⚡ electrical engineering

Secure Rate-Splitting and RIS Beamforming with Untrusted Energy Harvesting Receivers

This paper proposes a secure rate-splitting multiple access (RSMA) scheme aided by a UAV-mounted reconfigurable intelligent surface (RIS) to maximize fairness-based secrecy energy efficiency in a heterogeneous network where untrusted energy-harvesting receivers may act as eavesdroppers, utilizing an alternating optimization framework with sequential convex approximation to jointly design transmission and reflection parameters.

Original authors: Hamid Reza Hashempour, Le-Nam Tran, Duy H. N. Nguyen, Hien Quoc Ngo

Published 2026-03-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hamid Reza Hashempour, Le-Nam Tran, Duy H. N. Nguyen, Hien Quoc Ngo

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 high-stakes delivery scenario in a busy, obstacle-filled city. Here is the story of the paper, translated into everyday language with some creative metaphors.

The Cast of Characters

The Base Station (The Master Chef): A powerful kitchen (the transmitter) sitting on the ground. It has many arms (antennas) and wants to cook up delicious meals (data) for its loyal customers.
The Legitimate Customers (IHRs): These are the good guys. They want to eat the meal (get information) and they have special solar-powered plates that can also charge their batteries using the energy in the radio waves.
The Untrusted Guests (UEHRs): These are the tricky neighbors. They also have solar plates and need to charge their batteries. However, they are sneaky; while they are charging, they are also trying to peek at the Chef's secret recipes (eavesdropping on the data).
The Drone with a Magic Mirror (UAV-RIS): This is the star of the show. A drone is hovering in the sky carrying a giant, smart mirror made of thousands of tiny tiles. This mirror can bend and bounce signals around buildings that block the Chef's view.

The Problem: The "Blockage" and the "Spy"

In this city, tall buildings block the direct line of sight between the Chef and the customers.

The Challenge: The Chef needs to send food to the good customers.
The Catch: The good customers need energy to charge their plates, but the bad neighbors are also hungry for energy.
The Risk: If the Chef sends the message too loudly or in the wrong direction, the bad neighbors might not only steal the energy but also steal the secret recipe.

The Solution: A Three-Part Strategy

The paper proposes a clever three-step plan to solve this mess, combining Rate-Splitting, Beamforming, and the Magic Mirror.

1. The "Split Menu" Strategy (Rate-Splitting)

Instead of sending one giant, complex dish to everyone, the Chef uses a Rate-Splitting technique. Think of it like this:

The Common Sauce: The Chef prepares a "common sauce" that everyone (both good customers and bad neighbors) can taste. It's not the main course, but it's necessary.
The Private Steaks: The Chef then prepares individual, secret steaks for each good customer.
The Trick: The Chef sends the "Common Sauce" first. Because the bad neighbors are busy decoding this sauce (thinking it's the main event), they get confused and can't easily figure out the secret steaks hidden underneath. It's like a magician distracting the audience with a red scarf while hiding the rabbit in the other hand.

2. The "Smart Mirror" (RIS Beamforming)

The Chef can't see the customers directly because of the buildings. So, the Drone with the Magic Mirror steps in.

The mirror is made of tiny tiles. The Chef tells each tile exactly how to tilt.
The Analogy: Imagine a game of "Pin the Tail on the Donkey" but with light. The Chef shoots a laser at the mirror. The mirror tilts its tiles to bounce the laser around the building and hit the customer's plate perfectly.
The Security Twist: The mirror is also programmed to bounce the signal away from the bad neighbors, or in a way that makes the signal look like static noise to them, while keeping it crystal clear for the good customers.

3. The "Fairness" Goal (Max-Min SEE)

The goal isn't just to send data; it's to be Energy Efficient and Fair.

The Metric: They want to maximize "Secrecy Energy Efficiency" (SEE). In plain English: How much secret data can we send per unit of electricity used, while making sure no single customer is left out?
The Balancing Act: The system has to ensure the bad neighbors get just enough energy to charge their plates (so they don't complain or jam the system) but not so much that they become powerful enough to steal the secrets. It's a delicate dance of giving the enemy a crumb of energy while keeping the cake safe.

How They Solved the Math Puzzle

The math behind this is incredibly hard (non-convex), like trying to solve a Rubik's Cube while blindfolded. The authors used a method called Alternating Optimization:

Step A: Fix the mirror angles and figure out the best way to split the menu (Common vs. Private).
Step B: Fix the menu and figure out the best way to aim the Chef's arms (Precoding).
Step C: Fix the arms and menu, then tweak the mirror tiles again.
Repeat: They do this over and over, getting slightly better at each step, until they find the perfect balance.

The Results: Why It's Better

The paper tested this against two other methods:

SDMA: Sending separate beams to everyone (like shouting at each person individually).
NOMA: Sending a super loud signal where everyone tries to filter out the others (like a crowded party where you shout to be heard).

The Verdict:
The RSMA + RIS combo (The Split Menu + The Magic Mirror) won hands down.

It handled interference better.
It was more energy-efficient.
It scaled up well: Even if you add more customers or more bad neighbors, the system adapts and keeps working, whereas the other methods start to fail.

The Takeaway

This paper is about using a smart drone mirror and a clever splitting strategy to deliver secret messages and energy to good people in a city full of obstacles and spies. It proves that by being smart about how you split your message and where you bounce your signal, you can keep your secrets safe and your batteries charged, even when the odds are stacked against you.

1. Problem Statement

The paper addresses the challenge of securing wireless communications in a Beyond-5G heterogeneous network that integrates Unmanned Aerial Vehicles (UAVs) and Reconfigurable Intelligent Surfaces (RIS). The specific scenario involves:

Network Topology: A multi-antenna Base Station (BS) communicates with $K$ legitimate Information-Harvesting Receivers (IHRs) via a UAV-mounted RIS.
Threat Model: There are $J$ Untrusted Energy-Harvesting Receivers (UEHRs). These nodes are legitimate in that they harvest energy from the RF signals, but they are untrusted because they may act as eavesdroppers attempting to decode confidential information.
Constraints:
- Physical Layer Security (PLS): The system must maximize the secrecy rate for IHRs while preventing UEHRs from decoding the data.
- Energy Harvesting (EH): The system must ensure that UEHRs harvest a minimum required amount of energy, modeled via a non-linear energy harvesting function.
- Channel Conditions: Due to obstacles, there is no direct Line-of-Sight (LoS) between the BS and users; communication relies on the UAV-RIS relay.
Objective: Maximize Fairness-based Secrecy Energy Efficiency (SEE), defined as the ratio of the minimum secrecy rate among all users to the total power consumption (transmit + circuit power).

2. Methodology

The authors propose a Secure Rate-Splitting Multiple Access (RSMA) framework aided by the RIS. The solution involves a joint optimization of three variables:

Common message allocation coefficients ( $a_k$ ).
Active precoding vectors at the BS ( $P$ ).
Passive phase shifts at the RIS ( $\Theta$ ).

A. System Model & Signal Design

RSMA Strategy: The message for each user is split into a common stream (decoded by all users) and a private stream (decoded only by the intended user).
Security Mechanism: The common stream is designed such that legitimate users can decode it, but the UEHRs (eavesdroppers) cannot. The private streams are treated as interference for other users and eavesdroppers.
Channel Model: The system uses a Rician fading model for air-to-ground links. The received signal at a UEHR includes both the direct link (BS-to-UEHR) and the cascaded link (BS-to-RIS-to-UEHR).

B. Optimization Framework

The problem is formulated as a non-convex fractional programming problem due to the coupling of variables and non-linear constraints (specifically the EH model and SINR ratios). To solve this, the authors employ an Alternating Optimization (AO) framework decomposed into three sub-problems:

Common Message Allocation ( $a$ ):
- Given fixed precoders and RIS phases, this sub-problem maximizes the minimum secrecy rate.
- It is formulated as a Linear Programming (LP) problem and solved efficiently.
Active Precoding Optimization ( $P$ ):
- Given fixed $a$ and $\Theta$ , the goal is to optimize the BS precoders.
- The fractional objective is transformed using Dinkelbach's algorithm into a subtractive form.
- Non-convex constraints (SINR and EH) are handled using Sequential Convex Approximation (SCA). The authors derive first-order Taylor expansions to approximate non-convex terms (e.g., $|h^H x|^2$ ) with convex affine functions.
RIS Phase Shift Optimization ( $\Theta$ ):
- Given fixed $a$ and $P$ , the RIS phase shifts are optimized.
- The unit-modulus constraint ( $|s_m|=1$ ) is non-convex. The authors use a penalty-based method combined with SCA to linearize the objective and constraints, transforming the problem into a convex form solvable iteratively.

The overall algorithm (Algorithm 3) iterates between these three steps until convergence.

3. Key Contributions

Novel Framework: This is the first work to jointly design RSMA precoding and RIS beamforming for Secrecy Energy Efficiency (SEE) in a system with untrusted energy-harvesting receivers.
Algorithmic Innovation: The paper proposes an efficient AO-based solution that integrates Dinkelbach's transform (for fractional programming), SCA (for non-convex constraints), and Linear Programming (for rate allocation).
Non-Linear EH Modeling: The study incorporates a realistic logistic non-linear energy harvesting model, making the constraints more practical than linear approximations used in prior works.
Robustness Analysis: The design explicitly accounts for the worst-case scenario where UEHRs have direct links to the BS and attempt to decode both common and private streams.

4. Simulation Results

The authors validate the proposed scheme through numerical simulations comparing RSMA against SDMA (Space-Division Multiple Access) and NOMA (Non-Orthogonal Multiple Access) benchmarks.

Performance vs. Antennas ( $N_t$ ): As the number of BS antennas increases, SEE improves and eventually saturates. RSMA consistently outperforms SDMA and NOMA because it manages interference more flexibly, leading to higher secrecy rates.
Performance vs. RIS Elements ( $M$ ): Increasing the number of RIS elements ( $M$ ) significantly boosts SEE. The results show that a large RIS with low transmit power can achieve similar SEE to a small RIS with high power, highlighting the energy-saving potential of RIS.
Scalability:
- As the number of legitimate users ( $K$ ) increases, SEE drops due to increased eavesdropping probability and resource contention. However, increasing $N_t$ can offset this degradation significantly (e.g., doubling antennas from 4 to 8 at $K=6$ yields a 4x SEE gain).
- Increasing the number of untrusted users ( $J$ ) causes only a slight performance drop, indicating the robustness of the RSMA-RIS scheme against multiple eavesdroppers.

5. Significance

This work is significant for the development of secure, green 6G networks.

Synergy of Technologies: It demonstrates the powerful synergy between RSMA (for spectral efficiency and interference management) and RIS (for coverage extension and signal enhancement).
Security-Energy Trade-off: It provides a practical solution for scenarios where energy harvesting is necessary but security is compromised, offering a way to maximize energy efficiency without sacrificing data confidentiality.
UAV Integration: By utilizing UAV-mounted RISs, the paper addresses the challenge of blockage in dense urban environments, offering a dynamic solution for coverage extension in secure communications.

In conclusion, the proposed AO-based RSMA-RIS framework offers a superior, scalable, and energy-efficient approach to secure downlink transmission in the presence of untrusted energy-harvesting nodes.