March 2008  

  Figuring out wireless transmission distance

When planning or updating a wireless LAN installation, it's often necessary to determine if your wireless equipment can achieve a certain transmission distance. However, this information is not printed in the specs for wireless devices and antennas. The reason is simple – there are too many factors that affect the transmission distance, particularly the combination of transmission power and antenna gain. In this article, you can learn how to use your wireless device and antenna specifications to quickly determine the theoretical transmission distance.

First, the basics
The theoretical transmission distance that can be achieved between two wireless devices can be calculated from just a few key specifications.

Tx power = transmission power of device
This is the wireless device's transmission power and is typically measured in dBm. With greater Tx power, greater transmission distances can be achieved.

Data rate
The data rate is the number of bits that are conveyed or processed per unit of time. Since higher data rates require greater transmission power, a wireless device may offer different Tx power specifications for different data rates.

Rx sensitivity = receiver sensitivity of device
This is the wireless device's receiver sensitivity and is typically measured in dBm. With greater Rx sensitivity, the device is able to receive weaker signals, which means greater transmission distances can be supported

Don't forget that wireless communication occurs between two devices. If two devices have different Tx power and Rx sensitivity specifications, the theoretical transmission distance may be different depending on which direction the data is being transmitted. You will need to consider the Tx power and Rx sensitivity in both directions. In most cases, it is simpler to make sure that every wireless device in your network adheres to the same specifications for Tx power and Rx sensitivity.

Antenna gain
The gain for an antenna is typically measured in dBi and basically indicates how much the signal is boosted by the antenna. Although high gain antennas mean greater transmission distances, they are usually highly directional.

The frequency is typically measured in MHz or GHz and indicates which electromagnetic band is used for wireless communication. The frequency is determined by the IEEE 802.11 standard that you have selected for your network. All IEEE 802.11b and IEEE 802.11g devices use the 2.4 Ghz band, while IEEE 802.11a devices use the 5 Ghz band. The selection of IEEE 802.11 standard (and therefore frequency) is usually determined by factors such as national restrictions and existing device support.

If you have the information above for your wireless devices, you can easily determine the theoretical transmission distance between two wireless devices.

The formula explained
The formula for calculating the theoretical transmission distance is based on the Friis Transmission Equation for free space loss:

In this equation, R is the range and is the wavelength. We can take a look at the following figure to see how this corresponds with the specifications of our devices and antennas.

The Friis Transmission Equation requires a bit of modification to suit our needs. What we want is an equation that tells us the transmission distance directly. Also, it's easier for us to work with communication frequency rather than wavelength. We can modify the Friis Transmission Equation to fit our needs more closely, as follows:

Let's try an example
With this equation, we can quickly determine whether we will need new wireless equipment to reach a particularly remote site. Suppose you need to connect wirelessly to a node that is 4 km away. You are running an IEEE 802.11b network and you are currently using wireless devices with the following specifications:

  • Tx power: 18 dBm @ 11 Mbps
  • Rx sensitivity: -90 dBm @ 11 Mbps
  • Antenna gain: 2 dBi

With our formula, you have all the information you need to determine the theoretical transmission range that is possible with this set of equipment.

2442 MHz (all IEEE 802.11b devices )
Tx power
18 dBm
Tx antenna gain
2 dBi
Rx antenna gain
2 dBi
Rx sensitivity
-81 dBm

When you plug these numbers into our formula, you get a value of 1.38 km. This is the theoretical transmission distance that can be achieved by your wireless equipment. We could use the same formula to see how much further wireless signals would travel using 9-dBi antennas instead of 2-dBi antennas. (The theoretical transmission distance goes up to 6.92 km). Another way to increase the transmission distance would be to employ wireless devices that offer higher Tx power and/or lower Rx sensitivity.

Now for the fine print
Of course, there can be a big difference between the theoretical transmission distance and the actual results in the field. These calculations are based on an unobstructed line-of-sight signal with no electronic interference. However, the real world presents many variables that result in less-than-perfect wireless performance, such as mismatched impedance, electronic noise, building obstructions, reflected signals, etc.

This is why it is so important to conduct a thorough site survey in order to determine what is actually happening to your wireless signals in the field. Before you conduct that site survey, however, you still need some way to evaluate the different options you have for wireless hardware. This formula provides a straightforward way to perform that evaluation. With this formula, you can now easily estimate whether you will be able to achieve your desired transmission distance with a given set of hardware. Using this formula, you can make an informed decision when selecting antennas and devices for different wireless applications.

* Example of wireless AP specs
* Example of wireless antenna specs
* Wireless guidebook

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