Saturday, December 10, 2011

Effective Isotropic Radiated Power (EIRP)

Some would say that this is a very simple topic with which to start a blog about wireless deployments, but if there is one thing that most people often get wrong it is the simple matter of correctly setting their transmit power on their Access Point for use with a specific antenna.

While many vendors of enterprise wireless equipment allow the power to be set by simply selecting a country code, this is a fundamental topic that should be understood by ANYONE looking at deploying an enterprise wireless solution in any market vertical. It is important not just for the benefit of being on the correct side of the law in the country you are operating in but also for making sure that enough wireless access points are installed to achieve a high enough Received Signal Strength across the coverage area.

This post aims to provide a complete definition of EIRP and the implications of the laws that regulate it in different territories complete with a few vendor examples. Regulation of EIRP and how it applies to 802.11n MIMO is also included.


To properly define EIRP one must first define the term "isotropic". An isotropic source is one that radiates power evenly in all directions. A good example of an isotropic source is the sun. Think of using a square solar panel perhaps 1 square metre in dimension. No matter where you are in space, as long as you are a certain distance away from the sun, you will receive the same amount of power on that solar panel. You can think of this as the amount of power per square metre at a certain distance. As you move further from the sun, the amount of power per square metre becomes lower as the sun's power spreads out into space. The power per square metre is referred to as the Power Density. This is an important concept when beginning to understand EIRP.

Non-isotropic sources are those that do NOT radiate their power evenly in all directions, but rather in a specific direction better than others. That is, in one direction the power per square metre is greater than another. To put this yet another way, if an Isotropic source radiates all of its power equally in all directions, a non isotropic source takes all of the power fed into it and concentrates it in a specific direction. We call this the Directivity of a source but it is also referred to as the Gain although in my opinion this is technically incorrect.

Effective (or Equivalent) Isotropic Radiated Power is the amount of power that would have to be fed into an isotropic source to achieve a certain power density at a specific distance away from the source. It is important to realise that EIRP regulation does not define the total power fed into a source, but rather the power density at a specific distance from the source in the direction of the maximum directivity.

Let us use an example:
Imagine the sun again. The sun has a specific amount of power (let us pretend it is a bajillion million zillion watts of power) that is radiated in all directions. By the time all that power reaches earth it lands at about 1300 Watts per square metre. If we moved anywhere else in the solar system and maintained our distance from the sun, the power per square metre would be 1300 watts.

Now let us pretend that the sun concentrated its available power toward the earth twice as well as it currently does. For those of you familiar with dB measures we would say the sun now had a 3dBi (decibels above isotropic) gain in the earth's direction. The directivity of the sun would be 3dBi. It is a simple deduction that the power per square metre on the earth would increase to about 2600 Watts.

It is important to note that in our example, the total power radiated by the sun has not increased, but the EIRP of the sun is now double what it used to be. A completely isotropic sun would have to have DOUBLE the amount of total power (radiated in all directions) to achieve 2600 watts per square metre on the surface of the earth.

Conversely, using our pretend example, if we limited the EIRP of the sun to a bajillion million zillion watts and it started radiating towards the earth twice as well as an isotropic source, it would have to use only half of a billion million zillion watts to maintain the EIRP.

If you have followed my example, then it becomes obvious that the EIRP of a source is equal to the total power fed into a source multiplied by the directivity of the source. A perfectly isotropic source has a directivity of 1 or expressed in decibels: 0 dBi.

Using our example of the sun and now transferring it to something like a wireless access point, the total power of the sun is analogous to the transmit power of a radio in the AP. The way the sun radiates its power in various directions is analogous to the directivity of the antenna you have attached to the radio.

Expressed in decibels:

EIRP = Transmit Power (dBm) + Antenna Directivity (dBi)

If you stop to consider that the antenna and the power source are connected by a cable then you can include the loss through the cable in this equation:

EIRP = Tx Power (dBm) - Cable Loss (dB) + Antenna Directivity (dBi)

I want to look at the application of EIRP limitations with regard to certain regulatory domains, specifically ETSI (European) vs FCC (American) regulatory domains.

Using typical European regulations, the maximum EIRP for Wireless devices on the 2.4GHz band is 20dBm or 100mWatts. That means for a radio using different antennas (assuming no cable losses):

Antenna Gain Maximum Transmit Power Resulting EIRP
| | dBm | mWatts | |
| 2.1dBi | 17.9dBm | 61.6 | 20dBm |
| 5dBi | 15dBm | 31.62 | 20dBm |
| 7.5dBi | 12.5dBm | 17.8 | 20dBm |
| 10dBi | 10dBm | 10 | 20dBm |
| 14dBi | 6dBm | 4 | 20dBm |
| 21dBi | -1dBm | 0.79 | 20dBm |
| 24.5dBi | -4.5dBm | 0.35 | 20dBm |

Using FCC regulations, the maximum EIRP for a Wireless Device on the 2.4GHz band is 30dBm (1000mWatt) with a 6dBi additional allowance for antenna directivity. Thus the maximum total EIRP of a wireless AP is 36dBm.

Using the same Antennas as in the European example:

Antenna Gain Maximum Transmit Power Resulting EIRP
| | dBm | mWatts | |
| 2.1dBi | 30dBm | 1000 | 32.1dBm |
| 5dBi | 30dBm | 1000 | 35dBm |
| 7.5dBi | 28.5dBm | 708 | 36dBm |
| 10dBi | 26dBm | 398 | 36dBm |
| 14dBi | 22dBm | 158.5 | 36dBm |
| 21dBi | 15dBm | 31.6 | 36dBm |
| 24.5dBi | 11.5dBm | 14.12 | 36dBm |

WHAT ABOUT 802.11n and MIMO?
In older wireless chipsets there is only a single radio chain and a single stream of information. In newer chipsets as in 802.11n there are multiple radio chains and multiple streams of information.

The number of radio chains contained in a chipset is denoted typically in the following format:
Tx Chains x Rx Chains : Number of Spatial Streams.

An access point using two transmit chains, two receive chains and two spatial streams would be denoted as 2x2:2

The important thing to keep in mind here is that a typical 802.11n access point has 2 or more transmit radio chains. In older 802.11a/b/g access points the transmit power was defined per chip. In 802.11n access points the transmit power is defined in hardware per tx radio chain. The defined EIRP limit for the access point however has not changed. The implication is therefore that the total calculated Transmit Power of the Wireless Access Point must be split evenly among the radio chains in the chipset.

So let us look at an example:
Assuming you are using a 3x3:2 802.11n Access Point, you have 3 Tx Radio Chains. This translates to a -5dBm adjustment to the configured Tx Power per radio chain. That is, the TX Power allowed per radio chain must be divided by three.

To make a general rule, the Tx Power configured on an 802.11n AP must be the Maximum total allowed power divided by the number of transmit radio chains. to add this to our equation for EIRP we now say:

EIRP = Tx Power (dBm) + TxChains (dB) - Cable Loss (dB) + Antenna Directivity (dBi)

For both the FCC and European standards the following adjustments must be made to the configured Tx Power per Radio Chain:

| Tx Chains | Transmit Power
| | Adjustment |
| 1 | 0dB |
| 2 | 3dB |
| 3 | 5dB |
| 4 | 6dB |

There are some vendors who build APs with multiple radios inside them that work together to produce a single received signal. Each radio is typically fitted with a dedicated omni-directional antenna. The radios inside the AP are centrally controlled and fed a phase shifted version of the same transmit signal allowing the six radios to work together as a single phase shifted array. Based on the phase shifts between the signals fed into the radios the AP can perform beamforming by making the transmitted signal from each radio constructively interfere at a specified point in spac.

This is quite a technical topic to discuss on a blog. So here are the key take aways:
Using multiple radios to work together is allowed by both the FCC and European regulations, but the way they specify the behaviour of such a setup differs quite dramatically.

Let us use an example to illustrate this concept.
Assume you have an Access Point with six radios each with a dedicated 7.5dBi antenna. If beamforming is used then there exists a possibility that the received signal strength at a certain point in space could be the sum of the received power from all six radios (perfect constructive interference). That would translate to an 8dB gain in signal strength.

The FCC Regulations:
The FCC rules (here: define the following limits for beamforming and non-beamforming devices:

Maximum Conducted Output Power (Summed over all antenna elements):
1 Watt or 30dBm
Antenna Gain Allowance: 6dBi

Non-Beamforming Devices:
For every increase in Antenna gain in dB over the 6dBi limit the conducted output power of the device must be reduced by a corresponding amount. This means if you use a 10dBi Antenna, the maximum conducted output power must be set to no more than 26dBm.

Beamforming Devices:
For each added 3dBi of antenna gain above the 6dBi limit (due either to the directivity of the antenna or due to beamforming operation) the maximum conducted output power must be reduced by 1dB.

In addition, the directional gain is defined as follows:
"The directional gain shall be calculated as the sum of 10 log (number of array elements or staves) plus the directional gain of the element or stave having the highest gain."

Using six 7.5dBi antenna elements as in our example the maximum transmit power configured on the device is then calculated by:

Transmit Power = 30dBm - (Total Directional Gain - 6dBi)/3

Transmit Power = 30dBm - (7.5dBi + 8dBi - 6dBi)/3

Transmit Power = 30dBm - (3.167dB) = 26.83dBm

The total allowable EIRP is then:

Maximum EIRP = 26.83dBm + 7.5dBi + 8dBi = 42.33dBm

The ETSI Regulations:
According to the European telecommunications standards applied by most countries no additional allowance is provided for beamforming or antenna gain in the Maximum EIRP calculation for an access point. This makes things considerably simpler when calculating the maximum configurable power for an access point.

Again assuming an Access Point that uses six 7.5dBi antennas the total allowable configured power of the Access Point is caclulated as follows:

Max Transmit Power (dBm) = Maximum EIRP (dBm) - Antenna Directivity (dBi) - Beamforming Gain (dBi) + Cable Loss (dB)

Max Tx Pwr = 20dBm - 7.5dBi - 8dBi
= 4.5dBm (2.81 milliWatt)

Edit: At this point there are still a few things I would like to add but am currently a little distracted. I'll get around to fixing the spelling mistakes and adding a few more pieces to this.
In the meantime please bear with me and feel free to add comments or suggestions.

--That's all for now.--