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.
Highlights
In the design of a Nyquist filter the robustness to timing jitter is a prime factor
We propose to use the second derivative of the time response evaluated at t/T = 1 as a figure of merit related to the size of the largest sidelobe
To explain the improved performance of Nyquist pulses in the presence of timing errors three figures of merit based on fractional energy, first and second derivative of the time response, in short velocity and acceleration, evaluated at first zero crossing of the impulse response have been proposed and verified on pulses that have been reported in the corresponding literature and on a novel family of pulses
Summary
In the design of a Nyquist filter the robustness to timing jitter is a prime factor. A solution is to redistribute the tail energy of impulse response by diminishing the size of the largest sidelobe and in turn increase the size of the subsequent sidelobes. In order to obtain comparable performance in terms of spectral regrowth, one should increase the number of filter taps, resulting in bigger latency and implementation costs. In some applications where the latency is not critical these disadvantages are counteracted by the fact that one obtains increased performance in terms of lower bit error rate (BER). Several researchers embraced this idea known as improved Nyquist filter (INF) or pulse and produced on heuristic bases novel pulses that performed better than the ones previously reported [3,4,5,6,7,8,9,10,11]. A novel family of Nyquist pulses, denoted as power sine was introduced in order to check the validity of the approach to expedite the design process
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