3D 6G Networks: Volumetric Coverage

• 3D coverage in 6G networks is a volumetric extension of traditional 2D cellular architectures, enabling connectivity across terrestrial, aerial, and satellite layers.
• It employs advanced channel modeling, FD-MIMO beamforming, and RIS-assisted reconfiguration alongside AI-based orchestration to optimize network performance.
• Key performance metrics like coverage probability, SINR, and throughput are enhanced through integrated multi-tier architectures and cross-layer optimization.

Three-dimensional (3D) coverage in 6G networks denotes the volumetric extension of service cells to provide pervasive connectivity, capacity, and edge intelligence for users distributed in all spatial dimensions. This paradigm subsumes integration of terrestrial, aerial, and satellite nodes, advanced electromagnetic channel modeling, joint optimization of communication and computation resources, and new hardware capabilities such as reconfigurable intelligent surfaces (RIS) and ultra-massive MIMO arrays. The following sections present the foundational principles, system architectures, modeling frameworks, performance metrics, and deployment guidelines as established in recent literature.

1. Volumetric 6G Network Architectures

3D coverage in 6G networks is realized via hierarchical, multi-tiered architectures that blend terrestrial, aerial, and satellite platforms (Farré et al., 12 Jun 2025, Strinati et al., 2020, Strinati et al., 2019). The following spatial layers are canonical:

• Terrestrial Layer: Macro and small-cell gNodeBs are typically deployed at heights $h_B \approx 45$ m and may be co-located with passive RIS panels at $h_R \approx 35$ m. These anchor the ground segment and deliver high-density coverage, computation, and caching.
• Aerial Layer: Includes Low-Altitude Platforms (LAPs, e.g., UAV-BS) at 50–300 m, and High-Altitude Platforms (HAPS) at $\sim$20 km. These nodes provide rapid deployment, capacity offload, and persistent wide-area augmentation.
• Non-Terrestrial Network (NTN) Layer: LEO satellite constellations at $h_s \approx 600$ km (or more generally, 500–1000 km) deliver macro-scale volumetric coverage with spot beams (diameters 100–500 km).
• User Layer: User equipment (UE), IoT devices, and aerial vehicles are distributed arbitrarily in $0 \leq z_U \leq 100$ m, while fixed VSAT gateways connect NTNs to terrestrial core networks.

Orchestration of these tiers enables dynamic association, load balancing, and seamless mobility for ground, elevated, and aerial UEs. Virtualized network functions (VNFs) and mobile edge computing (MEC) extend cloud services into the 3D spatial domain (Strinati et al., 2020).

2. Physical Layer Models and Propagation in 3D

Accurate 3D coverage analysis depends on channel models that capture distance, elevation, and angular dependencies, as well as platform mobility and diverse propagation regimes (Yang et al., 7 Jan 2025, Kirik et al., 2024, Wang et al., 2021, Strinati et al., 2019). Key elements include:

• 3D Path-Loss Models: Path loss is modeled as $$PL(d, \theta) = PL_0 + 10\,\alpha\,\log_{10}(d/d_0) + \xi(\theta)$$, where $d$ is the 3D separation and $\xi(\theta)$ encapsulates elevation-dependent losses (e.g., shadowing, scintillation) parameterized per 3GPP TR 38.811 (Farré et al., 12 Jun 2025). For NTNs, $\alpha \approx 2.2$–2.5; for sub-6 GHz RIS links, $\alpha = 2.0$–3.0. Molecular absorption and frequency-dependent effects are included in THz bands (Wang et al., 2021).
• Multi-Tier LoS Probability: The probability of line-of-sight (LoS) as a function of elevation angle is $$P_\mathrm{LoS}^{(k)}(\theta) = 1/(1+a_k\,\exp(-b_k(\theta-a_k)))$$, adapted to node tier and environment.
• Small-Scale Fading: Channel gain for each tier is modeled as Rice($K_k(\theta)$) or Rayleigh distributions. For tri-polarized channels, dyadic Green’s function expansions and spherical vector harmonics rigorously resolve electromagnetic fields in 3D (Yang et al., 7 Jan 2025).
• Doppler and Mobility: In aerial and HAP-to-HAP links, Doppler shift is analytically characterized to correct the instantaneous effective channel and SNR, crucial for non-stationary scenarios (Kirik et al., 2024).

3D beamforming employs full-dimensional MIMO (FD-MIMO), supporting precise joint azimuth/elevation control. Volumetric cell design is further enhanced by RIS or IRS-enabled programmable environments (Long et al., 2021).

3. 3D Coverage Optimization, Beamforming, and Resource Allocation

Volumetric coverage and throughput maximization require joint optimization of spatial resource configurations, beam patterns, and embedded computation (Farré et al., 12 Jun 2025, Gopi et al., 2021, Strinati et al., 2020, Long et al., 2021):

• Beamforming + RIS Phase Control: Coverage and capacity are optimized via

$$\max_{w, \Phi} \sum_{k=1}^K \log_2(1+\mathrm{SINR}_k)\qquad \text{subject to}\quad |\Phi_{mn}|=1,\ \|w\|^2 \leq P_\text{max}$$

where $w$ and $\Phi$ represent analog/digital precoders and RIS phase-shift matrices, respectively (Farré et al., 12 Jun 2025, Long et al., 2021).

• Cooperative 3D Beamforming: In both cell-based and cell-free 6G, joint zero-forcing across spatially separated BSs (or access points) eliminates "angle-collision" in 3D, maximizing volumetric spectral efficiency (VSE):

$$\mathrm{VSE} = \frac{1}{V} \mathbb{E}\left[\log_2(1+\mathrm{SINR})\right]$$

with $V$ denoting the service volume (Gopi et al., 2021).

• AI-Based Orchestration: Distributed reinforcement learning orchestrates resource allocation, association, and function placement, converging (in aggregate) to an $\epsilon$-Nash equilibrium for joint communication, computation, and caching (C$^3$) (Strinati et al., 2020). Multi-agent RL leverages local state (channel, battery, queue) and federated policy updates.

The effects of RIS size, element quantization, and adaptive beam scanning on coverage depth and reliability are quantified by volumetric metrics such as $P_\mathrm{cov}$ and $V_\mathrm{cov}$ (Long et al., 2021, Farré et al., 12 Jun 2025).

4. Advanced 3D Channel Modeling and Metrics

6G research advances rigorous continuous-space electromagnetic channel models and 3D stochastic geometry frameworks for user/channel distributions (Yang et al., 7 Jan 2025, Wang et al., 2021):

• Continuous-Space EM Models: Dyadic Green’s function methods with vector spherical harmonics provide closed-form SVD expansions of channel matrices for arbitrary tri-polarized multi-user setups. Degrees of freedom (DoF) and statistical channel capacity depend on transmit/receive aperture sizes, sampling intervals, and scatterer densities.
• THz 3D GBSM: At THz bands, cluster-based geometric stochastic models include frequency-dependent diffuse scattering, leading to intricate angle and delay spreads. Performance metrics such as spatial correlation functions, RMS delay spread, and statistical coverage formulas are provided in closed form (Wang et al., 2021).
• Numerical Analysis: Simulation recipes discretize 3D domains via "method of equal area" (MEA) angle quantization and evaluate 3D coverage probability and SNR heatmaps as a function of system parameters.

Analytical coverage probability for arbitrary user elevations integrates over LoS/NLoS distributions and SINR/threshold events, supporting both physical-layer and network-level planning (Strinati et al., 2020, Strinati et al., 2019).

5. Reconfigurable Intelligent Surfaces and Full 3D Coverage

RIS/IRS have emerged as key enablers for coverage shaping and extension in 6G, capable of enhancing or restoring connectivity in 3D space (Long et al., 2021, Jeon et al., 25 Jan 2026, Farré et al., 12 Jun 2025):

• Passive RIS: By optimizing the phase-profile across an $N_x\times N_y$ array ($N\geq256$), passive RIS can redirect beams towards coverage nulls, supporting elevation ranges up to $z_U=100$ m (Farré et al., 12 Jun 2025). Quantization of 2–4 bits per element suffices for near-continuous main-lobe gain (Long et al., 2021).
• Active RIS / Aerial RIS: Integrating active amplification on an aerial platform (active-RIS) overcomes multiplicative fading and enables robust 3D backhaul for both UAV-BS and ground UEs (Jeon et al., 25 Jan 2026). The optimal RIS placement is solved analytically for multi-user scenarios using Fermat–Torricelli geometry, maximizing 3D energy efficiency under practical power constraints.
• Hardware and Control: 3D IRS deployment must address pilot overhead in cascaded channel estimation, rapid reconfiguration for mobile aerial users, and scaling control traffic to thousands of RIS elements.

RIS placement and element count crucially affect achieved SNR, cell radius, and sustained throughput. For example, increasing RIS elements from $N=64$ to $N=256$ increases the average DL rate from 260 Mbps to 420 Mbps, extending coverage radii from 55 m to 80 m (for sub-6 GHz RIS-TN) (Farré et al., 12 Jun 2025). Energy trade-offs between active and passive RIS are explicitly modeled, with active solutions cutting total power by 30–36 dB compared to passive designs (Jeon et al., 25 Jan 2026).

6. Performance Metrics, Simulation Results, and Trade-offs

Exact system-level metrics and empirical results contextualize capabilities and limitations of 3D 6G networks:

UE Altitude (m)	Coverage Probability (%)	Avg. SINR (dB)	Avg. Throughput (Mbps)
1.5	99.2	12.1	420
30	96.8	10.5	380
60	93.5	8.7	320
100	89.4	7.1	270

• Increasing LEO satellite count from 1 to 4 boosts total downlink capacity from 2.34 Gbps to 6.20 Gbps (+165%) (Farré et al., 12 Jun 2025).
• Using UAV relays to supplement saturated satellite coverage ensures 100% session retention at 10 Mbps for all 50 UEs in a mobile scenario, as opposed to substantial session drops without relay (Strinati et al., 2020).
• Coverage probability and average SNR decrease with elevation, attributed to increased path loss and reduced diffraction/scattering at higher altitudes.

Trade-offs in 3D coverage emerge between coverage volume, spectral efficiency, interference management, and hardware deployment. Detailed analytical formulas for $P_\mathrm{cov}(T)$, end-to-end latency, and volumetric spectral efficiency are provided for both stochastic and deterministic network layouts (Strinati et al., 2020, Gopi et al., 2021, Strinati et al., 2019).

7. Deployment Guidelines and Open Challenges

Field deployment of 3D 6G coverage-capable networks is governed by:

• RIS Placement: Install at $h_R=30$–40 m, spaced every 150–250 m along perimeters to ensure overlap of reflected beams and coverage up to 100 m spatial elevation (Farré et al., 12 Jun 2025).
• LEO Orbit and Beam Footprint Planning: Select $h_s \approx 600$ km (for $\leq10$ ms delay), with scanning Ka-band beams for high-density events and S-band for macro coverage. Satellite ephemeris must guarantee minimum $30^\circ$ elevation during peak demand.
• Handover and Spectrum Sharing: Dual-trigger handover (RSSI and elevation-angle) with dynamic spectrum sharing (FFR/FR3) between NTN and TN for reuse in hotspots (Farré et al., 12 Jun 2025).
• Aerial Active-RIS Deployment: Optimize array partitioning and amplification gain for joint service to UAV-BS and ground UEs; decentralize RIS placement via Pareto-optimal algorithms (Jeon et al., 25 Jan 2026).

Persistent challenges include robust 3D channel estimation at scale, real-time adaptation to platform mobility, robust interference mitigation under dense spatial reuse, and security/control for distributed RIS-enabled architectures.

---

3D coverage characterizes a foundational shift in 6G, transitioning from legacy 2D cells to volumetric, AI-optimized networks integrating terrestrial, UAV, HAP, and NTN components, with RIS and advanced electromagnetic design playing central roles (Farré et al., 12 Jun 2025, Strinati et al., 2020, Long et al., 2021, Yang et al., 7 Jan 2025, Jeon et al., 25 Jan 2026).