Quick Performance Assessment of Improved Nyquist Pulses

Abstract

An explanation is proposed for the improved behavior of the improved Nyquist pulses with an asymptotic decay rate of t-2 when sampled with a timing offset. Three figures of merit that indicate the energy distribution into the sidelobes of the time response and allow a quick assessment of their performance in terms of error probability when the impulse response is sampled with a timing error have been proposed and verified on several improved Nyquist pulses reported in the literature. In order to check the validity of the proposed figures of merit a novel family of Nyquist pulses denoted as power sine was introduced. Using the proposed approach the design process was expedited as the volume of necessary calculations was significantly decreased. To explain the difference in close pulse performance a figure of merit based on limited ISI distortion was introduced.

A New Family of Nyquist Pulses With Improved Performance

“…In Table 6, it is assumed that α = 0.25 whereas in Table 7, α = 0.35. BER results for the pulses with which comparison is carried out are available in [27,Table 5] and [27,Table 6], for α = 0.25 and α = 0.35, respectively. Note that the Poly and Power pulses, as well as the proposed pulses do not not have a fixed form for a given value of α but depend on one, three, or four parameters, respectively.…”

“…The performance of digital communication systems employing improved Nyquist pulses has further been addressed in several past research works, including [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37] Further insights on the performance of several state-of-the-art pulses are available in [27]. In [28], a method of improving the error probability performance of various Nyquist pulses, by multiplying them with a specific compactly supported function, has been proposed.…”