Hybrid Analog-Digital Beamforming via Matrix Decomposition for Distributed MIMO LEO Satellites with Channel-matched Warm Start

Abstract— Cooperative transmission from low-earth orbit (LEO) satellites equipped with large planar arrays is a leading sixth-generation (6G) candidate for satellite-to-ground multiple-input multiple-output (MIMO) links. Fully digital (FD) beamforming over such arrays is impractical because each antenna element requires a dedicated radio-frequency (RF) chain. This paper develops a hybrid analog-digital beamforming scheme for a distributed MIMO LEO satellite serving multi-antenna ground users. The proposed design decomposes the FD precoder via alternating minimization between a constant-modulus analog precoder and a low-dimensional digital baseband precoder, both solved via weighted minimum mean-square error (WMMSE). A key design decision is a channel-matched warm start, which initializes the analog precoder with uniform planar array (UPA) steering vectors for the scheduled users. Simulations with a 64×64 UPA at each satellite and L = 4 cooperating satellites serving K = 4 multi-antenna ground users at the Ka-band show that the proposed warm-started alternating minimization reduces the matrixdecomposition residual by over eleven orders of magnitude relative to random initialization, and that the resulting hybrid precoder with NRF = K RF chains achieves the FD upper bound on the sum spectral efficiency. This indicates that, for the rank-one line-of-sight channels characteristic of LEO scenarios, the number of RF chains required equals the number of spatially multiplexed users, yielding a three-order-ofmagnitude reduction in RF-chain count relative to FD while retaining optimal performance.

 Index Terms—6G, distributed MIMO, LEO satellite, hybrid beamforming, uniform planar array, alternating minimization, WMMSE.