The geometry of fusion inspired channel design

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. •Orthogonal decomposition, generalized signal-to-noise-ratio matrix.•Factorization of the optimal channel matrix.•Mercury/waterfilling interpretation for power allocation.•Extrinsic and intrinsic gradient search algorithm.•Minimum dimension of the secondary measurement.