# Optimal Beamforming for Hybrid Satellite Terrestrial Networks with Nonlinear PA and Imperfect CSIT

## TL;DR

This paper develops an optimal beamforming strategy for hybrid satellite-terrestrial networks that accounts for nonlinear power amplifiers and imperfect channel information, improving spectrum sharing efficiency.

## Contribution

It introduces a novel beamforming optimization considering PA nonlinearity and large-scale CSIT, which was not addressed in prior work.

## Key findings

- Proposed beamforming scheme outperforms existing methods in simulations.
- Maximized satellite system rate while controlling interference.
- Derived optimal amplitude and phase for desired beams.

## Abstract

In hybrid satellite-terrestrial networks (HSTNs), spectrum sharing is crucial to alleviate the "spectrum scarcity" problem. Therein, the transmit beams should be carefully designed to mitigate the inter-satellite-terrestrial interference. Different from previous studies, this work considers the impact of both nonlinear power amplifier (PA) and large-scale channel state information at the transmitter (CSIT) on beamforming. These phenomena are usually inevitable in a practical HSTN. Based on the Saleh model of PA nonlinearity and the large-scale multi-beam satellite channel parameters, we formulate a beamforming optimization problem to maximize the achievable rate of the satellite system while ensuring that the inter-satellite-terrestrial interference is below a given threshold. The optimal amplitude and phase of desired beams are derived in a decoupled manner. Simulation results demonstrate the superiority of the proposed beamforming scheme.