# Optimal Preamble Length for Spectral Efficiency in Grant-Free RA with Massive MIMO

## TL;DR

This paper investigates the optimal preamble length in grant-free massive MIMO systems to maximize spectral efficiency, considering collision, overhead, and channel estimation, revealing system parameter influences and differences from granted access.

## Contribution

It introduces an analysis of the optimal preamble length for spectral efficiency in grant-free massive MIMO, accounting for multiple system effects.

## Key findings

- Existence of an optimal preamble length for SE maximization
- Longer preamble length needed in grant-free compared to granted access
- Properties of optimal preamble length relative to system parameters

## Abstract

Grant-free random access (RA) with massive MIMO is a promising RA technique for massive access with low signaling overhead. In the grant-free RA with massive MIMO, preamble length has a critical impact on the performance of the system. In this paper, the optimal preamble length is investigated to maximize spectral efficiency (SE) of the grant-free RA with massive MIMO, where effects of the preamble length on the preamble collision and preamble overhead as well as channel estimation accuracy are taken into account. Simulation results agree well with our analyses and confirm the existence of optimal preamble length for SE maximization in the grant-free RA with massive MIMO. Moreover, properties of the optimal preamble length with respect to system parameters are revealed. Compared to the granted access, it is shown that longer preamble length is required for SE maximization in the grant-free RA.