On the Connection Between Compactness of Pulse Shaping Function and ISI

Abstract

This letter investigates the effect of compactness of a pulse shaping filter on the inter-symbol interference (ISI) by presenting a theoretical equation which directly expresses the bit error rate (BER) in terms of quantified compactness of the pulse. We numerically compute time-bandwidth product (TBP) of the considered pulses as the measure of compactness. To compute the TBP, we use four definitions of pulse width (i.e., time duration in time domain and bandwidth in frequency domain) including root mean square (RMS), full width at half maximum (FWHM), 99% energy concentration and - 40 dB bounded energy duration. We show that the standard pulses poses different compactness properties based on the defined TBP and the - 40 dB definition is the most effective definition to study ISI versus TBP. We also propose a new pulse which offers the least TBP based on - 40 dB definition among all standard pulses and show that this pulse outperforms these well-known pulses in terms of BER and bandwidth efficiency.