Efficient Riemannian algorithms for optimization under unitary matrix constraint

In this paper we propose practical algorithms for optimization under unitary matrix constraint. This type of constrained optimization is needed in many signal processing applications. Steepest descent and conjugate gradient algorithms on the Lie group of unitary matrices are introduced. They exploit the Lie group properties in order to reduce the computational cost. Simulation examples on signal separation in MIMO systems demonstrate the fast convergence and the ability to satisfy the constraint with high fidelity.