Propagation Models

We concentrate on cellular operation. There is a fixed station (FS) and mobile stations (MSs) moving through the cell. A cell is the area of responsibility of the fixed station, a cell site. It usually is pictured as a hexagon in shape, although its propagation profile is more like a circle with the fixed station in its center. Cell radii vary from 1 km (0.6 mi) in heavily built-up urban areas to 30 km (19 mi) or somewhat more in rural areas.

18.3.2.1 Path Loss or Transmission Loss. We recall the free-space loss (FSL) formula in Section 9.2.3. It simply stated that FSL was a function of the square of the distance and the square of the frequency plus a constant. It is a very useful formula if the strict rules of obstacle clearance are obeyed. Unfortunately, in the cellular situation, it is impossible to obey these rules. Then to what extent must this free-space loss formula be modified by the proximity of the earth and by the effects of trees, buildings, and hills in, or close to, the transmission path?

There have been a number of models that have been developed that are used as a basis for the calculation of transmission loss, several assumptions are made:

• That we will always use the same frequency band, often 800 or 900 MHz. Thus it is common to drop the frequency term (the 20 log F term) in the FSL formula and include a constant that covers the frequency term. If we wish to use the model for another band, say 1800 MHz, a scaling factor is added.

• That we will add a term to compensate for the usual great variance between the cell site antenna height when compared to the mobile (or hand-held) antenna height. We often call this the height-gain function, and it tends to give us an advantage. It is often expressed as -20 log(hThR), where hT is the height of the transmit antenna (cell site) and hR is the height of the receive antenna (on the mobile platform). These are comparative heights. Commonly, the mobile platform antenna height is taken as 6 ft or 3 m.

• That there is a catch-all term for the remainder of the losses, which in some references is expressed as ¡3 (in dB).

• That at least three models express the free-space loss as just 40 log dm (dm is distance in meters).

18.3.2.2 The Okumura Model. Okumura et al. (Ref. 3) carried out a detailed analysis for path predictions around Tokyo for mobile terminals. Hata (Ref. 4) published an empirical formula based on Okumura's results to predict path loss. The Okumura/Hata model is probably one of the most widely applied path loss models in the world for cellular application. The formula and its application follow.

where r is between 150 MHz and 1500 MHz, ht is between 30 m and 300 m, and d is the path distance and is between 1 km and 20 km.

A(hr) is the correction factor for mobile antenna height and is computed as follows: For a small- or medium-size city,

A(hr) = (1.1 log f - 0.7)hr - (1.56 log f - 0.8)(dB), (18.2a)

where hr is between 1 and 10 m. For a large city,

Example. Let f = 900 MHz, ht = 40 m, hr = 5 m, and d = 10 km. Calculate A(hr) for a medium-size city.

A(hr) = 12.75 - 3.8 = 8.95 dB LdB = 69.55 + 72.28 - 22.14 - 8.95 + 34.4 = 145.15 dB.

18.3.2.3 Building Penetration. For a modern multistory office building at 864 and 1728 MHz, transmission loss (Lde) includes a value for clutter loss L(v) and is expressed as follows:

where the attenuation in decibels of the floors and walls was af and aw, and the number of floors and walls along the line d were nf and nw, respectively. The values of L(v) at 864 MHz and 1728 MHz were 32 dB and 38 dB, with standard deviations of 3 dB and 4 dB, respectively (Ref. 2).

Another source (Ref. 5) provided the following information: At 1650 MHz the floor loss factor was 14 dB, while the wall losses were 3-4 dB for double plasterboard and 7-9 dB for breeze block or brick. The parameter L(v) was 29 dB. When the propagation frequency was 900 MHz, the first floor factor was 12 dB and L(v) was 23 dB. The higher value for L(v) at 1650 MHz was attributed to a reduced antenna aperture at this frequency compared to 900 MHz. For a 100-dB path loss, the base station and mobile terminal distance exceeded 70 m on the same floor, was 30 m for the floor above, and was 20 m for the floor above that, when the propagation frequency was 1650 MHz. The corresponding distances at 900 MHz were 70 m, 55 m, and 30 m. Results will vary from building to building, depending on the type of construction of the building, the furniture and equipment it houses, and the number and deployment of the people who populate it.