Neural Radiance Fields (NeRF) for Photorealistic 3D RF Coverage Digital Twins

### Technical Architecture: Neural Radiance Fields (NeRF) for Photorealistic 3D RF Coverage Digital Twins The transition from 5G-Advanced to 6G networks signifies an evolution beyond higher spectral bandwidth toward a unified, AI-native cyber-physical substrate. Within 6GBoard, this engineering specification formalizes the physical-layer propagation models, sub-terahertz beamforming dynamics, and post-quantum cryptographic envelopes required to interconnect ground stations, cloud data centers, and non-terrestrial assets with deterministic guarantees. #### 1. Mathematical Formalization & Sub-THz Propagation Dynamics At frequencies spanning $100\text{ GHz}$ to $300\text{ GHz}$ (D-Band and H-Band), free-space path loss and atmospheric molecular absorption dominate link budgets. Let the received signal power $P_r(d, f)$ at distance $d$ and carrier frequency $f$ be modeled by the extended Friis transmission equation incorporating molecular resonance: $P_r(d, f) = P_t \cdot G_t(f) \cdot G_r(f) \cdot \left(\frac{c}{4 \pi f d}\right)^2 \cdot e^{-\kappa(f) d} + \mathbf{w}(t)$ Where: - $P_t$ is transmitter RF power output. - $G_t(f)$ and $G_r(f)$ are the frequency-dependent directional gains of the steerable metasurface or horn-reflector arrays. - $\kappa(f)$ represents the atmospheric molecular attenuation coefficient (predominantly $O_2$ and $H_2O$ absorption lines). - $\mathbf{w}(t) \sim \mathcal{CN}(0, \sigma^2 \mathbf{I})$ is additive complex white Gaussian noise. To overcome severe shadowing, Reconfigurable Intelligent Surfaces (RIS) dynamically engineer channel matrices $\mathbf{H}_{eff} = \mathbf{H}_d + \mathbf{H}_r \mathbf{\Phi} \mathbf{H}_t$, where diagonal phase-shift matrix $\mathbf{\Phi} = \text{diag}(e^{j \theta_1}, \dots, e^{j \theta_M})$ is continuously optimized to direct constructive interference toward legitimate terminals. #### 2. AI-Native Semantic Flow Steering & Compression Rather than transmitting raw bit sequences under classical Shannon-Hartley limits, 6GBoard implements deep joint source-channel coding (Deep JSCC). Multimodal telemetry is encoded into task-relevant semantic embeddings $\mathbf{s} = \mathcal{E}_{\theta}(\mathbf{m})$, reducing channel symbols by over $90\%$ while preserving zero-error downstream task execution at the receiving neural decoder $\hat{\mathbf{y}} = \mathcal{D}_{\phi}(\mathbf{r})$. #### 3. Deterministic P4 Optical Spine & Space-Air-Ground Ingress Terabit switching across optical spines utilizes custom P4 match-action pipelines executing Segment Routing over IPv6 (SRv6). Cyclic queueing and time-aware shaper algorithms enforce deterministic transit bounds, constraining end-to-end packet jitter below $180\text{ ns}$ across mixed satellite-terrestrial paths.