STAR-BD-RIS: Dual-Sector Beyond-Diagonal RIS

• STAR-BD-RIS is a concept that integrates simultaneous transmission and reflection using beyond-diagonal (non-diagonal) reconfigurable surfaces, enabling richer analog processing.
• It employs a coupled impedance network to support wave-domain functions like beamforming and full-space operation in both communication and sensing applications.
• Optimization challenges and hardware constraints motivate research into algorithmic designs that balance circuit complexity with enhanced spectral and energy efficiencies.

STAR-BD-RIS generally denotes a simultaneously transmitting and reflecting beyond diagonal reconfigurable intelligent surface: a reconfigurable surface intended to provide transmission-side and reflection-side operation while departing from the conventional diagonal, elementwise-independent RIS model. The term is not yet used uniformly across the literature. Some papers explicitly adopt the acronym in FIM-assisted downlink and NOMA systems, whereas the transceiver-integrated BD-RIS literature does not introduce a separate STAR-BD-RIS acronym and instead treats BD-RIS itself as a wave-domain analog processing unit embedded within the transceiver aperture (Eftekhari et al., 19 Sep 2025, Farhadi et al., 6 Sep 2025, Raeisi et al., 10 May 2026). A closely related line of work places STAR-RIS as the two-sector special case of multi-sector BD-RIS, which makes STAR-BD-RIS best understood as part of a broader family of full-space, sectorized, and beyond-diagonal reconfigurable surfaces rather than as a single settled hardware architecture (Samy et al., 2024).

1. Terminology and conceptual scope

At its core, BD-RIS stands for beyond diagonal reconfigurable intelligent surface. “Beyond diagonal” means that the surface is not limited to a diagonal reflection or transfer matrix with independent per-element phase shifts; instead, the elements are interconnected by a reconfigurable impedance network, so the transfer or scattering matrix can be full or structured non-diagonal. This enables richer analog transformations, including amplitude and phase control, unlike conventional RISs that usually realize only diagonal phase control (Raeisi et al., 10 May 2026).

The STAR component refers to simultaneous transmission and reflection. In the NTN-oriented BD-RIS literature, this appears as hybrid or multi-sector operation, with transmission and reflection supported simultaneously across different sides or sectors of the surface. In the multi-sector BD-RIS framework, STAR-RIS is explicitly treated as the case with two sectors, so one sector corresponds to transmission and the other to reflection (Khan et al., 2024, Samy et al., 2024).

A second conceptual axis is whether the “beyond-diagonal” property is interpreted electromagnetically, circuit-theoretically, or only at the level of system terminology. A physics-compliant treatment models BD-RIS as a coupled load circuit attached to RIS auxiliary ports, and shows that BD-RIS can be rewritten in the same mathematical structure as a conventional diagonal RIS after replacing the radio environment by the cascade of the radio environment and the BD-RIS load circuit (Hougne, 2024).

Usage in the literature	Defining feature	Representative source
Transceiver-integrated BD-RIS	Wave-domain analog processing unit embedded within the transceiver aperture; no separate STAR-BD-RIS acronym	(Raeisi et al., 10 May 2026)
Multi-sector BD-RIS	Sectorized full-space operation; STAR-RIS is the 2-sector special case	(Samy et al., 2024)
Explicit STAR-BD-RIS	Dual-sector STAR-BD-RIS with CW-SC or cell-wise single-connected implementation	(Farhadi et al., 6 Sep 2025, Eftekhari et al., 19 Sep 2025)

This suggests that “STAR-BD-RIS” currently names a research direction more than a single canonical realization. In some papers it denotes a dual-sector, simultaneously transmitting and reflecting surface with a BD-RIS motivation; in others the STAR behavior is absorbed into multi-sector or hybrid BD-RIS models.

2. Physical and mathematical foundations

A generic transceiver-integrated BD-RIS relation is described as a cascaded analog transfer,

$$\mathbf{y} = \mathbf{H}_{\text{BR}} \mathbf{\Phi}_{\text{BD}} \mathbf{H}_{\text{TB}} \mathbf{x} + \mathbf{n},$$

where $\mathbf{H}_{\text{TB}}$ is the transceiver-to-BD-RIS channel, $\mathbf{\Phi}_{\text{BD}}$ is the beyond-diagonal surface transfer or scattering matrix, and $\mathbf{H}_{\text{BR}}$ is the BD-RIS-to-user channel. The transceiver-integration viewpoint treats the end-to-end channel as a cascade of the transceiver–BD-RIS and BD-RIS–user links, which preserves reciprocity (Raeisi et al., 10 May 2026).

The standard contrast is with the conventional RIS model

$$\mathbf{\Phi}_{\text{RIS}} = \operatorname{diag}\!\left(e^{j\phi_1}, \ldots, e^{j\phi_M}\right),$$

for which each auxiliary port is terminated by its own independent tunable load. In the physics-compliant BD-RIS formulation, the effective load matrix seen by the RIS ports is induced by a coupled multi-port load circuit,

$$\mathbf{\Phi} = \mathbf{Z}^\mathrm{LC}_\mathcal{SS} - \mathbf{Z}^\mathrm{LC}_\mathcal{SC} \left( \mathbf{Z}^\mathrm{LC}_\mathcal{CC} + \mathbf{\Psi} \right)^{-1} \mathbf{Z}^\mathrm{LC}_\mathcal{CS},$$

and the measurable antenna-port impedance retains the same algebraic structure as in the D-RIS case after replacing the original environment by the cascaded environment $\mathbf{Z}^{\mathrm{casc}}$ and the effective tuning matrix by the diagonal load matrix $\mathbf{\Psi}$ (Hougne, 2024).

For STAR- or multi-sector operation, the literature uses joint conservation constraints rather than independent reflection-only control. Representative forms are

$$\boldsymbol{\Phi}_t^H\boldsymbol{\Phi}_t+\boldsymbol{\Phi}_r^H\boldsymbol{\Phi}_r={\bf I}_{K/2}$$

for hybrid two-side operation and

$$\sum_{s=1}^S\boldsymbol{\Phi}_s^H\boldsymbol{\Phi}_s={\bf I}_{K/S}$$

for $\mathbf{H}_{\text{TB}}$0-sector control. In cell-wise single-connected or CW-SC implementations, these matrix relations reduce to diagonal sector matrices with per-element conservation laws such as $\mathbf{H}_{\text{TB}}$1 (Khan et al., 2024, Farhadi et al., 6 Sep 2025).

A recurrent modeling point is that the same optimization protocols as for D-RIS can be used for the BD-RIS case once the cascaded multi-port network is adopted. The accompanying caution is that many published comparisons between BD-RIS and D-RIS fix the number of RIS elements while allowing the BD-RIS to use more tunable lumped elements, which can make the comparison unfair or at least incomplete (Hougne, 2024).

3. Architectural realizations

The most distinctive architectural proposal in the current literature is the transceiver-integrated BD-RIS. In this architecture, the BS-side active antennas excite the surface, the wave is processed in the electromagnetic domain by the BD-RIS, and the processed field then propagates to the user or sensing target. The BD-RIS is therefore treated not just as an environment-mounted reflector, but as an analog processing unit attached to the transceiver aperture. The paper positions this as a balance between MiLAC and SIM: high flexibility like MiLAC, modularity like SIM, and better modeling robustness than multi-layer SIM because it involves a single near-field channel between the transceiver aperture and the surface (Raeisi et al., 10 May 2026).

A second taxonomy classifies BD-RIS by interconnection structure. The standard categories are single-connected, group-connected, and fully-connected. In the NTN survey, these correspond respectively to diagonal-like, block-diagonal, and unitary matrix structures. Fully-connected BD-RIS offers the richest control but also the highest circuit complexity, while group-connected structures trade control for reduced hardware burden (Khan et al., 2024).

A third axis is space partitioning. Multi-sector BD-RIS divides the surface into $\mathbf{H}_{\text{TB}}$2 sectors arranged as a polygon prism, each covering $\mathbf{H}_{\text{TB}}$3 of space. Under this view, STAR-RIS is the special case $\mathbf{H}_{\text{TB}}$4. This reframes STAR-type simultaneous transmission and reflection as a specific point inside a broader sectorized BD-RIS design space (Samy et al., 2024).

Dual-polarized BD-RIS adds a further degree of architectural realism. In that setting, the RIS is split between vertical and horizontal polarizations. A central result is that a group-connected RIS with group size $\mathbf{H}_{\text{TB}}$5, where each pair contains two RIS elements with opposite polarization, achieves the fully-connected performance upper bound in opposite-polarization LoS channels while reducing circuit complexity from $\mathbf{H}_{\text{TB}}$6 to $\mathbf{H}_{\text{TB}}$7 (Nerini et al., 2024).

Non-reciprocal BD-RIS extends the beyond-diagonal paradigm still further by allowing non-symmetric scattering matrices. In full-duplex settings, this enables a wave incident from one direction to experience a different transformation than a wave incident from the opposite direction, which is not possible under reciprocal symmetric scattering (Li et al., 2024). Although this is not a STAR-specific model, it broadens the feasible class of advanced RIS architectures relevant to STAR-BD-RIS taxonomy.

4. Signal-processing functions and system roles

The transceiver-integrated literature presents BD-RIS as a wave-domain signal processing platform. The representative wave-domain functions listed for this architecture include beamforming and beam focusing in far field and near field, linear processing such as SVD-based precoding and zero-forcing, interference management for integrated sensing and communications, transform-domain channel conditioning including DFT-like angular decomposition and discrete Fresnel transforms for near-field shaping, and spatiotemporal processing, including STBC-like behavior through time-varying surface configurations. By moving such functions from digital baseband into the electromagnetic domain, BD-RIS is argued to reduce arithmetic load in the baseband, relax ADC/DAC requirements, lower latency, and cut overall power consumption (Raeisi et al., 10 May 2026).

Communication and sensing are both recurrent target applications. In a representative downlink case, beamforming is based on the dominant right singular vector of the channel matrix. MiLAC achieves the best benchmark performance, but BD-RIS comes close while remaining modular; the slight loss is attributed mainly to multiplicative path loss in the cascaded channel. In sensing, BD-RIS also performs close to MiLAC when a sweeping codebook of unit-modulus steering vectors is used. The same work notes that BD-RIS can support localization-related functions by conditioning the wavefront in the near field (Raeisi et al., 10 May 2026).

On the STAR side, pulse-Doppler radar provides a concrete full-space sensing example. A STAR-RIS-based radar separates transmissive-half-space and reflective-half-space echoes by imposing different slow-time modulation codes on the two sides. Two scanning policies are defined: simultaneous scanning, which uses all $\mathbf{H}_{\text{TB}}$8 pulses for both sides and yields Doppler resolution $\mathbf{H}_{\text{TB}}$9, and sequential scanning, which illuminates the two sides in separate halves of the CPI and yields Doppler resolution $\mathbf{\Phi}_{\text{BD}}$0. The detector is based on a generalized information criterion and chooses among $\mathbf{\Phi}_{\text{BD}}$1, $\mathbf{\Phi}_{\text{BD}}$2, $\mathbf{\Phi}_{\text{BD}}$3, and $\mathbf{\Phi}_{\text{BD}}$4 (Grossi et al., 2024).

In ISAC, STAR-RIS has also been combined with RSMA. The BS jointly optimizes common rates, active beamforming, and passive transmission/reflection beamforming to maximize sensing SINR while meeting communication-rate requirements. A key theorem shows that, in the single-target setting considered there, the dedicated sensing waveform can be removed without loss of sensing SINR because its covariance can be absorbed into the communication-waveform covariance (Liu et al., 2024). This is not a BD-RIS paper, but it illuminates the STAR-side full-space sensing role that STAR-BD-RIS systems are expected to inherit.

5. Optimization and algorithmic design

Optimization problems in this area are typically highly non-convex because beamforming, phase or scattering matrices, user grouping, rate allocation, and hardware constraints are tightly coupled. In STAR-RIS-enhanced cell-edge communication, one transmitted user and one reflected user are paired as a NOMA pair, multiple NOMA pairs are served via TDMA, and a two-layer iterative algorithm jointly optimizes user pairing, decoding order, passive beamforming, power allocation, and time allocation to maximize the minimum downlink rate (Lei et al., 2023).

Robust formulations further incorporate hardware impairments and CSI uncertainty. In STAR-RIS-empowered multi-user RSMA, robust sum-rate maximization under bounded channel-estimation errors and transceiver impairments is decomposed into active and passive subproblems. The solution pipeline uses SCA and SDR to convert the original problem into convex SDP subproblems, then applies Gaussian randomization when higher-rank solutions arise (Asif et al., 20 Oct 2025).

Learning-based control has been introduced in papers that explicitly use the STAR-BD-RIS acronym. In a hybrid downlink multiuser MISO system with an FIM antenna at the BS and a STAR-BD-RIS along the transmission path, the goal is to maximize achievable sum rate under short block length by jointly optimizing the FIM surface configuration, the transmit beamforming vector, and the STAR-BD-RIS phase shift matrix. The proposed solver is Meta-TD3, which augments TD3 with a meta-critic through a bi-level optimization structure (Eftekhari et al., 19 Sep 2025). In a related FIM-assisted BS and STAR-BD-RIS-aided NOMA system, the objective is energy-efficiency maximization over beamforming, subcarrier assignment, FIM morphing, and STAR-BD-RIS configuration, and the proposed optimizer is Meta-SAC (Farhadi et al., 6 Sep 2025).

Low-complexity configuration search remains a major topic on the BD-RIS side. For MU-MISO communication systems with a fully-connected symmetric unitary BD-RIS, a depth-first tree search algorithm explores the discrete phase-configuration space with pruning, targeting a trade-off between channel-strength maximization performance and computational-complexity scalability. Its reported upper-bound complexity without pruning is $\mathbf{\Phi}_{\text{BD}}$5, while practical branch-pruned behavior is much lower in the tested regime (Souza et al., 8 Apr 2026).

6. Applications, performance analyses, and empirical findings

A central motivation for STAR-BD-RIS-style architectures is full-space coverage in scenarios where conventional reflecting RIS is inadequate. In non-terrestrial networks, the stated drivers include long distances and severe path loss, mobility and fast-varying geometry, coverage holes and blocked LoS, interference between terrestrial and non-terrestrial layers, the need for 360° coverage, and strict power and hardware constraints. In the LEO NOMA case study, the joint optimization of satellite transmit power and BD-RIS phase response increases achievable sum rate, and the sum rate increases as the number of BD-RIS elements increases (Khan et al., 2024).

In multi-user MIMO OFDM broadcast channels, several RIS technologies are compared under the important restriction that RIS coefficients are constant across all subbands. The main conclusion is that STAR-RIS and multi-sector BD-RIS can outperform a regular RIS, especially when the regular RIS cannot assist the communications for all the users. The same study states that multi-sector BD-RIS can significantly outperform STAR-RIS and regular RIS because it can create more directional beams per sector and optimize user channels in different sectors more independently (Soleymani et al., 2024).

Sectorization tradeoffs have been analyzed explicitly. For a fixed number of configurable elements, increasing the number of sectors improves outage performance at the expense of reduced diversity order compared to STAR-RIS. Yet the reported practical gains from sectorization are large: transitioning from a 2-sector to a 6-sector configuration yields a notable $\mathbf{\Phi}_{\text{BD}}$6 increase in spectral efficiency and a $\mathbf{\Phi}_{\text{BD}}$7 increase in energy efficiency. At outage probability $\mathbf{\Phi}_{\text{BD}}$8, a 6-sector configuration needs about $\mathbf{\Phi}_{\text{BD}}$9 elements whereas the 2-sector STAR-RIS case needs about $\mathbf{H}_{\text{BR}}$0 (Samy et al., 2024).

Dual-polarized analysis sharpens the performance-complexity picture. In same-polarization Rayleigh fading, the asymptotic gain of fully-connected BD-RIS over conventional single-connected RIS is

$\mathbf{H}_{\text{BR}}$1

In opposite-polarization Rayleigh fading, the gain becomes

$\mathbf{H}_{\text{BR}}$2

which tends to $\mathbf{H}_{\text{BR}}$3 as $\mathbf{H}_{\text{BR}}$4. In opposite-polarization LoS channels, the group-size-2 design achieves the fully-connected bound, which makes it a particularly important architectural result for practical dual-polarized implementations (Nerini et al., 2024).

Placement and geometry are also decisive. In STAR-RIS-assisted NOMA systems, optimizing the deployment location significantly enhances weighted sum rate, and both beamformer-based and cluster-based NOMA prefer asymmetric STAR-RIS deployment. The stated physical reason is the double-fading loss $\mathbf{H}_{\text{BR}}$5, which makes the surface position directly influence the cascaded channel strength and the SIC hierarchy (Gao et al., 2022).

7. Limitations, unresolved issues, and common misconceptions

The present literature also defines a substantial set of limitations. For transceiver-integrated BD-RIS, the stated challenges are physically consistent modeling under strong coupling, mutual coupling, and near-field effects; calibration of near-field transceiver-to-surface channels; hardware impairments such as fabrication tolerances, insertion losses, finite-resolution tuning, and imperfect impedance loads; circuit complexity for fully connected designs; configuration algorithms under differing objectives and constraints; multi-function simultaneity, where one configuration may need to support beamforming, sensing, interference suppression, and channel conditioning simultaneously; and limited experimental validation, with a call for prototypes and measurements (Raeisi et al., 10 May 2026).

In NTNs, additional open problems are adaptive channel realization and channel estimation, RF circuitry constraints, receiver sensitivity under weak long-distance signals, control signaling overhead, synchronization among satellite/UAV/BD-RIS/ground terminals, and robustness under atmospheric turbulence and mobility (Khan et al., 2024). In OFDM, the inability to tune the RIS independently on each subcarrier means that gains tend to shrink as the number of subbands grows (Soleymani et al., 2024).

A recurring misconception concerns what counts as “beyond diagonal” in named STAR-BD-RIS implementations. The 2025 FIM-assisted papers use the term STAR-BD-RIS, but their actual formulations adopt a cell-wise single-connected or CW-SC architecture in which the sector matrices are diagonal, with unit-modulus or per-element conservation constraints, rather than a fully populated non-diagonal matrix realization (Eftekhari et al., 19 Sep 2025, Farhadi et al., 6 Sep 2025). This suggests that the acronym is sometimes used at the level of architectural motivation and scattering-network interpretation even when the implemented optimization model is diagonal per sector.

A second misconception is that BD-RIS necessarily requires an entirely new end-to-end channel formalism. The physics-compliant multi-port treatment shows the opposite: once the load circuit is modeled explicitly and cascaded with the radio environment, the BD-RIS problem can be mapped into the conventional D-RIS formalism. The more serious issue is benchmarking fairness, since fixed-element-count comparisons often hide a larger number of tunable lumped elements in the BD-RIS hardware (Hougne, 2024).

Overall, a plausible implication is that STAR-BD-RIS remains a moving target shaped by three partially overlapping threads: STAR-RIS full-space operation, BD-RIS coupled or structured non-diagonal scattering, and sectorized or dual-sector implementations that interpolate between the two. The literature consistently points to gains in coverage, controllability, spectral efficiency, and energy efficiency, but it is equally consistent in showing that those gains depend on hardware topology, calibration, model fidelity, and the exact meaning assigned to “beyond diagonal” in a given system model.