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

TL;DR

This paper introduces a matrix factorization approach for hybrid precoding in mmWave MIMO systems, providing conditions for optimal precoding, removing power constraints without loss, and proposing an efficient BFGS-based algorithm.

Contribution

It offers new conditions for optimal hybrid precoding, removes coupled power constraints, and develops a BFGS-based algorithm for improved performance.

Findings

The proposed algorithm outperforms existing hybrid precoding methods.

Conditions for exact realization of unconstrained optimal precoders are established.

Power constraints can be removed without affecting optimality.

Abstract

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 we treat it as a matrix factorization problem with power and constant modulus constraints. Our work 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 Ns satisfies Ns = minfrank(H);Nrfg, where H represents the channel matrix and Nrf is the number of radio frequency (RF) 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 (BFGS)-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.