain new formulas for the symbol error rate in MDPSK, to calculate the distribution of instantaneous frequency, to study the error rate in digital FM with partial-bit integration in the postdetection filter, and to obtain a simplified expresion for the error rate in DPSK with a phase error in the reference signal. In the degenerate case in which one of the vectors is noise free, the results lead to the symbol error rate in MPSK.     

Improving differential detection of MDPSK by nonlinear noiseprediction and sequence estimation

A new technique is proposed to improve the performance of differential detection (DD) of M-ary differential phase-shift keying (MDPSK) significantly, applying sequence estimation. In order to obtain an appropriate representation of the received signal, a nonlinear time-variant finite impulse response or infinite impulse response prediction-error filter is used. For both filter structures the optimum coefficients are derived, assuming transmission over an additive white Gaussian noise (AWGN) channel. Delayed decision-feedback sequence estimation (DDFSE) is employed to estimate the transmitted symbol sequence. It is shown by simulations that even for decision-feedback equalization, which is a simple special case of DDFSE, a significant performance improvement of conventional DD under AWGN conditions results. In contrast to other noncoherent low-complexity receivers proposed in literature, this receiver is very robust under flat fading (Rayleigh and Ricean) conditions     

光MDPSK通用调制解调结构构建及仿真

新型相位调制格式技术能够有效地减少光传输损伤,是光传输系统中的重要技术。从理论上分析了光MDPSK(M进制差分相移键控)的调制解调原理,构建了通用的调制解调结构,并首次推导出MDPSK的通式和解调公式,最后以基于CSRZ(载波抑制归零,占空比为67%)码的DQPSK(差分正交相移键控)、8DPSK(3阶差分相移键控)和16DPSK(4阶差分相移键控)为例,用MATLAB软件仿真得到了其调制后的频谱图和解调后的眼图。仿真结果表明,随着级数的增加,MDPSK调制格式的频谱宽度会逐渐变窄,且解调后的眼图也令人满意。     

Decision-feedback differential detection of MDPSK for flat Rayleighfading channels

In this paper, decision-feedback differential detection (DF-DD) of M-ary differential phase-shift keying (MDPSK) signals, which has been introduced previously for the additive white Gaussian noise (AWGN) channel by Leib et al. (1988) and Edbauer (1992), is extended to flat Rayleigh fading channels. The corresponding DF-DD metric is derived from the multiple-symbol detection (MSD) metric and for genie-aided DF-DD, an exact expression for the bit-error rate (BER) of QDPSK (M=4) is calculated. Furthermore, the dependence of BER on the power spectrum of the fading process is investigated for feedback filters of infinite order. It is shown that in this case, for ideally bandlimited fading processes, the error floor of conventional differential detection (DD) can be removed entirely. Simulation results confirm that both MSD and DF-DD with feedback filters of finite order can reduce the error floor of conventional DD significantly. DF-DD thereby causes considerably less computational load