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 demonstrate that the downlink signals received at the ground station from multiple LEO satellites can be represented as a structured tensor using mode-n products. Based on this tensor representation, we formulate the channel estimation problem as a tensor decomposition problem to mitigate beam squint effects and inter-satellite interference in downlink communication. To solve this problem, we propose constrained versions of CANDECOMP/PARAFAC (CP) and Tucker decompositions. Specifically, our modified approach incorporates additional constraints, such as a power constraint, which are not considered in the standard CP and Tucker decompositions. Finally, we validate the proposed methods through numerical simulations. Results show that the Tucker-based method achieves lower computational error than the CP-based method, albeit with higher computational cost. Furthermore, the proposed methods incorporating power constraints demonstrate comparable convergence performance to conventional approaches while requiring fewer iterations.