The Geometry of Fusion Inspired Channel Design

TL;DR

This paper explores the geometric design of secondary channels in MIMO systems to optimize information transfer, proposing algorithms that leverage manifold geometry and demonstrating their effectiveness through simulations.

Contribution

It introduces a geometric approach to secondary channel design in MIMO systems, including new algorithms based on manifold geometry and analytical solutions for special cases.

Findings

Algorithms effectively approximate optimal secondary channels

Intrinsic algorithm exploits sphere geometry for efficiency

Simulation results validate the proposed methods

Abstract

This paper is motivated by the problem of integrating multiple sources of measurements. We consider two multiple-input-multiple-output (MIMO) channels, a primary channel and a secondary channel, with dependent input signals. The primary channel carries the signal of interest, and the secondary channel carries a signal that shares a joint distribution with the primary signal. The problem of particular interest is designing the secondary channel matrix, when the primary channel matrix is fixed. We formulate the problem as an optimization problem, in which the optimal secondary channel matrix maximizes an information-based criterion. An analytical solution is provided in a special case. Two fast-to-compute algorithms, one extrinsic and the other intrinsic, are proposed to approximate the optimal solutions in general cases. In particular, the intrinsic algorithm exploits the geometry of the unit sphere, a manifold embedded in Euclidean space. The performances of the proposed algorithms are examined through a simulation study. A discussion of the choice of dimension for the secondary channel is given.