# Directivity-Beamwidth Tradeoff of Massive MIMO Uplink Beamforming for High Speed Train Communication

## TL;DR

This paper explores the tradeoff between beam directivity and beamwidth in massive MIMO uplink beamforming for high-speed train communication, proposing a location-aware design that enhances transmission efficiency and rate region in high traffic scenarios.

## Contribution

It introduces a low-complexity, location-based beamforming method that optimizes directivity under varying positioning accuracies without complex eigen-decomposition, and analyzes performance in high-density HST networks.

## Key findings

- Optimal beamforming improves achievable rate region.
- Less than a certain positioning error guarantees performance.
- Real-time location info enhances transmission efficiency.

## Abstract

High-mobility adaption and massive Multiple-input Multiple-output (MIMO) application are two primary evolving objectives for the next generation high speed train (HST) wireless communication system. In this paper, we consider how to design a location-aware beamforming for the massive MIMO system in the high traffic density HST network. We first analyze the tradeoff between beam directivity and beamwidth, based on which we present the sensitivity analysis of positioning accuracy. Then, in order to guarantee a high efficient transmission, we derive an optimal problem to maximize the beam directivity under the restriction of diverse positioning accuracies. After that, we present a low-complexity beamforming design by utilizing location information, which requires neither eigen-decomposing (ED) the uplink channel covariance matrix (CCM) nor ED the downlink CCM (DCCM). Finally, we study the beamforming scheme in future high traffic density HST network, where a two HSTs encountering scenario is emphasized. By utilizing the real-time location information, we propose an optimal adaptive beamforming scheme to maximize the achievable rate region under limited channel source constraint. Numerical simulation indicates that a massive MIMO system with less than a certain positioning error can guarantee a required performance with satisfying transmission efficiency in the high traffic density HST scenario and the achievable rate region when two HSTs encounter is greatly improved as well.