Engineers who build and operate cellular networks have to prove their sites are safe. Every mast, rooftop panel, and 5G small cell must sit far enough from homes, offices, and walkways to keep the public’s exposure to radio-frequency (RF) energy below strict limits set by bodies such as the ICNIRP in Europe and the FCC in the United States.
Traditionally, those “compliance distances” are estimated with software that represents each antenna as a simplified mathematical model and then “ray-traces” how energy spreads into the environment. The process works, but it can be overly cautious. Extra-wide exclusion zones waste rooftop space and force operators to lower transmit power or add fill-in sites.
A master’s dissertation by Raynard Swanepoel under supervision of Dr. D.I.L. De Villiers tackles this problem head-on. The study asks three straightforward questions:
- Can we describe common base-station antennas with spherical wave functions instead of the usual ray-tracing building blocks?
- If we do, will the predicted RF fields match full-physics (so-called “full-wave”) simulations more closely?
- Can the entire modelling process be automated so that engineers no longer manually tune parameters?
What Are Spherical Wave Functions—And Why Bother?
Figure 1: Example antenna site generated in IXUS RF Safety Software
Imagine dropping a pebble into a pond. Ripples spread out evenly in every direction. Mathematicians describe similar three-dimensional ripples with spherical wave functions. By adding many of these functions together—each with its own strength and phase—you can reproduce almost any radiation pattern, including the tightly focused beams and quirky side-lobes of real-world cellular antennas.
Swanepoel’s insight is that a small set of spherical modes can stand in for the hundreds of point sources normally used in ray tracing. Fewer—but smarter—building blocks promise a cleaner match to lab-measured patterns, especially in tricky regions close to the main beam where ray-tracing tends to over- or under-shoot.
Building the Models Automatically
To turn theory into practice, the study created an automated synthesis pipeline. It starts with a manufacturer’s two-dimensional pattern (the familiar polar plot you find on antenna datasheets). A Random Forest regression model provides an initial estimate for physical dimensions, such as reflector size.
A Nelder–Mead optimiser then tweaks the number of elements, their spacing, and the phase-and-amplitude “weights” until the synthesised pattern hugs the supplier’s curve as closely as possible. The same pipeline can output either a spherical-wave model or a classic ray-tracing model, allowing the researcher to compare them like-for-like.
Three Very Different Antennas, One Clear Winner
The thesis tested both approaches on three industry-standard cases:
- Cross-dipole panel (a sector antenna often found on macro sites)
- IEC 62232 reference panel (a benchmark defined in the key human-exposure standard)
- Omnidirectional collinear (the can-shaped sticks mounted on many rooftops)
For each antenna, a full-wave model produced with FEKO served as the ground truth. Compared with ray-tracing, the spherical-wave version cut the average 3D far-field error by up to 48% for the cross-dipole panel and trimmed the worst-case error by 26%.
The benefit was smaller for the very clean IEC panel pattern, but the new method still halved the median error. Even better, when the optimiser handled every setting itself, the finished model beat a hand-tuned equivalent by 38% on average.
Where Next?
The dissertation suggests three avenues for future work:
- Build a dedicated, open-source spherical-wave engine that skips the heavyweight full-wave solver during optimisation.
- Blend methods—for example, use spherical waves in most of the space but switch to Huygens-based techniques or Friis transmission inside the minimum sphere.
- Optimise at mode level by adjusting the weight of each individual spherical harmonic instead of tweaking physical reflector plates, unlocking even closer matches for antennas with exotic side-lobes.
Final Thoughts
This research shows that spherical-wave synthesis isn’t just academic curiosity. It’s a pragmatic tool that can slot into existing RF-safety workflows, output familiar far-field files, and deliver up to twice the accuracy of today’s ray-tracing models with no human fine-tuning. Automated scripts shoulder the heavy lifting, freeing engineers to focus on site design rather than performing tedious tasks.
If network operators, regulators, and software vendors adopt this approach, the public could see faster rollouts, stronger signals, and confident reassurance that every mast and panel meets the safety standard—no more, no less. That’s a win for everyone who depends on a phone in their pocket and a tower on the horizon.
Download and read the full research paper here: https://scholar.sun.ac.za/bitstreams/9d92c738-a4d6-4fe2-8aba-bb499938a527/download
