Delay-Doppler Diversity Analysis of ODDM Modulation in Satellite Communication Systems

Orthogonal delay-Doppler division multiplexing (ODDM) modulation offers a promising solution to the problem of severe Doppler effects in low earth orbit (LEO) satellites communications. It has been suggested in the recent literature that ODDM modulation can extract full delay-Doppler (DD) diversity, yet a rigorous analysis has not been presented. In this paper, we present a formal analysis of the DD diversity achieved by ODDM modulation along with supporting simulations. Specifically, the analysis and simulations reveal that the asymptotic DD diversity order of ODDM modulation is one, and this order is achieved at lower bit error rate (BER) values for increased frame sizes. We also present low-complexity detector for ODDM modulation based on the Orthogonal approximate message passing (OAMP) algorithm, and show that this detector extracts full DD diversity with the reduced complexity.