⚡ electrical engineering

Millimeter Wave Path Loss for Diverse Antenna Patterns in Outdoor Environment

This paper proposes a novel approach based on a multi-elliptical propagation model to modify empirical path loss models, enabling accurate estimation for millimeter-wave antenna systems with diverse radiation patterns and beam widths in outdoor environments.

Original authors: Jaroslaw Wojtun, Cezary Ziolkowski, Jan M. Kelner, Pawel Skokowski, Niraj Narayan, Rajeev Shukla, Aniruddha Chandra, Radek Zavorka, Tomas Mikulasek, Jiri Blumenstein, Ondrej Zeleny, Ales Prokes

Published 2026-03-18

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jaroslaw Wojtun, Cezary Ziolkowski, Jan M. Kelner, Pawel Skokowski, Niraj Narayan, Rajeev Shukla, Aniruddha Chandra, Radek Zavorka, Tomas Mikulasek, Jiri Blumenstein, Ondrej Zeleny, Ales Prokes

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: The "Flashlight" Problem

Imagine you are trying to send a secret message using a flashlight in a dark, crowded city.

The Old Way (Omnidirectional): You use a standard lightbulb that shines light in all directions (360 degrees). It's easy to set up, but the light gets weak very quickly, and it wastes energy lighting up empty walls and the sky.
The New Way (Millimeter Wave/5G): To send more data (like high-definition video), we need to use "Millimeter Waves." These are like super-fast, high-frequency light beams. But they are fragile; they get blocked easily by buildings, rain, and even people.
The Solution (Directional Antennas): To make these waves work, we use directional antennas. Think of these as laser pointers or spotlights. Instead of flooding the whole room with light, you aim a tight, powerful beam directly at your friend. This gives you a stronger signal and less interference from neighbors.

The Problem: Engineers have great formulas (maps) to predict how far a "lightbulb" signal travels. But they don't have easy maps for "spotlights." Every time you change the shape of the spotlight (make it wider or narrower) or change the lens, the old maps don't work anymore. Calculating a new map for every single new antenna is like trying to draw a new map of a city every time you change your car's headlights. It takes too much time and computer power.

The Paper's Solution: The "Shape-Shifting" Calculator

This paper introduces a clever, low-effort trick to fix this. The authors created a method to take the "lightbulb" map and instantly adjust it to work for any "spotlight" shape.

Here is how they did it, using a creative metaphor:

1. The "Multi-Elliptical" Bubble (The MPM)

Imagine the space between the transmitter (the sender) and the receiver (the friend) is filled with invisible, floating oval bubbles (ellipses).

The sender and receiver are at the two ends (foci) of these bubbles.
These bubbles represent where the radio waves bounce off buildings and scatter around the city.
Some waves go straight through (Line-of-Sight), while others bounce off walls (Non-Line-of-Sight).

The authors use a mathematical model to fill these bubbles with "traffic" (radio waves). This helps them see exactly how the waves are moving through the city.

2. The "Sunglasses" Adjustment

Once they know how the waves are moving inside the bubbles, they apply the "antenna pattern."

The Analogy: Imagine the radio waves are a crowd of people running through a hallway.
- An Omnidirectional antenna is like an open door; everyone runs through.
- A Directional antenna is like putting on a pair of narrow sunglasses. You can only see (or receive) the people running directly in front of you. The people running to the side are blocked out.

The paper's method calculates exactly how much "signal" is lost when you put on those sunglasses. It asks: "If we narrow the beam, how much of the bouncing signal do we miss?"

What They Found (The Results)

The researchers tested this with two different "colors" of light (28 GHz and 39 GHz) in two different city scenarios:

Scenario A: Clear Line of Sight (LOS)

The Situation: You and your friend are looking straight at each other with no buildings in between.
The Finding: It doesn't matter if your "spotlight" is wide or narrow. As long as you are looking at each other, the signal is strong.
The Analogy: If you are shining a laser pointer directly at a friend's face, it doesn't matter if the beam is the width of a pencil or a finger; they will still see the dot clearly.

Scenario B: Blocked View (NLOS)

The Situation: There is a building between you and your friend. The signal has to bounce off other buildings to reach them.
The Finding: This is where the beam width matters a lot.
- Wide Beam: If your antenna is wide, it catches many bouncing signals from different angles.
- Narrow Beam: If your antenna is very narrow (like a tight laser), it might miss the bouncing signals entirely because they are coming from the side.
The Analogy: Imagine you are trying to catch rain in a bucket.
- If the rain is falling straight down (LOS), a small cup works fine.
- If the rain is blowing sideways and bouncing off walls (NLOS), a wide bucket catches much more water than a narrow straw. If you use a narrow straw, you might miss the rain completely.

Why This Matters

Speed: Instead of running massive, slow computer simulations for every new antenna design, engineers can use this "shortcut" to get the answer instantly.
Flexibility: It allows engineers to design antennas with any shape or beam width and know exactly how well they will work in a real city.
Better 5G: This helps us build better 5G networks that are faster and more reliable, even in crowded cities where signals bounce off skyscrapers.

Summary in One Sentence

The authors invented a smart "calculator" that takes a simple map of how radio waves travel and instantly adjusts it to predict how well any specific type of "spotlight" antenna will work, saving engineers hours of complex math and helping us build faster 5G networks.

1. Problem Statement

The rapid deployment of 5G systems in the millimeter-wave (mmWave) spectrum (Frequency Range 2: 24.25–71 GHz) relies heavily on directional antennas (e.g., massive MIMO) to overcome high signal attenuation and path loss. However, existing empirical path loss (PL) models face two main limitations:

Omnidirectional Bias: Standard models (e.g., 3GPP TR 38.901) are primarily designed for omnidirectional antennas. Adapting them for directional antennas requires complex algorithms with high computational costs.
Lack of Flexibility: Existing empirical models derived from measurements are typically tied to specific antenna systems with fixed radiation patterns and beam widths. They cannot easily be adapted to estimate path loss for antennas with different beam shapes or Half-Power Beam Widths (HPBWs) without new, costly measurements.

2. Methodology

The authors propose a novel, low-complexity method to modify an existing omnidirectional path loss model to estimate directional path loss for any arbitrary antenna pattern and beam width. The core of the methodology involves the Multi-Elliptical Propagation Model (MPM).

Input Basis: The method starts with a baseline omnidirectional PL model (derived from 3GPP TR 38.901 or synthesized measurements).
Geometric Modeling (MPM): The authors utilize a 2D Multi-Elliptical Propagation Model, a Geometry-Based Stochastic Model (GBSM).
- The model constructs coaxial multi-elliptical scattering structures where the Transmitter (Tx) and Receiver (Rx) are at the foci.
- The size of the ellipses is determined by the Power Delay Profile (PDP) delays (time-clusters), while the power of these clusters defines path amplitudes.
- This allows for the calculation of the Power Azimuth Spectrum (PAS), $P(\phi, D)$ , which describes how signal power is distributed across different angles for a specific distance.
Correction Factor Calculation: The directional path loss ( $PL_{out}$ ) is calculated by adding a correction coefficient to the input omnidirectional path loss ( $PL_{in}$ ):
$PL_{out}(D) = PL_{in}(D) + PL_{corr}(D)$
The correction coefficient ( $PL_{corr}$ ) is derived by comparing the integrated PAS of the omnidirectional antenna against the PAS of the specific directional antenna, weighted by their respective gains. This effectively accounts for how the antenna pattern filters specific propagation paths (scattering components).

3. Key Contributions

Novel Adaptation Framework: A method to convert a generic omnidirectional PL model into a directional one for any antenna pattern shape and HPBWs without requiring new field measurements.
Low Computational Complexity: Unlike deterministic ray-tracing simulations, the MPM-based approach offers a compromise between simple empirical models and complex simulations, providing realistic results with significantly lower computational overhead.
Comprehensive Pattern Analysis: The study evaluates diverse antenna models, including:
- Simplified mathematical models: Gaussian (main lobe only) and Sinc (includes side lobes).
- Realistic 3GPP/ITU-compliant models: A massive MIMO gNodeB (12x8 elements) and a User Equipment (UE) single-element pattern.
Parametric Study: The method analyzes the impact of varying HPBWs (specifically 8°, 16°, and 24°) on path loss estimation.

4. Results and Analysis

The study was conducted for 28 GHz and 39 GHz frequencies in an outdoor urban macro (UMa) environment, covering both Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) conditions.

Impact of Antenna Pattern Models:
- Path loss increases with frequency.
- Gaussian and Sinc models yielded similar results, despite the Sinc model accounting for side lobes.
- The realistic gNodeB pattern resulted in slightly higher path loss compared to the simplified models.
- Key Insight: While directional antennas introduce higher path loss values compared to omnidirectional baselines (due to spatial filtering), they improve the overall link power budget through high antenna gain and reduce interference/phase differences.
Impact of Beam Width (HPBW):
- LOS Conditions: Increasing the HPBW causes a decrease in path loss. For wide beams (e.g., 24°), the path loss approaches that of omnidirectional antennas because the dominant direct path is captured regardless of beam width.
- NLOS Conditions: The effect is more pronounced. Narrow beams significantly filter out delayed scattering components arriving from directions outside the main lobe. Consequently, narrow-beam antennas exhibit higher path loss in NLOS scenarios compared to wider beams, as they miss critical multipath components necessary for signal reception.

5. Significance

This research provides a critical tool for network planners and researchers in the mmWave domain. By decoupling path loss modeling from specific hardware measurements, the proposed method allows for:

Rapid System Design: Engineers can simulate network performance for custom or future antenna configurations without conducting new physical campaigns.
Optimization of Beamwidth: It quantifies the trade-off between beam width and path loss in NLOS environments, aiding in the design of beam management strategies for 5G/6G networks.
Scalability: The approach is computationally efficient, making it suitable for large-scale network simulations where deterministic ray tracing is too slow.

The authors note that future work will extend this methodology to 3D (including the elevation plane) and provide further empirical verification.