Leveraging Autoencoder for Joint Pilot Waveforming and Compressive Sensing in Beamspace Channel Estimation for LEO Satellite Communications

Beamspace channel estimation is crucial for unlocking the potential of millimeter-wave (mmWave) communications in low Earth orbit (LEO) satellite networks. Effective channel estimation tailored to the unique characteristics of LEO channels, including hybrid beamforming architectures, is imperative. This paper presents a novel joint design framework integrating transmit pilot waveforming and receive compressive sensing (CS) for downlink beamspace channel estimation in LEO satellite communications. By exploiting channel sparsity and deep learning with an autoencoder (AE), the joint design is formulated as a sensing matrix design problem. We explore a simple AE training method utilizing 1-sparse channel patterns, enabling efficient decoding with orthogonal matching pursuit (OMP) and its variants. Subsequently, a low-rank approximation method is employed to extract the precoder and compressor from the trained sensing matrix. We further propose a machine learning (ML)-OMP method using a customized multilayer perceptron (MLP) network for iterative support selection. Simulation results demonstrate that the proposed transmit pilot waveforming and receive CS methods significantly enhance beamspace channel estimation performance with fewer pilot time slots. Furthermore, the proposed ML-OMP method outperforms conventional OMP, particularly in scenarios with non-customized precoders and compressors.