  Inspired by the orthogonal time frequency space (OTFS) modulation, in this
paper, we consider designing a multicarrier (MC) modulation on delay-Doppler
(DD) plane, to couple the modulated signal with a doubly-selective channel
having DD resolutions. A key challenge for the design of DD plane MC modulation
is to investigate whether a realizable pulse orthogonal with respect to the DD
plane's fine resolutions exists or not. To this end, we first indicate that a
feasible DD plane MC modulation is essentially a type of staggered multitone
modulation. Then, analogous to orthogonal frequency division multiplexing, we
propose an orthogonal delay-Doppler division multiplexing (ODDM) modulation,
and design the corresponding transmit pulse. Furthermore, we prove that the
proposed transmit pulse is orthogonal with respect to the DD plane's
resolutions and therefore a realizable DD plane orthogonal pulse does exist.
The orthogonality of this particular pulse significantly eases the derivation
of the ODDM's DD domain channel input-output relation, and yields a channel
matrix with an elegant block-circulant-like structure. We demonstrate that the
ODDM outperforms the OTFS in terms of out-of-band emission and bit error rate,
by achieving perfect coupling between the modulated signal and the DD channel.
