# Orthogonal Frequency Division Multiplexing

It seems like I run into this term with just about every new digital transmission technology. What the heck does “orthogonal” mean when applied to frequencies? What are the advantages of this modulation scheme?

It was this paper written back in 1994, by Phil Karn, an amateur radio operator, that made it make sense for me. He explains the concept in great detail along with the math behind it and also proposes one particular coding scheme (but there are many possible).

After gaining an understanding, I am curious if this isn’t what the proprietary Telebit protocol PEP is. They didn’t have the high end digital signal processors to work with but they had the Motorola 68000 CPU.

Now that I have a reasonable understanding of the protocol and the math behind it, I understand the reason it is being so widely implemented and why folks are pursing ultra-wideband transmission schemes. The potential benefits of this protocol are so great that I wonder if any other modulation schemes will still be in use in a couple of decades.

My question with respect to how “Orthogonal”, a geometrical term, applies to “frequency”. Imagine an old linear radio dial, the type with the numbers from one end to the other with a little pointer that moves when you twist a knob to select a station. Now imagine that dial is linear. Now on this linear dial you have lines marking off frequency divisions equally spaced apart. You’ve got a bunch of parallel equally spaced lines on the dial, they are orthogonal. Now that you can visualize that you can see how orthogonal can apply to frequencies.

Orthogonal frequency division multiplexing divides up bandwidth into a bunch of narrow channels using equally spaced carriers each modulated at a slow symbol rate. This is realized by using fast Fourier transforms rather than attempting to create hardware to modulate and demodulate each carrier. It is the advent of fast digital signal processors that has made it practical to encode high bit rate streams suitable for digital video or local area network applications.

There are a number of very interesting ramifications. If you use a large number of channels, this modulation technique can approach the Shannon limit which defines the theoretical maximum data transmission rate possible with a given bandwidth and signal to noise ratio. Another way of putting it is that OFDM utilizes the available spectrum with near perfect efficiency.

OFDM can transmit data over a channel in which the noise is much higher than the signal. That makes it possible for multiple devices to share the same spectrum without interfering with each other.

Each channel operates at a very low rate relative to the total speed. Each symbol transmitted is smeared out over a long time frame and in the receiver integrated over a long time frame. Ordinary modulation would suffer severe interference with even brief interruptions, but because of the way OFDM smears the transmitted symbols out over time, a brief interruption in the received signal will not cause a loss of data. Those of you who’ve been annoying by the swish-swish on FM while driving down the road can appreciate this.

By itself this scheme is still sensitive to selective channel interference. Additional coding can be done to reduce this. When this is done, OFDM becomes CODFM. Again the article references above gives one example.

In addition to making efficient use of bandwidth OFDM also makes efficient use of transmitted power since it can allow the maximum transmission rate for a given signal to noise ratio.

As the cost of digital signal processors continue to drop and the power of digital signal processors continues to increase, I expect that it’s a matter of time before CODFM pretty much displaces conventional modulation schemes altogether.