Tensor-Based Channel Estimation Considering Beam Squint Effects in LEO Satellite Communications

In this paper, we propose a tensor based channel estimation framework for beam squint-aware low Earth orbit (LEO) downlink communication at a ground station. We first show that the downlink signals received at the ground station from multiple LEO satellites can be represented as a mathematically structured tensor using mode-n products. Based on this tensor representation, we established the channel estimation problem as a tensor decomposition problem, to mitigate beam squint effects and inter-satellite interference in the downlink communication. To solve the problem, we propose a constrained version of CANDECOMP/PARAFAC (CP) and Tucker decomposition. Specifically, our modified method is designed to incorporate additional constraints such as a power constraint, which is not considered in the original CP and Tucker decomposition. Finally, we validate our proposed methods through numerical simulations. We observed that Tucker methods yielded low computational error compared to CP method at extreme computation cost. Our proposed methods, incorporating an additional power constraint, achieved comparable converged performance to conventional methods but offered advantages in requiring fewer iterations.