在這篇論文中，我們探討了基於Extended 𝐻∞ filter 所設計的載
波頻率偏移估測方法且應用在多重輸入多重輸出之低軌衛星(Low
Earth orbit)通訊系統。由於衛星與地面接收站之間的高相對速度所引
起的多普勒偏移會導致接受訊號的失真。因此本文提出基於正交分頻
多工(OFDM)的衛星傳輸適應性通訊演算法進而改善多普勒偏移問題，
並且利用衛星是沿著地球進行圓軌道運動的特性以及多普勒特徵來
進一步更新衛星移動到下一個時間位置時的多普勒值。模擬結果表明，
提出的估測器與擴展卡爾曼濾波器(EKF)相比，由於提出的估測器是
不需要對干擾有任何的了解，因此能夠在非高斯雜訊下以及模型有誤
差的情況中，依然有著良好的估計性能和在有限樣本的情況下能快速
的收斂。以及在均方誤差(mean square error) 的精確度上也能夠貼近
於克拉瑪界線(Cramer-Rao Bound)。

In this paper, we investigate the adaptive carrier frequency offset (CFO) estimation method based on the Extended 𝐻∞ filter and maximum likelihood estimation of channel coefficients for MIMO-OFDM in low Earth orbit (LEO) satellite communication system. Since the Doppler shift is caused by the high relative velocity between the satellite and the ground receiving station causes the distortion of the received signal. Consequently, to overcome this problem, this study proposes an adaptive communication algorithm and turbo iteration to make the estimated value be close to the
exact value based on MIMO-OFDM for satellite transmission to improve the Doppler effect problem, and further update the Doppler value when the satellite moves to the next time index by using the characteristics that the satellite is moving in a circular orbit along the Earth and the Doppler
feature. The simulation results show that the proposed estimator has good performance under model error and Bernoulli Gaussian impulse noise, and can fast convergence in limited sample sizes, also, compared with the Extended Kalman filter (EKF), because the Extended 𝐻∞ filter does not require any information about the interference. The mean square error (MSE) is also near to the Cramer-Rao Bounds (CRBs).

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