Vertical Heterogeneous Networks (vHetNets)

• Vertical Heterogeneous Networks (vHetNets) are integrated multi-layer architectures combining terrestrial base stations, HAPS, UAVs, and satellites to deliver ubiquitous wireless access.
• They converge radio access, edge computing, sensing, and AI-driven optimization to efficiently manage dynamic interference, spectrum sharing, and resource allocation.
• vHetNets enhance capacity and energy efficiency through techniques like dynamic cell switching, coordinated multi-point beamforming, and distributed optimization strategies.

Vertical Heterogeneous Networks (vHetNets) represent an integrated wireless network paradigm in which multiple strata of communication platforms—including terrestrial base stations, high altitude platform stations (HAPS), uncrewed aerial vehicles (UAVs), and, potentially, satellite nodes—jointly deliver connectivity, capacity, and advanced services over broad and diverse geographic domains. This multi-layer architecture enables the convergence of space, air, and ground networks into a unified infrastructure capable of addressing the escalating demands of 6G and beyond for ultra-reliable, ubiquitous, and sustainable wireless access. The technical features of vHetNets encompass harmonized-spectrum operation (where tiers share spectral resources), dense and dynamic deployment scenarios, integrated compute/sensing capabilities, and the pervasive use of advanced network optimization and artificial intelligence for management and control.

1. Architectural Principles and Layered Composition

A typical vHetNet consists of at least two vertically differentiated tiers, often extending to three or more. Core instantiations include:

• Terrestrial tier: Macro and small cell base stations (MBSs, SBSs), typically deployed at heights of tens of meters, provide foundational coverage and capacity for ground-based user equipment (UE).
• Aerial/stratospheric tier: HAPS located at 20–50 km altitude operate as super-macro base stations (SMBSs), delivering wide-area line-of-sight (LoS) coverage, backhaul, and edge resources. UAVs act as mobile aerial base stations (ABSs) or relays in the lower-altitude airspace.
• Space (satellite) tier (optional): LEO, MEO, and GEO satellites supply global reach and additional redundancy (Farajzadeh et al., 2021, Wang et al., 2022).

Inter-tier links (terrestrial↔HAPS, HAPS↔satellite, UAV↔ground/HAPS) use a combination of RF (sub-6 GHz, mmWave, or THz) and, in some architectures, free-space optical (FSO) channels (Tekbıyık et al., 2020, Kurt et al., 2020). A single vHetNet may support direct device-to-device, backhaul, fronthaul, and cascade associations, with inter-tier relaying, hierarchical computation/caching, and multi-hop routing.

Key architectural rationales include:

• Coverage complementarity: HAPS and UAVs bridge coverage gaps in rural and high-mobility settings, while terrestrial tiers serve dense urban demand (Shamsabadi et al., 2023, Salamatmoghadasi et al., 15 Jan 2026).
• Capacity scaling and load offloading: Load-aware allocation schemes allow HAPS to offload terrestrial SBSs and macro cells, especially under energy-saving or cell-sleeping regimes (Salamatmoghadasi et al., 2024, Salamatmoghadasi et al., 15 Jan 2026).
• Integrated compute/sensing: HAPS/UAVs can provide edge compute and wide-area sensing, supporting IoT, autonomous vehicular systems, and next-generation delivery networks (Kurt et al., 2020, Wang et al., 2022).

2. Propagation, Channel, and Association Models

Vertically integrated networks exhibit highly heterogeneous channel characteristics. Critical models include:

• Terrestrial MBS–UE Links: Rayleigh or Nakagami-m fading with log-normal shadowing, 3GPP path-loss models (e.g., TR 38.901 UMa) (Shamsabadi et al., 2024, Shamsabadi et al., 2023).
• HAPS–UE Links: Dominantly LoS, modeled as 3D Rician fading with a typically high Rician K-factor (e.g., K=10), and free-space path-loss. The path-loss exponent and link distance (20 km scale) drive receive power; LoS probability is deterministically high for HAPS-UE links (Shamsabadi et al., 2024, Shi et al., 14 Dec 2025).
• UAV–UE Links: Nakagami fading, typically LoS with lower elevation (Shi et al., 14 Dec 2025). UAVs' highly dynamic positioning creates additional geometric diversity.
• Interference and Spectrum Reuse: Harmonized-spectrum scenarios (co-channel operation of multiple tiers) introduce severe inter- and intra-tier interference. SINR is given generally as

$$\gamma_u = \frac{\sum_{b=1}^{B+1}|(h_u^b)^H w_u^b|^2}{\sum_{b=1}^{B+1}\sum_{k\neq u}|(h_u^b)^H w_k^b|^2 + \sigma_n^2}$$

capturing all cross-talk between tiers (Shamsabadi et al., 2024, Shamsabadi et al., 2024, Shamsabadi et al., 2023).

Association rules in vHetNets are governed by maximizing long-term average received power or received SINR, taking into account heterogeneous path-loss, probabilistic LoS/NLoS effects, and directional gains (Cherif et al., 2019, Shi et al., 14 Dec 2025). In cell-free vHetNets, UEs may be served simultaneously by multiple BSs via coordinated multi-point (CoMP) beamforming (Shamsabadi et al., 11 Jul 2025, Shi et al., 14 Dec 2025).

3. Resource Allocation, Interference Management, and Optimization

Resource management in vHetNets is dominated by joint beamforming, power allocation, user association, and subcarrier/resource block scheduling to mitigate interference and achieve operator goals—e.g., maximizing throughput, fairness, or energy efficiency.

Centralized Formulations:

• Weighted Sum Rate (WSR): Maximize aggregate spectral efficiency, favoring throughput (Shamsabadi et al., 2024).
• Proportional Fairness (PF): Maximize the sum of log-SE, balancing fairness and aggregate rate (Shamsabadi et al., 2024, Shamsabadi et al., 2023, Shamsabadi et al., 11 Jul 2025).
• Max–Min Fairness (MMF): Maximize the worst-case user SE, ensuring strong QoS guarantees for cell-edge or underserved users (Shamsabadi et al., 2024, Shamsabadi et al., 2022).

All such formulations are inherently nonconvex, frequently mixed-integer nonlinear programs (MINLPs) due to binary association variables, bilinear SINR structure, and nonconcave objectives. State-of-the-art solution methods employ successive convex approximation (SCA), transforming the problem into a sequence of second-order cone programs (SOCPs) or convex relaxations and updating slack/linearization variables at each iteration. Fast convergence (typically <10 outer iterations) is observed (Shamsabadi et al., 2024, Shamsabadi et al., 2023, Shamsabadi et al., 2022).

Distributed and AI-Driven Strategies:

• Multi-level ADMM/ALM: Distributed coordination where each node (HAPS, MBS) optimizes local variables, periodically reconciling with consensus constraints (Shamsabadi et al., 11 Jul 2025, Shamsabadi et al., 2024).
• Deep Reinforcement Learning (DRL): Multi-agent RL (e.g., DDPG, CA2C) for distributed resource allocation, trajectory planning, and node selection in AI-native vHetNets (Wang et al., 2022, Shamsabadi et al., 2024).
• Cell-Free/CoMP Beamforming: Cell-free topologies leverage distributed beamforming to serve each UE collectively, with interference mitigation arising from multi-point coordination (Shamsabadi et al., 11 Jul 2025, Shi et al., 14 Dec 2025).

Numerical results consistently demonstrate:

• WSR maximizes overall SE but may degrade edge-user performance.
• PF and MMF objectives yield substantial improvements (up to 2 bps/Hz increases in the 5th-percentile SE) for underserved UEs and fairness metrics, especially with HAPS integration (Shamsabadi et al., 2024, Shamsabadi et al., 2023).
• Distributed optimization (ADMM/ALM) and DRL achieve $>90\%$ of centralized SE at greatly reduced computation and signaling cost, essential for scalability in dense deployments (Shamsabadi et al., 2024, Shamsabadi et al., 11 Jul 2025, Wang et al., 2022).

4. Energy Efficiency and Sustainable Operation

Energy efficiency is a defining concern for vHetNets, given the proliferation of small cells and high energy consumption by RAN infrastructure.

• Cell Switching: Dynamic ON/OFF control of SBSs with HAPS providing LoS offloading/support allows substantial energy savings (up to 77% at low load, 40% at high loads vs. all-ON baselines) without traffic loss (Salamatmoghadasi et al., 15 Jan 2026, Salamatmoghadasi et al., 2024).
• Load Estimation Under Sleep Mode: Multi-level clustering (MLC) estimation for sleeping SBSs achieves sub-1% estimation error and power consumption deviation, unlocking practical deployment of traffic-aware cell switching in vHetNets (Salamatmoghadasi et al., 2024).
• Sustainability-Leveraging Solar-Powered HAPS: Persistent, solar-powered HAPS minimize carbon impact and support 6G/Industry 5.0 targets for green telecom (Salamatmoghadasi et al., 15 Jan 2026, Wang et al., 2022).

5. Advanced Applications: Positioning, Sensing, and Computing

Positioning:

vHetNets improve localization accuracy, especially vertical precision, in urban areas where standalone GNSS fails. Joint use of HAPS, terrestrial 5G gNBs, and GNSS satellites reduces 90%-tile vertical error from ≈18 m (GPS-only) to ≈5 m in urban canyons, with VDOP improved to 2–3 (Zheng et al., 2023).

Edge Computing and Caching:

HAPS-enabled vHetNets facilitate ultralow-latency computation offloading, edge caching, and wide-area sensing. Offloading algorithms balance local and HAPS computation to minimize task delay subject to capacity and QoS constraints (Kurt et al., 2020). Caching at HAPS improves content delivery latency and reduces backhaul demand.

Sensing:

High-resolution sensors onboard HAPS platforms enable wide-area coverage, data fusion, and situational awareness for fleet management, anomaly detection, and UAV/IoT coordination (Kurt et al., 2020, Wang et al., 2022).

6. AI-Integrated vHetNets and Self-Evolving Networks

Vertical integration unlocks the synergy of distributed AI for both network operation and native services:

• AI for vHetNets: DRL and federated learning manage dynamic association, UAV trajectories, energy, and spectrum. Actor–critic frameworks, e.g., CA2C, jointly optimize continuous (trajectory) and discrete (association) actions in energy- and traffic-constrained settings, achieving strong gains in anomaly-detection F1 scores and energy savings (Wang et al., 2022).
• VHetNets for AI: Layered FL (e.g., UAV-local GANs, periodic global aggregation at HAPS) achieves robust distributed anomaly detection under stringent privacy, energy, and bandwidth constraints (Wang et al., 2022).
• Self-Evolving VHetNets (SEI-VHetNets): Embedding SE units across layers, leveraging RL/meta-learning/FL, enables closed-loop telemetry-driven reconfiguration—adapting topology, resource allocation, and policies in real time with minimal human oversight (Farajzadeh et al., 2021).

Challenges include handling heterogenous and non-IID data distributions, ensuring privacy/security (Byzantine/poisoning resilience), and managing communication/computation constraints, especially in energy-limited aerial nodes (Wang et al., 2022, Farajzadeh et al., 2021).

7. Key Performance Trade-offs and Design Guidelines

Empirical, analytical, and optimization studies yield the following guidelines:

Objective	Key Benefits	Suitable Scenario
Weighted Sum Rate (WSR)	Highest aggregate throughput	Bulk data offloading
Network-Wide PF (NW-PF)	Balance sum SE and edge-user fairness	General-purpose/SLAs
Network-Wide MMF (NW-MMF)	Maximizes minimum user SE, steepest fairness CDF	Emergency/QoS-critical services

• HAPS augmentation enhances network-wide SE, lifts cell-edge performance, and supports aggressive energy-saving policies, even with strict outage-based QoS (Shamsabadi et al., 2024, Shamsabadi et al., 2023, Salamatmoghadasi et al., 15 Jan 2026).
• Distributed and cell-free architectural modes scale efficiently to large networks, closely tracking centralized benchmarks with dramatically reduced computational and signaling overhead (Shamsabadi et al., 11 Jul 2025, Shamsabadi et al., 2024).
• UAV/ABS deployment and geometry-aware clustering (e.g., coverage-weighted k-means) optimally balances coverage, interference, and backhaul (Shi et al., 14 Dec 2025).
• Cell switching and energy-efficient operation require robust, low-error traffic load forecasting for SBSs—multi-level clustering achieves negligible (<1%) power deviations (Salamatmoghadasi et al., 2024).
• Network design must tightly couple objective-function selection, resource allocation method, and site-specific constraints (capacity, backhaul, spectrum, hardware capabilities) to meet differentiated requirements (Shamsabadi et al., 2024, Shamsabadi et al., 2023).

• "Impact of Objective Function on Spectral Efficiency in Integrated HAPS-Terrestrial Networks" (Shamsabadi et al., 2024)
• "Downlink Coverage and Rate Analysis of an Aerial User in Vertical Heterogeneous Networks (VHetNets)" (Cherif et al., 2019)
• "Interference Management Strategies for HAPS-Enabled vHetNets in Urban Deployments" (Shamsabadi et al., 2024)
• "VHetNets for AI and AI for VHetNets: An Anomaly Detection Case Study for Ubiquitous IoT" (Wang et al., 2022)
• "Addressing the Load Estimation Problem: Cell Switching in HAPS-Assisted Sustainable 6G Networks" (Salamatmoghadasi et al., 2024)
• "Self-Evolving Integrated Vertical Heterogeneous Networks" (Farajzadeh et al., 2021)
• "Communication, Computing, Caching, and Sensing for Next Generation Aerial Delivery Networks" (Kurt et al., 2020)
• "Sustainable Vertical Heterogeneous Networks: A Cell Switching Approach with High Altitude Platform Station" (Salamatmoghadasi et al., 15 Jan 2026)
• "Vertical Heterogeneous Networks Beyond 5G: CoMP Coverage Enhancement and Optimization" (Shi et al., 14 Dec 2025)
• "Enhancing Next-Generation Urban Connectivity: Is the Integrated HAPS-Terrestrial Network a Solution?" (Shamsabadi et al., 2023)
• "Handling Interference in Integrated HAPS-Terrestrial Networks through Radio Resource Management" (Shamsabadi et al., 2022)
• "Two-Level Distributed Interference Management for Large-Scale HAPS-Empowered vHetNets" (Shamsabadi et al., 11 Jul 2025)
• "A Positioning System in an Urban Vertical Heterogeneous Network (VHetNet)" (Zheng et al., 2023)
• "A Holistic Investigation on Terahertz Propagation and Channel Modeling Toward Vertical Heterogeneous Networks" (Tekbıyık et al., 2020)
• "I am 4 vho: new approach to improve seamless vertical hanover in heterogeneous wireless networks" (Khattab et al., 2013)
• "An Overview of Context-Aware Vertical Handover Schemes in Heterogeneous Networks" (Alhazmi et al., 2011)