⚡ electrical engineering

Robust Sparse Channel Estimator for RIS-Assisted Hybrid MIMO Millimeter Wave Communication Under Impulsive Noise

This paper proposes a robust sparse-aware maximum correntropy criterion (SA-MCC) algorithm for channel estimation in RIS-assisted hybrid MIMO mmWave systems, demonstrating superior performance over conventional methods in the presence of impulsive noise and hardware impairments.

Original authors: Ankit Chouhan, Sandesh Jain, Rangeet Mitra, Pragya Swami, Somesh Kumar

Published 2026-07-10

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CC BY 4.0

Original authors: Ankit Chouhan, Sandesh Jain, Rangeet Mitra, Pragya Swami, Somesh Kumar

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ 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 you are trying to send a secret message across a crowded, noisy city using a flashlight. In the future, to make these messages super fast and clear, we want to use a special kind of "super-light" called millimeter waves. But there's a catch: these waves are like shy ghosts. They get blocked easily by walls, rain, or even a person walking by, and they lose their strength very quickly.

To fix this, engineers are building giant, invisible mirrors in the sky called Reconfigurable Intelligent Surfaces (RIS). Think of these mirrors as a team of thousands of tiny, smart robots. When the shy ghost-light hits them, the robots can instantly tilt and twist to bounce the light around obstacles and straight to your receiver, creating a clear path where there was none before.

The Problem: The "Static" in the Room
However, there's a big troublemaker. The equipment that sends and receives these signals isn't perfect. It has "hardware impairments," which act like a broken radio that adds weird, sudden bursts of static. In the real world, this isn't just a gentle hiss; it's like someone randomly shouting or dropping a heavy drum in the middle of a quiet library. This is called impulsive noise.

The old ways of trying to figure out the path of the light (called channel estimation) are like trying to listen to a whisper while someone is banging drums. The old methods, which assume the noise is a steady, gentle hum, get completely confused by these sudden shouts. They try to average out the noise, but the shouts are so loud and weird that the average doesn't make sense. The paper argues that these old methods, like LMS and ZA-LMS, simply aren't tough enough for this kind of chaotic environment.

The New Solution: A Smart Filter
The authors of this paper propose a new, tougher way to listen. They call it a Robust Sparse Channel Estimator based on the Maximum Correntropy Criterion (MCC).

Here is how it works, using a fun analogy:
Imagine you are trying to find a few specific friends in a massive, dark stadium (the channel). You know your friends are sitting in only a few specific seats (this is called sparsity).

The Old Way: You shout, "Where are you?" and listen to everyone's answer. If someone screams (impulsive noise), you get confused and think they are your friend.
The New Way (MCC): You use a special "noise-canceling ear." This ear is designed to ignore the crazy, loud screams. It focuses only on the clear, consistent voices. It knows that the screams are outliers and doesn't let them mess up your search.

The paper introduces three layers of improvement to this new method:

ZA-MCC: This version adds a rule that says, "If a seat looks empty, assume it's empty." It helps ignore the empty seats so you only focus on the friends who are actually there.
SA-MCC: This is even smarter. Instead of just ignoring empty seats, it uses a fancy mathematical trick (involving something called a Gauss-Hypergeometric function) to be very precise about which seats are truly empty and which ones have your friends. It's like having a super-sharp flashlight that only lights up the exact spots where your friends are sitting.
VSS-SA-MCC: This is the champion. It adds a "variable step-size." Imagine you are walking through the stadium. If the path is clear, you take big, fast steps. If you hit a bump or hear a weird noise, you slow down to be careful. This algorithm automatically changes how fast it learns based on how messy the noise is.

What the Simulations Show
The authors didn't just guess; they ran thousands of computer simulations to test their idea. They set up virtual cities with different sizes of mirror teams (RIS) and different numbers of antennas (32x32 and 64x64). They made the noise very "impulsive" (using a model called $\alpha$ -stable noise where the parameter $\alpha = 1$ ).

The results were clear:

The old methods (LMS, ZA-LMS) struggled and got confused by the noise.
The new VSS-SA-MCC method was the fastest to find the path and the most accurate.
In one specific test with a 32x32 setup and 32 mirror elements, the new method achieved a Normalized Mean-Squared Error (NMSE) of -35.15 dB, while the older MCC method only reached -24.40 dB.
When they increased the mirror team to 64 elements, the new method got even better, reaching -36.22 dB.

The paper suggests that this new method is much better at handling the "shouts" of impulsive noise than the current standard methods. It proves that by being "sparse-aware" (knowing that most of the path is empty) and using the "correntropy" trick (ignoring the crazy noise), we can keep our super-fast connections stable even when the hardware is imperfect.

So, while this isn't a finished product you can buy at a store yet, the simulations strongly suggest that if we want our future 5G and beyond networks to work in messy, real-world cities with broken hardware, we need to switch to this smarter, tougher way of listening.

Technical Summary: Robust Sparse Channel Estimator for RIS-Assisted Hybrid MIMO Millimeter Wave Communication Under Impulsive Noise

Problem Statement
The integration of Reconfigurable Intelligent Surfaces (RIS) with millimeter-wave (mmWave) Multi-Input Multi-Output (MIMO) architectures is critical for achieving ultra-high data rates in next-generation wireless networks. However, accurate Channel Estimation (CE) in these systems faces significant challenges. RIS-assisted links suffer from severe path loss and are highly susceptible to non-Gaussian distortions arising from nonlinear hardware impairments (HIs) in power amplifiers, as well as impulsive interference common in dense urban environments.

Conventional CE techniques, such as Orthogonal Matching Pursuit (OMP) and Zero-Attracting Least Mean Square (ZA-LMS), rely on Minimum Mean Square Error (MMSE) criteria. These methods consider only second-order error statistics and assume Gaussian noise distributions. Consequently, they exhibit degraded performance and instability when applied to RIS-assisted hybrid MIMO-mmWave systems impaired by heavy-tailed, non-Gaussian, or impulsive noise. Furthermore, while mmWave channels possess inherent sparsity in the angular domain, existing sparse-aware estimators often fail to maintain robustness under these specific non-ideal conditions.

Methodology
The paper proposes a unified framework for robust, sparsity-aware (SA) channel estimation based on the Maximum Correntropy Criterion (MCC). The MCC is a robust statistical measure that utilizes higher-order error statistics, making it inherently resilient to impulsive noise and outliers compared to traditional MMSE approaches.

The authors develop a progressive algorithmic framework:

ZA-MCC Estimator: The initial proposal integrates an $\ell_1$ -norm regularization term into the MCC cost function. This promotes sparsity in the channel coefficients while leveraging the robustness of the MCC against non-Gaussian noise.
SA-MCC Estimator: To address the limitation of $\ell_1$ -norm regularization, which uniformly attracts all coefficients toward zero (potentially degrading significant channel taps), the authors propose a more flexible sparsity constraint. This utilizes a generalized Gauss-hypergeometric approximation of the $\ell_0$ -norm. This approach allows for better suppression of insignificant channel taps while preserving dominant paths.
VSS-SA-MCC Estimator: The final proposed algorithm introduces a Variable Step-Size (VSS) strategy to the SA-MCC framework. Unlike existing VSS-ZA-LMS algorithms that update step sizes based on instantaneous error energy (which can be unstable due to outliers), this method adapts the learning rate based on the energy of the MCC-induced error kernel. This dynamic adaptation aims to accelerate convergence and reduce steady-state Normalized Mean-Squared Error (NMSE) without increasing computational complexity.

The system model considers a downlink scenario where the direct Base Station (BS) to User Equipment (UE) line-of-sight is blocked, necessitating signal transmission via an RIS. The channel is modeled geometrically with sparse multipath components, and the noise is modeled using a symmetric $\alpha$ -stable distribution to simulate impulsive interference.

Key Contributions
The paper claims the following specific contributions:

Novel Framework: It presents the first study to employ MCC-based sparsity-aware algorithms for RIS-assisted hybrid MIMO mmWave CE in the presence of non-Gaussian distortions.
Robust Sparsity: The proposed ZA-MCC framework leverages higher-order error statistics to offer improved resilience over conventional MMSE-based estimators against impulsive noise.
Enhanced Sparsity Constraint: A novel SA-MCC estimator is introduced using a generalized Gauss-hypergeometric approximation of the $\ell_0$ -norm, enabling superior suppression of insignificant channel taps.
Adaptive Learning: The introduction of a VSS strategy (VSS-SA-MCC) that dynamically adapts the learning rate based on the MCC error kernel energy, resulting in accelerated convergence and reduced steady-state NMSE.
Comprehensive Validation: Extensive simulations validate the framework across various MIMO and RIS configurations, demonstrating superiority over state-of-the-art benchmarks.

Simulation Results
The performance of the proposed VSS-SA-MCC algorithm was evaluated against LMS, ZA-LMS, standard MCC, ZA-MCC, and fixed-step SA-MCC algorithms under $\alpha$ -stable noise ( $\alpha=1$ ). Key findings include:

Convergence: The VSS-SA-MCC algorithm demonstrated the fastest convergence rate among all tested methods. In a $32 \times 32$ MIMO system with 32 RIS elements, it achieved a steady-state NMSE of $-35.15$ dB, outperforming the fixed-step SA-MCC ( $p=2$ ) which reached $-33.21$ dB.
SNR Robustness: Across SNR values ranging from $-20$ dB to $20$ dB, the proposed SA-based approaches consistently outperformed LMS, ZA-LMS, and standard MCC. The SA-MCC ( $p=2$ ) and VSS-SA-MCC variants exhibited the lowest NMSE and minimal fluctuation, particularly in low SNR regimes where ZA-LMS showed significant oscillations.
IRS Scaling: Increasing the number of RIS elements (from 32 to 64) improved NMSE performance for all algorithms. However, the proposed SA-MCC ( $p=2$ ) and VSS-SA-MCC showed the most significant gains, achieving a steady-state NMSE of $-36.22$ dB in a $64 \times 64$ MIMO system with 64 RIS elements.
Parameter Sensitivity: The use of the Gauss-hypergeometric approximation with $p=2$ consistently yielded lower NMSE compared to $p=1$ , validating the effectiveness of the specific $\ell_0$ -like penalty formulation.

Significance and Claims
The authors conclude that the proposed VSS-SA-MCC methodology provides a promising solution for channel estimation in future wireless communication systems, specifically in scenarios characterized by hardware impairments, severe fading, and non-Gaussian disturbances. The work addresses a critical research gap by demonstrating that robust, sparsity-aware estimation is feasible and superior to existing methods when dealing with the impulsive noise inherent in practical RIS-assisted mmWave deployments. The paper positions this approach as a viable alternative to conventional estimators that fail under non-Gaussian conditions, offering a balance of high accuracy, fast convergence, and robustness without incurring significant computational overhead.

Technical Summary: Robust Sparse Channel Estimator for RIS-Assisted Hybrid MIMO Millimeter Wave Communication Under Impulsive Noise

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