OAMP-Aided Joint Channel Estimation and Data Detection for ODDM Systems

In this work, to address the challenge of joint channel estimation and data detection (JED) for orthogonal delay-Doppler (DD) division multiplexing (ODDM) in doubly selective channels, we propose an orthogonal approximate message passing (OAMP)-aided JED (OAMP-JED) receiver. We first formulate a bilinear cross-domain JED model, which can be linearized into separate channel estimation and data detection subproblems. The proposed OAMP-JED receiver alternately executes two OAMP modules for these subproblems, effectively coupled through a variational noise term to account for model uncertainty. Leveraging OAMP's error orthogonality, we derive closed-form scalar-variance updates to enable efficient and principled soft information exchange between the modules, thereby mitigating error propagation during JED. Simulation results show that, for both uncoded and coded ODDM, OAMP-JED achieves a lower bit error rate (BER) than benchmark schemes. Moreover, its BER performance closely approaches that of OAMP with perfect CSI.

A Novel ISAC Waveform Based on Orthogonal Delay-Doppler Division Multiplexing with FMCW

In this work, we propose the orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation with frequency modulated continuous wave (FMCW) (ODDM-FMCW) waveform to enable integrated sensing and communication (ISAC) with a low peak-to-average power ratio (PAPR). We first propose a square-root-Nyquist-filtered FMCW (SRN-FMCW) waveform to address limitations of conventional linear FMCW waveforms in ISAC systems. To better integrate with ODDM, we generate SRN-FMCW by embedding symbols in the DD domain, referred to as a DD-SRN-FMCW frame. A DD chirp compression receiver is designed to obtain the channel response efficiently. Next, we construct the proposed ODDM-FMCW waveform for ISAC by superimposing a DD-SRN-FMCW frame onto an ODDM data frame. A comprehensive performance analysis of the ODDM-FMCW waveform is presented, covering peak-to-average power ratio, spectrum, ambiguity function, and Cramer-Rao bound for delay and Doppler estimation. Numerical results show that the proposed ODDM-FMCW waveform delivers excellent ISAC performance in terms of root mean square error for sensing and bit error rate for communications.

Achieving Full Multipath Diversity by Random Constellation Rotation: a Theoretical Perspective

Diversity is an essential concept associated with communication reliability in multipath channels since it determines the slope of bit error rate performance in the medium to high signal-to-noise ratio regions. However, most of the existing analytical frameworks were developed for specific modulation schemes while the efficient validation of full multipath diversity for general modulation schemes remains an open problem. To fill this research gap, we propose to utilize random constellation rotation to ease the conditions for full-diversity modulation designs. For linearly precoded cyclic-prefix orthogonal frequency division multiplexing (OFDM) systems, we prove that maximum multipath diversity can be attained as long as the spread matrix does not have zero entries, which is a sufficient but easily satisfied condition. Furthermore, we derive the sufficient and necessary condition for general modulation schemes, whose verification can be divided into validation tasks for each column of the modulation matrix. Based on the proposed conditions, maximum diversity order can be attained with the probability of 1 by enabling a randomly generated rotation pattern for both time and doubly dispersive channels. The theoretical analysis in this paper also demonstrates that the diversity evaluation can be concentrated on the pairwise error probability when the number of error symbols is one, which reduces the complexity of diversity-driven design and performance analysis for novel modulation schemes significantly in both time and doubly dispersive channels. Finally, numerical results for various modulation schemes confirm that the theoretical analysis holds in both time and doubly dispersive channels. Furthermore, when employing practical detectors, the random constellation rotation technique consistently enhance the transmission reliability for both coded and uncoded systems.

Performance of orthogonal delay-doppler division multiplexing modulation with imperfect channel estimation

The orthogonal delay-Doppler division multiplexing (ODDM) modulation is a recently proposed multi-carrier modulation that features a realizable pulse orthogonal with respect to the delay-Doppler (DD) plane's fine resolutions. In this paper, we investigate the performance of ODDM systems with imperfect channel estimation considering three detectors, namely the message passing algorithm (MPA) detector, iterative maximum-ratio combining (MRC) detector, and successive interference cancellation with minimum mean square error (SIC-MMSE) detector. We derive the post-equalization signal-to-interference-plus-noise ratio (SINR) for MRC and SIC-MMSE and analyze their bit error rate (BER) performance. Based on this analysis, we propose the MRC with subtractive dither (MRC-SD) and soft SIC-MMSE initialized MRC (SSMI-MRC) detector to improve the BER of iterative MRC. Our results demonstrate that soft SIC-MMSE consistently outperforms the other detectors in BER performance under perfect and imperfect CSI. While MRC exhibits a BER floor above $10^{-5}$, MRC-SD effectively lowers the BER with a negligible increase in detection complexity. SSMI-MRC achieves better BER than hard SIC-MMSE with the same detection complexity order. Additionally, we show that MPA has an error floor and is sensitive to imperfect CSI.