# SNR, RSSI, EIRP and Free Space Path Loss

## Introduction

SNR, RSSI, EIRP and Free Space Path Loss

## Signal to Noise Ratio

The power level of the RF signal relative to the power level of the noise floor is known as the Signal-to-Noise ratio or SNR. It is the ratio of signal power to the noise power corrupting the signal.

In simple words, SNR (Signal-to-Noise Ratio) is a ratio based value that evaluates your signal based on the noise being seen. SNR is measured as a positive value between 0dB and 120dB and the closer the value is to 120dB, the better.

Let’s look at the components of the SNR and then understand how SNR is determined.  SNR is comprised of 2 values.

• a) Signal
• b) Noise

RSSI (Received Signal Strength Indicator) is a more common name for the Signal value. It is the strength that one device is hearing another device. This value is measured in decibels from 0 (zero) to -120 (minus 120). The closer this value to 0 (zero), stronger the signal.

Typically voice networks require a -65dBm or better signal level while a data network needs -80dBm or better. Normal range in a network would be -45dBm to -87dBm depending on power levels and design.  The Signal is also affected by the APs transmit power & antenna as well as the client’s antenna.

Noise is any signal that interferes with your signal. Noise can be due to other wireless devices such as cordless phones, microwave devices etc. This value is measured in decibels from 0 (zero) to -120 (minus 120). Noise level is the amount of interference in your wireless signal, so lower is better. Looking at this value, if the value is closer to -120 (minus 120) it is better because that means there is little to no interference. Typical environments range between -90dBm and -98dBm.

To calculate the SNR value, we add the Signal Value to the Noise Value and it generates (or should) a positive number that is expressed in decibels (db).  For example, lets say your Signal value is -55dBm and your Noise value is -95dBm.

-55dBm + -95dBm = 40db this means you have an SNR of 40, the general rule of thumb is that any SNR above 20 is good.

Other important terminologies that we need to understand is the EIRP and Free Space Path Loss.

## EIRP (Effective Isotropic Radiated Power)

EIRP (Effective Isotropic Radiated Power) is the actual amount of signal leaving the antenna and is a value measured in db and is based on 3 values:
a) Transmit Power (dBm)
b) Cable Loss (dB)
c) Antenna Gain (dBi)

The dB measures the power of a signal as a function of its ratio to another standardized value. The abbreviation dB is often combined with other abbreviations in order to represent the values that are compared. Here are two examples:

dBm—The dB value is compared to 1 mW.

dBw—The dB value is compared to 1 W.

You can calculate the power in dBs from this formula:

Power (in dB) = 10 * log10 (Signal/Reference)
This list defines the terms in the formula:

log10 is logarithm base 10.

Signal is the power of the signal (for example, 50 mW).

Reference is the reference power (for example, 1 mW).

## How to find EIRP

To determine EIRP follow this equation:

<Transmit Power> – Cable Loss + Antenna Gain = EIRP

For example we have a Cisco 1242AG access points running at full power with a 6dBi antenna on the 802.11a radio and a 2.5dBi antenna on the 802.11bg radio.

802.11a EIRP = 17dBm (40mw) – 0dB + 6dBi = 23dBm = 200mw of actual output power

802.11bg EIRP = 20dBm (100mw) – 0dB + 2.5dBi = 22.5dBm = 150mw (approx) of actual output power

Based on the example above, in theory, if you were to measure it right at the antenna you could get an RSSI of -23dBm or -22.5dBm respectively.

## Free Space Path Loss

Free space path loss is a weakening of the RF signal due to a broadening of the wave front.

It is a measure of how much signal power the device loses over a given distance. Typically the device loses about 0.020 dB per foot in an outdoor or wide open office; doors, walls, glass, and etc. affect this. This is why as a client walks away from an AP,  the signal gets weaker.

All this relates to the client because it determines the signal the client receives, also keep in mind that when looking at the client you have to account for it’s antenna as well much like the EIRP.

So if a client card has a 2 dBi antenna (although they are typically either 0dBi or 2.2dBi) that boosts the incoming signal, and assuming the actual  RSSI signal being seen is -68dBm, then:

-68dBm + 2dBm = -66dBm

Check out the Cisco Enterprise Mobility Design Guide for more detail information on WLAN Radio Frequency Design Considerations.

## Free Space Path loss

free space path loss is a major issue when dealing with RF links at a long distance, particularly outdoors. Cisco has a couple of good calculator tools to allow for free space path loss in the RF link budget design calculations. To explain free space path loss use the following formula.

FSPL       = (   4   π   d / λ   ) 2
= (   4   π   d   f   / c   ) 2
Where:
FSPL is the Free space path loss
d is the distance of the receiver from the transmitter (metres)
λ is the signal wavelength (metres)
f is the signal frequency (Hertz)
c is the speed of light in a vacuum (metres per second)

This is actually part of the MESH RF boot camp class that was required to get your Outdoor MESH ATP. If you fail to consider free space path loss on an outdoor MESH network the MESH links will surely fail.