High-Frequency Hybrid Beamsteering

• High-frequency hybrid beamsteering is an approach that combines analog beamforming with digital precoding to form highly directional mmWave and THz wireless links under strict hardware and propagation constraints.
• It employs hybrid architectures—such as fully-connected, subarray, and switch-based networks—to balance flexible beamforming performance with reduced RF chain complexity and power consumption.
• Practical designs mitigate wideband issues like beam squint using delay-based and angular strategies, ensuring robust performance in evolving 5G, 6G, and future high-throughput wireless networks.

High-frequency hybrid beamsteering refers to the design and implementation of beamforming architectures, algorithms, and hardware suitable for mmWave and terahertz (THz) frequencies, with hybrid analog-digital control, to achieve highly directional transmission, spatial multiplexing, and reliable link establishment under extreme physical, hardware, and propagation constraints. This approach consolidates advantages of analog beamsteering via phased arrays or switching or lens networks with the flexibility and multiplexing of digital precoding, while minimizing the number of RF chains and mixed-signal hardware required to support ultra-massive arrays and wide bandwidths. Hybrid beamsteering is a foundational technology for 5G NR, 6G, and future high-throughput wireless networks.

1. Mathematical Foundations of Analog Beamsteering

Analog beamsteering at high frequency is rooted in array response modeling and geometric propagation. For a narrowband, LOS or sparse mmWave/THz MIMO channel with $L$ dominant paths, the channel can be written as

$H = A_U\,\mathrm{diag}(g)\,A_B^H,$

where $A_B$ and $A_U$ are transmit/receive array response matrices constructed from steering vectors $a_B(\phi_\ell)$ and $a_U(\theta_\ell)$, and $g$ collects complex path gains. For uniform linear arrays (ULAs),

$$a_B(\phi) = [1, e^{-j2\pi d\sin\phi/\lambda}, \ldots, e^{-j2\pi (N_B-1)d\sin\phi/\lambda}]^T,$$

and similarly for $a_U(\theta)$. Analog beamformers select $F_A = A_B$, $W_A = A_U$, steering along dominant spatial directions.

After analog-only steering, the effective channel matrix collapses to a near-diagonal structure:

$$H_{\text{eff}} = W_A^H H F_A \approx \mathrm{diag}(g),$$

as cross-coupling terms are suppressed by array orthogonality for $N_{B}, N_{U} \gg L$ (Zou et al., 2017).

The achievable rate with pure analog beamsteering, and the gap to full digital SVD-based beamforming,

$$R_{\mathrm{AB},\infty} \approx \mathbb{E}\left[\sum_{\ell=1}^L \log_2\left(1 + \frac{P_s}{\sigma_n^2}|g_\ell|^2\right)\right]$$

tracks the digital-optimal rate closely at low and medium SNR, but a finite gap emerges at high SNR as off-diagonal interference cannot be completely eliminated (Zou et al., 2017).

Practical constraints enforce implementation via codebooks of quantized phase-shifter settings, leading to rate loss that depends on the codebook size $C$, antenna count $N$, and SNR. Analytical bounds show that codebook sizes $C\gtrsim N$ suffice for $\leq3$ dB loss, while $C\approx 2N$ yields near-infinite-precision performance (Zou et al., 2017).

2. Hybrid Architectures and Their Physical Realizations

Hybrid beamforming architectures enable high-frequency steering by partitioning beamforming across (i) an analog/RF network realized by phase shifters, switches, or lens arrays, and (ii) a digital/baseband stage. The analog layer rapidly coarsely aligns energy along the dominant paths, while the digital layer provides fine spatial multiplexing or interference suppression within a lower-dimensional subspace.

Classes of architectures include:

• Fully-connected phase-shifter networks: Each RF chain drives all $N$ antennas through dense PS-Networks (Sohrabi et al., 2017), supporting arbitrary beam combinations but at high power and insertion loss.
• Subarray/partially-connected networks: Each RF chain addresses a subset of antennas, reducing hardware at the cost of less flexible beams; block-diagonal analog matrices are typical (Sohrabi et al., 2017).
• Switch-based or lens-based beamspace architectures: Selection among fixed beams using binary switches or passive lens arrays, optimized via discrete beam index selection (Shuang et al., 2018, Ma et al., 2022).
• MA-aided or tile-based architectures: Hierarchical grouping of antennas into tiles/panels with partial physical repositioning (slow geometric DOF) to emulate wideband focusing in the absence of TTD hardware (Zhang et al., 11 Nov 2025).
• Fixed or dynamic true-time-delay (TTD) arrays: Incorporation of frequency-agnostic delay lines to overcome beam squint in wideband THz; dynamic-subarray with fixed TTD achieves high energy efficiency without expensive variable-delay elements (Yan et al., 2022).

Hybrid structures can flexibly accommodate different numbers of streams and RF chain counts, with the practical minimum to achieve full spatial multiplexing set by channel sparsity (in mmWave, $N_{\text{RF}}=L$ is sufficient in large arrays with $L$ paths (Sohrabi et al., 2017, Zou et al., 2017)).

3. Wideband, Beam Squint, and Beam Split Effects

Wideband high-frequency systems suffer from frequency-dependent deviations in array responses, generically termed beam squint (in the far-field, ULA) or beam split (in THz ultra-massive and near-field). Fixed phase-shifter arrays produce beams whose maxima shift with frequency; the misalignment increases linearly with array size, bandwidth, and element spacing.

• Beam squint ratio (BSR): $BSR \approx N b \Delta / 8$, with $b=B/f_c$ fractional bandwidth, $N$ antennas, element spacing $\Delta$ (Ma et al., 2022).
• Array gain collapse: For large BSR, the per-frequency array gain drops, and fully-connected phase-shifter-based HBF is bounded by $\approx1/3$ the narrowband gain (Ma et al., 2022). Switch-based HBF is more robust, with higher minimum broadband gain for the same array size.

Mitigation strategies:

• Delay-phased or TTD-based architectures: Application of frequency-dependent delays per element flattens frequency response, at high power/hardware cost (Yan et al., 2022).
• Angular-based hybrid beamforming: By broadening the analog beamwidth according to measured or assumed angular spread (i.e., selecting analog steering vectors covering a support region), beam split can be mitigated without additional TTD hardware (Yildirim et al., 24 Mar 2025). Effective beamwidths $$\Delta\theta_{\rm eff} = \Delta\theta_0 + 2 \sigma_\theta$$ accommodate the needed frequency variation.
• MA-aided architectures: Reconfiguring antenna/tile positions provides a geometric analog to TTD, flattening array gain across band edges in near-field wideband scenarios (Zhang et al., 11 Nov 2025).

4. Hybrid Beamsteering Algorithms and Optimization

High-frequency hybrid beamsteering algorithms must jointly solve analog and digital beamformer design under constant-modulus, switch, or delay-based constraints, typically leveraging the channel’s sparse or structured nature.

Representative algorithm classes include:

• Alternating minimization: For partially-connected or fully-connected architectures, alternate between LS/SVD update for digital precoder and coordinate-descent or quantized update for analog phase-shifters (Sohrabi et al., 2017, Sohrabi et al., 2016).
• Angular support expansion: Select analog steering vectors spread over the angular region of significant channel paths; alternate with digital SVD update per subcarrier (Yildirim et al., 24 Mar 2025).
• Beam selection via structured search: For switch/lens-based HBF, select the subset of analog beams or DLA index set to minimize Gram-matrix inverse trace (i.e., condition number), via ACO, greedy or exhaustive assignment (Shuang et al., 2018).
• Low-complexity/implicit CSI approaches: Beamforming based on coupling coefficients or beam training—selecting analog beams with the largest energy or Frobenius-norm effective channel over subcarrier measurements (Chiang et al., 2018, Chiang et al., 2017).
• Row-decomposition for TTD/SW-HBF: Alternating update of switches (for fixed TTD) and digital block via minimal-score selection, with digital blocks solved in closed form (e.g., orthogonal Procrustes) (Yan et al., 2022). Switch-based HBF also leverages PGA-TS algorithms combining projected gradient and tabu search for binary realization (Ma et al., 2022).
• Hierarchical/flat-top beam codebook in beam management: Hierarchical flat-top codebooks with variable width are designed for fast, reliable beam training during initial access and under mobility constraints (Alexandropoulos et al., 2021, Jiang et al., 2022).

5. Performance, Hardware Tradeoffs, and Implementation Insights

Numerical and experimental evaluations demonstrate:

• Near-optimality vs. digital beamforming: For mmWave and THz, properly configured hybrid schemes achieve $\lesssim1$–$2$ dB rate loss versus fully-digital SVD-based designs at low-to-medium SNR, with residual gap primarily from inter-stream interference at high SNR (Zou et al., 2017, Sohrabi et al., 2017, Yildirim et al., 24 Mar 2025).
• RF hardware scaling: Subarray, switch-based, and lens-based architectures reduce the count of active RF devices (phase shifters, TTDs, amplifiers), and partially-connected schemes achieve nearly the same spectral efficiency with an order-of-magnitude fewer RF chains (Sohrabi et al., 2017).
• Robustness to channel state information (CSI) error: Angular-based and DS-FTTD architectures maintain $\geq80\%$ efficiency even when CSI NMSE is as high as 0.4 (Yan et al., 2022, Yuan et al., 2019).
• Beam training latency: Multi-level, hierarchical codebooks and flat-top analog beams reduce initial access and handover delays from tens of slot sweeps to a few macro time slots (Alexandropoulos et al., 2021, Jiang et al., 2022).
• Energy efficiency: DS-FTTD and switch-based HBF enable up to 3$\times$ improvement in energy efficiency over FC-TTD and phase-shifter networks in large wideband arrays at THz (Yan et al., 2022, Ma et al., 2022).
• MA-aided and tile-based designs: Tile positioning enhances beam squint mitigation performance, matches or exceeds TTD benchmarks, and increases the sum rate by up to 140% in extreme bandwidth, multi-user near-field THz settings (Zhang et al., 11 Nov 2025).

Table: Key High-Frequency Hybrid Beamsteering Architectures

Architecture	Physical Mechanism	Beam Squint Mitigation	Complexity/Cost
Phase-shifter FC	Dense phase shifters	Poor	High power, high loss
Switch-based	Antenna switches	Good at wideband	Low power, fast reconfig
DS-FTTD	Fixed delay + switches	Excellent	Modest, no var. TTDs
MA/tile-based	Movable array elements	Excellent (geometric)	Low-speed mechanical adj.
Lens-array	Passive spatial FT	Limited	Ultra-low insertion loss

6. Extensions: Multiuser, Near-Field, and Cell-Free Scenarios

Hybrid beamsteering frameworks extend beyond single-user links to multiuser massive MIMO, uplink beam management, and cell-free cooperative architectures.

• Multiuser MIMO: Joint hybrid precoding/combining strategies maximize sum rate or weighted sum rate via WMMSE, ZF, or SCA algorithms, adapted to channel sparsity and analog hardware constraints. Performance approaches digital ZF with only slightly increased RF chains (Sohrabi et al., 2017, Sohrabi et al., 2016).
• Cell-free and distributed MIMO: Hierarchical DRL-based hybrid beamsteering enables dynamic clustering and RF nulling among subnetworks, with analog beamsteering learned and digital ZF optimized per subnetwork, providing up to 28% sum-rate gain versus all-digital baselines (Al-Eryani et al., 2021).
• Near-field LoS beam focusing: Beam focusing with wide-aperture arrays leverages prolate-Landau eigenstructure and 2D-DFT asymptotics for closed-form hybrid beam designs, enabling spatial multiplexing in the spherical regime under hybrid hardware constraints (Yun et al., 7 Apr 2024).

7. Practical Design Guidelines and Future Directions

For system designers, high-frequency hybrid beamsteering involves:

1. Angular estimation: Low-rate pilot schemes suffice for initial angle, spread, and codebook adaptation (Yildirim et al., 24 Mar 2025).
2. Analog beam selection: Use array response vectors or geometric/tile parameterization covering the sparse angular support; set codebook size to $C\geq N$ for minimal quantization loss (Zou et al., 2017).
3. Digital stage configuration: Align digital baseband beamforming (SVD or WMMSE) to the effective lower-dimensional channel.
4. Periodic codebook/dictionary update: Track channel changes on the order of coherence time; practical with agile analog selection or slow MA repositioning (Zou et al., 2017, Zhang et al., 11 Nov 2025).
5. Switch and delay network selection: For extreme wideband/THz, implement DS-FTTD or switch-based architectures to suppress squint/beam split with O(10–30) W total network power at k-antenna scales (Ma et al., 2022, Yan et al., 2022).

Current trends indicate a pivot to geometric and hardware-based innovations (tile-motion, lens/delay hybrids), robust multiuser protocol integration, and autonomous adaptation via reinforcement learning for scalable real-world deployments (Al-Eryani et al., 2021, Zhang et al., 11 Nov 2025).

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References:

• (Zou et al., 2017) Analog Beamsteering for Flexible Hybrid Beamforming Design in Mmwave Communications
• (Sohrabi et al., 2017) Hybrid Analog and Digital Beamforming for mmWave OFDM Large-Scale Antenna Arrays
• (Ma et al., 2022) Switch-based Hybrid Beamforming Transceiver Design for Wideband Communications with Beam Squint
• (Yildirim et al., 24 Mar 2025) Angular-Based Hybrid Beamforming for Wideband THz Massive MIMO Systems: Mitigating Beam Split by Leveraging Angular Spread
• (Yan et al., 2022) Energy-efficient Dynamic-subarray with Fixed True-time-delay Design for Terahertz Wideband Hybrid Beamforming
• (Zhang et al., 11 Nov 2025) MA-Aided Hierarchical Hybrid Beamforming for Multi-User Wideband Beam Squint Mitigation
• (Yun et al., 7 Apr 2024) Analog-Digital Beam Focusing for Line of Sight Wide-Aperture MIMO with Spherical Wavefronts
• (Alexandropoulos et al., 2021) Uplink Beam Management for Millimeter Wave Cellular MIMO Systems with Hybrid Beamforming
• (Al-Eryani et al., 2021) Self-Organizing mmWave MIMO Cell-Free Networks With Hybrid Beamforming: A Hierarchical DRL-Based Design
• (Sohrabi et al., 2016) Hybrid Digital and Analog Beamforming Design for Large-Scale Antenna Arrays
• (Shuang et al., 2018) Beam Selection for MmWave Massive MIMO Systems Under Hybrid Transceiver Architecture
• (Chiang et al., 2018) Frequency-Selective Hybrid Beamforming Based on Implicit CSI for Millimeter Wave Systems
• (Jiang et al., 2022) Initial Access for Millimeter-Wave and Terahertz Communications with Hybrid Beamforming
• (Yuan et al., 2019) Hybrid Beamforming for Terahertz Multi-Carrier Systems over Frequency Selective Fading