# Optimal Design Method of MIMO Antenna Directivities and Corresponding Current Distributions by Using Spherical Mode Expansion

## TL;DR

This paper introduces an analytical method using spherical mode expansion to design near-optimal MIMO antenna directivities and current distributions, improving efficiency over traditional iterative approaches.

## Contribution

It presents a novel analytical optimization technique for MIMO antenna design that eliminates the need for iterative greedy searches by deriving directivity and current distributions directly.

## Key findings

- Achieves near-optimal channel capacity with the proposed method.
- Provides explicit current distributions for limited antenna surfaces.
- Validates effectiveness through numerical simulations.

## Abstract

This paper proposes a new methodology to design optimal antennas for MIMO (Multi-Input Multi-Output) communication systems by using spherical mode expansion. Given spatial channel properties of a MIMO channel, such as the angular profile at both sides, the optimal MIMO antennas should provide the largest channel capacity with a constraint of the limited implementation space (volume). In designing a conventional MIMO antenna, first the antenna structure (current distribution) is determined, second antenna directivity is calculated based on the current distribution, and thirdly MIMO channel capacity is calculated by using given angular profiles and obtained antenna directivity. This process is repeated by adjusting the antenna structure until the performance satisfies a predefined threshold. To the contrary, this paper solves the optimization problem analytically and finally gives near optimal antenna structure (current distribution) without any greedy search. In the proposed process, first the optimal directivity of MIMO antennas is derived by applying spherical mode expansion to the angular profiles, and second a far-near field conversion is applied on the derived optimal directivity to achieve near optimal current distributions on a limited surface. The effectiveness of the proposed design methodology is validated via numerical calculation of MIMO channel capacity as in the conventional design method while giving near optimal current distribution with constraint of an antenna structure derived from proposed methodology.