⚡ electrical engineering

Cell-Free Massive MIMO-Assisted SWIPT Using Stacked Intelligent Metasurfaces

This paper proposes a deep reinforcement learning-based centralized training and decentralized execution framework to jointly optimize stacked intelligent metasurface phase shifts, access point mode selection, and power allocation in cell-free massive MIMO-assisted SWIPT systems, effectively maximizing harvested energy while satisfying spectral efficiency constraints under practical impairments.

Original authors: Thien Duc Hua, Mohammadali Mohammadi, Hien Quoc Ngo, Michail Matthaiou

Published 2026-02-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Thien Duc Hua, Mohammadali Mohammadi, Hien Quoc Ngo, Michail Matthaiou

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 a future where your smartphone never runs out of battery because it charges itself wirelessly while you are reading a text message or watching a video. This is the dream of SWIPT (Simultaneous Wireless Information and Power Transfer).

However, getting enough power to charge a device while also sending a clear message is like trying to shout a secret to a friend across a noisy, crowded stadium while simultaneously trying to light a candle on a table. It's incredibly difficult to do both well at the same time.

This paper proposes a brilliant new way to solve that problem using a combination of three high-tech concepts: Cell-Free Networks, Stacked Metasurfaces, and AI.

Here is the breakdown in simple terms:

1. The Setup: The "Cell-Free" Stadium

Traditionally, cell towers are like giant spotlights. If you are far away, the signal is weak.

The New Idea: Instead of a few big towers, imagine hundreds of small, friendly "access points" (like smart streetlights) scattered everywhere in a city. This is Cell-Free Massive MIMO. They all work together to cover the area perfectly, so no one is ever in a "dead zone."

2. The Problem: The "Traffic Jam"

In this crowded stadium of signals, two things are happening at once:

Information: Sending data (text, video) to your phone.
Power: Beaming energy to charge your phone.

The problem is that the signals can get in each other's way. If the "power beam" is too strong, it might drown out the "message." If the "message" is too loud, it might waste the energy meant for charging. Plus, the hardware needed to manage this is usually expensive and eats up a lot of electricity itself.

3. The Hero: The "Stacked Intelligent Metasurface" (SIM)

This is the paper's star invention. Think of a standard radio antenna as a simple megaphone. It can shout, but it can't really shape the sound perfectly.

Now, imagine a Stacked Intelligent Metasurface (SIM) as a high-tech, multi-layered "smart lens" attached to every one of those streetlights.

How it works: Instead of just shouting, these lenses can bend, twist, and focus the invisible radio waves like a laser.
The "Stacked" part: Unlike older technology (RIS) which is like a single sheet of glass, these are stacked layers (like a sandwich). This gives them much more control. They can act like a "traffic cop" for radio waves, directing the "power waves" straight to the battery and the "data waves" straight to the screen, ensuring they don't crash into each other.
The Benefit: They do this using "analog computing" (manipulating waves directly) rather than heavy digital processing, which saves massive amounts of energy.

4. The Brain: The "Decentralized AI" (CTDE)

Now, how do you control hundreds of these smart streetlights and their complex lenses at the same time?

The Old Way (Centralized): Imagine one giant super-computer in a basement trying to control every single streetlight in the city. As the city grows, this computer gets overwhelmed, slows down, and eventually crashes. This is called Centralized Training and Execution (CTCE).
The New Way (This Paper): The authors propose Centralized Training, Decentralized Execution (CTDE).
- Training: The AI "brain" learns in a simulation (the classroom) where it sees the whole city. It learns the best rules for how to move the lenses and split the power.
- Execution: Once trained, the AI is split up. Each streetlight gets its own tiny "brain" (a local AI agent). When the system is running, each streetlight looks at its immediate surroundings and makes its own decisions instantly, without asking the central computer.
- The Analogy: Think of a soccer team. The coach (Centralized Training) teaches the team the strategy. But during the game, the players (Decentralized Execution) don't wait for the coach to yell every move; they react instantly to the ball and their teammates based on what they learned. This makes the team faster and more scalable.

5. The Goal: The "Perfect Balance"

The paper uses this AI to solve a complex math puzzle:

Maximize Energy: Get as much power as possible to the devices.
Guarantee Speed: Make sure the internet speed is fast enough for video calls.
Handle Imperfections: Real life is messy. The AI accounts for bad weather, signal interference, and imperfect hardware.

The Results

The researchers tested their idea with computer simulations. They found that:

It works: The "Smart Lens" (SIM) technology significantly boosts both charging speed and internet speed compared to current methods.
It's fast: The decentralized AI makes decisions much faster than the old "giant computer" method, especially in large networks.
It's smart: The AI learns to navigate the "traffic jams" of signals better than traditional math-based methods, achieving results that are nearly perfect but with much less computing power.

Summary

This paper presents a blueprint for the future of wireless networks. By combining distributed smart antennas, multi-layered "smart lenses" that bend radio waves, and decentralized AI that lets each antenna think for itself, we can create a world where our devices are always charged and always connected, without needing massive, energy-hungry servers to manage it all.

1. Problem Statement

The paper addresses the challenge of optimizing Simultaneous Wireless Information and Power Transfer (SWIPT) in Cell-Free Massive MIMO (CF-mMIMO) systems enhanced by Stacked Intelligent Metasurfaces (SIMs).

Context: While CF-mMIMO improves spectral efficiency (SE) and energy harvesting (HE), it faces scalability issues due to high hardware costs (RF chains) and energy consumption. Traditional Reconfigurable Intelligent Surfaces (RISs) have limited degrees of freedom (DoF). SIMs, with their multi-layered structure, offer superior signal manipulation capabilities.
Core Challenge: The system must jointly optimize three complex, interdependent variables:
1. Access Point (AP) Mode Selection: Deciding whether an AP acts as an Information-AP (I-AP) or an Energy-AP (E-AP).
2. Power Allocation: Distributing transmit power among users.
3. SIM Phase Shifts (PS): Configuring the electromagnetic wave propagation through the stacked layers.
Constraints & Impairments: The optimization must satisfy:
- Minimum SE Quality-of-Service (QoS) for information receivers (IRs).
- Minimum Harvested Energy (HE) QoS for energy receivers (ERs).
- Practical impairments: Non-linear energy harvesting (NLEH) models, pilot contamination (PC), channel estimation errors, and reliance on long-term statistical Channel State Information (CSI).
Optimization Nature: The resulting problem is a mixed-integer non-convex optimization problem, which is computationally intractable for large-scale networks using traditional methods.

2. Methodology

A. System Modeling & Performance Analysis

Architecture: A CF-mMIMO system where $M$ APs, each equipped with a multi-layer SIM, serve single-antenna IRs and ERs.
Precoding: The authors employ Protective Partial Zero-Forcing (PPZF).
- I-APs use Zero-Forcing (ZF) to eliminate inter-user interference.
- E-APs use Protective Maximum Ratio Transmission (PMRT), projecting energy signals into the null space of IR channels to prevent interference with information transmission.
Derivations: Closed-form expressions are derived for:
- Ergodic Spectral Efficiency (SE) for IRs.
- Average Non-Linear Harvested Energy (HE) for ERs, utilizing a logistic function model to account for circuit saturation.

B. Proposed Solution: CTDE Framework based on DRL

To overcome the "curse of dimensionality" inherent in centralized optimization, the authors propose a Centralized Training, Decentralized Execution (CTDE) framework using Deep Reinforcement Learning (DRL).

Markovian Environment: The problem is transformed into a Markov Decision Process (MDP) where each AP acts as an agent.
Decentralized Execution: Unlike Centralized Training and Centralized Execution (CTCE), where a single agent controls the whole network, CTDE equips each AP with its own DNN-based actor. Each AP makes decisions based on local observations (large-scale fading coefficients), significantly reducing the action space dimensionality.
Constraint Satisfaction:
- Normalization: A specific normalization process is applied to the actor's output to ensure binary mode selection (I-AP vs. E-AP) and power constraints are met.
- Reward Function: A normalized joint reward function is designed to balance the trade-off between maximizing total harvested energy and maintaining SE QoS. It includes a penalty term for SE violations and a term based on the Frobenius norm of the SIM channel to encourage effective beamforming.
Algorithms: The framework is tested using both off-policy (MADDPG) and on-policy (MAPPO) algorithms.

C. Benchmark: Two-Phase Convex-Based Solution

To provide a theoretical performance bound, a robust two-stage convex-based optimization is developed:

Phase 1 (Heuristic): Optimizes SIM phase shifts using a layer-by-layer heuristic search to maximize the channel trace.
Phase 2 (SCA): Uses Successive Convex Approximation (SCA) to jointly optimize AP mode selection and power allocation, relaxing binary constraints and linearizing non-convex terms.

3. Key Contributions

Novel Framework: First integration of Stacked Intelligent Metasurfaces (SIMs) into CF-mMIMO SWIPT systems, explicitly modeling non-linear energy harvesting and pilot contamination.
Closed-Form Analysis: Derivation of analytical expressions for achievable SE and average harvested energy under statistical CSI and PPZF precoding.
CTDE DRL Strategy: Introduction of a scalable CTDE framework that solves the mixed-integer non-convex problem without manual convexification. It effectively handles high-dimensional decision spaces by distributing the learning load across APs.
Stability Mechanisms: Development of a normalized joint reward function and constraint-satisfied normalization to stabilize training and ensure feasible solutions.
Robust Benchmark: A two-phase convex-based solution (HPS + SCA) serving as a high-complexity performance benchmark.

4. Numerical Results

Extensive simulations validate the proposed approach against baselines (Random AP mode, Equal Phase Shifts, CTCE strategies, and the convex benchmark).

SIM Impact:
- SIMs significantly outperform traditional RISs.
- Heuristic Phase Shifts (HPS) yield 1.05x (SE) and 1.52x (HE) gains over Equal Phase Shifts (EQPS).
- Increasing the Ricean factor ( $\kappa$ ) improves harvested energy significantly (up to 2x improvement as $\kappa$ goes from 2 to 12).
DRL Performance:
- CTDE vs. CTCE: The CTDE framework (MADDPG/MAPPO) achieves performance comparable to the centralized CTCE but with significantly better scalability and lower inference latency.
- Convergence: CTDE agents converge faster and more stably than single-agent (CTCE) counterparts in large-scale networks, avoiding the curse of dimensionality.
- Reward Normalization: The proposed normalized reward function prevents training collapse (loss explosion) seen in non-scaled reward scenarios.
Comparison with Convex Benchmark:
- The DRL-based CTDE solution achieves SWIPT performance comparable to the convex-based JAPPA solution (which is near-optimal) but with a massive reduction in computational complexity.
- Inference Time: DRL inference is instantaneous (milliseconds), whereas the convex-based solution requires iterative loops taking seconds to minutes, especially as the number of APs increases.
- Gain: The proposed DRL approach outperforms random/heuristic baselines by significant margins (e.g., 30%+ gain in sum-HE over centralized SADDPG).

5. Significance

This paper makes a significant contribution to the field of 6G and next-generation wireless networks by:

Bridging the Gap: It successfully bridges the gap between theoretical optimization (convex methods) and practical, real-time implementation (DRL) in complex, large-scale SWIPT systems.
Scalability: It demonstrates that CTDE is the viable path for deploying CF-mMIMO systems with intelligent surfaces, solving the scalability bottleneck that plagues centralized control.
Energy Efficiency: By enabling efficient joint optimization of information and power transfer using low-cost SIMs, it paves the way for sustainable, self-sustaining IoT networks.
Practicality: The inclusion of non-linear harvesting models, pilot contamination, and statistical CSI makes the results highly relevant for real-world deployment scenarios.

In conclusion, the study proves that a DRL-based CTDE framework can autonomously manage complex resource allocation in SIM-assisted CF-mMIMO SWIPT systems, achieving near-optimal performance with the low latency and scalability required for future wireless networks.