In the era of sixth-generation (6G) wireless communication, numerous applications are expected to be realized, including environmental monitoring, smart agriculture, remote education, security protection, and intelligent transportation systems. These scenarios require large-scale, continuous Internet services in forests, rivers, oceans, and road networks, to name a few, where optical cables are difficult to deploy. High-altitude platform stations (HAPSs) emerge as a promising solution, offering low-latency, high-capacity services while facilitating the establishment of vertical heterogeneous networks (vHetNets) in fiber-less areas. This article investigates three HAPS-based solutions, where HAPSs can serve wireless devices directly or via gateway (GW) networks: the HAPS-to-device (H2D) scheme, the HAPS-to-GW-to-device (H2G2D) scheme, and the hybrid scheme. Leveraging percolation theory, we study the feasibility of large-scale continuous Internet coverage, where the key performance indicator (KPI) is the percolation probability. We discuss the subcritical and supercritical cases in different coverage schemes, and prove that the phase transition from zero to nonzero percolation probability appears when increasing the HAPS density or GW density. Numerical results verify that the curve of the critical condition of the phase transition exists between the derived lower bound and upper bound, which can help reduce the upfront cost of HAPS-based vHetNet solutions.

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