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.

Meeting Name

2017 IEEE Global Communications Conference, GLOBECOM 2017 (2017: Dec. 4-8, Singapore, Singapore)


Electrical and Computer Engineering


National Science Foundation (U.S.)
Natural Science Foundation of China
Shanghai Key Fundamental Research Project
Guangxi NSFC
National Science and Technology Major Project of China
Ministry of Science and Technology of the People's Republic of China. 863 Program


The work of Y.R. Zheng and C. Xiao was supported in part by US National Science Foundation under grants ECCS-1231848, ECCS-1408316 and ECCS1539316. The work of W. Chen was supported by NSFC 61671294, by Shanghai S&T Key Project 16JC1402900, by Guangxi NSFC 2015GXNSFDA139037, by National Major Project 2017ZX03001002-005, and by National 863 project 2015AA01A710.

Keywords and Phrases

Factorization; Matrix algebra; Millimeter waves (mmwave); MIMO systems; Newton-Raphson method; Constant modulus constraints; Finite-alphabet inputs; Joint optimization; Matrix factorizations; Necessary optimality condition; Radio frequency chains; Sufficient and necessary condition; Problem solving

International Standard Book Number (ISBN)


Document Type

Article - Conference proceedings

Document Version


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Publication Date

01 Dec 2018