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.

Spectrum and Orthogonality of Orthogonal Delay-Doppler Division Multiplexing Modulation Waveforms

Orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation has recently emerged as a promising paradigm for ensuring reliable communications in doubly-selective channels. This work investigates the spectra and orthogonality characteristics of analog (direct) and approximate digital implementations of ODDM systems. We first determine the time and frequency domain representations of the basis functions for waveform in analog and approximate digital ODDM systems. Thereafter, we derive their power spectral densities and show that while the spectrum of analog ODDM waveforms exhibits a step-wise behavior in its transition regions, the spectrum of approximate digital ODDM waveforms is confined to that of the ODDM sub-pulse. Next, we prove the orthogonality characteristics of approximate digital ODDM waveforms and show that, unlike analog ODDM waveforms, the approximate digital ODDM waveforms satisfy orthogonality without the need of additional time domain resources. Additionally, we examine the similarities and differences that implementations of approximate digital ODDM share with the other variants of DD modulations, focusing on the domain changes the symbols undergo, the type of pulse shaping and windowing used, and the domains and the sequence in which they are performed. Finally, we present numerical results to validate our findings and draw further insights.

Sum-Rate Maximization for Pinching Antenna-assisted NOMA Systems with Multiple Dielectric Waveguides

This paper investigates the resource allocation design for a pinching antenna (PA)-assisted multiuser multiple-input single-output (MISO) non-orthogonal multiple access (NOMA) system featuring multiple dielectric waveguides. To enhance model accuracy, we propose a novel frequency-dependent power attenuation model for dielectric waveguides in PA-assisted systems. By jointly optimizing the precoder vector and the PA placement, we aim to maximize the system's sum-rate while accounting for the power attenuation across dielectric waveguides. The design is formulated as a non-convex optimization problem. To effectively address the problem at hand, we introduce an alternating optimization-based algorithm to obtain a suboptimal solution in polynomial time. Our results demonstrate that the proposed PA-assisted system not only significantly outperforms the conventional system but also surpasses a naive PA-assisted system that disregards power attenuation. The performance gain compared to the naive PA-assisted system becomes more pronounced at high carrier frequencies, emphasizing the importance of considering power attenuation in system design.

Parallel Coding for Orthogonal Delay-Doppler Division Multiplexing

This paper proposes a novel parallel coding transmission strategy and an iterative detection and decoding receiver signal processing technique for orthogonal delay-Doppler division multiplexing (ODDM) modulation. Specifically, the proposed approach employs a parallel channel encoding (PCE) scheme that consists of multiple short-length codewords for each delay-Doppler multicarrier (DDMC) symbol. Building upon such a PCE transmission framework, we then introduce an iterative detection and decoding algorithm incorporating a successive decoding feedback (SDF) technique, which enables instant information exchange between the detector and decoder for each DDMC symbol. To characterize the error performance of the proposed scheme, we perform density evolution analysis considering the finite blocklength effects. Our analysis results, coupled with extensive simulations, demonstrate that the proposed PCE scheme with the SDF algorithm not only showcases a better overall performance but also requires much less decoding complexity to implement, compared to the conventional benchmark scheme that relies on a single long channel code for coding the entire ODDM frame.

On the Time-Frequency Localization Characteristics of the Delay-Doppler Plane Orthogonal Pulse

In this work, we study the time-frequency (TF) localization characteristics of the prototype pulse of orthogonal delay-Doppler (DD) division multiplexing modulation, namely, the DD plane orthogonal pulse (DDOP). The TF localization characteristics examine how concentrated or spread out the energy of a pulse is in the joint TF domain, the time domain (TD), and the frequency domain (FD). We first derive the TF localization metrics of the DDOP, including its TF area, its time and frequency dispersions, and its direction parameter. Based on these results, we demonstrate that the DDOP exhibits a high energy spread in the TD, FD, and the joint TF domain, while adhering to the Heisenberg uncertainty principle. Thereafter, we discuss the potential advantages brought by the energy spread of the DDOP, especially with regard to harnessing both time and frequency diversities and enabling fine-resolution sensing. Subsequently, we examine the relationships between the time and frequency dispersions of the DDOP and those of the envelope functions of DDOP's TD and FD representations, paving the way for simplified determination of the TF localization metrics for more generalized variants of the DDOP and the pulses used in other DD domain modulation schemes. Finally, using numerical results, we validate our analysis and find further insights.

Channel Spreading Function-Inspired Channel Transfer Function Estimation for OFDM Systems with High-Mobility

In this letter, we propose a novel channel transfer function (CTF) estimation approach for orthogonal frequency division multiplexing (OFDM) systems in high-mobility scenarios, that leverages the stationary properties of the delay-Doppler domain channel spreading function (CSF). First, we develop a CSF estimation model for OFDM systems that relies solely on discrete pilot symbols in the time-frequency (TF) domain, positioned at predefined resource elements. We then present theorems to elucidate the relationship between CSF compactness and pilot spacing in the TF domain for accurate CSF acquisition. Based on the estimated CSF, we finally estimate the CTF for data symbols. Numerical results show that, in high-mobility scenarios, the proposed approach outperforms traditional interpolation-based methods and closely matches the optimal estimator in terms of estimation accuracy. This work may pave the way for CSF estimation in commercial OFDM systems, benefiting high-mobility communications, integrated sensing and communications, and related applications.

Uplink Multiple Access with Heterogeneous Blocklength and Reliability Constraints: Discrete Signaling with Treating Interference as Noise

We consider the uplink multiple access of heterogeneous users, e.g., ultra-reliable low-latency communications (URLLC) and enhanced mobile broadband (eMBB) users. Each user has its own reliability requirement and blocklength constraint, and users transmitting longer blocks suffer from heterogeneous interference. On top of that, the decoding of URLLC messages cannot leverage successive interference cancellation (SIC) owing to the stringent latency requirements. This can significantly degrade the spectral efficiency of all URLLC users when the interference is strong. To overcome this issue, we propose a new multiple access scheme employing discrete signaling and treating interference as noise (TIN) decoding, i.e., without SIC. Specifically, to handle heterogeneous interference while maintaining the single-user encoding and decoding complexities, each user uses a single channel code and maps its coded bits onto sub-blocks of symbols, where the underlying constellations can be different. We demonstrate theoretically and numerically that the proposed scheme employing quadrature amplitude modulations and TIN decoding can perform very close to the benchmark scheme based on Gaussian signaling with perfect SIC decoding. Interestingly, we show that the proposed scheme does not need to use all the transmit power budget, but also can sometimes even outperform the benchmark scheme.

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.

Wireless Communications in Doubly Selective Channels with Domain Adaptivity

Wireless communications are significantly impacted by the propagation environment, particularly in doubly selective channels with variations in both time and frequency domains. Orthogonal Time Frequency Space (OTFS) modulation has emerged as a promising solution; however, its high equalization complexity, if performed in the delay-Doppler domain, limits its universal application. This article explores domain-adaptive system design, dynamically selecting best-fit domains for modulation, pilot placement, and equalization based on channel conditions, to enhance performance across diverse environments. We examine domain classifications and connections, signal designs, and equalization techniques with domain adaptivity, and finally highlight future research opportunities.