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## SNR, RSSI, EIRP and Free Space Path Loss   Beginner

## 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.

## Source   Rising star

Excellent information for the beginning RF professional. I would like to add the 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   Rising star

Rajesh,

I am im pressed with what you did with my post and I am glad it will be able to help so many others out.

Dennis,

Thanks for the kudos on the document, it was generated from years in the industry dealing with wireless. and your comments are valid and extremely valuable and I remember them from my Mesh ATP training a few years ago.

Thanks Guys, I hope this document helps many people moving forward.

Kayle   Beginner

Thanks for providing this useful information Kayle.  And yes, the idea is to convert useful and informative posts into documents so that many more CSC users will be benefitted

Rajesh   Beginner

Signal is measured in dBm (or Watt, or milliwatt, or whatever), NOT in dB!

dB are used to indicate ANY ratio:

x dB = 10 * Log a / b.

If you have doubled your incomes, you have increased them by 3dB. That's because Log 2 is very close to 0.3.

If you have halved them, they have decreased by 3dB (or increased by -3dB)

Log 1/2 = - Log 2 = - 0.3

Remember the rules concerning Logarithms.

Therefore:

x dBm + (or -) y dB = z dBm

x dB + (or -) y dB = z dB

Pay attention!!   Beginner

you are right man. signal level is not measured via dB but in dBm.   Engager

Good doc Rajesh.

Just I want to mention that 17 dBm is equivalent to 50 mW, not 40 mW as mentioned above.

+5 from me.   Rising star

Actually above it's correct, but the math line is where i made the typo.. Good catch though.  Community Member

Thanks a lot for your explicit explanation on the terms used in Wi-Fi. Only one thing I'm confused is in the section

How to find EIRP

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.

I'm confused why RSSI equals to negative value of EIRP. In case of EIRP=17dBm, then is RSSI measured right at the antenna will be equal to -17dBm. It is strange that if the EIRP is lower, the RSSI measured will be higher.   Beginner

That's a good question I have here as well.

Also, what if the output power is less than 1mw, let say 0.2 mw, then it is -13dbm.  let say cable loss is 1db, antenna gain is 2dbi, then what is the EIRP?  Community Member

According to your question, the EIRP would be -13dbm - 1db + 2dbi = -12dbm. However, I wonder what is the RSSI measured right at the antenna. If there is any misunderstanding, please let me know.   Beginner

RSSI doesn't turn to minus right way.  it will very close to EIRP when very close to the transmitter's antenna.  So, if EIRP is 20dbm RSSI will be close to 20dbm if it is very close by.

The reason we often see EIRP is positive dbm, but RSSI is negative dbm, is because there is often a 69db free path loss taken in count like a default assumption(at least Cisco wireless exam takes that assumption).

So, a 20dbm EIRP, -69 db free path loss, you will see RSSI -49dbm.  Community Member

Thanks a lot for your sharing. I think I figured out as well. I was confused the relationship between RSSI and Received Power, as several reference reveal there is no relationship between RSSI and power level, such as wikipedia. So I wonder the Signal Strength measured by inSSIDer is RSSI or Received Power.

After finding out the definition from MetaGeek, they give me clearer meaning to RSSI. Actually the measured value from inSSIDer are Received Power. The original RSSI value should not be displayed in dBm. The link below is the definition of RSSI from MetaGeek.

Moreover, I have tried to calculate the free-space path loss for 5GHz in 1cm,5cm,10cm,50cm and 1m. The outcomes are

1cm: 6.43dB

5cm: 20.40dB

10cm: 26.43dB

50cm: 40.41dB

1m: 46.43dB

It is discovered that Received Power become 0dBm with a distance of 5cm from Tx only, with EIRP of 20dBm. So the Received Power drops from positive to zero only within a distance from 1cm to 5cm apart. Moreover, if I measure with 50cm and 1m apart respectively, the Received Power will be around (20-40.41=-20.41dBm) and (20-46.43=-26.43dBm), which the values are approx. to that I measured with my wireless router, with 20dBm EIRP. The measured Received Power would be lower(i.e. more negative) due to real environment, such as obstacles to cause reflection and diffraction, and interference from other wireless devices.  Community Member

A point of note. There is actually an error in the explanation from

------------------------------------------------------------------------------------------------------------------------------

"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. "

------------------------------------------------------------------------------------------------------------------------------

SNR (which stands for signal To Noise ratio) is a ratio of Signal Power to the Noise Power. So, that will be subtracting the Noise Power from the Signal Power. So from the Rajesh post, it should have been -55dBm - (-95dBm) = -55dBm + 95dBm = 40dB

Just thought I should point that out. Thank you.

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