Phase Only RF Precoding for Massive MIMO Systems With Limited RF Chains

Abstract

Massive MIMO systems promise high spectrum efficiency by deploying <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M \gg 1$</tex></formula> antennas at the base station (BS). However, to achieve the full gain provided by massive MIMO, the BS requires <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M$</tex> </formula> radio frequency (RF) chains, which are expensive. This motivates us to consider RF-chain limited massive MIMO systems with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M$</tex> </formula> antennas but only <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$S \ll M$</tex></formula> RF chains. We propose a two-stage precoding scheme to efficiently exploit the large spatial degree of freedom (DoF) gain in massive MIMO systems with limited RF chains and reduced channel state information (CSI) signaling overhead. In this scheme, the MIMO precoder is partitioned into a high-dimensional phase only RF precoder followed by a low-dimensional baseband precoder. The RF precoder is adaptive to the spatial correlation matrices for inter-cluster interference mitigation. The baseband precoder is adaptive to the reduced dimensional “effective” CSI for intra-cluster spatial multiplexing. We formulate the two stage precoding problem such that the minimum (weighted) average data rate of users is maximized under the phase only constraint on the RF precoder and the limited RF chain constraint. This is a combinatorial optimization problem which is in general NP-hard. We propose a low complexity solution based on a novel bi-convex approximation approach. Simulations show that the proposed design has significant gain over various baselines.