Studying the Physical Layer – OFDM Symbols

I am currently involved in studying for the CWAP exam. I wish to take advantage of the CWNP Free Retake Offer so that if I need to I can retake the exam without having to pay for it. Being the person I am, however, I can’t just approach this as “I’ll try and see what happens”. I actually am studying to pass it, so because of this I am trying to actually understand the material and gain enough insight into it that I understand how everything works. The difficulty with this is that there are bits that are glossed over in the CWAP study guide by necessity, as they are not important to the exam, but I still want to know how it works, how it all fits together. So I necessarily have to go out and find for myself the information I want.

I have been steadily going through the physical layer descriptions, if you haven’t yet studied this material its quite fascinating. The basic idea is that each station has to sit and listen to the channel (if its not sending) to detect the beginning of any signal it can receive. A transmitting station will first of all send a preamble. The preamble consists of a stream of 0’s or 1’s that the receiving station can synchronize with, then after this the transmitting station sends the Start Frame Delimiter (SFD) which is a set 16 bits that indicates the PLCP Header is next. This process is all pretty straight forward to understand, however the problem is it just describes how DSSS works and not OFDM.

In the OFDM world the PLCP preamble is also called a training structure, which consists of 10 short symbols and 2 long symbols. These are described as the 10 short symbols are used for AGC (automatic gain control), diversity selection and coarse frequency offset estimation of the carrier signal. The 2 long symbols are used for channel and fine frequency offset. We also get additional information, that the total training length is 16 microseconds and a short training symbol has 12 subcarriers and a long training symbol has 52 subcarriers. Leaving aside for a second that some of this (such as frequency offset estimation) may not immediately make sense one thing that struck me in reading all this was that I wasn’t sure I understood what the word ‘symbol’ meant in this context. It seemed to me that one of the core things to understand about how OFDM works is to understand what an OFDM symbol actually is.

I actually have both editions of the CWAP study guide. I find while studying that it helps sometimes to get two different views on a certain section in order to gain understanding. My first reaction was to look in the index, glossary and list of terms to see if it was more defined. Nope, its assumed to be something known. Maybe it was in CWNA and I just missed it, so I go back to my CWNA guide and find that there is an index entry for symbols. It turns out to be pretty thin, however, and part of a discussion on guard intervals in 802.11n in that book. Not really enough for my purposes. Now this becomes a mission for me, I simply must understand what symbol means in this context.

I first of all hit Google and discover that Wikipedia has Symbol rate as an entry. It begins that a symbol can be described as either a pulse (in digital baseband transmission) or a “tone” (in passband transmission using modems) representing an integer number of bits. It then goes on to give some examples of the relationship between baud rate and bit rate. This is useful but for me I still cannot quite grasp from this explanation how it relates to the usage in OFDM. I post to twitter as well to get input from other WLAN pro’s on this question and get some great answers (as much as you can in 140 characters). Finally my friend Matthew Gast comes out with ‘A symbol is a change in amplitude & phase that carries a defined number of bits’. ‘Data bits get mapped into a constellation by amplitude and phase change; constellation has 2^(# of data bits)’. This to me seems to be getting closer to something I can understand. Matthew adds ‘All PHYs use symbols, CCK, DSSS and FHSS are all simpler than OFDM though’. That to me points out even more its important to understand what symbols are.

I continued to search and found a page on modulation in Wikipedia, which is also very useful in adding to my knowledge as it describes the process of modulating a signal. The analogy to music seems to be common in describing how radio signals work, which is not surprising in that radio signals quite commonly as shown to be waveforms. In the section of this article that talks about digital modulation methods it describes how telephones lines were designed for transferring audible sounds and I’m sure we are all used to the noise of a modem as it syncs with its partner at the other end. The process that is going on here is that the digital computer is using an analog sound, a set of “tones”, to represent data that is being sent. Each tone can be thought of as a symbol of the data it represents. As long as both ends understand what the tone or symbol means, then they can map this to a piece of data.

Now that I have isolated that a symbol is a represenatation of some piece of data that is being sent, I want to dig a bit further and figure out how it works in particular for wireless. Now in case you need a refresher, the last stage before a piece of data is sent over the air is handled by the PCLP (Physical Layer Convergence Protocol). Its function is to take the PSDU (PLCP service data units) and add a PLCP header and preamble to them to form the PPDU. The PPDU is what is actually sent by the PMD over the air. In my mind the PLCP is preparing everything and then instructing the PMD to modulate the data and send it over the air. This means that the PLCP also is responsible for generating the symbols that represent the data that is being sent.

Mathew confirms my supposition and additionally tells me exactly where in 802.11-2007 the process is described (its in clause and an example is given in Annex G). So now with this reading my understanding finally has the process down. Lets go over it;

  1. OFDM is a signaling technique that breaks down a stream of data into subcarriers. This is roughly analogous to a chord on a guitar, which is made up of individual notes played together. You can read a much better explanation of this here.
  2. Each of those subcarriers is modulated by using BPSK, QPSK, 16-QAM or 64-QAM depending on the rate needed. The preamble in OFDM is always sent using the lowest rate.
  3. This data is goes through a couple of other processes to prepare it and then is broken down into groups of 1, 2, 4 or 6 bits  and then converted into complex numbers representing BPSK, QPSK, 16-QAM or 64-QAM constellation points.
  4. These complex numbers are a mathematical representation of the original data and as such can be used to form a signal to be sent to the receiver.
  5. The complex numbers then are our symbols as each symbol is a mathematical representation of a change in the waveform.

As an aside, the reason for using the constellation diagrams as shown in the 802.11-2007 standard is that this incorporates defined bit patterns, so that is one bit has an error the receiver can correct it because it knows that the bit should be a different value. This is a property of Gray codes.

I hope you have enjoyed my small explanation of what symbols are, please do let me know if I have made any mistakes in this (hopefully not) or if some part requires further explanation.

5 Responses to “Studying the Physical Layer – OFDM Symbols”

  1. Leonardo Mezzanotti says:

    Great post man. CWDP study guide has a good but tiring explanation for symbols.

  2. WildDev says:

    Yes I just looked at that now on pg 31. For me at least it doesn’t quite go deep enough in explaining it and the relationship to the constellation diagrams. Well I hope my post helps others who are wanting to understand the concept better.

  3. Jose says:

    Very interesting blog. Im involved in TSCM services and some of the info you are providing is very useful for my job. Thanks for sharing, I will visit your blog often.

  4. spencer says:

    I am very impressed by the quality and detail of this blog. I will keep referring back here while studying for the CWNA.

    Thanks for sharing

  5. Greg Kamer says:

    This is a great write up! Thanks for the time you took to put this here. I did want to bring some thing your attention; your link the OFDM blog post on CWNP’s site is broken. Here is the correct link:

    Thanks again and keep up the good work!

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