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.     

Modeling of intersymbol-interference in a Rayleigh fast fadingchannel with typical delay power profiles

By applying a propagation model which combines Rayleigh fast fading with typical, prescribed delay power profiles, the authors analyze intersymbol interference error performance of a single-bit differential detector. A quadrature modulation with ±π/2 phase rotation within one symbol period, which is the case for MSK, is assumed. An analytic expression is derived for the error probability as a function of the ratio of the average energies of the relevant symbol and the preceding interfering symbols. This interference is caused by the channel time dispersion. The error probability lies between an upper and a lower bound with a margin that never exceeds 3 dB. The upper bound error probability turns out to be almost identical to the cochannel interference as calculated by the model of K. Hirade et al. (1979). Using typical delay power profiles of European propagation environments, the authors calculate error probability versus symbol duration. For bad-urban and hilly-terrain cases, in which error bursts may last for a few milliseconds, several tens to several hundreds of successive symbols will be corrupted, unless proper signal recovery measures are taken     

Probability of error in PAM systems with intersymbol interference and additive noise

The effect of intersymbol interference and additive noise on the performance of a digital data transmission system is considered. The data sequence is assumed to be independent and equiprobable. The additive noise is independent of the signal but is not restricted to be Gaussian. A simple lower bound, an upper bound, and a simple approximation to the upper bound, on the probability of error are derived. The approximation to the upper bound is twice the lower bound; hence, either can be taken as an approximation to the actual error probability.     

Maximum likelihood sequence detection for intersymbol interference channels: A new upper bound on error probability

Maximum likelihood sequence detection of digital signaling subject to intersymbol interference and additive white Gaussian noise is considered. A new approach to the error probability analysis results in an upper bound which is tighter than the Forney bound. In addition, in the case of infinite-length intersymbol interference a locally convergent bound is shown to hold under fairly general assumptions on the signal autocorrelation.     

An upper bound on the error probability in decision-feedback equalization

An upper bound on the error probability of a decision-feedback equalizer which takes into account the effect of error propagation is derived. The bound, which assumes independent data symbols and noise samples, is readily evaluated numerically for arbitrary tap gains and is valid for multilevel and nonequally likely data. One specific result for equally likely binary symbols is that if the worst case intersymbol interference when the firstJfeedback taps are Set to zero is less than the original signal voltage, then the error probability is multiplied by at most a factor of2^Jrelative to the error probability in the absence of decision errors at highS/Nratios. Numerical results are given for the special case of exponentially decreasing tap gains. These results demonstrate that the decision-feedback equalizer has a lower error probability than the linear zero-forcing equalizer when there is both a highS/Nratio and a fast roll-off of the feedback tap gains.     

The evaluation of error probabilities for low-frequency attenuationchannels

Channels having large low-frequency attenuation are of much interest. Low-frequency removal may result from transformer or capacitor coupling. Examples include ISDN loop transmission (transformer coupling) and wireless systems (capacitor coupled amplifiers). Despite this interest, few works have explicitly examined the problem of calculating the average probability of error for these systems, in which the intersymbol interference from a single pulse may extend over hundreds or even thousands of symbols. Efficient series techniques for evaluation of the error probabilities of multilevel pulse amplitude modulations and multilevel duobinary signaling are derived. The method is applicable to any additive noise possessing an even probability density function. The Gaussian noise case is examined in detail. Examples of Nyquist I signaling and suboptimal detection of nonreturn-to-zero pulse codes are considered. The results are compared to previous published results. It is seen that an often cited upper bound, though within a factor of about ten in error probability for small to medium intersymbol interference conditions, may significantly overestimate the system degradation due to low-frequency attenuation when the intersymbol interference is large     

Probability of error in digital communication systems with intersymbol interference and dependent symbols (Corresp.)

An upper and lower bound to the probability of error is presented for a digital communication system with dependent symbols affected by additive noise and intersymbol interference. Explicitly considered are two systems in which independent binary symbols are encoded into ternary dependent symbols, i.e., a bipolar code and a dicode. The bounds practically coincide under a proper choice of certain integers; hence the true value of probability of error can be computed as a function of signal to noise ratio.     

On ML Bit Detection of Binary Signals with Intersymbol Interference in Gaussian Noise

Various forms and properties of the maximum-likelihood (ML) bit detector structure for binary signals with intersymbol interference in the presence of additive stationary Gaussian noise are presented and two receiver implementation forms are considered. A simple analytical approximation which also has a heuristic interpretation as a lower bound on the bit probability of error for this detector is presented. The performance of this detector for typical small and moderate degrees of intersymbol interference is presented and compared to other detectors. Both cases indicate that the analytical approximation is quite tight and thus useful in predicting the performance of this highly nonlinear device.     

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.     

Performance of Multiphase CPSK Systems with Intersymbol Interference

An upper bound on the probability of error for multiphase coherent phase-shift-keying (CPSK) systems with intersymbol interference and additive Gaussian noise is presented. The bound is derived through the Chernoff bounding technique and is given by a simple closed-form expression. To demonstrate its applicability the bound is computed for quaternary and octonary CPSK systems with various "typical" pulse responses. Graphical comparisons with other measures of the probability of error show the relative efficacy of the bound.     

Performance of coherent phase-shift-keyed systems with intersymbol interference

In order to optimize the design of a coherent phase-shift-keyed (CPSK) system, it is necessary to estimate the amount of degradation produced by intersymbol interference. In this paper, an upper bound to the probability of error ofm-ary CPSK systems is given when an ideal CPSK signal is passed through a linear time-invariant noisy filter. This bound can be used to estimate the maximum amount of deterioration produced by intersymbol interference, and hence to choose the filter and channel parameters appropriately. It is assumed that allmsymbols have equal a priori probabilities and that the noise is Gaussian.     

Analysis of the effects of time delay spread on TCM performance

We investigate the effect of time delay spread on trellis coded modulation (TCM) in a wireless radio environment where equalization is not employed to mitigate the effects of frequency selective fading when the time delay spread is small. Using a random variable decomposition technique and a Gaussian approximation of the intersymbol interference terms, we obtain explicit bounds for the pairwise error probability of TCM over multipath Rayleigh fading channels characterized by various power delay profiles. A method to calculate an upper bound of the bit error rate (BER) based on Jamali and LeNgoc (1995) bound is also presented. These bounds are used to evaluate TCM performance as well as investigate the delay spread tolerance limit of TCM, including I-Q TCM, over frequency selective fading channels     

Error probability of reduced-state sequence estimation fortrellis-coded modulation on intersymbol interference channels

The error probability of reduced-state sequence estimation (RSSE) for trellis-coded modulation (TCM) on intersymbol interference channels is evaluated. A method based on a stack algorithm is proposed to evaluate the union bound on the error probability for ideal RSSE, which is a good approximation to the error probability of real RSSE. The stack algorithm is employed because it provides a good tradeoff between computer memory and computing time     

Random geometric series and intersymbol interference

An interesting and long-standing problem in probability theory is surveyed, and its applications to analyzing the effects of intersymbol interference in digital transmission systems are discussed. Old and new results are presented which enable one to obtain analytical forms for the probability density function of the intersymbol interference in special eases. The probability of error is then computed and compared with some popular upper bounds.     

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     

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     

Error performance of mismatched receivers for linear-codedmodulation

Optimum demodulation of intersymbol interference may be performed using maximum-likelihood sequence estimation receivers. Standard performance analysis of these receivers assume that the receiver has perfect knowledge of the channel. We assume instead a mismatched receiver that uses an imperfect estimate of the channel to decode the information sequence. A free-distance expression for a mismatched ML receiver is derived and applied to the case of linear-coded modulation. A truncated union bound approximation accurately predicts the error probability     

Lower Bounds on Error Probability in the Presence of Large Intersymbol Interference

A lower bound on the symbol error probability achieved by any estimator of a digital pulse-amplitude-modulated sequence in the presence of white Gaussian noise and intersymbol interference is presented. The bound reduces to the well-known single-pulse error probability bound when intersymbol interference is small, but is tighter when interference is large. For example, on the singlepole (RC) channel, the effective signal-to-noise ratio for any estimator is shown to decrease by at least 3 dB for every doubling in pulse rate T^-1asT rightarrow 0and, on the double-pole channel, by at least 9 dB, thus disproving a recent conjecture [2] on the performance of nonlinear receivers.     

Improved Prabhu upper bound for PAM systems with noise and interference

The authors present an improved modification of the upper bound on error probability of the canonical binary system with additive interference and Gaussian noise. The proposed modification is illustrated by a sinusoidal interference example. It is shown that in this case, for a signal-to-noise ratio of 0 dB and signal-to-interference ratio of 3 dB, the modified upper bound is 9% larger than the exact value, which is approximately 8.5 times smaller than the error resulting from the Prabhu upper bound on error probability.<>     

Multiple-access capability of frequency-hopped spread-spectrumrevisited: an analysis of the effect of unequal power levels

A method for the evaluation of the probability of error of uncoded asynchronous frequency-hopped spread-spectrum multiple-access communications is presented. For systems with binary FSK modulation this method provides an accurate approximation and a tight upper bound to the bit error probability; for systems with M-ary FSK modulation, it provides tight upper bounds to the symbol error probability. The method enables the computationally efficient averaging of the error probability with respect to the delays, phase angles, and data streams of the different users. It relies on the integration of the product of the characteristic function of the envelope of the branch of the BFSK demodulator, which carries the desired signal, and of the derivative of the characteristic function of the envelope of the other branch. For sufficient frequency separation between the BFSK tones, the method can achieve any desirable accuracy. Moreover, the computational effort required for its evaluation grows linearly with the number of interfering users. In the M-ary case, tight upper bounds based on the union bound and the results of the binary case are derived. The method allows the effect of unequal power levels on other-user interference in FH/SSMA systems to be quantified accurately for the first time. The results indicate that the FH/SSMA systems suffer from the near-far problem, although less seriously than direct-sequence SSMA systems