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Hybrid Beamforming for Massive MIMO - A Survey

Andreas F. Molisch, Vishnu V. Ratnam, Shengqian Han, Zheda Li, Sinh Le Hong Nguyen, Linsheng Li, Katsuyuki Haneda

arXiv:1609.05078v2cs.IT

TL;DR

Massive MIMO needs lower-cost, lower-overhead transceivers without giving up the benefits of large antenna arrays. The paper surveys hybrid analog-digital architectures, classifies them by CSI, complexity, and carrier frequency, and concludes that designs must match application and channel characteristics.

  • Problem

    Massive MIMO requires reducing hardware cost and CSI-acquisition overhead while retaining the spatial benefits of many antenna elements.

  • Method

    The paper surveys hybrid transceivers that combine large-dimensional analog processing with lower-dimensional digital processing and categorizes them by CSI, complexity, and carrier frequency.

  • Results

    The survey finds that hybrid beamforming can achieve fully digital performance when the number of RF chains is no smaller than the number of data streams, while different structures trade complexity against performance.

  • Takeaways & Limitations

    There is no universally best hybrid structure or algorithm; designs should be adapted to application and channel characteristics.

  • Takeaways & Limitations

    Important millimeter-wave multi-user implementation issues, including scheduling and two-dimensional and three-dimensional lens-array design, remain open research topics.

Abstract

from arXiv · show

Hybrid multiple-antenna transceivers, which combine large-dimensional analog pre/postprocessing with lower-dimensional digital processing, are the most promising approach for reducing the hardware cost and training overhead in massive MIMO systems. This paper provides a comprehensive survey of the various incarnations of such structures that have been proposed in the literature. We provide a taxonomy in terms of the required channel state information (CSI), namely whether the processing adapts to the instantaneous or the average (second-order) CSI; while the former provides somewhat better signal-to-noise and interference ratio (SNIR), the latter has much lower overhead for CSI acquisition. We furthermore distinguish hardware structures of different complexities. Finally, we point out the special design aspects for operation at millimeter-wave frequencies.

I. INTRODUCTION

Massive MIMO improves spectral efficiency but creates substantial RF-chain cost, energy consumption, and CSI-acquisition overhead. Hybrid transceivers address these challenges by combining analog and digital processing with fewer conversion chains, while exposing complexity and optimization trade-offs.

  • Massive MIMO increases data streams, simplifies processing, provides channel hardening, and reduces transmission energy through large beamforming gain.
  • Each-antenna RF chains raise hardware cost and energy consumption, while antenna-pair CSI acquisition consumes considerable spectral resources.
  • Hybrid transceivers combine RF-domain analog beamformers with baseband digital beamforming and use fewer up/downconversion chains.
  • The survey organizes hybrid beamforming by instantaneous versus average CSI, hardware complexity, and specialized mm-wave constraints.
  • Full-complexity structures connect each RF chain to all antenna elements, reduced-complexity structures use subsets, and virtual-sectorization structures separate processing by sectors.
  • Hybrid beamformer optimization is difficult because transmit and receive analog and digital matrices are coupled, phase shifters impose constraints, and finite resolution can produce NP-hard integer programs.

A. Approximating the optimal beamformer

For instantaneous-CSI design, the survey approximates fully digital beamformers and evaluates three hybrid structures. Full-complexity processing can match fully digital performance under sufficient RF-chain resources, whereas reduced or sectorized structures introduce different losses and overhead trade-offs.

  • A. Approximating the optimal beamformer: The fully digital SU-MIMO solution uses dominant left and right singular vectors of the channel matrix obtained by SVD.
  • A. Approximating the optimal beamformer: Hybrid beamformers approximate the fully digital solution by minimizing Euclidean distance, yielding quasi-optimal solutions in sparse channels and alternating optimization in non-sparse channels.
  • A. Approximating the optimal beamformer: The full-complexity structure matches fully digital performance when the number of RF chains is no smaller than the number of users or streams.
  • A. Approximating the optimal beamformer: The reduced-complexity structure incurs substantial loss in the considered MU-MIMO case, although its loss is much smaller for SU-MIMO.
  • A. Approximating the optimal beamformer: Virtual-sectorization can suffer a performance floor from inter-group interference, while its reduced training overhead is not represented in the comparison.

B. Decoupling the design of the analog and digital beamformers

Decoupling analog and digital beamformer design reduces optimization complexity by imposing receiver, digital-precoder, or phase-only assumptions. The resulting sequential and heuristic designs provide tractable alternatives, including asymptotic SINR guarantees for normalized conjugate beamforming.

  • B. Decoupling the design of the analog and digital beamformers: Assuming a fully digital MMSE receiver can eliminate the combiner's impact on SU-MIMO precoder optimization.
  • B. Decoupling the design of the analog and digital beamformers: Assuming a unitary digital precoder enables column-by-column analog optimization under phase-only antenna constraints, followed by closed-form digital-precoder computation.
  • B. Decoupling the design of the analog and digital beamformers: Element-wise normalized conjugate beamforming offers a simple heuristic analog precoder for hybrid beamforming.
  • B. Decoupling the design of the analog and digital beamformers: As antenna elements and streams grow while their ratio remains fixed, the heuristic's asymptotic SINR is reduced by a factor of π/4 relative to fully digital beamforming.
  • B. Decoupling the design of the analog and digital beamformers: For MU-MIMO with hybrid receivers, strongest receive-beam selection and normalized eigenbeamforming are applied before block diagonalization over the projected channel.

C. Wideband hybrid beamforming

Wideband hybrid beamforming must accommodate frequency-selective channels because analog weights cannot vary across subcarriers. Hybrid structures can match fully digital performance when enough RF chains are available, while practical constraints still require frequency-domain scheduling and control-coverage considerations.

  • Wideband constraints: Analog beamformers use common weights across subcarriers, so strongly frequency-selective wideband channels require adaptation to average channel state.The limitation follows because the analog beamformer extends over the whole available band.
  • Wideband constraints: Frequency-domain scheduling remains necessary for hybrid transceivers under practical array-size constraints, even though it was considered unnecessary for fully digital massive MIMO.Serving UEs on different subcarriers makes existing narrowband hybrid precoders inapplicable.
  • Control signaling: Narrow analog beams suit user data, whereas wide beams suit broadcast control signals, motivating separate treatment of signaling and data planes.The paper notes that splitting them across carrier frequencies may solve the coverage problem.
  • Performance: Hybrid beamforming can provide the same functionality as digital beamforming by combining desired multipath components and suppressing interfering components with phase shifters and variable gain amplifiers.This equivalence is stated for narrowband operation.
  • Performance: With full-instantaneous CSI at the transmitter, narrowband hybrid beamforming matches fully digital performance when NS ≤ NRF.For wideband systems, the corresponding requirement is NRF ≥ min(NBS, NS,wb).
  • Performance: Phase-only hybrid structures can achieve fully digital performance in narrowband systems when NRF ≥ 2NS.Two phase-only analog entries can represent one unconstrained amplitude-and-phase entry.

III. HYBRID BEAMFORMING BASED ON AVERAGED CSI

Average-CSI hybrid beamforming reduces the CSI burden by basing analog processing on slowly varying channel statistics while retaining instantaneous effective CSI for digital processing. JSDM groups users by channel covariance to create virtual sectors and reduce training and feedback overhead, but overlapping covariances constrain grouping and can leave inter-group interference.

  • Motivation: Full-CSI massive MIMO is limited by coherence-block size, motivating transmission strategies based on reduced-dimensional, slowly varying second-order CSI.In FDD systems, downlink training and uplink feedback for each antenna further increase overhead.
  • JSDM: JSDM groups users with similar transmit channel covariance and uses hybrid beamforming to reduce downlink training and uplink feedback burden.The supplied passage identifies JSDM as an average-CSI approach for multi-user systems.
  • JSDM design: JSDM represents each channel using covariance eigenstructure and constructs the analog precoder from group-specific interference null spaces and dominant eigenvectors.The supplied passages define U as the covariance eigenmatrix and describe Eg and Gg as the relevant design components.
  • JSDM: JSDM forms virtual sectors in which downlink training occurs in parallel, while users feed back only intra-group channels, reducing training and feedback overhead by the number of virtual sectors.The reduction factor is explicitly tied to the number of virtual sectors.
  • JSDM limitations: JSDM conservatively uses few groups because users’ transmit channel covariances partially overlap, limiting overhead reduction and preventing effective suppression of inter-group interference when orthogonality fails.Eliminating overlapping beams is described as a heuristic remedy.
  • Extensions: Non-orthogonal virtual sectorization has been paired with a modified MMSE algorithm that optimizes multi-group digital precoders for a lower bound on average sum rate.This is presented as a generalization of JSDM.
  • Extensions: UE grouping extensions include K-means clustering and fixed quantization, while online iterative tracking can reduce JSDM complexity under time-varying channels.The passage also discusses stream optimization using users’ angle-of-departure statistics and spreads.

B. Decoupling of Analog and Digital Beamformers

With average CSI for analog processing and instantaneous effective CSI for digital processing, optimal hybrid-beamformer design becomes a coupled long-term and per-snapshot problem. The paper therefore motivates decoupled designs to make the mathematical treatment more manageable.

  • CSI separation: Average-CSI designs use average CSI for analog and instantaneous effective CSI for digital beamformers.Finding optimal beamformers requires designing digital processing for each channel snapshot before deriving the analog beamformer from its long-term average.
  • Design challenge: The resulting optimization is difficult because digital beamformers must be designed per snapshot before the analog beamformer is obtained from their long-term time-average.The passage explicitly characterizes the mathematical treatment as difficult.

C. Full-dimensional (FD) MIMO in 3GPP

The paper describes full-dimensional MIMO architectures and a selection-based hybrid structure relevant to 3GPP CSI acquisition. Analog processing can be fixed or based on average statistics while switches select ports per channel realization, reducing hardware or training demands.

  • 3GPP FD MIMO: 3GPP Release 13 CSI acquisition protocols for FD MIMO include non-precoded and beamformed pilots, with the non-precoded beamformer related to a reduced-complexity hybrid structure.A possibly static analog precoder is applied to part of an antenna array to reduce training overhead.
  • Selection structure: Hybrid beamforming with selection places a selection stage before transmit-side or after receive-side analog processing.The selection stage is the defining feature of this special class.
  • Selection structure: A switch matrix feeds data streams to the best NRF ports among L analog-block input ports, typically with L = NBS_RF.The structure uses more available ports than selected RF chains when L ≥ NBS_RF.
  • Selection rationale: Because phase shifters and amplifiers may not track rapidly varying instantaneous channels, the analog precoder is fixed or average-CSI-based while switches select ports for each realization.Switching networks are also presented as advantageous relative to full-complexity analog beamforming.

A. Design of analog precoding/combining block

Analog precoding before antenna selection exploits spatial multipath components and can provide beamforming gains, but searching for the best analog ports becomes exponentially complex as the number of RF chains grows.

  • A. Design of analog precoding/combining block: Analog precoding before antenna selection exploits spatial multipath components by processing signals in the beam-space.DFT-based and TX-correlation-based eigenmode designs are described for the analog precoder.
  • A. Design of analog precoding/combining block: Eigenmode beamforming based on the TX correlation matrix shows better performance in correlated channels than the simpler selection architecture.
  • A. Design of analog precoding/combining block: Searching for the best ports in the analog block has exponentially increasing complexity with the number of RF chains.
  • A. Design of analog precoding/combining block: Greedy, restricted, and iterative selection algorithms reduce the search and hardware complexity of analog-port selection.Restricted architectures limit each RF chain to a subset of analog ports, while iterative algorithms span linear to sub-exponential search complexity.

V. HYBRID BEAMFORMING AT MM-WAVE

At mm-wave frequencies, hybrid beamforming exploits sparse multipath channels to combine analog array gains with digital multiplexing, while antenna, beam, and codebook selection offer lower-dimensional implementations.

  • V. HYBRID BEAMFORMING AT MM-WAVE: Mm-wave propagation has higher loss, making antenna-array gain and practical RF-aware hybrid beamforming important design considerations.
  • V. HYBRID BEAMFORMING AT MM-WAVE: Sparse-channel hybrid beamforming focuses RF array gains on a limited number of multipaths while baseband processing multiplexes streams and allocates power.This architecture is asymptotically optimum for large antenna arrays.
  • V. HYBRID BEAMFORMING AT MM-WAVE: Codebook-based beamforming uses predefined beams for downlink training and feeds back selected beam IDs instead of estimating the full CSI matrix at the receiver.
  • V. HYBRID BEAMFORMING AT MM-WAVE: Spatially sparse precoding approximates the unconstrained beamformer using array-response vectors and a sparsity-constrained matrix reconstruction.The approximation can be sufficiently close to the optimal precoder with finite antenna arrays when dominant multipaths are few.
  • V. HYBRID BEAMFORMING AT MM-WAVE: Fast greedy antenna-subset selection performs as robustly as exhaustive search in sparse mm-wave channels.With equal spectral efficiency, hybrid antenna selection can outperform a sparse hybrid combiner with coarsely quantized phase shifters in power consumption.
  • V. HYBRID BEAMFORMING AT MM-WAVE: CAP-MIMO uses a lens antenna and feed-array beam selector to select high-gain beams in the low-dimensional beamspace of sparse multipath channels.

B. Hybrid beamforming in mm-wave MU scenarios

In mm-wave multi-user scenarios, hybrid beamforming combines analog beam selection with digital interference mitigation, but RF imperfections degrade spectral efficiency and several implementation questions remain open.

  • B. Hybrid beamforming in mm-wave MU scenarios: Hybrid beamforming at the base station transmits multiplexed data streams to multiple UEs equipped with one antenna or fully analog beamforming arrays.
  • B. Hybrid beamforming in mm-wave MU scenarios: ZF digital precoding mitigates inter-user interference, enabling hybrid beamforming to significantly outperform analog beamsteering in multi-cell scenarios.
  • B. Hybrid beamforming in mm-wave MU scenarios: The achievable-rate comparison considers randomly selected groups of n = 2, ..., 5 associated UEs under single-path and blockage-based line-of-sight conditions.
  • B. Hybrid beamforming in mm-wave MU scenarios: Multi-user scheduling and 2D and 3D lens-array design remain open research issues for mm-wave hybrid beamforming.
  • C. Impact of transceiver imperfections: RF imperfections, including 6-bit phase-shifter quantization and residual transceiver impairments, significantly degrade the spectral efficiency of spatially sparse hybrid precoding.

D. Spectral-energy efficiency tradeoff

The survey examines the energy-efficiency–spectral-efficiency relationship of a millimeter-wave hybrid structure and finds that the number of RF chains can be optimized for each target spectral efficiency. Hybrid beamforming seeks this tradeoff by combining analog and digital processing while limiting expensive, energy-consuming RF chains.

  • EE-SE tradeoff: An optimal number of RF chains achieves maximal EE for any given SE in the considered mm-wave hybrid structure.The structure uses sub-arrays at the base station to serve users individually.
  • EE-SE tradeoff: The EE-SE relationship is evaluated for Structure B with NBS = 800 and a 200 MHz system bandwidth.The figure assumes a noise power spectral density of 10−17 dBm/Hz, average channel gain of −100 dB, and fixed power-consumption parameters.
  • Design context: Hybrid beamforming combines analog and digital beamforming to exploit large arrays while keeping expensive and energy-hungry RF chains within reasonable limits.The survey categorizes designs by CSI requirements, hardware complexity, and carrier-frequency range, with no single structure best across all categories.
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