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 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 reduction for differential MSK bynonredundant error correction

A theoretical analysis and experimental results for differential detection of minimum-shift keying (MSK) with nonredundant error correction are described. The proposed demodulator utilizes the output detected from the difference in phase over two or three time slot intervals along with the conventional detector output. A single error can be corrected by using two differential detectors, and a single and a double error can be corrected by using three detectors. It is shown that the error rate performance is improved, especially in the presence of intersymbol interference (ISI), without the addition to the transmitted data of redundant bits. Simulation and experimental results agree with the theoretical analysis, which shows that the degradation of differential detection relative to coherent detection is reduced from 2.2 dB without error correction to 1.2 dB with single error correction and to 0.7 dB with double error correction. The method can be applied effectively to mobile communications over a fading channel or to time-division multiple-access (TDMA) communications using burst mode transmission     

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.     

Bit error probability of phase-coherent communication systems in the presence of noise and interference

The signal, interference and noise are applied at the input to the phase-coherent communication receiver and an expression for the bit error probability is derived. Error curves are calculated for the case when the reference carrier is not ideal. The reference carrier is extracted by the first order loop.<>     

Standard-quadrature-rules approach to the evaluation of error probability in multilevel digital systems

A method for computing the probability of error for multilevel pulse-amplitude modulation data transmission systems is presented. It is based on the use of standard quadrature rules, and allows one to obtain very accurate results in a short computer time. Results and comparisons with previously known methods show the satisfactory performance of the proposed approach, even in critical situations.     

Error probability for multilevel digital systems in presence ofintersymbol interference and additive noise

Generalization of a recently published technique for the evaluation of error probability in fiber-optic communication systems is described. The crux of the method is a minimax approximation of the cumulative distribution function of the additive noise. The additive noise is not constrained to be Gaussian. Examples and comparisons with previously published techniques are presented     

Moment space upper and lower error bounds for digital systems with intersymbol interference

A method for the evaluation of upper and lower bounds to the error probability of a linear pulse-amplitude modulation (PAM) system with bounded intersymbol interference and additive Gaussian noise is obtained via an isomorphism theorem from the theory of moment spaces. These upper and lower bounds are seen to be equivalent to upper and lower envelopes of some compact convex body generated from a set of kernel functions. Depending on the selection of these kernels and their corresponding moments, different classes of bounds are obtained. In this paper, upper and lower bounds that depend on the absolute moment of the intersymbol interference random variable, the second moment, the fourth moment, and an "exponential moment" are found by analytical, graphical, or iterative approaches. We study in detail the exponential moment case and obtain a family of new upper and a family of new lower bounds. Within each family, expressions for these bounds are given explicitly as a function of an arbitrary real-valued parameter. For two channels of interest, upper and lower bounds are evaluated and compared. Results indicate these bounds to be tight and useful.     

Probability of error for digital systems with inaccurately known interference (Corresp.)

The "moment bound theory" is known to provide a useful technique to evaluate error probabilities for digital communication systems in the presence of additive noise and random interference. In this correspondence this theory is extended to the case where the moments of the interference are known only within certain intervals, and upper and lower bounds to the error probabilities are sought. A situation like this can occur in several applications. For example, the exact statistics of the interference may not be known, and only estimates of the first moments may be available. Another example arises when the signal is disturbed by intersymbol interference generated by a channel impulse response whose samples are known only in a certain interval--either because they have been measured with finite accuracy, or because we want to estimate the error probability for a class of channel impulse responses. Several numerical examples are provided which show the range of applicability of this technique.     

Worst-case error probability of a spread-spectrum system inenergy-limited interference

We consider a communication channel corrupted by thermal noise and by an unknown and arbitrary interference of bounded energy. For this channel, we derive a simple upper bound to the worst-case error probability suffered by a direct sequence (DS) communication system with error-correction coding, pseudorandom interleaving, and a correlation receiver. This bound is exponentially tight as the block length of the error correcting code becomes large. Numerical examples are given that illustrate the dependence of the bound on the choice of error correcting code, the type of interleaving used, and the relative energy of the Gaussian noise and arbitrary interference     

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.     

Intermodulation interference probability distribution in mobile radiocommunication systems

The problem of mobile radio system outage in the presence of two signal third order intermodulation interferences is presented. The probability that the desired signal level exceeds the interference level by a predetermined value is defined, computed and graphically illustrated. For all signals the superposition of lognormal and Rayleigh distributions is assumed.<>     

Moments of correlated digital signals for error probability evaluation

In digital communication systems, the error probability in the presence of intersymbol interference (II) and additive noise may be calculated to any desired degree of accuracy by well-known approximation methods which avoid the exponential computation growth (with the number of interferers) inherent in an exhaustive method, on the condition that a fast technique for computing II moments is available. Such a technique is indeed available at present, but it is strongly limited by the assumption that the data symbols are mutually independent. In this paper, this limitation is removed, and a fast procedure is given for computing H moments of correlated digital signals. The computations grow linearly with the number of interferers. The assumption made is that correlated symbols are produced by a general finite-state sequential machine. As illustrative examples, the fast procedure is applied to bipolar and Franaszek MS-43 codes.     

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.     

Average error probability of digital cellular radio systems using MRC diversity in the presence of multiple interferers

The performance of digital cellular radio systems employing maximal ratio combining diversity is analyzed in a flat-fading channel with cochannel interference and additive white Gaussian noise. It is assumed that the desired signal may experience Rice fading (due to the presence of a line-of-sight component), while the interferers are Rayleigh-faded and may have similar or dissimilar average powers. Exact expressions are derived for the average symbol-error probability of M-ary phase-shift keying modulation in the presence of multiple independent Rayleigh-faded interferers.     

Semidefinite programming bounds on the probability of error of binary communication systems with inexactly known intersymbol interference

We consider the problem of evaluating the probability of error of binary communication systems in the presence of additive noise and intersymbol interferences whose statistics are inexactly known due to the estimation errors of the channel coefficients. We present a new method using semidefinite programming to evaluate tight bounds on the error probability based on the upper and lower bounds on the moments of those interferences. Numerical results are provided and compared with a previously published technique.     

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 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.