Fixed Intelligent Surfaces in Wireless Systems

• Fixed Intelligent Surface (FIS) is a passive architecture using preconfigured, non-tunable reflection matrices to adjust wireless signals via transmitter frequency tuning.
• FIS exploits the movable signals paradigm by altering the carrier frequency to achieve coherent phase alignment across array elements, maximizing link gains in LOS scenarios.
• Advanced FIS designs, such as Beyond-Diagonal FIS, employ polarization-swapping techniques to mitigate cross-polarization losses and yield up to a fourfold power gain compared to RIS.

A Fixed Intelligent Surface (FIS) is a class of passive electromagnetic surfaces with static—preconfigured and non-tunable—scattering properties. In FIS-aided wireless systems, the surface reflection matrix remains strictly fixed during operation. Instead of surface-side reconfiguration, performance optimization is accomplished by adjusting the carrier frequency of the transmitter. This contrasts with Reconfigurable Intelligent Surfaces (RIS), which achieve control by dynamically altering the local electromagnetic response (e.g., via tunable impedance states). The FIS paradigm has received recent attention due to its minimal in-surface hardware requirements—enabling scalable implementations—while still offering substantial, and sometimes superior, end-to-end link gains by leveraging the movable-signal principle, particularly in line-of-sight (LOS) SISO scenarios with dual polarization (Nerini et al., 3 Dec 2025). FIS architectures support a wide array of applications, including indoor/outdoor mmWave and multi-band communications.

1. System Model and Channel Representation

FIS-enabled systems are typically modeled as LOS single-input single-output (SISO) or modest MIMO links, where the direct Tx–Rx path is absent and communication is exclusively relay-assisted by a passive dual-polarized intelligent surface of $N$ elements arranged as a uniform linear array (ULA). The array is composed of $N/2$ co-located vertical-polarized and $N/2$ horizontal-polarized elements (Nerini et al., 3 Dec 2025). The input–output relation is

$$y = h\,x + n, \qquad h = h_\mathrm{R}\,\Theta\,h_\mathrm{T} - h_\mathrm{R}\,h_\mathrm{T}$$

where $x$ is the transmit symbol, $y$ is the observed signal, $n$ is complex additive noise, $h_\mathrm{T}$ is the link from Tx to surface (column vector), $h_\mathrm{R}$ is the surface to Rx (row vector), and $\Theta\in \mathbb{C}^{N\times N}$ is the fixed reflection (scattering) matrix. Channels are structured as Kronecker products over polarization vectors $\mathbf{p}_\mathrm{T}$, $\mathbf{p}_\mathrm{R}$—encoding cross-polar discrimination—and analytic LOS phasor vectors $\mathbf{g}_\mathrm{T}$, $\mathbf{g}_\mathrm{R}$ determined by geometry and wavelength.

In FIS, $\Theta$ is not changed during operation. Instead, frequency selection at the transmitter alters the wavelength $\lambda$, modulating phase terms in $\mathbf{g}_\mathrm{T}$ and $\mathbf{g}_\mathrm{R}$ for coherent combining.

2. Fixed Reflection Matrix Configurations

FIS operation depends on the type of reflection matrix:

• Diagonal FIS (D-FIS): The matrix is $$\Theta_{\mathrm{diag}} = \mathrm{diag}(e^{j\theta_1},\ldots,e^{j\theta_N})$$, with entries set offline and fixed for all transmissions. No per-element tuning is performed after deployment (Nerini et al., 3 Dec 2025).
• Beyond-Diagonal FIS (BD-FIS): $\Theta$ is an arbitrary unitary matrix ($\Theta^H\Theta=I_N$), commonly comprising block-off-diagonal or polarization-swapping structures. Example: For dual-polarized FIS with orthogonal Tx–Rx polarizations, a block-off-diagonal configuration enables engineered cross-polar coupling, mitigating polarization mismatch losses.

Physical meaning: Diagonal entries induce per-port phase shifts with no mutual coupling; off-diagonal elements allow cross-coupling/crosstalk, which is especially advantageous in the dual-polarized setting for unlocking otherwise orthogonally polarized signal routes.

3. Movable Signals Paradigm

The core innovation in FIS systems is the "movable signals" concept: The transmitter changes its carrier frequency $f$, equivalently adjusting the wavelength $\lambda$, with the aim to align the phases of surface reradiation across all ports. Under fixed $\Theta$, spectrum agility permits compensation for array geometries and path differences. The optimal choice is

$$\lambda^* = d_A\cdot|\sin\theta_\mathrm{R} + \sin\theta_\mathrm{T}|,\qquad f^* = \frac{c}{d_A\cdot|\sin\theta_\mathrm{R} + \sin\theta_\mathrm{T}|}$$

where $d_A$ is the antenna spacing and $\theta_\mathrm{R,T}$ are Rx and Tx angles relative to the surface normal. This selects $f^*$ such that all reradiated rays sum coherently, maximizing $|h|$. Optimal frequency tuning achieves full array gain with the fixed surface (Nerini et al., 3 Dec 2025).

4. Performance Analysis and Fundamental Gains

The received power at the Rx is $$P_R = |h|^2 = |h_\mathrm{R}\,\Theta\,h_\mathrm{T} - h_\mathrm{R}\,h_\mathrm{T}|^2$$. Key analytic results include:

• Diagonal FIS: For $\Theta=-I_N$, full phase opposition is set to cancel specular reflection and double the reradiated amplitude:

$P_R^{\mathrm{D\text{-}FIS}} = (1+\chi)^2 N^2$

where $\chi$ is the inverse cross-polar-discrimination. Frequency adjustment ($f^*$) yields phase alignment on both polarization axes.

• Comparison to RIS: Diagonal RIS surface achieves at most a quarter of this power due to inability to compensate structural scattering:

$$P_R^{\mathrm{D\text{-}RIS}} \approx \frac{(1+\chi)^2N^2}{4}$$

For all polarization scenarios, D-FIS provides a strict $4\times$ power advantage as $N\to\infty$ (Nerini et al., 3 Dec 2025).

• Beyond-Diagonal FIS: BD-FIS, with proper polarization-swapping, further recovers lost paths under polarization mismatch:

$$P_R^{\mathrm{BD\text{-}FIS}} = \frac{[1+\chi+2\sqrt{\chi}]^2N^2}{4}$$

As $\chi \to 0$ (complete polarization orthogonality), this gain factor diverges, indicating robustness to polarization alignment.

5. Dual-Polarization Effects and Polarization Management

The presence of dual-polarized elements introduces significant polarization-dependent behaviors. For diagonal surfaces, cross-polarization mismatch directly limits achievable gain, with high attenuation as $\chi\to 0$. BD-FIS with polarization-swapping matrices restores signal paths by engineering port coupling, recovering losses and ensuring link reliability regardless of the relative polarization of Tx and Rx (Nerini et al., 3 Dec 2025). This effect is unique to beyond-diagonal matrix designs and is provably absent in standard diagonal FIS or RIS.

6. Design Guidelines and Application Scenarios

• Optimal Matrix Selection: For D-FIS, $\Theta=-I_N$ is universally optimal. For BD-FIS under orthogonal polarizations, block-off-diagonal matrices with per-port $\pi$ phase swaps maximize throughput.
• Frequency Tuning Range: The required operating frequency must span $$f^*=c/[d_A|\sin\theta_\mathrm{R}+\sin\theta_\mathrm{T}|]$$ across the anticipated geometries. Applications with wide available bandwidth (e.g., mmWave or sub-THz) are especially well-suited.
• Implementation Considerations: FIS requires zero active hardware on the surface—no power or reconfigurable control lines—all complexity is shifted to a frequency-agile transmitter. FIS is thus attractive in large deployments, mobility settings, or energy-constrained scenarios, provided transmitter agility and spectrum flexibility are available.
• Limitations: In spectrum-constrained environments or for channels varying faster than the achievable tuning rate, the relative merit of FIS may be reduced due to the fundamental requirement for frequency adaptation.

7. Connection to Fixed HR-RIS and Binary FIS Architectures

Related work on hybrid relay–reflecting surfaces (HR-RIS) with fixed configurations (Nguyen et al., 2021) and narrowband binary-state FIS (Björnson, 2021) affirms the benefits of fixed-surface architectures. HR-RIS augments a mostly passive fixed surface with a small number of active relay elements, showing $15$–$20\%$ SE gains over RIS-only, confirming the potential of architectures with hardware simplicity and minimal dynamic control. In binary FIS systems, pilot-aided channel recovery combined with per-element quantized phase selection ($\theta_n\in\{0,\pi\}$) achieves substantial array gain (sum-power increases of $10$–$20$ dB, rate gains $2$–$5\times$) using only $O(N\log N)$ complexity and nanosecond-class reconfiguration via simple switches (Björnson, 2021). Both approaches reinforce the FIS principle: passive hardware, with insightfully chosen (fixed) control, can provide near-coherent combining and scalable link gain when paired with transmitter-side adaptation.

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In summary, Fixed Intelligent Surfaces exploit transmitter frequency agility and static, globally predesigned reflection matrices to achieve optimal coherent signal combining—realizing up to fourfold power gains over classical RIS in LOS scenarios and extreme robustness to polarization alignment when beyond-diagonal coupling is leveraged (Nerini et al., 3 Dec 2025). The paradigm offers compelling scalability and deployment simplicity, provided spectrum agility can be guaranteed at the transmitter side.