ULA factorization theorem

An algebraic theorem called the ULA factorization theorem (Miyashita et al. (2003)) has been proved for a uniform linear array (ULA) with co-phase excitations. It ultimately governs the arrays of arrays principle of uniformly spaced ULA in that all possible topologies of feeding networks with equal amplitude and co-phase dividers are determined. Further physical insight yields the corollary of the theorem called the feed network factorization theorem, where an isomorphism is found between the factorization formulas and certain analogue of trees in the discrete mathematics. Applications to simple ULA geometries and related mathematical considerations are described.