---
kind: concept
slug: air-to-ground-path-loss
title: Air-to-ground path loss
summary: >-
  Models for the signal loss between an aerial platform and a ground user, split into a clear-line-of-sight and a blocked-path case weighted by an elevation-angle probability. Five variants (low altitude, indoor users, high altitude, cellular-to-UAV, UAV-to-UAV). The constants are not given in the surveyed source, so each model needs values from its original study or from measurement.
tags: [wireless, uav, path-loss, channel-model]
papers: ["1805.00881"]
related: []
status: draft
updated_at: 2026-10-19
---

## Overview

A platform in the air, such as a drone or a balloon, talks to a receiver on
the ground, and the received power falls with distance. Most air-to-ground
models write the loss in dB as a distance term plus an extra loss. The extra
loss depends on whether the direct path is clear, and that depends on the
elevation angle from the user to the platform [arxiv:1805.00881 §XI]. The
clear-path and blocked-path cases each get an average loss, and the model
mixes them with a probability [arxiv:1805.00881 eq. 1].

The invariant the variants share is a distance-dependent free-space style
term plus environment-dependent extra losses. The constants that tune these
terms are environment-specific. The surveyed source does not give numbers for
most of them [arxiv:1805.00881 §XI]. The corpus has one paper for this
concept, so every claim below comes from it, and the models are reported as
the survey describes them, not checked against their original studies.

## Variants

### Low altitude platform, outdoor users

The mean loss is a weighted sum of a line-of-sight (LOS) branch and a
non-line-of-sight (NLOS) branch. The LOS probability depends on the elevation
angle, and both branches use a free-space style term plus an extra loss per
environment [arxiv:1805.00881 eq. 1] [arxiv:1805.00881 eq. 2]
[arxiv:1805.00881 eq. 3] [arxiv:1805.00881 eq. 4]. The survey says the model
comes from a simulation with ray tracing of direct, reflected and diffracted
paths. Its receivers fall into three groups, and the model is fitted to the
first two. The third group, in deep fading, is about 3% of receivers and is
left out [arxiv:1805.00881 §XI]. Card:
[UAV civil-applications survey (2018)](/papers/1805.00881).

### Outdoor-to-indoor (UAV to an indoor user)

The loss is a sum of three parts: a free-space term that grows with the
outdoor distance, a building penetration term that depends on the incidence
angle, and an indoor term that grows with the distance inside the building
[arxiv:1805.00881 eq. 5]. The survey gives the reviewed model's values for
its constants: w = 20, g1 = 32.4, g2 = 14, g3 = 15 and g4 = 0.5, without
units [arxiv:1805.00881 §XI]. As the horizontal distance grows, the free-space
part rises and the penetration part falls with the incidence angle
[arxiv:1805.00881 §XI]. The model is the survey's answer to the outdoor-only
scope of the low altitude model [arxiv:1805.00881 §XI].

### High altitude platform, built-up areas

The LOS probability is a logistic-type curve in the elevation angle, with
five empirical parameters a to e [arxiv:1805.00881 eq. 7]
[arxiv:1805.00881 eq. 8]. The LOS and NLOS losses are written in km and GHz,
with a constant of 92.4 and, for the NLOS case, a shadowing term that depends
on the elevation angle [arxiv:1805.00881 eq. 9] [arxiv:1805.00881 eq. 10]. The
survey says the model covers 2 to 6 GHz and four built-up area types:
suburban, urban, dense urban and urban high-rise [arxiv:1805.00881 §XI].

### Cellular base station to UAV

This model describes the link from a terrestrial cellular base station up to a
flying UAV, not the link from a UAV down to the ground. The loss is a
terrestrial term in 10 α log(d), an excess aerial term that depends on the
depression angle, and a zero-mean Gaussian shadowing term whose spread also
depends on the angle [arxiv:1805.00881 eq. 6]. The survey says the fit comes
from field measurements that cover both terrestrial and aerial samples
[arxiv:1805.00881 §XI]. Its comparison table lists the setting as uplink at
850 MHz [arxiv:1805.00881 §XI].

### UAV to UAV

The survey says UAV-to-UAV channels are mostly line of sight, so free-space
path loss can be used. It adds that high Doppler shifts are a problem,
especially for fixed-wing UAVs [arxiv:1805.00881 §XI]. This is a default
rather than a fitted model.

## When to use which

The survey does not compare the models on accuracy. The table below uses only
the scope and limits the survey states.

| Situation | Use | Why |
|---|---|---|
| Ground users outdoors, low-altitude UAV | Low altitude platform | Its LOS probability is a function of elevation angle and its branch terms are simpler than the high altitude model's. The survey lists 2D outdoor users as its scope [arxiv:1805.00881 §XI] |
| Users inside buildings | Outdoor-to-indoor | The survey says the outdoor low altitude model does not cover indoor users [arxiv:1805.00881 §XI] |
| Built-up areas at 2 to 6 GHz, high-altitude platform | High altitude platform | It is fitted for that band and those four area types [arxiv:1805.00881 §XI] |
| Base station measuring a flying UAV | Cellular-to-UAV | It is built from field samples for that direction. The survey notes it does not cover denser urban areas or millimetre-wave bands [arxiv:1805.00881 §XI] |
| UAV-to-UAV link | Free-space loss | The survey describes these channels as mostly line of sight [arxiv:1805.00881 §XI] |
| Dense urban areas, 5G bands, or other bands not listed above | None of these without new data | The comparison table lists unconsidered 5G bands for every model except UAV-to-UAV [arxiv:1805.00881 §XI] |
| Any model, no site data | Take constants from the original study or measure them | The survey gives no numeric values for α, β, ζ, a to e, A, B or the shadowing terms [arxiv:1805.00881 §XI] |

## Implementation sketch

The shared core is a probability-weighted mix of two branch losses. The
branch losses differ by variant. Pseudocode below, in our own words, with
citations to the equations it follows.

```pseudocode
# Low altitude platform: LOS-weighted mean loss [eq. 1] [eq. 2] [eq. 3] [eq. 4]
# Input:  elevation theta (radians), distance d (m), carrier fc (Hz)
# Output: mean path loss in dB

def lap_path_loss(theta, d, fc, alpha, beta, zeta_los, zeta_nlos):
    c = 3e8  # speed of light, m/s
    # LOS probability from the elevation in degrees  [eq. 2]
    deg = 180 / pi * theta
    p_los = 1 / (1 + alpha * exp(-beta * (deg - alpha)))
    # Free-space style term shared by both branches  [eq. 3] [eq. 4]
    fspl = 20 * log10(4 * pi * fc * d / c)
    l_los = fspl + zeta_los
    l_nlos = fspl + zeta_nlos
    # Weight the two branches by the LOS probability  [eq. 1]
    return p_los * l_los + (1 - p_los) * l_nlos
```

```pseudocode
# High altitude platform: same mixing, different terms  [eq. 7] to [eq. 10]
# Input:  elevation theta, distance d_km (km), frequency f_ghz (GHz)
# Output: mean path loss in dB

def hap_path_loss(theta, d_km, f_ghz, a, b, c_, d_, e,
                  zeta_los, zeta_nlos, l_s):
    # Empirical LOS probability; c_ and d_ are not the speed of light  [eq. 8]
    p_los = a - (a - b) / (1 + ((theta - c_) / d_) ** e)
    # Base loss in dB with the constant 92.4  [eq. 9] [eq. 10]
    base = 20 * log10(d_km) + 20 * log10(f_ghz) + 92.4
    l_los = base + zeta_los
    l_nlos = base + l_s + zeta_nlos  # l_s: shadowing, depends on theta
    return p_los * l_los + (1 - p_los) * l_nlos
```

```pseudocode
# UAV to indoor user: three additive terms  [eq. 5]
# Input:  outdoor distance d_out, frequency f, incidence angle theta_i,
#         indoor distance d_in
# Output: total loss (units not stated in the source)

def indoor_path_loss(d_out, f, theta_i, d_in):
    # Constants of the reviewed model  [eq. 5] [§XI]
    w, g1, g2, g3, g4 = 20, 32.4, 14, 15, 0.5
    l_free = w * log10(d_out) + w * log10(f) + g1  # free-space part
    l_pen = g2 + g3 * (1 - cos(theta_i)) ** 2      # penetration part
    l_in = g4 * d_in                               # indoor part
    return l_free + l_pen + l_in
```

Notes on where the variants differ:

- The source writes "20 log" without a base. The sketches use base 10, which
  is the usual meaning, but the survey does not state it.
- Units differ. The low altitude model uses SI units, implied by the speed of
  light in its equation. The indoor model does not state units for its
  distances or frequency. The high altitude model uses km and GHz.
- The angle units differ. In the low altitude model, the LOS probability
  multiplies θ by 180/π, so θ is in radians there. The high altitude model
  uses θ directly and does not state a unit.
- In the low altitude model, α is both a constant and the offset inside the
  exponent [arxiv:1805.00881 eq. 2]. Check the original study before coding
  it.
- The cellular-to-UAV spread is written as aθ + σ_o, but the text calls it an
  angle-dependent standard deviation. The survey does not define a or σ_o
  [arxiv:1805.00881 eq. 6] [§XI].

## Contradictions

None known. The corpus has one paper for this concept, so no two papers
disagree. The survey has its own inconsistencies, listed in the notes above.
One citation issue is worth knowing: the comparison table names an ITU
guideline as the source of the indoor model, while the text attributes that
model to a different reviewed study [arxiv:1805.00881 §XI].

## Papers

- [UAV civil-applications survey (2018)](/papers/1805.00881): a 2018 survey whose wireless-coverage section reviews the air-to-ground and cellular-to-UAV path-loss models on this page. It has no new method or experiments.