Mathematical Cell Deployment Optimization for Capacity and Coverage of Ground and UAV Users

We present a general mathematical framework for optimizing cell deployment and antenna configuration in wireless networks, inspired by quantization theory. Unlike traditional methods, our framework supports networks with deterministically located nodes, enabling modeling and optimization under controlled deployment scenarios. We demonstrate our framework through two applications: joint fine-tuning of antenna parameters across base stations (BSs) to optimize network coverage, capacity, and load balancing, and the strategic deployment of new BSs, including the optimization of their locations and antenna settings. These optimizations are conducted for a heterogeneous 3D user population, comprising ground users (GUEs) and uncrewed aerial vehicles (UAVs) along aerial corridors. Our case studies highlight the framework's versatility in optimizing performance metrics such as the coverage-capacity trade-off and capacity per region. Our results confirm that optimizing the placement and orientation of additional BSs consistently outperforms approaches focused solely on antenna adjustments, regardless of GUE distribution. Furthermore, joint optimization for both GUEs and UAVs significantly enhances UAV service without severely affecting GUE performance.

Disentangling Observed Causal Effects from Latent Confounders using Method of Moments

Discovering the complete set of causal relations among a group of variables is a challenging unsupervised learning problem. Often, this challenge is compounded by the fact that there are latent or hidden confounders. When only observational data is available, the problem is ill-posed, i.e. the causal relationships are non-identifiable unless strong modeling assumptions are made. When interventions are available, we provide guarantees on identifiability and learnability under mild assumptions. We assume a linear structural equation model (SEM) with independent latent factors and directed acyclic graph (DAG) relationships among the observables. Since the latent variable inference is based on independent component analysis (ICA), we call this model SEM-ICA. We use the method of moments principle to establish model identifiability. We develop efficient algorithms based on coupled tensor decomposition with linear constraints to obtain scalable and guaranteed solutions. Thus, we provide a principled approach to tackling the joint problem of causal discovery and latent variable inference.