Channel Estimation using 5G Sounding Reference Signals: A Delay-Doppler Domain Approach

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.

Unique Word Channel Estimation for Oversampled OTFS

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.

Waveform-domain NOMA: An Enabler for ISAC in Uplink Transmission

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.

A Unified Framework for Adaptive Waveform Processing in Next Generation Wireless Networks

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.

Time and Frequency Synchronization for Multiuser OTFS in Uplink

In this paper, we propose time and frequency synchronization techniques for uplink multiuser OTFS (MU-OTFS) systems in high-mobility scenarios. This work focuses on accurately estimating and correcting timing offsets (TOs) and carrier frequency offsets (CFOs). Specifically, TO estimation is essential for locating users' pilots on the delay-time plane, while CFO estimation enhances channel estimation accuracy. First, we propose a TO estimation technique for an existing multiuser pilot structure in MU-OTFS. We replace the impulse pilot (IMP) in this pilot structure with a more practical pilot with a cyclic prefix (PCP), referred to as single-user-inspired PCP (SU-PCP). This structure employs different Zadoff-Chu (ZC) sequences, which enables pilot separation via correlation at the receiver side. Consequently, we introduce a correlation-based TO estimation technique for uplink MU-OTFS using this pilot structure. Next, a spectrally efficient and practical pilot pattern is proposed, where each user transmits a PCP within a shared pilot region on the delay-Doppler plane, referred to as MU-PCP. At the receiver, the second TO estimation technique utilizes a bank of filters to separate different users' signals and accurately estimate their TOs. Then, we derive a mathematical threshold range to enhance TO estimation accuracy by finding the first major peak in the correlation function rather than relying solely on the highest peak. After locating the received users' pilot signals using one of the proposed TO estimation techniques, our proposed CFO estimation technique reduces the multi-dimensional maximum likelihood (ML) search problem into multiple one-dimensional search problems. In this technique, we apply the Chebyshev polynomials of the first kind basis expansion model (CPF-BEM) to effectively handle the time-variations of the channel in obtaining the CFO estimates for all the users.

PAPR of DFT-s-OTFS with Pulse Shaping

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.

Time Frequency Localized Pulse for Delay Doppler Domain Data Transmission

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.

Delay-Doppler Multiplexing With Global Filtering

This paper proposes a novel modulation technique called globally filtered orthogonal time frequency space (GF-OTFS) which integrates single-carrier frequency division multiple access (SC-FDMA)-based delay-Doppler representation with universal filtered multi-carrier (UFMC) modulation. Our proposed technique first arranges the frequency-Doppler bins of an orthogonal time frequency space (OTFS) frame in adjacency using SC-FDMA and then applies universal filtering to the neighboring signals to mitigate inter-Doppler interference (IDI). By employing this approach, GF-OTFS achieves superior spectral containment and effectively mitigates interference caused by Doppler shifts in dynamic, time-varying channels. This paper also presents a detailed mathematical formulation of the proposed modulation technique. Furthermore, a comprehensive performance evaluation is conducted, comparing our GF-OTFS approach to state-of-the-art techniques, including Doppler-resilient UFMC (DR-UFMC) and receiver windowed OTFS (RW-OTFS). Key performance metrics, such as bit error rate (BER) and out-of-band (OOB) emissions, as well as the Doppler spread reduction are analyzed to assess the effectiveness of each approach. The results indicate that our proposed technique achieves comparable BER performance while significantly improving spectral containment.

Windowed Dictionary Design for Delay-Aware OMP Channel Estimation under Fractional Doppler

Delay-Doppler (DD) signal processing has emerged as a powerful tool for analyzing multipath and time-varying channel effects. Due to the inherent sparsity of the wireless channel in the DD domain, compressed sensing (CS) based techniques, such as orthogonal matching pursuit (OMP), are commonly used for channel estimation. However, many of these methods assume integer Doppler shifts, which can lead to performance degradation in the presence of fractional Doppler. In this paper, we propose a windowed dictionary design technique while we develop a delay-aware orthogonal matching pursuit (DA-OMP) algorithm that mitigates the impact of fractional Doppler shifts on DD domain channel estimation. First, we apply receiver windowing to reduce the correlation between the columns of our proposed dictionary matrix. Second, we introduce a delay-aware interference block to quantify the interference caused by fractional Doppler. This approach removes the need for a pre-determined stopping criterion, which is typically based on the number of propagation paths, in conventional OMP algorithm. Our simulation results confirm the effective performance of our proposed DA-OMP algorithm using the proposed windowed dictionary in terms of normalized mean square error (NMSE) of the channel estimate. In particular, our proposed DA-OMP algorithm demonstrates substantial gains compared to standard OMP algorithm in terms of channel estimation NMSE with and without windowed dictionary.

Reduced Overhead Channel Estimation for OTFS With Split Pilot

Orthogonal time frequency space modulation (OTFS) is currently one of the most robust modulation techniques for high Doppler channels. However, to reap the benefits of OTFS, an accurate channel estimation is crucial. To this mean, the widely used embedded pilot structures use twice the channel length size as a delay guard to avoid interference between the pilot and data symbols. Hence, incurring a large spectral efficiency loss, especially in wideband systems where the channel length is large. To reduce the pilot overhead, we propose a novel split pilot structure with two impulse pilots. With two pilots, we can use one to cancel the other, thus, capable of removing the pilot interference over data. To remove the data interference from the pilot, we also propose an iterative joint channel estimation and detection technique tailored to the proposed split pilot structure. With the interference caused by the delay spread solved, we reduce the number of delay guards in our system by half, significantly improving the spectral efficiency. To corroborate our claims, we numerically demonstrate that our proposed method can achieve performance levels comparable to that of the full-guard method while using only half the delay guard. Additionally, we show that our proposed iterative channel estimating technique has a fast convergence speed, requiring only two iterations.