Space-Time Adaptive Beamforming for Satellite Communications: Harnessing Doppler as New Signaling Dimensions

Abstract

Low Earth orbit (LEO) satellite downlinks are fundamentally limited by severe channel correlation: the line-of-sight (LoS)-dominant propagation and high orbital altitude confine users to a narrow angular region, rendering the multiuser channel matrix ill-conditioned. This paper provides a rigorous characterization of this limitation by exploiting the Vandermonde structure of the channel. Specifically, we link the minimum eigenvalue of the channel Gram matrix to user crowding through a balls-and-bins abstraction, and derive asymptotic sum rate scaling laws for both uniform linear arrays and uniform planar arrays. Our analysis reveals a sharp density threshold beyond which zero-forcing (ZF) precoding provably fails. To overcome this spatial multiplexing breakdown, we propose space-time adaptive beamforming (STAB), which exploits user-dependent residual Doppler shifts as an additional discrimination dimension. By constructing a time-extended channel in the joint space-Doppler domain, STAB restores a non-vanishing sum rate in regimes where purely spatial ZF collapses. We further develop a space-Doppler user selection (SDS) algorithm that leverages both spatial and Doppler separability for scheduling. Numerical results corroborate the analytical predictions and demonstrate that STAB with SDS achieves substantial sum rate gains over conventional methods in dense LEO downlink scenarios.

Figures (7)

• Figure 1: Large orbital altitudes inducing user channel correlation and MU-MIMO limitations.
• Figure 2: Considered system model for STAB with repetition length $L=3$.
• Figure 3: Balls-and-bins interpretation of spatial user distribution across sparse, critical, and dense regimes.
• Figure 4: Empirical cumulative distribution function of the ZF and the STAB sum rate for $M_x = M_y = 16, K = 16, L = 3$, and $P = 40 \text{ dBm}$, under different cell sizes $R$ and UPA.
• Figure 5: Validation of the upper-bound chain in Lemma \ref{['lem:zf_sumrate']} for the average ZF sum rate of a ULA with $M=256$, $K=16$, and $P= 30\text{ dBm}$, 16 bins, and maximum load $n$ where all users are uniformly randomly distributed.

Theorems & Definitions (20)

• Remark 1: Intuition on STAB
• Remark 2: Interpretation of the scaling regime
• Lemma 1: Max load scaling in the balls-and-bins model
• proof
• Lemma 2: Upper bound on $\lambda_1$ under a single cluster
• proof
• Lemma 3: ZF sum rate upper bound
• proof
• Theorem 1: Upper scaling law of the average sum rate $R_{\Sigma}$
• proof