The article presents a novel two-stage hierarchical beam training approach for large-scale intelligent reflecting surfaces (RISs), which can improve the accuracy of user positioning while reducing the training overhead. The proposed approach consists of two stages: stage 1 uses an angular-domain codebook to estimate the user’s angular information, and stage 2 employs a hierarchical polar-domain codebook to estimate the user’s distance information.
Hierarchical Polar-Domain Codebooks
The hierarchical polar-domain codebooks used in stage 2 are designed to comprehensively represent the entire angular and distance domains in each layer, while ensuring that the polar domain of a codeword within a particular layer encompasses the union of polar domains represented by several codewords in subsequent layers. This design allows for an efficient representation of the complex angular and distance information.
Training Overhead
The article highlights that the proposed two-stage approach can significantly reduce the training overhead compared to traditional methods, which require a single codebook for both stages. The use of hierarchical polar-domain codebooks in stage 2 enables a more efficient estimation of the user’s distance information, resulting in a lower training overhead.
Numerous Layers
The total number of layers, Lt = L1 + L2, is determined by the total number of RIS elements denoted by N, with Lt = log2 (N). This means that as the number of RIS elements increases, the number of layers also increases, allowing for a more accurate estimation of the user’s position.
Main Procedure
The main procedure for each stage can be formulated as follows:
Stage 1
- Use an angular-domain codebook to estimate the user’s angular information
- Compute the likelihood of the observed angle measurements given the estimated angular information
- Select the most likely L1 and L2 values based on the likelihood function
Stage 2
- Use a hierarchical polar-domain codebook to estimate the user’s distance information
- Compute the likelihood of the observed range measurements given the estimated distance information
- Select the most likely L1 and L2 values based on the likelihood function
Conclusion
The proposed two-stage hierarchical beam training approach offers a promising solution for large-scale intelligent RIS systems, providing improved accuracy while reducing the training overhead. By using hierarchical polar-domain codebooks in stage 2, the approach can efficiently represent the complex angular and distance information, leading to a more accurate estimation of the user’s position. The article provides detailed explanations of the codebook design and the main procedure for each stage, making it easier for readers to understand the concepts and their applications.
