Efficient Hybrid Beamfocusing in Near-Field Systems

• Energy-efficient hybrid beamfocusing is the design of transceivers that exploit near-field spherical-wave propagation to focus energy jointly in range and angle, enhancing spatial multiplexing.
• It integrates wideband OFDM and polar-domain channel models to manage frequency-dependent focal patterns and mitigate beam-squint through true-time-delay compensation.
• Hybrid architectures combine phase shifters, TTD networks, and dynamic subarrays to balance spectral efficiency and hardware constraints, achieving superior energy efficiency.

Energy-efficient hybrid beamfocusing is the design of hybrid analog–digital transceivers that exploit near-field spherical-wave propagation to concentrate electromagnetic energy at prescribed spatial locations while constraining RF-chain count, analog-network losses, DAC/ADC power, and baseband complexity. In extremely large-scale antenna arrays operating at mmWave and THz frequencies, the Rayleigh distance $R_{\mathrm{Rayleigh}}=2D^2/\lambda$ can extend over microcell scales, so communication often occurs in the Fresnel region rather than the far field. In that regime, beam control is inherently joint in range and angle, and energy efficiency depends not only on radiated power but also on how accurately hybrid hardware can realize frequency-dependent focal patterns under practical impairments (An et al., 2023).

1. Near-field regime and the meaning of beamfocusing

For an aperture of size $D$ and wavelength $\lambda$, the far-field approximation ceases to be accurate once the link distance is comparable to $R_{\mathrm{Rayleigh}}=2D^2/\lambda$. At mmWave and THz, large apertures make this boundary operationally important: planar-wave steering no longer captures the propagation phase across the array, and spherical-wavefront models become necessary. Near-field communication therefore targets the radiating Fresnel region, not the reactive near field, and the array response depends on user range as well as direction (An et al., 2023).

This distinction separates beamfocusing from conventional far-field beamforming. Far-field beamforming is angle-only: its weights are determined by direction-of-arrival or direction-of-departure, and users with similar angles are difficult to separate in line-of-sight channels. Near-field beamfocusing instead creates a localized focal spot in range–angle space. The transmit beampattern for a precoder $f\in\mathbb{C}^{N_t}$,

$B_t(r,\theta)=\left|a_t(r,\theta)^H f\right|^2,$

is therefore distance-aware, and leakage can be suppressed between users that are angularly aligned but range-separated. A plausible implication is that the near-field aperture itself becomes a multiplexing resource, not merely an array-gain resource (An et al., 2023).

A standard single-path free-space model already reflects this shift. If the $m$-th element is at $p_m\in\mathbb{R}^3$ and the user is at $u\in\mathbb{R}^3$, then

$$h_m(u)=\alpha \frac{e^{-j(2\pi/\lambda)\|u-p_m\|}}{\|u-p_m\|},$$

so both phase and amplitude vary across the aperture. For a ULA, the element-to-user distance is

$D$0

with steering coefficient

$D$1

These expressions make explicit that near-field focusing is fundamentally a spherical-wave synthesis problem rather than a plane-wave steering problem (An et al., 2023).

2. Channel, waveform, and energy-efficiency models

The near-field MIMO channel is commonly represented in a polar-domain form. A compact multipath model is

$D$2

with each path parameterized by range and angle. In wideband OFDM, each subcarrier has a frequency-dependent channel $D$3, and the focusing parameters vary across frequency because the array response itself is frequency dependent. This is the origin of near-field beam-squint or beamsplit: a focal spot synthesized at the carrier frequency drifts in both angle and distance over the band unless the analog network compensates group delay (An et al., 2023).

A frequency-domain formulation used in wideband near-field systems writes the propagation delay from antenna $D$4 to position $D$5 as $D$6, with steering coefficient

$D$7

Under a second-order approximation for a ULA,

$D$8

where

$D$9

This captures the range–angle coupling that hybrid beamfocusing must preserve or compensate (Zhou et al., 4 Dec 2025).

Energy efficiency is usually measured in bits per Joule. A common communication-centric definition is

$\lambda$0

with

$\lambda$1

The corresponding spectral-efficiency expression is often written through an effective channel $\lambda$2,

$\lambda$3

This model makes clear that EE is shaped jointly by radiated power, insertion loss, RF-chain scaling, and the computational load of channel estimation and precoding (An et al., 2023).

Security- and sensing-oriented variants refine the numerator while preserving the same denominator logic. In near-field wideband secure transmission, secrecy energy efficiency is defined as

$\lambda$4

where $\lambda$5, and the total power includes transmit power plus $\lambda$6, $\lambda$7, $\lambda$8, and $\lambda$9. In near-field ISAC, the same bits-per-Joule perspective is coupled to CRB or BCRB constraints, exposing an explicit estimation–energy tradeoff (Zhang et al., 2023).

3. Hybrid architectures and their energy implications

The architectural spectrum is broad, but its tradeoffs are structurally consistent. Fully digital arrays provide the highest near-field fidelity because each element has its own RF chain, yet at THz/mmWave with ELAAs they are constrained by RF-chain power, data-converter energy, clocking, and thermal load. Phase-shifter-based hybrid arrays reduce active-chain count and are therefore more energy-friendly, but their analog weights are frequency-flat, so wideband near-field focusing suffers from beam-squint, quantization loss, and insertion loss through large PS networks (An et al., 2023).

True-time-delay networks address the frequency-flat limitation by realizing delays rather than static phases. In wideband near-field links, they provide frequency-consistent focal spots and are therefore the standard remedy for spatial wideband effects. Their cost is higher hardware complexity, potential group-delay error, additional control energy, and extra insertion loss. This makes TTD architectures attractive when spectral-efficiency loss from misfocus dominates, but not automatically EE-optimal when the band is narrow or the aperture is moderate (An et al., 2023).

Sub-connected and switch-based architectures refine this tradeoff. In TTD-based wideband beamfocusing, a fully-connected analog network maximizes combining gain but requires many TTDs and PSs; a sub-connected network lets each RF chain drive only a subarray, reducing TTD count, maximum delay requirements, insertion loss, and control power, at a modest performance penalty. In one RSMA-based wideband design, the sub-connected TTD architecture is stated to have a performance gap of approximately $R_{\mathrm{Rayleigh}}=2D^2/\lambda$0 bps/Hz relative to the fully-connected counterpart in the reported setup, while improving energy efficiency through lower hardware burden (Zhou et al., 4 Dec 2025).

A more hardware-constrained THz variant is the dynamic-subarray with fixed true-time-delay architecture. It replaces adjustable TTDs and dense PS networks with low-cost fixed delays and a binary switch network. The analog mapping is

$R_{\mathrm{Rayleigh}}=2D^2/\lambda$1

combined with a binary switch matrix $R_{\mathrm{Rayleigh}}=2D^2/\lambda$2 whose rows each contain exactly one nonzero entry. This architecture was designed specifically to combat beam squint while keeping high energy efficiency, because fixed delays and switches consume markedly less power than adjustable TTD fabrics (Yan et al., 2022).

Metasurface and electromagnetic-domain implementations extend the same logic. Lens arrays, dynamic metasurface antennas, and stacked intelligent metasurfaces reduce active power and heat at the expense of focusing granularity, calibration burden, and limited per-subcarrier flexibility (An et al., 2023). A more recent tri-hybrid architecture adds an electromagnetic layer through radiation-center reconfigurable antenna arrays, combining digital beamforming, analog beamforming, and electromagnetic beamforming via radiation-center selection. This introduces extra spatial degrees of freedom without scaling RF chains proportionally, and the reported EE gains are especially pronounced for partially connected implementations (Li et al., 21 Aug 2025).

4. Optimization frameworks and algorithmic design

Near-field channel estimation is usually posed in a polar sparse domain rather than a Fourier angular domain. Reported algorithmic families include simultaneous OMP and gridless iterative weighted methods adapted to spherical steering vectors, sparse Bayesian learning that jointly estimates channels and beam-split parameters, and geometry-aided estimation for RIS-assisted localization. These methods exploit the fact that line-of-sight-dominant mmWave/THz channels are sparse in range–angle coordinates rather than in pure angle (An et al., 2023).

Hybrid precoding then becomes a constrained approximation problem over constant-modulus phases, delay sets, or switch graphs. Standard strategies include codebook-based focusing, alternating optimization, OMP over spherical-wave atoms, and manifold or projected-gradient methods. The “$R_{\mathrm{Rayleigh}}=2D^2/\lambda$3” design decomposes three-dimensional focusing into two-dimensional far-field beamsteering plus one-dimensional range compensation, thereby reducing codebook size and pilot overhead. Low-complexity designs also exploit LDMA, where near-field steering vectors become asymptotically orthogonal in range, simplifying precoder construction (An et al., 2023).

Wideband RSMA-enabled beamfocusing makes this structure more explicit. One formulation maximizes the minimum user rate by jointly optimizing frequency-dependent analog beamfocusing, frequency-independent analog beamfocusing, digital beamfocusing, and common-rate allocation. The transmitted signal on subcarrier $R_{\mathrm{Rayleigh}}=2D^2/\lambda$4 is

$R_{\mathrm{Rayleigh}}=2D^2/\lambda$5

with $R_{\mathrm{Rayleigh}}=2D^2/\lambda$6 implementing TTD-based frequency-dependent analog beamfocusing and $R_{\mathrm{Rayleigh}}=2D^2/\lambda$7 implementing PS-based frequency-independent analog beamfocusing. The resulting nonconvex problem is solved through a penalty-based iterative algorithm with block coordinate descent across three blocks, including closed-form updates for $R_{\mathrm{Rayleigh}}=2D^2/\lambda$8, phase updates for $R_{\mathrm{Rayleigh}}=2D^2/\lambda$9, and one-dimensional searches for TTD delays (Zhou et al., 4 Dec 2025).

Secure near-field beamfocusing adds a second layer of fractional optimization. In wideband physical-layer security, one reported approach first solves a semi-digital per-subcarrier secrecy design using alternating optimization, fractional programming, and BSUM, then performs an analog approximation step that fits a TTD–PS cascade to the semi-digital target. A low-complexity beamsplit-aware initializer, BALA, line-searches an endpoint on the wideband focus trace and provides robust initial delays for the analog optimization. This two-stage structure is specifically motivated by secrecy energy efficiency: analog TTD compensation keeps more subcarriers usable, so power does not need to be concentrated on a few “good” frequencies (Zhang et al., 2023).

In near-field ISAC, beamfocusing can be optimized against estimation bounds rather than rate alone. One formulation minimizes the CRB of joint distance-and-angle estimation for a point target, or the BCRB of the target response matrix for an extended target, while satisfying user QoS and an EE threshold. The first stage solves a fully digital penalty-based successive convex approximation; the second stage matches that solution with a hybrid analog–digital factorization through alternating optimization under fully-connected or partially-connected constant-modulus constraints (Hu et al., 6 Aug 2025).

5. Reported performance trends

The clearest communication-side evidence for beamfocusing comes from near-field line-of-sight multiplexing and positioning. For a $f\in\mathbb{C}^{N_t}$0-element transmit ULA at $f\in\mathbb{C}^{N_t}$1 GHz with aperture approximately $f\in\mathbb{C}^{N_t}$2 m, the achievable degrees of freedom increase from $f\in\mathbb{C}^{N_t}$3 to $f\in\mathbb{C}^{N_t}$4 as propagation distance shrinks from $f\in\mathbb{C}^{N_t}$5 m to $f\in\mathbb{C}^{N_t}$6 m. In the same frequency regime, increasing aperture from $f\in\mathbb{C}^{N_t}$7 to $f\in\mathbb{C}^{N_t}$8 elements moves the user into the near field and reduces CEP from approximately $f\in\mathbb{C}^{N_t}$9 cm to approximately $B_t(r,\theta)=\left|a_t(r,\theta)^H f\right|^2,$0 cm. These results are not EE numbers by themselves, but they establish the SE and sensing gains that hybrid architectures attempt to preserve at lower power (An et al., 2023).

Wideband TTD-based hybrid beamfocusing shows that much of the fully digital rate can be retained with far fewer RF chains. In one RSMA-enabled design with $B_t(r,\theta)=\left|a_t(r,\theta)^H f\right|^2,$1, $B_t(r,\theta)=\left|a_t(r,\theta)^H f\right|^2,$2, $B_t(r,\theta)=\left|a_t(r,\theta)^H f\right|^2,$3 GHz, and $B_t(r,\theta)=\left|a_t(r,\theta)^H f\right|^2,$4 subcarriers, TTD-based frequency-dependent analog beamfocusing yields gains up to approximately $B_t(r,\theta)=\left|a_t(r,\theta)^H f\right|^2,$5 bps/Hz for the fully-connected architecture and approximately $B_t(r,\theta)=\left|a_t(r,\theta)^H f\right|^2,$6 bps/Hz for the sub-connected architecture relative to PS-only hybrid beamforming. The same study reports that with $B_t(r,\theta)=\left|a_t(r,\theta)^H f\right|^2,$7 instead of $B_t(r,\theta)=\left|a_t(r,\theta)^H f\right|^2,$8 RF chains, the TTD hybrid remains within approximately $B_t(r,\theta)=\left|a_t(r,\theta)^H f\right|^2,$9 bps/Hz of full digital, and that RSMA with TTD hybrid outperforms SDMA with TTD hybrid by approximately $m$0 bps/Hz under increasing user load (Zhou et al., 4 Dec 2025).

THz dynamic-subarray fixed-TTD designs demonstrate a more direct EE payoff. At $m$1 GHz with $m$2, $m$3 GHz, and $m$4 fixed delays per RF chain, the average array gain grows from $m$5 dB at $m$6 to $m$7 dB at $m$8, while the average loss relative to the ideal becomes about $m$9 dB for $p_m\in\mathbb{R}^3$0. Spectral efficiency saturates around $p_m\in\mathbb{R}^3$1, but EE peaks around $p_m\in\mathbb{R}^3$2, and the reported EE is $p_m\in\mathbb{R}^3$3 to $p_m\in\mathbb{R}^3$4 higher than TTD-aided baselines for $p_m\in\mathbb{R}^3$5 while maintaining comparable SE (Yan et al., 2022).

Security-oriented results show the same rate–power pattern from a different metric. In TTD-assisted analog near-field wideband secrecy design, secrecy energy efficiency is reported to be markedly higher than for fully digital across a broad range of $p_m\in\mathbb{R}^3$6, with peak secrecy spectral efficiency attained at a moderate number of TTDs and EE decreasing thereafter because hardware power keeps rising while secrecy-rate gains diminish. In another near-field RSMA secure design, a fully-connected hybrid architecture with $p_m\in\mathbb{R}^3$7 and $p_m\in\mathbb{R}^3$8 RF chains approaches fully digital secrecy performance; when $p_m\in\mathbb{R}^3$9, the loss is less than $u\in\mathbb{R}^3$0 bps/Hz, and the RF-chain count is reduced by $u\in\mathbb{R}^3$1, with scenarios in the paper highlighting reductions up to $u\in\mathbb{R}^3$2 (Zhang et al., 2023).

Near-field ISAC introduces an explicit counterexample to the common assumption that better communication efficiency automatically improves sensing. In one hybrid beamfocusing study, focal maps align at approximately $u\in\mathbb{R}^3$3 m and $u\in\mathbb{R}^3$4, confirming distance–angle focusing, and at high radar SNR the distance CRB reaches centimeter-level accuracy in the near field. However, increasing EE worsens both $u\in\mathbb{R}^3$5 and $u\in\mathbb{R}^3$6, and hybrid architectures degrade distance estimation relative to fully digital due to reduced degrees of freedom. This establishes a nontrivial sensing–EE tradeoff rather than a monotone improvement (Hu et al., 6 Aug 2025).

6. Practical constraints, recurring misconceptions, and open problems

A recurring misconception is that hybrid beamfocusing is simply conventional beam steering with fewer RF chains. In fact, near-field focusing must preserve spherical phase curvature and, in wideband systems, group-delay consistency across subcarriers. Phase-only analog networks designed at $u\in\mathbb{R}^3$7 do not generally maintain focal alignment over bandwidth, and insertion loss from long PS or TTD paths can erase some of the radiated-power savings if not modeled explicitly (An et al., 2023).

Another misconception is that passive or metasurface-style architectures are automatically the most energy-efficient. Passive lenses, DMAs, SIMs, and switch-controlled holographic surfaces reduce active power, but they also introduce calibration complexity, finite tuning precision, transmission or reflection loss, and limited per-subcarrier adaptivity. Switch-controlled RHS architectures nevertheless demonstrate that, when hardware impairments are incorporated into the design, EE can exceed both fully digital and conventional PSA-based hybrids; the same work also reports that impairment-aware beamforming design yields further EE improvements over impairment-agnostic baselines (Li et al., 2024).

The dominant practical bottlenecks remain hardware and model fidelity. THz oscillator phase noise increases EVM and shortens coherence intervals; finite-resolution PS and TTD elements generate sidelobes and focal loss; mutual coupling and effective aperture variation distort range–angle patterns; insertion loss raises the PA burden; and near-field calibration is more demanding than far-field calibration because amplitude and phase must be maintained per element over temperature and frequency. Thermal and reliability constraints become especially acute in ELAAs, making sub-connected or passive-heavy architectures attractive even when their idealized SE is slightly lower (An et al., 2023).

Open research directions are correspondingly multi-layered. The literature identifies scalable low-loss analog fabrics, hierarchical subarrays, joint communication–positioning–sensing design, RIS-aided focusing, dynamic user clustering in range, AI-based EE–SE tradeoff learning, robust optimization under coupling and calibration drift, and wideband metasurface co-design that exploits rather than suppresses frequency selectivity. A plausible implication is that future progress will depend less on any single beamforming algorithm than on co-optimizing hardware topology, waveform structure, and polar-domain inference under realistic power models (An et al., 2023).