OTFS Fractional Doppler Channel Estimation and Detection Paper Collection 2 (Abstract)

Written in front: This article was written on June 1, 2023, and compiled the latest top papers on OTFS in IEEE (mostly published in 2023), mainly related to the fractional Doppler problem (44 papers in total, 5 papers updated each time). The original intention of writing this article is to understand the background of the fractional Doppler problem and to understand some of the existing mature solutions to the fractional Doppler problem. Therefore, under the premise of limited time, I only focus on the core parts of the abstract (problem background, solution, Brief details) make a translation (the accuracy of the translation is for reference only, any inaccuracies are welcome to be corrected), and the core parts of the abstract are marked in red or underlined, and the English abstract is split for everyone's convenience Quickly find the content you need. At the end of the abstract, I write a summary, which is mostly a summary and some of my simple thoughts.

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一、论文6：Message Passing-Based Structured Sparse Signal Recovery for Estimation of OTFS Channels With Fractional Doppler Shifts

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Message Passing-Based Structured Sparse Signal Recovery for Estimation of OTFS Channels With Fractional Doppler Shifts
Liu, Fei and Yuan, Zhengdao and Guo, Qinghua and Wang, Zhongyong and Sun, Peng
2021 Dec
IEEE Transactions on Wireless Communications
original:
背景：The orthogonal time frequency space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To enable efficient OTFS detection in the delay-Doppler (DD) domain, the DD domain channels need to be acquired accurately. 问题背景：To achieve the low latency requirement in future wireless communications, the time duration of the OTFS block should be small, therefore fractional Doppler shifts have to be considered to avoid significant modelling errors due to the assumption of integer Doppler shifts. However there lack investigations on the estimation of OTFS channels with fractional Doppler shifts in the literature. 本文方法：In this work, we develop a channel estimator for OTFS with particular attention to fractional Doppler shifts, and both bi-orthogonal waveform and rectangular waveform are considered. Instead of estimating the DD domain channel directly, we estimate the channel gains and (fractional) Doppler shifts that parameterize the DD domain channel. 算法细节：The estimation is formulated as a structured sparse signal recovery problem with a Bayesian treatment. Based on a factor graph representation of the problem, an efficient message passing algorithm is developed to recover the structured sparse signal (thereby the OTFS channel). The Cramer-Rao Lower Bound (CRLB) for the estimation is developed and the effectiveness of the algorithm is demonstrated through simulations.

translate:

Message passing-based sparse structure signal recovery method for fractional Doppler shift OTFS channel estimation Abstract: Orthogonal time-frequency air conditioning is a promising modulation scheme in high mobility scenarios. In future wireless communications, in order to achieve low latency requirements, the time length of the OTFS block will be reduced, so fractional Doppler frequency offset must be considered to avoid modeling errors caused by the integer Doppler assumption. However, most current papers lack research on OTFS channel estimation considering fractional Doppler frequency offset. In this paper, we propose an OTFS channel estimation method that specifically considers fractional Doppler shifts, while also considering biorthogonal and rectangular waveforms. On the contrary, we did not directly estimate the channel in the DD domain, but first estimated parameters such as channel gain and fractional Doppler shift in the DD domain channel. In terms of estimation algorithm, we model it as a sparse signal recovery problem that introduces Bayesian method. By representing the problem as a factor graph, an effective message passing algorithm is introduced to recover the sparse signal structure (of the OTFS channel). Finally, the Cramer-Rod lower bound is derived and the effectiveness of the algorithm is proved through simulation experiments.

Summary: Bayesian sparse signal representation, factor graph, message passing and other algorithms are introduced to solve the OTFS channel estimation problem considering fractional Doppler.

2. Paper 7: A Two-stage Channel Estimation Algorithm for OTFS in Fractional Doppler Channels

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A Two-stage Channel Estimation Algorithm for OTFS in Fractional Doppler Channels
He, Xiaolin and Fan, Pingzhi and Wang, Qianli
2023
IEEE Communications Letters

original:
背景：Orthogonal time-frequency space (OTFS) modulation is a promising modulation technology, which can provide superior performance under high-mobility radio scenarios. 问题背景：However, fractional Doppler shift brings inter-Doppler interference (IDI), leading to performance deterioration of channel estimation. 本文方法：This paper proposes a two-stage algorithm for estimating the fractional Doppler channels.算法细节： In the first stage, a rough position of each nonzero Doppler shift is estimated through the correlation of the basis function in the delay-Doppler (DD) domain. In the second stage, a quasi-Newton method is employed to iteratively re-estimate the fractional Doppler channel based on the prior estimation, thus resulting in significantly reduced estimation error caused by the IDI. 性能分析：Simulation results demonstrate that the proposed algorithm for channel estimation can achieve a much lower normalized mean square error (NMSE) than the baseline algorithms. Moreover, the achieved bit error rate (BER) is very close to that of perfect channel estimation.

translate:

Two-stage channel estimation method for OTFS fractional Doppler channel Abstract: Orthogonal time-frequency air conditioning is a promising modulation scheme in high mobility scenarios. However, the fractional Doppler problem brings IDI (Inter-Doppler Interference), which degrades channel estimation performance. This paper proposes a two-stage estimation algorithm suitable for fractional Doppler channels. In the first stage, a preliminary non-zero Doppler frequency shift is obtained through the correlation of the basis functions in the DD domain. In the second stage, the quasi-Newton method is introduced to iteratively obtain a new estimate of fractional Doppler based on the previous estimate, thus significantly reducing the estimation error caused by IDI. Performance analysis shows that compared with the basic algorithm, it can achieve lower NMSE and at the same time, it is close to the perfect channel estimation performance in terms of bit error performance.

Summary: The channel estimation problem is divided into two stages. First, a preliminary Doppler frequency shift is obtained through the relevant budget, and then the quasi-Newton method is introduced to further update the estimated value through iteration. The simulation shows that it has good results in both NMSE and BER. .

三、论文8：Efficient Channel Estimation for OTFS Systems in the Presence of Fractional Doppler

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Efficient Channel Estimation for OTFS Systems in the Presence of Fractional Doppler
Li, Zhongjie and Yuan, Weijie and You, Changsheng and Cui, Yuanhao
2023 March
2023 IEEE Wireless Communications and Networking Conference (WCNC)

原文：
本文算法：In this paper, we propose an efficient channel estimation algorithm for orthogonal time frequency space (OTFS) systems in the presence of fractional Doppler.算法细节： The proposed algorithm first employs the well-known threshold-based estimator to obtain the effective channel response. With the effective channel matrix in hand, we then utilize the linear system to recover the Doppler shifts and channel gains of different resolvable paths. The interference between different paths is also considered. 性能分析：Our simulation results verify that, by selecting appropriate samples in the effective channel matrix, the Doppler shifts and channel gains can be estimated robustly even in poor signal-to-noise ratio (SNR) conditions.

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Effective channel estimation of OTFS system considering fractional Doppler Abstract: This paper proposes an efficient channel estimation algorithm considering fractional Doppler. The algorithm first sets an estimator based on existing thresholds to obtain an effective channel response. Since the effective channel matrix is ​​known (possibly translated inaccurately), we then use a linear system to recover the Doppler shifts and channel gains for different decomposable paths. In this process, we consider the interference between different paths. Performance analysis shows that by selecting reasonable samples in the effective channel matrix, preliminary estimates of Doppler shift and channel gain can be achieved even under low signal-to-noise ratio conditions.

4. Paper 9: Hybrid Message Passing Detection for OTFS Modulation

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Hybrid Message Passing Detection for OTFS Modulation
Li, Xiang and Yuan, Weijie and Li, Zhongjie
2023 March
2023 IEEE Wireless Communications and Networking Conference (WCNC)

original:
背景：Orthogonal time frequency space (OTFS) modulation which multiplexes data symbols in the delay Doppler (DD) domain has been proved to be an effective scheme for high-mobility scenarios. To realize the full time and frequency diversity promised, some promising detectors have been developed. The existence of fractional Doppler imposes new challenges to the performance and complexity of the detector. 本文方法：In this paper, we proposed a hybrid message passing detector for OTFS in the presence of the fractional OTFS. Based on the system model, we derive the probabilistic model of OTFS detector and represent it by a factor graph. For one Doppler index, we choose the path with the highest gain which is referred to as the main path. Then, a hybrid message passing (MP) scheme is developed, where we apply the non-approximate MP algorithm for the main paths while the Gaussian approximation-based MP algorithm is executed for the remaining paths.

translate:

Hybrid messaging detection algorithm for OTFS modulation Orthogonal time-frequency air conditioning is a promising modulation scheme in high mobility scenarios. In order to achieve full-time and full-frequency diversity, there are currently some excellent detectors. The existence of fractional Doppler poses new challenges in terms of detector performance and complexity. This paper proposes a hybrid message passing method to implement OTFS signal detection considering fractional Doppler. Based on this system model, this paper derives the probabilistic model of the OTFS detector and represents it with a factor graph. For the same Doppler value, we select the path with the largest gain as the main path (to facilitate the subsequent use of corresponding algorithms). Among them, the non-approximate message passing algorithm is used for the main path and the MP algorithm based on Gaussian approximation is used for the remaining paths.

Summary: The hybrid MP algorithm is introduced, and its "hybrid" lies in using different algorithms to analyze the main path and non-main path.

五、论文10:A Low Complexity OTFS Channel Estimation Method For Fractional Delay-Doppler Scenarios

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A Low Complexity OTFS Channel Estimation Method For Fractional Delay-Doppler Scenarios
Khan, Imran Ali and Mohammed, Saif Khan
2023
IEEE Wireless Communications Letters

原文：
本文方法：We propose a low-complexity channel estimation method for Orthogonal Time Frequency Space (OTFS) modulation based systems. 算法细节：Two important aspects of OTFS modulation, namely, (i) fine delay-Doppler (DD) resolution which results in path separation and, (ii) the separability of the effective DD domain channel gain| expression into delay domain and Doppler domain terms, are used to propose an iterative channel estimation method which separately estimates the delay, Doppler shift and the channel gain for each channel path. 性能分析：The proposed estimation does not require matrix inversion and therefore has lower complexity when compared to other known methods. The proposed method is shown to achieve a normalized mean square estimation error (NMSE) performance better than other methods.

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A low-complexity OTFS channel estimation method considering fractional delay-Doppler scenarios Abstract: This paper proposes a low-complexity channel estimation method for system-based OTFS modulation. Regarding OTFS modulation, there are two important aspects to consider: (i) Selecting a good delay-Doppler resolution to achieve path separation. (ii) The expression of the effective DD domain channel gain is divided into time domain and Doppler domain forms, and then an iterative channel estimation method is proposed to estimate the delay and Doppler frequency shift as well as the channel gain of each path respectively. Simulation results show that the proposed algorithm does not require matrix inversion and therefore has lower complexity. At the same time, the performance is better in NMSE.

Summary: First implement delay-Doppler path separation, and then introduce an iterative algorithm to estimate three parameters: delay, Doppler frequency shift and channel gain.