In this paper, we propose time and frequency synchronization techniques for the uplink of multiuser orthogonal time frequency space (MU-OTFS) in high-mobility scenarios. We introduce a spectrally efficient and practical pilot pattern where each user utilizes a pilot with a cyclic prefix (PCP) within a shared pilot region on the delay-Doppler plane. At the receiver, a bank of filters is deployed to separate the users' signals and accurately estimate their timing offsets (TOs) and carrier frequency offsets (CFOs). Our technique employs a threshold-based approach that provides precise TO estimates. Our proposed CFO estimation technique reduces the multi-dimensional maximum likelihood (ML) search problem into multiple one-dimensional search problems. Furthermore, 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. Finally, we numerically investigate the error performance of our proposed synchronization technique in high mobility scenarios for the MU-OTFS uplink. Our simulation results confirm the efficacy of the proposed technique in estimating the TOs and CFOs which also leads to an improved channel estimation performance.

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 the existing literature on joint timing and frequency synchronization of orthogonal time frequency space modulation (OTFS), practically infeasible impulse pilot with large peak-to-average power ratio (PAPR) is deployed. Hence, in this paper, we propose a timing offset (TO) and carrier frequency offset (CFO) estimation for OTFS over a linear time-varying (LTV) channel, using a low PAPR pilot structure. The proposed technique utilizes the recently proposed practically feasible pilot structure with a cyclic prefix (PCP). We exploit the periodic properties of PCP in both delay and time domains to find the starting point of each OTFS block. Furthermore, we propose a two-stage CFO estimation technique with over an order of magnitude higher estimation accuracy than the existing estimator using the impulse pilot. In the first stage, a coarse CFO estimate is obtained which is refined in the second stage, through our proposed maximum likelihood (ML) based approach. The proposed ML-based approach deploys the generalized complex exponential basis expansion model (GCE-BEM) to capture the time variations of the channel, absorb them into the pilot and provide an accurate CFO estimate. Since our proposed synchronization technique utilizes the same pilot deployed for channel estimation, it does not require any additional overhead. Finally, we evaluate the performance of our proposed synchronization technique through simulations. We also compare and show the superior performance of our proposed technique to the only other existing joint TO and CFO estimation method in OTFS literature.

The widely used embedded impulse pilot for channel estimation of orthogonal time frequency space modulation (OTFS) has a prohibitively large peak to average power ratio (PAPR). Hence, in this paper, we propose a novel embedded pilot with cyclic prefix (PCP) that has a significantly reduced PAPR compared to the impulse pilot. This is achieved by spreading the pilot power along the delay dimension using a constant amplitude Zadoff-Chu (ZC) sequence with a cyclic prefix (CP). We analytically derive upper bound PAPR expressions for the impulse pilot and the proposed PCP. Together with our numerical results, these upper bounds attest the significant PAPR improvement that is achieved by PCP. We also develop a two-stage channel estimation technique with a superior performance to the threshold-based channel estimation for the impulse pilot. At the first stage, the channel is estimated by a linear estimator under the assumption of the channel being locally linear time invariant over each time-slot within the OTFS block. Taking advantage of the benefits that are offered by the CP in our proposed pilot structure, we develop a low complexity least squares based estimator for implementation of the first stage. At the second stage, we use the channel estimate from the first stage and the generalized complex exponential basis expansion model (GCE-BEM) to accurately estimate the full channel. Finally, we numerically analyse and show the superior estimation performance of our proposed channel estimator for PCP to the threshold-based estimator for the impulse pilot.

In this paper, we consider the problem of joint estimation and equalization of doubly selective channels and all radio frequency impairments, namely transmitter IQ imbalance (TIQI), receiver IQI (RIQI) and carrier frequency offsets (CFO) in the uplink of single carrier frequency division multiple access (SC-FDMA) and orthogonal frequency division multiple access (OFDMA) systems with direct conversion transceiver architecture and high mobility users. We combine the effect of TIQI, RIQI and DSC to a new effective channel and propose the use of a Hermite polynomial based basis expansion model for approximating it to avoid the identifiability issue associated with this complete parameter estimation problem. As the maximum likelihood solution to this joint estimation problem requires complex multi-dimensional searches, we propose a novel subspace nulling based iterative estimation technique that effectively reduces the multi-user interference and replaces the multi-dimensional search with single-dimensional searches. Further, without much compromise on the performance, we also derive a low complexity version of the proposed technique. Additionally, we derive the Cramer-Rao bound for the joint estimation of CFO and effective channel. Moreover, we propose two equalization techniques for iteratively equalizing the mirror subcarrier pairs. The proposed techniques do not put any restriction on the carrier assignment scheme and provide good performance even at high mobile speeds.