Optimal Wireless Transmitter Placement in Realistic Urban Environments

1. High-Fidelity Signal Propagation

Standard placement heuristics often rely on simplified "disk" models. Our method utilizes Sionna RT to perform site-specific ray tracing. This accounts for:

• Diffuse scattering and specular reflections from building facades.
• Material-specific attenuation (e.g., concrete vs. glass).
• Complex 3D diffraction over rooftops (Knife-edge diffraction).

The figure on the right illustrates ray-traced signal propagation in an urban environment. Each colored path represents a signal ray bouncing between buildings, capturing the complexity that simple disk models miss entirely.

2. The Objective Functional \(\mathcal{S}(T)\)

We consider the problem of optimally placing a set of transmitters \(T = \{t_1, \dots, t_n\} \subset \Omega\) in a physical environment \(\Omega \subseteq \mathbb{R}^n\), where signal propagation is governed by a spatially varying medium \(\mu(x)\). Each location \(y \in \Omega\) receives signal contributions from all transmitters through a propagation model \(P(y,x)\). A natural performance measure is the Signal-to-Interference-and-Noise Ratio (SINR):

\[ \text{SINR}(y, T) = \frac{\max_{t \in T} P(y, t)} {\sum_{t \in T} P(y, t) - \max_{t \in T} P(y, t) + \sigma^2} \]

While physically accurate, this formulation induces a non-convex optimization landscape with many local optima. To overcome this, we introduce a family of aggregated surrogate measures \(\mathcal{P}_{\text{MAX}}\) and \(\mathcal{P}_{\text{SUM}}\), and define a spatially aggregated objective functional:

\[ \mathcal{S}(T) = \mathbb{E}_{Y \sim f}\left[\bar{W}(\mathcal{P}(Y, T))\right] \]

where \(f(y)\) is a spatial density encoding region importance and \(\bar{W}(\kappa) = \int_0^\kappa w(s)\,ds\) is the anti-derivative of a monotone utility function \(w\). We formulate two equivalent placement problems:

\[ \min_{T \subseteq \Omega} |T| \quad \text{s.t.} \quad \mathcal{S}(T) \geq \beta \qquad \text{or} \qquad \max_{T \subseteq \Omega} \mathcal{S}(T) \quad \text{s.t.} \quad |T| \leq \beta. \]

3. IA-SPA: Interference-Aware Submodular Placement Algorithm

Placement isn't just about coverage — it's about managing interference. IA-SPA specifically targets areas where the SINR is lowest, ensuring robust "edge-of-cell" performance for every user in the network.

4. Case Study: San Francisco

To establish a realistic baseline, we utilized building footprint data and existing tower locations for AT&T and T-Mobile sourced from open-source network datasets. This allows us to compare IA-SPA directly against real-world engineering deployments in a dense 3D environment.

High-fidelity 3D model of San Francisco used for ray-tracing simulations.

Quantitative Comparison against Real-World Baselines

The table below summarizes performance of IA-SPA compared to existing carrier deployments using the same number of towers.

Data rate coverage maps: AT&T baseline (left) vs. IA-SPA optimized placement (right) in San Francisco.

Interference maps: AT&T baseline (left) vs. IA-SPA optimized placement (right). IA-SPA dramatically reduces peak interference.

5. Case Study: Florence

For Florence, we demonstrate IA-SPA's ability to handle exclusionary zones (historical landmarks where tower placement is prohibited) and continuous deployment scenarios (expanding an existing network around pre-placed towers).

High-fidelity 3D model of Florence used for ray-tracing simulations.

Exclusionary zone (red) where tower placement is prohibited.

Continuous deployment scenario with existing towers (red points).

Coverage Results: Florence with Exclusionary Zone

Data rate coverage with exclusionary zone: Iliad baseline (left) vs. IA-SPA (right).

Interference maps with exclusionary zone: Iliad baseline (left) vs. IA-SPA (right).

Coverage Results: Florence Continuous Deployment

Data rate coverage in continuous deployment scenario: Iliad baseline (left) vs. IA-SPA (right).

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