Orthogonal Delay-Doppler Division Multiplexing (ODDM) Over General Physical Channels

This paper investigates the characteristics and performance of orthogonal delay-Doppler division multiplexing (ODDM) modulation over doubly selective physical channels with general delay and Doppler. Assuming that the implementation of the ODDM is based on 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 (ESDD) domain channel in terms of the parameters of the physical channel and the DD plane orthogonal pulse (DDOP). The established IO relation can describe the patterns of inter-symbol-interference (ISI) and inter-carrier-interference (ICI) for more general delay and Doppler shifts of the physical channel. Based on the results, we also examine the influence of the transmitter configuration on the sparsity of the ESDD channel and on the resulting performance-complexity tradeoff of ODDM. We further introduce a pilot-assisted method of estimating the physical channel parameters by leveraging the derived IO relation and the root-MUSIC algorithm. We also present a low-complexity symbol detector for ODDM systems based on conjugate gradients (CG). Simulation results under various settings show that the error performance of ODDM based on the estimate of the physical channel approaches that with perfect channel state information (CSI) at a low-to-medium signal-to-noise ratio (SNR), but has an increased gap from the perfect CSI case when the SNR increases.