OTFS分数多普勒信道估计与检测论文整理2（摘要）

写在前面：该文写于2023.6.1，整理了IEEE上最新OTFS方面（大多为2023年发表）顶刊论文，主要涉及到分数多普勒问题（一共44篇，每次更新5篇）。写文的初衷是为了理解分数多普勒的问题背景，并了解现有针对分数多普勒问题的一些成熟解决方案，因此在时间有限的前提下只针对摘要核心部分（问题背景、解决方法、简要细节）做出翻译（关于翻译的准确性仅供参考，对于不准确的地方欢迎指正），并对摘要中核心的部分进行标红或划线处理，同时对英文摘要进行拆分，方便大家快速找到所需要的内容，摘要最后写了总结，大多为概括以及本人的一些简单想法。

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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
原文：
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.

翻译：

基于消息传递的稀疏结构信号恢复方法用于分数多普勒频移OTFS信道估计 摘要：正交时频空调制是高移动性场景下的有前景的调制方案。在未来的无线通信中，为了实现低时延的要求，OTFS块的时间长度将会减小，因此必须考虑分数多普勒频偏以避免整数多普勒假设带来的建模误差。然而，目前的论文中大多缺乏关于考虑分数多普勒频偏的OTFS信道估计方面的研究。在本文中，我们提出了一个特别考虑分数多普勒偏移的OTFS信道估计方法，同时也考虑了双正交波形和矩形波形。相反，我们并没有在DD域直接进行信道估计，而是先在DD域信道中估计了信道增益与分数多普勒偏移等参数。估计算法方面，我们建模成一个引入贝叶斯方法的稀疏信号恢复的问题。通过将问题进行因子图表示，引入了一个有效的消息传递算法去恢复（OTFS信道的）稀疏信号结构。最后，推导了克拉美-罗下界并通过仿真实验证明算法有效性。

总结：引入贝叶斯稀疏信号表示、因子图、消息传递等算法，以解决考虑分数多普勒的OTFS信道估计问题。

二、论文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

原文：
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.

翻译：

用于OTFS分数多普勒信道的两阶段信道估计方法 摘要：正交时频空调制是高移动性场景下的有前景的调制方案。然而，分数多普勒问题带来了IDI（多普勒间干扰），使得信道估计性能下降。该论文提出了适用于分数多普勒信道的两阶段估计算法。在第一阶段，通过基函数在DD域的相关性得到一个初步的非零多普勒频移。第二阶段引入拟牛顿法，在先前估计的基础上迭代得到分数多普勒的新的估计值，从而大幅降低由于IDI产生的估计误差。性能分析表明，与基本算法相比可以达到更低的NMSE同时，在误码性能方面与完美信道估计性能接近。

总结：将信道估计问题分成两个阶段进行， 先通过相关预算得到一个初步的多普勒频移，再引入拟牛顿法通过迭代进一步更新估计值，仿真表明在NMSE和BER方面均有较好效果。

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.

翻译：

考虑分数多普勒的OTFS系统有效信道估计 摘要：该论文提出了一个考虑分数多普勒的有效的信道估计算法。该算法首先设置了一个基于现有阈值的估计器以获得有效的信道响应。由于已知有效的信道矩阵（可能翻译的不准确），然后我们使用线性系统去恢复不同可分解路径的多普勒频移以及信道增益。在这一过程中，我们考虑了不同路径间的干扰。性能分析表明，通过在有效信道矩阵中选择合理的样本，即使在低信噪比条件下也可以实现多普勒频移和信道增益的初步估计。

四、论文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)

原文：
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.

翻译：

用于OTFS调制的混合消息传递检测算法 正交时频空调制是高移动性场景下的有前景的调制方案。为实现在全时间和全频率分集，目前已有一些优秀的检测器。由于分数多普勒的存在对于检测器的性能和复杂度方面提出新的挑战。该论文提出了一个混合消息传递方法实现考虑分数多普勒的OTFS信号检测。基于这一系统模型，该论文推导了OTFS检测器的概率模型并用因子图进行表示。对于同一个多普勒值，我们选择增益最大的路径作为主径（方便后续分别使用对应算法）。其中，对于主径使用非近似消息传递算法而对于剩余路径使用基于高斯近似的MP算法。

总结：引入混合MP算法，其“混合”在于对于主径和非主径分别用不同算法进行分析。

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.

翻译：

考虑分数时延-多普勒场景的低复杂度OTFS信道估计方法 摘要：该论文提出了一个低复杂度的信道估计方法用于基于系统的OTFS调制。关于OTFS调制主要从两个重要方面考虑：(i) 选定一个好的时延-多普勒分辨率从而实现路径分离。(ii) 有效DD域信道增益的表达式分为时域和多普勒域的形式，接着提出一个迭代信道估计方法分别估计时延和多普勒频移以及每条路径的信道增益。仿真结果表明，所提算法不需要矩阵求逆因此复杂度更低。同时在NMSE方面性能更优。

总结：首先实现时延-多普勒的路径分离，再引入迭代算法分别估计三个参数：时延、多普勒频移以及信道增益。