Hybrid Analog and Digital Beamforming for mmWave OFDM Large-Scale Antenna Arrays

Abstract: Hybrid analog and digital beamforming is a promising candidate for large-scale mmWave MIMO systems because of its ability to significantly reduce the hardware complexity of the conventional fully-digital beamforming schemes while being capable of approaching the performance of fully-digital schemes. Most of the prior work on hybrid beamforming considers narrowband channels. However, broadband systems such as mmWave systems are frequency-selective. In broadband systems, it is desirable to design common analog beamformer for the entire band while employing different digital beamformers in different frequency sub-bands. This paper considers hybrid beamforming design for systems with OFDM modulation. First, for a SU-MIMO system where the hybrid beamforming architecture is employed at both transmitter and receiver, we show that hybrid beamforming with a small number of RF chains can asymptotically approach the performance of fully-digital beamforming for a sufficiently large number of transceiver antennas due to the sparse nature of the mmWave channels. For systems with a practical number of antennas, we then propose a unified heuristic design for two different hybrid beamforming structures, the fully-connected and the partially-connected structures, to maximize the overall spectral efficiency of a mmWave MIMO system. Numerical results are provided to show that the proposed algorithm outperforms the existing hybrid beamforming methods and for the fully-connected architecture the proposed algorithm can achieve spectral efficiency very close to that of the optimal fully-digital beamforming but with much fewer RF chains. Second, for the MU-MISO case, we propose a heuristic hybrid percoding design to maximize the weighted sum rate in the downlink and show numerically that the proposed algorithm with practical number of RF chains can already approach the performance of fully-digital beamforming.

• The paper introduces a hybrid beamforming approach for mmWave OFDM systems that achieves near-optimal fully-digital performance using fewer RF chains.
• It develops heuristic algorithms for both fully-connected and partially-connected architectures to optimize spectral efficiency and reduce hardware complexity.
• The study demonstrates practical applications in SU-MIMO and MU-MISO configurations, emphasizing energy efficiency and scalable design for large-scale antenna arrays.

Hybrid Analog and Digital Beamforming for mmWave OFDM Large-Scale Antenna Arrays

Introduction

This paper presents an in-depth exploration of hybrid analog and digital beamforming as a viable technique for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems, focusing on orthogonal frequency division multiplexing (OFDM) modulation in large-scale antenna arrays. The central challenge addressed is the considerable hardware complexity inherent in fully-digital beamforming methods, which necessitate a separate radio frequency (RF) chain for each antenna element. This architecture poses practical difficulties, especially with the advent of advanced wireless systems that employ large-scale antenna arrays. Hybrid beamforming is proposed as a solution that can maintain performance close to fully-digital beamforming while substantially reducing hardware requirements.

System Architecture and Problem Formulation

The hybrid beamforming architecture integrates a low-dimensional digital beamformer with a high-dimensional analog beamformer, the latter implemented using analog phase shifters that are shared across subcarriers in OFDM systems. This shared nature presents a unique challenge in frequency-selective environments, where designing a common analog beamformer for the entire band, while employing distinct digital beamformers in different frequency sub-bands, becomes critical.

The paper delineates two prominent beamforming architectures:

1. Fully-Connected Architecture: Every RF chain is connected to all antenna elements through a network of phase shifters, imposing a constant modulus constraint on the elements of the analog beamforming matrices.
2. Partially-Connected Architecture: Each RF chain connects only to its respective sub-array, reducing the hardware complexity and power consumption.

The problem is framed as an optimization challenge to maximize the overall spectral efficiency under power spectral density constraints for each subcarrier. Hybrid beamforming designs for single-user MIMO (SU-MIMO) and multiuser multiple-input single-output (MU-MISO) systems are proposed to address this challenge, utilizing heuristic algorithms optimized to maximize the spectral efficiency while minimizing hardware resources such as radio frequency (RF) chains.

Main Contributions and Methodology

• Asymptotic Analysis for SU-MIMO Systems: For a sufficiently large antenna array, hybrid beamforming approaches the performance of fully-digital beamforming by leveraging the sparse nature of mmWave channels. With large transceiver antennas, hybrid beamforming with fewer RF chains can achieve similar performance as using a complex conventional fully-digital beamforming architecture.
• Hybrid Beamforming Design for SU-MIMO: The paper proposes a unified heuristic algorithm optimized for practical use with a moderate number of antennas, supporting both fully-connected and partially-connected hybrid beamforming structures. The strategy involves separately designing the transmitter and receiver beamformers.
• Transmitter Design: A coordinated descent algorithm is introduced for locally optimizing the fully-connected and partially-connected beamforming matrices, $\mathbf{V}_\text{RF}$, in asymptotically large antenna arrays, relaxing the constraints for practical application.
• For the multiuser MISO (MU-MISO) configuration, the paper develops a heuristic hybrid precoding design maximizing the downlink weighted sum rate. The approach assumes perfect CSI and uses iterative weighted minimum mean squared error (WMMSE) methodology to address inter-user interference and priority weighting. The analog precoder optimizes sub-carrier selection, while digital precoders are iteratively adjusted.

\section{Conclusion} This paper discusses hybrid analog and digital beamforming strategies for OFDM-based mmWave MIMO systems using large-scale antenna arrays. For both single-user MIMO (SU-MIMO) and multiuser MISO (MU-MISO) configurations, it presents heuristic algorithms for hybrid precoding that can achieve spectral efficiencies close to those of optimal fully digital beamformers with a reduced number of RF chains. This approach offers reduced power consumption and hardware complexity, while maintaining near-optimal spectral efficiency, by capitalizing on the unique properties of mmWave communications, such as channel sparsity and the capability to leverage large-scale antenna arrays. The discussion suggests future exploration into extending these techniques to scenarios with practical limitations on phase shifter resolutions and other potential real-world constraints, to further the practical applicability of hybrid beamforming architectures.