---
title: Active Reconfigurable Intelligent Surface
url: https://www.emergentmind.com/topics/active-reconfigurable-intelligent-surface-ris
type: topic
---

# Active Reconfigurable Intelligent Surface

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 [2103.00709] 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 [2103.00709] 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.

Source: https://www.emergentmind.com/topics/active-reconfigurable-intelligent-surface-ris