# The Wireless Propagation Models Engineering Essay

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The wireless transmission is dependent on the medium of transmission. The atmospheric conditions such as temperature, humidity and rain affect the wireless transmission by absorbing the electromagnetic waves. The variations in the atmospheric layers also affect the transmission characteristics and causes transmission losses or fading. Apart from the atmospheric effects the received power varies due to reflection, diffraction and scattering. The electromagnetic waves are reflected by the objects whose dimension is very large compared to wavelength of transmission, e.g. the buildings, earth's surface etc. When the radio waves are obstructed by a sharp edge surface, they tend to bend around the obstruction due to diffraction and allows wave to reach even non line of sight areas. The scattering occurs when the medium of transmission has dense particles of size smaller than the wavelength of transmitted wave. For example, street signs, foliage etc. In case of mobile communication all these obstacles play very important roles especially in urban areas making the calculations using free space propagation invalid in such environments.

The network planning and designing requires that all the above mentioned parameters be taken into account. The propagation models are used to emulate the actual conditions and allow network designing as per the site conditions. Various type of models exist for various type of environmental and site conditions and they are used extensively for conducting feasibility studies, network planning and network deployment. These models are used for number of other functions such as performing interference studies etc.

This paper looks into some popular and most used propagation models for path loss in outdoor environment and their applications in real life scenarios.

propagation models

The propagation models can be broadly categorized into three types (Abhayawardhana et al., 2005):

Empirical models: These models use measurements and observations to arrive at the results. These types of models are used for path loss, rain fades and multipath fade predictions. (Abhayawardhana et al., 2005)

Deterministic models: These determine the received signal power at a particular point by making use of the laws governing electromagnetic wave propagation. The obstacles such as buildings, foliage etc. is taken into account to arrive at results. In order to see the effects of environment these models used detailed 3D maps of the propagation environment. Ray tracing model is a deterministic model. (Abhayawardhana et al., 2005)

Stochastic models: These models provide predictions based on environmental variables. Though these are not very accurate but also require less significant environmental information as well as require less processing for generating predictions. The wave propagation model based on random walk is one such model (Franceschetti, 2004).

## Empirical Path-Loss Models

The empirical models are used in complex propagation scenarios such as in case of mobile communication, where it is difficult to predict the path loss-using ray tracing models. The empirical models can be further categorized into time dispersive models and non-time dispersive models. The time dispersive models take into account the time dispersive characteristics of the channel such as multipath delay spread etc. The non-time dispersive models predict mean path loss as a function of variables such as distance antenna heights etc. Number of models have been developed for many different scenarios and are used depending on the environment. The empirical models are used extensively in designing mobile networks. (Abhayawardhana et al., 2005)

## Stanford University Interim (SUI) channel models

SUI is a time dispersive model and was developed by Stanford University for the Institute of Electrical and Electronic Engineers (IEEE) 802.16 (Wi-Max) working group (Abhayawardhana et al., 2005). The model was developed for 2.5 GHz to 2.7 GHz Multipoint Microwave Distribution System (MMDS) frequency band. The SUI model is defined for three type of terrains named A, B and C. The terrain A is for hilly areas with moderate to heavy foliage densities and provides maximum path loss. The type B terrain is for hilly terrains with light tree densities or flat terrain with moderate to heavy tree densities. The type C terrain provides minimum path loss for flat terrain with light tree densities. The path loss equation given by SUI model is (Abhayawardhana et al., 2005)

PL = A+10Î³ log10 (d/d0) + Xf + Xh + s for d > d0

Where, d is the distance between the base station and the CPE ( Customer premises equipment) antennas in meters, d0 = 100 m. In order to account for shadow fading owing to trees and other clutter a lognormally distributed factor s is used . s has a value between 8.2 dB and 10.6 dB.

Parameter A = 20 log10 ( 4Ï€d0/ Î») and Î³ = a âˆ’ bhb + c/hb

hb the base station height above ground in meters. The range of hb is from 10 m and 80 m. The value of constants a, b and c are given in Table 1. The Î³ is path loss exponent and determined by hb for a given terrain.

Table 1 numerical values for the SUI model parameters

Model Parameter

Terrain A

Terrain B

Terrain C

a

4.6

4.0

3.6

b(mâˆ’1)

0.0075

0.0065

0.005

c(m)

12.6

17.1

20

Thus, SUI model can be used for predictions in rural suburban and urban environments.

## Okumura Model

Okumura et al. (1968) conducted extensive studies around city of Tokyo in 150 MHz and 1500 MHz band and developed set of graphs depicting median attenuation relative to free space of signal propagation in irregular terrain. The height of base station taken was between 20 to 200 meters, the height of mobile was between 1 to 10 meter, and the distance between transmitter and receiver was 1 to 100 Kms. The model, developed by authors is known as Okumara model and it provides empirical path loss formula as follows:

PL(d ) dB = L(fc, d) + AÎ¼(fc, d) âˆ’ G(ht ) âˆ’ G(hr ) âˆ’ GAREA,

Where, d is distance, fc is center frequency of transmission, L(fc, d) is free space path loss at distance d, AÎ¼(fc, d) is the median attenuation for various environments, G(ht ) is height gain factor for base station antenna, G(hr ) is height gain factor for mobile station antenna and GAREA is the gain due to the type of environment. The values of GAREA and AÎ¼(fc, d) are provided by Okumura's empirical plots. The empirical formulas for G(ht ) and G(hr ) are (Okumura et al., 1968):

G(ht ) = 20 log10(ht/200), for 30m< ht < 1000 m; (2.29)

G(hr ) = 10 log10(hr/3), for hr â‰¤ 3 m,

G(hr ) = 20 log10(hr/3), for 3 m < hr < 10 m.

## Hata Model

The graphical curves provided in Okumara model were difficult to use. Hata (1980) provided empirical formulas for calculation of path loss in different scenarios keeping the basic parameters such as frequency range same as in case of Okumara model. The Hata model defines three prediction areas; open areas with no obstructions in path, suburban area with scattered obstacles like trees, buildings etc. and urban area with large buildings as in cities.

The standard empirical path loss formula for urban areas is (Hata, 1980):

PL,urban(d ) = 69.55 + 26.16 log10(fc) âˆ’13.82 log10(ht ) âˆ’ a(hr ) + (44.9 âˆ’ 6.55 log10(ht )) log10(d )

a(hr ) is a correction factor for the mobile antenna height and depends on the size of the coverage area. Thus, for small cities a(hr ) is given by (Hata, 1980)

a(hr ) = (1.1log10(fc) âˆ’ .7)hr âˆ’ (1.56 log10(fc) âˆ’ .8) dB

For larger cities a(hr ) at frequencies fc > 300 MHz is given by

a(hr ) = 3.2(log10(11.75hr ))2 âˆ’ 4.97 dB.

The path loss for suburban areas is given by:

PL,suburban(d ) dB = PL,urban(d ) dB âˆ’ 2[log10(fc/28)]2 âˆ’ 5.4

The path loss for rural areas is given by:

PL,rural(d ) dB = PL,urban(d ) dB âˆ’ 4.78[log10(fc)]2 +18.33 log10(fc) - K

Where, K varies from 35.94 for countryside to 40.94 for desert.

For distances greater than 1 Km the Hata model approximates Okumara model and provides good predictions for first-generation cellular systems. However, the model does not provide good prediction for smaller cell size and indoor environment (Goldsmith, 2005).

## COST 231 Hata Model

European cooperative for scientific and technical research (EURO-COST) extended the Hata model to 2 GHz from original 1.5 GHz for urban areas. The path loss as per COST231 model is given by

PL,urban(d ) = 46.3 + 33.9 log10(fc) âˆ’13.82 log10(ht ) âˆ’ a(hr )+ (44.9 âˆ’ 6.55 log10(ht )) log10(d ) + CM

Where, CM is taken as 0 dB for medium sized cities and suburbs. For metropolitan areas CM is taken as 3 dB . Since this model extends Hata model it is called as COST 231 extension to the Hata model. The model is applicable for only following parameters: 1.5 GHz < fc < 2 GHz, 30 m < ht < 200 m, 1 m < hr < 10 m, and 1 km < d < 20 km. (Goldsmith, 2005)

## COST 231-Walfisch-Ikegami Model

This model is made up by combining models of J. Walfisch and F. Ikegami. It was further enhanced under COST231 project. It is a semi empirical model and takes into account the characteristics such as heights of buildings, widths of roads, building separation, road orientation with respect to the direct radio path. The buildings in the vertical plane between the transmitter and the receiver are considered. Due to these considerations, this model gives predictions with higher accuracy especially in cases where the antenna is mounted on rooftop of buildings. The model operates with Frequency f between 800 MHz and 2000 Mhz, TX height hBase between 4 and 50 m, RX height hMobile between 1 and 3 m and distance d between 0.02 and 5 km. The path loss for LOS and NLOS are given below (Ranvier, 2004):

LOS: LLOS [dB] = 42.6 + 26 log10 d[km] + 20 log10 f [MHz]

NLOS: LNLOS [dB] = LFS + Lrts (wr, f, Î”hMobile , Î¦ ) + LMSD (Î”hBase, hBase, d, f, bS )

Where, LFS = free space path loss = 32.4 + 20 log10 d[km] + 20 log10 f [MHz]

Lrts= roof-to-street loss, LMSD= multi-diffraction loss, Lori = street orientation function

LMSD= Lbsh + ka + kd log10 (d [km] ) + kf log10 ( f [MHz] ) - 9 log10 ( b )

Lbsh = -18 log10 ( 1 + Î”hBase ) for hBase > hRoof and is 0 for hBase â‰¤ hRoof

ka = 54 for hBase > hRoof , ka = 54 - 0.8 Î”hBase for d â‰¥ 0.5 km, hBase â‰¤ hRoof and

ka = 54 - 0.8 Î”hBased /0.5 for d <0.5 km, hBase â‰¤ hRoof

kd = 18 for hBase > hRoof , ka = 18 - 15 Î”hBase / hRoof for hBase â‰¤ hRoof

kf = - 4 + 0.7 ( f / 925 - 1 ) for medium sized city and kf = - 4 + 1.5 ( f / 925 - 1 ) for metropolitan center.

## ECC-33 Path Loss Model

The Hata- Okumara model and COST231 were based on measurements in Japan and worked only upto 2 GHz. Electronic Communication Committee (ECC) extrapolated the measurements in Okumara model and made some modification in assumptions so that it can be used for fixed wireless access (FWA) in European countries (ECC Report 33, 2006). The path loss defined by ECC 33 is:

PL = Afs + Abm âˆ’ Gb âˆ’ Gr

Where, Afs is the free space attenuation, Abm is basic median path loss, Gb is the base station height gain factor and Gr the terminal (CPE) height gain factor and are given as follows (ECC Report 33, 2006):

Afs = 92.4 + 20 log10(d) + 20 log10(f)

Abm = 20.41+ 9.83 log10(d) + 7.894 log10(f) + 9.56[ log10(f)]2

Gb = log10(hb/200){13.958 + 5.8[log10(d)]2}

and for medium city environments, Gr = [42.57 + 13.7 log10(f)][log10(hr) âˆ’ 0.585]

where, f is the frequency in GHz, d is the distance between base station and CPE in km, hb is the base station antenna height in metres and hr is the CPE antenna height in metres .

Most of the European cities fall under the medium city model. The model can be used for Point-to-Multipoint (PMP) and Fixed Wireless Systems in the frequency band of 3.4 - 3.8 GHz

## Simplified Path-Loss Model

It is very difficult to find a single model that can take care of all the characteristics of various environments. In order to simplify design in many cases a simple model is needed that can take care of basic characteristics of propagation and provide an approximation for real scenario. For this purpose a simple path loss model that is commonly used for system design is (Goldsmith, 2005):

Pr dBm = Pt dBm + K dB âˆ’10Î³ log10 (d0/d)

Where, K is a constant and depends on the average channel attenuation and the antenna characteristics. d0 is a reference distance for the antenna far field, and Î³ is the path-loss exponent. The values of K, Î³ and d0 can be find out by approximating either empirical or analytical model. The above equation is only valid for the cases where d > d0 and d0 is 1-10 m indoors and 10-100 m outdoors.

While approximating empirical measurements using simplified model the value of K < 1 is made equal to free-space path gain at distance d0 assuming omnidirectional antennas.

K = 20 log10(Î»/ 4Ï€d0).

The value of Î³ is taken as between 2 to 4 when propagation follows free space or two ray model. The value of Î³ has also been derived empirically for various environments. (Goldsmith, 2005)

## Deterministic models

## Ray Tracing

The transmitted signal arrives at the receiver end taking multiple paths after reelections from many obstacles on the way. The ray-tracing model assumes that locations of the reflectors and their dielectric properties are fixed. The propagation of radio waves through these obstacles can be solved using Maxwell's equation but that makes calculations very complex. In order to simplify the calculations simple geometric equations are used in ray tracing models to reflect the effect of reflection, diffraction, and scattering on transmitted waves. The ray tracing models provide best results when distance between the reflector/scatterer is multiple wavelengths of the transmitted wave. (Goldsmith, 2005)

## Two-Ray Model

In two ray model the received signal is assumed to consists of direct or LOS component and a component reflected from the ground as shown in Figure 1 . Thus, it is useful in cases where there is a dominance of single ground reflection. The received signal consists of signal attenuated by normal path loss and the signal attenuated along the path x and x'.

Figure 1 (Goldsmith, 2005)

The received signal power in two-ray model is given by (Goldsmith, 2005):

Pr dBm = Pt dBm +10 log10(Gl) + 20 log10(hthr ) âˆ’ 40 log10(d ), where Pr is received power, Pt is transmitted power and Gl =âˆš(GaGb) is the product of the transmit and receive antenna field radiation patterns in the LOS direction.

This shows that for large d the received signal power is independent of wavelength because the combination of direct path and signal effectively forms an antenna array. The plot of distance verses received power (Figure 2) shows that for a certain critical distance dc the sum of direct and reflected wave forms a maxima and minima pattern due to interference between two waves and after the distance dc the final maxima is reached and the signal attenuates proportionally with d âˆ’4. This critical distance can be used in system design. In case of cellular system, the critical distance will be minimum cell radius, as path loss inside the cell will be much less than path loss outside the cell.

Figure 2. Received power versus distance for two-ray model. (Goldsmith, 2005)

## Ten-Ray Model (Dielectric Canyon)

Ten-Ray Model was developed by Amitay (Goldsmith, 2005) for urban microcells. The model assumes flat streets, with buildings on both the sides, that intersect with each other at an angle of ninety degrees and the height of transmitting and receiving antenna is at street level. The buildings on either side of street act like dielectric conduit to the propagating signal. The ten ray model assumes that ten reflected rays are there and the experimental data showed that this closely approximated the signal propagation though dielectric conduit formed by the buildings. The ten rays (paths) constituting the received signal are one LOS path, "one ground-reflected (GR), single-wall (SW) reflected, double-wall (DW) reflected, triple-wall (TW) reflected, wall-ground (WG) reflected, and ground-wall (GW) reflected paths" (Goldsmith, 2005). Figure 3 shows the overhead view of ten ray model paths.

Figure 3 Overhead view of the ten-ray model

The power fall off in case of ten ray model is inversely proportional to the square of the distance d for antennas located below and above the buildings. The path loss exponent is almost independent of the transmitter height. (Goldsmith, 2005)

## General Ray Tracing

The General ray tracing is used for prediction of field strength and delay spread for the locations where the exact transmitter and receiver antenna placement (height), location and dielectric properties of the building etc. can be specified. Since this model requires exact information, it is used for a definite link design. The general ray tracing method uses geometrical optics methodology for calculation of losses due to LOS, reflections, diffraction and scattering.

The ray-tracing models provide accurate predictions for rural areas, in city streets when receiver as well as transmitter is close to ground and in indoor environments with appropriate diffraction coefficients. The ray-tracing models do not take cater for power variations such as delay spread of the multipath etc. (Goldsmith, 2005)

## Free space + RMD

The Freespace + RMD (Reï¬‚ection/Multiple Diffraction) model was developed by EDX Engineering for propagation analysis in 30 MHz to 40 GHz frequency band. It has been selected by FCC (Federal Communication Corporation) for two way MMDS systems. The model takes into account following characteristics (Anderson, 2003):

"Free-space propagation and partial Fresnel zone obstruction for LOS paths,

Single reï¬‚ection contribution for LOS paths and

Single and multiple diffraction loss for NLOS paths" (Anderson, 2003).

This model can be used for engineering of point-to-point microwave links. The model first assesses using calculations whether path is LOS or not. In case path is LOS, two ray propagation model is used for path loss estimation. In case obstruction is found, the diffraction loss over the obstacles is calculated and added to normal LOS path loss calculation. In case of multiple obstructions, Epstein-Peterson method is used for calculating path loss.

## Longley-Rice Model

TheÂ Longley-Rice radio propagationÂ model was proposed for predicting path loss for point to pint communication links in 40 MHz to 100 MHz frequency range, over various types of terrains. The model uses path geometry of the terrain and the refractivity of troposphere for calculating the transmission losses. The 2-Ray model is used for prediction of signal strength within the horizon and Fresnel-Kirchoff knife edge model is used for estimation of diffraction over isolated obstacles. The troposcatter predications are made using forward scatter theory. The model can be used in two ways. It provides point-to-point mode prediction when detailed path profile is available and provides area prediction when details of path profile are not available by providing techniques to estimate various path specific parameters. The model is also available as computer program for 20 MHZ to 10 GHz range. (Anderson, 2003)

Conclusion

The wireless transmission not only depends on the environment but also on various obstacles coming in the way of electromagnetic waves. It also depends on reflection, diffraction and scattering of electromagnetic wave as they travel form transmitter to the receiver. The proper design of network requires accurate predictions of signal strength received at the receiver. It is simple when the LOS exists but become complicated in scenarios such as mobile network where the receiver can be anywhere in city. In order to properly asses the signal strength in various environment the propagation models have been developed. These allow network designer to engineer the links and network properly so that the communication is available in the designed area. The deterministic and empirical models are most commonly used models. The fixed wireless networks mainly use deterministic models such as two-ray model etc. The mobile networks mostly used empirical models such as Okumara and Hata models. General simplified models have also been suggested to avoid complicated calculations in simplified scenarios. The various models are also available in form of computer programs for easy path profiling and network design.