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Historical Note: Okumura's Measurements and Hata's Formula

In the 1960s, Yoshihisa Okumura conducted extensive propagation measurements in Tokyo. His results, published as sets of curves, were widely used but inconvenient for computation. In 1980, Masaharu Hata fitted Okumura's data with empirical formulae, creating the Okumura–Hata model — still one of the most widely used path-loss models for cellular planning at frequencies below 1.5 GHz.

Definition:
Okumura–Hata Model

Valid for $f_0 \in [150, 1500]$ MHz, $d \in [1, 20]$ km, $h_t \in [30, 200]$ m, $h_r \in [1, 10]$ m.

Urban (large city):

$PL = 69.55 + 26.16\log_{10}(f_0) - 13.82\log_{10}(h_t) - a(h_r) + (44.9 - 6.55\log_{10}(h_t))\log_{10}(d)$

where $f_0$ is in MHz, $d$ in km, heights in metres, and

$a(h_r) = 3.2[\log_{10}(11.75\,h_r)]^2 - 4.97 \quad \text{(large city)}$

$a(h_r) = (1.1\log_{10}(f_0) - 0.7)h_r - (1.56\log_{10}(f_0) - 0.8) \quad \text{(small/medium city)}$

Suburban:

$PL_{\text{sub}} = PL_{\text{urban}} - 2\left[\log_{10}\!\left(\frac{f_0}{28}\right)\right]^2 - 5.4$

Open (rural):

$PL_{\text{open}} = PL_{\text{urban}} - 4.78[\log_{10}(f_0)]^2 + 18.33\log_{10}(f_0) - 40.94$

,

Definition:
COST-231 Hata Model

Extends the Hata model to $f_0 \in [1500, 2000]$ MHz:

$PL = 46.3 + 33.9\log_{10}(f_0) - 13.82\log_{10}(h_t) - a(h_r) + (44.9 - 6.55\log_{10}(h_t))\log_{10}(d) + C_M$

where $C_M = 0$ dB for suburban/open areas and $C_M = 3$ dB for metropolitan centres.

This model is widely used for 2G/3G network planning in the 1800–2000 MHz band.

Hata/COST-231 Path-Loss Model

Compare path loss predictions for urban, suburban, and rural environments. Adjust frequency, base station height, and distance to see how the Hata model behaves.

Parameters

Carrier frequency (MHz)900

BS antenna height (m)30

Mobile height (m)1.5

Definition:
3GPP Path-Loss Models

The 3GPP TR 38.901 standard defines path-loss models for frequencies up to 100 GHz across several scenarios:

Urban Macro (UMa) — LOS:

$PL = 28.0 + 22\log_{10}(d) + 20\log_{10}(f_0)$

Urban Macro (UMa) — NLOS:

$PL = 13.54 + 39.08\log_{10}(d) + 20\log_{10}(f_0) - 0.6(h_r - 1.5)$

Urban Micro (UMi) — LOS:

$PL = 32.4 + 21\log_{10}(d) + 20\log_{10}(f_0)$

Indoor Hotspot (InH) — LOS:

$PL = 32.4 + 17.3\log_{10}(d) + 20\log_{10}(f_0)$

Here $d$ is in metres, $f_0$ in GHz. These models include breakpoint distances, LOS probabilities, and O2I (outdoor-to-indoor) penetration loss.

The 3GPP models are the de facto standard for 4G/5G system-level simulations. They are calibrated from extensive measurement campaigns worldwide.

Path-Loss Model Comparison

Model	Frequency range	Distance range	Use case
Free-space (Friis)	Any	Any (LOS)	Satellite, LOS microwave links
Two-ray	Any	$> d_c$	Open areas with ground reflection
Okumura–Hata	150–1500 MHz	1–20 km	2G/3G macro cells
COST-231 Hata	1500–2000 MHz	1–20 km	2G/3G/4G macro cells
3GPP UMa/UMi	Up to 100 GHz	10 m–5 km	4G/5G system simulations
CI/ABG (mmWave)	28–73 GHz	1–200 m	5G mmWave small cells

Definition:
Close-In (CI) and ABG Models for mmWave

For millimeter-wave frequencies, two models are commonly used:

Close-In (CI) free-space reference model:

$PL(d) = PL_{\text{fs}}(1\,\text{m}) + 10n\log_{10}(d) + X_\sigma$

where $PL_{\text{fs}}(1\,\text{m}) = 20\log_{10}(4\pi/\lambda)$ and $n$ is the PLE (fitted to measurements).

Alpha-Beta-Gamma (ABG) model:

$PL = 10\alpha\log_{10}(d) + \beta + 10\gamma\log_{10}(f_0) + X_\sigma$

where $\alpha$ , $\beta$ , $\gamma$ are fitted parameters. The CI model is preferred for its physical basis (anchored to free-space at 1 m), while ABG offers better flexibility for multi-frequency fitting.

Common Mistake: Using Models Outside Their Valid Range

Mistake:

Applying the Hata model at 3.5 GHz or at distances below 1 km.

Correction:

Every empirical model has a defined validity range (frequency, distance, antenna height). Using a model outside its range can give wildly inaccurate predictions. For 5G frequencies, use the 3GPP TR 38.901 models or the CI/ABG mmWave models.

Quick Check

In the Hata model, what is the purpose of the correction factor $a(h_r)$ ?

It accounts for antenna polarisation

It corrects for mobile antenna height

It models rain attenuation

It accounts for building penetration loss

Correction:

It corrects for mobile antenna height

Correct. $a(h_r)$ is the mobile antenna height correction factor, which adjusts the path loss based on the mobile terminal height relative to the default (1.5 m).

⚠️Engineering Note

Path-Loss Model Calibration and Accuracy

Empirical path-loss models are calibrated to specific measurement campaigns and environments. Applying them without local calibration introduces systematic errors:

Hata model: derived from measurements in Tokyo (1960s). Urban morphology differs significantly in European, American, and Asian cities. The RMSE against local measurements is typically 6–10 dB without local tuning.
3GPP models: calibrated from multi-city campaigns, but the LOS/NLOS probability functions assume specific street layouts. For deployment planning, operators run local drive tests and fit the path-loss exponent $n$ and shadow fading $\sigma$ to measured data.
O2I penetration loss: 3GPP TR 38.901 defines low-loss and high-loss building types. Modern energy-efficient buildings with metalised glass can add 25–35 dB of penetration loss at 3.5 GHz, severely limiting indoor coverage from outdoor cells.
mmWave: human body blockage adds 20–35 dB at 28 GHz. Foliage loss is 0.4–1.0 dB/m, making tree-lined streets problematic for mmWave coverage.

For engineering purposes, always validate models against local measurements before committing to a network design.

Practical Constraints

•
Hata model valid only for 150-1500 MHz, 1-20 km, BS height 30-200 m
•
3GPP O2I high-loss buildings add 25-35 dB at 3.5 GHz
•
Human body blockage at 28 GHz: 20-35 dB
•
Foliage loss at mmWave: 0.4-1.0 dB/m

📋 Ref: 3GPP TR 38.901, §7.4

Okumura–Hata Model

An empirical path-loss model for 150–1500 MHz, based on Okumura's measurements in Tokyo. Widely used for macro-cell planning.

3GPP Path-Loss Model

Standardised models (TR 38.901) for system-level simulations, covering UMa, UMi, InH, and RMa scenarios up to 100 GHz.

Empirical and Semi-Empirical Models