What is the difference between the metropolitan correction factor Cm of 0 dB and 3 dB?

COST 231-Hata adds a constant Cm term to the path loss to distinguish environment density. Cm equals 0 dB for medium-sized cities and suburban centers with moderate tree density, and 3 dB for dense metropolitan centers with tall, closely spaced buildings. The 3 dB increment reflects the additional clutter loss from heavy urban construction. Choosing the wrong Cm shifts every predicted path-loss value by 3 dB, which translates directly into a cell-radius error of roughly 10 to 15 percent during coverage planning.

How does the COST 231 model handle the mobile antenna height correction?

The mobile antenna height correction a(hm) is identical to the original Hata small-to-medium city term: a(hm) = (1.1 log10 f - 0.7) hm - (1.56 log10 f - 0.8) dB. For a typical handset at hm = 1.5 m and f = 1800 MHz this correction is only about 0.0 to 0.1 dB, so it is frequently neglected in handheld coverage studies. The term becomes significant only for elevated mobiles such as vehicle-mounted or fixed-wireless terminals where hm reaches 3 to 10 m.

Electromagnetic Theory

COST 231 Model

Q: What frequency range is the COST 231-Hata model valid for?

The COST 231-Hata model is calibrated for 1500 to 2000 MHz, base station antenna heights of 30 to 200 m, mobile antenna heights of 1 to 10 m, and link distances of 1 to 20 km. It was developed specifically because the original Okumura-Hata model only covered 150 to 1500 MHz, leaving the 1800 MHz DCS and 1900 MHz PCS bands without a validated formula. Outside its stated ranges the prediction error grows quickly, and for distances below 1 km or microcell geometries the Walfish-Ikegami model is preferred.

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Developed by the European COST 231 research action and often called the COST-Hata model, this empirical formula extends the Hata model upward in frequency to cover 1500 to 2000 MHz, the band occupied by 1800 MHz DCS and 1900 MHz PCS networks. Building on Okumura's measurement curves, it predicts the median path loss between a base station and a mobile as a function of frequency, antenna heights, and link distance, with a metropolitan correction term C_m that distinguishes dense city cores from suburban areas. Valid for base heights of 30 to 200 m and ranges of 1 to 20 km, it remains a workhorse for macrocell coverage prediction in PCS and 2G/3G cellular planning.

Category: Electromagnetic Theory

Frequency Range: 1500 to 2000 MHz

Valid Distance: 1 to 20 km

Why the COST 231 Extension Was Needed

The original Okumura-Hata formulation, published in 1980, fit Yoshihisa Okumura's Tokyo measurement curves to closed-form equations valid from 150 to 1500 MHz. When European operators began deploying GSM 1800 (DCS-1800) and North American carriers rolled out 1900 MHz PCS, that upper bound of 1500 MHz left the new bands without a validated path-loss tool. The COST 231 working group, part of the European Cooperation in Science and Technology program, re-fitted the Hata equations against propagation data gathered in the 1500 to 2000 MHz range and published the result in 1991 as the COST 231-Hata model.

The structure mirrors Hata closely: a frequency-dependent constant, a base-station antenna-height term that scales the distance dependence, a mobile-antenna-height correction, and a slope on the logarithm of distance. The two visible changes are the revised numeric coefficients on the frequency and constant terms and the addition of the C_m metropolitan factor, which is 0 dB for medium cities and suburbs and 3 dB for dense metropolitan centers. Because it is purely empirical, the model carries no explicit terrain or building-geometry input; clutter is captured statistically rather than ray-traced.

In a coverage-planning workflow the model output feeds directly into the path-loss budget that sets cell radius. A 3 dB error from picking the wrong C_m shifts the predicted edge-of-cell field strength by 3 dB, which moves the usable cell radius by roughly 10 to 15 percent and can change the count of base stations needed to blanket a service area.

Governing Equation and Correction Terms

COST 231-Hata Median Path Loss (urban):
L₅₀ = 46.3 + 33.9·log₁₀(f) − 13.82·log₁₀(h_b) − a(h_m) + (44.9 − 6.55·log₁₀(h_b))·log₁₀(d) + C_m dB

Mobile-Height Correction (small/medium city):
a(h_m) = (1.1·log₁₀(f) − 0.7)·h_m − (1.56·log₁₀(f) − 0.8) dB

Metropolitan Factor:
C_m = 0 dB (medium city / suburban), C_m = 3 dB (dense metropolitan)

Where f = frequency in MHz (1500 to 2000), h_b = base antenna height in m (30 to 200), h_m = mobile antenna height in m (1 to 10), d = distance in km (1 to 20). Example: f = 1800 MHz, h_b = 50 m, h_m = 1.5 m, d = 5 km, C_m = 3 dB → L₅₀ ≈ 160 dB (about 48 dB above the 111.5 dB free-space loss at the same range).

How It Compares to Related Propagation Models

Model	Frequency Range	Distance Range	Environment	Method	Best Use
COST 231-Hata	1500 to 2000 MHz	1 to 20 km	Urban / suburban macrocell	Empirical	PCS / DCS coverage
Okumura-Hata	150 to 1500 MHz	1 to 20 km	Urban / suburban / rural	Empirical	VHF/UHF cellular
COST 231 Walfish-Ikegami	800 to 2000 MHz	0.02 to 5 km	Urban microcell, street canyon	Semi-deterministic	Dense urban microcell
Free-Space	Any	Line of sight	Unobstructed	Analytic	Link-budget baseline
Longley-Rice (ITM)	20 MHz to 20 GHz	1 to 2000 km	Irregular terrain	Deterministic + statistical	Long-haul, terrain-aware

Common Questions

Frequently Asked Questions

What frequency range is the COST 231-Hata model valid for?

It is calibrated for 1500 to 2000 MHz, base heights of 30 to 200 m, mobile heights of 1 to 10 m, and distances of 1 to 20 km. The original Okumura-Hata only covered 150 to 1500 MHz, leaving the 1800 MHz DCS and 1900 MHz PCS bands unsupported. Below 1 km or for microcell geometries, the Walfish-Ikegami model is preferred.

What is the difference between the metropolitan factor C_m of 0 dB and 3 dB?

C_m = 0 dB applies to medium-sized cities and suburban centers with moderate clutter; C_m = 3 dB applies to dense metropolitan cores with tall, closely spaced buildings. The 3 dB increment captures extra urban clutter loss. Selecting the wrong value shifts every predicted path-loss figure by 3 dB, changing planned cell radius by roughly 10 to 15 percent.

How is the mobile antenna height correction a(h_m) calculated?

It uses the Hata small/medium-city term a(h_m) = (1.1·log₁₀(f) − 0.7)·h_m − (1.56·log₁₀(f) − 0.8) dB. At h_m = 1.5 m and 1800 MHz it is only about 0.0 to 0.1 dB, so it is often neglected for handsets, becoming significant only for elevated vehicle or fixed-wireless terminals at 3 to 10 m.

Related Terms

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