⚡ electrical engineering

Low-Complexity Channel Parameter Estimation for Coprime HRIS-Assisted MIMO Systems

This paper proposes a low-complexity channel parameter estimation scheme for uplink MIMO systems assisted by a Hybrid Reconfigurable Intelligent Surface (HRIS) with sparse coprime active elements, utilizing Khatri-Rao and Kronecker factorizations alongside spatial smoothing and Root-MUSIC to achieve robust angular extraction and superior accuracy compared to fully passive architectures.

Original authors: Jean C. S. Ferreira, Melryllin G. O. Sousa, Fazal-E Asim

Published 2026-08-14

📖 5 min read🧠 Deep dive

CC0 1.0

Original authors: Jean C. S. Ferreira, Melryllin G. O. Sousa, Fazal-E Asim

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the air around us is filled with invisible radio waves, carrying our texts, videos, and calls. For decades, we've tried to catch these waves with antennas, hoping they bounce off buildings or travel straight to us. But sometimes, the signal gets lost, blocked, or too weak to hear. Enter a new kind of technology called a "Reconfigurable Intelligent Surface" (RIS). Think of a RIS as a giant, high-tech mirror made of thousands of tiny, low-power tiles. Instead of just reflecting light like a bathroom mirror, this digital mirror can be programmed to bend and steer radio waves exactly where we want them to go, turning a dead zone into a strong signal.

However, there's a catch. To steer the mirror perfectly, the system needs to know exactly where the signal is coming from and where it needs to go. This is like trying to aim a laser pointer at a moving target while wearing thick foggy glasses. If the mirror is "passive" (meaning it only reflects and doesn't "see" the signal), it has to guess the path based on a round-trip echo, which is often blurry and full of errors. This paper tackles that guessing game. It proposes a smarter mirror that doesn't just reflect, but also "listens" to a few of the incoming signals directly, allowing it to figure out the path with much sharper precision, all while keeping the hardware simple and cheap.

The Smart Mirror with Ears

In this study, researchers Jean C. S. Ferreira, Melryllin G. O. Sousa, and Fazal-E Asim propose a clever upgrade to these intelligent mirrors, which they call a "Hybrid Reconfigurable Intelligent Surface" (HRIS). Imagine a massive wall of 121 tiny tiles (arranged in an 11 by 11 grid). In a traditional setup, every single tile is just a reflector. In their new design, only a tiny handful of these tiles—specifically 11 of them—are given "ears" (active sensors) to listen to the incoming signal directly. The rest of the 110 tiles remain passive, doing what they do best: reflecting the signal to the receiver.

The researchers arranged these 11 listening tiles in a special, sparse pattern called a "coprime" geometry. You can think of this like a musical rhythm where you only play certain beats to create a complex sound; here, the specific spacing of the sensors allows them to "hear" a much wider range of angles than their small number would suggest. This setup solves a major problem: usually, having so few sensors makes it hard to pinpoint exactly where a signal is coming from. But by using this special spacing and some advanced math tricks (like "spatial smoothing" and "Root-MUSIC"), the system can fill in the missing pieces of the puzzle and figure out the signal's direction with high accuracy.

How It Works: The Two-Step Dance

The paper describes a two-step process to find the signal's path. First, the 11 "listening" tiles at the mirror catch the signal coming from the user's phone. Because they are right there at the source, they get a clear, direct snapshot of the signal's angle. This is like having a security camera right at the front door.

Second, the rest of the mirror reflects the signal toward the base station (the receiver). The base station receives this reflected signal, which has traveled a longer, more complex path. The researchers use a mathematical technique called "Khatri-Rao and Kronecker factorizations" to untangle this complex reflection. It's like taking a tangled ball of yarn and finding the two separate strings that were woven together. By combining the clear "listening" data from the 11 sensors with the "reflection" data from the whole mirror, the system fuses the information to get a super-accurate map of the signal's journey.

What the Simulations Show

The authors ran computer simulations to test if this idea actually works. They compared their "Hybrid" mirror against a standard "All-Passive" mirror (where no tiles have ears). The results were promising. In these simulations, the Hybrid mirror with its 11 active sensors was much better at guessing the correct angles of the signal, especially for the path between the user and the mirror.

The study found that even though only about 9% of the tiles (11 out of 121) were active, the system performed significantly better than the fully passive version. The "listening" tiles provided a strong, clear signal that helped the system ignore the noise that usually plagues the reflection-only method. Interestingly, the researchers noted that the accuracy of the final signal direction depends on how much power is split between listening and reflecting. If the mirror listens too much, it reflects too little; if it reflects too much, it can't hear well. The simulations showed that there is a sweet spot (around splitting the power 50/50) where the system gets the best of both worlds.

Why It Matters

The main takeaway from this paper is that you don't need to turn the entire mirror into a complex, expensive computer to get great results. By adding just a few smart, listening tiles in a specific pattern, you can get a much clearer picture of the wireless world. The authors suggest that this approach offers a great balance: it keeps the hardware simple and cheap (since most tiles remain passive) while dramatically improving the accuracy of the signal tracking. While these results are based on simulations and assume a clear line-of-sight (no buildings blocking the view), the findings suggest a practical path forward for making 6G networks faster and more reliable without breaking the bank on expensive equipment.

Technical Summary: Low-Complexity Channel Parameter Estimation for Coprime HRIS-Assisted MIMO Systems

Problem Statement
Reconfigurable Intelligent Surfaces (RISs) offer significant potential for beyond-5G and 6G systems by programmatically controlling signal propagation. However, effective deployment relies on accurate Channel State Information (CSI). Conventional fully passive RISs lack direct sensing capabilities, forcing the Base Station (BS) to estimate the cascaded UE-RIS-BS channel indirectly. This indirect observation complicates parameter estimation, particularly as the number of RIS elements increases, leading to high pilot overhead and reduced identifiability. While Hybrid RIS (HRIS) architectures introduce active sensing elements to mitigate this, fully connected or subarray-based hybrid designs often incur prohibitive hardware complexity, power consumption, and cost. Furthermore, utilizing sparse array geometries to reduce sensor counts introduces rank-deficiency issues in covariance matrices, hindering high-resolution angle estimation.

Methodology
The paper proposes a low-complexity parameter estimation framework for uplink MIMO systems assisted by an HRIS employing a sparse, "L"-shaped coprime geometry. The system model assumes a dominant Line-of-Sight (LoS) component where the HRIS consists of a large number of passive reflecting elements and a small subset of active sensing elements ( $N_A \ll N$ ).

The estimation scheme operates in three phases:

Local Sensing at HRIS: Active elements, connected to individual RF chains, simultaneously sense a portion of the incident UE signal while reflecting the remainder. The received signal at the HRIS sensing chains is processed to directly estimate the UE departure angle (AoD) and HRIS arrival angles (AoA) using a rank-1 extraction followed by spatial decoupling of the horizontal and vertical array signatures.
Reflection-Based Processing at BS: The BS receives the signal reflected by the entire HRIS aperture. The cascaded channel is modeled using the Khatri-Rao product structure. The proposed method employs vectorization and least-squares Khatri-Rao factorization (LSKRF) to decouple the cascaded channel into the UE-HRIS and HRIS-BS links. Subsequently, least-squares Kronecker factorization (LSKronF) is used to separate the multi-dimensional spatial signatures.
Rank Restoration and Data Fusion: To address the rank deficiency caused by the sparse coprime geometry, coarray-domain spatial smoothing is applied. Root-MUSIC is then utilized to extract high-resolution angular parameters from the restored covariance matrices. Finally, a data fusion step averages the angular estimates obtained from the local sensing branch and the reflection-based branch to produce the final channel parameters.

Key Contributions
The paper outlines four primary contributions:

Architecture: A novel HRIS design where only a few selected elements are active and arranged in a sparse, L-shaped coprime array, while the majority of elements remain passive reflectors. This minimizes hardware complexity while maintaining a large reflection aperture.
Framework: A channel parameter estimation framework that integrates local HRIS sensing with BS-side cascaded-channel processing, utilizing Khatri-Rao and Kronecker factorizations to decouple channel components.
Algorithm: The application of coarray-domain spatial smoothing and Root-MUSIC to overcome the rank deficiency inherent in sparse coprime geometries, enabling robust angular extraction.
Validation: Simulation results demonstrating that the proposed strategy yields higher estimation accuracy compared to fully passive RIS baselines and remains robust across varying power-splitting factors and active element configurations.

Simulation Results
Monte Carlo simulations were conducted comparing the proposed coprime HRIS against a fully passive RIS baseline and conventional unstructured matrix estimators.

Angular Estimation: The proposed HRIS consistently achieved lower Root Mean Square Error (RMSE) for UE-HRIS parameters (AoD and AoA) compared to the passive baseline. This improvement is attributed to the local sensing capability, which avoids the double path loss and noise amplification associated with the cascaded channel. The BS AoA performance remained similar between both architectures, as it relies primarily on the reflected signal.
Channel Reconstruction: The proposed method achieved the lowest Normalized Mean Square Error (NMSE) for the structured cascaded channel matrix, outperforming direct Least Squares (LS) and Khatri-Rao Factorization (KRF) methods used with passive RISs.
Power Splitting: Results indicated a trade-off where increasing the reflection power fraction ( $\rho$ ) improved reflection-based estimates but degraded local sensing estimates. The proposed architecture's ability to fuse both sources of information provided robustness against this trade-off.
Active Elements: Increasing the number of active elements improved sensing accuracy by expanding the virtual aperture, while having a negligible impact on the reflection gain, confirming that high accuracy can be achieved with a small fraction of active hardware.

Significance
The paper claims that the proposed architecture offers a favorable trade-off between estimation accuracy, reflection gain, power consumption, and implementation cost. By leveraging sparse coprime sensing, the system achieves high-resolution parameter estimation without the hardware burden of fully connected hybrid surfaces. The integration of local sensing with cascaded channel processing allows for robust channel acquisition that surpasses the limitations of fully passive RISs, making it a practical candidate for future 6G deployments. The authors note that future work should address extensions to non-line-of-sight (NLoS) conditions, dynamic environments, and multi-user scenarios.

More like this