Intersymbol interference and error probability

Using a criterion of minimum average error probability we derive a method for specifying an optimum linear, time invariant receiving filter for a digital data transmission system. The transmitted data are binary and coded into pulses of shapepm s(t). The linear transmission medium introduces intersymbol interference and additive Gaussian noise. Because the intersymbol interference is not Gaussian and can be correlated with the binary digit being detected, our problem is one of deciding which of two waveforms is present in a special type of correlated, non-Gaussian noise. For signal-to-noise ratios in a range of practical interest, the optimum filter is found to be representable as a matched filter followed by a tapped delay line--the same form as that of the least mean square estimator of the pulse amplitude. The performance (error probability vs.S/N) of the optimum filter is compared with that of a matched-filter receiver in an example.     

Intersymbol interference and probability of error in digital systems

Intersymbol interference and additive Gaussian noise are two important sources of distortion in digital systems, and a principal goal in the analysis of such systems is the determination of the resulting probability of error. Earlier related work has sought to estimate the error probability either by calculating an approximation based upon a truncated version of the random pulse train or by obtaining an upper bound which results from consideration of the worst case intersymbol interference. In this paper a new upper bound is derived for the probability of error which is computationally simpler than the truncated pulse-train approximation and which never exceeds the worst case bound. Moreover, the new bound is applicable in a number of cases where the worst case bound cannot be used. The bound is readily evaluated and depends upon three parameters: the usual signal-to-noise ratio; the ratio of intersymbol interference power to total distortion power; and the ratio of the maximum intersymbol interference amplitude to its rms value. To illustrate the utility of the bound, it is compared with the earlier methods in three cases which are representative of the most important situations occurring in practice.     

Intersymbol interference error bounds with application to ideal bandlimited signaling

An upper bound is derived for the probability of error of a digital communication system subject to intersymbol interference and Gaussian noise. The bound is applicable to multilevel as well as binary signals and to all types of intersymbol interference. The bound agrees with the exponential portion of a normal distribution in which the larger intersymbol interference components subtract from the signal amplitude, and the smaller components add to the noise power. The results are applied to the case of random binary signaling with sinx/xpulses. It is shown that such signals are not so sensitive to timing error as is commonly believed, nor does the total signal amplitude become very large with significant probability. However, the error probability does grow very rapidly as the system bandwidth is reduced below the Nyquist band.     

Intersymbol interference in duobinary systems

An upper bound for the error probability due to intersymbol interference and Gaussian noise is calculated for duobinary signalling systems. The duobinary system with twice the binary signalling speed has an error rate in excess of that of a binary system using identical filters.     

Intersymbol interference in misequalised coaxial systems

A study of digital system degradation in under- and over-equalised coaxial channels is presented. Particular emphasis is paid to the analysis of the dependence of intersymbol interference on the extent of misequalisation and the chosen line code. Line codes of practical importance are considered.     

Intersymbol interference on a continuous-time Gaussian channel

The effect on the probability of error from intersymbol interference caused by a repeated use of a continuous-time Gaussian channel is examined. The model assumes that signals that are power constrained are put through a linear filter after which Gaussian noise is added to produce the received signal. One can view the linear filter as a frequency constraint on the inputs. Because of the memory in the filter, past inputs affect the filter output for the current input. It is shown that this interference can be treated as an additional input whose reproducing kernel Hilbert space (RKHS) norm is upper bounded by a function that tends to 0 with increasing block length. Describing the channel in RKHS terms, we show that the exponential error bounds obtained by Gallager are unchanged if one takes intersymbol interference into account.     

Frequency offset receiver diversity for differential MSK

A new receiver diversity scheme for differential detection of minimum shift keying (MSK) is proposed. The signal from each receiving branch is translated to a different IF frequency. The IF signals are summed and then detected by a common differential detector. The diversity scheme does not need phase adjusters, signal quality measurement circuits or a switching controller; moreover the error rate performance is equivalent to that of postdetection equal gain combining diversity, which needs plural complete receiving systems. Theoretical analysis and computer simulation results show that the diversity gain of the proposed scheme is about 13 dB at a 10^-3error rate under Rayleigh fading and 5 dB under Rician fading when the signal-to-interference power ratio is 10 dB. The static error rate performance improvement was confirmed by experimental test results. Simulation results with data from mobile propagation studies are also shown. Even in heavily shadowed cases, the probability that fading attenuation is less than 17 dB is improved from 80 to 99 percent, and a 7 to 13 dB improvement in margin requirement for 99 percent of time operation is achieved.     

Intersymbol interference cancellation in CDMA 1xEVDO network

This paper presents the BER performance of the physical layer of the code division multiple access 1x Evolution Data Only (EVDO) standard for different data transmission formats, and shows the improvement on the BER performance of the EVDO system over intersymbol interference channel by adapting the low complexity turbo equalization scheme at the receiver. The radio frequency, channel condition, and mobile user data speeds were extracted from a mobile user with a drive experiment on a live wireless EVDO network. Then, the real data were utilized to simulate the actual mobile user's data speeds in our simulations to show the overall BER performance of the EVDO system application. The simulation results are shown over Gaussian and Proakis A channels and the results indicate that significant intersymbol interference cancellation is obtained with an adapted code division multiple access system and the advantages of turbo equalization on the EVDO system are discussed in this research. Copyright © 2012 John Wiley & Sons, Ltd.     

Intersymbol interference due to linear and nonlinear distortion

The paper provides a recursion model for the calculation of the probability density function (pdf) of intersymbol interference (ISI) which is caused by the combined effect of linear channel dispersion and of nonlinear distortion. The nonlinearity introduces statistical interdependencies between the interfering symbols and these dependencies are implicitly taken into account in a trellis-structured recursion rule. The results were verified by time consuming Monte Carlo simulation and show, e.g., that the nonlinear characteristic of a high power amplifier (HPA) reduces in some cases the error probability caused by the linear dispersion. Surprisingly, the ISI due to the nonlinear amplifier is increased in the case of offset modulation     

Intersymbol interference effects on BPSK and QPSK carrier trackingloops

The tracking performance of three conventional carrier tracking loops in the presence of intersymbol interference (ISI) is analyzed. The closed-form expressions for the squaring losses of BPSK (binary phase-shift-keyed) low-SNR (signal-to-noise ratio), BPSK high-SNR, and QPSK (quaternary phase-shift-keyed) low-SNR loops are derived. ISI is shown to affect the BPSK high-SNR loop as much as the I-Q loop despite the nonlinear effect of the hard-limiter. For the QPSK carrier tracking loop, the degradation is shown to be greater due to the modulation of both components of the carrier. In this case, ISI, in addition to modifying the coefficients in the squaring loss, adds a new term not present in wideband channels. In all cases, a unity squaring loss could not be achieved because of the irreducible error due to pattern noise. This noise is only present in band-limited channels and is dependent on the data model used     

双光纤点衍射干涉投影系统误差校正及优化

条纹投影测量技术为复杂曲面提供了一种大动态范围的非接触式三维形貌检测方式。在基于双光纤点衍射干涉的条纹投影检测系统中,系统结构参数对最终面形检测精度影响较大。通过建立系统结构几何分析模型,对系统结构参数进行了优化。针对双光纤点衍射探头投射角标定误差的影响,传统基于零级亮条纹定位的投射端投射角标定方法由于临近级次条纹光强较为接近难以区分而导致存在较大误差,为此提出了一种基于基准平面的投射角迭代校正方法,在原标定方法的基础上进一步提高了其标定精度,进而有效提高了面形检测精度。为验证所提出方法的可行性,搭建实验系统对不同斜率动态范围的待测物测量比对,结果表明校正前后的测量系统与三坐标测量机的测量结果偏差从0.418 2 mm减小至0.021 1 mm,实现了微米级的检测精度,为各类复杂曲面的高精度检测提供了一种可行的方法。     

Intersymbol interference resilient interleaving architecture for multi-stream interleaved frequency division multiple access system

A multi-stream cyclic interleaving architecture for an interleaved frequency division multiple access (IFDMA) system is proposed. The proposed scheme exploits the full benefits of maximal length sequence ( $m$-sequence), in contrast to single data stream transmission scheme proposed in earlier works, thereby allowing simultaneous transmission of multiple data streams by each user. The cyclic spreading allows the separation of multiple data streams for each user in addition to intersymbol interference (ISI) minimization. The assignment of orthogonal subcarriers to each user compensates multiuser interference (MUI). The increase in the number of data stream transmission improves the data rate of the system. The proposed scheme employs maximal ratio combining (MRC) to maximize the instantaneous signal-to-noise ratio (SNR) of the multipath signal. The performances of the proposed interleaving scheme are compared with the minimum mean square error frequency domain equalization (MMSE-FDE)-based conventional interleaving scheme. Despite the simultaneous transmission of multiple data streams, the proposed scheme retains the performance of single data stream transmission.     

Simple Expression for Interchannel and Intersymbol Interference Degradation in MSK Systems with Application to Systems with Gaussian Filters

In this paper, we derive a simple expression for the degradation in signal-to-noise ratio caused by intersymbol and adjacent channel interference in MSK systems for which the total response is nonnegative and the response is such that only two intersymbol and one adjacent channel terms are dominant. An MSK system with Gaussian filters in transmitter and receiver satisfy this condition. The resulting expression is simple because we simultaneously maximize the signal value from the main channel (by selecting the sampling time) and the degradation caused by the signals in the interfering channels. For such systems we derive the relation between the optimal filter bandwidth and channel frequency separation. Numerical results are presented for the case of Gaussian filters in both transmitter and receiver or receiver only and either one or two adjacent interfering channels.     

A transmitter diversity for MSK with two-bit differential detection

Transmitter diversity is a technique that is effective for mitigating signal transmission degradation caused by multipath fading which is one of the most serious problems in land mobile radio. A frequency-offset transmitter diversity is proposed for a land mobile radio system that employs minimum-shift keying (MSK) and two-bit differential detection. It is shown that high transmission efficiency can be obtained in comparison with the other frequency-offset transmitter diversity. In addition, the diversity effect on the bit error rate (BER) performance is equivalent to that of postdetection equal gain combining diversity. The BER performance improvement was confirmed by the experimental test results.     

基于CRC纠错与迭代干扰消除的星载AIS接收机

为了提升星载船舶自动识别系统( AIS)的卫星接收性能,提出了一种采用4 b循环冗余校验( CRC)纠错与迭代干扰消除算法的星载AIS接收方案。针对星载AIS系统中多路信号碰撞明显的情况,首先,通过分析星载AIS系统中CRC错误类型,采用比特反转的方式进行纠错;其次,对纠错后的序列进行AIS数据重构,采用迭代干扰消除方法消除重构信号,并将余下信号作为输入信号再次进入系统进行解调。仿真结果表明,和传统的CRC纠错系统相比,针对典型的两路信号碰撞情况,基于4 b CRC校验与迭代干扰消除的星载AIS系统能够带来1~2 dB的误码率增益,对星载AIS系统的性能提升有重要指导意义。     

Sharp error bounds for intersymbol interference

Sharp upper and lower bounds of the Chebyshev type are established for the probability of error due to intersymbol interference and additive Gaussian noise in a digital communication system. The results are in relatively closed form, and the only statistical knowledge assumed about the interference is the peak eye opening and the variance. The bounds apply to correlated and uncorrelated signals and for any signal to noise ratio.     

Sparse-graph codes for quantum error correction

Sparse-graph codes appropriate for use in quantum error-correction are presented. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse-graph codes keep the number of quantum interactions associated with the quantum error-correction process small: a constant number per quantum bit, independent of the block length. Third, sparse-graph codes often offer great flexibility with respect to block length and rate. We believe some of the codes we present are unsurpassed by previously published quantum error-correcting codes.     

Comparison of DPSK and MSK bit error rates for K andRayleigh-lognormal fading distributions

The composite Rayleigh-lognormal distribution is mathematically intractable for the analytical evaluation of such a communication system performance metric as bit error rate. The composite K distribution closely approximates the Rayleigh-lognormal and is potentially useful for analytical manipulations. In this contribution we derive the bit error rates of differential phase-shift keying (DPSK) and minimum shift keying (MSK), in manageable closed forms, for the K distribution model of multipath fading and shadow fading, and show, numerically, the close agreement between these results and those based on the Rayleigh-lognormal distribution     

Reduction of the error floor of MSK by selection diversity

We examine the error floor of minimum shift keying (MSK) when the receiver uses selection diversity. Both received signal strength indication (RSSI)-driven diversity and bit error rate (BER)-driven diversity are analyzed. The considered channel is a two-delay Rayleigh-fading channel; detection is done by differential detectors with either fixed or adaptive determination of the sampling time. Analysis is based on the method of error regions, where the instantaneous impulse response is represented by phasors in the complex plane. We first compute the joint probability density function (pdf) of the phasors of the two diversity branches. Depending on the selection criterion, the error probability is then computed as an integral over certain functions of this pdf. In the limit of small delay spreads S, the integrals are evaluated analytically. For fixed sampling, the admissible delay spread for BER=10^-3 is increased by about a factor of three (as compared to the no-diversity case) for RSSI-driven diversity and a factor of four for BER-driven diversity. For adaptive sampling, RSSI-driven diversity gives little improvement in the admissible S for BER=10^-3 while BER-driven diversity increases it by some 50%. Results are confirmed by comparison with Monte Carlo simulations and measurements     

Mathematical problems in error calculations for interference

Several treatments of interference problems are examined with a view to determine whether doubtful mathematical assumptions about the existence of probability density functions affect the conclusions. Most derivations can be recast so that the existence of a density function is not necessary for the conclusions to be valid