On the bit error probability of QAM modulation

This paper presents some closed-form bit error probability expressions for coherent demodulation of both Gray coded and differentially decoded Gray coded QAM modulations in nonfading and frequency nonselective Rayleigh fading channels. These results demonstrate that as QAM constellation sizes get larger the BEP degradation due to differential encoding and decoding becomes negligible.     

Symbol error probability of two-dimensional signaling in Ricean fading with imperfect channel estimation

In this paper, a general analytical framework is developed for calculating the symbol error rate of two-dimensional (2-D) signaling in Ricean fading with imperfect channel estimation. We show that in the presence of channel estimation errors, the symbol error rate of arbitrary 2-D signaling in Ricean fading can be expressed as a two-fold proper integral with finite integration limits, which is suitable for numerical evaluation. This new analysis is applicable to any channel estimation scheme where the estimated and the actual channel gains are jointly complex-Gaussian. System parameters related to specific channel estimation schemes are optimized and the effect of Doppler frequency shift in the channel line-of-sight component on the error performance is investigated using our analysis.     

Upper bound on the bit error probability of TCM overfrequency-selective Rayleigh fading channel

A new upper bound on the bit error probability using Chernoff's bound of trellis code modulation (TCM) is introduced. It can be applied to a frequency-selective Rayleigh fading channel. The bound indicates a new design criterion, which is the product of the intersymbol interference (ISI) distance     

Approximate average bit error probability for DQPSK over fading channels

The bit error probability (BEP) of DQPSK with Gray coding over an AWGN channel can be computed simply, although it is hard to integrate and derive the average BEP for fading channels. Presented are novel approximations of the average BEP of DQPSK with Gray coding over fading channels. Numerical results show that the novel formulations are quite accurate.     

Soft decision metric generation for QAM with channel estimation error

The channel code bit log likelihood ratio (LLR) for soft decision decoding is derived for quadrature amplitude modulated signals (QAM). The effect of imperfect channel knowledge on soft decision decoding performance is studied. Our results indicate this effect increases with channel estimation error and/or QAM modulation level. A metric based on generalized log likelihood ratio (GLLR) is derived for soft decision channel decoding with imperfect channel knowledge. Numerical results show that the GLLR-based metric outperforms the conventional minimum distance decoding metric that does not take into account channel estimation error.     

Outage analysis of ANC in the FDD two-way fading channel with channel estimation error

This paper considers a frequency-division duplex (FDD) two-way channel with channel estimation error, where channel gains are independent of each other. It derives the exact closed-form outage probability expressions in the FDD system with analog network coding (ANC) by use of probability theory. To provide more insights, an approximated version for the exact outage probability is also developed in the medium-to-high signal-to-noise ratio (SNR) region. The simulation results show that the derived exact outage probabilities match the results of Monte Carlo simulations in all SNR regions, while the approximated outage probabilities also approach the simulation results when the channel condition is good. It is interesting that ANC in the FDD two-way channel is proved to outperform that of in the time-division duplex (TDD) channel by the computer simulation.     

BER analysis of arbitrary QAM for MRC diversity with imperfect channel estimation in generalized ricean fading channels

Imperfect channel estimation (ICE) can severely degrade the bit error rate (BER) of digital modulations with maximum ratio combining (MRC) diversity reception. The resulting performance analysis problem in its most general setting has not been addressed before. In this paper, the effect of ICE on the BER of an arbitrary square/rectangular Gray-coded quadratic amplitude modulation (QAM) in generalized Ricean fading channels when MRC reception is employed is analyzed. A general expression for the bit error probability of an arbitrary square/rectangular QAM scheme is first derived. This general formula requires a number of conditional probabilities, which is derived in closed form for independent and nonidentically distributed (i.n.d.) Rayleigh-fading channels with MRC and ICE. An efficient numerical method is also presented to compute the conditional probabilities for i.n.d. and correlated Ricean fading. In addition, extensive Monte Carlo simulations that agree excellently with the analytical results are presented.     

A symbol-by-symbol channel estimation receiver for space-time block coded systems and its performance analysis on the nonselective rayleigh fading channel

We present a symbol-by-symbol channel estimation receiver for an orthogonal space-time block coded system, and derive its analytical performance on a slow, nonselective, Rayleigh fading channel. Exact, closed-form expressions for its bit error probability (BEP) performance for M-ary phase shift-keying modulations are obtained, which enable us to theoretically predict the actual performance achievable under practical conditions with channel estimation error. Our BEP expressions show explicitly the dependence of BEP on the mean square error of the channel estimates, which in turn depend on the channel fading model and the channel estimator used. Tight upper bounds are presented that show more clearly the dependence of the BEP on various system parameters. Simulation results using various fading models are obtained to demonstrate the validity of the analysis.     

Expressions for bit error probability

The bit error probability (BEP) for many wireless communications networks can be expressed in the form R = Pr (X₂ < X₁) where X₁ and X₂ are independent random variables. Here, a comprehensive collection of formulas is derived for R by assuming the most commonly known models for X₁ and X₂. A discussion is provided of four possible applications to problems in wireless communications. Copyright © 2007 John Wiley & Sons, Ltd.     

Exact bit error rate calculations for synchronous MC-CDMA over aRayleigh fading channel

The bit error rate of a synchronous multicarrier code-division multiple-access system operating in a Rayleigh fading channel is calculated based on a moment generating function method, without any assumption on the distribution of multiple access interference. Two closed-form BER expressions are derived. Moreover, the BER can be accurately evaluated by using a Gauss-Chebyshev quadrature rule based numerical approach     

Efficient bit error probability expression and very tight bound for maximal ratio combining diversity systems over Rayleigh fading channel

Bit Error Probability （BEP） provides a fundamental performance measure for wireless diversity systems. This paper presents two new exact BEP expressions for Maximal Ratio Combining （MRC） diversity systems. One BEP expression takes a closed form, while the other is derived by treating the squared-sum of Rayleigh random variables as an Erlang variable. Due to the fact that the extant bounds are loose and could not properly characterize the error performance of MRC diversity systems, this paper presents a very tight bound. The numerical analysis shows that the new derived BEP expressions coincide with the extant expressions, and that the new approximation tightly bounds the accurate BEP.     

频率选择性衰落信道GMSK误码性能分析

通过对数字移动信道脉冲响应时延展宽包络 ( PDSP)波形的研究 ,分析了GMSK调制下的脉冲时延展宽包络与误码率之间的变化关系 ,建立了两者之间关系的理论模型和计算机仿真模型 ,同时给出了在四种较为典型的 PDSP作用下 ,GMSK误码率特性的计算机仿真结果。     

信道估计误差对Rayleigh衰落下多天线CDMA系统信道容量影响

目前对多天线信道容量的研究几乎都是集中在具有精确信道估计的假设上,但是它实现起来有一定的难度.在Walsh扩频地址码、多码检测和最大似然接收机的基础上,研究了Rayleigh衰落情况下信道估计误差对MIMO CDMA系统的影响.分析及仿真结果均表明:信道容量随着信道估计误差的增加迅速下降;对于N×N系统,在固定的信道估计误差和信噪比下容量和天线的数目呈线性关系,容量增加的斜率随信道估计误差的增大而减小.     

A simple approach to error probability with binary signaling over generalized fading channels with maximal ratio combining and noisy channel estimates

In this letter, we study the performance of binary signaling on generalized fading channels with maximal ratio combining (MRC) and imperfect channel estimates. With the assumption of the channel estimate being corrupted by a complex Gaussian random variable, an expression for the average probability of error is provided in the form of a simple single integral which involves the moment generating function of the normalized signal-to-noise ratio corresponding to the case of ideal MRC. Various examples are given to illustrate the usefulness of the derived expression under various fading conditions with different distributions, and with a possible correlation between the diversity branches.     

Probability of bit error for MPSK modulation with diversityreception in Rayleigh fading and log-normal shadowing channel

In an additive white Gaussian noise channel subject to Rayleigh fading and log-normal shadowing, consideration is given to diversity reception with K-port macroscopic selection and L-branch microscopic maximal-ratio combining, and analytical expressions are derived for upper and lower bounds on the bit error probabilities for BPSK, QPSK, 8-PSK, and 16-PSK modulations. The derived expressions can be evaluated at any location in the serving cell. Error-probability can be calculated by averaging over all possible locations within the serving cell. By evaluating these bounds, numerical results for the following cases are presented: without diversity reception, microdiversity combining, macrodiversity selection, and simultaneous use of macrodiversity selection and microdiversity combining. For symmetrical arrangement of macrodiversity ports against the lognormal shadowing, error probability at the equidistant point gives upper bounds on the error probabilities for most of the area in the serving cell. Error probability at the equidistant point is a good estimate of the error probability obtained by averaging over all possible locations in the cell     

Performance analysis of bit error rate of data link system under pulse LFM interference in time-varying rayleigh channel

Wireless Networks - In such mobile platforms as ships and aircraft, the detection and reconnaissance devices are near to the communication facilities. When working at the same time, they will...     

Optimal and mismatched detection of QAM signals in fast fading channels with imperfect channel estimation

In this paper, we derive an optimal detector for pilot-assisted transmission in Rayleigh fading channels with imperfect channel estimation. The classical approach is based on obtaining channel estimates and treating them as perfect in a minimum distance detector (this is called mismatched detector). The optimal detector jointly processes the received pilot and data symbols to recover the data. The optimal detector is specified for fast frequency-flat fading channels.We consider spline approximation of the channel gain time variations and compare the detection performance of different mismatched detectors with the optimal one. Further, we investigate the detection performance of an iterative receiver in a system transmitting turbo-encoded data, where a channel estimator provides either maximum likelihood estimates, minimum mean square error (MMSE) estimates or statistics for the optimal detector. Simulation results show that the optimal detector outperforms the mismatched detectors. However, the improvement in the detection performance compared to the mismatched detector with the MMSE channel estimates is modest.     

Average error probability for quadriphase modulated DS-SSMA communications through Nakagami fading channel

An asynchronous direct sequence spread spectrum multiple access system using quadrature phase shift keying modulation through Nakagami'sm-distributed fading channel is considered for nondiversity reception. Approximation to the average error probability is evaluated in two steps. Using the Gauss quadrature rule, the moments of the multiple interferences are used to evaluate the conditional probability conditioned on a fixed fading amplitude of the desired signal. The probability density function of the desired signal is Nakagami distributed. The average error probability which is the expected value of the conditional probability is evaluated by the trapezoidal integration method. This method provides a good approximation to the average error probability for a small to a fairly large number of users. Numerical results are presented for a set of Gold code of code length 127.     

A general analysis of bit error probability for reference-basedBPSK mobile data transmission

Unified analysis of the performance of binary phase shift keying (BPSK) under static and mobile operating conditions is presented for the case in which a separate reference tone is used for channel sounding and subsequent `coherent' data detection. It is shown that under both Rician and Rayleigh fading conditions, the use of a reference can eliminate the irreducible error rate phenomenon, with minimal sacrifice in bit error rate performance over an ideal BPSK system