Abstract--Phase-time arrays, which integrate phase shifters (PSs) and true-time delays (TTDs), have emerged as a cost-effective architecture for generating frequency-dependent rainbow beams in wideband sensing and localization. This paper proposes an end-to-end deep learning-based scheme that simultaneously designs the rainbow beams and estimates user positions. Treating the PS and TTD coefficients as trainable variables allows the network to synthesize task-oriented beams that maximize localization accuracy. A lightweight fully connected module then recovers the user's angle-range coordinates from its feedback of the maximum quantized received power and its corresponding subcarrier index after a single downlink transmission. Compared with existing analytical and learning-based schemes, the proposed method reduces overhead by an order of magnitude and delivers consistently lower two-dimensional positioning error .

The evolution of cooperation has been extensively studied using abstract mathematical models and simulations. Recent advances in Large Language Models (LLMs) and the rise of LLM agents have demonstrated their ability to perform social reasoning, thus providing an opportunity to test the emergence of norms in more realistic agent-based simulations with human-like reasoning using natural language. In this research, we investigate whether the cooperation dynamics presented in Boyd and Richerson's model persist in a more realistic simulation of the Diner's Dilemma using LLM agents compared to the abstract mathematical nature in the work of Boyd and Richerson. Our findings indicate that agents follow the strategies defined in the Boyd and Richerson model, and explicit punishment mechanisms drive norm emergence, reinforcing cooperative behaviour even when the agent strategy configuration varies. Our results suggest that LLM-based Multi-Agent System simulations, in fact, can replicate the evolution of cooperation predicted by the traditional mathematical models. Moreover, our simulations extend beyond the mathematical models by integrating natural language-driven reasoning and a pairwise imitation method for strategy adoption, making them a more realistic testbed for cooperative behaviour in MASs.