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.     

Combined Effects of Intersymbol, Interchannel, and Co-Channel Interferences in M-ary CPSK Systems

An expression for the error probability of multilevel coherent phase-shift-keyed (CPSK) systems in the presence of intersymbol, interchannel, and co-channel interferences and additive Gaussian noise is derived. An exact expression is given for the binary CPSK system, whereas upper and lower bounds are presented for the multilevel systems. The approach proposed in this paper overcomes the difficulties of the exhaustive methods and allows accurate and fast evaluation of the character error probability. Only the impulse responses of the overall channels are needed, and the computational labor is reduced to the numerical evaluation of one particular type of integral, whose computation is based upon nonclassical Gaussian quadrature rules. The model of the system is general enough to allow the choice of a rectangular or otherwise-shaped modulating pulse and a constant or shaped envelope of the modulating carrier. Phase incoherence between adjacent carriers is also assumed, and a random misalignment among the modulating bit streams can be taken into account, if necessary. Extensive numerical results are presented for 2- and 4-level systems. The presentation of the results stresses a possible utilization of them in system design problems.     

On Minimum Average Probability of Error Expression for a Binary Pulse-Communication System With Intersymbol Interference

Results useful in the calculation of the exact closed-form expression for the minimum average probability of errorP_eof a binary pulse linear communication system with2Nintersymbol interferences and additive colored Gaussian noise are given. By first performing statistical averaging and then using the variational method, a compact form ofP_ethat depends only on the overall system impulse response taken overNtime instants is obtained. TheseNunknowns are given as the solution ofNsimultaneous nonlinear equations. Specific examples illustrating this approach are considered.     

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.     

Intersymbol Interference Performance of Systems with Correlated Digital Signals

For a digital system with correlated digital symbols, we derive upper and lower bounds on the probability of error when the system is subject to intersymbol interference and additive Gaussian noise. The bounds are expressed in terms of the error probability obtained with a finite number of intersymbol interference terms and some parameters associated with the remainder terms. We also show that the difference between the upper and lower bounds can be made arbitrarily small and that the error probability can be computed to any desired degree of accuracy. We give some examples to illustrate the method.     

On the Probability Density of Intersymbol Interference

The paper presents a simple and rapid algorithm for numerically evaluating the probability density function (pdf) of intersymbol interference (ISI) in digital transmission systems. The results coincide with the analytical solutions available for very few cases only. The biterror rate calculated from the pdf's of ISI and of Gaussian noise agree with upper and lower bounds as published by many authors. Examples of the pdf of ISI in some cases of practical interest are given for various QAM-modulation schemes.     

Error Probability of a Binary Signal Perturbed by Intersymbol Interference and Impulsive Atomopheric Noise

This paper analyzes the performance of baseband polar signals in the presence of impulsive atmospheric noise and intersymbol interference (ISI). Different levels of ISI have been considered to make the analysis more meaningful. Possible explanations for the results are offered. A comparison has also been made with the system operating in Gaussian noise.     

Error Probability in the Presence of Intersymbol Interference and Additive Noise for Multilevel Digital Signals

A new method is presented to compute the average probability of error in the presence of intersymbol interference and additive noise for multilevel pulse-amplitude-modulation (PAM) and partial-response-coded (PRC) signaling schemes. The method is based upon nonclassical Gauss quadrature rules (GQR) and suffers no limitation on noise statistics, so that it applies also for non-Gaussian noise. Moreover it yields some remarkable advantages as compared with other methods, in particular, with the series expansion method that has recently received considerable attention. Expressions for the truncation error are also given and their derivation is reported in the Appendix. Finally, examples of applications are presented and comparisons with other methods are carried out.     

On Differential Detection of M-ary DPSK with Intersymbol Interference and Noise Correlation

In this paper we study differential detection ofM-ary differential phase-shift-keyed (DPSK) signals with intersymbol interference and noise correlation. With these impairments there can be a wide variation in the error rate of the individual symbols, with this variation increasing withM. However, by adding a phase shift offset and adjusting the decision boundaries in the detector, this variation can be reduced and the average symbol error rate can be decreased. For example, for quaternary DPSK with a signal to adjacent (from the previous and next symbols) intersymbol interference power ratio of 17 dB, these methods can reduce the variation in symbol error rates by more than two orders of magnitude and decrease the required signal-to-thermal noise ratio for a 10^-6symbol error rate by more than 2 dB.     

Matched-Transmission Technique for Channels With Intersymbol Interference

A new transmission scheme for channels with intersymbol interference named "matched-transmission (MT) technique" is proposed. An implementation of the MT system is presented and its relations with conventional techniques are described. It is shown that the partial response scheme is a special case of our new technique. The performance of the MT technique is discussed from the view point of the output signal-to-noise ratio and the system is shown to attain asymptotically the bound performance predicted by the information theory.     

Lower Bounds for Finite Intersymbol Interference Error Rates

Some simple lower bounds for the probability of error for band-restricted digital communication are presented. The bounds revolve two values of the complementary error function, the system SNR, the peak value, second moment, and sometimes, the fourth moment of the intersymbol interference. Contrary to other available lower bounds, no parameter searches or infinite series computations are required. The bounds hold when the system "eye" is open and in some cases when the source symbols are correlated.     

Calculating Error Probabilities for Intersymbol and Cochannel Interference

The probability of error in a binary symmetric channel with intersymbol interference and additive noise is efficiently calculated by numerical quadrature of a Laplace inversion integral along a contour in the complex plane passing through a saddlepoint of the integrand. For Gaussian noise, a bound is set on the truncation error incurred by necessarily restricting the integration to a finite interval. The probability of error resulting from cochannel interference is calculated by a similar technique.     

Error Probabilities for Orthogonal Multiplex Systems in the Presence of Intersymbol Interference and Gaussian Noise

The transmission model for anN-dimensional system is extended to handle additive noise and timing error. An orthogonal multiplex system operating in the presence of additive noise and channel introduced inter- and intra-symbol interference is analyzed. Error probabilities are derived and results are reported for carder sets comprising trigonometric product waveforms, Walsh functions, parabolic cylinder functions, and prolate spheroidal wave functions.     

Error Performance of M-ary Noncoherent FSK in the Presence of CW Tone Interference

The error probability performance ofM-ary noncoherent frequency-shift-keying (NCFSK) digital systems when under the influence of continuous wave (CW) interference is determined. Exact expressions are derived in terms of the signal-to-noise and the signal-to-interference ratios. Numerical results are given for quarternary and octonary NCFSK with the signal-signal-to-interference ratio as a parameter.     

Cochannel and Intersymbol Interference in Quadrature-Carrier Modulation Systems

A method is presented for determining the performance of a quadrature-carrier modulation system in terms of probability of error in the presence of additive white Gaussian noise, intersymbol interference, and cochannel interference. This method has been applied to determine the error rate of several quadrature-carrier modulation systems using Butterworth receiving filters of different orders. It has been foand that among the different quadrature-carrier modulation systems studied, sinusoidal frequency-shift keying seems to exhibit the best overall performance in a cochannel and intersymbol interference environment. These results are shown through a number of performance curves that provide useful data for the systems designer.     

Binary Error Rate Caused by Intersymbol Interference and Gaussian Noise

The probability of error in a binary signal owing to intersymbol interference and Gaussian noise is computed by approximation of the expression for the probability of error by a finite sum of squareintegrable functions. The approximating functions should be chosen so that their averages over all bit combinations can be easily determined. The projection of the error function on the subspace of polynomials results in a series which converges more rapidly to the exact error rate than does the Taylor series expansion used previously. The negative exponential functions have the same general form as the error function and, as expected, also result in rapid convergence to the average error rate.     

Fast Error Rate Evaluation in the Presence of Intersymbol Interference

In this paper, we present a general framework which describes a class of fast methods of error rate evaluation in the presence of additive noise and intersymbol interference. An analysis of this framework led us to propose a new method based on a Fourier series expansion which does not make use of the moments of the intersymbol interference. Its computing cost is low and it handles various kinds of noise as well as current coherent amplitude or phase modulation techniques.     

Error Analysis for Noncoherent M-ary Orthogonal Communication Systems in the Presence of Arbitrary Gaussian Interference

A general error analysis for the noncoherentM-ary orthogonal keyed receiver in the presence of arbitrary Gaussian interference is presented. Relations to well-known formulas which apply to the broadband white Gaussian noise environment are given. Numerical results for various special interference situations are presented, and the impact of unequal values of the noise power in the different receiver channels on the error performance is discussed.