Impact of Objective Function on Spectral Efficiency in Integrated HAPS-Terrestrial Networks

TL;DR

This paper investigates how the choice of objective function affects spectral efficiency in a harmonized vHetNet that combines a High Altitude Platform Station (HAPS) with terrestrial base stations. It formulates three joint user association and beamforming design problems for weighted sum rate (WSR), network-wide proportional fairness (NW-PF), and network-wide max-min fairness (NW-MMF), and solves them via a successive convex approximation (SCA) framework with SOC and exponential-cone relaxations to handle non-convexities. Key findings show that WSR achieves the highest sum SE, NW-MMF yields the best minimum SE, and NW-PF offers a balanced trade-off between sum SE and fairness, with HAPS-enabled vHetNets improving the performance of the worst-affected UEs. The results highlight the practical value of HAPS integration and indicate that NW-PF is a favorable default choice when balancing total throughput and user fairness in urban vHetNets.

Abstract

Integrating non-terrestrial networks (NTNs), in particular high altitude platform stations (HAPS), with terrestrial networks, referred to as vHetNets, emerges as a promising future wireless network architecture for providing ubiquitous connectivity. In this context, optimizing the performance of vHetNets has become a paramount concern, particularly in harmonized spectrum vHetNets, where HAPS and terrestrial networks share the same frequency band, resulting in severe inter-/intra-tier interference. This paper provides a comparative analysis of different objective functions, specifically focusing on weighted sum rate (WSR), network-wide proportional fairness (NW-PF), and network-wide max-min fairness (NW-MMF), with an aim to design a joint user association scheme and multiple-input multiple-output (MIMO) beamforming weights in a vHetNet, operating in an urban area. The simulation results comprehensively compare the behavior of different objective functions in vHetNets and standalone terrestrial networks. This analysis aims to shed light on the impact of diverse objective functions on the achievable spectral efficiency (SE) of vHetNets.

Figures (3)

• Figure 1: Network architecture.
• Figure 2: Statistical behavior of SE in a vHetNet (4 MBSs + 1 HAPS) for different objective functions.
• Figure 3: Comparison between statistical behavior of SE in a vHetNet (4 MBSs + 1 HAPS) and standalone terrestrial network (5 MBSs).