MBX Model for Macro Cell

This model proposes path loss formula for urban area by considering path loss as a result of signal reduction due to free space wavefront spreading, multiple diffraction past rows of buildings, and building shadowing it [1]. The geometry for this model is given in following figure 1.

Figure 1. [1 ], geometry for MBX model

This model can be applied to cases when base station antenna is above, below and near the average rooftop level. However, in this section, formulas could be applied only case when base station antenna is above the rooftop levels.

(1)

This model approaches the problem as Walfisch-Bertoni approaches. It finds that plane wave multiple diffraction fields reduces to

(2)

where,

n is number of buildings, Dh_b is base station antenna height with respect to the average rooftop level, and b is the separation between buildings as shown in figure 1.

(3)

By using above approximations, and including free space loss and diffraction from the rooftop to street loss following formula is derived:

(4)

In this equation, diffraction loss from rooftop to street L_rts is given by following formula:

where,

, in meters

q=tan^-1(Dh_m/x) in radians

The comparison of the model with measurements is given in [1]. The comparison of the model in [1] is done with measurements carried out by Lee [2]. The obtained figure is given below:

Figure 2 [1] Comparison of MBX Model with measurements.

This figure shows that predicted curves for suburban area are lower than the measured value. The predicted signal for urban are (four story houses) is above the measured level.

The comparison of the model is also done with Okumura’s measurements. The obtained plot for comparison is given below by using Wireless Simulator Program given in Figure 3.

In this plot, it is observed that MBX models correlates with Okumura-Hata results for suburban case. Actually, it is expected because it is difficult to have terrain type valid for MBX model in urban and open area. MBX model has 3.3 dB differences for suburban area case, 15 dB for open area and 13.26 dB for urban area case.

Terrain Parameters:

Average Width: 73.8 m

Average Building Height: 11.25m

Percentage of Buildings: 37%

Study Parameters:

Frequency: 900 MHz,

TX Height (hb)=51m

Mobile Height (hm)=1.5m

TX Gain: 13 dBi

City Size: Small/Medium

Area Type :

Okumura-Hata Path Loss :Suburban Area

Okumura-Hata Path Loss (1) : Open Area

Okumura-Hata Path Loss (2) : Urban Area

Figure 3 Comparison of MBX model with Okumura Measurements.

The model is valid for 0.3<R<11 km and frequency 800<f<2000 MHz.

[1] Howard H.Xia, “A simplified Analytical Model for Predicting Path Loss in Urban and Suburban Environments”, IEEE Trans. Veh. Technol. Vol VT-46,No.4, 1997.

[2] W.C.Y.Lee, “ Mobile Cellular Telecommunications Systems”, New York,McGraw-Hill, 1989