Propagation & Channels

COST 231 Walfish-Ikegami

Q: What is the valid frequency and distance range for the COST 231 Walfish-Ikegami model?

The model is defined for frequencies from 800 MHz to 2000 MHz, base station antenna heights of 4 to 50 m, mobile heights of 1 to 3 m, and transmitter-to-receiver separations of 0.02 km to 5 km. It was calibrated against COST 231 measurement campaigns in European cities, so it is most accurate for dense and medium-density urban environments with reasonably uniform building heights. Outside these limits, the multiscreen diffraction terms lose physical validity and the prediction error grows; for ranges below 20 m or above 5 km, or for frequencies into the millimeter-wave bands, ray-tracing or higher-frequency models are preferred.

Q: How does the model differentiate between line-of-sight and non-line-of-sight conditions?

For a line-of-sight street canyon where the base station is below the rooftops, the model uses a simple two-term street-canyon equation: L = 42.6 + 26 log d + 20 log f, valid for d of at least 20 m. For the more common non-line-of-sight case the total loss is the sum of free-space loss, the rooftop-to-street diffraction and scatter term Lrts, and the multiscreen diffraction term Lmsd. When Lrts plus Lmsd is negative or zero, the model collapses to free-space loss alone. This branching is why the model is described as semi-empirical: the LOS branch is empirical while the NLOS branch is built on Walfisch-Bertoni multiscreen diffraction physics.

Q: What is the difference between the Walfish-Ikegami model and the Okumura-Hata model?

Okumura-Hata is a fully empirical model derived from Tokyo drive-test curves and uses only frequency, antenna heights, and distance with a coarse urban or suburban correction; it extends down to about 1 km and up to about 1500 MHz (extended to 2000 MHz in the COST 231-Hata variant). Walfish-Ikegami adds explicit building geometry: average building height, building separation, street width, and street orientation angle, plus a physical rooftop diffraction mechanism. This lets it predict microcell scenarios with base antennas below rooftop level and short ranges down to 20 m, where Hata is undefined. The cost is that Walfish-Ikegami needs detailed morphology data that Hata does not require.

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Widely used for cellular coverage planning, this semi-empirical model predicts median path loss in built-up urban areas from 800 MHz to 2 GHz. Rather than treating the city as a single clutter factor, it combines free-space path loss with two physical mechanisms: rooftop-to-street diffraction and multiscreen diffraction across rows of buildings. By accepting explicit morphology inputs (average building height, building separation, street width, and the angle of the incident wave relative to the street), it captures microcell behavior where the base antenna sits below the rooftop line, a regime where simpler models such as Okumura-Hata are undefined. The result is a model accurate enough for dense European-style city grids yet light enough to run over thousands of pixels in a coverage tool.

Frequency: 800 MHz to 2 GHz

Range: 20 m to 5 km

Base Height: 4 to 50 m

How the Walfish-Ikegami Model Estimates Urban Loss

The model emerged from the European COST 231 research action of the early 1990s, which combined the rooftop-diffraction theory of Walfisch and Bertoni with the street-level scattering work of Ikegami. It splits the propagation problem into a line-of-sight (LOS) street-canyon case and a non-line-of-sight (NLOS) case. In the LOS branch, when the mobile and base antenna can see each other down a street, a two-parameter formula based on Stockholm measurements applies. The far more common NLOS branch treats the signal as a wave that propagates over the rooftops by multiple forward diffraction across building rows, then diffracts down from the last rooftop edge into the street where the mobile sits.

The NLOS total loss is the sum of three components: ordinary free-space loss L₀, the rooftop-to-street diffraction and scatter loss L_rts, and the multiscreen diffraction loss L_msd. The L_rts term depends on street width w, the height difference between the rooftop and the mobile, and a street-orientation correction that accounts for whether the street runs toward or across the base station. The L_msd term is the most involved: it models the cumulative diffraction over a series of equally spaced building screens and changes form depending on whether the base antenna is above, level with, or below the average rooftop height h_roof.

Because L_rts and L_msd can individually go negative under favorable geometry, the model clamps their sum at zero; when L_rts + L_msd ≤ 0 the prediction reverts to pure free-space loss. This guard prevents the unphysical result of urban clutter improving the signal relative to free space, and it is one of the practical details engineers must implement carefully when coding the model into a planning tool.

Governing Equations

Line-of-sight street canyon (d ≥ 20 m):
L_LOS = 42.6 + 26·log₁₀(d) + 20·log₁₀(f) dB

Non-line-of-sight total loss:
L_NLOS = L₀ + L_rts + L_msd (when L_rts + L_msd > 0)
L_NLOS = L₀ (when L_rts + L_msd ≤ 0)

Free-space term:
L₀ = 32.4 + 20·log₁₀(d) + 20·log₁₀(f) dB

Rooftop-to-street diffraction:
L_rts = −16.9 − 10·log₁₀(w) + 10·log₁₀(f) + 20·log₁₀(Δh_mobile) + L_ori

Where d = distance in km, f = frequency in MHz, w = street width in m, Δh_mobile = h_roof − h_mobile, and L_ori is the street-orientation correction (range −10 to +4 dB). Example: f = 900 MHz, d = 1 km, w = 25 m, h_roof = 30 m, h_base = 12 m (base below rooftop), with b = 50 m typically yields a total NLOS loss near 160 dB (about 150 dB for a street running toward the base, rising to roughly 165 dB for a perpendicular street).

Geometry Inputs and Typical Values

Input Parameter	Symbol	Typical Range	Role in Model
Frequency	f	800 to 2000 MHz	Sets free-space and diffraction loss slope
Base antenna height	h_base	4 to 50 m	Selects above/below-rooftop L_msd branch
Mobile height	h_mobile	1 to 3 m	Drives rooftop-to-street drop Δh
Average building height	h_roof	9 to 50 m	Defines rooftop diffraction edge
Building separation	b	20 to 50 m	Number of multiscreen diffractions
Street width	w	b/2 (typ. 10 to 25 m)	Sets L_rts magnitude
Street orientation	φ	0° to 90°	Orientation correction L_ori

Common Questions

Frequently Asked Questions

What is the valid frequency and distance range for the COST 231 Walfish-Ikegami model?

The model is defined for 800 MHz to 2000 MHz, base antenna heights of 4 to 50 m, mobile heights of 1 to 3 m, and distances of 0.02 km to 5 km. It was calibrated on COST 231 measurements in European cities, so it is most accurate for dense and medium-density urban grids with fairly uniform building heights. Below 20 m, beyond 5 km, or into the millimeter-wave bands, the multiscreen diffraction terms lose validity and ray-tracing is preferred.

How does the model differentiate between line-of-sight and non-line-of-sight conditions?

For an LOS street canyon with the base below rooftop level it uses L = 42.6 + 26·log₁₀(d) + 20·log₁₀(f), valid for d ≥ 20 m. For NLOS the loss is L₀ + L_rts + L_msd; when L_rts + L_msd ≤ 0 the model reverts to free-space loss alone. The LOS branch is empirical while the NLOS branch is built on Walfisch-Bertoni multiscreen diffraction physics.

What is the difference between the Walfish-Ikegami model and the Okumura-Hata model?

Okumura-Hata is fully empirical, using only frequency, antenna heights, and distance with a coarse clutter correction, and is defined down to about 1 km. Walfish-Ikegami adds explicit building geometry (height, separation, street width, orientation) and a physical rooftop diffraction mechanism, letting it model microcells with antennas below rooftop level down to 20 m. The trade-off is that it needs detailed morphology data Hata does not require.

Related Terms

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