Tag Archives: Path Loss

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:

WINNER-II Path Loss Equation
WINNER-II Path Loss Equation

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.

WINNER-II Propagation Scenarios
WINNER-II Propagation Scenarios
WINNER-II Path Loss Models
WINNER-II Path Loss Models


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:


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)


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:


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
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
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.
5. Shadowing factor (s).

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:


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
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.