Full diversity sets of unitary matrices from orthogonal sets of idempotents

TL;DR

This paper presents a method to construct full diversity sets of unitary matrices using orthogonal idempotents, enabling algebraic analysis of their properties for applications in space-time communication systems.

Contribution

It introduces a novel approach to design unitary matrices from orthogonal idempotents, simplifying the construction and analysis of space-time constellations.

Findings

Constructed unitary matrices with guaranteed diversity properties

Algebraic methods to evaluate differences between matrices

Applications to space-time communication system design

Abstract

Orthogonal sets of idempotents are used to design sets of unitary matrices, known as constellations, such that the modulus of the determinant of the difference of any two distinct elements is greater than $0$. It is shown that unitary matrices in general are derived from orthogonal sets of idempotents reducing the design problem to a construction problem of unitary matrices from such sets. The quality of the constellations constructed in this way and the actual differences between the unitary matrices can be determined algebraically from the idempotents used. This has applications to the design of unitary space time constellations.