Hata Propagation Model

A closed-form empirical model that estimates median land-mobile path loss from frequency, distance, antenna heights, and environment-specific corrections inside a declared validity envelope.

Version

v2 · 2026-09-19 · History

Domain-specific #

1984

Domain group

Natural Sciences

Origin domain

Physics

Subdomains

Radio Propagation, Land Mobile Path Loss → Physics

Aliases

Okumura–Hata model

Core Idea

The Hata propagation model is a closed-form empirical estimator of median transmission path loss for VHF/UHF land-mobile links. Masaharu Hata fitted formulas to the measurement-based Okumura method so that planners could compute urban loss from carrier frequency, transmitter–receiver distance, effective base-station antenna height, mobile antenna height, and an environment correction without reading families of curves. Suburban and open-area forms subtract calibrated corrections from the urban baseline.

The identity includes its empirical envelope. Hata's original paper states 100–1500 MHz, 1–20 km, base height 30–200 m, mobile height 1–10 m, quasi-smooth terrain, and isotropic-antenna propagation loss; many engineering summaries use a conservative lower frequency of 150 MHz.

How would you explain it like I'm…

Signal Fading Recipe

When a radio tower sends a signal to a phone or walkie-talkie, the signal gets weaker as it travels, especially through a city. People measured how much weaker it got in lots of places, and someone turned all those measurements into one easy recipe. You put in how far away you are, how tall the antennas are, and what the area is like, and it guesses the weakening. It only works well for the kinds of places and sizes they measured.

Signal-Loss Guessing Formula

The Hata Propagation Model is a formula for guessing how much a radio signal fades on its way from a base station to a mobile radio. It came from fitting simple formulas to an older method based on real measurements that used lots of charts. You plug in the radio frequency, the distance, the heights of both antennas, and a correction for the type of place, like city, suburbs, or open country. It gives a typical (median) amount of signal loss, not the exact loss at every spot. It's only trusted inside the range of frequencies, distances and heights it was built from.

Empirical Median Path-Loss Model

The Hata Propagation Model estimates path loss, how much a radio signal weakens between a base station and a mobile receiver, for VHF/UHF land-mobile radio. It is empirical. Masaharu Hata fitted closed-form formulas to the measurement-based Okumura method, so planners could compute loss directly instead of reading families of curves. The inputs are carrier frequency, distance, effective base-station antenna height, mobile antenna height, and an environment correction. The output is a median loss for urban areas, and suburban and open-area versions subtract corrections from the urban result. Hata's paper covers 100–1500 MHz, 1–20 km, base heights of 30–200 m, mobile heights of 1–10 m, and quasi-smooth terrain. Many summaries use 150 MHz as a safer lower limit. Outside these ranges, using it is extrapolation.

 

The Hata Propagation Model is a closed-form empirical estimator of median transmission path loss for VHF/UHF land-mobile links. Masaharu Hata derived it by fitting formulas to the Okumura method, which was built from measurement curves. The urban formula takes carrier frequency, transmitter–receiver distance, effective base-station antenna height, mobile antenna height, and an environment-dependent correction. Suburban and open-area variants subtract calibrated corrections from the urban baseline. Because it is empirical, its validated envelope is part of what the model is. Hata's original paper states 100–1500 MHz, 1–20 km, base heights of 30–200 m, and mobile heights of 1–10 m, with quasi-smooth terrain and isotropic-antenna propagation loss. Many engineering summaries conservatively take 150 MHz as the lower frequency bound. Applying the formulas outside these ranges is extrapolation, not an application of the validated model. It also yields only median loss, not location-specific predictions.

Scope of Application

Hata was designed for land-mobile system planning where a base antenna stands substantially above a vehicular or portable terminal. Engineers use the model for early coverage contours, link-budget comparison, candidate-site screening, and sensitivity studies across distance, height, frequency, and broad clutter class. Its computational simplicity made the Okumura measurement program usable in large planning calculations.

The urban equation is the reference. A small/medium-city mobile-height correction differs from the large-city piecewise correction. Suburban and open forms modify urban loss. Uses should state which branch was chosen and why the terrain and morphology resemble its calibration class.

Clarity

For a small or medium city, the urban median-loss equation is

\[ L_U=69.55+26.16\log_{10}f-13.82\log_{10}h_b-a(h_m) +(44.9-6.55\log_{10}h_b)\log_{10}d, \]

with

\[ a(h_m)=(1.1\log_{10}f-0.7)h_m-(1.56\log_{10}f-0.8). \]

Manages Complexity

The model compresses a difficult environment-dependent propagation field into a few interpretable coordinates. Frequency, distance, two antenna heights, and a morphology branch replace exhaustive drive-test curves at the preliminary-planning stage. The distance coefficient itself changes with base height, so the model retains an interaction that a single universal path-loss exponent would discard.

Abstract Reasoning

Within the envelope, increasing distance increases predicted loss because the distance coefficient remains positive for allowed base heights. Raising the base antenna generally lowers the predicted loss, though the full change includes its effect on distance slope. Increasing frequency generally raises the urban baseline in this range. Applying the suburban or open correction lowers loss relative to the urban reference for the same numeric inputs.

Knowledge Transfer

The exact model transfers among qualifying land-mobile planning cases because the same variables, coefficients, branches, and median-loss output recur. It transfers from urban to suburban or open settings through defined correction formulas, not by metaphor. COST-231 and other derivatives demonstrate instrument lineage, but their altered ranges and coefficients keep them distinct models.

The portable skeleton—signal source, medium, attenuation, distance, and reach—belongs to Propagation. Empirical calibration and prediction travel more broadly as modeling practices, but a traffic forecast or epidemiological spread curve does not instantiate Hata.

Relationships to Other Abstractions

Current abstraction Hata Propagation Model Domain-specific

Parents (1) — outgoing typed relations

• Hata Propagation Model presupposes Propagation Prime

  The broader abstraction is Propagation: the model estimates how a radio signal attenuates while spreading from a source through a cluttered environment.

Hierarchy path (1) — routes to 1 parentless root

• Hata Propagation Model → presupposes Propagation

Neighborhood in Abstraction Space

Hata Propagation Model sits in a sparse region of the domain-specific corpus (92^nd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2769 abstractions)

Nearest neighbors

• Rugosity — 0.80
• Wireless triangulation — 0.79
• Ziggurat Algorithm — 0.79
• Variogram — 0.79
• Floor Effect — 0.78

Computed from structural-signature embeddings · 2026-10-25