Considerations on Error Probability in Correlated-Symbol Systems

An approach to evaluate the error probability in conventional PAM digital data transmission systems with correlated symbols in the presence of intersymbol interference and additive noise is formulated in general and it is applied to the Gram-Charlier series expansion method. It is shown that the technique of conditioning few symbols before and/or after the symbol to be detected increases substantially the range of signal-to-noise ratios with an acceptable increase of numerical work. This technique also improves existing bounds on error probability, as, e.g, Glave's bound.     

Effect of Channel Estimation Error on Bit Error Probability in OFDM Systems over Rayleigh and Ricean Fading Channels

A characteristic function-based method is used to derive closed-form bit error probability (BEP) expressions for orthogonal frequency-division multiplexing (OFDM) systems in the presence of channel estimation error over frequency-selective Rayleigh fading channels and frequency-selective Ricean fading channels. Both single channel reception and diversity reception with maximal ratio combining (MRC) are examined. The BEP expressions are shown to be sums of several conditional probability functions which can be calculated by using proper complex Gaussian random variable theory and a characteristic function method. The closed-form BEP expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models. The performances of two interpolation methods, a sine interpolator with Hamming windowing and a Wiener interpolator, are compared.     

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.     

Accurate Approximation of QAM Error Probability on Quasi-Static MIMO Channels and Its Application to Adaptive Modulation

An accurate approximation for the conditional error probability on quasi-static multiple-input multiple-output (MIMO) antenna channels is proposed. For a fixed channel matrix, it is possible to accurately predict the performance of quadrature amplitude modulations (QAM) transmitted over the MIMO channel in presence of additive white Gaussian noise. The tight approximation is based on a simple Union bound for the point error probability in the n-dimensional real space. Instead of making an exhaustive evaluation of all pairwise error probabilities (intractable in many cases), a Pohst or a Schnorr-Euchner lattice enumeration is used to limit the local theta series inside a finite radius sphere. The local theta series is derived from the original lattice theta series and the point position within the finite multidimensional QAM constellation. In particular, we take into account the number of constellation facets (hyperplanes) that are crossing the sphere center. As a direct application to the accurate approximation for the conditional error probability, we describe a new adaptive QAM modulation for quasi-static multiple antenna channels     

On the Error Probability Evaluation in Lightwave Systems With Optical Amplification

We review the time domain, frequency domain, and Fourier series Karhunen-Loeve series expansion (KLSE) methods for exact BER evaluation in intensity- and phase-modulated direct-detection optically amplified systems. We compare their complexity and computational efficiency, and discuss the most relevant implementation issues. We show that the method based on a Fourier series expansion has the simplest implementation and requires the minimum number of eigenvalues to converge to the exact BER value for various kind of optical filters. For this method, we also introduce an equivalent form of the moment generating function, that avoids the singularity for eigenvalues equal to zero, and derive an alternative expansion where signal and noise are expanded on the same orthonormal basis.     

与窄带微波系统共享频段的CDMA系统性能分析

本文分析了与窄带微波系统共享频段的ＣＤＭＡ系统的误码性能，给出了ＤＳ／ＣＤＭＡ接收机使用一个多径判决反馈滤波器后的计算机模拟数值结果。     

Error Probability Performance of M-ary CPSK Systems With Intersymbol Interference

We derive upper and lower bounds on the probability of error ofM-ary CPSK systems subject to intersymbol interference and additive Gaussian noise. The bounds are expressed in terms of the error probability obtained with a finite pulse train and some parameters associated with the residual pulse train. Methods are given to compute the probability of error with a finite number of interference terms and it is shown that the difference between the upper and the lower bounds is a monotone decreasing function of the number of pulses in the finite pulse train. The applicability of the method to compute the probability of error with any desired degree of accuracy is illustrated by examples for quaternary and octonary systems.     

Bit Error Probability for Baseband and Subcarrier Optical Communication Systems

Digital baseband and digital subcarrier noncoherent optical communication systems are considered in this paper. Expressions are developed for the bit error probability of optical subcarrier systems which use a nonliner polarization modulator and either a one-detector or a two-detector receiver, The expressions are evaluated numerically, and the results are used to compare the one- and two-detector subcarrier systems with the corresponding one- and two-detector baseband systems for a fLxed bit error probability.     

Error control codes for QAM signalling

A class of block codes is described which exploits the properties of quadrature amplitude modulation signal constellations whose points lie on a square grid. The simplest codes in the class have block lengths 4 and 8 and offer coding gains of 3 dB and 4.5 dB, respectively.     

相位噪声对多天线QAM性能影响分析

正交幅度调制系统(QAM)对载波的相位噪声非常敏感,多天线技术的使用可以提高通信系统的性能。对QAM系统在当今通信系统中的应用及相位噪声对QAM系统性能影响进行介绍,对多天线QAM系统受相位噪声影响进行了理论分析及仿真验证,并给出了闭式误差向量幅度(EVM)表达式。给出的理论公式及仿真结果对多天线QAM系统相位噪声指标的确定及系统性能分析具有参考意义。     

An Exact Error Probability Analysis of OFDM Systems with Frequency Offset

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for orthogonal frequency division multiplexing (OFDM) systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in additive white Gaussian noise (AWGN), frequency flat and frequency selective Rayleigh fading channels. The BER/ SER performances of BPSK and QPSK modulation schemes are analyzed for AWGN and frequency-flat Rayleigh fading channels while BPSK is considered for frequency-selective Rayleigh fading channels. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions.     

A Comment on "Probability of Error in PN-Modulated Spread Spectrum Binary Communication Systems"

Examination of the interference power of spread spectrum PN systems gives a result approximately twice as large as that reported by Hopkins and Simpson [1]. The additional factor is due to a correlation between intersymbol interferences at different chip times. A corrected characteristic function for the interference is given here.     

The Effect of Bandlimiting Filters on Probability of Error of MSK

Minimum Shift Keying (MSK) is a method of modulation which can be viewed as a special case of Frequency Shift Keying or a special form of Offset Quadrature Phase Shift Keying; therefore, it can be detected either by a discriminator or with a pair of matched filters. In the latter case, the system is optimal, provided there are no bandlimiting filters in the transmitter and receiver. These filters introduce intersymbol interference and hence degrade the performance of the system. In this paper we investigate analytically the effect of a bandlimiting filter in the receiver on the error probability of the system, presenting numerical results when that filter is of the Butterworth type. It is shown that a very simple suboptimal detector outperforms the matched filter detector so long as2W/R_{b} < 1.3, where Rbis the bit rate andWis the single sided 3 dB bandwidth of the bandlimiting filter.     

Coded Error Probability for DS Spread-Spectrum Systems with Periodic Pulsed Multiple-Tone Interference

The coded error probability for direct sequence (DS) BPSK or QPSK spread-spectrum systems, used with or without interleaving, and operating in the presence of pulsed multiple-tone interference, is investigated. We consider the worst-case channel error probability under conditions of pulsed multiple-tone jamming for the various systems, and present coded error probability as a function of interleaving delay for(n, k)block codes with hard-decision decoding. It is shown that when the maximum level of continuous multiple-tone interference does not exceed the level of the desired signal, the duty cycle of the corresponding pulsed interference which yields the worst-case error probability is usually small, and that the smaller the duty factor of the jamming, the more considerable is the performance improvement due to the use of interleaving in conjunction with the coding.     

Noise in Remote-Sensing Systems: The Effect on Classification Error

Several types of noise in remote-sensing systems are treated. The purpose is to provide enhanced understanding of the relationship of noise sources to both analysis results and sensor design. The context of optical sensors and spectral pattern recognition analysis methods is used to enable tractability for quantitative results. First, the concept of multispectral classification is reviewed. Next, stochastic models are discussed for both signals and noise, including thermal, shot and quantization noise along with atmospheric effects. A model enabling the study of the combined effect of these sources is presented, and a system performance index is defined. Theoretical results showing the interrelated effects of the noise sources on system performance are given. Results of simulations using the system model are presented for several values of system parameters, using some noise parameters of the Thematic Mapper scanner as an illustration. Results show the relative importance of each of the noise sources on system performance, including how sensor noise interacts with atmospheric effects to degrade accuracy     

A New Union Bound on the Error Probability of Binary Coded OFDM Systems in Wireless Environments

Orthogonal Frequency Division Multiplexing (OFDM) systems are commonly used to mitigate frequency-selective multipath fading and provide high-speed data transmission. In this paper, we derive new union bounds on the error probability of a coded OFDM system in wireless environments. In particular, we consider convolutionally coded OFDM systems employing single and multiple transmit antennas over correlated block fading (CBF) channels with perfect channel state information (CSI). Results show that the new union bound is tight to simulation results. In addition, the bound accurately captures the effect of the correlation between sub-carriers channels. It is shown that as the channel becomes more frequency-selective, the performance get better due to the increased frequency diversity. Moreover, the bound also captures the effect of multi-antenna as space diversity. The proposed bounds can be applied for coded OFDM systems employing different coding schemes over different channel models.     

Probability of Error in Pseudonoise (PN)-Modulated Spread Spectrum Binary Communication Systems

The probability of error in a binary communication system using pseudonoise (PN) modulation to spread the transmitted spectrum is influenced by noise, bandlimiting, and synchronization errors. In this paper the average probability of error is determined, using a series expansion of the characteristic function of the intersymbol interference. It is shown that the effects of intersymbol interference are reduced by spreading and that local code synchronization errors become the dominant factor in the probability of error when the system bandwidth is large.     

Envelope-Derived Timing Recovery in QAM and SQAM Systems

The problem of continuously recovering timing phase and frequency in a high-rate carrier-modulated data communication device is addressed. The communication link is assumed narrowband with respect to the baud rate of the device, thus necessitating the use of some type of equalization in the receiver. The receiver demodulator is assumed coherent in nature. A timing recovery technique based on narrow-band filtering and squaring of the received demodulated waveform(s) is examined. Analysis of the first moment of the waveforms so generated reveals a convenient indicator of sampling instants. If the timing recovery filters are properly designed, then these sampling instants exactly satisfy a requirement previously derived, ensuring efficient operation of the equalizer. Design criteria for the filters are given. Two principal types of linear modulation techniques are considered. These are quardrature-carrier amplitude modulation (QAM) and staggered QAM (SQAM). A set of experimental waveforms observed in a QAM modem signaling at 2400 Bd is included for illustration. Several conclusions are drawn as a result of the study. First, the mean timing waveforms in QAM and SQAM systems bear fixed time relationships to suitable receiver sampling instants. Second, adequate timing filter design is attained with very narrowband filters centered on frequencies equal to half the baud rate and the full baud rate. Third, recovery circuits used in QAM systems may be designed so as to have negligible timing jitter. In SQAM systems and, consequently, in vestigial sideband-amplitude modulation (VSB-AM) systems, this advantage is generally not found.     

Probability of Error Analysis of BPSK OFDM Systems with Random Residual Frequency Offset

In this paper, we derive closed form bit error rate (BER) expressions for orthogonal frequency division multiplexing (OFDM) systems with residual carrier frequency offset (CFO). Most of the published work treats CFO as a nonrandom parameter. But in our study we consider it as a random parameter. The BER performance of binary phase shift keying (BPSK) OFDM system is analyzed in the cases of additive white Gaussian noise (AWGN), frequency-flat and frequency-selective Rayleigh fading channels.We further discuss how these expressions can be related to systems with practical estimators. The simulation results are provided to verify the accuracy of these error rate expressions.     

RS乘积码在QAM系统中的应用

由Reed-Solomon码构成的RS乘积码有很强纠随机错误和突发错误的能力,本文将RS乘积码和正交幅度调制技术结合起来用于提高正交调制通信系统的可靠性,这种系统不需要解调器输出的软信息而采用硬判决迭代译码,可以大大简化系统的复杂性.