Written in front: This article was written on July 27, 2023. It compiles 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) are translated, and the core parts of the abstract are marked in red or underlined. At the same time, the English abstract is split to facilitate everyone to quickly find the content they need. At the end of the abstract, a summary is written, which is mostly a summary summary and Some simple thoughts or questions of mine.
OTFS considers fractional Doppler channel estimation and detection related papers collection 3 (Abstract)
- 1. Paper 11: A Novel OTFS System Based on DFrFT-OFDM
- 二、论文12:Channel Estimation and Equalization for CP-OFDM-based OTFS in Fractional Doppler Channels
- 三、论文13：Deterministic Pilot Design and Channel Estimation for Downlink Massive MIMO-OTFS Systems in Presence of the Fractional Doppler
- 四、论文14:Embedded Delay-Doppler Channel Estimation for Orthogonal Time Frequency Space Modulation
- 五、论文15:Low-Complexity Channel Matrix Calculation for OTFS Systems with Fractional Delay and Doppler
1. Paper 11: A Novel OTFS System Based on DFrFT-OFDM
10
Mallaiah, Renikunta and Mani, V. V. 2022 June
IEEE Wireless Communications Letters
original:
背景：Orthogonal Time Frequency Space modulation (OTFS) is a promising modulation technique expected to counter the severe Doppler effects encountered in a doubly dispersive channel. OTFS scheme is developed on the basis of Orthogonal Frequency Division Multiplexing (OFDM) systems to support communication between high-speed vehicles, whose superiority lies in the domain of the equivalent channel. OTFS converts the Time-Frequency (TF) domain channel in the OFDM system to Delay-Doppler (DD) domain channel that becomes a handy tool to overcome the difficulties faced in a frequency selective channel. 本文方法：This letter presents an OTFS system design that is developed on the Discrete Fractional Fourier Transform (DFrFT) based OFDM system, which is designed to perform better compared to the conventional OTFS system with the same design complexity. The simulation results evidentially show 1 dB gain in power at a Bit-Error-Rate (BER) of and a significant 3 dB decrement in the PAPR when a high power pilot with a 25 dB is inserted in the OTFS data frame.
translate:
Summary: The paper introduces the discrete fractional Fourier transform (DFrFT) based on the design of the OTFS system, which does not increase the complexity and has advantages in reducing PAPR.
二、论文12:Channel Estimation and Equalization for CP-OFDM-based OTFS in Fractional Doppler Channels
11
Hashimoto, Noriyuki and Osawa, Noboru and Yamazaki, Kosuke and Ibi, Shinsuke
2021 June
2021 IEEE International Conference on Communications Workshops (ICC Workshops)
original:
背景：Orthogonal time frequency and space (OTFS) modulation is a promising technology that satisfies high-Doppler requirements for future mobile systems. OTFS encodes information symbols and pilot symbols into the two-dimensional (2D) delay-Doppler (DD) domain. The received symbols suffer from inter-Doppler interference (IDI) in fading channels with fractional Doppler shifts sampled at noninteger indices in the DD domain. The IDI has been treated as an unavoidable effect because the fractional Doppler shifts cannot be obtained directly from the received pilot symbols. 本文方法：This paper provides a solution to channel estimation for fractional Doppler channels with lower computational complexity than a conventional channel estimation method using a pseudo sequence. The proposed estimation provides new insight into the OTFS input-output relation in the DD domain as a 2D circular convolution with a small approximation. According to the input-output relation, we also provide a low-complexity channel equalization method using the estimated channel information. 性能分析：We demonstrate the error performance of the proposed channel estimation and equalization in a high-Doppler channel by simulations. The simulation results show that the proposed channel estimation method outperforms the conventional channel estimation. The results also show that the proposed equalization method has a similar performance to the minimum mean square error equalizer using matrix inversion.
translate:
Summary: This paper aims at the IDI caused by the fractional Doppler influence, which is difficult to remove directly through the received pilot signal. It makes an approximation to the OTFS input-output relationship and proposes a low-cost calculation for the fractional Doppler channel. Complexity channel estimation method.
三、论文13：Deterministic Pilot Design and Channel Estimation for Downlink Massive MIMO-OTFS Systems in Presence of the Fractional Doppler
9
Shi, Ding and Wang, Wenjin and You, Li and Song, Xiaohang and Hong, Yi and Gao, Xiqi and Fettweis, Gerhard
2021 Nov
IEEE Transactions on Wireless Communications
original:
背景（OTFS与MIMO结合的意义与不足）：Although the combination of the orthogonal time frequency space (OTFS) modulation and the massive multiple-input multiple-output (MIMO) technology can make communication systems perform better in high-mobility scenarios, there are still many challenges in downlink channel estimation owing to inaccurate modeling and high pilot overhead in practical systems. 本文方法：In this paper, we propose a channel state information (CSI) acquisition scheme for downlink massive MIMO-OTFS in presence of the fractional Doppler, including deterministic pilot design and channel estimation algorithm. 算法细节（四点）：First, we analyze the input-output relationship of the single-input single-output (SISO) OTFS based on the orthogonal frequency division multiplexing (OFDM) modem and extend it to massive MIMO-OTFS. |Moreover, we formulate an accurate model for the practical system in which the fractional Doppler is considered and the influence of subpaths is revealed. A deterministic pilot design is then proposed based on the model and the structure of the pilot matrix to reduce pilot overhead and save memory consumption. Since channel geometry changes very slowly relative to the communication timescale, we put forward a modified sensing matrix based channel estimation (MSMCE) algorithm to acquire the downlink CSI. 性能分析：Simulation results demonstrate that the proposed downlink CSI acquisition scheme has significant advantages over traditional algorithms.
translate:
Summary: This paper studies the issues such as inaccurate modeling and high pilot overhead that may exist in MIMO-OTFS in actual systems. This paper proposes a downlink MIMO-OTFSCSI equalization scheme suitable for fractional Doppler. This solution makes improvements in four aspects: input-output relationship, accurate modeling, pilot design, and sensing matrix.
四、论文14:Embedded Delay-Doppler Channel Estimation for Orthogonal Time Frequency Space Modulation
14
Raviteja, P. and Phan, Khoa T. and Hong, Yi and Viterbo, Emanuele
2018 Aug
2018 IEEE 88th Vehicular Technology Conference (VTC-Fall)
original:
背景：hogonal time frequency space (OTFS) modulation was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) over delay-Doppler channels. The channel impulse response is needed at the receiver to perform OTFS detection. 本文方法：In this work, we analyze OTFS-based channel estimation using a pilot symbol embedded in the data frame: 嵌入式导频the pilot symbol with a number of guard zero-symbols is suitably located on the delay-Doppler grid containing the information symbols. Different symbol arrangements are proposed depending on whether the channel has integer or fractional Doppler paths relative to an integer grid. The channel information is first estimated from a group of received symbols using a simple 信道估计：threshold method. The estimated information is then used for data detection within the same frame, via a message passing (MP) algorithm. 性能分析：Numerical results compare the error performance of the proposed schemes and the OTFS scheme with ideal channel estimation under similar spectral and energy efficiency. Moreover, our results show that OTFS with non-ideal channel estimation can still outperform OFDM with ideal channel estimation.
translate:
Summary: This paper was carefully read in the previous blog , and the embedded pilot design was proposed, and the input-output relationship under integer/fractional Doppler was derived respectively. Channel estimation uses a simple threshold estimation method, and signal detection uses the MP algorithm.
五、论文15:Low-Complexity Channel Matrix Calculation for OTFS Systems with Fractional Delay and Doppler
17
Wang, Zheng and Liu, Lingjia and Yi, Yang and Calderbank, Robert and Zhang, Jianzhong
2022 Nov
MILCOM 2022 - 2022 IEEE Military Communications Conference (MILCOM)
original:
背景：Orthogonal Time Frequency Space (OTFS) modulation has been introduced to manage channel induced high Doppler shifts in mobile communication networks. In an OTFS system, the information carrying symbols are placed in the data frames in the delay-Doppler (DD) domain before transformed into the time domain for transmission. Accordingly, the DD domain channel matrix can be estimated using the corresponding pilots in the DD domain. For OTFS systems with integer delay and Doppler values, the underlying channel matrix in the DD domain is sparse. 问题：1.分数多普勒矩阵失去了稀疏性：However, the counterpart channel matrix is no longer sparse when the delay and Doppler values are fractional.2. 整数情况由于矩阵尺寸大仍是个耗时的问题： In fact, even for the integer case calculating the sparse channel matrix is still time-consuming due to its large size. 本文方法：To significantly reduce the computational complexity, in this paper, we introduce a low complexity algorithm for calculating the channel matrix of OTFS systems with fractional delay and Doppler. The introduced algorithm leverages the circulant property of the underlying channel matrix in the DD domain and calculates a small portion of elements in one initial block. Through some simple operation, the elements in the initial block can be replicated into other parts of the channel matrix. 性能分析：Both theoretical complexity analysis and simulation results demonstrate that our method can significantly reduce the computation complexity when computing the channel matrix. Since DD domain channel matrix is crucial for OTFS receive processing, we believe this is an important step to bring OTFS towards practical communication systems.
translate:
Summary: Due to the loss of sparsity of the channel matrix of OTFS in the DD domain under fractional Doppler, it becomes complicated. At the same time, the solution of the sparse channel matrix is still a time-consuming problem due to the large matrix size. Therefore, the paper captures the cyclic characteristics of OTFS and proposes a low-complexity (the initial block is continuously copied to obtain the complete matrix) OTFS fractional delay/Doppler channel matrix calculation method.