A Coherence-Based Algorithm for Optimizing Rank-1 Grassmannian Codebooks

An iterative algorithm for the numerical optimization of rank-1 Grassmannian codebooks is presented. This algorithm achieves the same results as the current state-of-the-art algorithm, but requires a median of 9.52 times less computation time. This improvement is achieved by reformulating the optimization problem to directly minimize coherence instead of maximizing the Euclidean distance between codewords, thereby removing the need to consider large numbers of complex antipodals. The runtime improvement achieved allows the optimization of the larger codebooks required in many applications.