Hybrid Precoding for Millimeter Wave MIMO Systems With Finite-Alphabet Inputs

This paper investigates the hybrid precoding design for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems with finite alphabet inputs. The precoding problem is a joint optimization of analog and digital precoders, and it imposes nonconvex constant modulus constraints on the analog precoder. We treat this problem as a matrix factorization problem with constant modulus constraints. The main contributions of our work are listed as follows: First, we propose sufficient and necessary conditions for hybrid precoding schemes to realize any unconstrained optimal precoders exactly when the number of data streams is equal to the number of radio frequency chains. Second, we show that the power constraint in the hybrid precoding problem can be removed without loss of optimality. Third, we present a trust region Newton method to solve our problem using gradient and Hessian information, and the proposed algorithm converges to a stationary point satisfying the first and second order necessary optimality conditions. Several numerical examples are provided to show that the proposed algorithm outperforms existing hybrid precoding algorithms.