Air-to-ground path loss

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 1805.00881 §XI. The clear-path and blocked-path cases each get an average loss, and the model mixes them with a probability 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 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 1805.00881 eq. 1 1805.00881 eq. 2 1805.00881 eq. 3 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 1805.00881 §XI. Card: UAV civil-applications survey (2018).

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 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 1805.00881 §XI. As the horizontal distance grows, the free-space part rises and the penetration part falls with the incidence angle 1805.00881 §XI. The model is the survey's answer to the outdoor-only scope of the low altitude model 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 1805.00881 eq. 7 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 1805.00881 eq. 9 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 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 1805.00881 eq. 6. The survey says the fit comes from field measurements that cover both terrestrial and aerial samples 1805.00881 §XI. Its comparison table lists the setting as uplink at 850 MHz 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 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.

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.

# 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

# 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

# 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 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 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 1805.00881 §XI.

Papers

• UAV civil-applications survey (2018): 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.