The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
MIMO transceiver design via majorization theory
Foundations and Trends in Communications and Information Theory
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
IEEE Transactions on Information Theory
Linear precoding for mutual information maximization in MIMO systems
ISWCS'09 Proceedings of the 6th international conference on Symposium on Wireless Communication Systems
MIMO Gaussian channels with arbitrary inputs: optimal precoding and power allocation
IEEE Transactions on Information Theory
Optimal designs for space-time linear precoders and decoders
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Optimal Design of Non-Regenerative MIMO Wireless Relays
IEEE Transactions on Wireless Communications
Mutual information and minimum mean-square error in Gaussian channels
IEEE Transactions on Information Theory
Gradient of mutual information in linear vector Gaussian channels
IEEE Transactions on Information Theory
Optimum power allocation for parallel Gaussian channels with arbitrary input distributions
IEEE Transactions on Information Theory
Globally Optimal Linear Precoders for Finite Alphabet Signals Over Complex Vector Gaussian Channels
IEEE Transactions on Signal Processing
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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.