WINNER-II Path Loss Model

In simple terms the path loss is the difference between the transmitted power and the received power of a wireless communication system. This may range from tens of dB to more than a 100 dB e.g. if the transmitted power of a wireless communication system is 30 dBm and the received power is -90 dBm then the path loss is calculated as 30-(-90)=120 dB. Path loss is sometimes categorized as a large scale effect (in contrast to fading which is a small scale effect).

According to the WINNER-II model the path loss can be calculated  as:

Here d is the separation between the transmitter and receiver in meters, fc is the frequency in GHz, A is the path loss exponent, B is the intercept and C is the frequency dependent parameter. X is the environment specific parameter such as path loss due to a wall. PLfree is the path loss in a free space line of sight environment (here A=20, B=46.4 and C=20).

The table below describes the different environments defined in the WINNER-II model. Once an environment is selected the path loss parameters A, B and C can be selected from the table further down e.g. A1 is the in-building scenario with A=18.7, B=46.8 and C=20 for the LOS case. The PL for a T-R separation of 100 m and frequency of 2 GHz is calculated as:

PL=18.7*log10(100)+46.8+20*log10(2/5)=76.42 dB

A separate equation for the path loss is given where the parameters A, B and C are not sufficient to describe the scenario.

Note:

1. Here CG is the concept group that developed the particular scenario. This is either Local Area (LA), Metropolitan Area (MA) or Wide Area (WA).

2. For more details visit:

L. Hentilä, P. Kyösti, M. Käske, M. Narandzic , and M. Alatossava. (2007, December.) MATLAB implementation of the WINNER Phase II Channel Model ver1.1 [Online]. Available: https://www.ist-winner.org/phase_2_model.html

Base Station Antenna Tilt and Path Loss

Path loss is basically the difference in transmit and receive powers of a wireless communication link. In a Free Space Line of Sight (LOS) channel the path loss is defined as:

L=20*log10(4*pi*d/lambda)

where ‘d’ is the transmit receive separation and ‘lambda’ is the wavelength. It is also possible to include the antenna gains in the link budget calculation to find the end to end path loss (cable and connector losses may also be factored in). Antenna gains are usually defined along a horizontal plane and vertical plane passing through the center of the antenna. The antenna gain can then be calculated at any angle in 3D using the gains in these two planes.

Although 3D antenna gains are quite complex quantities simplified models are usually used in simulations e.g. a popular antenna Kathrein 742215 has the following antenna gain models [1] along the horizontal and vertical planes:

Gh(phi)=-min(12*(phi/HPBWh)^2, FBRh)+Gm

Gv(theta)=max(-12*((theta-theta_tilt)/HPBWv)^2, SLLv)

where

Gm=18 dBi
HPBWh=65 degrees
HPBWv=6.2 degrees
SLLv=-18 dB

We are particularly interested in the gain in the vertical plane and the effect of base station antenna tilt on the path loss. We assume that the mobile antenna station has uniform gain in all directions. The path loss can be then calculated as:

L=20*log10(4*pi*d/lambda)+Gv(theta)+Gh(phi)

where we have assumed that Gh(phi)=0 for all phi (this is a reasonable simplification since changing the distance along the line of sight would not change Gh(phi) ). Using the above expression the path loss in free space is calculated for a frequency of 1805 MHz, base station antenna height of 30 m and an antenna tilt of 5 degrees.

Effect of Antenna Tilt on Path Loss

It is observed that there is a sudden decrease in path loss at distances where the antenna main beam is directed. If the antenna tilt is increased this behavior would be observed at smaller distances. Since we have used a side lobe level that is fixed at -18 dB we see a rapid change in behavior at around 100 m. If a more realistic antenna model is used we would see a gradual decrease in path loss at this critical distance.

[1] Fredrik Gunnarsson, Martin N Johansson, Anders Furuskär, Magnus Lundevall, Arne Simonsson, Claes Tidestav, Mats Blomgren, “Downtilted Base Station Antennas – A Simulation Model Proposal and Impact on HSPA and LTE Performance”,
Ericsson Research, Ericsson AB, Sweden. Presented at VTC 2008.

WiMAX Path Loss and Antenna Height

As discussed previously the SUI (Stanford University Interim) model can be used to calculate the path loss of a WiMAX link. The SUI model is given as:

SUI Path Loss Equation

It has five components:

1. The free space path loss (A) up to the reference distance of ‘do’.
2. Additional path loss for distance ‘d’ with path loss exponent ‘n’.
3. Additional path loss (Xf) for frequencies above 2000 MHz.
4. Path gain (Xh) for receive antenna heights greater than 2 m.

The most important factor in this equation is the distance dependent path loss. The impact of this factor is controlled by the path loss exponent ‘n’. It is well known that in free space the path loss exponent has a value of 2. In more realistic channels its value ranges anywhere from 2 to 6. For SUI model the path loss exponent is calculated as:

n=a-(b*hb)+(c./hb)

where a, b and c are SUI model specific parameters. It is obvious that the path loss exponent decreases with increase in base station antenna height ‘hb’. The path loss exponent for various antenna heights is shown below.

Path Loss Exponent

It is observed that as the base station antenna height is varied from 10 m to 80 m the path loss exponent for the three scenarios varies from around 5.5-6.0 to 3.5-4.5. Basically what this means is that for higher base station antenna heights the cell radius would be larger. However we need to be careful when making this statement. Higher antenna heights also sometimes results in a weak signal area close to the base station. This is where the antenna downward tilt becomes an important factor. Antenna downward tilt usually has a value around 5-10 degrees. It is somewhat surprising that although it is such an important factor none of the well known empirical models take it into account.

Note: SUI Model was initially formulated based upon the data collected by AT&T Wireless across the United States in 95 existing macrocells at 1.9 GHz.

WiMAX Path Loss Calculation

Calculation of the path loss is fundamental to Wireless System Design. There are many models available for calculating the path loss such as Okumura Model, Hata Model, COST-231 Model and more recently the SUI (Stanford University Interim) Model. The SUI Model has been specifically proposed for Broadband Wireless Access Systems such as WiMAX. It defines three types of environments namely A, B and C which are equivalent to the urban, suburban and rural environments defined in the earlier models. According to this model the path loss can be calculated as:

PL=A+10*n*log10(d/do)+Xf+Xh+s

where

n=a-(b*hb)+(c/hb)
A=20*log10(4*pi*do/lambda)
Xf=6.0*log10(f/2000)
Xh=-10.8*log10(hr/2) for A&B
Xh=-20.0*log10(hr/2) for C

and

frequency of operation = f = >2000MHz
transmit receive separation = d = 100 m to 8000 m
reference distance = do = 100 m
base station antenna height = hb = 10 m to 80 m
receive antenna height = h = 2 m to 10 m
shadowing factor with lognormal distribution = s = 8.2 dB to 10.6 dB

The values for the parameters a,b and c for the three environment are given in the table below.

Doing a quick calculation for f=2500 MHz, hb=30 m, hr=2 m, s=8.2, do=100 m and d=1000 m gives us a path loss 137.13 dB for Type-A channel. Increasing the frequency to 3500 MHz (another WiMAX band) increases the path loss to 140.93 dB i.e. there is a 3.8 dB increase in the path loss.

So to recap the path loss given by the SUI model is composed of 5 elements:

1. The free space path loss (A) up to the reference distance of ‘do’.
2. Additional path loss for distance ‘d’ with path loss exponent ‘n’.
3. Additional path loss (Xf) for frequencies above 2000 MHz.
4. Path gain (Xh) for receive antenna heights greater than 2 m.

LTE Path Loss at 700 MHz

In the previous post we had compared the path loss of LTE at 728 MHz and 1805 MHz in a free space line of sight channel. This is a very simplistic channel model which tells us that ratio of the received signal strengths at these frequencies can be simply found as:

(f1/f2)^2=(1805/728)^2=6.15

That is the received signal strength at 728 MHz is 6.15 times higher than the received signal strength at 1805 MHz.

Now let us consider a more realistic channel model known as the COST-231 model. According to this model the path loss (difference between the transmit power and receive power) is given as:

L=46.3+33.9*log10(f)-13.82*log(ht)-a+(44.9-6.55*log10(ht))*log10(d)+C

where

f=frequency in MHz (0.1500 MHz – 2000 MHz)

ht=base station antenna height in m (30 m – 200 m)

hr=mobile station antenna height in m (1 m – 10 m)

d=transmit receive separation in km (1 km – 20 km)

C=3 dB for metropolitan centres

and mobile station antenna correction factor is given as:

a=3.2*log10(11.75*hr)^2-4.97

Using the above equations with ht=30 m, hr=1 m and d=1 km the path loss at 728 MHz and 1805 MHz is found out to be 100.63 dB and 114.00 dB respectively i.e. there is a gain of 13.37 dB when using the lower frequency. In simpler terms the received signal at 728 MHz would be 21.72 times stronger than the signal at 1805 MHz.

Such a remarkable improvement in signal strength or in signal to noise ratio (SNR) has the potential of increasing the throughput four folds. For example at an SNR of 1.5 dB QPSK 1/2 would give a throughput of 6.00Mbps whereas at an SNR of 14.7 dB a modulation coding scheme (MCS) of 64QAM 2/3 would result in a throughput of 24.01 Mbps.

Modulation Coding Schemes

Propagation and In-Building Penetration at 700MHz

It is quite well known that wireless signals travel further at lower frequencies. This phenomenon has become particularly important in the context of LTE where a frequency band has been allocated at 700MHz. We would like to quantify the benefits that can be achieved by using this frequency band.

Firstly we find the received signal power at 728 MHz (lowest downlink frequency) and at 3600 MHz (highest downlink frequency) in a free space line of sight channel. The transmit power is set to 1 W and omnidirectional antennas are considered at the transmitter and receiver. The received power for these two frequencies at a distance of 1000 m is found out to be -59.68dBm and -73.57dBm respectively i.e. there is a gain of 13.88 dB by using the lower frequency band. In simpler terms the signal power would be more than 20 times stronger at the lower frequency. This result can also be simply obtained by taking the square of the ratio the two frequencies.

(3600/728)^2 = 24.45

Similarly compared to a frequency of 1805 MHz, the signal at 728 MHz would be more than 6 times stronger.

(1805/728)^2 = 6.1474

Now we turn our attention to the penetration loss i.e. how much would the signal attenuate when passing through a concrete wall. For this we would have to calculate the attenuation constant (alpha) which is given as:

Propagation Constant

Alpha, the attenuation constant is the real part of the propagation constant gamma whereas Beta, the phase constant, is the imaginary part. These quantities depend upon the frequency, relative permittivity, relative permeability and conductivity of the material. The penetration loss can then be found as -20*log10(exp(-alpha*thickness)). Using the properties of concrete the penetration loss at 728 MHz and at 1805 MHz is found out to be 4.16 dB and 10.38 dB i.e. there is a gain of 6.22 dB when using the lower frequency. In simpler terms the signal at the lower frequency would be more than 4 times stronger. We have considered a concrete wall of 10 cm thickness.

It is quite evident that the frequency of operation plays a big role in determining the propagation loss and the penetration loss. The frequency band of 728-746 MHz would thus be a prized commodity and operators would be willing to pay handsome amount to secure it.

Note:

1. We have ignored the reflection that occurs at the interface as its effect is comparably quite small.

2. Following were the material properties of concrete used in the calculation for penetration loss.

```728 MHz
Relative permittivity = 4.5775
Relative permeability = 1.0000
Conductivity = 0.055

1805 MHz
Relative permittivity = 4.1000
Relative permeability = 1.0000
Conductivity = 0.1300```