Resource Allocation for STAR-RIS-enhanced Metaverse Systems with Augmented Reality

1. Problem Statement

The paper addresses the critical challenge of service latency in Augmented Reality (AR)-enabled Metaverse systems. In these systems, AR users (e.g., vehicles in an IoV scenario) capture environmental data (images/video) and offload them to a Metaverse server located at a Base Station (BS) for real-time object detection. The processed results are then returned to the users to render immersive virtual scenarios.

Key Challenges:

• Latency Sensitivity: High latency causes user discomfort (e.g., motion sickness) and safety risks in delay-sensitive applications like autonomous driving.
• Resource Constraints: Mobile users have limited computation power and battery energy, while wireless channels are stochastic and prone to blockage.
• Coverage Limitations: Traditional Reconfigurable Intelligent Surfaces (RIS) only reflect signals, providing 180-degree coverage. Users on the opposite side of the RIS suffer from poor connectivity.
• Coupled Optimization: Minimizing latency requires jointly optimizing communication resources (power, bandwidth, RIS coefficients) and computation resources (CPU frequency, edge server allocation), creating a highly non-convex and coupled optimization problem.

Objective:
To minimize the maximum service latency experienced by any AR user (a min-max fairness objective) by jointly optimizing:

1. Local CPU-cycle frequency of AR users.
2. Transmit power of AR users.
3. Transmit/Reflect coefficient matrices of the STAR-RIS.
4. Computation resource allocation (CPU frequency) at the BS.

2. System Model

The authors propose a system model comprising:

• Entities: A BS with an integrated edge Metaverse server, a Simultaneously Transmitting and Reflecting RIS (STAR-RIS) with $N$ elements, and $K$ AR users.
• Topology: Users are divided into two groups based on their location relative to the STAR-RIS:
  • Reflection Users: Located on the same side as the BS; signals are reflected.
  • Transmission Users: Located on the opposite side; signals are transmitted through the STAR-RIS.
• Workflow:
  1. Local Processing: AR users convert image formats (YUV to RGB) locally.
  2. Transmission: Processed data is sent to the BS via STAR-RIS using either SDMA (Spatial Division Multiple Access) or FDMA (Frequency Division Multiple Access).
  3. Edge Computing: The BS performs object detection.
  4. Result Delivery: Results are sent back to the user (assumed negligible latency due to small result size).
• Latency Components: Total latency = Local processing delay + Transmission delay + Edge processing delay.

3. Methodology

The formulated optimization problem is strictly non-convex due to the fractional structure of the transmission rate, interference terms, and the rank-one constraint on the RIS coefficient matrices. The authors propose an Alternating Optimization (AO) framework to solve this iteratively:

1. Problem Transformation:

   • The max-min problem is reformulated using an auxiliary variable $t$ to represent the maximum latency.
   • The non-convex transmission rate expression is approximated using Fenchel conjugate arguments (Lemma 1) to transform it into a tractable concave form.

2. Decomposition into Subproblems:
   The AO method decouples the variables into four blocks, optimizing them while keeping others fixed:

   • Transmit Power Control: Solved as a convex optimization problem using standard tools (e.g., CVX).
   • STAR-RIS Coefficient Matrix Optimization: This is the most complex part due to the non-convex rank-one constraint. The authors propose a Penalty Function-based method. They relax the rank constraint and add a penalty term to the objective function. A Successive Convex Approximation (SCA) technique is used to linearize the non-convex part of the penalty term, ensuring convergence to a rank-one solution.
   • Local CPU Frequency: Derived analytically as a closed-form solution based on energy constraints and latency requirements.
   • BS Computation Resource Allocation: Solved using the Lagrange Duality method and KKT conditions. Theoretical analysis proves that under optimal allocation, all AR users achieve the same service latency, ensuring fairness.

3. FDMA Extension:
   The framework is extended to FDMA-based systems, where bandwidth allocation ratios are added as optimization variables. The problem remains convex and is solved similarly.

4. Key Contributions

• Novel Framework: First investigation of STAR-RIS integration into AR-enabled Metaverse systems for joint communication and computation optimization.
• Min-Max Latency Optimization: Unlike previous works focusing on total throughput or energy, this paper targets the maximum service latency to ensure Quality of Experience (QoE) for all users, particularly in safety-critical scenarios.
• Algorithm Design: Development of a low-complexity, convergent algorithm combining:
  • Penalty function-based method for STAR-RIS configuration.
  • Closed-form solutions for CPU frequencies.
  • Lagrange duality for edge resource allocation.
• Theoretical Insights:
  • Proved that optimal resource allocation equalizes service latency across all users.
  • Demonstrated that the BS allocates more computing resources to users with higher transmission or local processing delays.

5. Numerical Results

Extensive simulations compare the proposed method against benchmarks:

• Benchmarks: Reflecting-only RIS, Transmitting-only RIS, and STAR-RIS with random phase shifts.
• Key Findings:
  • Latency Reduction: The proposed method significantly reduces maximum service latency compared to benchmarks (e.g., >18% reduction vs. Reflecting RIS).
  • STAR-RIS Advantage: STAR-RIS outperforms single-mode RIS because it serves users on both sides of the surface, eliminating coverage holes.
  • SDMA vs. FDMA:
    • FDMA generally performs better, especially with high transmit power or large data sizes, as it eliminates co-channel interference.
    • SDMA is more suitable for power-constrained scenarios or when bandwidth is abundant.
  • Scalability: Performance improves as the number of STAR-RIS elements ($N$) increases, providing more spatial degrees of freedom.
  • Convergence: The proposed alternating algorithm converges rapidly (within a few iterations).

6. Significance

This paper provides a critical blueprint for deploying 6G-enabled Metaverse and IoV systems. By leveraging STAR-RIS, it solves the fundamental coverage limitation of traditional RIS, ensuring that users in "shadowed" areas receive the same low-latency service as those in line-of-sight. The joint optimization of communication and computation resources ensures that the system remains robust under strict energy and delay constraints, which is essential for immersive, real-time AR applications like autonomous driving and remote surgery. The proposed algorithms offer a practical, computationally efficient approach for network operators to manage these complex, heterogeneous networks.