5G-NTN低轨卫星通信中载波频偏和采样频偏低复杂度联合估计算法

龚险峰; 李颖; 刘明洋; 翟盛华

doi:10.11999/JEIT251086

5G-NTN低轨卫星通信中载波频偏和采样频偏低复杂度联合估计算法

doi: 10.11999/JEIT251086 cstr: 32379.14.JEIT251086

龚险峰^{1, 2},
李颖^1, ,,
刘明洋^{1, 2},
翟盛华²

1.
西安电子科技大学通信工程学院西安 710071
2.
中国空间技术研究院西安分院西安 710010

基金项目: 国家自然科学基金(62131016, 62471363)

详细信息

作者简介:
龚险峰：男，博士生，研究方向为宽带通信卫星载荷设计、卫星5G/6G通信技术

李颖：女，教授，研究方向为大规模随机多址接入、智能信号处理与传输技术

刘明洋：男，博士生，研究方向为深空通信技术、宽带通信技术

翟盛华：男，研究员，研究方向为卫星通信系统设计、通信信号处理技术

通讯作者:
李颖　yli@mail.xidian.edu.cn

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出版历程
- 修回日期: 2025-12-02
- 录用日期: 2025-12-02
- 网络出版日期: 2025-12-05

Low-Complexity Joint Estimation Algorithm for Carrier Frequency Offset and Sampling Frequency Offset in 5G-NTN Low Earth Orbit Satellite Communications

GONG Xianfeng^{1, 2},
LI Ying^{1
, ,},
LIU Mingyang^{1, 2},
ZHAI Shenghua²

1.
School of Telecommunications Engineering, Xidian University, Xi’an 710071, China
2.
China Academy of Space Technology (CAST)-Xi’an Institute of Space Radio Technology, Xi’an 710010, China

Funds: The National Natural Science Foundation of China(62131016, 62471363)

摘要

摘要: 在5G非地面网络(5G-NTN)低轨卫星通信系统中，多普勒效应会带来载波频偏(CFO)、采样频偏(SFO)以及子载波间频偏(ISFO)。研究发现，当正交频分复用(OFDM)信号子载波数量较大且采用高阶调制时，ISFO会成为制约接收机性能的关键因素。现有算法多针对CFO和SFO的估计及补偿展开研究，极少考虑ISFO的影响。另外，采用传统的最大似然估计算法对CFO和SFO进行联合估计时，需要进行一维或二维网格搜索，计算复杂度非常高。针对上述问题，本文利用5G-NTN中导频信号的分布特点，提出了两种低复杂度的CFO和SFO联合估计算法。首先，利用5G-NTN中解调参考信号的互相关向量在主瓣内的单峰特性，设计了一种基于二分搜索的联合估计算法，可以实现快速收敛。然后，设计了基于观测量自相关的L&R估计算法，推导了待估参数的近似闭式解。典型实例分析和仿真表明，两种算法性能接近采用一维或二维搜索的最大似然估计算法，且所提二分搜索估计算法运算量仅为二维搜索最大似然估计算法的4%、一维搜索最大似然估计算法的44%。
- 5G非地面网络 /
- 低轨卫星通信 /
- 多普勒效应 /
- 子载波间频偏
Abstract: Objective The Doppler effect presents a major impairment in Low Earth Orbit (LEO) satellite communications within 5G Non-Terrestrial Networks (5G-NTN), introducing Carrier Frequency Offset (CFO), Sampling Frequency Offset (SFO), and Inter-Subcarrier Frequency Offset (ISFO) across subcarriers. Although existing estimation algorithms focus mainly on CFO and SFO, the effect of ISFO remains inadequately addressed. ISFO becomes particularly detrimental to receiver performance when OFDM systems utilize a large number of subcarriers and high-order modulation. Moreover, under joint CFO and SFO conditions, conventional maximum likelihood estimation (MLE) methods often involve one- or two-dimensional grid searches, incurring high computational complexity. To mitigate these issues, this paper proposes two novel joint estimation algorithms for CFO and SFO. Methods This paper analyzes the influence of non-ideal factors at the transmitter, receiver, and channel, such as local oscillator offset, sampling frequency offset in Digital-to-Analog and Analog-to-Digital converters, and Doppler effect. A mathematical model for the received OFDM signal is developed, and the mechanism through which SFO and ISFO distort the phase of frequency-domain subcarriers is derived. Leveraging the pilot structure of 5G-NTN, two joint CFO and SFO estimation algorithms are introduced: (1) Algorithm 1 exploits the sequence correlation between the received frequency-domain DMRS signal vectors, denoted as and . After phase pre-compensation is applied to , the normalized cross-correlation vector is computed. An objective function is constructed based on this vector, and its unimodal property within the main lobe is utilized to efficiently estimate the parameters via a bisection search. (2) Algorithm 2 treats the estimation parameters as analogous to carrier frequency offsets in single-carrier systems and adopts an L&R-based autocorrelation approach to derive approximate closed-form expressions. Results and Discussions A computational complexity analysis is performed comparing the proposed algorithms with conventional one-dimensional (1D-ML) and two-dimensional (2D-ML) grid-search MLE methods. Numerical results demonstrate that Algorithm 1 achieves substantial complexity reduction. Specifically, the number of complex multiplications—the dominant computational cost—is only 4% of that of the 2D-ML method, 8% of that of Algorithm 2, and 44% of that of the 1D-ML method. Although Algorithm 2 is computationally heavier, it provides a closed-form estimation expression. The performance of each algorithm is evaluated in terms of the mean square error (MSE) of the estimated parameters. Simulations show that for a subcarrier number of 3072, the 1D-ML algorithm slightly outperforms others at SNRs below 5 dB. However, since robust modulation schemes (e.g., BPSK, QPSK) typically used at low SNRs can tolerate larger offsets, the medium-to-high SNR regime is of greater practical interest, where all four algorithms exhibit comparable estimation performance. Conclusions This paper addresses the impact of Doppler effect in 5G-NTN LEO satellite communications by analyzing the mechanism and influence of ISFO and proposing two joint estimation algorithms for CFO and SFO. First, a mathematical model of the received signal is established considering non-ideal factors such as CFO, SFO, and ISFO. It is derived that the combined effect of SFO and ISFO on OFDM signals is equivalent to their linear superposition, effectively expanding the range of the equivalent SFO. Second, the objective function is defined using the cross-correlation vector of two DMRS sequences. Leveraging its unimodal characteristic within the main lobe, a binary search algorithm is employed to achieve rapid convergence. Subsequently, the parameter to be estimated—determined by SFO and ISFO—is analogized to the carrier frequency offset in single-carrier systems. An approximate closed-form solution for parameter estimation is derived using the L&R algorithm. Finally, complexity analysis and performance simulations are conducted. The results demonstrate that the proposed algorithms not only significantly reduce computational complexity but also exhibit excellent estimation performance. The outcomes of this research can be applied to the development of 5G-NTN LEO satellite payloads and terminal products, demonstrating promising potential for widespread application.
- 5G Non-Terrestrial Networks (5G-NTN) /
- Low Earth Orbit (LEO) satellite communications /
- Doppler effect /
- Inter-Subcarrier Frequency Offset (ISFO)

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图 1 多普勒效应导致的ISFO

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图 2 低轨卫星通信系统模型

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图 3 DMRS信号在时域和频域的分布

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图 4 算法1搜索过程示意图

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图 5 参数$ \alpha $的估计MSE

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图 6 参数$ {\varepsilon }_{0} $的估计MSE

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图 7 不同子载波数量和MCS下的解调损失

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1 二分搜索估计算法

输入：$ {\boldsymbol{Y}}_{M1} $，$ {\boldsymbol{Y}}_{M2} $，$ \rho $，$ {k}_{0} $，$ d $，$ I $，$ {\alpha }_{\max } $，$ N{}_{\text{fi}} $
1：if $ \rho dI{\alpha }_{\max } > 2text{π} $ then
2：　确定粗搜索次数：$ {N}_{\text{co}}=2\times \left\lceil \rho dI{\alpha }_{\max }/(2text{π} )\right\rceil $，并设置　　　 $ \boldsymbol{Z}={[Z(1),Z(2),\cdots ,Z({{N}_{\text{co}}})]}^{\mathrm{T}} $；
3：　for $ l=1\cdots {N}_{\text{co}} $ do
4：　　获取粗搜索点：$ \beta =2text{π} (l-({N}_{\text{co}}+1)/2)/(\rho dI) $；
5：　　根据公式(10)～公式(12)依次计算$ {\mathbf{\tilde{\boldsymbol{Y}}}}_{\text{M2}} $、$ \boldsymbol{R}(\beta ) $和$ f(\beta ) $，　　　　并将$ f(\beta ) $存入$ Z(l) $中；
6：　end
7：　搜索得到$ \boldsymbol{Z} $中最大值的序号$ {l}_{\max } $，计算粗估计值　　　 $ {\overline{\alpha }}_{mid}=2text{π} ({l}_{\max }-({N}_{\text{co}}+1)/2)/(\rho dI) $；
8：else
9：　粗估计值$ {\overline{\alpha }}_{mid}=0 $；
10：end
11：确定精搜索的初始基准点$ \gamma ={\overline{\alpha }}_{mid} $及步进$ \Delta =text{π} /(\rho dI) $；
12：for $ n=1\cdots N{}_{\text{fi}} $ do
13： if $ f(\gamma +\Delta ) > f(\gamma -\Delta ) $ then
14：　调整基准点和步进：$ \gamma =\gamma +\Delta $，$ \Delta =\Delta /2 $；
15： else
16：　调整基准点和步进：$ \gamma =\gamma -\Delta $，$ \Delta =\Delta /2 $；
17： end
18：end
19：计算多普勒参数估计值：$ \overline{\alpha }=\gamma $，　　　 $ {\overline{\varepsilon }}_{0}=\arctan (\displaystyle\sum\nolimits_{i=0}^{I-1}{R}_{i}(\overline{\alpha }))/\rho $；
输出：$ \overline{\alpha } $，$ {\overline{\varepsilon }}_{0} $

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表 1 算法复杂度比较

算法名称	复数乘	实数乘	复数加
本文算法1	73728	36864	36864
本文算法2	893568	4608	768
2D-ML算法	1658880	0	829440
1D-ML算法	165888	0	82944

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表 2 仿真系统参数

参数名称	参数值
子载波数量($ K $)	768(64RB)、3072(256RB)
导频子载波间隔($ d $)	2
DMRS信号序号	M1=2，M2=6
SFO($ \eta $)	30 ppm
CFO($ {\varepsilon }_{0} $)	0.02
ISFO($ \Delta \varepsilon $)	24 ppm
信道类型	AWGN
编码调制方式	MCS10(BPSK、码率308/1024)、 MCS25(16QSK、码率873/1024)
天线配置	SISO

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