⚡ electrical engineering

Blockage-aware Hierarchical Codebook Design for RIS-Assisted Movable Antenna Systems

This paper proposes a novel blockage-aware hierarchical beamforming framework for RIS-assisted movable antenna systems that integrates Gerchberg-Saxton-based blockage detection and a two-stage optimization approach to significantly improve energy efficiency and reduce beam training overhead.

Original authors: Yan Zhang, Indrakshi Dey, Nicola Marchetti

Published 2026-03-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yan Zhang, Indrakshi Dey, Nicola Marchetti

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 conversation with a friend in a crowded, noisy park. You both have walkie-talkies, but the signal is weak because there are huge trees, buildings, and even people walking between you.

In the world of 6G wireless networks, this is exactly the problem engineers are facing. They want to send data at lightning speeds (like terabits per second), but high-frequency signals are easily blocked by obstacles like walls or even a person walking by.

This paper proposes a clever new way to solve this problem by combining three futuristic technologies: Movable Antennas, Smart Mirrors (RIS), and Smart Search Patterns.

Here is the breakdown of their idea using simple analogies:

1. The Problem: The "Blind Search"

Imagine you are trying to find the best spot to talk to your friend.

Old Way (Fixed Antennas): You are stuck in one spot. If a tree blocks the path, you can't talk.
Standard Movable Antenna Way: You can walk around to find a clear path. But, you don't know where the clear paths are. So, you have to walk in every direction, check if you can talk, and then walk back. This takes a long time and burns a lot of battery (energy).
The "Blockage" Issue: In a real city, obstacles move. A bus drives by, or a group of people gathers. If your system blindly checks directions that are blocked, it wastes time and energy shouting into a wall.

2. The Solution: The "Smart Map" and the "Two-Stage Plan"

The authors propose a system that acts like a smart navigator that knows the map of obstacles before you even start walking.

Part A: The "Smart Mirror" (RIS)

First, they use a Reconfigurable Intelligent Surface (RIS). Think of this as a giant, smart mirror on a building wall.

How it works: If the direct path to your friend is blocked, the mirror can catch the signal, bounce it off the wall, and send it around the obstacle to your friend.
The Trick: The authors set up this mirror first using a "slow" calculation based on general patterns (like knowing where the big buildings usually are). This prepares the environment before the fast action starts.

Part B: The "Blockage-Aware" Search (The Codebook)

This is the core innovation. Instead of checking every possible direction, the system builds a Hierarchical Codebook.

The Analogy: Imagine you are looking for a lost key in a house.
- Traditional Method: You check every single drawer in every single room, one by one. (Very slow, very tiring).
- Their Method: You have a "Blockage Map." You know the kitchen is locked (blocked), so you don't even look there. You know the living room is open, so you start there.
- The "Gerchberg-Saxton" Algorithm: This is the math engine that draws the map. It's like a GPS that says, "Don't aim the beam (your voice) at that wall; aim it at the open window instead." It rotates the signal beam away from obstacles and toward open spaces.

Part C: The Two-Stage Process

To make this fast and efficient, they split the work into two stages:

Stage 1 (The Setup): Set the "Smart Mirror" (RIS) to bounce signals around big obstacles. This is done once every few minutes because big obstacles don't move fast.
Stage 2 (The Sprint): Now that the mirror is set, the movable antennas quickly scan only the open directions. Because they skip the blocked directions, they find the best connection in a fraction of the time.

3. Why is this a Big Deal? (The Results)

The paper ran simulations to see how this works in a busy city. Here is what they found:

Energy Savings: Because the system doesn't waste time shouting at walls (blocked directions), it saves a massive amount of battery power. It's like not walking into a dead-end alley.
Speed: It finds the connection much faster. While other systems might take 100 steps to find the right path, this one takes about 20 because it skips the dead ends.
The Trade-off: The authors admit that the absolute maximum speed might be slightly lower than a perfect, theoretical system that checks everything. However, in the real world, where obstacles are everywhere, their system is much more practical because it is faster and uses less energy.

Summary

Think of this paper as a guide for a smart, energy-efficient delivery driver.

Old Driver: Drives every single street in the city to find the customer, even if they know a street is closed. They get tired and run out of gas.
New Driver (This Paper): Checks a live map of road closures (Blockage Detection). They set up a drone (RIS) to drop packages over the closed roads. Then, they drive only the open streets, finding the customer quickly and saving fuel.

This approach makes future 6G networks more reliable, faster to connect, and much friendlier to the environment by saving energy.

1. Problem Statement

The paper addresses critical challenges in 6G millimeter-wave (mmWave) and Terahertz (THz) communication systems, specifically focusing on the integration of Movable Antennas (MA) and Reconfigurable Intelligent Surfaces (RIS).

The Context: While MA systems offer dynamic spatial diversity by mechanically repositioning antennas to find better channel conditions, and RIS can create alternative propagation paths, their joint deployment faces significant hurdles.
The Core Challenges:
1. Blockage Sensitivity: mmWave signals are highly susceptible to environmental blockages (buildings, humans). Existing MA designs often ignore "dual blockage": environmental obstacles and blockages caused by the MA's own position (self-shadowing).
2. Training Overhead: Exhaustive beam search in MA-RIS systems is computationally prohibitive due to the vast search space (combinations of antenna positions and beam directions).
3. Energy Inefficiency: Continuous mechanical movement and exhaustive beam training in blocked directions waste significant energy, which is critical for battery-constrained IoT and mobile deployments.
4. Complexity: Jointly optimizing MA positions and RIS phase shifts is a non-convex, high-complexity problem that scales poorly with system size.

2. Methodology

The authors propose a Blockage-Aware Hierarchical Codebook (HCB) framework utilizing a two-stage optimization approach to decouple the complex joint problem.

A. System Model

Setup: A Base Station (BS) equipped with $M$ movable antennas communicates with $K$ users via an RIS with $N$ elements.
Channel: Modeled using geometric channel models for MA-RIS and RIS-UE links, incorporating realistic path loss and blockage probabilities (LOS/NLOS).
Energy Efficiency (EE): Defined as the ratio of sum-rate to total power consumption (including mechanical motion power, static circuit power, and transmission power).

B. Two-Stage Optimization Strategy

To reduce computational complexity, the problem is split into two stages:

Stage I: RIS Phase-Shift Optimization (Slow Timescale)
- Goal: Optimize RIS phase shifts using Statistical Channel State Information (CSI) (large-scale parameters like angles, path loss, and blockage statistics) rather than instantaneous CSI.
- Method: Maximizes the expected effective channel gain across users. This is solved using a convex optimization solver (e.g., MATLAB fmincon) once per coherence interval.
- Benefit: Drastically reduces feedback overhead and computational load compared to optimizing RIS phases for every beam candidate.
Stage II: Blockage-Aware Hierarchical Beam Training (Fast Timescale)
- Goal: Efficiently find the optimal MA positions and beamforming vectors using a hierarchical codebook.
- Blockage Detection: The system calculates geometric intersection between the MA-RIS line-of-sight and obstacles to determine "blocked angular ranges."
- Gerchberg-Saxton (GS) Algorithm Integration:
  - Instead of standard codebooks, the authors design a GS-based hierarchical codebook.
  - The GS algorithm is modified to incorporate blockage masks. In the angular domain, the algorithm enforces zero gain (or strict penalties) in blocked directions while shaping the beam toward available (unblocked) angles.
  - Hard vs. Soft Constraints: The design can enforce exact nulls in blocked directions (Hard) or penalize leakage (Soft).
- Hierarchical Structure: A binary tree structure is used where the search space is progressively narrowed (coarse-to-fine). Blocked branches are pruned early, skipping unnecessary evaluations.

3. Key Contributions

Novel Blockage-Aware Codebook: The first framework to integrate blockage detection directly into the codebook design for MA systems. It uses the GS algorithm to rotate beams away from blocked regions, effectively handling "dual blockage" (environmental + MA-induced).
Two-Stage Decoupled Optimization: A practical approach that separates RIS configuration (based on statistical CSI) from beam training. This significantly lowers the computational complexity of the joint MA-RIS optimization problem.
Energy and Overhead Reduction: By intelligently skipping blocked directions and using a hierarchical search, the method minimizes the number of beam evaluations and mechanical movements required.
Theoretical Analysis: The paper provides rigorous complexity analysis and convergence proofs for the adapted GS algorithm, showing that it converges rapidly (within ~20-40 iterations) and that higher blockage densities actually accelerate convergence by reducing the feasible search space.

4. Simulation Results

The proposed method was evaluated against traditional Hierarchical, DFT, and Subspace Codebook (SC) baselines under mmWave conditions (60 GHz).

Achievable Rate vs. Overhead:
- The proposed method achieves a stable operating point with ~80% less training overhead compared to the Subspace Codebook (SC) and traditional hierarchical methods.
- While it sacrifices a small amount of peak rate (~0.1 Gbps) compared to the SC codebook, it reaches its maximum rate much faster due to the pruning of blocked directions.
Energy Efficiency (EE):
- The proposed scheme demonstrates the highest Energy Efficiency among all compared methods.
- It achieves a peak EE of approximately 4.2 Mbits/Joule at moderate transmit power. The reduction in mechanical movement and pilot transmission time directly contributes to this gain.
Robustness to Blockage:
- As blockage density increases, the training overhead for the proposed method remains low and stable, whereas traditional methods suffer from increased complexity or require exhaustive searches in blocked areas.
- Convergence analysis shows that the GS algorithm stabilizes quickly (median residual drops significantly within 20 iterations), and higher blockage densities lead to faster stabilization.

5. Significance and Conclusion

This paper presents a pivotal advancement for the practical deployment of MA-RIS systems in future 6G networks.

Practical Viability: It addresses the "energy vs. performance" trade-off that has hindered MA adoption. By reducing the mechanical control burden and training time, it makes MA systems viable for energy-constrained scenarios (e.g., IoT, vehicular networks).
Intelligent Resource Management: The shift from "blind" exhaustive search to "blockage-aware" intelligent pruning represents a fundamental change in how beam training is approached in dynamic, obstructed environments.
Scalability: The two-stage approach and the mathematical guarantees on convergence suggest that the solution is scalable to large-scale MIMO systems without prohibitive computational costs.

In summary, the authors successfully demonstrate that integrating blockage awareness into the codebook design via the Gerchberg-Saxton algorithm, combined with a statistical RIS optimization stage, yields a system that is more energy-efficient, faster to train, and more robust to real-world environmental challenges than existing state-of-the-art methods.