Ray Tracing

Ray tracing operates on the high-frequency approximation of Maxwell's equations, treating electromagnetic waves as localized rays that travel in straight lines within homogeneous media. This approach is valid when the wavelength is much smaller than the dimensions of surrounding objects, making it ideal for mmWave and sub-THz frequencies used in 5G and 6G systems.

• Rays obey Snell's law of reflection and refraction at material boundaries
• Diffraction is modeled using the Uniform Theory of Diffraction (UTD) to account for wave bending around edges
• Each ray carries complex amplitude, phase, delay, and polarization information

Unlike statistical channel models, ray tracing requires a high-fidelity 3D digital map of the physical environment, including building geometries, material electromagnetic properties, and terrain elevation data. This deterministic approach captures the unique multipath signature of a specific location.

• Material databases assign complex permittivity and conductivity to surfaces like concrete, glass, and foliage
• Diffuse scattering models account for surface roughness and small-scale irregularities
• The resulting Channel Impulse Response is unique to the exact transmitter-receiver geometry

Two primary algorithmic approaches exist for identifying valid propagation paths between transmitter and receiver. Ray launching shoots rays uniformly from the transmitter and tests which reach the receiver, while image-based ray tracing computes exact reflection paths by mirroring the source across planar surfaces.

• Shooting and Bouncing Rays (SBR): Launches a dense fan of rays and recursively traces reflections up to a maximum depth
• Image method: Computes exact specular paths deterministically but scales poorly with complex geometries
• Hybrid approaches combine both techniques for efficiency in dense urban canyons

Ray tracing outputs a detailed list of multipath components (MPCs) — each representing a discrete propagation path with measurable physical parameters. This granular data enables precise Angle of Arrival estimation and spatial channel characterization essential for beamforming design.

• Each MPC records delay, azimuth/elevation departure and arrival angles, complex amplitude, and Doppler shift
• The coherent summation of all MPCs produces the full Channel Impulse Response
• Spatial consistency across closely spaced receiver locations is naturally preserved

Ray tracing accuracy scales directly with computational effort. GPU acceleration has made real-time ray tracing feasible for dynamic scenarios, but the technique remains more computationally intensive than stochastic models. Optimization strategies balance fidelity against runtime.

• Ray density and maximum reflection/diffraction depth control accuracy vs. runtime
• Pre-computed visibility trees accelerate repeated queries in static environments
• Angular z-buffer techniques reduce redundant ray intersection tests
• Typical simulation times range from milliseconds for simple indoor scenes to minutes for dense urban macro-cells

A hybrid modeling framework that combines deterministic ray tracing for strong specular paths with a stochastic model for weaker, diffuse scattering clusters. This approach captures the dominant propagation mechanisms precisely while efficiently approximating the complex diffuse background, balancing computational cost with physical accuracy. The QD model is the foundation of modern mmWave and sub-THz channel standards.

The time-domain characterization of a wireless channel's multipath profile, representing received signal power as a function of delay when a perfect impulse is transmitted. Ray tracing directly computes the CIR by summing the complex amplitude, delay, and phase of each traced path. The CIR is the fundamental output used to derive:

• Power delay profile
• Delay spread
• Coherence bandwidth

The direction from which a propagating radio wave impinges upon a receiver antenna array. Ray tracing inherently computes AoA by tracking the final ray segment's vector before reception. This spatial information is critical for:

• Beamforming codebook design
• MIMO spatial correlation matrices
• Angle spread characterization for 3D channel models

A domain adaptation technique where a model trained entirely on ray-traced synthetic RF data is refined to maintain accuracy in a live physical environment. The ray tracer generates labeled training data for neural receivers and classifiers, but subtle discrepancies in material properties and geometry require transfer learning to bridge the sim-to-real gap. Domain randomization during ray tracing improves generalization.