Reconfigurable Intelligent Surface (RIS)

Updated 6 July 2025

Reconfigurable Intelligent Surfaces (RIS) are programmable planar arrays of passive elements that manipulate electromagnetic waves to enhance wireless channels.
RIS technology transforms passive radio environments into active systems by applying tunable phase shifts to reflected waves, boosting signal quality and coverage.
Empirical studies show that RIS-assisted channels can achieve near-unity condition numbers, simplifying receiver design and reducing error rates.

A reconfigurable intelligent surface (RIS) is a planar structure composed of an array of electronically controllable elements that manipulate the propagation of incident electromagnetic waves in a programmable manner. RIS technology is leveraged in wireless communications to create "smart radio environments," where the wireless channel is no longer a passive conduit but an active and optimizable system component designed to enhance link performance, spatial multiplexing, and coverage. Unlike traditional relaying or active antenna approaches, the RIS is primarily passive, altering the phase and/or amplitude of the reflected waves rather than generating new signals, thereby enabling energy- and cost-efficient management of the radio environment.

1. Working Principles of RIS

The central operational mechanism of an RIS is its ability to tailor the spatial characteristics of reflected electromagnetic waves through locally tunable phase shifts and, in some architectures, amplitude adjustments. For a narrowband flat-fading scenario, the received signal $y$ in an RIS-assisted link can be formulated as:

$y = \sqrt{G_e} H_e x + \sqrt{G_r} H_\text{RIS} x + n = H_\text{eff} x + n$

Here, $x$ is the transmit vector, $H_e$ is the "environment" channel without the RIS, $H_\text{RIS}$ captures the RIS-modulated channel, and $n$ is additive white Gaussian noise. The effective channel $H_\text{eff} = \sqrt{G_e} H_e + \sqrt{G_r} H_\text{RIS}$ reflects the additive nature of RIS augmentation, contrasting the multiplicative effect found in conventional MIMO precoding.

Each RIS element, or unit cell, applies a tunable phase (and possibly amplitude) through a coefficient of the form $q_i = \beta_i e^{j\theta_i}$ , with $0 \le \beta_i \le 1$ and $0 \le \theta_i < 2\pi$ . By appropriate choice of $\theta_i$ across the array, the RIS produces constructive interference at the receiver, thereby enhancing specific channel metrics, such as gain or eigenchannel structure.

2. Candidate Implementations

Two main classes of physical realizations are discussed:

Reflectarray-Based RIS: Elements are sized on the order of $\lambda/2$ and controlled electronically to apply the desired phase shift. These systems are characterized by simplicity and relatively low cost but require a large number of elements to achieve high spatial resolution due to the antenna-like scattering nature and limited spatial sampling.
Metasurface-Based RIS: Built from arrays of engineered subwavelength meta-atoms, metasurfaces allow for quasi-continuous and finer-grained control over the amplitude and phase of the reflected wavefront. Such surfaces can engineer anomalous reflection, not necessarily following Snell's law, and achieve highly specular responses when elements are electrically large relative to wavelength. Compared to reflectarrays, metasurfaces require more sophisticated element design and control circuits but offer greater flexibility in wavefront manipulation.

3. Channel Modeling and Estimation

RIS-affected channel models must capture the new physical phenomena introduced by programmable reflections:

Dyadic Backscatter Model: Models the RIS as a bank of individual scattering antennas, leading to $H_\text{RIS} = F Q G$ , where $G$ and $F$ are the transmitter-to-RIS and RIS-to-receiver channels, respectively, and $Q$ is the diagonal phase shift matrix. This approach models the RIS contribution as a product of independent fading distributions from both links. Large numbers of RIS elements improve diversity.
Spatial Scattering Model: Particularly suited to metasurface-based RIS, this model represents the RIS channel as a sum over spatial paths with tunable coefficients:

$H_\text{RIS} = \sum_{\ell=1}^{L} \alpha_\ell q_\ell \mathbf{a}_R(\theta_{R,\ell}, \phi_{R,\ell}) \mathbf{a}_T^*(\theta_{T,\ell},\phi_{T,\ell})$

This enables the incorporation of angular information and is expandable to scenarios with beamsteering or anomalous reflection.

Channel estimation presents unique challenges because RIS elements are passive and cannot directly transmit or process pilots. Two techniques are discussed:

Feedback-based adaptation at the receiver (e.g., beam search with received signal strength feedback)
Equipping a minority of RIS elements with active receiving capability for compressed sensing or machine learning-based channel inference

4. Optimization and Challenges

RIS configuration diverges from traditional MIMO optimization:

Additive Channel Effect: The RIS creates an additive enhancement to the existing environment channel ( $H_\text{eff} = \sqrt{G_e} H_e + \sqrt{G_r} H_\text{RIS}$ ), as opposed to the multiplicative effect of TX-side precoding. This additive contribution delivers additional degrees of freedom for improving the channel condition number or shaping the channel towards more favorable singular value spectra.
Optimization Objectives: Key objectives include maximizing effective channel gain, improving channel rank and conditioning, or diagonalizing the effective channel for multi-user interference management. Maximization of spectral entropy,

$SE(H_\text{eff}) = -\sum_{i} \frac{\sigma_i}{\sum_j \sigma_j} \ln\left(\frac{\sigma_i}{\sum_j \sigma_j}\right)$

(where $\sigma_i$ are the singular values of $H_\text{eff}$ ), is cited as a measure leading to more orthogonal channels.

Computational Complexity: The optimization is highly nonconvex and NP-hard, especially with hardware-related phase constraints ( $-\pi \leq \theta_i \leq \pi$ ) and in the presence of partial or imperfect CSI. Algorithms utilize heuristic, gradient-based, or machine learning approaches to find tractable suboptimal solutions compatible with channel coherence times.

5. Empirical Performance and System Implications

Numerical evaluations demonstrate the potential of RIS-assisted systems to substantially improve channel properties and simplify receiver designs:

Channel Condition Number: Optimized RISs can produce channel realizations with condition numbers approaching unity (i.e., $\kappa \approx 1$ ), signaling strong channel orthogonality and enabling improved spatial multiplexing.
Receiver Performance: Zero-forcing (ZF) receivers benefit from noise enhancement mitigation and approach matched filter optimality in the RIS-assisted regime, even surpassing maximum likelihood detectors in the traditional scenario without RIS.
Simulation Studies: Empirical distributions of channel condition numbers across $10^4$ realizations show marked improvements with RIS optimization. Symbol error rate is notably reduced at ZF receivers for both increased channel gain and better channel conditioning.

6. Significance and Future Directions

RIS technology represents a transformative shift in wireless communication, enabling the intentional and adaptive control of the radio environment. The passive nature of RIS results in low energy consumption, while its capability to provide programmable phase and (optionally) amplitude modulation leads to significant improvements in link reliability, spatial multiplexing, and system capacity. Key differentiators from existing techniques include passive, additive channel enhancement, and nonconvex optimization under strict hardware constraints.

Ongoing research addresses topics such as the development of efficient optimization algorithms, hardware realizations that push the boundaries of spatial and spectral control, scalable channel estimation strategies, and the effective integration of RIS in MIMO and multi-user scenarios. The empirical results support the vision that RIS will play a foundational role in simplifying receiver architectures and enhancing the overall efficiency of next-generation wireless communication systems (2005.00938).

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References (1)

Reconfigurable Intelligent Surfaces for Wireless Communications: Principles, Challenges, and Opportunities (2020)