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.

翻译：受正交时频空间（OTFS）调制的启发，本文考虑在延迟-多普勒（DD）平面上设计一种多载波（MC）调制，使调制信号与具有DD分辨率的双选择性信道耦合。DD平面MC调制的设计关键在于探究是否存在一种可实现且正交于DD平面精细分辨率的脉冲。为此，我们首先指出，可行的DD平面MC调制本质上是一种交错多音调制。随后，类比于正交频分复用，我们提出了一种正交延迟-多普勒复用（ODDM）调制，并设计了相应的发射脉冲。此外，我们证明所提出的发射脉冲在DD平面分辨率上满足正交性，从而证实了可实现的正交DD平面脉冲确实存在。该脉冲的正交性显著简化了ODDM在DD域信道输入-输出关系的推导，并得到具有优雅的块循环类结构的信道矩阵。我们证明，ODDM在带外发射和误码率方面优于OTFS，实现了调制信号与DD信道的完美耦合。