Designing Hierarchical Codebooks with Weighted Hamming Distance for Robust UWB Multi-Service Indication

The rising demand for diverse service requirements under limited resources necessitates designing codeword indicators with variable distance metrics to exploit prior information, such as data rate, coding schemes, and Signal-to-Noise Ratio (SNR). Traditional codebook designs that maximize the minimum Hamming distance provide a global lower bound but often overlook the specific distance requirements of individual codewords. To address this limitation, the weighted Hamming distance metric is introduced, prioritizing codewords with varying distance attributes. Maximizing the weighted Hamming distance leads to the development of hierarchical codebooks, enabling the selection of codewords tailored to specific distance needs. Building on the classical Plotkin bound, an upper bound is derived, revealing trade-offs among the number of codewords, distance layers, and lengths. Optimal hierarchical codebooks are designed using a cyclotomy structure to maintain the desired Hamming distance properties and incorporate a heuristic algorithm to allow flexibility in codebook length and multi-layer attributes. In ultra-wideband multi-service scenarios, allocating higher-distance codewords to lower-SNR services enhances overall performance by matching codeword distances to service demands. Simulations demonstrate that, informed by deep learning-based SNR predictions, this approach reduces packet error rates and improves efficiency compared to existing IEEE 802.15.4z convolutional schemes and classical Hadamard codebooks.