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

GONG Xianfeng; LI Ying; LIU Mingyang; ZHAI Shenghua

doi:10.11999/JEIT251086

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GONG Xianfeng, LI Ying, LIU Mingyang, ZHAI Shenghua. Low-Complexity Joint Estimation Algorithm for Carrier Frequency Offset and Sampling Frequency Offset in 5G-NTN Low Earth Orbit Satellite Communications[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT251086

Citation:

GONG Xianfeng, LI Ying, LIU Mingyang, ZHAI Shenghua. Low-Complexity Joint Estimation Algorithm for Carrier Frequency Offset and Sampling Frequency Offset in 5G-NTN Low Earth Orbit Satellite Communications[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT251086

Citation:

GONG Xianfeng, LI Ying, LIU Mingyang, ZHAI Shenghua. Low-Complexity Joint Estimation Algorithm for Carrier Frequency Offset and Sampling Frequency Offset in 5G-NTN Low Earth Orbit Satellite Communications[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT251086

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

doi: 10.11999/JEIT251086 cstr: 32379.14.JEIT251086

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)

Received Date: 2025-10-13
Accepted Date: 2025-12-02
Rev Recd Date: 2025-12-02

Available Online: 2025-12-05

Abstract

Abstract

Objective The Doppler effect is a major impairment in Low Earth Orbit (LEO) satellite communications within 5G Non-Terrestrial Networks (5G-NTN). It introduces 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 is insufficiently addressed. ISFO becomes highly detrimental to receiver performance when Orthogonal Frequency-Division Multiplexing (OFDM) systems use a large number of subcarriers and high-order modulation. Moreover, under joint CFO and SFO conditions, conventional Maximum Likelihood Estimation (MLE) methods often require one- or two-dimensional grid searches. This results in high computational cost. To reduce this cost, two joint estimation algorithms for CFO and SFO are proposed. Methods The influence of non-ideal factors at the transmitter, receiver, and channel, such as local oscillator offset, SFO in Digital-to-Analog Converters (DACs) and Analog-to-Digital Converters (ADCs), and the Doppler effect, is analyzed. 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 proposed. (1) Algorithm 1 uses the sequence correlation between the received frequency-domain Demodulation Reference Signal (DMRS) vectors. After phase pre-compensation is applied, the normalized cross-correlation vector is computed. An objective function is constructed from this vector, and its unimodal behavior in the main lobe is used to estimate the parameters through a bisection search. (2) Algorithm 2 treats the estimation parameter as analogous to a CFO in single-carrier systems and adopts an L&R-based autocorrelation method to derive approximate closed-form expressions. Results and Discussions A computational complexity analysis compares the proposed algorithms with one-dimensional (1D-ML) and two-dimensional (2D-ML) grid-search MLE methods. Numerical results show that Algorithm 1 reduces complexity substantially. The number of complex multiplications, which represent the main computational cost, is 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 more computationally demanding, it yields a closed-form estimation expression. The performance of each algorithm is evaluated through the Mean Square Error (MSE) of the estimated parameters. Simulations show that for a subcarrier number of 3072, the 1D-ML algorithm performs slightly better than the others at Signal-to-Noise Ratios (SNRs) below 5 dB. However, because robust modulation schemes such as BPSK and QPSK typically used at low SNRs tolerate larger offsets, the medium-to-high SNR range is of greater practical relevance. In this range, all four algorithms demonstrate comparable estimation performance. Conclusions This study addresses the effect of Doppler in 5G-NTN LEO satellite communications by analyzing the mechanism and influence of ISFO and by 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. The combined effect of SFO and ISFO on OFDM signals is derived to be equivalent to their linear superposition, which expands the range of the equivalent SFO. Second, the objective function is defined using the cross-correlation vector of two DMRS sequences. By using its unimodal behavior within the main lobe, a binary search enables fast convergence. Subsequently, the parameter determined by SFO and ISFO is then treated as analogous to the CFO in single-carrier systems, allowing an approximate closed-form estimation solution to be obtained through the L&R method. Finally, complexity analysis and performance simulations show that the proposed algorithms provide significant computational savings and strong estimation performance. These results can support the development of 5G-NTN LEO satellite payloads and terminal products.

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References(17)

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