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

TL;DR

This paper rigorously analyzes the delay-Doppler diversity of ODDM modulation in satellite communications, revealing its asymptotic diversity order and proposing a low-complexity detector that achieves full diversity.

Contribution

It provides the first formal analysis of ODDM's delay-Doppler diversity and introduces an efficient detector based on OAMP algorithm.

Findings

ODDM achieves an asymptotic delay-Doppler diversity order of one.

Larger frame sizes improve BER performance at the same diversity order.

The proposed OAMP-based detector extracts full delay-Doppler diversity with reduced complexity.

Abstract

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.