The emergence of alternative multiplexing domains to the time-frequency domains, e.g., the delay-Doppler and chirp domains, offers a promising approach for addressing the challenges posed by complex propagation environments and next-generation applications. Unlike the time and frequency domains, these domains offer unique channel representations which provide additional degrees of freedom (DoF) for modeling, characterizing, and exploiting wireless channel features. This article provides a comprehensive analysis of channel characteristics, including delay, Doppler shifts, and channel coefficients across various domains, with an emphasis on their inter-domain relationships, shared characteristics, and domain-specific distinctions. We further evaluate the comparative advantages of each domain under specific channel conditions. Building on this analysis, we propose a generalized and adaptive transform domain framework that leverages the pre- and post-processing of the discrete Fourier transform (DFT) matrix, to enable dynamic transitions between various domains in response to the channel conditions and system requirements. Finally, several representative use cases are presented to demonstrate the applicability of the proposed cross-domain waveform processing framework in diverse scenarios, along with future directions and challenges.

Orthogonal Time Frequency Space (OTFS) modulation is a promising waveform for future wireless networks. However, its resilience to RF impairments remains relatively understudied. Low-cost RF front ends are crucial for next-generation wireless systems, yet their performance is often degraded by RF impairments such as transmit IQ imbalance (IQI), phase noise (PN), timing offset (TO), and carrier frequency offset (CFO). Hence, this paper addresses the estimation and compensation of these RF impairments in OTFS systems under high mobility. A unified system model is developed that incorporates TO, CFO, PN, IQI and other channel effects into an effective channel representation. Using the pilot with cyclic prefix (PCP), a low-peak to average power ratio (PAPR) pilot suitable for OTFS, we propose a pilot-aided synchronization and estimation framework. The dual periodicity of PCP is exploited in our proposed TO estimation technique. A maximum-likelihood-based technique is also proposed to jointly estimate the CFO and effective channel using a complex exponential basis expansion model (CE-BEM). Finally, a linear detection model is formulated in the delay-Doppler domain to mitigate residual interference caused by RF impairments. Our simulation results corroborate the efficacy of our proposed synchronization and channel estimation techniques.

Practical aspects of orthogonal time frequency space (OTFS), such as channel estimation and its performance in fractional delay-Doppler (DD) channels, are a lively topic in the OTFS community. Oversampling and pulse shaping are also discussed in the existing literature, but not in the context of channel estimation. To the best of our knowledge, this paper is the first to address the problem of data-to-pilot and vice versa energy leakage caused by oversampling and pulse shaping in OTFS. Theoretical analysis is performed on an oversampled, pulse-shaped OTFS implementing the embedded pilot channel estimation technique, revealing a trade-off between the amount of energy leakage and excess bandwidth introduced by the pulse shape. Next, a novel variant of OTFS is introduced, called UW-OTFS, which is designed to overcome the leakage problem by placing the pilot in the oversampled time domain instead of the DD domain. The unique structure of UW-OTFS offers 36 percent higher spectral efficiency than the OTFS with embedded pilot. UW-OTFS also outperforms traditional OTFS in terms of bit error ratio and out-of-band emissions.

In this paper, we investigate the performance of RIS-aided orthogonal time frequency space (OTFS) and orthogonal frequency division multiplexing (OFDM) systems in the presence of oscillator phase noise. OFDM is known to be sensitive to phase noise, which could limit the potential gains promised by RIS systems. OTFS, on the other hand, is a compelling potential waveform for RIS-aided systems in the presence of phase noise due to it's resilience to time-varying channels. However, the effect of phase noise on OTFS has not been fully analyzed in the literature as of yet. Additionally, no existing works in the literature consider the effect of phase noise on an RIS-aided OTFS system. Hence, we propose a joint RIS channel and phase noise estimation technique using a Wiener filtering approach. Our proposed method exploits the statistical nature of both the phase noise and the Doppler spread channel in a setup with RIS. Our numerical analysis demonstrates the significant gain of RIS-aided OTFS offers compared to RIS-aided OFDM in the presence in the presence of phase noise. Additionally, our results demonstrate the superiority of our proposed estimation technique, with gains of up to 3 dB in terms of bit error rate (BER), over existing methods in the literature.

The standardization of the sixth-generation (6G) has recently commenced to address the rapidly growing demands for enhanced wireless network services. Nevertheless, existing wireless systems, particularly at the physical layer waveform level, remain inadequate for achieving the ambitious key performance indicators (KPIs) envisioned for 6G. Specifically, orthogonal frequency division multiplexing (OFDM), the widely adopted waveform in fifth-generation new radio (5G-NR) networks, suffers from inherent limitations in satisfying these stringent requirements. In practice, OFDM can experience severe inter-carrier interference (ICI), resulting in a pronounced data rate error floor caused by high Doppler shifts. Additionally, the repetitive usage of cyclic prefixes (CPs), intended to combat multipath delays, results in significant spectral inefficiency. These fundamental drawbacks pose critical obstacles to fulfilling 6G performance objectives. Orthogonal time frequency space (OTFS) modulation has recently emerged as a promising waveform candidate, addressing the aforementioned challenges by exploiting the unique characteristics of the delay-Doppler (DD) domain channel. Unlike OFDM, OTFS is inherently resilient to channel distortions induced by delay and Doppler effects, while remaining sensitive to time and frequency shifts. Such intrinsic properties are instrumental in enabling OTFS, with joint communication and sensing capabilities, to embrace, rather than combat, dynamic channel conditions. Motivated by these compelling advantages, this article investigates the feasibility and practical implementation of OTFS modulation leveraging the current OFDM-based wireless systems. Furthermore, we present a practical precoding scheme for OTFS-based multiple-input multiple-output (MIMO) systems, characterized by near-linear computational complexity and compared with conventional OFDM-based MIMO systems. We also highlight the advantages of the DD waveform for integrated sensing and communications (ISAC). Through these explorations, we reveal that the DD waveform has substantial potential to achieve scalable, efficient, and robust wireless communication and sensing capabilities, positioning it as a critical technology for future 6G networks.

Affine frequency division multiplexing (AFDM) has recently emerged as a promising waveform for high-mobility communications due to its resilience to Doppler effects and its advantages for integrated sensing and communication (ISAC). AFDM modulates transmit data symbols using chirp subcarriers with two adjustable parameters. One is used for dealing with the Doppler effect and the second parameter can be used for physical layer security (PLS). In this paper, we focus on designing the second chirp parameter in the form of a generic phase function to enhance the robustness of the waveform against brute-force demodulation by the eavesdropper. In particular, we first derive a design criterion that reveals the brute-force demodulation complexity depends on the first derivative of the phase function. Then, we introduce a family of phase functions that can increase the brute-force demodulation complexity in an unbounded and controllable manner, while preserving chirp structure of AFDM. Our simulation results demonstrate that the proposed phase function design enhances the PLS performance of AFDM by several orders of magnitude compared with the conventional AFDM in terms of brute-force demodulation complexity.

According to the recent 3GPP decisions on 6G air interface, orthogonal frequency-division multiplexing (OFDM)-based waveforms are the primary candidates for future integrated sensing and communication (ISAC) systems. In this paper, we consider a monostatic sensing scenario in which OFDM is used for the downlink and its reflected echo signal is used for sensing. OFDM and discrete Fourier transform-spread OFDM (DFT-s-OFDM) are the options for uplink transmission. When OFDM is used in the uplink, the power difference between this signal and the echo signal leads to a power-domain non-orthogonal multiple access (PD-NOMA) scenario. In contrast, adopting DFT-s-OFDM as uplink signal enables a waveform-domain NOMA(WD-NOMA). Affine frequency-division multiplexing (AFDM) and orthogonal time frequency space (OTFS) have been proven to be DFT-s-OFDM based waveforms. This work focuses on such a WD-NOMA system, where AFDM or OTFS is used as uplink waveform and OFDM is employed for downlink transmission and sensing. We show that the OFDM signal exhibits additive white Gaussian noise (AWGN)-like behavior in the affine domain, allowing it to be modeled as white noise in uplink symbol detection. To enable accurate data detection performance, an AFDM frame design and a noise power estimation (NPE) method are developed. Furthermore, a two-dimensional orthogonal matching pursuit (2D-OMP) algorithm is applied for sensing by iteratively identifying delay-Doppler components of each target. Simulation results demonstrate that the WD-NOMA ISAC system, employing either AFDM or OTFS, outperforms the PD-NOMA ISAC system that uses only the OFDM waveform in terms of bit error rate (BER) performance. Furthermore, the proposed NPE method yields additional improvements in BER.

Future 6G non-terrestrial networks aim to deliver ubiquitous connectivity to remote and undeserved regions, but unmanned aerial vehicle (UAV) base stations face fundamental challenges such as limited numbers and power budgets. To overcome these obstacles, high-altitude platform station (HAPS) equipped with a reconfigurable intelligent surface (RIS), so-called HAPS-RIS, is a promising candidate. We propose a novel unified joint multi-objective framework where UAVs and HAPS-RIS are fully integrated to extend coverage and enhance network performance. This joint multi-objective design maximizes the number of users served by the HAPS-RIS, minimizes the number of UAVs deployed and minimizes the total average UAV path loss subject to quality-of-service (QoS) and resource constraints. We propose a novel low-complexity solution strategy by proving the equivalence between minimizing the total average UAV path loss upper bound and k-means clustering, deriving a practical closed-form RIS phase-shift design, and introducing a mapping technique that collapses the combinatorial assignments into a zone radius and a bandwidth-portioning factor. Then, we propose a dynamic Pareto optimization technique to solve the transformed optimization problem. Extensive simulation results demonstrate that the proposed framework adapts seamlessly across operating regimes. A HAPS-RIS-only setup achieves full coverage at low data rates, but UAV assistance becomes indispensable as rate demands increase. By tuning a single bandwidth portioning factor, the model recovers UAV-only, HAPS-RIS-only and equal bandwidth portioning baselines within one formulation and consistently surpasses them across diverse rate requirements. The simulations also quantify a tangible trade-off between RIS scale and UAV deployment, enabling designers to trade increased RIS elements for fewer UAVs as service demands evolve.

Delay-Doppler multiplexing has recently stirred a great deal of attention in research community. While multiple studies have investigated pulse-shaping aspects of this technology, it is challenging to identify the relationships between different pulse-shaping techniques and their properties. Hence, in this paper, we classify these techniques into two types, namely, circular and linear pulse-shaping. This paves the way towards the development of a unified framework that brings deep insights into the properties, similarities, and distinctions of different pulse-shaping techniques. This framework reveals that the recently emerged waveform orthogonal delay-Doppler multiplexing (ODDM) is a linear pulse-shaping technique with an interesting staircase spectral behaviour. Using this framework, we derive a generalized input-output relationship that captures the influence of pulse-shaping on the effective channel. We also introduce a unified modem for delay-Doppler plane pulse-shaping that leads to the proposal of fast convolution based low-complexity structures. Based on our complexity analysis, the proposed modem structures are substantially simpler than the existing ones in the literature. Furthermore, we propose effective techniques that not only reduce the out-of-band (OOB) emissions of circularly pulse-shaped signals but also improve the bit-error-rate (BER) performance of both circular and linear pulse-shaping techniques. Finally, we extensively compare different pulse-shaping techniques using various performance metrics.

As sixth-generation (6G) networks move toward higher carrier frequencies and larger antenna apertures, wireless systems increasingly operate in the near-field, demanding a physically consistent model that explicitly highlights the wavenumber-domain channel characteristics. In this paper, we establish an analytical wavenumber-domain channel modeling for multiple-input single-output (MISO) transmissions based on the Weyl expansion. Our model reveals that the effective channel coefficients of uniform linear arrays (ULAs) can be derived as a one-dimensional integral with respect to the zeroth-order Hankel function of the first kind in the wavenumber-domain. This modeling allows us to exploit the channel characteristics directly in the wavenumber-domain. Particularly, we derive the wavenumber-domain expression of multiuser interference, whose value is sensitive to the wavenumber-domain aliasing due to the presence of the Dirichlet kernel. The asymptotical orthogonality condition that eliminates the aliasing is then derived, which requires the antenna spacing is no larger than half of the wavelength. The avoidance of wavenumber-domain aliasing can significantly reduce the multiuser interference (MUI) and improve the communication performance, which is explicitly verified by our numerical results under the same aperture size and transmit power.

Modern waveform design faces a fundamental trade-off between the computational simplicity of channel estimation (CE) and the maximization of diversity gains. While orthogonal frequency division multiplexing (OFDM) enables low-complexity one-tap equalization, it inherently suppresses multipath diversity by collapsing resolvable delay components into a single frequency-domain coefficient. Conversely, although affine-domain processing captures full channel diversity, its performance is often bottlenecked by estimation errors. This paper proposes a hybrid domain processing framework that aggregates path diversity to enhance the effective signal-to-noise ratio (SNR) without altering the existing frame structures. Firstly, we highlight the limitations of conventional iterative-search CE in the affine domain, demonstrating that fractional delay spreading induces severe estimation error floors. To resolve this, we propose a cross-domain framework that decouples estimation from data multiplexing. Our design utilizes frequency-domain demodulation reference signals (DMRS) for robust, low-complexity CE, followed by a derived full-rank mapping to an affine-domain data block for coherent path aggregation. Furthermore, we analyze the impact of Doppler-induced channel aging and subcarrier spacing constraints to mitigate inter-carrier interference (ICI). Simulation results under standardized 3GPP channel models demonstrate that the proposed scheme eliminates the error floors of native affine CE and achieves bit-error-rate (BER) performance approaching multi-antenna MIMO baselines, while maintaining the hardware simplicity of a single-antenna transceiver.

We study channel parameter estimation for multiuser orthogonal time frequency space (OTFS) systems in the delay-Doppler (DD) domain. To enable structured parametric estimation, we adopt a multi-user pilot cyclic prefix (MU-PCP) design, which multiplexes users along the Doppler dimension while preserving a separable exponential structure. This structure facilitates high-resolution estimation of fractional delay and Doppler parameters in the multiuser setting. Building on this framework, we extend weighted MUSIC (W-MUSIC) to multiuser OTFS, providing a computationally efficient approach with mild grid dependency, and develop a matrix pencil (MP)-based method that achieves fully grid-independent delay-Doppler parameter estimation. Numerical results demonstrate the effectiveness of the proposed methods and reveal a robustness-complexity tradeoff: W-MUSIC performs better at low SNR, while MP achieves higher estimation accuracy at moderate-to-high SNR with significantly lower computational complexity.

Orthogonal time frequency space (OTFS) modulation is promising for low Earth orbit (LEO) satellite systems to combat mobility-induced channel variations. However, existing researches are confined to single-frame, single-antenna architectures, overlooking the spatio-temporal correlations inherent in the equivalent delay-Doppler (DD) domain channel in multi-frame LEO satellite multiple-input multiple-output (MIMO)-OTFS systems. Therefore, in this paper, we first establish a multi-frame LEO satellite MIMO-OTFS system with transmitter-windowed under fractional Doppler, derive the input-output relationship, and formulate a structured sparse signal recovery problem. Then, we propose an expectation propagation-based spatio-temporal channel estimation algorithm (EP-ST), which employs a spike-and-slab prior embedded in a hierarchical Gaussian process to exploit the spatio-temporal correlations of the channel, while efficiently tackling high-dimensional posterior intractability via the EP framework. Simulation results demonstrate that the proposed method effectively captures channel characteristics and substantially improves estimation accuracy.

This paper investigates the effect of oscillator phase noise in orthogonal time frequency space (OTFS) systems. The paper provides in-depth analysis of the interference due to phase noise in the delay-Doppler domain and derives expressions for SINR for three different oscillator types, namely free-running oscillators, continuous-time phase locked loops (PLLs) and discrete-time PLLs. The analysis demonstrates the OTFS is sensitive to phase noise and requires appropriate estimation and compensation. In particular, the analysis shows phase noise imposed inter-Doppler-interference (IDI) is severe and that existing phase noise estimation techniques which only consider the common-phase-error (CPE) can not compensate this IDI effectively. Additionally, the existing methods in the OTFS literature on phase noise assume the channel to be a known single tap channel. Hence, in this paper, we propose a method for joint channel and phase noise estimation using a Wiener filtering approach. Our proposed method exploits the statistical nature of both the phase noise and the Doppler spread channel. Our numerical results demonstrate the superior performance of our proposed technique, with gains of up to 8 dB in terms of bit error rate (BER) over existing methods in the literature.

This paper presents novel time and frequency synchronization techniques for uplink multiuser orthogonal time frequency space (MU-OTFS) systems in high-mobility scenarios. This work focuses on accurately estimating and correcting timing offsets (TOs) and carrier frequency offsets (CFOs), which are essential for reliable user pilot localization and channel estimation, respectively. A TO estimation method is first developed for an existing MU-OTFS pilot structure by replacing the conventional impulse pilot (IMP) with a more practical pilot with a cyclic prefix (PCP), referred to as the single-user-inspired PCP (SU-PCP). This structure employs different Zadoff-Chu (ZC) sequences, enabling pilot separation via correlation at the receiver and facilitating a correlation-based TO estimation technique for uplink MU-OTFS using this pilot structure. A multiuser PCP (MU-PCP) pilot pattern is subsequently proposed, where each user transmits a PCP within a shared pilot region on the delay-Doppler plane. The second TO estimation technique utilizes a bank of filters to separate user signals and accurately estimate their TOs. To further improve estimation accuracy, a mathematical threshold range is derived to identify the first major peak in the correlation function rather than relying solely on the maximum peak. Following TO estimation, a CFO estimation technique is proposed that transforms the multidimensional maximum-likelihood (ML) search into multiple one-dimensional searches. By employing the Chebyshev polynomials of the first-kind basis expansion model (CPF-BEM), the method effectively accounts for channel time variations in estimating CFOs for all users. Simulation results verify high-accuracy TO and CFO estimation and improved channel performance in high-mobility MU-OTFS uplinks.

Delay-Doppler multicarrier modulation (DDMC) techniques have been among the central topics of research for high-Doppler channels. However, a complete transition to DDMC-based waveforms is not yet practically feasible. This is because 5G NR based waveforms, orthogonal frequency division multiplexing (OFDM) and discrete Fourier transform-spread OFDM (DFT-s-OFDM), remain as the modulation schemes for the sixth-generation radio (6GR). Hence, in this paper, we demonstrate how we can still benefit from DD-domain processing in high-mobility scenarios using 5G NR sounding reference signals (SRSs). By considering a DFT-s-OFDM receiver, we transform each received OFDM symbol into the delay-Doppler (DD) domain, where the channel is then estimated. With this approach, we estimate the DD channel parameters, allowing us to predict the aged channel over OFDM symbols without pilots. To improve channel prediction, we propose a linear joint channel estimation and equalization technique, where we use the detected data in each OFDM symbol to sequentially update our channel estimates. Our simulation results show that the proposed technique significantly outperforms the conventional frequency-domain estimation technique in terms of bit error rate (BER) and normalized mean squared error (NMSE). Furthermore, we show that using only two slots with SRS for initial channel estimation, our method supports pilot-free detection for more than 25 subsequent OFDM symbols.

Orthogonal Time Frequency Space (OTFS) suffers from high peak-to-average power ratio (PAPR) when the number of Doppler bins is large. To address this issue, a discrete Fourier transform spread OTFS (DFT-s-OTFS) scheme is employed by applying DFT spreading across the Doppler dimension. This paper presents a thorough PAPR analysis of DFT-s-OTFS in the uplink scenario using different pulse shaping filters and resource allocation strategies. Specifically, we derive a PAPR upper bound of DFT-s-OTFS with interleaved and block Doppler resource allocation schemes. Our analysis reveals that DFT-s-OTFS with interleaved allocation yields a lower PAPR than that of block allocation. Furthermore, we show that interleaved allocation produces a periodic time-domain signal composed of repeated quadrature amplitude modulated (QAM) symbols which simplifies the transmitter design. Based on our analytical results, the root raised cosine (RRC) pulse generally results in a higher maximum PAPR compared to the rectangular pulse. Simulation results confirm the validity of the derived PAPR upper bounds. Furthermore, we also demonstrate through BER simulation analysis that the DFT-s-OTFS gives the same performance as OTFS without DFT spreading.

The intrinsic channel tap diversity is lost in the frequency domain one-tap channel estimation (CE), where all multipath components collapse into a single equivalent complex coefficient. Therefore, diversity enhancement solutions are typically shifted toward channel coding or multiple input multiple output (MIMO) schemes. In this paper, we propose a cross-domain path diversity aggregation to enhance the effective signal to noise ratio (SNR) of the received signal while maintaining full compatibility with the existing frame structure. Although affine domain can theoretically achieve high diversity order, we first demonstrate the limitations of iterative search based CE under frequency selective channels with fractional spreading. To overcome these issues, we introduce a hybrid-domain processing that employs the frequency-domain pilots-only symbol for CE, followed by a block of data symbols multiplexed in the affine domain. This design enables simple and accurate CE in the frequency domain while harnessing the diversity and equalization benefits of the affine domain, thereby providing inherent SNR enhancement without additional channel coding or MIMO extensions. Simulation results confirm that the proposed method achieves low BER and high achievable rates under severe frequency-selective conditions, approaching the performance of MIMO systems with significantly lower complexity.

Orthogonal time frequency space (OTFS) is a strong candidate waveform for sixth generation wireless communication networks (6G), which can effectively handle time varying wireless channels. In this paper, we analyze the effect of fractional delay in delay Doppler (DD) domain multiplexing techniques. We develop a vector-matrix input-output relationship for the DD domain data transmission system by incorporating the effective pulse shaping filter between the transmitter and receiver along with the channel. Using this input-output relationship, we analyze the effect of the pulse shaping filter on the channel estimation and BER performance in the presence of fractional delay and uncompensated fractional timing offset (TO). For the first time, we propose the use of time-frequency localized (TFL) pulse shaping for the OTFS waveform to overcome the interference due to fractional delays. We show that our proposed TFL-OTFS outperforms the widely used raised cosine pulse-shaped OTFS (RC-OTFS) in the presence of fractional delays. Additionally, TFL-OTFS also shows very high robustness against uncompensated fractional TO, compared to RC-OTFS.

In this paper, we propose a novel network architecture where two types of aerial infrastructures together with a ground station provide connectivity to a remote area. A high altitude platform station (HAPS) is equipped with reconfigurable intelligent surface (RIS), called HAPS-RIS, to be exploited to assist the unmanned aerial vehicle (UAV)-based wireless networks. A key challenge in such networks is the restricted number of UAVs, which limits full coverage and leaves some users unsupported. To tackle this issue, we propose a hierarchical bilevel optimization framework including a leader and a follower problem. The users served by HAPS-RIS are in a zone called the HAPS-RIS zone and the users served by the UAVs are in another zone called the UAV zone. In the leader problem, the goal is to establish the zone boundary and practical RIS phase shift design that maximizes the number of users covered by HAPS-RIS while ensuring that users in this zone meet their rate requirements. This is achieved through our proposed practical relaxation method and the proposed dynamic radius-based zone association with RIS clustering (DyRaZARC) technique. The follower problem focuses on minimizing the number of UAVs required, ensuring that the rate requirements of the users in the UAV zone are met. This is addressed through our proposed novel geometry-informed machine learning method, called k-means adaptive dynamic UAV selection (KADUS) technique. Our study reveals that increasing the number of RIS elements significantly decreases the number of required UAVs.