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Hybrid Beamforming for 5G and Beyond Millimeter-Wave Systems: A Holistic View
Jun Zhang, Xianghao Yu, Khaled B. Letaief
TL;DR
Mm-wave systems need beamforming that avoids the cost and power burden of one RF chain per antenna while preserving high spectral efficiency. The paper develops a taxonomy and systematically compares hybrid structures across hardware, computational, and spectral efficiency, finding that suitable structures can approach fully digital performance with low hardware complexity. Its conclusions identify RF-chain counts comparable to data streams, fixed phase-shifter designs, and flexible mappings as promising directions, while practical adoption remains constrained by hardware and algorithmic challenges.
Problem
Fully digital beamforming is costly and power-hungry for large mm-wave arrays, while hybrid beamforming still requires jointly addressing hardware complexity, algorithmic complexity, and spectral efficiency.
Method
The paper proposes a taxonomy of hybrid beamforming structures and compares their mapping strategies, hardware implementations, algorithms, and spectral efficiency.
Results
Suitable hybrid structures can approach fully digital performance with low hardware complexity; fixed phase shifter designs need only a small number of phase shifters, approximately 10.
Takeaways & Limitations
Hybrid beamforming is promising for 5G and beyond mm-wave systems when analog-network structure is chosen to balance hardware, computational, and spectral efficiency.
Takeaways & Limitations
Practical applicability remains limited by hardware complexity and the non-convex, computationally challenging nature of hybrid beamforming design.
Abstract
from arXiv · showhide
Millimeter-wave (mm-wave) communication is a key technology for future wireless networks. To combat significant path loss and exploit the abundant mm-wave spectrum, effective beamforming is crucial. Nevertheless, conventional fully digital beamforming techniques are inapplicable, as they demand a separate radio frequency (RF) chain for each antenna element, which is costly and consumes too much energy. Hybrid beamforming is a cost-effective alternative, which can significantly reduce the hardware cost and power consumption by employing a small number of RF chains. This paper presents a holistic view on hybrid beamforming for 5G and beyond mm-wave systems, based on a new taxonomy for different hardware structures. We take a pragmatic approach and compare different proposals from three key aspects: 1) hardware efficiency, i.e., the required hardware components; 2) computational efficiency of the associated beamforming algorithm; and 3) achievable spectral efficiency, a main performance indicator. Through systematic comparisons, the interplay and trade-off among these three design aspects are demonstrated, and promising candidates for hybrid beamforming in future wireless networks are identified.
I. INTRODUCTION
The paper frames hybrid beamforming as a response to mm-wave hardware and algorithmic challenges, and evaluates structures through hardware, spectral, and computational efficiency. It introduces new analog-network implementations and a flexible mapping strategy to balance these objectives.
- Motivation: Mm-wave 5G offers abundant spectrum and supports large-scale antenna arrays, but implementation must meet stringent rate, efficiency, and latency demands.The introduction cites orders-of-magnitude goals for peak data rate, area spectral efficiency, and network energy efficiency, with about 1 ms roundtrip latency.
- Challenges: Fully digital beamforming is impractical for large mm-wave arrays because its mixers, ADCs/DACs, and power amplifiers impose prohibitive cost and power burdens.The increased beamformer dimension also creates stringent computational-efficiency requirements.
- Prior approaches: Analog beamforming reduces complexity but supports only single-stream transmission, motivating hybrid beamforming to exploit more spatial resources.Prior work developed low-complexity and higher-spectral-efficiency hybrid designs for mm-wave systems.
- Open challenges: Hybrid beamforming still faces hardware-cost and non-convex algorithm-design challenges that affect practical applicability.These issues motivate structures that improve hardware efficiency while retaining tractable beamforming algorithms.
- Paper scope: The paper compares hybrid beamforming through hardware efficiency, computational efficiency, and spectral efficiency, emphasizing their interplay.The desired design uses few hardware components, low-complexity algorithms, and spectral efficiency close to fully digital beamforming.
- Contributions: The paper presents state-of-the-art structures, identifies their limitations, introduces two analog implementations, and proposes flexible RF-chain-to-antenna mapping.The stated goals include simplifying algorithm design, reducing hardware complexity, and balancing hardware complexity against spectral efficiency.
II. A PRIMER ON HYBRID BEAMFORMING
A hybrid beamformer combines a digital component implemented with RF chains and an analog network shared across users and subcarriers. The analog network is the main structural differentiator, linking hardware requirements to algorithmic difficulty and spectral efficiency.
- System model: The considered system is a downlink multiuser mm-wave MIMO-OFDM system with an Nt-antenna base station serving K users over F subcarriers.Each user receives Ns data streams per subcarrier, with a limited number of BS RF chains.
- Hybrid architecture: The hybrid beamformer contains digital and analog components, with RF chains forming the common digital-side structure.The digital component can be designed per user and subcarrier.
- Hybrid architecture: The analog network is shared by all users and subcarriers because analog RF beamforming occurs after the IFFT.This differs from the user- and subcarrier-specific digital beamformers.
- Design focus: The analog network is the key differentiator because its structure affects hardware efficiency, algorithm design, and achievable spectral efficiency.The paper therefore focuses its structural comparison on the analog network.
- Hardware criteria: Hardware efficiency is compared by counting key components rather than explicitly evaluating energy efficiency.The paper argues that changing hardware choices makes direct energy-efficiency comparisons difficult, although hardware efficiency largely determines it.
- Hardware criteria: Phase shifters and switches dominate analog-network hardware trade-offs because power amplifiers are required for each antenna element.Switches reduce implementation complexity, power consumption, and cost, but their binary operation can reduce spectral efficiency.
B. A Taxonomy of Hybrid Beamforming Structures
Hybrid beamforming structures are classified by how RF chains connect to antennas and by the hardware used for each connection. These choices determine the analog-matrix constraints and consequently influence algorithm design and performance.
- Taxonomy: The taxonomy separates analog-network design into mapping strategy and hardware implementation.Mapping determines RF-chain-to-antenna connectivity, while implementation specifies the components used for each connected pair.
- Basic structures: Fully-connected mapping links every RF chain to every antenna, whereas partially-connected mapping links each RF chain to a non-overlapping subset of neighboring antennas.The basic comparison uses the single-phase-shifter implementation.
- Design formulation: The paper formulates hybrid design as approximation of a fully digital beamformer under transmit-power and hardware-dependent analog-network constraints.The formulation is applicable to any given digital beamformer and supports tractable algorithm design.
- Taxonomy: Table I organizes candidate structures by combining a mapping choice from part (a) with a hardware implementation from part (b).The table uses FRF for the analog beamforming matrix and fi and Fi for a column vector and matrix, respectively.
- Design formulation: The analog feasible set determines the structural constraints, while the digital component is optimized through a least-squares subproblem with a closed-form solution.The analog constraints are the main source of design difficulty.
B. SPS Fully-Connected Structure
The SPS fully-connected structure is analyzed as a constrained hybrid-beamforming design in which RF-chain and antenna connectivity determines the analog-network problem. OMP offers a lower-complexity codebook approach, while manifold optimization improves performance at higher complexity.
- Operating regimes: When N_RF ≥ 2KNs, SPS fully-connected hybrid beamforming can realize fully digital beamforming, making algorithm design trivial.The general case of interest has N_RF < 2KNs.
- Algorithms: For N_RF < 2KNs, OMP selects analog-beamformer columns from a codebook, typically formed by mm-wave channel array-response vectors.The codebook restriction inevitably causes some performance loss relative to fully digital beamforming.
- Algorithms: MO-AltMin treats the unit-modulus analog constraints as a complex-circle Riemannian manifold and outperforms OMP at increased complexity.It optimizes the full analog matrix rather than relying only on codebook column selection.
- Algorithms: Phase-shifter-by-phase-shifter optimization analytically evaluates each phase shifter's contribution to spectral efficiency and iteratively updates the analog network.This provides a finer-grained alternative to column-wise OMP and whole-matrix MO-AltMin updates.
C. SPS Partially-Connected Structure
The SPS partially-connected structure reduces hardware complexity to the level of analog beamforming, but its design methods impose performance or flexibility limitations.
- Hardware and algorithms: The SPS partially-connected structure uses as many phase shifters as analog beamforming, equal to the antenna size.Codebook-based methods have low complexity but incur performance loss, while SIC constrains the digital beamformer and requires RF chains to match data streams.
- Hardware and algorithms: Codebook-based design offers low complexity for narrowband and OFDM systems but may leave additional performance gains unclear.
- Hardware and algorithms: SIC decomposes rate optimization into per-RF-chain subproblems but forces a diagonal digital beamforming matrix and matching RF-chain and stream counts.
- Performance: SDR-AltMin achieves strong performance by obtaining globally optimal analog and digital subproblem solutions during alternating iterations.The design problem is decoupled across RF chains and their connected antenna elements.
- Performance: SDR-AltMin outperforms other benchmarks for the SPS partially-connected structure, whose simpler hardware also lowers computational complexity.
D. Limitations of Basic Structures
The basic structures expose a three-way trade-off: fully connected architectures can approach fully digital spectral efficiency but require high hardware or computational complexity, whereas partially connected designs reduce hardware at substantial performance cost.
- Performance trade-offs: The fully-connected structure provides much higher spectral efficiency than the partially-connected structure in the Fig. 3 comparison.The comparison uses six data streams at 0 dB SNR and varies the numbers of RF chains at both sides.
- Limitations: MO-AltMin has much higher computational complexity than other algorithms because it contains nested iterations.
- Performance trade-offs: With MO-AltMin, the fully-connected structure approaches fully digital performance when RF-chain count is comparable to data-stream count, unlike OMP.
- Performance trade-offs: The limited RF-chain count is not itself a performance bottleneck; the analog network structure has a decisive effect.
- Limitations: The fully-connected structure retains high analog-network hardware complexity, while the partially-connected structure reduces phase shifters but substantially degrades performance.
- Design challenge: Future designs must balance hardware efficiency, computational efficiency, and spectral efficiency through more flexible structures.
IV. TWO NEW ANALOG NETWORK IMPLEMENTATIONS
Two analog network implementations improve on the SPS design in different ways: DPS simplifies algorithm design and improves spectral efficiency, while FPS reduces hardware requirements and also performs well computationally and spectrally.
- DPS implementation: The DPS implementation simplifies algorithm design and improves spectral efficiency at the cost of additional phase shifters.Its investigation also motivates a convex-relaxation approach for efficient beamforming algorithms.
- FPS implementation: The FPS implementation uses a small number of fixed phase shifters with switches to improve hardware efficiency.It also performs well in computational efficiency and spectral efficiency.
A. Double Phase Shifter (DPS) Implementation
The DPS implementation improves hybrid beamforming by using two phase-shifter sets, enabling efficient algorithms and stronger spectral-efficiency performance than SPS structures. Its benefits trade increased phase-shifter hardware against reduced RF-chain requirements and improved performance.
- Hardware implementation: DPS uses two phase-shifter sets, allowing each analog-network connection to combine outputs from two phase shifters.The DPS partially-connected structure uses 2N_t phase shifters, between the SPS partially-connected and DPS fully-connected structures.
- Beamforming algorithms: The DPS fully-connected design reduces beamforming to a low-rank matrix approximation with a closed-form solution, while its SPS counterpart can use phase extraction from the DPS solution.The phase-extraction approach requires only an SVD operation, yielding a low-complexity SPS algorithm.
- Fully-connected mapping: For single-carrier systems, DPS fully-connected beamforming perfectly decomposes a fully digital beamformer with the minimum N_RF = N_s RF chains.This reduces the RF-chain requirement by half compared with the SPS fully-connected implementation, which needs 2KN_s RF chains for fully digital beamforming.
- Performance and trade-offs: DPS fully-connected structures achieve near-optimal spectral efficiency, while dynamic mapping halves the performance gap between fixed mapping and fully digital beamforming in the partially-connected case.The SPS fully-connected convex-relaxation algorithm outperforms the state-of-the-art algorithm in [27] with much lower computational complexity.
- Partially-connected mapping: In the DPS partially-connected structure, each RF-chain optimization is an eigenvalue problem with closed-form solutions, improving computational efficiency.The associated mapping design remains combinatorial; greedy and modified K-means algorithms are proposed instead of exhaustive search.
- Performance and trade-offs: DPS performance and algorithmic gains require more phase shifters, so deployment may depend on the availability of low-cost, low-power phase shifters.The DPS approach nevertheless provides design guidance for other hybrid beamforming structures and supports theoretical analysis through low-rank or eigenvalue formulations.
B. Fixed Phase Shifter (FPS) Implementation
The FPS implementation uses a small number of fixed phase shifters followed by adaptive switches, reducing hardware complexity while retaining channel-adaptive connections. Its binary switch formulation supports relatively simple algorithm design, but switch count remains substantial.
- Architecture: The FPS implementation lets each signal pass through multiple phase shifters, using a small number of quantized, fixed-phase devices.This contrasts with approaches using many unquantized phase shifters and targets lower cost and power consumption.
- Architecture: A dynamic switch network selects and combines fixed-phase outputs to adapt the RF-chain-to-antenna connections to channel states.The network compensates for the limited channel adaptability of fixed phase shifters.
- Hardware requirements: The FPS implementation requires N_tN_RF N_c adaptive switches while using only N_c fixed phase shifters.The fixed phase shifters process RF-chain outputs in parallel, and selected outputs are combined for each antenna connection.
- Trade-offs: The FPS structure can have hardware complexity comparable to or lower than analog beamforming, although partially connected FPS designs may incur significant performance loss.An efficient alternating-minimization algorithm was proposed for the associated switch-network problem.
- Algorithm design: Its analog-network design determines binary switch states, with the switch matrix S and fixed-phase operation matrix C defining the formulation.This replaces continuous analog-phase optimization with a binary-variable design problem.
C. Performance Comparison
The DPS and FPS fully connected structures approach fully digital spectral efficiency in the evaluated multicarrier multiuser system. FPS achieves similar performance with far fewer phase shifters, making it attractive for practical deployment.
- Spectral-efficiency comparison: Both DPS and FPS fully connected structures achieve spectral efficiency close to fully digital beamforming.The comparison uses a general multicarrier multiuser system where the MO-AltMin algorithm is considered too complex to apply.
- Hardware-performance comparison: Around 10 fixed phase shifters suffice for FPS, compared with 1152 for SPS and 2304 for DPS.FPS therefore retains performance close to DPS while using substantially fewer phase shifters.
- Deployment implications: DPS is attractive for cost-insensitive applications or systems with low-cost, high-resolution commercial phase shifters.Under those conditions, DPS is described as favorable in both spectral and computational efficiency.
V. A FLEXIBLE MAPPING STRATEGY FOR HARDWARE-PERFORMANCE TRADE-OFFS
The flexible group-connected mapping strategy divides RF chains and antennas into groups, allowing hardware complexity and spectral efficiency to be adjusted through the group count. It preserves compatibility with existing analog-network implementations and algorithms.
- Mapping structure: The group-connected strategy divides antennas and RF chains into η groups, with each RF-chain group connected to its corresponding antenna group.The grouping is flexible, and different groups may contain different numbers of RF chains and antennas.
- Algorithm design: The block-diagonal analog beamforming matrix decouples the design of each group, so existing fully connected algorithms can be reused without additional design difficulty.Each block corresponds to one antenna and RF-chain group.
- Mapping structure: η = 1 gives fully connected mapping, whereas η = N_RF gives partially connected mapping.Intermediate η values provide mapping strategies with different hardware complexities.
- Hardware scaling: For SPS and DPS implementations, the group-connected mapping uses 1/η of the fully connected number of phase shifters.The same group-connected mapping can also be combined with the other analog implementations considered in the paper.
- Trade-off: Varying η balances hardware complexity and spectral efficiency, while the strategy provides a flexible performance–hardware trade-off compatible with different implementations.The paper identifies compatibility with different analog networks and existing beamforming algorithms as key properties.
VI. CONCLUSIONS AND FUTURE DIRECTIONS
The paper’s systematic comparison shows that suitable hybrid beamforming structures can approach fully digital performance with low hardware complexity, motivating FPS group-connected mapping as a promising candidate. Future work must address channel acquisition, algorithm complexity, ADC quantization, hardware–algorithm co-design, and network-level effects.
- Conclusions: The comparison evaluates hybrid beamforming structures across hardware efficiency, spectral efficiency, and computational efficiency.It shows that hardware implementation affects both algorithm design and achievable spectral efficiency.
- Conclusions: RF chains comparable to the number of data streams and approximately 10 fixed phase shifters can suffice for near-fully-digital performance with FPS.The FPS group-connected structure is identified as a promising candidate for 5G and beyond mm-wave systems.
- Future directions: Perfect CSI is assumed, while acquiring large-scale CSI with reduced RF chains remains challenging.Different hybrid beamforming structures may require different training methods, particularly under low-SNR training conditions.
- Future directions: Further work is needed on lower-complexity beamforming algorithms and on extending the structures to systems with low-resolution ADCs.The paper highlights deep learning as one possible direction for reducing algorithmic complexity and identifies ADC quantization as an unresolved digital-domain issue.
- Future directions: Hardware–algorithm co-design and network-level analysis are needed because hybrid beamforming creates more intricate signal and interference distributions.The FPS implementation is presented as a preliminary hardware–algorithm co-design effort.