ISI-Free Linear Combination Pulses with Better Performance

Abstract

SUMMARY In this letter we proposed the linear combination of twoISI-free pulses with different decay rates in order to obtain a new Nyquistpulse. The proposed pulse contains a new design parameter β,givinganadditional degree of freedom to minimize the bit error probability perfor-mance in the presence of symbol-timing errors, for a given roll-offfactorα. Several practical tools are implemented for evaluating the performanceof the proposed filter. The novel pulse is evaluated in terms of the bit errorprobability performance in the presence of symbol-timing errors. Eye dia-grams are presented to visually assess the vulnerability of the transmissionsystem to ISI, and the maximum distortion is estimated as a quantitativemeasure of performance. key words: intersymbol interference (ISI), linear combination, Nyquistpulses 1. Introduction In the last few years, the demand for higher data rates incommunication systems has increased due to the need tosupport the wide range of internet and multimedia services;hence, better bandwidth reuse and higher error-free datarates are required. In data communications, Nyquist’s firstcriterion guarantees that a sequence of pulses sampled at theoptimum sampling time will have zero intersymbol interfer-ence (ISI) [1]. Besides the ISI-free prerequisite, pulse shap-ing filters have to exhibit low sensitivity to timing errors.In practical receivers, the presence of timing jitter causesthe actual sampling points to deviate from the optimal ones;hence, symbol timing errors are produced.At the moment, the most popular Nyquist pulse for dis-tortionless data transmission is the raised-cosine (RC) pulse[1]. Furthermore, the so-called better-than-raised cosine fil-ter (BTRC), outperforms the RC pulse in terms of largereye openings and smaller average error rate [2],[3]. Othersuperior pulses, that do not have an explicit time-domainexpression, have also been formulated [4],[5].In this letter, a linear combination between two Nyquistpulses was proposed. The new family of Nyquist pulses ischaracterized by a new design parameter, giving an addi-tional degree of freedom to design a pulse less sensitive totiming errors for a fixed roll-offfactor. To provide immunityagainst timing jitter, the relative magnitudes of the impulsesidelobes should be reduced. Hence, our analysis for obtain-