# Forum

## ERP-OFDM (802.11g) channel bandwidth

17 posts by 6 authors in: Forums > CWNA - Enterprise Wi-Fi Admin
Last Post: January 20, 2012:
• Despite this should be clear and obvious on the book, I am not really sure which is the actual bandwidth of 802.11g channels.

On one hand, on 802.11n's Chapter 18, pg. 598, one can read "As you learned in Chapter 6 [...] 802.11a and [b]802.11g radios use 20 MHz[/b] OFDM channels". Good and clear as a diamond bullet.
However, in this very Chapter 6, "2.4 GHz Channels", pg. 205, it is said that "[b]Each [of the 14 channels] is 22 MHz wide[/b]". [b][i]In general, regardless of the encoding technology[/i][/b]. I assume that implicitly it meant DSSS/HR-DSSS, but then again this is confusing.

So, which is the real bandwith of 802.11g channels?

• This confused me for a while. ERP-OFDM is 20Mhz, DSSS/HR-DSSS is 22Mhz.

• 802.11a,g,n,and the new ac all use OFDM an all have a primary channel width of 20 Mhz.

• Remember it's related to the Spectrum mask of each Modulation method, not a redefinition of the channel spacing.

• Jamrb1963

You have hit upon an area that can be very confusing. Wirelessman is absolutely correct in what he is saying. In some cases it is a bit like ?how long is a piece of string ??

A full reply to the question, in terms of understanding why and where we measure bandwith can involve a lot of signal theory and mathematics. In order to avoid that here, we?ll use some analogies.

Imagine that someone gave you a rectangular box and asked you to measure it?s width. You?d probably say ?That?s easy??let me take a ruler and line it up along it?s width, and there?s the answer?. Nice and straightforward. No problems.

Now, we take you out into the middle of the Sequoia trees in a forest in California, and say ?OK, now measure the width of that huge tree there?.

http://myknownbuzz.com/giant-sequoia-trees/

Now this becomes a bit more complex. Your first questions would probably be:
?Hang on a minute. That tree starts off wide at the bottom and tapers off towards the top. Where do you want me to measure ? At the base ? Half way up ? At the top ??

What is missing from the equation here is a point of reference at which we can measure. This is the complex part and varies according to who is doing the measuring, as well as the shape of the thing being measured.

Going back to measuring our nice square box, we often see diagrams in RF engineering showing nice square boxes in diagrams showing frequency layouts. These are represented for convenience in drawing and do not represent the actual RF signal shape as viewed on say, a spectrum analyzer. In other words, we could draw a series of little square boxes on a graph showing amplitude on the axis and frequency along the x-axis. On these diagrams ( we are not just talking about Wi-Fi here, but all types of RF signals?satellite, microwave etc ). These diagrams are simply a quick and dirty way of showing channel spacing. Channel spacing is different from bandwidth in general.

Now, if we look at a digitally modulated signal, will it appear as a box ? The answer is no, but depending upon circumstances ( to be discussed later ), it can appear ?squarish or boxish? for want of a better expression.

A digitally modulated signal has a complex shape. Many have a flattish top, and tapering sides. Depending upon circumstances, you may see other ?bits? to the left and right of the main signal part. Most of us are familiar with the sidelobes present on all practical antennas. We can imagine a main lobe, then moving a little away spatially, we find a smaller lobe. Moving further away still, we may find even more sidelobes. We can plot the antenna pattern on paper showing relative power versus angle on a circular type of layout known as a polar plot. Figure 2 below:

If we imagine that we had a polar plot drawn on a magical piece of rubbery type of paper that could be stretched into any shape, and we take the middle of the diagram and cut it through the center and strecth it out left and right, we would have an x-y plot with relative power on the x-axis and amplitude on the y axis. This is called a cartesian plot. This can be seen in Figure 1 of the link above.

We would now see a main lobe, with little side lobes to the left and right.

With some types of digital signals ( highly dependent on the modulation method etc used ), we could see a ?similarish? type of thing. In other words ( and we have to be careful not to carry the analogy too far?.antennas and modulated outputs are totally different beasts, but often share a similar sinx/x pattern ) we may see a center ?lobe? and a number of ?sidelobes?. In digital communications, we do not use the term sidelobe ( although you will see it used at times in popular literature ). We usually use the term sideband.

http://zone.ni.com/devzone/cda/tut/p/id/8551

So, now we have a main central signal and a number of sidebands. Do we always see those sidebands ? That depends.

Imagine an island in the middle of the ocean. The island looks like the one shown below, but has symmetry about the center.

http://www.traveljournals.net/pictures/113443.html

We are in a boat and observing the island from a distance. The water ( noise floor ) is nice and calm. The island is mainly a big mountain in the middle ( main signal ) with a number of smaller mountains to the left and right ( sidebands ). You know that beneath the water there must be more of the island. In fact it must go all the way to the ocean floor . What is preventing us from seeing more of the island ( which spreads out left and right, the further we go down below the surface ) is the water level. Using a magical pump, we start to pump out the ocean. As the water level ( noise ) drops, we see more and more of the island, including more small mountains to the left and right of the ones that we saw above the surface. In other words, a big mountain in the middle with progressively smaller mountains to the left and right. Eventually we hit the bottom of the ocean floor.

Now, we get the magical pump back in action and fill up the water back to it?s original level.

A huge tide comes in and suddenly we can only see part of the island. The increase in water level has obscured some of the smaller mountains.

We start the motor in the boat up and start to move away from the island. Gradually, the main mountain becomes smaller and smaller. Eventually we can?t see the smaller mountains at all ( we know that they are there, but just can?t see them from where we are ).

Thermal noise is present everywhere except for bodies at absolute zero ( roughly minus 273 degrees Kelvin ). We can see this noise on a spectrum analyzer. If we look at the output of say a HR-DSSS modulator, we could see a main signal, plus some some smaller ?bumps? or sidebands.

Now we take that amplifier and surround it with a cryogenic refrigerator which contains liquid helium as it?s coolant. We drop the physical temperature of the device down to an extremely low value. On the spectrum analyzer, we can see the noise floor physically dropping down. As this happens ( just as when we used our magical pump to lower the water level of the island ), more features are visible. We see that the main signal has spread out at it?s base. This is not make-believe. Most international satellite communications facilities used cryogenic cooling of LNAs ( low noise amplifiers ) in order to physically lower noise levels and increase SNR. One of my first jobs was doing maintenance on these devices. NASA and the military still use these systems for picking up very low level signals ( Mars rover vehicles etc ).

http://tmo.jpl.nasa.gov/progress_report/42-157/157C.pdf
http://www.ustream.tv/recorded/16743753

In practice, however, this is very difficult and expensive. This example was to show that there is more ?lurking under the water/noise level? than first meets the eye.

We now connect the output of the modulator to an amplifier. The amplifier does two things. It increases the level of the signal ( plus the sidebands ), but it also increases the noise level. In fact even though the signal level increases, the noise ( and this is highly dependent on the quality of the amplifier etc ) will also increase and obscure some of the finer details ( part or all of the sidelobe ?bumps? ). This is equivalent to the tide coming in at the same time as an undersea movement causes the whole island to move up a bit.

Now, we connect the modulator to our Wi-Fi card and start moving away from the device while still looking at the spectrum analyzer. The noise floor ( water level ) stays the same, but the main signal lobe and the sidebands begin to drop in height, due to free space attenuation. This is just what happened when we moved away from the island ( that used the horizon effect, so the analogy can only go so far ). Eventually we get far enough away from the device that we can?t see the sidebands at all. The noise floor does not drop. I won?t go into the reasons for that here, as it involves quite a bit of math and quantum theory. We will see in a later post that the thermal noise floor can vary in another type of communication system.

Now we go back to our measuring problem with the trees. As the trees ( main signal lobe ) taper off towards the top, we need to come up with a reference point from which to measure. It is important to mention here that we are using a linear tape measure and not a logarithmic measure ( our analogy can only go so far ). We know that these Suqioia trees are all the same shape. We decide to measure the total height of the tree above ground ( noise level ). Once this has been done, we say ?OK, we are now going to find the point on the tree where the height has dropped to one half of the height measured at the top. This will be our reference point.? One half corresponds to 3 dB ( yes, we can even use decibels in height measurement ). This has now become our reference point to measure the width of our trees.

In many non Wi-Fi applications, we use a 3 dB bandwidth as a standard. In other words, measuring from the flattish top ( more about that later ), we come down 3 dB in power ( on a spectrum analyzer for example ) and measure what frequency bandwidth that corresponds to on the x-axis ( frequency ) of the spectrum analyzer.

To summarize:

1. Digital signals can have complex shapes. OFDM is in a class of it?s own, and will be discussed later. We need to establish a reference point for bandwidth measurement. This is critical and will be discussed later.

2. Digital signals can have a main lobe and a number of sidebands.

3. If we are going to measure the ?width? of a digital signal, we must have some form of reference to use, due to the fact that no digital signal is perfectly square ( there are some complex mathematics behind that statement which I won?t go into here )

I?ll cover more about signal shapes in the next post, followed by how the IEEE specs for bandwidth are meant to be read.

Dave

• Dave,

Sorry I don't have a "tree stump" analogy to go along with your nature comparisons.

You've probably seen this, but for others who may not have, they should look at an OFDM signal that has an (increasing and) over-amplifed signal. The OFDM signals really do begin to look like overly fat tree stumps. The spectrum masks get fatter and shorter as the signal output is increased.

This is from the amplifier operating out of its linear amplification region. The effect is called "spectral re-growth". There is a really good description of this in the CWDP text, which also discusses some financial aspects of amplifier choice.

Another "odd" view of an OFDM signal is when the (say horizontally polarized) antenna is rotating. The normally flat-topped signal looks like a kids seesaw, with alternate sides moving up and down. I haven't seen this described anywhere, but is very evident if you are rotating the radio on a turntable in a semi-anechoic chamber or screen room and testing for FCC compliance.

In fact, if your test antenna is not polarized to the radio's antenna, even in a static setup, the flat top can look more like a steep slide pointing to one side or the other.

• Now we need to look at the issue of channel separation, and then we?ll come back to bandwidth later. The RF spectrum is a limited resource. There are only so many MHz of unlicenced bandwidth available at any one time ( future bands are being planned ). Many different users, such as the military, the scientific community etc, share that bandwidth. Most of them were ?at home? in the unlicenced bandwidth well before Wi-Fi showed up. Many of the regulations produced by regulatory bodies such as the FCC in the United States are designed to try to miminze the effects of interference from one system into another. Even though it may be thought that ?everybody should be treated equally? in terms of regulations, it just doesn?t work like that. If we consider for example, the co-existence of Wi-Fi and radar systems, then the question could be asked ?Does radar bow to Wi-Fi or the other way around?. I think we all know the answer to that one. If there is an important system such as radar, Wi-Fi is going to have to do what it is told ( DFS etc ), and so it should be. At the same time, the regulators want to make sure that they can cram as many channels as possible into the limited spectrum available. But how do they figure that out ? If we cram ?too many? in, we will definitely have interference. If we put ?too few? in, we are potentially wasting useful RF spectrum. It?s like Goldilocks.

Let?s imagine that the sidebands of a particular signal overlapped our wanted signal by say 10% of the wanted signal. Does that mean that the quality or SNR or packet error rate or any other metric of the signal would drop by 10% ? No, we cannot say that. It is extremely complex to figure out. Even mathematically, certain assumptions have to be made. It depends upon multiple factors, including modulation and coding type etc.

So, most values of channel separation ( the distance between the center frequencies of adjacent signals ) are determined in test labs and ranges. They increase the power a bit here, shift the carriers closer together there etc, until they come up with an acceptable Goldilocks value that is neither too close to cause ?excessive interference? nor too far away to waste bandwidth. Just like the porridge?.neither too hot nor too cold.

Signal shapes vary depending upon the modulation scheme etc. OFDM is unusual, because what we do is to take a whole bunch of narrow band modulated carriers and multiplex them together in frequency to produce a signal. When viewed on a spectrum analyzer, differences can be seen between OFDM and 802.11b signals for example. The raw signal from a modulator, which may show a sinx/x pattern will be filtered to reduce sideband levels. The shape changes. Even what may appear to be a ?flat top? on a modulated signal when viewed on a spectrum analyzer, can often be seen to have ?ripples? when viewed under greater magnification.

In the latest CWNA Study Guide on PP 206 ? 209 there are some diagrams showing spectral masks. So what are these masks ? They basically set limits on power not only for the main signal or ?lobe?, but also for the sidebands on either side of the main lobe. They are like a fitted blanket or dress that goes over the ?customer? or signal. It basically says ?If you can?t fit into this dress size, you need to lose a bit of weight?. The values given are often expressed in dBr ( decibels relative to something ). In the case of channel masks, the ?something? is often the peak value of power ( center of the signal main lobe ).

So, channel separation is determined experimentally ( or should be ). But what about bandwidth ? Now we have to go back to the square box and the trees. We can rule out the square box, as digitally modulated signals can never be perfectly square. So how we do we determine the bandwidth of the signal ? Well, unfortunately, there are many ways to determine bandwidth. One way is to look at the 3dB bandwidth ( where power has dropped down by half ). That?s well and fine, but doesn?t really tell us much. Another way would be too look at a spectrum like that of Figure 6.7 in the CWNA guide and look at where the signal drops off into the noise floor. Another way would be to almost arbitrarily look at the bandwidth between the first nulls ( drop down points between the main lobe and the first sideband ) on either side of the main lobe or carrier. You could also measure between the second nulls. Each would have it?s own place in an engineering analysis. In FM radio engineering, often a ratio is taken between the 3 and 60 dB bandwidths, which give a ?shape factor?. In other words, what is the ratio of the widths measured at the halfway down and one millionth of the way down the tree ? This tells us information on the shape of the tree half way up compared with a place toward the bottom.

In Wi-Fi, we are mostly interested in channel separation rather than bandwidth, as bandwidth can be defined in so many ways. It?s one of the least understood concepts in all of communications, in terms of a modulated signal as opposed to a frequency range of bandwidth ( e.g. UNII 1, 100 MHz plain and simple ). One satellite organization defined occupied bandwidth as containing 90% of the signal energy. Plots would be made on graph paper and you would have to count each square and then use a formula to get the occupied bandwidth value. Modern digital systems make light of that.

What has the following horrible little creature to do with all this ?

http://bartsimpsonpictures.squarelogic.net/

http://www.eetimes.com/design/communications-design/4009233/Don-t-Let-Linearity-Squeeze-Your-WLAN-performance

Actually when you look at some outputs closely, they have the exact ripples that you see on Mr Simpson?s head, hence the term.

More in the next post.

Dave

• That reminded me of something, but unrelated to WLANs. Digital TV (DVB-T) uses OFDM, and where I am the channel bandwidth is 7MHz.

In my IPTV server, one of the channels I just could not receive, even though I had a very good signal. The problem was, that there were 2 channels in use adjacent to each other. The first was from 174 to 181 MHz and the second from 181 to 188 MHz. The corresponding centre frequencies are therefore 177.5 MHz and 184.5 MHz.

If I set the two tuners to the centre frequencies, as they should be, only one of the channels came in. I realised that the TV cards didn't just magically stop listening at the end of their 7MHz bandwidth. I overcame the problem by setting the higher channel's centre frequency to 184.625, which is slightly off-centre, but for the most part where it should be. Everything was then fine.

This was just a real life situation where the bandwidth of something doesn't mean that that's the only thing in the equation.

• When we look at a satellite communication signal received from space on a spectrum analyzer, one of the first things we notice is how much higher the noise floor is ( with similar analyzer settings ) to the noise seen with a Wi-Fi system. What causes this ? There are several reasons, but one of the main ones concerns the fact that the satellite has an antenna facing earth. This antenna integrates all the noise ( highly complex mathematical theory involving multiple integrations ) ?seen? by the antenna. The antenna looking towards the earth picks up thermal noise from the physically warm earth. On the uplink from the earth to the satellite, the earth station antenna ?sees? the cold of space:

http://www.dxsatcs.com/content/insat-3a4b-935-e-c-band-packet-doordarshan-quality

Here, we can see a number of spectrum plots:

http://zone.ni.com/devzone/cda/tut/p/id/8551

With Wi-Fi, we generally refer to spectrum masks rather than actual bandwidth in the specs. One exception was the now obsolete 802.11 FHSS, where the following mention was made:

?14.6.6 Occupied channel bandwidth
Occupied channel bandwidth shall meet all applicable local geographic regulations for 1 MHz channel
spacing. The rate at which the PMD entity will hop is governed by the MAC. The hop rate is an attribute
with a maximum dwell time subject to local geographic regulations.?

If you look at the plot in the following document ( Google Search ), you will see an example of occupied bandwidth with respect to a mobile system:

ieee c802.20-03/112r1

Going back to our previous mention of rough diagrams used for frequency planning or layout purposes, we can see the following:
http://en.wikipedia.org/wiki/List_of_WLAN_channels

In summary, then:

An excellent question, but with a complex series of answers. In general, the IEEE docs tend to refer to channel separation values as opposed to bandwidth values.

If we wish to define bandwidth, we must set parameters on how we wish to measure it, taking the signal shape etc into consideration ( remember measuring the ?width? of the tree ).

Sideband power levels are very important in interference analysis

Some more pictures of the mighty and beautiful Sequoia trees. The General Sherman is one of the oldest living things on earth.

http://ustravels2.freeservers.com/sequoia1.html
http://en.wikipedia.org/wiki/General_Sherman_(tree)

Dave

• As an example of how we must be careful in accepting certain terminology, we can take a look at PP 208 and 209 of the CWNA study guide.

On P208, 5 GHz Channels, lines 3 and 4:

"The original three UNII bands each have four nonoverlapping channels with 20 MHz separation between the center frequencies".

Imagine now that you are at a company picnic. People are sitting by a wooden table, on benches.Four of you are sat side by side. Each person has a placemat. The placemats are separated from each other, and have a little name tag, with the company employee ID: 36, 40, 44 and 48. Each person is completely separate from each other in terms of space. They all have "their own individual, personal space". There is a slight separation of the placemats one from the other.

http://www.magicjumprentals.com/pages/company-picnics
http://www.outdoorfactory.com.au/product90.html

As the picnic goes on, long speeches are given. People's rear ends are starting to hurt, so they shuffle about in their seats side to side. Because of the slight gap between placemats, it means that if two adjacent employees, 36 and 40 say, move towards each other at the same time, they will not bump into each other. The placemats do not overlap each other and even if there is a slight shuffling along the bench, each person will not bump into the other. However, if the speeches go on for hours, people may start shuffling even more, and start to bump into each other.

Now, some people who said they weren?t coming show up. The employees are told to put more placemats down. The only way they can do that is if they overlap the old and new placemats. People now have to sit closer together. It?s not as pleasant as the previous situation, but it?s ?not bad?.

Now a bunch of other people show up. More placemats are put on the table. People are squeezed together. Now complaints start happening ?Sir !!...Sir!! you are in my personal space? ( as they say in the States ). Nobody is very happy.

Just like Goldilocks, there has to be a happy medium. With just a few people at the table, there is room enough for eveyone, but there is space that is being unused.

When just a few more people show up, there is less space, but those extra people can be accommodated.
When too many people show up, they can be accommodated, but a lot of bumping into each other occurs.

So it was when the regulatory groups were determining channel spacing. If they went for the first situation ( within a limited, fixed frequency space ), you could fit everyone nicely, but you weren?t making maximum use of the space.

In the third situation, there were just too many users ( too many channels ). Mutual interference from overlap would be too much.

The second option was chosen. A ?fair number? of channels, with an ?acceptable amount? of overlap.

Wi-Fi signals are transmitted from APs, STA cards etc. Inside those devices are oscillators. Those oscillators usually have a crystal and probably a programmable divider frequency synthesizer arrangement with phase locked loops etc. However, there is a certain amount of drift. When we have two channels side by side with different STAs using them, we have no idea whether the two frequencies will be coming closer together at a point in time or farther apart upon initial viewing ( you can usually see a pattern long term ). A ?guard band? is usually put in place to account for this frequency drift ( the IEEE has specs for this?temperature changes are a major factor which have to be contended with ). In the picnic analogy, this represents people shuffling side to side.

Now, let?s go back to the phasing used in the CWNA book: ??.four non-overlapping channels?.?.

There is a picture on page 209 showing the channel layout a la ?IEEE 802.11?.

Because it said ?non overlapping?, we should see every channel completely and totally separated from each other with absolutely no ?bumping together? whatsoever of any kind. After all, at the picnic table, the placemats are either overlapping or they are not. There is no in between.

However, when we look at Figure 6.9, do we see completely separate channels without any touching or bumping whatsoever ? No. We see what I would say is a fair amount of overlap.

So does this mean that there is a mistake in the book ? No, it doesn?t. The terms have been taken straight from official documents.

So how can we be talking about ?non overlapping? one minute, yet see obvious overlap the next, in the figure ?

We?re straight back to measuring the trees ?.where do we measure the width ? In this case, the question is how do they define non-overlapping ? From the looks of it, they have decided to say it is when the ?top squarish parts? of adjacent channels are not touching each other ( it?s more complex than that, but we won?t go into that here ).

In other words, we are back to Goldilocks. Not too much space and not too little space. The values of overlap that gave ?acceptable performance? were determined experimentally.

What started off as a relatively simple question about bandwith in Wi-Fi, can be seen to be actual quite complicated in terms of a response.

Transmit mask specs and channel separation values are two important parameters. We must be careful of terminology and points of reference for measuring.

The next time you are in coach on an international flight, and a portly person sits down beside you, all of these concepts will suddenly come to mind, especially five hours in.

Dave

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