Sub-Connected Active RIS Architectures

• Sub-connected active RIS architectures are designs that share amplifier resources across groups of elements to reduce hardware complexity and power consumption.
• They employ grouping and clustering strategies that enable coherent signal combining while mitigating double fading and long-distance path loss.
• Simulation studies reveal that moderate grouping can achieve over 90% of the full sum-rate with significant energy efficiency gains compared to fully-connected systems.

Searching arXiv for the cited papers on sub-connected active RIS architectures and closely related work. Sub-connected active RIS architectures are reconfigurable intelligent surface designs in which signal amplification is shared across multiple elements, sub-arrays, clusters, or selected active partitions rather than assigned independently to every element. The common purpose is to mitigate double fading and long-distance path loss while reducing the amplifier count, static power, and hardware complexity of fully active implementations. Within the recent literature, this architectural principle appears in diagonal active RIS for MU-MISO and HAPS-assisted links, in hybrid active/passive RIS with active reflecting sub-surfaces, in sub-array-based double-faced active RIS, and in group-connected beyond-diagonal RIS with clustered reflect-type amplifiers (Karaman et al., 18 Jul 2025, Zhu et al., 2022, Ntougias et al., 2024, Cao et al., 2024, Ntougias et al., 7 May 2026, Sankar et al., 2023).

1. Architectural concept and taxonomy

In the diagonal active RIS setting, a sub-connected architecture typically means that multiple RIS elements share one reflection-type power amplifier while retaining phase reconfigurability. In the HAPS-based active RIS system, the total number of RIS elements is $N$, partitioned into $Q$ groups of size $T=N/Q$; within each group all $T$ elements share a single power amplifier and an amplification gain $\beta_g$, while each element keeps its own tunable phase shift $\phi_i$. Four schemes are considered there: Scheme I with $T=1$ and $Q=N$, Scheme II with $T=512$, Scheme III with $T=1024$, and Scheme IV with $Q$0 (Karaman et al., 18 Jul 2025).

A related MU-MISO formulation groups $Q$1 RIS elements into $Q$2 sub-arrays, each driven by a single amplifier. In that model, the group size is $Q$3, and the sub-array combines the incident signals coherently, amplifies them with gain $Q$4, and re-divides them equally among the $Q$5 elements. This differs from the element-wise fully-connected active RIS, which uses $Q$6 amplifiers, and directly changes both the signal model and the RIS power consumption (Zhu et al., 2022).

Hybrid architectures extend the same principle to a coarser granularity. In one model, the RIS is partitioned into reflecting sub-surfaces $Q$7, and an SC-active sub-surface $Q$8 shares a single power amplifier across all $Q$9 elements, so that $T=N/Q$0 with common $T=N/Q$1. Only a subset $T=N/Q$2 may be active, turning the design into a hybrid active/passive RIS (Ntougias et al., 2024). A more fine-grained hybrid interpretation activates exactly $T=N/Q$3 of the $T=N/Q$4 RIS elements through a binary selection vector $T=N/Q$5, with active elements using $T=N/Q$6 and passive ones using $T=N/Q$7 (Sankar et al., 2023).

Sub-connection also appears in architectures beyond conventional reflection-only diagonal models. In the sub-array-based DFA-RIS, the surface contains $T=N/Q$8 aligned reflecting-element pairs, grouped into $T=N/Q$9 non-overlapping sub-arrays of size $T$0; all reflection amplifiers in sub-array $T$1 share a binary switch $T$2, allowing the amplification function to be activated or deactivated dynamically (Cao et al., 2024). In hybrid beyond-diagonal RIS, each reflecting subsurface is divided into groups and then clustered, and each cluster is fed by a single low-cost reflect-type amplifier with amplitude $T$3, while every group implements a unitary-symmetric coupling matrix $T$4 (Ntougias et al., 7 May 2026).

Across these formulations, the phrase “fully-connected” is model-dependent. In diagonal active RIS it often denotes one amplifier per element. In the beyond-diagonal RIS family it denotes a full coupling block per reflecting subsurface, with one large tunable impedance network per subsurface rather than per group. The unifying distinction is therefore not the label itself, but the degree of active-resource sharing and coupling granularity.

2. Signal models and matrix representations

A central mathematical feature of sub-connected active RIS is that the reflection or scattering matrix remains structured, typically block-diagonal or group-mapped, with group-shared amplitude variables and element-wise or block-wise phase control. In the HAPS formulation, the indicator matrix is

$T$5

so that group $T$6 controls elements $T$7, and the overall RIS reflection matrix is

$T$8

where $T$9 collects element-wise phase shifts and $\beta_g$0 collects per-group amplification gains. The received signal at user $\beta_g$1 is

$\beta_g$2

with amplifier noise $\beta_g$3 of variance $\beta_g$4 and AWGN $\beta_g$5 of variance $\beta_g$6 (Karaman et al., 18 Jul 2025).

The improved sub-connected signal model for MU-MISO makes the internal combining stage explicit. For group $\beta_g$7, the incident vector is $\beta_g$8, the phase-shift vector is $\beta_g$9, and the coherently combined scalar is

$\phi_i$0

After amplification by $\phi_i$1 and equal redistribution over the $\phi_i$2 ports, the sub-array output becomes

$\phi_i$3

with

$\phi_i$4

The full RIS matrix is block-diagonal: $\phi_i$5 This model departs from the simpler diagonal-amplification view because intra-group coherent combination and redistribution alter both the useful signal and the amplified noise term (Zhu et al., 2022).

Double-faced and beyond-diagonal architectures add further structure. For DFA-RIS, the reflected and transmitted outputs are

$\phi_i$6

where $\phi_i$7 is the active sub-array matrix, $\phi_i$8 and $\phi_i$9 implement power division, and $T=1$0 carry unit-modulus phases (Cao et al., 2024). For the group-connected SC-active BD-RIS, the per-group block is

$T=1$1

with $T=1$2 and $T=1$3. The global scattering matrix is block-diagonal across groups and reflecting subsurfaces, and the end-to-end channel is

$T=1$4

This construction shows that sub-connection is compatible with beyond-diagonal coupling rather than confined to element-wise diagonal reflection (Ntougias et al., 7 May 2026).

3. Performance metrics and optimization problems

The principal metrics are SINR, sum-rate, power consumption, and energy efficiency. In the HAPS-based model, the SINR under the sub-connected structure is

$T=1$5

the sum-rate is

$T=1$6

the total power consumption is

$T=1$7

and the energy efficiency is

$T=1$8

Because $T=1$9, increasing the group size decreases the number of power amplifiers and directly reduces the $Q=N$0 term (Karaman et al., 18 Jul 2025).

The same rate-versus-power logic appears in multi-user MISO and DFA-RIS designs, but with richer power models. In the MU-MISO sub-connected array architecture, the RIS power is

$Q=N$1

which separates dynamic forwarding power from the static costs of phase shifters and amplifiers (Zhu et al., 2022). In the hybrid SC-active/passive formulation, each active reflecting sub-surface consumes

$Q=N$2

and the system-level energy efficiency is

$Q=N$3

subject to BS and RIS power budgets, modulus constraints, and amplification limits (Ntougias et al., 2024).

DFA-RIS introduces binary activation into the energy model. The RIS power there is

$Q=N$4

so the number of active sub-arrays enters explicitly through an $Q=N$5-type count (Cao et al., 2024). In the hybrid RIS with channel-aware active-element placement, the received SNR is

$Q=N$6

which isolates the coherent signal gain and the RIS-noise penalty generated only by the active branches (Sankar et al., 2023).

These objective functions lead to closely related optimization problems: sum-rate maximization, energy-efficiency maximization, and power minimization under QoS constraints. The common constraints are BS transmit budgets, RIS reflect-power or total-power budgets, unit-modulus phase shifts, bounded amplification gains, and, in sub-connected formulations, the requirement that all elements in the same group share the same amplification variable.

4. Solution methodologies

The optimization problems for sub-connected active RIS are consistently nonconvex because of coupled beamformers and RIS coefficients, unit-modulus constraints, amplifier noise terms, group-sharing constraints, and, in some models, binary or $Q=N$7-type activation variables. The literature therefore uses decompositions that separate power allocation, phase control, amplification, and activation patterns (Zhu et al., 2022, Cao et al., 2024, Ntougias et al., 2024, Karaman et al., 18 Jul 2025, Sankar et al., 2023, Ntougias et al., 7 May 2026).

For the HAPS problem, the sum-rate objective is simplified by relaxing discrete $Q=N$8 and $Q=N$9 to continuous variables and approximating $T=512$0 at high SNR. The resulting expressions are re-cast as posynomials and solved via geometric programming, after which $T=512$1 may be quantized to the nearest discrete levels if needed and $T=512$2 is set at its computed value or at its maximum if saturated. Power allocation $T=512$3 is obtained within the same GP procedure (Karaman et al., 18 Jul 2025).

For MU-MISO with the improved sub-connected signal model, sum-rate maximization is handled through fractional programming, block coordinate descent, ADMM, and MM. Auxiliary variables $T=512$4 and $T=512$5 convert the logarithmic sum-rate into a tractable surrogate; the BS precoders are updated through convex QP or SOCP subproblems; the RIS phase-shift update is handled by ADMM-MM; and the RIS amplification update becomes a convex QP in the group gains. A companion power-minimization problem under QoS constraints is likewise reformulated as SOCP for the BS precoder and RIS gains, with ADMM-MM used for the phase variables. Empirical convergence is reported in about $T=512$6 outer iterations and about $T=512$7 inner ADMM-MM iterations (Zhu et al., 2022).

The DFA-RIS energy-efficiency design uses a more layered construction. Dinkelbach’s transform turns the fractional objective into $T=512$8; quadratic and Lagrangian dual transforms introduce auxiliary $T=512$9 and $T=1024$0; alternating optimization updates beamformers, power-division coefficients, phase matrices, amplifier gains, and activation patterns; Penalty-Dual-Decomposition handles the unit-modulus phase constraints; MM smooths the $T=1024$1-like activation term; and CVX is used for convex QCQP and QP subproblems. Under imperfect CSI, Constrained Stochastic Majorization-Minimization replaces expectations by sample-based convex surrogates and converges to a stationary point of the expected-value problem (Cao et al., 2024).

Hybrid active/passive RIS with SC-active partitions also follows the Dinkelbach route, combined with Lagrangian dual and quadratic transforms. The BS beamformer update has a KKT-based closed form,

$T=1024$2

while the active RIS block update is a small convex QCQP in the vector of diagonal entries, solved by bisection on the dual multiplier. Passive partitions are updated through MM under unit-modulus constraints (Ntougias et al., 2024).

Two other methodological endpoints are noteworthy. In the active/passive element-placement model, alternating optimization reduces the transmit beamformer to MRT and the active-set update to sorting the per-element gains $T=1024$3, yielding $T=1024$4 complexity per joint RIS/selection update (Sankar et al., 2023). In the group-connected SC-active BD-RIS, the optimization separates into a spatial design and a power design: Takagi factorization yields the optimal unitary-symmetric group matrices $T=1024$5, and a Cauchy–Schwarz argument gives a closed-form optimal cluster amplification factor $T=1024$6 under the reflect-power budget, with an optional one-dimensional line search over a scalar $T=1024$7 to refine the signal-versus-noise trade-off (Ntougias et al., 7 May 2026).

5. Reported trade-offs and comparative performance

The central empirical result across the literature is that sub-connected active RIS architectures usually sacrifice some instantaneous beamforming degrees of freedom in exchange for substantial savings in amplifier count and power, and that this trade-off frequently improves energy efficiency. In the HAPS study, fully-connected active RIS achieves the highest sum-rate for all $T=1024$8, but Schemes II, III, and IV achieve approximately $T=1024$9–$Q$00 of the fully-connected sum-rate with far fewer power amplifiers. Scheme II yields the best energy-efficiency operating point under the reported settings, and a key guideline from that study is that sub-connected schemes with moderate group size $Q$01 offer $Q$02 of full sum-rate at approximately $Q$03 less PA power consumption (Karaman et al., 18 Jul 2025).

The MU-MISO sub-connected array study reports even stronger gains under RIS power constraints. With $Q$04 dBm, the sub-connected architecture with $Q$05 yields $Q$06 higher sum-rate than the fully-connected architecture while using only one quarter of the amplifiers. When the RIS power budget is below $Q$07 dB, the fully-connected structure yields zero sum-rate, whereas sub-connected configurations with $Q$08 or $Q$09 remain operational. For power minimization, achieving $Q$10 dB with sub-connected $Q$11 requires only $Q$12 of the total power and one eighth of the amplifiers used by the fully-connected benchmark (Zhu et al., 2022).

Hybrid architectures reveal a similar non-monotonic optimum in the number of active partitions. In the SC-active/passive multi-user MISO formulation, simulations indicate that $Q$13 maximizes energy efficiency under moderate $Q$14 and low $Q$15, outperforming both fully-connected active RIS and passive RIS by up to $Q$16–$Q$17. The representative EE values reported for one fixed-budget example are approximately $Q$18 bit/J for $Q$19, $Q$20 bit/J for $Q$21, and $Q$22 bit/J for $Q$23, showing that fully activating all sub-surfaces is not necessarily optimal (Ntougias et al., 2024).

Sub-array control is also effective in full-space and beyond-diagonal settings. The DFA-RIS study reports that the sub-array-based architecture outperforms fully-connected DFA-RIS and passive STAR-RIS by approximately $Q$24–$Q$25 in energy efficiency at $Q$26 dBm, with negligible sum-rate loss, and remains robust to CSI errors up to $Q$27 MSE (Cao et al., 2024). In the hybrid BD-RIS family, the SC/SC-BD design achieves approximately $Q$28 dB receive SNR at $Q$29 while using only $Q$30 amplifiers, exceeding the $Q$31 dB of the fully-connected active diagonal RIS in the reported SISO scenario, and it attains the highest rate at about $Q$32 b/s/Hz, saturating once the reflect-power budget exceeds about $Q$33 dBm (Ntougias et al., 7 May 2026).

Placement-based hybrid RIS further emphasizes that active resources should be allocated where the cascaded channel is strongest. With only $Q$34 active elements, the channel-aware placement scheme matches fully active performance while saving approximately $Q$35 of RIS power, and random placement is reported to be $Q$36–$Q$37 dB worse in SNR (Sankar et al., 2023). Taken together, these studies show that the operating point is governed not by a single universal rule, but by the interaction among amplifier count, power budgets, path loss, dynamic amplifier noise, and the granularity at which amplification is shared.

6. Interpretation, misconceptions, and design implications

A frequent misconception is that adding more active components necessarily improves system-level performance. The reported results do not support that as a general statement. Fully-connected active RIS often maximizes spectral efficiency or raw sum-rate, but energy efficiency can peak at intermediate group sizes, intermediate numbers of active partitions, or sparse active-element placements. In the HAPS setting, Scheme II is optimal for EE at $Q$38 dBm, while Scheme IV becomes optimal at $Q$39 dBm; in hybrid multi-user MISO, half-active operation can dominate both fully passive and fully active extremes; and in sub-array DFA-RIS, dynamic activation of only selected sub-arrays is beneficial for EE (Karaman et al., 18 Jul 2025, Ntougias et al., 2024, Cao et al., 2024).

A second misconception is that sub-connection eliminates meaningful beamforming flexibility. The surveyed designs retain considerable control. Group-shared amplification is routinely combined with element-wise phase shifts, binary RA operating patterns, or unitary-symmetric beyond-diagonal group couplers. In the BD-RIS family, sub-connected active operation is not merely a reduced diagonal architecture; it coexists with structured inter-element coupling and closed-form coherent design through Takagi factorization (Ntougias et al., 7 May 2026). In the diagonal MU-MISO and HAPS formulations, sub-connected operation still permits per-element phase tuning even when the amplifier gain is shared across many elements (Zhu et al., 2022, Karaman et al., 18 Jul 2025).

A third misconception is that amplifier output power should always be driven to its maximum. The HAPS study explicitly states that PA output power $Q$40 need not be pushed to its maximum because, beyond a critical $Q$41, the marginal gain in $Q$42 is dominated by dynamic noise $Q$43 and EE falls (Karaman et al., 18 Jul 2025). This observation is consistent with the broader active-RIS literature, where the denominator of SINR always contains an amplified-noise term.

Several design guidelines recur. For energy-constrained HAPS payloads, the recommendation is to choose sub-connected architectures with $Q$44 in the few-hundreds to low-thousands and to adapt $Q$45 to site-specific altitude, channel, and path-loss conditions. In hybrid active/passive RIS, the number of active sub-surfaces should increase with the available $Q$46, but remain small when PA budgets are tight. In placement-based hybrid RIS, one should activate the elements with the strongest end-to-end gains $Q$47. In DFA-RIS, the RA on/off pattern becomes an additional control dimension, and under imperfect CSI the design should satisfy QoS and power constraints in expectation (Karaman et al., 18 Jul 2025, Ntougias et al., 2024, Sankar et al., 2023, Cao et al., 2024).

These results suggest a unifying interpretation of sub-connected active RIS architecture: it is not a single hardware blueprint, but a family of sparsified active front-ends that redistribute a limited number of amplifiers across groups, sub-surfaces, faces, or clusters. The common research direction is therefore adaptive architectural selection rather than fixed amplifier topology—choosing grouping size, activation pattern, and coupling structure jointly with beamforming, under the specific channel, QoS, and power constraints of the deployment scenario.