On the Input-Output Relation of ODDM Modulation over General Physical Channels

This paper considers orthogonal delay-Doppler division multiplexing (ODDM) modulation over doubly selective physical channels with general delay and Doppler. Assuming the implementation based on the IDFT/DFT and sample-wise pulse-shaping/receiver-filtering, we study the input-output (IO) relation for ODDM and characterize the equivalent sampled delay-Doppler (DD) domain channel in terms of the parameters of the physical channel and the DD plane orthogonal pulse. The established IO relation can describe the pattern of inter-symbol-interference (ISI) and inter-carrier-interference (IeI) for arbitrary delay and Doppler of the physical channel. The results of this paper are useful for developing signal processing algorithms for ODDM-based communication and sensing applications.