Active Reconfigurable Intelligent Surface

• Active RIS is a wireless paradigm where each reflecting element uses an active load to amplify signals and enable precise phase control beyond passive RIS limitations.
• It employs alternating optimization via MMSE beamforming and SCA-based methods to jointly manage signal enhancement and noise amplification under strict power constraints.
• Simulation results reveal that active RIS can achieve higher SNR and data rates with fewer elements, making it ideal for compact deployments in challenging environments.

Active Reconfigurable Intelligent Surface (RIS) is a paradigm in wireless communications in which each reflecting element (RE) is augmented with an active load, such as a negative resistance, enabling both phase control and radio frequency (RF) signal amplification. Unlike conventional passive RIS, which can only introduce phase shifts and may require a large surface with many elements to overcome the severe double-fading attenuation of product (cascaded) wireless links, the active RIS introduces additional RF power at the electromagnetic (EM) front end via active circuits, thereby providing a mechanism to directly amplify the reflected signal. This approach fundamentally alters the traditional tradeoff space, supporting higher link budgets and smaller physical sizes under a fixed power budget, but necessitates sophisticated joint optimization of the reflection coefficients and receiver signal processing due to noise amplification.

1. Fundamental Principles and Signal Model

In a passive RIS, each element’s complex reflection coefficient $\phi_m$ is given by $|\phi_m| \leq 1$, typically constrained to $|\phi_m|=1$ for pure phase shifters. The reflection mechanism is passive: for load impedance $Z_L$ and antenna impedance $Z_A$, the reflection coefficient is

$\Gamma = \frac{Z_L - Z_A^*}{Z_L + Z_A}$

With $Z_L$ positive real, $|\Gamma|^2 \leq 1$. In the active RIS, each RE uses a load impedance with negative resistance, i.e., $Z_L = -R_L + jX_L$ ($R_L>0$), yielding $|\Gamma|^2 > 1$. This setup amplifies the incident field at each RE by “injecting” additional RF power (sourced by a DC bias) through active electronic components (e.g., tunnel diodes).

System-level analysis in (Long et al., 2021) considers a single-input multiple-output (SIMO) architecture:

• A single-antenna transmitter.
• An active RIS with $M$ REs, each characterized by a reflection coefficient $\phi_m = a_m e^{j\theta_m}$ (with $a_m>1$ possible).
• An $N$-antenna receiver.

The received signal before combining is

$$y(n) = \sqrt{p_t} \left(\mathbf{h}_1 + \mathbf{G} \boldsymbol{\Phi} \mathbf{h}_2\right) s(n) + \mathbf{G} \boldsymbol{\Phi} \mathbf{z}_2(n) + \mathbf{z}_1(n)$$

with $\mathbf{h}_1$ as direct Tx–Rx channel, $\mathbf{h}_2$ as Tx–RIS channel, $\mathbf{G}$ as RIS–Rx channel, and $\mathbf{z}_1, \mathbf{z}_2$ as noise at Rx and RIS, respectively.

2. Noise Amplification and System Trade-Offs

Unlike their passive counterparts, active RISs not only amplify the signal but also the RIS-local noise $\mathbf{z}_2(n)$. This creates a conflict: increasing the amplification gain $a_m$ enhances the received signal but also enhances correlated noise arriving via the RIS-to-Rx channel. The design must balance:

• High received signal power (favoring high $a_m$ and more active REs).
• Control of RIS-correlated noise (favoring lower $a_m$ or fewer REs).

The end-to-end post-combiner SNR can be written as

$$\gamma_s = \frac{p_t | \mathbf{w}^H (\mathbf{h}_1 + \mathbf{G}\boldsymbol{\Phi}\mathbf{h}_2) |^2 }{ \sigma_2^2 \| \mathbf{w}^H \mathbf{G}\boldsymbol{\Phi} \|^2 + \sigma_1^2 \|\mathbf{w}\|^2 }$$

with receiver beamformer $\mathbf{w}$. The total active RIS power constraint accounts for the amplification consumed in each RE’s bias circuitry and the power delivered to the signal:

$$p_t \| \boldsymbol{\Phi} \mathbf{h}_2 \|^2 + \sigma_2^2 \| \boldsymbol{\Phi} \|^2 \leq P_\text{out}$$

and $a_m \leq a_{m,\text{max}}$.

A key system behavior—observed in LOS channel analysis—is that, unlike passive RIS (where achievable SNR increases with the number of REs $M$), in the active RIS context there exists an optimal $M^*$, as spreading the total power among more REs reduces per-RE amplification. For uniform $a$ across all REs,

$$\gamma_{s,a} = \frac{p_t \rho_2^2 \rho_g^2 M^2 a^2}{\rho_g^2 \sigma_2^2 M a^2 + \sigma_1^2}$$

where $\rho_2$, $\rho_g$ are deterministic channel coefficients. The numerator is quadratic in $M$, but the denominator penalizes both $M$ and $a^2$ by noise and power constraints.

3. Joint Optimization Methodology

Given the coupled impact of active RIS on signal power and noise, the system employs alternating optimization:

(a) Rx Beamforming Update:

For fixed RIS coefficients, the MMSE beamformer is optimal,

$$\mathbf{w}^* = \left( \mathbf{h} \mathbf{h}^H + \frac{\sigma_2^2}{p_t}\mathbf{G}\boldsymbol{\Phi}\boldsymbol{\Phi}^H \mathbf{G}^H + \frac{\sigma_1^2}{p_t} \mathbf{I}_N \right)^{-1} \mathbf{h}$$

with $$\mathbf{h} = \mathbf{h}_1 + \mathbf{G}\boldsymbol{\Phi} \mathbf{h}_2$$.

(b) RIS Reflecting Coefficient Update:

For fixed $\mathbf{w}$, the optimal $\theta_m$ aligns the reflected path with the direct channel. With fixed phases, the magnitude vector $\mathbf{a}$ is optimized subject to the overall and per-element constraints. The challenge arises from the quadratic fractional structure and non-convex constraints. This is efficiently handled using sequential convex approximation (SCA), employing first-order Taylor expansions to approximate convex surrogates of nonconvex constraints over auxiliary variables (such as $\tau$ and $\kappa$ representing signal and amplified noise powers).

Through iterations of these two substeps, convergence to an effective solution is achieved.

4. Performance Evaluation and System Behavior

Simulation results (Long et al., 2021) comparing the proposed active RIS with passive RIS under identical power budgets demonstrate:

• Substantial SNR and achievable rate improvements when the amplification is effectively managed.
• For a given power budget, active RIS requires fewer elements and/or a smaller physical surface for a target SNR, which is especially beneficial when the surface size is limited.
• The achievable rate does not always monotonically increase with $M$ (unlike passive RIS). There is an optimal point in the tradeoff between more elements and higher per-element amplification.
• If the RIS is positioned near the receiver (where the Tx–RIS link is weak), the benefit of active amplification is particularly pronounced, especially under tight power budgets.
• The alternating optimization/SCA-based method yields convergence within several iterations, and the performance improvement over passive RIS is more visible when RIS elements are power constrained or when deployment size is a limiting factor.

5. Practical Considerations and Implementation

Benefits

• Reduced Surface Size for Target Performance: Active RIS alleviates the need for physically large RIS, offering designers more flexibility in deployment (including where space is limited).
• Power Efficiency: Greater signal strength can be achieved at a fixed power budget via a judicious mix of amplification and beamforming, rather than purely increasing the number of passive elements.
• Deployment Flexibility: Sites close to the receiver, which would have been less effective with passive RIS, can be exploited since active amplification can compensate for the weak incident signal power.
• Algorithmic Efficiency: The closed-form MMSE solution and the SCA-based approach maintain tractability even as the number of elements increases.

Limitations

• Noise Amplification: Since the RIS amplifies both the incident signal and local noise, it is essential that RIS and Rx beamforming be jointly optimized; otherwise, performance may degrade instead of improve.
• Hardware Complexity: Each active RE requires a negative resistance generator (e.g., tunnel diode) and associated biasing circuitry, introducing cost, stability, and linearity considerations; the implementation of a large number of stable active reflection amplifiers remains a hardware challenge.
• Power Allocation Tradeoff: The finite power budget must be split between circuit biasing, control logic, and signal amplification, constraining net gain if too many elements are active without sufficient available power.
• Potential for System Instability: Negative resistance circuits can be susceptible to oscillations or nonlinearity if not carefully designed.

A plausible implication is that while active RIS enables new design regimes (compactness, flexibility, energy efficiency), meaningful performance gains require closed-loop, cross-layer optimization that explicitly accounts for signal, noise, and hardware properties. This approach, by mitigating the multiplicative double-fading effect of cascade links and offering fine-grained control of power allocation, is likely to underpin future wireless systems in both coverage-challenged and power-constrained scenarios.

6. Outlook and Research Implications

The paper demonstrates that the physical-layer benefits of active RIS—chiefly, the mitigation of double-fading loss—can be harvested through joint optimization of receiver combining and RIS configuration, using an alternating MMSE/SCA algorithm. The explicit modeling of amplified RIS-introduced noise is essential for accurate system design; naively maximizing signal power will generally result in suboptimal (or even degraded) end-to-end performance.

Future research avenues include:

• Scalability analysis as system dimensions grow (impact of thousands of REs).
• Robustness to hardware non-idealities, e.g., nonlinearities or variability in negative-resistance generation.
• Adaptive algorithms for dynamic environments or mobile users.
• Integration of more advanced channel state estimation for active RIS control.

The methods and insights developed for the single-input multiple-output scenario generalize directly to broader multiantenna and multistream settings, providing a foundational methodology for the joint signal processing/hardware optimization of next-generation active RIS-assisted wireless networks.