Bayesian Learning Aided Sparse Channel Estimation for Orthogonal Time Frequency Space Modulated Systems

Srivastava, Suraj; Singh, Rahul Kumar; Jagannatham, Aditya K.; Hanzo, Lajos

doi:10.1109/tvt.2021.3096432

Cited by 36 publications

(19 citation statements)

References 15 publications

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“…In the Delay-Doppler domain, due to the transmit symbol arrangement in (14), the received pilot symbols can be expressed in the same way as (12), where k…”

Section: Problem Formulationmentioning

confidence: 99%

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Sparse channel estimation algorithms for OTFS system

et al. 2022

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Orthogonal time-frequency space (OTFS) modulation, which has recently been proposed in the literature, is one of the promising techniques designed in the 2D Delay-Doppler domain adapted to combat high Doppler fading channels. However, channel estimation in high Doppler scenarios in advanced mobile-communication systems is still a challenging task. In this paper, the problem of channel estimation in the Delay-Doppler domain of the OTFS is focused on. First, a simple adaptation of the generalized orthogonal matching pursuit procedure, which will serve as a baseline method in this work, is proposed. Then, iterative algorithms are derived beneficiating from the sparsity of the channel. The unknown channel vector is separated into an unknown sparse support vector corresponding to the delay and Doppler taps, and an unknown vector of channel gains. These algorithms involve 𝓁 1 -norm minimization and a two-stage iterative procedure to recover alternatively the channel support and its coefficients. The estimation problem is also addressed from a Bayesian point of view. The sparse representation is reformulated as a specific marginalization of the maximum a posteriori problem on the support of the channel. To deal with the intractability of this problem, two existing techniques are adapted to this context, namely: The Monte Carlo Markov chain with the Gibbs sampler and variational mean-field approximation with the variational Bayesian expectation-maximization procedure. Finally, to assess the performance of the proposed algorithms, their complexity and performance are compared against existing methods. Experimental tests, conducted in high-mobility scenarios and low-latency applications, show that the proposed schemes are slightly more expensive in terms of complexity load but perform significantly better in terms of normalized mean square error and bit error rate.

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“…In the Delay-Doppler domain, due to the transmit symbol arrangement in (14), the received pilot symbols can be expressed in the same way as (12), where k…”

Section: Problem Formulationmentioning

confidence: 99%

“…In [12], a Bayesian learning-aided sparse CE scheme for OTFS modulated systems are featured. The pilots are directly transmitted over the time-frequency domain grid for estimating the Delay-Doppler domain channel state information (CSI).…”

Section: Introductionmentioning

confidence: 99%

Sparse channel estimation algorithms for OTFS system

et al. 2022

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“…This problem is further exacerbated in MIMO OTFS systems, especially for a large number of antennas, since one has to place multiple guard intervals at each transmit antenna. The recent proposal in [31] and its MIMO extension [32] have addressed this issue by considering TF-domain pilots, where the pilot symbols of all the transmit antennas are transmitted in a common TF resource block, thereby leading to a significant reduction in the pilot overhead.…”

Section: A Literature Reviewmentioning

confidence: 99%

“…where w P,v ∈ C Np,2×1 represents the noise vector comprising the N p,2 samples of the combined noise at the vth RF chain. Using (31), the DD-domain sparse CSI estimation model of estimating the equivalent channel Hp , similar to (20), can be formulated as…”

Section: B Stage-2 (F Rf Design and Equivalent Sparse Dd-domain Csi E...mentioning

confidence: 99%

OTFS Transceiver Design and Sparse Doubly-Selective CSI Estimation in Analog and Hybrid Beamforming Aided mmWave MIMO Systems

Srivastava

Singh

Jagannatham

et al. 2022

IEEE Trans. Wireless Commun.

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Orthogonal time frequency space (OTFS) waveform based millimeter wave (mmWave) MIMO systems are capable of achieving high data rates in high-mobility scenarios. Hence, transceivers are designed for both analog beamforming (AB) and hybrid beamforming (HB), where we commence by deriving the delay-Doppler (DD)-domain input-output relationship considering a delay-Doppler-angular domain channel model. Subsequently, a novel two-stage procedure is developed for transmit beamformer (TBF)/ precoder (TPC) and receiver combiner (RC) design, and for estimating the DD-domain's equivalent channel state information (CSI). The key feature of the proposed framework is that the RF TBF/ TPC and RC design maximizes the directional beamforming gains. It is also demonstrated that the low-dimensional baseband CSI of the DD-domain becomes sparse for mmWave-AB MIMO OTFS systems, and blocksparse for mmWave-HB MIMO OTFS systems. Subsequently, Bayesian learning (BL) and block-sparse BL (BS-BL) solutions are developed for improved CSI estimation. We also derive the Bayesian Cramer-Rao lower bounds (BCRLB) for benchmarking the mean-squared-error (MSE) of the CSI estimates. Finally, our simulation results demonstrate the improved efficacy of the proposed transceiver designs and confirm the enhanced CSI estimation performance of the BL-based schemes over other competing sparse signal recovery schemes.

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“…The existing treatises, which address channel estimation in OTFS systems, can be broadly classified into two categories: 1) Approaches that exploit the 2-dimensional (2D)-circular convolution based relationship [1], [9], [11] between the transmit symbols and the channel in the DD-domain; 2) Alternative schemes that benefit from the limited number of dominant multipath components, i.e., the DD-domain sparsity [10], [12], [13]. The initial solutions of [1], [11] developed impulse-based CSI estimation techniques for SISO OTFS systems, which were then extended to MIMO OTFS in [14].…”

Section: A Literature Surveymentioning

confidence: 99%

Delay-Doppler and Angular Domain 4D-Sparse CSI Estimation in OTFS Aided MIMO Systems

Srivastava

Singh

Jagannatham

et al. 2022

IEEE Trans. Veh. Technol.

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A convenient delay, Doppler and angular-(DDA) domain representation of the multiple-input multiple-output (MIMO) wireless channel is conceived for deriving the end to end relationship in the delay-Doppler (DD)-domain for orthogonal time frequency space (OTFS)-based communications. Subsequently, a time-domain pilot based model is developed for estimating the DDA-domain channel state information (CSI) of our MIMO OTFS system. The key differentiating feature of the CSI estimation model derived is its ability to exploit the 4-dimensional (4D)-sparsity arising in the DDA-domain, given the limited number of dominant scatterers. Furthermore, the training overhead of the proposed framework is low, and the pilot placement is quite flexible, necessitating no guard-interval. Finally, an orthogonal matching pursuit (OMP) framework is employed for 4D-sparse CSI acquisition, followed by deriving the Oracle minimum mean squared error (Oracle-MMSE) and its Bayesian Cramer-Rao lower bound (BCRLB). Our simulation results confirm the improved CSI estimation performance attained over the benchmarks.

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Bayesian Learning Aided Sparse Channel Estimation for Orthogonal Time Frequency Space Modulated Systems

Cited by 36 publications

References 15 publications

Sparse channel estimation algorithms for OTFS system

Sparse channel estimation algorithms for OTFS system

OTFS Transceiver Design and Sparse Doubly-Selective CSI Estimation in Analog and Hybrid Beamforming Aided mmWave MIMO Systems

Delay-Doppler and Angular Domain 4D-Sparse CSI Estimation in OTFS Aided MIMO Systems

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