A Generalized Framework for Pulse-Shaping on Delay-Doppler Plane
arXiv (Cornell University)(2023)
摘要
The primary objective of this paper is to establish a generalized framework
for pulse-shaping on the delay-Doppler plane. To this end, we classify
delay-Doppler pulse-shaping techniques into two types, namely, circular and
linear pulse-shaping. This paves the way towards the development of a
generalized pulse-shaping framework. Our generalized framework provides the
opportunity to compare different pulse-shaping techniques under the same
umbrella while bringing new insights into their properties. In particular, our
derivations based on this framework reveal that the recently emerged waveform
orthogonal delay-Doppler multiplexing modulation (ODDM) is a linear
pulse-shaping technique. By presenting ODDM under our generalized framework, we
clearly explain the observed staircase behavior of its spectrum which has not
been previously reported in the literature. Another contribution of this paper
is proposal of a simple out-of-band (OOB) emission reduction technique by
inserting a small number of zero-guard (ZG) symbols along the delay dimension
of the circularly pulse-shaped signals. Additionally, inserting the zero-guards
improves the bit-error-rate (BER) performance of both circular and linear
pulse-shaping techniques. Finally, our simulation results confirm the validity
of our mathematical derivations, claims and the effectiveness of the ZGs in OOB
reduction and BER performance improvement.
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