Investigation of Modified Hata Propagation Models

Spectrum Planning Team Radiofrequency Planning Group Australian Communications Authority

Document: SP 2/01 Date: April 2001

INTRODUCTION ........................................................................................................................................ 3 BACKGROUND........................................................................................................................................... 3 EMPIRICAL HATA MODEL .................................................................................................................... 3 MODIFIED MODELS ................................................................................................................................. 4 ITU-R P.529-2 ........................................................................................................................................... 5 ITU-R P.529-3 ........................................................................................................................................... 5 ERC REPORT 68 ...................................................................................................................................... 6 COMPARISON OF MODIFIED MODELS.............................................................................................. 6 RECOMMENDATIONS ............................................................................................................................. 7 BIBLIOGRAPHY......................................................................................................................................... 7 ATTACHMENTS......................................................................................................................................... 8 OKUMURA AND HATA CURVES 150 MHZ ..................................................................................................... 8 OKUMURA AND MODIFIED HATA CURVES 150 MHZ ..................................................................................... 9 OKUMURA AND MODIFIED HATA CURVES 450 MHZ ................................................................................... 10 OKUMURA AND MODIFIED HATA CURVES 900 MHZ ................................................................................... 11 OKUMURA AND MODIFIED HATA CURVES 1500 MHZ ................................................................................. 12 CONVERTING PROPAGATION LOSS AT RECEIVER TO FIELD STRENGTH ....................................................... 13

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INTRODUCTION The purpose of this paper is to review several modified Hata models. The different modified Hata models are compared against the Okumura field strength curves from which the original Hata model was derived. The models are compared for different frequencies, distances and base transmitter heights. The mobile antenna height in all cases was assumed to be 1.5m and the field strength values are calculated for a 1 kW ERP transmitter. A recommendation is made on which model most closely approximates the Okumura field strength curves.

BACKGROUND The original Hata model was published in 1980 by Masaharu Hata [1]. Hata took the information in the field strength curves produced by Yoshihisa Okumura [2] and produced a set of equations for path loss. Okumura carried out a number of propagation studies in and around Tokyo City and produced a set of curves of field strength against distance. Two of the limitations of the Hata model are that it has a limited path length and a limited frequency range. A number of modified models have been produced to extend the path length and frequency range. These modified models vary slightly from each other and some of these models more closely match the Okumura curves than others do.

EMPIRICAL HATA MODEL The Hata empirical model uses a propagation equation split up into two terms, a term that has a logarithmic dependence on distance and a term that is independent of distance. The Hata model also includes adjustments to the basic equation to account for Urban, Suburban and Open area propagation losses. For more detail see reference [1]. The variables are described in the attachments at the end of this report. The Hata equation for propagation loss in an urban area is given by: L p = 69.55 + 26.16 log( f ) − 13.82 log(hb ) − a (hm ) + (44.9 − 6.55 log(hb )) * log(d ) Where, in the case of propagation loss in a medium to small city: a (hm ) = (1.1 log( f ) − 0.7) * hm − (1.56 log( f ) − 0.8) The adjustment for propagation loss in a suburban area is: L ps = L p (urban area) − 2 * (log( f / 28)) 2 − 5.4

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The adjustment for propagation loss in an open area is: L po = L p (urban area) − 4.78(log( f )) 2 + 18.33 log( f ) − 40.94 The model is suitable for use over the ranges: Frequency range 150 − 1500 MHz Base station height 30 − 200 m Mobile height 1 − 10 m Distance range 1 − 20 km Figure 1 in the Attachments compares the field strength curves generated by the Hata model against the Okumura field strength curves for urban areas. At distances below 30 km the Hata curves compare very well, to within ±1dB of the Okumura curves. At distance above 30 km the Okumura curves drop below the Hata curves. At 100 km the difference varies from 7 dB to 15 dB.

MODIFIED MODELS The modified Hata models were produced to improve on the range limitation that the original Hata model had. The first modified model appeared in a CCIR report [6] in an attempt to extend the Hata model to cover greater distance. An ambiguous equation in the CCIR report lead to an uncertain interpretation. In particular as to how the distance term was raised. There was uncertainty about whether the power term includes the whole log term or just the distance term. The equation in the CCIR report was written as shown below. E= 69.82 − 6.16 log f + 13.82 log hb + a(hm) − (44.9 − 6.55 log hb) * log d b Some later models included just the distance term raised to the power b and some included the whole log distance term raised to the power b. In general the original equation was kept with new terms added to extend the distance range. To aid comparison with the original Okumura curves all models have been converted to calculate field strength from a 1 kW ERP transmitter. Some of the modified models have been published in this form and there is some small variation in some of the constants in the different models due to rounding errors. Three models that were compared are the ITU-R P.529-2 [4], ITU-R P.529-3 [5] and the model used in the ERC Report 68 [3].

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ITU-R P.529-2 The equation in this model has the distance term only, raised to the power b . The equation is stated as: E = 65.55 − 6.16 log( f ) + 13.82 log(hb ) + a (hm ) − (44.9 − 6.55 log(hb )) * log(d b ) Where: a (hm ) = (1.1 log( f ) − 0.7) * hm − (1.56 log( f ) − 0.8) b = 1 for d 20 km

These equations are meant to be extensions of the original Hata equation. When the distance is less than 20 km, which is in the useable range of the original Hata equation, the modified equation should equal the original equation. This equation does not equal the original equation for a distance of less than 20 km. The first constant 65.55 should have been 69.82. This model claims to be suitable for use over the ranges: Frequency range 150 − 1500 MHz Base station height 30 − 200 m Mobile height 1 − 10 m Distance range 1 − 100 km ITU-R P.529-3 The equation in this model has the whole log distance term raised to the power b . It also includes a modification to the base height term. This equation does equate to the original Hata equation for distances less than 20km. The equation is: E = 69.82 − 6.16 log( f ) + 13.82 log(hb ) + a (hm ) − (44.9 − 6.55 log(hb )) * (log(d )) b Where: a (hm ) = (1.1 log( f ) − 0.7) * hm − (1.56 log( f ) − 0.8) b = 1 for d