All boldface letters stand for vectors (lower case) or matrices (upper case). Representative numerical results are given in Section 5 before we conclude the paper in Section 6. Section 4 proposes an adaptive DFO compensation algorithm in LEO-MIMO satellite systems. Section 3 considers the DFO effects, deriving the approximation expressions of achievable rate with MRT and MASLNR precoding. Section 2 introduces the system model including system configuration and satellite channel model. The remainder of this paper is organized as follows. In order to improve the estimation accuracy, we adopt the beam alignment (BA) algorithm for fine compensation in the receiver (iii) Simulation results verified the correctness of approximation expressions, and the average system SE can be improved after using the proposed compensation algorithm in LEO-MIMO satellite systems Based on information of orbit, user location, and velocity, precompensation is performed in the transmitter. The SE of LEO-MIMO satellite communication systems is analyzed (ii) We propose an adaptive DFO compensation algorithm. (i) Considering the DFO effects, we derived the approximation expressions of achievable rate with maximum ratio transmission (MRT) and maximum average signal-to-leakage-plus-noise ratio (MASLNR) precoding. The contributions of this work are summarized as follows. Taking DFO into account, we analyze the SE performance of the system and design an adaptive DFO compensation algorithm. In this paper, we investigate robust downlink transmission for LEO-MIMO satellite systems. However, incorporating MIMO into satellite communication systems is still a challenge. MIMO can substantially increase the number of antennas and spatial resolution and achieve a high transmission rate. MIMO has been widely applied in the terrestrial wireless network. Thus, to achieve better performance in LEO-MIMO satellite systems, a lightweight and effective adaptive DFO compensation algorithm is needed. However, the solutions discussed above cannot be substantially applied to high-speed systems. Paper discussed a maximum frequency shift estimation algorithm based on the level pass rate, which needs loss information of transmission process to calculate the average power of the signal. In, frequency offset and the Doppler shift joint estimation algorithm in high mobility environment based on orthogonal angle domain subspace projection was proposed.
Some works improved the accuracy of estimation by adding CP, which can be applied to the scenario of large frequency offset. But the estimation range of the algorithm was less than half of a subcarrier interval. In, by adding a cyclic prefix (CP) and training data in orthogonal frequency-division multiplexing (OFDM) systems, a high-dynamic DFO estimation approach was presented. Yet, it assumed the angular velocity of the satellite relative to the user is constant, which was unrealistic. In, a geographic method to estimate DFO in a condition that satellites communicate with fixed earth stations was proposed. Many works have been conducted toward the development of DFO estimation. Therefore, the receiver is difficult to obtain the instantaneous channel state information (iCSI). Then Doppler frequency offset (DFO) inevitably causes intersymbol interference (ISI) and fast time variation of the channel. Firstly, due to the long distance of transmission links, it always results in large channel attenuation. However, there are many challenges in LEO multiple-input and multiple-output (LEO-MIMO) satellite communication systems. In the 6G space-air-earth integrated network, a low earth orbit (LEO) satellite communication network will be combined with a ground communication network to provide wide coverage and high dynamic. In recent years, the application of satellite communication has been increasing. Numerical results verify the effectiveness of the proposed DFO compensation algorithm. In order to relieve the impact of DFO, we propose an adaptive DFO compensation algorithm based on the precompensation design and beam alignment. Numerical results show that the derived closed-form expressions are accurate and the DFO severely affects system performance. Considering the impact of DFO, we derive the closed-form expressions for the downlink achievable rates with maximum ratio transmission (MRT) and maximum average signal-to-leakage-plus-noise ratio (MASLNR) precoding. In this paper, we investigate downlink transmission schemes robust to the Doppler frequency offset (DFO) induced by high mobility for low earth orbit multiple-input and multiple-output satellite communication systems.
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