Active Reconfigurable Intelligent Surfaces

• Active RIS are programmable metasurfaces with built-in amplification, enabling precise control over phase and amplitude of reflected signals.
• They overcome passive RIS limitations by amplifying impinging signals, achieving 20–40 dB SNR gains in high-frequency and NLOS environments.
• Practical implementations must balance increased noise, thermal challenges, and nonlinear distortions with optimized hybrid designs and circuit-aware strategies.

Active Reconfigurable Intelligent Surfaces (RIS) are programmable metasurfaces in which each scattering element is equipped with an amplification mechanism—typically a low-noise amplifier (LNA) or negative-resistance device—enabling not only phase but also amplitude control of the reflected electromagnetic waves. Unlike passive RIS, which suffer from multiplicative (double) path-loss and rely solely on phase manipulation, active RIS can amplify impinging signals, thereby enhancing end-to-end channel power gain and overcoming coverage and rate limitations intrinsic to passive implementations. This capability is particularly significant for high-frequency (mmWave/THz) and non-line-of-sight (NLOS) environments, as well as for realizing ultra-reliable communications in 6G wireless systems.

1. Fundamental Principles and Signal Models

An active RIS consists of an array of $N$ elements, each operating as an independent reflect-and-amplify unit. At the element level, the incident narrowband signal $x$ from the transmitter is received through a channel $h_{\mathrm{in},n}$, subject to additive noise $w_n \sim \mathcal{CN}(0, \sigma_w^2)$. Each element applies a programmable complex gain $g_n$ (typically $|g_n| > 1$ for amplification), yielding an amplified signal $$y_n^{\mathrm{amp}} = g_n (h_{\mathrm{in},n} x + w_n)$$, which is then reradiated towards the user via an output channel $h_{\mathrm{out},m}^{(n)}$.

The aggregate signal at a receiver $m$ is

$$r_m = \sum_{n=1}^N h_{\mathrm{out},m}^{(n)} g_n (h_{\mathrm{in},n} x + w_n) + v_m$$

with $v_m \sim \mathcal{CN}(0, \sigma_v^2)$ denoting receiver noise. Defining the composite end-to-end channel as $$h_{m,\mathrm{eff}} = \sum_{n=1}^N h_{\mathrm{out},m}^{(n)} g_n h_{\mathrm{in},n}$$, the instantaneous output SNR becomes

$$\mathrm{SNR}_m = \frac{P_t |h_{m,\mathrm{eff}}|^2}{\sigma_v^2 + \sum_{n=1}^N |g_n|^2 \sigma_w^2}$$

where $P_t$ is the transmit symbol power (Basar et al., 2021).

This is generalized in MIMO and multi-user cases by collecting element gains and phase-shifts into a diagonal matrix $$\Theta = \mathrm{diag}\{\theta_1, \dots, \theta_N\}$$ with $\theta_n = \alpha_n e^{j\phi_n}$, allowing the RIS to perform compound spatial beamforming and amplitude control (Yigit et al., 2022, Gavriilidis et al., 31 Mar 2025).

2. Performance Gains, Trade-Offs, and Architectural Variants

Active RIS fundamentally alters end-to-end power scaling. While passive RIS exhibits SNR scaling as $\sim N^2 P_t / (d_{SR}^2 d_{RD}^2 \sigma^2)$, active RIS achieves SNR $$\sim N P_t P_A / (P_A\sigma_v^2 d_{SR}^2 + \sigma^2 d_{RD}^2 + \dots)$$, transitioning from a multiplicative to an additive path-loss regime. In high-dispersion or high-loss settings (e.g., $d_{SR}, d_{RD} > 50$ m), active RIS can outperform passive RIS by $20$–$40$ dB SNR, or equivalently yield the same link budget with orders-of-magnitude fewer elements (Basar et al., 2021, Long et al., 2021).

There is a trade-off, as higher amplification increases efficiency but also raises thermal noise and hardware complexity. The RIS-induced noise, scaling with $\sum |g_n|^2 \sigma_w^2$, eventually dominates at excessive gain or element count. This introduces an optimal region for per-element gain and overall active surface size, often favoring sparse or hybrid (mixed active/passive) arrays for limited power budgets (Gavriilidis et al., 31 Mar 2025).

Nonlinear distortion and memory effects in practical amplifiers must be accounted for, as they can induce beamformed in-band and out-of-band spectral regrowth into unintended spatial directions. For large arrays, this can become a limiting factor for high-SNR and highly multiplexed scenarios, motivating distortion-aware scheduling and power back-off strategies (Kolomvakis et al., 2024).

In recent years, centralized active RIS (CA-RIS) architectures—which employ a single (or few) high-power amplifiers at the focal point of a passive phase-controlled array—have been introduced. These structures provide moderate amplification (e.g., $9.6$ dB net measured gain at $4$ GHz), greatly reduce hardware costs and array noise, and are scalable to large apertures, with measured performance well above that of passive RIS and only $3$–$7$ dB below full distributed active RIS (Liu et al., 2024).

Architecture	Per-Element Amplification	Noise Accumulation	Complexity/Scalability
Passive RIS	None	Only thermal	Minimal
Active Distributed	Yes	Sums over $N$ amps	High (scaled with $N$)
Centralized (CA-RIS)	One/few shared	Single amplifier	Low, high scalability

3. Power Consumption, Circuit Modeling, and Physical Limits

Active RIS elements utilize either low-noise amplifiers (conventional method) or analog negative-resistance circuits, such as tunnel diodes. Recent physical modeling captures the inherent phase-amplitude coupling, circuit-induced amplitude bounds, and the precise DC bias power required for each level of negative resistance or amplification (Gavriilidis et al., 31 Mar 2025). The per-element reflection coefficient is

$$\gamma_n(C_n, R_n) = \frac{Z_n(C_n, R_n) - Z_0}{Z_n(C_n, R_n) + Z_0}, ~\gamma_n = \alpha_n e^{j\phi_n}$$

where $Z_n$ is the tunable impedance implemented via parallel L, C, and negative R. For a target phase shift $\phi_n$, only a subset of amplitude gains $\alpha_n$ are feasible, with closed-form boundaries governed by the circuit's stable bias range.

Practical power budgeting is dictated by

$\sum_{n=1}^N P(R_n) \leq P_{\mathrm{RIS}}$

with $P(R_n)$ determined by the DC operating point of each tunnel diode, typically $8$–$26.5$ mW per element in S-band experimental realizations. Excessive distribution of available power over too many elements leads to diminished per-element gain and thus suboptimal performance. Empirical optimization demonstrates that, for a fixed RIS power budget, it is preferable to activate only a subset ($\sim 1.2\times$ the number that can be fully powered), with the rest behaving as passive phase shifters (Gavriilidis et al., 31 Mar 2025).

4. Optimization Methodologies

Active RIS-empowered transmission strategies center on joint optimization of the array (element gains/phases) and system-level resources (precoding, user assignment). Key methodologies include:

• Alternating/block coordinate descent: Alternates between receiving beamformer and RIS coefficients, leveraging closed-form updates for MMSE combining, and sequential convex approximation (SCA) for nonconvex amplitude optimization (Long et al., 2021, Yigit et al., 2022, Peng et al., 2022).
• Semidefinite relaxation (SDR): Converts nonconvex quadratic RIS optimization problems into semidefinite programs (SDP), then approximates the rank-one solution via principal component or randomization (Yigit et al., 2022).
• Physical circuit aware design: Incorporates phase-amplitude dependencies and realistic amplifier noise/power constraints using convex optimization over identified feasible sets (Gavriilidis et al., 31 Mar 2025).
• Stochastic successive convex approximation (SSCA): Integrated in systems with self-sustainable energy harvesting and imperfect CSI to balance rate, reliability, and energy availability, alternating between variable blocks (e.g., beamforming, harvesting duration, RIS parameters) (Cao et al., 2024).
• Ergodic/sum-rate maximization: For THz and multi-user scenarios, ergodic rate (or sum-rate) is maximized with respect to RIS parameters subject to hardware constraints, often via alternating optimization and moment-matching approximations of SNR distributions (Khalid et al., 2024).
• Distortion-aware scheduling: In scenarios where nonlinear distortion from RIS amplifiers is non-negligible, user-subcarrier assignments are managed to avoid overlap between intended beams and distortion lobes (Kolomvakis et al., 2024).

5. Applications, Deployment Scenarios, and Empirical Results

Active RIS are particularly effective in the following use cases:

• Macro-cell coverage extension: Effective at $d_{SR}, d_{RD} > 50$ m where passive RIS fail due to double fading; empirical SNR gains of $20$–$40$ dB have been demonstrated (Basar et al., 2021).
• THz and mmWave communications: The extreme path loss is mitigated by per-element amplification, with measured SNR improvements of $3$–$5$ dB and coverage extension of $20$–$30$\% at $0.3$ THz, $M=100$ (Khalid et al., 2024).
• Self-sustainable anti-jamming: Active RIS powered via TD-SWIPT harvesting circuits achieve high anti-jamming rates, outperforming passive RIS by more than $30\%$ in throughput under identical base station transmit power (Cao et al., 2024).
• Mobile edge computing (MEC): For offloading, active RIS yield $30$–$40$\% lower maximum computational latency than passive RIS, and require $4\times$ fewer elements for a target latency, at a fixed power budget (Peng et al., 2022).
• Radar detection: Active RIS enable spatial diversity for radar, achieving up to $9$ dB SNR gain for a fixed probability of detection, provided sufficient per-element gain (e.g., $a_{\max}^2 \geq 40$ dB) (Rihan et al., 2022).
• Cooperative backscatter and index modulation: Active RIS-APSK schemes deliver $3$–$5$ dB SER gain at $10^{-3}$ in backscatter channels and support high-rate spatial symbol mapping (Li et al., 2024).

6. Practical Implementation, Hardware, and Limitations

Active RIS deployment imposes distinct challenges beyond traditional phased arrays:

• Power/thermal management: Fully distributed active RIS can require substantial aggregate DC power and are subject to thermal constraints, especially for large apertures. CA-RIS addresses this via centralized amplification (Liu et al., 2024).
• Noise amplification: Each active element injects and amplifies noise; measured impact is negligible at moderate gain/range but dominates at close range or excessive element count. Optimization of the active/passive mix is essential (Gavriilidis et al., 31 Mar 2025, Long et al., 2021).
• Nonlinear distortion: Nonlinear PAs can generate strong in-band and out-of-band distortion beams, necessitating distortion-aware resource allocation and, where possible, digital predistortion (Kolomvakis et al., 2024).
• Phase-amplitude quantization: Practical requirements are satisfied with $2$–$4$ bit quantization per element. Algorithms support such discrete control (Peng et al., 2022).
• Calibration and synchronization: Active elements require periodic amplitude-phase calibration and closed-loop control to mitigate drift and aging effects.
• Self-sustainability: Energy harvesting RIS have been experimentally demonstrated, supporting amplitude gains up to $40$ dB with realistic efficiencies ($60$–$80\%$), enabling green deployments (Cao et al., 2024).

7. Outlook, Hybridization, and Research Directions

Active RIS substantially reframe RIS system design, making achievable SNR, coverage, and rate gains possible for scenarios where passive RIS are infeasible due to physical or economic constraints. Future research directions include: optimizing hybrid (active/passive) topologies for fixed power budgets, characterizing nonlinearity effects for extremely large apertures, managing energy harvesting and sustainability at scale, and fully realizing CA-RIS in commercial platforms for low-complexity high-throughput systems. The essential requirement remains to account for the coupled phase-amplitude-gain, noise, and power dynamics introduced by amplification at the hardware level, as rigorously established in recent circuit-aware analyses (Gavriilidis et al., 31 Mar 2025, Basar et al., 2021, Liu et al., 2024).