Hybrid Precoding for Millimeter Wave MIMO Systems: A Matrix Factorization Approach

This paper investigates the hybrid precoding design for millimeter wave multiple-input multiple-output systems with finite-alphabet inputs. The precoding problem is a joint optimization of analog and digital precoders, and we treat it as a matrix factorization problem with power and constant modulus constraints. This paper presents three main contributions. First, we present a sufficient condition and a necessary condition for hybrid precoding schemes to realize unconstrained optimal precoders exactly when the number of data streams N-s satisfies N-s = min{rank( H), N-rf}, where H represents the channel matrix and N-rf is the number of radio frequency chains. Second, we show that the coupled power constraint in our matrix factorization problem can be removed without loss of optimality. Third, we propose a Broyden-Fletcher-Goldfarb-Shanno-based algorithm to solve our matrix factorization problem using gradient and Hessian information. Several numerical results are provided to show that our proposed algorithm outperforms existing hybrid precoding algorithms.