Mohammad Taha Shah

Mohammad Taha Shah, Mohamed-Slim Alouini

This paper develops a stochastic-geometry framework for high-altitude platform station (HAPs) networks in which platforms execute cyclic patrol trajectories anchored to designated service regions. We introduce two small-circle ring Cox process models on the spherical Earth. In the small-circle ring Poisson Cox process (SCR-PCP), platforms form one-dimensional Poisson point processes on localized patrol rings, whereas in the small-circle ring binomial Cox process (SCR-BCP), each ring contains a fixed number of uniformly distributed platforms. We establish the isotropy of both models and derive spatial statistics, including the distributions of the nearest-anchor, nearest-ring, and nearest-HAPs distances, together with the joint serving distance and serving ring angle distribution required for SCR-BCP analysis. Building on these results, we derive coverage probability expressions under nearest-HAPs association by decomposing aggregate interference into same-ring and other-ring components and characterizing their conditional Laplace transforms. To account for the flight dynamics of patrol-based HAPs, we integrate a steady circular flight propulsion model with the communication analysis and introduce a coverage energy efficiency (CEE) metric. This yields an analytical condition for the energy-optimal patrol radius that balances coverage performance against the propulsion cost of circular flight. Numerical results reveal fundamental differences between intensity-driven (SCR-PCP) and finite-fleet (SCR-BCP) deployments and demonstrate that patrol geometry, platform density, and cruising velocity should be jointly optimized to achieve energy-efficient HAPs operation.

Mohammad Taha Shah, Sabrina Khurshid, Gourab Ghatak

In this paper, we investigate the problem of sequential decision-making for Sharpe ratio (SR) maximization in a stochastic bandit setting. We focus on the Thompson Sampling (TS) algorithm, a Bayesian approach celebrated for its empirical performance and exploration efficiency, under the assumption of Gaussian rewards with unknown parameters. Unlike conventional bandit objectives focusing on maximizing cumulative reward, Sharpe ratio optimization instead introduces an inherent tradeoff between achieving high returns and controlling risk, demanding careful exploration of both mean and variance. Our theoretical contributions include a novel regret decomposition specifically designed for the Sharpe ratio, highlighting the role of information acquisition about the reward distribution in driving learning efficiency. Then, we establish fundamental performance limits for the proposed algorithm \texttt{SRTS} in terms of an upper bound on regret. We also derive the matching lower bound and show the order-optimality. Our results show that Thompson Sampling achieves logarithmic regret over time, with distribution-dependent factors capturing the difficulty of distinguishing arms based on risk-adjusted performance. Empirical simulations show that our algorithm significantly outperforms existing algorithms.