Design of High-Dimensional Grassmannian Frames via Block Minorization Maximization

In this letter, we present an iterative algorithm for constructing high-dimensional incoherent Grassmannian Frames (GFs) which are sets of unit-norm vectors that are minimax optimal: the maximum absolute value of their inner products is a minimum. We formulate the GF design as a nonconvex optimization problem and solve it via an efficient iterative algorithm. The bulk of each iteration of the proposed algorithm is a Linear Program (LP) for which there are a host of efficient solvers. The proposed algorithm is based on the theoretically sound Minorization Maximization technique which, unlike some of the state-of-the-art design approaches, monotonically minimizes the design criterion and can construct GFs with low coherence values.