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

TL;DR

This work introduces a quantization-theory–inspired framework for optimizing cell deployment and antenna configuration in wireless networks with deterministic node placements and 3D user distributions, including UAV corridors. It formulates an NP-hard, nonconvex problem and solves it via alternating Lloyd-type partitioning and gradient-based updates of antenna tilts, transmit powers, and deployment parameters. Two KPI-driven applications are developed: (i) optimize existing BS tilts/power for a coverage-capacity trade-off and (ii) jointly optimize deployment locations/bearings with antenna settings. Case studies on ground and UAV users show deploying new BSs yields consistent performance gains over tilt-only approaches, with significant UAV benefits and limited GUE degradation, highlighting the framework’s ability to achieve 3D connectivity in heterogeneous networks.

Abstract

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.

Figures (5)

• Figure 1: Uptilted ($\theta_n>0$) and downtilted ($\theta_n<0$) BSs serving GUEs and UAV corridors, with $\theta_n$, $\theta_{\textrm{3dB}}$, $\phi_n$, and $\rho_n$ denoting vertical tilt, vertical HPBW, horizontal bearing, and transmit power, respectively. Also, $p_{n-2} = p_{n-1} = p_n$ denote the position of three co-located sectorized BSs.
• Figure 2: The CDF of SINR when the cell partitioning, antenna tilts, transmission powers, and the deployment of new BSs are jointly optimized via Algorithm \ref{['gamma_1_2_algorithm']}.
• Figure 3: Optimal deployment and cell partitioning when network is optimized via Algorithm \ref{['gamma_1_2_algorithm']} for $r = 0.5$ and GUEs are distributed according to the Gaussian mixture.
• Figure 4: Optimal BS antenna tilts (blue circles) and transmit powers (red triangles) for $r = 0.5$ when network is optimized via Algorithm \ref{['gamma_1_2_algorithm']} and GUEs have Gaussian mixture distribution.
• Figure 5: The CDF of spectral efficiency (bps/Hz) when cell partitioning, antenna tilts, transmit powers, and the deployment of new BSs are jointly optimized via Algorithm \ref{['gamma_2_2_algorithm']}.