⚡ electrical engineering

RIS-Enabled Wireless Channel Equalization: Adaptive RIS Equalizer and Deep Reinforcement Learning

This paper proposes and evaluates two approaches for RIS-enabled wireless channel equalization: a classical adaptive method (ARISE) that relies on channel estimation and a deep reinforcement learning framework that optimizes RIS coefficients directly from received signals, demonstrating that the Soft Actor-Critic (SAC) algorithm achieves comparable performance with lower complexity by eliminating the need for explicit channel estimation.

Original authors: Gal Ben-Itzhak, Ender Ayanoglu

Published 2026-03-04

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Gal Ben-Itzhak, Ender Ayanoglu

Original paper licensed under CC BY 4.0 (http://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 have a clear conversation with a friend in a massive, echoey cathedral. Every time you speak, your voice bounces off the stone walls, creating a messy mix of your original words and delayed echoes. By the time your friend hears you, the words are garbled, overlapping, and hard to understand. This is exactly what happens in wireless communication (like your phone connecting to a cell tower) when signals bounce off buildings and mountains, creating "echoes" called multipath interference.

This paper tackles a new way to fix this problem using a high-tech mirror called a Reconfigurable Intelligent Surface (RIS).

The Problem: The Echo Chamber

Normally, when your phone receives a garbled signal, it tries to fix it after the signal arrives, using digital software inside the phone. It's like trying to clean up a muddy painting after it's already been splashed with paint.

The authors propose a smarter idea: Why not fix the signal before it even reaches the phone?

The Solution: The "Smart Mirror" (RIS)

Think of the RIS as a giant wall of thousands of tiny, adjustable mirrors placed between the cell tower and your phone.

Traditional approach: The mirrors are static; they just reflect whatever hits them.
This paper's approach: The mirrors are "smart." They can instantly change their angle to steer the signal.

The goal is to use these mirrors to act as an "Over-the-Air Equalizer." Instead of waiting for the signal to arrive and then cleaning it up, the mirrors reshape the signal in mid-air so that when it finally hits your phone, it's already clean, strong, and free of echoes.

The Two Competing Strategies

The paper compares two different ways to tell these smart mirrors what to do.

1. The "Map Reader" Approach (ARISE)

The first method is called ARISE (Adaptive RIS Equalization).

How it works: Imagine a surveyor who first spends hours mapping every single wall, floor, and corner of the cathedral to understand exactly how sound bounces. Once they have a perfect 3D map, they calculate exactly how to tilt every mirror to fix the echo.
The Catch: Getting this perfect map takes a lot of time and effort. The surveyor has to shout test sounds, listen to the echoes, and do complex math. In a real-world scenario where people are moving, the map becomes outdated before it's even finished. It's accurate, but it's slow and requires a lot of "pilot" signals (test sounds) to work.

2. The "Trial and Error" Approach (DRL)

The second method uses Deep Reinforcement Learning (DRL), specifically an algorithm called SAC (Soft Actor-Critic).

How it works: Imagine a blindfolded musician trying to tune a guitar. They don't need a map of the room. They just pluck a string, listen to the sound, and say, "That was too sharp, I'll loosen the peg." They try again, listen, and adjust. Over time, through thousands of tiny attempts, they learn exactly how to tune the instrument to sound perfect in that specific room.
The Magic: The AI doesn't need to know why the echo exists or have a map of the walls. It just looks at the result (the sound) and adjusts the mirrors to make it better. It learns by doing.

The Showdown: Who Wins?

The authors ran thousands of computer simulations to see which method works better in different scenarios (moving users, different room sizes, different amounts of echo).

The Map Reader (ARISE): It works very well and produces a very clean signal. However, it is slow to start because it has to spend so much time "mapping" the environment first. If the environment changes quickly (like a car driving by), the map is useless.
The Trial-and-Error Learner (SAC): It starts learning immediately. It doesn't need a map. It adapts instantly to changes.
- The Result: The SAC algorithm eventually achieved the same high-quality signal as the Map Reader.
- The Bonus: It did it without needing the complex, time-consuming mapping process. It was faster, more flexible, and easier to implement.

The Takeaway

Think of it like navigating a city:

ARISE is like a GPS that requires you to download a full, high-definition 3D map of the city before you can drive. It's great if the city never changes, but if a road closes, you're stuck waiting for a new map.
SAC (DRL) is like a driver who learns the city by driving. They don't need a map; they just look at the traffic and turn left or right based on what they see. They might make a few wrong turns at first, but they quickly learn the best route and can adapt instantly if a road is blocked.

Conclusion:
This paper proves that using AI (specifically the SAC algorithm) to control these smart mirrors is a practical, powerful, and efficient way to fix wireless signals. It allows our future 6G networks to be faster and more reliable without needing to constantly measure and map the entire environment first. The "blind musician" (AI) can tune the "guitar" (wireless signal) just as well as the "surveyor" (mathematical model), but much faster and with less hassle.

1. Problem Statement

The paper addresses the challenge of signal equalization in wideband wireless links utilizing Reconfigurable Intelligent Surfaces (RIS).

Context: In high-speed wireless communications, multipath propagation causes Inter-Symbol Interference (ISI), degrading symbol recovery. Traditional equalizers (e.g., Feed-Forward Equalizers) operate at the receiver using digital baseband processing and delay elements.
The Gap: While RISs can reshape the wireless environment to improve Signal-to-Noise Ratio (SNR), their application as an "over-the-air equalizer" (performing equalization before the signal reaches the receiver) is underexplored.
Key Challenge: Effective RIS equalization requires configuring a large number of passive elements. Classical methods rely on accurate Channel State Information (CSI) of the cascaded Base Station-RIS-User Equipment (BS-RIS-UE) link. However, acquiring full CSI for high-dimensional RIS arrays is computationally expensive, introduces significant communication overhead (pilot signaling), and creates latency, making it impractical for dynamic environments.

2. Methodology

The authors propose and compare two distinct approaches to RIS-assisted equalization: a classical adaptive method and model-free Deep Reinforcement Learning (DRL).

A. Adaptive RIS Equalization (ARISE)

Concept: A novel adaptation of the Steepest Descent (SD) algorithm. Unlike traditional equalizers that update filter coefficients after reception, ARISE configures the RIS coefficients ( $\Gamma_m$ ) before the signal reaches the UE to shape the pulse response.
Mechanism:
- It minimizes a cost function $J$ defined as the mean squared error between the desired pulse (a single peak at $t=0$ ) and the received pulse, while simultaneously maximizing the main tap power.
- The algorithm requires explicit knowledge of the cascaded channel matrix ( $h_{BRU}$ ) to compute gradients.
- It updates reflection coefficients using a gradient descent rule derived from the channel estimates.
Limitation: It is heavily dependent on accurate, high-dimensional channel estimation, which creates a bottleneck in terms of pilot overhead and latency.

B. Model-Free Deep Reinforcement Learning (DRL)

To overcome the CSI dependency of ARISE, the authors implement three DRL algorithms that optimize RIS coefficients directly from received pulse responses without explicit channel estimation.

Formulation: The problem is modeled as a Markov Decision Process (MDP):
- State ( $s_t$ ): The real and imaginary parts of the received pulse response samples.
- Action ( $a_t$ ): The RIS reflection coefficients (real and imaginary parts).
- Reward ( $r_t$ ): A normalized metric ( $\eta_n$ ) that rewards a strong main tap and penalizes ISI energy.
Algorithms Evaluated:
1. DDPG (Deep Deterministic Policy Gradient): An actor-critic algorithm using deterministic policies.
2. TD3 (Twin Delayed DDPG): Improves DDPG by using twin critics to reduce overestimation bias and delayed policy updates.
3. SAC (Soft Actor-Critic): A maximum entropy algorithm that learns a stochastic policy, encouraging exploration and robustness.

3. Key Contributions

ARISE Framework: The development of a steepest descent-based algorithm (ARISE) that treats the RIS as a spatial equalizer, optimizing reflection phases to mitigate multipath distortion and boost SNR simultaneously.
DRL for RIS Control: The application and evaluation of DDPG, TD3, and SAC for RIS configuration, demonstrating that model-free approaches can bypass the need for explicit CSI.
Comprehensive Comparative Analysis: A rigorous comparison of ARISE and DRL methods across diverse metrics: convergence speed, computational complexity, communication overhead, and performance under varying channel conditions (Rician factor, number of RIS elements, and ISI paths).
Identification of SAC: The demonstration that Soft Actor-Critic (SAC) offers the best trade-off, achieving performance comparable to the CSI-dependent ARISE while eliminating the channel estimation bottleneck.

4. Simulation Results

The authors conducted extensive simulations with a single-antenna BS, single-antenna UE, and varying RIS sizes ( $M$ ) and channel conditions.

Performance vs. ARISE:
- SAC achieved equalization performance (measured by normalized objective function $\eta_n$ and SNR) nearly identical to ARISE.
- TD3 converged slower than SAC but eventually reached stable, high-performance states.
- DDPG struggled with local optima and showed the lowest performance, often failing to converge effectively in complex scenarios.
Convergence Speed: SAC demonstrated rapid convergence (often within 1,000 steps) and maintained stability even when the UE moved (random walk model) or channel conditions changed.
Scalability:
- As the number of RIS elements ( $M$ ) increased, all algorithms improved, though DRL performance eventually plateaued due to fixed neural network hidden layer sizes.
- As the number of delayed paths (ISI) increased, SAC maintained high performance without needing to re-estimate the growing channel matrix, unlike ARISE.
Robustness: In Rayleigh fading scenarios (no Line-of-Sight), DRL algorithms (especially SAC) performed significantly better than in Rician scenarios where the geometry was easier to learn, yet SAC still outperformed DDPG and TD3.
Complexity Trade-off:
- ARISE: Low per-step computational complexity but extremely high communication complexity due to the need for full CSI acquisition.
- DRL (SAC): Moderate computational complexity (due to neural network training) but negligible communication complexity as it operates directly on received signals.

5. Significance and Conclusion

This work highlights a paradigm shift in RIS control strategies. While classical adaptive filtering (ARISE) offers theoretical optimality, its reliance on full CSI makes it impractical for large-scale, dynamic RIS deployments.

Practicality: The study proves that Deep Reinforcement Learning, specifically SAC, is a viable, scalable, and robust solution for real-time RIS control.
Efficiency: SAC achieves "over-the-air" equalization without the heavy pilot overhead required by ARISE, making it suitable for future 6G and dynamic wireless systems where channel conditions change rapidly.
Hardware Realism: The model-free nature of DRL allows it to inherently accommodate hardware imperfections (nonlinearities, coupling effects) that are difficult to model analytically, further enhancing its practical utility.

In summary, the paper establishes that SAC-based RIS control provides a practical path to deploying RIS as an active equalizer, balancing high performance with implementation feasibility.