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The primary objective of this paper is to establish a generalized frameworkfor pulse-shaping on the delay-Doppler plane. To this end, we classifydelay-Doppler pulse-shaping techniques into two types, namely, circular andlinear pulse-shaping. This paves the way towards the development of ageneralized pulse-shaping framework. Our generalized framework provides theopportunity to compare different pulse-shaping techniques under the sameumbrella while bringing new insights into their properties. In particular, ourderivations based on this framework reveal that the recently emerged waveformorthogonal delay-Doppler multiplexing modulation (ODDM) is a linearpulse-shaping technique. By presenting ODDM under our generalized framework, weclearly explain the observed staircase behavior of its spectrum which has notbeen previously reported in the literature. Another contribution of this paperis proposal of a simple out-of-band (OOB) emission reduction technique byinserting a small number of zero-guard (ZG) symbols along the delay dimensionof the circularly pulse-shaped signals. Additionally, inserting the zero-guardsimproves the bit-error-rate (BER) performance of both circular and linearpulse-shaping techniques. Finally, our simulation results confirm the validityof our mathematical derivations, claims and the effectiveness of the ZGs in OOBreduction and BER performance improvement.

A Generalized Framework for Pulse-Shaping on Delay-Doppler Plane