SIM-Assisted Fully-Analog Beamforming

• SIM-assisted fully-analog beamforming is a wireless transceiver architecture that uses cascaded metasurface layers to shape electromagnetic fields without full digital processing.
• It relies on layered phase-only modulation and diffraction, which enables effective beam steering, beam shaping, and multiuser interference management through physical wave synthesis.
• Algorithmic designs such as alternating optimization and gradient-based methods address power allocation and discrete phase control, enhancing both near-field and far-field performance.

SIM-assisted fully-analog beamforming denotes a class of wireless transceiver architectures in which the dominant spatial processing operation is implemented directly in the electromagnetic wave domain by a stacked intelligent metasurface (SIM) or a closely related reconfigurable analog scattering network, rather than by a conventional high-dimensional digital precoder. In the SIM formulation most directly associated with the term, a base station-side stack of transmissive metasurface layers reshapes the transmitted field through cascaded phase modulation and inter-layer diffraction, so that beam steering, beam shaping, and part of the multiuser interference management are realized physically as waves propagate through the stack (An et al., 2023). The literature uses this concept in several related senses: as BS-integrated multilayer wave-domain precoding for multiuser downlink transmission, as a statistical-CSI beam synthesis framework with discrete meta-atom states, as a near-field focusing architecture, as a multi-objective integrated sensing-and-communication (ISAC) transmitter, and, more broadly, as a unified analog scattering platform that may simultaneously support active and passive beamforming functions (Nerini et al., 29 May 2026).

1. Wave-domain definition and architectural scope

In the SIM-based downlink architecture, the transmitter consists of a feeding antenna array followed by $L$ transmissive metasurface layers, each with $N$ independently configurable meta-atoms. For layer $l$, the phase response is modeled by

$$\phi_n^l=e^{j\theta_n^l}, \qquad \boldsymbol{\Phi}^l=\operatorname{diag}(\boldsymbol{\phi}^l)\in\mathbb{C}^{N\times N},$$

and the end-to-end stacked transformation is represented as a cascade of fixed propagation matrices and programmable diagonal phase matrices. In one canonical formulation,

$$\mathbf{G}=\boldsymbol{\Phi}^L\mathbf{W}^L\cdots \boldsymbol{\Phi}^2\mathbf{W}^2\boldsymbol{\Phi}^1\in\mathbb{C}^{N\times N},$$

so the SIM implements beam shaping by physically controlling the phase progression across multiple passive layers (Jiao et al., 21 Jan 2026).

This wave-domain viewpoint differs from conventional digital or hybrid beamforming in a precise sense. The SIM is not modeled as an abstract constant-modulus matrix with independently programmable entries. Rather, the effective analog precoder is a structured product of per-layer phase-only modulation and inter-layer diffraction. In the ISAC formulation, the corresponding transmit beamforming matrix is

$$\mathbf F_{\mathrm{SIM}}=\mathbf \Phi^L \mathbf W^L \mathbf \Phi^{L-1}\mathbf W^{L-1}\cdots \mathbf \Phi^1 \mathbf W^1,$$

with $$\mathbf F_{\mathrm{SIM}}\in\mathbb C^{M\times N_{\mathrm{BS}}}$$, which the literature explicitly interprets as a physically structured cascaded analog precoder rather than a conventional RF phase-shifter matrix (Li et al., 2024).

A recurrent point in the literature is that “fully-analog” refers primarily to the spatial precoding stage, not necessarily to the elimination of all digital control. Several works still optimize scalar per-user or per-stream powers, and some include user scheduling or feeder-side excitation vectors. This implies that SIM-assisted fully-analog beamforming is best interpreted as wave-domain analog beam synthesis with limited digital supervisory control, rather than as an architecture devoid of digital functionality in every subsystem. The same qualification appears in active/passive analog scattering architectures such as the microwave linear analog computer (MiLAC), where the beamforming/combining operation is fully analog, but the system objective is still expressed in rate-theoretic terms and optimized over physically constrained scattering parameters (Nerini et al., 29 May 2026).

2. Electromagnetic cascade models and hardware constraints

The central mathematical object in SIM-assisted fully-analog beamforming is the alternating product of layer responses and propagation operators. Inter-layer propagation is modeled explicitly by Rayleigh–Sommerfeld diffraction. In the discrete-phase statistical-CSI formulation, the $(n,n')$-th entry of the layer-to-layer propagation matrix is given by

$w^l_{n,n'}= \frac{d_x d_y \cos \varphi^l_{n,n'}}{d^l_{n,n'} \left(\frac{1}{2\pi d^l_{n,n'}-j\frac{1}{\lambda}\right) e^{j2\pi d^l_{n,n'}/\lambda},$

while related works use equivalent expressions with the same physical ingredients: meta-atom dimensions, propagation distance, incidence angle, and wavelength (Jiao et al., 21 Jan 2026). This modeling choice distinguishes SIM from single-layer RIS formulations that treat the programmable surface only as a diagonal phase mask.

The phase control model is usually unit-modulus and phase-only. For continuous-state meta-atoms,

$$\theta_m^l\in[0,2\pi), \qquad |[\mathbf \Phi^l]_{m,m}|=1.$$

For practical hardware, several works impose $N$0-bit quantization,

$N$1

and explicitly study $N$2-bit, $N$3-bit, and $N$4-bit phase control. In that setting the meta-atoms are treated as programmable passive elements, with no active RF chain per meta-atom assumed (Jiao et al., 21 Jan 2026).

The literature also includes an amplitude-and-phase generalization. In the mixed active/passive SIM model, each coefficient takes the form

$N$5

with phase-controlled nearly passive layers and amplitude-controlled active layers. The overall transformation is

$N$6

This extends phase-only SIM by introducing amplitude control through active layers integrated with amplifier chips, together with a per-stream power preserving constraint and amplitude constraints for active layers (Darsena et al., 2024). A plausible implication is that “fully-analog beamforming” in the SIM literature spans both strictly passive phase-only stacks and broader wave-domain analog processors with controlled gain.

A distinct but conceptually adjacent line replaces the multilayer metasurface by a physically realizable multiport microwave scattering network. In the MiLAC architecture, the reconfigurable analog network is characterized by a symmetric unitary scattering matrix

$N$7

partitioned into an RF-port reflection coefficient, an active beamforming vector, and a passive scattering submatrix. This shows that fully-analog beamforming can also be realized as a coupled multiport transformation rather than a diagonal phase-shifter network (Nerini et al., 29 May 2026).

3. Signal models, CSI regimes, and optimization formulations

The canonical SIM downlink signal model writes the received signal at user $N$8 as

$N$9

where $l$0 denotes power allocation, $l$1 is the feeder-to-first-layer excitation vector, and $l$2 is the stacked wave-domain precoder. The effective beam toward user $l$3 is therefore $l$4, and multiuser interference arises through the same analog transformation acting on all streams (Jiao et al., 21 Jan 2026).

Two CSI regimes appear prominently. One line assumes explicit channel knowledge for optimization of $l$5 or analogous end-to-end maps, as in multiuser wave-domain downlink beamforming and SIM-based ISAC. Another line centers on statistical CSI. In the latter, the channel from the last SIM layer to user $l$6 is modeled as correlated Rayleigh fading,

$l$7

with $l$8, and the sum-rate objective is replaced by a closed-form average-rate surrogate justified by channel hardening. This yields the approximation

$l$9

with each $$\phi_n^l=e^{j\theta_n^l}, \qquad \boldsymbol{\Phi}^l=\operatorname{diag}(\boldsymbol{\phi}^l)\in\mathbb{C}^{N\times N},$$0 written in terms of traces involving $$\phi_n^l=e^{j\theta_n^l}, \qquad \boldsymbol{\Phi}^l=\operatorname{diag}(\boldsymbol{\phi}^l)\in\mathbb{C}^{N\times N},$$1, the feeder vectors, and user covariances (Jiao et al., 21 Jan 2026). The statistical-CSI interpretation is that SIM reconfiguration can be performed on longer timescales, avoiding the prohibitive pilot overhead implied by large numbers of meta-atoms and layers.

The main discrete-phase optimization problem under statistical CSI is formulated as

$$\phi_n^l=e^{j\theta_n^l}, \qquad \boldsymbol{\Phi}^l=\operatorname{diag}(\boldsymbol{\phi}^l)\in\mathbb{C}^{N\times N},$$2

subject to the SIM cascade constraint, diagonal phase structure, discrete phase alphabet, total power constraint, and nonnegative powers. This is the mathematical statement of SIM-assisted analog beamforming with wave-domain precoding and scalar power allocation (Jiao et al., 21 Jan 2026).

In the ISAC formulation, the corresponding objective is multi-objective rather than purely communications-oriented: $$\phi_n^l=e^{j\theta_n^l}, \qquad \boldsymbol{\Phi}^l=\operatorname{diag}(\boldsymbol{\phi}^l)\in\mathbb{C}^{N\times N},$$3 with

$$\phi_n^l=e^{j\theta_n^l}, \qquad \boldsymbol{\Phi}^l=\operatorname{diag}(\boldsymbol{\phi}^l)\in\mathbb{C}^{N\times N},$$4

and

$$\phi_n^l=e^{j\theta_n^l}, \qquad \boldsymbol{\Phi}^l=\operatorname{diag}(\boldsymbol{\phi}^l)\in\mathbb{C}^{N\times N},$$5

Here SIM-assisted fully-analog beamforming is used to balance multiuser communication and transmit beampattern shaping for sensing, not merely to maximize user rate (Li et al., 2024).

A related near-field formulation emphasizes that SIM-assisted fully-analog beamforming is not restricted to far-field steering. In the near-field MIMO model, the user channel entries are

$$\phi_n^l=e^{j\theta_n^l}, \qquad \boldsymbol{\Phi}^l=\operatorname{diag}(\boldsymbol{\phi}^l)\in\mathbb{C}^{N\times N},$$6

so beam focusing depends jointly on angle and distance, while the stacked analog transformation remains

$$\phi_n^l=e^{j\theta_n^l}, \qquad \boldsymbol{\Phi}^l=\operatorname{diag}(\boldsymbol{\phi}^l)\in\mathbb{C}^{N\times N},$$7

This suggests that SIM-assisted fully-analog beamforming can be interpreted as range-angle focusing in the Fresnel region, not only angular beam steering in the Fraunhofer region (Papazafeiropoulos et al., 2024).

4. Algorithmic design methods

The algorithmic literature is dominated by alternating methods that exploit the layered structure of the analog beamformer. Under statistical CSI with discrete phases, sum-rate maximization is converted into a weighted minimum mean square error problem and solved by alternating optimization. The transformed problem introduces receive-like auxiliary variables and MSE weights, with closed-form updates

$$\phi_n^l=e^{j\theta_n^l}, \qquad \boldsymbol{\Phi}^l=\operatorname{diag}(\boldsymbol{\phi}^l)\in\mathbb{C}^{N\times N},$$8

$$\phi_n^l=e^{j\theta_n^l}, \qquad \boldsymbol{\Phi}^l=\operatorname{diag}(\boldsymbol{\phi}^l)\in\mathbb{C}^{N\times N},$$9

With phases fixed, power allocation is handled through a Lagrangian/KKT step; with powers fixed, each layer is isolated through

$$\mathbf{G}=\boldsymbol{\Phi}^L\mathbf{W}^L\cdots \boldsymbol{\Phi}^2\mathbf{W}^2\boldsymbol{\Phi}^1\in\mathbb{C}^{N\times N},$$0

reducing the phase update to a quadratic program over a discrete unit-modulus vector (Jiao et al., 21 Jan 2026).

The discrete-phase layer update is then treated by alternating direction method of multipliers. Introducing $$\mathbf{G}=\boldsymbol{\Phi}^L\mathbf{W}^L\cdots \boldsymbol{\Phi}^2\mathbf{W}^2\boldsymbol{\Phi}^1\in\mathbb{C}^{N\times N},$$1, the update sequence is

$$\mathbf{G}=\boldsymbol{\Phi}^L\mathbf{W}^L\cdots \boldsymbol{\Phi}^2\mathbf{W}^2\boldsymbol{\Phi}^1\in\mathbb{C}^{N\times N},$$2

followed by projection of each element onto the discrete alphabet

$$\mathbf{G}=\boldsymbol{\Phi}^L\mathbf{W}^L\cdots \boldsymbol{\Phi}^2\mathbf{W}^2\boldsymbol{\Phi}^1\in\mathbb{C}^{N\times N},$$3

The overall solver is therefore an outer alternating-optimization loop with inner WMMSE, power-update, and per-layer ADMM substeps (Jiao et al., 21 Jan 2026).

Continuous-phase SIM works often use gradient-based methods instead. In the ISAC transmitter, the proposed D$$\mathbf{G}=\boldsymbol{\Phi}^L\mathbf{W}^L\cdots \boldsymbol{\Phi}^2\mathbf{W}^2\boldsymbol{\Phi}^1\in\mathbb{C}^{N\times N},$$4 algorithm—Dual-Normalized Differential Gradient Descent—computes the sensing and communication gradients with respect to every $$\mathbf{G}=\boldsymbol{\Phi}^L\mathbf{W}^L\cdots \boldsymbol{\Phi}^2\mathbf{W}^2\boldsymbol{\Phi}^1\in\mathbb{C}^{N\times N},$$5, normalizes them elementwise,

$$\mathbf{G}=\boldsymbol{\Phi}^L\mathbf{W}^L\cdots \boldsymbol{\Phi}^2\mathbf{W}^2\boldsymbol{\Phi}^1\in\mathbb{C}^{N\times N},$$6

forms a weighted differential direction

$$\mathbf{G}=\boldsymbol{\Phi}^L\mathbf{W}^L\cdots \boldsymbol{\Phi}^2\mathbf{W}^2\boldsymbol{\Phi}^1\in\mathbb{C}^{N\times N},$$7

and applies a second normalization plus a decaying-step update

$$\mathbf{G}=\boldsymbol{\Phi}^L\mathbf{W}^L\cdots \boldsymbol{\Phi}^2\mathbf{W}^2\boldsymbol{\Phi}^1\in\mathbb{C}^{N\times N},$$8

This method balances multiple objectives at the gradient level rather than through a scalarized weighted-sum objective (Li et al., 2024).

Earlier multiuser SIM beamforming works employ alternating optimization with iterative water-filling for powers and gradient ascent for layer phases. There the SIM phase gradient is written explicitly in terms of layer-prefix and layer-suffix products, and the phase update uses an Armijo step size. The stated interpretation is that multilayer wave-domain processing can replace digital beamforming while retaining an optimization workflow over powers and programmable metasurface phases (An et al., 2023).

The literature also contains lower-complexity approximations. In amplitude-and-phase SIM design, a concentrated optimization first computes a target beamforming matrix and then fits the SIM coefficients through least-squares projected gradient descent, while a suboptimal zero-forcing design imposes

$$\mathbf{G}=\boldsymbol{\Phi}^L\mathbf{W}^L\cdots \boldsymbol{\Phi}^2\mathbf{W}^2\boldsymbol{\Phi}^1\in\mathbb{C}^{N\times N},$$9

to eliminate inter-user interference among scheduled streams (Darsena et al., 2024). In wideband SIM-assisted OFDMA, alternating optimization splits the problem between a MILP subcarrier-assignment step and a PCCP/SOCP phase-design step in order to approximate interference-free subcarrier-wise mappings under one common multilayer SIM configuration (Li et al., 10 Sep 2025).

5. Performance characteristics and demonstrated trade-offs

A consistent finding is that multilayer wave-domain beamforming improves with the number of metasurface layers and meta-atoms, up to saturation or hardware-limited regimes. In the statistical-CSI discrete-phase study, with carrier frequency $$\mathbf F_{\mathrm{SIM}}=\mathbf \Phi^L \mathbf W^L \mathbf \Phi^{L-1}\mathbf W^{L-1}\cdots \mathbf \Phi^1 \mathbf W^1,$$0 GHz, meta-atom size $$\mathbf F_{\mathrm{SIM}}=\mathbf \Phi^L \mathbf W^L \mathbf \Phi^{L-1}\mathbf W^{L-1}\cdots \mathbf \Phi^1 \mathbf W^1,$$1, $$\mathbf F_{\mathrm{SIM}}=\mathbf \Phi^L \mathbf W^L \mathbf \Phi^{L-1}\mathbf W^{L-1}\cdots \mathbf \Phi^1 \mathbf W^1,$$2, $$\mathbf F_{\mathrm{SIM}}=\mathbf \Phi^L \mathbf W^L \mathbf \Phi^{L-1}\mathbf W^{L-1}\cdots \mathbf \Phi^1 \mathbf W^1,$$3 dBm, $$\mathbf F_{\mathrm{SIM}}=\mathbf \Phi^L \mathbf W^L \mathbf \Phi^{L-1}\mathbf W^{L-1}\cdots \mathbf \Phi^1 \mathbf W^1,$$4 dBm, and users randomly placed in a $$\mathbf F_{\mathrm{SIM}}=\mathbf \Phi^L \mathbf W^L \mathbf \Phi^{L-1}\mathbf W^{L-1}\cdots \mathbf \Phi^1 \mathbf W^1,$$5–$$\mathbf F_{\mathrm{SIM}}=\mathbf \Phi^L \mathbf W^L \mathbf \Phi^{L-1}\mathbf W^{L-1}\cdots \mathbf \Phi^1 \mathbf W^1,$$6 m annulus, the proposed algorithm converges within about $$\mathbf F_{\mathrm{SIM}}=\mathbf \Phi^L \mathbf W^L \mathbf \Phi^{L-1}\mathbf W^{L-1}\cdots \mathbf \Phi^1 \mathbf W^1,$$7 iterations for all tested phase resolutions. The same work reports that $$\mathbf F_{\mathrm{SIM}}=\mathbf \Phi^L \mathbf W^L \mathbf \Phi^{L-1}\mathbf W^{L-1}\cdots \mathbf \Phi^1 \mathbf W^1,$$8-bit phase quantization achieves over $$\mathbf F_{\mathrm{SIM}}=\mathbf \Phi^L \mathbf W^L \mathbf \Phi^{L-1}\mathbf W^{L-1}\cdots \mathbf \Phi^1 \mathbf W^1,$$9 of the continuous-phase performance, that the achievable sum rate increases monotonically with the number of SIM layers, and that at $$\mathbf F_{\mathrm{SIM}}\in\mathbb C^{M\times N_{\mathrm{BS}}}$$0 the $$\mathbf F_{\mathrm{SIM}}\in\mathbb C^{M\times N_{\mathrm{BS}}}$$1-bit case reaches about $$\mathbf F_{\mathrm{SIM}}\in\mathbb C^{M\times N_{\mathrm{BS}}}$$2 bits/s/Hz while $$\mathbf F_{\mathrm{SIM}}\in\mathbb C^{M\times N_{\mathrm{BS}}}$$3-bit incurs only about $$\mathbf F_{\mathrm{SIM}}\in\mathbb C^{M\times N_{\mathrm{BS}}}$$4 loss relative to $$\mathbf F_{\mathrm{SIM}}\in\mathbb C^{M\times N_{\mathrm{BS}}}$$5-bit (Jiao et al., 21 Jan 2026).

Earlier discrete-phase multiuser downlink work reports that, for the same number of transmit antennas, the proposed SIM-based system achieves about $$\mathbf F_{\mathrm{SIM}}\in\mathbb C^{M\times N_{\mathrm{BS}}}$$6 improvement in terms of sum rate compared to conventional MISO systems, and that performance with more than four bits is almost identical to continuous tuning (An et al., 2023). In the continuous-phase predecessor, increasing the number of metasurface layers improves the sum rate, with about $$\mathbf F_{\mathrm{SIM}}\in\mathbb C^{M\times N_{\mathrm{BS}}}$$7 improvement at $$\mathbf F_{\mathrm{SIM}}\in\mathbb C^{M\times N_{\mathrm{BS}}}$$8 compared with a single-layer SIM when $$\mathbf F_{\mathrm{SIM}}\in\mathbb C^{M\times N_{\mathrm{BS}}}$$9 in the reported setting (An et al., 2023). These results support the specific claim that stacked layers provide more wave-domain degrees of freedom than a single programmable surface.

In ISAC beamforming, the reported performance emphasizes trade-off control rather than pure rate maximization. For $(n,n')$0, $(n,n')$1, and $(n,n')$2, the designed beampattern places strong peaks at the target directions, with

$(n,n')$3

Across $(n,n')$4 channel realizations, convergence is typically within $(n,n')$5 iterations, with average performance

$(n,n')$6

The paper also states that larger metasurface aperture and larger stack depth improve joint communication-and-sensing performance (Li et al., 2024).

Wideband beamforming introduces a different trade-off. Because one SIM configuration must serve many subcarriers simultaneously, the fully-analog beamformer cannot, in general, realize per-subcarrier zero-forcing. The OFDMA study therefore introduces a utilization ratio

$(n,n')$7

and shows a fundamental trade-off between subcarrier reuse and analog interference suppression. In the reported simulation with $(n,n')$8 GHz, $(n,n')$9, $w^l_{n,n'}= \frac{d_x d_y \cos \varphi^l_{n,n'}}{d^l_{n,n'} \left(\frac{1}{2\pi d^l_{n,n'}-j\frac{1}{\lambda}\right) e^{j2\pi d^l_{n,n'}/\lambda},$0, $w^l_{n,n'}= \frac{d_x d_y \cos \varphi^l_{n,n'}}{d^l_{n,n'} \left(\frac{1}{2\pi d^l_{n,n'}-j\frac{1}{\lambda}\right) e^{j2\pi d^l_{n,n'}/\lambda},$1, and $w^l_{n,n'}= \frac{d_x d_y \cos \varphi^l_{n,n'}}{d^l_{n,n'} \left(\frac{1}{2\pi d^l_{n,n'}-j\frac{1}{\lambda}\right) e^{j2\pi d^l_{n,n'}/\lambda},$2, the proposed system achieves its maximum sum rate around $w^l_{n,n'}= \frac{d_x d_y \cos \varphi^l_{n,n'}}{d^l_{n,n'} \left(\frac{1}{2\pi d^l_{n,n'}-j\frac{1}{\lambda}\right) e^{j2\pi d^l_{n,n'}/\lambda},$3, and $w^l_{n,n'}= \frac{d_x d_y \cos \varphi^l_{n,n'}}{d^l_{n,n'} \left(\frac{1}{2\pi d^l_{n,n'}-j\frac{1}{\lambda}\right) e^{j2\pi d^l_{n,n'}/\lambda},$4 out of $w^l_{n,n'}= \frac{d_x d_y \cos \varphi^l_{n,n'}}{d^l_{n,n'} \left(\frac{1}{2\pi d^l_{n,n'}-j\frac{1}{\lambda}\right) e^{j2\pi d^l_{n,n'}/\lambda},$5 is stated as the maximum utilization ratio that still preserves near-zero interference among shared subcarriers (Li et al., 10 Sep 2025). A plausible implication is that SIM-assisted fully-analog beamforming is especially effective when the communication architecture itself is co-designed to reduce the burden placed on one common analog configuration.

Near-field studies add a geometric performance interpretation. When users are inline in angle but separated in range, near-field spherical-wave channels provide additional focusing dimensions, and the SIM outperforms far-field beamforming because range information contributes to interference mitigation (Papazafeiropoulos et al., 2024). The MiLAC literature reveals a different trade-off: the same analog scattering network cannot maximize active and passive functions simultaneously, and the rate frontier is parameterized by

$w^l_{n,n'}= \frac{d_x d_y \cos \varphi^l_{n,n'}}{d^l_{n,n'} \left(\frac{1}{2\pi d^l_{n,n'}-j\frac{1}{\lambda}\right) e^{j2\pi d^l_{n,n'}/\lambda},$6

$w^l_{n,n'}= \frac{d_x d_y \cos \varphi^l_{n,n'}}{d^l_{n,n'} \left(\frac{1}{2\pi d^l_{n,n'}-j\frac{1}{\lambda}\right) e^{j2\pi d^l_{n,n'}/\lambda},$7

with $w^l_{n,n'}= \frac{d_x d_y \cos \varphi^l_{n,n'}}{d^l_{n,n'} \left(\frac{1}{2\pi d^l_{n,n'}-j\frac{1}{\lambda}\right) e^{j2\pi d^l_{n,n'}/\lambda},$8. This shows that in unified analog scattering platforms, active and passive beamforming gains are structurally coupled by physics rather than independently tunable (Nerini et al., 29 May 2026).

6. Relations to adjacent analog beamforming paradigms and open limitations

SIM-assisted fully-analog beamforming sits within a broader analog-beamforming landscape. Conventional analog beamsteering for sparse mmWave channels uses path-direction steering vectors as analog beams and can approach digital SVD beamforming in the low-to-medium SNR regime when paths are angularly separable. That literature emphasizes infinite-precision or codebook-based steering vectors rather than multilayer diffraction-based transformations, and its principal practical design rule is that the beam codebook size should be at least larger than the number of antennas and preferably about twice as large (Zou et al., 2017). This suggests that SIM-assisted fully-analog beamforming generalizes path-based analog beamsteering from a single phase-shifter stage to a deep wave-domain processor.

Receiver-side assisting mechanisms provide another adjacent paradigm. One work studies analog beamforming aided by full-dimension one-bit chains, where all array elements are observed through 1-bit digital chains during beam acquisition and a phase-only analog combiner is then configured for data transmission. The architecture is not a SIM, but it is explicitly described as an assisting subsystem for subsequent fully analog beamforming (Liu et al., 2024). A plausible implication is that “SIM assistance” in a wider sense may include low-resolution observation subsystems that infer angular structure without requiring full-resolution digital beamforming during data transmission.

Measurement-assisted and codebook-learning approaches address the beam acquisition side rather than the wave-domain beam synthesis side. Beamforming learning based on Bayesian clustering of likely high-gain directions reduces training time to only $w^l_{n,n'}= \frac{d_x d_y \cos \varphi^l_{n,n'}}{d^l_{n,n'} \left(\frac{1}{2\pi d^l_{n,n'}-j\frac{1}{\lambda}\right) e^{j2\pi d^l_{n,n'}/\lambda},$9 of that of exhaustive search while targeting a minimum beamforming gain, but it operates at the codebook level and does not realize the beamformer through a stacked metasurface (Chraiti et al., 2019). Analog-codebook design via a generalized Lloyd framework similarly addresses single-RF-chain constant-modulus beam sweeping and quantized phase shifters, not multilayer EM transformations (Ganji et al., 2019). These works are relevant to SIM-assisted fully-analog beamforming only in the sense that they can supply beam-search policies or priors for analog-only hardware.

Several limitations recur across the SIM literature. Many formulations assume perfect CSI or statistical CSI known to the transmitter; hardware experiments are generally absent; amplitude-phase coupling, insertion loss, mutual coupling, dispersive phase responses, and reconfiguration latency are often omitted; and fast wideband or high-mobility adaptation remains difficult. Discrete-phase statistical-CSI work is downlink-only with single-antenna users and includes scalar power allocation and feeder-side vectors, so it is not a pure metasurface-only formulation in the strongest possible sense (Jiao et al., 21 Jan 2026). Amplitude-and-phase SIM introduces more realistic power-preserving and active-layer constraints but also increases hardware complexity through amplifier-integrated layers (Darsena et al., 2024). MiLAC provides exact structural bounds for a unified analog scattering platform, but only for a single-stream active link and one passive-assisted link (Nerini et al., 29 May 2026).

A common misconception is that SIM-assisted fully-analog beamforming is equivalent to conventional hybrid beamforming with a different analog front-end. The literature instead presents it as a different computational locus: the high-dimensional spatial transform is carried out by propagation through reconfigurable physical media, while digital processing, when retained, is reduced to scalar power loading, low-dimensional stream management, or control-layer optimization. Another misconception is that a single metasurface layer and a stacked SIM provide equivalent beamforming expressivity. The multilayer works explicitly argue that stacking creates a richer cascade of propagation and modulation, which is why multilayer SIM is repeatedly shown to improve multiuser interference suppression, near-field focusing, or communication-sensing trade-off relative to single-layer structures (Li et al., 2024).

In this sense, SIM-assisted fully-analog beamforming is best understood not as one fixed architecture but as a family of wave-domain precoding schemes in which reconfigurable electromagnetic hardware absorbs a large fraction of the spatial processing burden traditionally assigned to digital baseband. Across the cited works, its defining traits are the structured cascade of phase-control layers and propagation operators, the use of physically realizable analog constraints, and the treatment of beamforming as electromagnetic field synthesis rather than only matrix multiplication (An et al., 2023).