---
title: SIM-Assisted Fully-Analog Beamforming
url: https://www.emergentmind.com/topics/sim-assisted-fully-analog-beamforming
type: topic
---

# SIM-Assisted Fully-Analog Beamforming

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 [2302.03188]. 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 [2605.31549].

## 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 [2601.14803].

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 [2409.03259].

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 [2605.31549].

## 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 [2601.14803]. 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 \(b\)-bit quantization,
\[
\theta_n^l\in \left\{ 0,\frac{2\pi}{2^b},\dots,\frac{(2^b-1)2\pi}{2^b} \right\},
\]
and explicitly study \(1\)-bit, \(2\)-bit, and \(3\)-bit phase control. In that setting the meta-atoms are treated as programmable passive elements, with no active RF chain per meta-atom assumed [2601.14803].

The literature also includes an amplitude-and-phase generalization. In the mixed active/passive SIM model, each coefficient takes the form
\[
\gamma_{\ell,q}=\alpha_{\ell,q}e^{j\phi_{\ell,q}},
\]
with phase-controlled nearly passive layers and amplitude-controlled active layers. The overall transformation is
\[
G=\Gamma_{L}W_{L}\Gamma_{L-1}W_{L-1}\cdots \Gamma_2W_2\Gamma_1W_1.
\]
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 [2408.16606]. 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
\[
\bar{\boldsymbol{\Theta}}\in\mathbb{C}^{(N+1)\times(N+1)},
\qquad
\bar{\boldsymbol{\Theta}}^H\bar{\boldsymbol{\Theta}}=\mathbf{I},
\qquad
\bar{\boldsymbol{\Theta}}=\bar{\boldsymbol{\Theta}}^T,
\]
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 [2605.31549].

## 3. Signal models, CSI regimes, and optimization formulations

The canonical SIM downlink signal model writes the received signal at user \(k\) as
\[
y_k = \bm h_k^{\mathrm H}\mathbf G \sum_{i=1}^K \mathbf w_i^1 p_i s_i + n_k,
\]
where \(p_i^2\) denotes power allocation, \(\mathbf w_i^1\) is the feeder-to-first-layer excitation vector, and \(\mathbf G\) is the stacked wave-domain precoder. The effective beam toward user \(k\) is therefore \(\mathbf G \mathbf w_k^1 p_k\), and multiuser interference arises through the same analog transformation acting on all streams [2601.14803].

Two CSI regimes appear prominently. One line assumes explicit channel knowledge for optimization of \(\mathbf H\mathbf F_{\mathrm{SIM}}\) 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 \(k\) is modeled as correlated Rayleigh fading,
\[
\bm h_k\sim \mathcal{CN}(\mathbf 0,\beta_k \mathbf R),
\]
with \(\operatorname{tr}(\mathbf R)=N\), and the sum-rate objective is replaced by a closed-form average-rate surrogate justified by channel hardening. This yields the approximation
\[
R=\sum_{k=1}^K \log_2(1+\gamma_k),
\]
with each \(\gamma_k\) written in terms of traces involving \(\mathbf G\), the feeder vectors, and user covariances [2601.14803]. 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
\[
\max_{\boldsymbol{\phi}^l,\mathbf p}\quad \sum_{k=1}^K \log_2\left(1+\frac{S_k}{I_k}\right)
\]
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 [2601.14803].

In the ISAC formulation, the corresponding objective is multi-objective rather than purely communications-oriented:
\[
\max_{\boldsymbol{\vartheta}} \quad R_{\mathrm{sum}},
\qquad
\min_{\boldsymbol{\vartheta}} \quad J_{\mathrm{MSE}},
\]
with
\[
J_{\mathrm{MSE}}=\left\| \overline{\mathbf P}_{\mathrm S}-\mathbf P_{\mathrm D} \right\|_2^2
\]
and
\[
[\mathbf P_{\mathrm S}]_{j,k} = \boldsymbol{\alpha}^H(\psi_j,\phi_k)\, \mathbf F_{\mathrm{SIM}}\mathbf F_{\mathrm{SIM}}^H\, \boldsymbol{\alpha}(\psi_j,\phi_k).
\]
Here SIM-assisted fully-analog beamforming is used to balance multiuser communication and transmit beampattern shaping for sensing, not merely to maximize user rate [2409.03259].

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
\[
[\mathbf{H}_{k}]_{mn}=\alpha_{mn}^{k}\exp(-j 2 \pi r_{mn}^{k}/\lambda),
\]
so beam focusing depends jointly on angle and distance, while the stacked analog transformation remains
\[
\mathbf{T}=\mathbf{W}^{L}\mathbf{\Phi}^{L} \cdots \mathbf{W}^{2}\mathbf{\Phi}^{2}\mathbf{W}^{1}\mathbf{\Phi}^{1}.
\]
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 [2408.01684].

## 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
\[
u_{w,k}^*= \frac{\mathbf R_k^{1/2}\mathbf G\mathbf w_k^1 p_k} {\sum_{i=1}^K p_i^2(\mathbf G\mathbf w_i^1)^{\mathrm H}\mathbf R_k(\mathbf G\mathbf w_i^1)+\sigma_k^2},
\]
\[
\rho_{w,k}^*= \left(1-u_{w,k}^*\mathbf R_k^{1/2}\mathbf G\mathbf w_k^1 p_k\right)^{-1}.
\]
With phases fixed, power allocation is handled through a Lagrangian/KKT step; with powers fixed, each layer is isolated through
\[
\mathbf G \mathbf w_i^1 p_i = \mathbf C_i^l \boldsymbol{\phi}^l,
\]
reducing the phase update to a quadratic program over a discrete unit-modulus vector [2601.14803].

The discrete-phase layer update is then treated by alternating direction method of multipliers. Introducing \(\bm x=\boldsymbol{\phi}^l\), the update sequence is
\[
(\boldsymbol{\phi}^l)^{\ell+1} = (\mathbf B+\beta \mathbf I_N)^{-1} \left(\bm d+\beta(\boldsymbol x^\ell+\boldsymbol\omega^\ell)\right),
\]
followed by projection of each element onto the discrete alphabet
\[
\left\{e^{j 2\pi m/2^b}\,:\, m=0,\dots,2^b-1\right\}.
\]
The overall solver is therefore an outer alternating-optimization loop with inner WMMSE, power-update, and per-layer ADMM substeps [2601.14803].

Continuous-phase SIM works often use gradient-based methods instead. In the ISAC transmitter, the proposed D\(^3\) algorithm—Dual-Normalized Differential Gradient Descent—computes the sensing and communication gradients with respect to every \(\theta_m^l\), normalizes them elementwise,
\[
\tilde g_{\mathrm{sens}}= \frac{\partial J_{\mathrm{MSE}}/\partial \theta_m^l}{\sqrt{(\partial J_{\mathrm{MSE}}/\partial \theta_m^l)^2+\epsilon}},
\qquad
\tilde g_{\mathrm{com}}= \frac{\partial R_{\mathrm{sum}}/\partial \theta_m^l}{\sqrt{(\partial R_{\mathrm{sum}}/\partial \theta_m^l)^2+\epsilon}},
\]
forms a weighted differential direction
\[
[\mathbf G]_{m,l}=w_1\tilde g_{\mathrm{sens}}-w_2\tilde g_{\mathrm{com}},
\]
and applies a second normalization plus a decaying-step update
\[
\theta_m^l \leftarrow \theta_m^l-\mu [\overline{\mathbf G}]_{m,l},
\qquad
\mu\leftarrow \mu\beta.
\]
This method balances multiple objectives at the gradient level rather than through a scalarized weighted-sum objective [2409.03259].

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 [2302.03188].

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
\[
\widetilde{ H} \, \widetilde{ G} =  \widetilde{ D}
\]
to eliminate inter-user interference among scheduled streams [2408.16606]. 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 [2509.08294].

## 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 \(2\) GHz, meta-atom size \(\lambda/2\), \(K=M=5\), \(P_{\max}=30\) dBm, \(\sigma^2=-80\) dBm, and users randomly placed in a \(60\)–\(80\) m annulus, the proposed algorithm converges within about \(10\) iterations for all tested phase resolutions. The same work reports that \(1\)-bit phase quantization achieves over \(85\%\) of the continuous-phase performance, that the achievable sum rate increases monotonically with the number of SIM layers, and that at \(L=7\) the \(3\)-bit case reaches about \(43\) bits/s/Hz while \(2\)-bit incurs only about \(4\%\) loss relative to \(3\)-bit [2601.14803].

Earlier discrete-phase multiuser downlink work reports that, for the same number of transmit antennas, the proposed SIM-based system achieves about \(200\%\) 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 [2309.02687]. In the continuous-phase predecessor, increasing the number of metasurface layers improves the sum rate, with about \(30\%\) improvement at \(L\approx 7\) compared with a single-layer SIM when \(N=49\) in the reported setting [2302.03188]. 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 \(M=100\), \(L=7\), and \(w_1=w_2=1\), the designed beampattern places strong peaks at the target directions, with
\[
J_{\mathrm{MSE}}\approx -12.79\ \mathrm{dB},
\qquad
R_{\mathrm{sum}}\approx 15\ \text{bit/s/Hz}.
\]
Across \(100\) channel realizations, convergence is typically within \(\sim 15\) iterations, with average performance
\[
R_{\mathrm{sum}} = 13.56\ \text{bit/s/Hz},
\qquad
J_{\mathrm{MSE}} = -12.82\ \mathrm{dB}.
\]
The paper also states that larger metasurface aperture and larger stack depth improve joint communication-and-sensing performance [2409.03259].

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
\[
\rho=\frac{K_c}{N_c}
\]
and shows a fundamental trade-off between subcarrier reuse and analog interference suppression. In the reported simulation with \(f_0=28\) GHz, \(N_c=16\), \(S=K=4\), \(M=100\), and \(L=7\), the proposed system achieves its maximum sum rate around \(\rho=62.5\%\), and \(K_c=10\) out of \(N_c=16\) is stated as the maximum utilization ratio that still preserves near-zero interference among shared subcarriers [2509.08294]. 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 [2408.01684]. 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
\[
R_{1}(t)=\log_2\left(1+P_M\frac{\left\Vert\mathbf{h}_1\right\Vert^2\left(1-t^2\right)}{\sigma_1^2}\right),
\]
\[
R_{2}(t)=\log_2\left(1+P_1\frac{\left(\left\vert h_{21}\right\vert+\left\Vert\mathbf{h}_2\right\Vert\left\Vert\mathbf{h}_1\right\Vert t\right)^2}{\sigma_2^2}\right),
\]
with \(t\in[0,1]\). This shows that in unified analog scattering platforms, active and passive beamforming gains are structurally coupled by physics rather than independently tunable [2605.31549].

## 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 [1705.04943]. 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 [2409.06819]. 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 \(5\%\) 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 [1912.12406]. 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 [1902.00838]. 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 [2601.14803]. Amplitude-and-phase SIM introduces more realistic power-preserving and active-layer constraints but also increases hardware complexity through amplifier-integrated layers [2408.16606]. MiLAC provides exact structural bounds for a unified analog scattering platform, but only for a single-stream active link and one passive-assisted link [2605.31549].

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 [2409.03259].

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 [2309.02687].

Source: https://www.emergentmind.com/topics/sim-assisted-fully-analog-beamforming