🔢 mathematics

Joint Movable Antenna Positioning and RIS Partitioning for Sum-Rate Maximization

This paper proposes a joint movable antenna positioning and RIS partitioning framework for downlink communications that maximizes network sum-rate by optimizing antenna locations, beamforming, and RIS element selection through an alternating optimization algorithm, demonstrating significant performance gains over conventional fixed-antenna schemes.

Original authors: Mohammed Saif

Published 2026-06-11

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Mohammed Saif

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 wireless network as a busy concert hall where a band (the Base Station) is trying to play music for two different groups of fans (the Users) sitting in different corners. Usually, the band is stuck in one spot, and the sound has to travel through a crowded room full of walls and obstacles, making the music muddy or hard to hear.

This paper proposes a clever new way to set up the concert using two high-tech tools: Movable Antennas (MAs) and Reconfigurable Intelligent Surfaces (RIS).

Here is the breakdown of their idea in simple terms:

1. The Problem: Stuck in a Bad Spot

In traditional setups, the band's speakers (antennas) are bolted to the wall. If the sound gets blocked or if the two groups of fans start hearing each other's music (interference), the band can't do much about it. They are stuck with a "fixed" view of the room.

2. The Solution: A Dynamic Stage and a Smart Mirror Wall

The authors suggest two upgrades:

Movable Antennas (The Flexible Speakers): Instead of being bolted down, the speakers can slide around on a small track. If the sound is blocked, the band can physically slide the speakers to a spot where the sound travels clearer.
The RIS (The Smart Mirror Wall): Imagine a giant wall covered in thousands of tiny, invisible mirrors. These mirrors can be programmed to catch the sound from the band and reflect it specifically toward the fans. The paper introduces a new twist: Partitioning. Instead of using the whole wall for everyone, they split the wall into two sections. One section reflects sound to Fan Group 1, and the other section reflects sound to Fan Group 2.

3. The "Joint" Strategy: Dancing Together

The core of this paper is that you can't just move the speakers or just adjust the mirrors; you have to do both at the same time to get the best result.

The authors created a mathematical "dance routine" (an algorithm) that figures out the perfect combination of:

Where to slide the speakers (MA Positioning).
How to aim the music (Beamforming).
How to split the mirror wall (RIS Partitioning).

They call this the Joint MA-RIS Framework. It's like a conductor who simultaneously tells the violinists to move left, tells the drummer to hit harder, and tells the sound engineers to adjust the echo, all to make sure both groups of fans hear the music perfectly without hearing the other group.

4. How They Solved the Puzzle

The math behind this is incredibly complex because moving the speakers changes how the sound hits the mirrors, which changes how the fans hear it. It's a giant, tangled knot of variables.

To untie it, the authors used a step-by-step approach called Alternating Optimization:

Step 1: Keep the speakers still, and figure out the best mirror settings.
Step 2: Keep the mirrors still, and figure out the best speaker positions.
Step 3: Keep both fixed, and adjust the power levels.
Repeat: They do this over and over until the music sounds perfect.

They also used a "Zero-Forcing" technique, which is like a noise-canceling headphone for the whole room. It actively creates "silence zones" (spatial notches) where the interference would be, ensuring Fan Group 1 doesn't hear Fan Group 2's music at all.

5. The Results: A Louder, Clearer Concert

When they tested this in a computer simulation (a virtual concert hall):

Better Sound: The "Joint" approach (moving speakers + smart mirrors) produced much clearer music (higher data rates) than just moving the speakers or just using fixed speakers.
More Fans: As they added more tiny mirrors to the wall, the sound quality got even better for everyone.
More Power: When they gave the band more power to play, the system handled it efficiently, delivering more music to the fans.

In a Nutshell

This paper claims that by letting the wireless antennas slide around and splitting a smart mirror wall into dedicated zones, we can create a much faster and clearer internet connection. It's about giving the network the freedom to move and adapt, rather than being stuck in a fixed, rigid position, resulting in a much stronger signal for everyone.

Technical Summary: Joint Movable Antenna Positioning and RIS Partitioning for Sum-Rate Maximization

Problem Statement
This paper addresses the challenge of maximizing the downlink sum-rate in a wireless communication system operating in dense urban environments where direct Base Station (BS)-to-User links are obstructed. The system utilizes a Reconfigurable Intelligent Surface (RIS) to facilitate communication. While Movable Antennas (MAs) offer spatial flexibility to enhance channel conditions, and RISs can shape the propagation environment, existing works have not fully exploited the synergy between MA sub-array positioning, RIS element partitioning, and beamforming. The core problem is formulated as a joint optimization of three coupled variables: the physical positions of MA sub-arrays, the transmit beamforming vectors, and the partitioning of RIS elements among users. This optimization is subject to constraints on minimum antenna separation (to prevent mutual coupling), transmit power budgets, and the total number of available RIS elements. The resulting mathematical problem is highly non-convex and difficult to solve directly.

Methodology
To solve the non-convex joint optimization problem, the authors propose an Alternating Optimization (AO) framework that decomposes the problem into three tractable subproblems, solved iteratively:

Transmit Beamforming Optimization: With fixed MA positions and RIS partitioning, the beamforming design is addressed using Zero-Forcing (ZF) principles. The problem is reformulated using Karush–Kuhn–Tucker (KKT) conditions to derive a closed-form solution for power allocation and beamformer direction, effectively suppressing inter-user interference.
RIS Partitioning Optimization: With fixed beamforming and MA positions, the allocation of RIS elements to different users is optimized. The authors demonstrate that this subproblem can be reduced to a one-dimensional search space by expressing the partitioning variables in terms of a single allocation factor, which is then solved via a low-complexity grid search.
MA Position Optimization: With fixed beamforming and RIS partitioning, the physical positions of the MAs are optimized. Due to the non-convex nature of the distance constraints and the non-linear relationship between position and channel phase, the authors employ a Block Coordinate Descent (BCD) approach. They utilize a first-order lower-bound approximation to convexify the minimum separation constraint, allowing the position update to be solved efficiently using convex optimization tools (specifically CVX with the MOSEK solver).

Key Contributions

Joint Framework: The paper introduces a novel system framework that jointly optimizes MA sub-array positioning, sub-array beamforming, and RIS element partitioning (selection) for sum-rate maximization.
Algorithmic Solution: It proposes a specific alternating optimization scheme that handles the non-convexity of the joint problem by decomposing it into solvable subproblems using KKT conditions, one-dimensional search, and BCD-based convex reformulation.
System Design: The work defines a specific architecture where a BS with two MA sub-arrays communicates with two users via a partitioned RIS, explicitly modeling the interference between non-aligned sub-arrays and RIS partitions.

Simulation Results
Numerical simulations were conducted in a scenario where a BS and RIS are located at fixed coordinates, and users are randomly distributed in a region with obstructed direct links. The proposed "Joint MA-RIS" scheme was compared against three benchmark schemes:

Fixed Position Antenna (random beamforming and RIS selection).
Random Position Antenna (random MA positions, optimized RIS/beamforming).
MA-Optimized (optimized MA positions, random RIS/beamforming).

The results indicate that the proposed joint framework consistently achieves the highest sum-rate across varying numbers of RIS elements ( $N$ ) and transmit power budgets ( $P$ ). Key findings include:

Performance Gain: The joint optimization significantly outperforms benchmarks, demonstrating that optimizing MA positions alone (MA-Optimized) is insufficient without coordinated RIS partitioning and beamforming.
Scalability: Sum-rate increases with the number of RIS elements and the number of MAs ( $M$ ), validating the utility of additional spatial degrees of freedom.
Convergence: The proposed algorithm demonstrates stable convergence within a practical number of iterations.

Significance and Claims
The paper claims that the integration of movable antennas with RIS-assisted propagation control offers a promising approach for future 6G systems by enabling adaptive spatial control and high spectral efficiency. The primary significance lies in demonstrating that the additional degrees of freedom provided by movable antennas, when jointly optimized with RIS partitioning, allow the system to establish stronger BS-RIS channels and form more effective directional beams. This leads to enhanced desired signal power and effective mitigation of inter-user interference, resulting in superior sum-rate performance compared to conventional fixed-antenna configurations or schemes that optimize only a subset of the system parameters. The authors note that their work specifically addresses the gap in existing literature regarding the joint design of RIS partitioning and MA sub-array structures.