# Asymptotic Performance Analysis of Spatially Reconfigurable Antenna Arrays

## TL;DR

This paper analyzes the asymptotic behavior of MIMO systems with spatially reconfigurable antenna arrays, showing that mutual information converges to a Gumbel distribution as the displacement area grows large, improving understanding of system performance.

## Contribution

It derives the asymptotic distribution of mutual information for large displacement areas, demonstrating the Gumbel distribution approximation for reconfigurable antenna arrays.

## Key findings

- Mutual information converges to a Gumbel distribution as displacement size increases.
- The mean of the mutual information grows proportionally with displacement size.
- Numerical results confirm the Gumbel approximation's accuracy even for finite displacement sizes.

## Abstract

A spatially reconfigurable antenna arrays consists of an antenna array of finite length and fixed geometry which is displaced within a given area. Using these reconfigurable components, the performance of MIMO systems is remarkably improved by effectively positioning the array in its displacement area. This paper studies the large-system performance of MIMO setups with spatially reconfigurable antenna arrays when the displacement area is large. Considering fading channels, the distribution of the input-output mutual information is derived, and the asymptotic hardening property is demonstrated to hold. As the size of the displacement area grows large, the mutual information is shown to converge in distribution to a type-one Gumbel random variable whose mean grows large proportional to the displacement size, and whose variance tends to zero. Our numerical investigations depict that the type-one Gumbel approximation closely tracks the empirical distribution even for a finite displacement size.