## Friday, July 19, 2013

### OFDM and COFDM

Engineers know that OFDM (orthogonal frequency-division multiplexing) is a multi-carrier transmission system i.e. it uses a number of narrow band sub-carriers, and is resilient in the face of multi-path interference, and narrow-band interference. Thouse is it sensitive to phase problems. It's used in both wireless and DTV. The problem with OFDM is that people just don't know what the word "orthagonal" means. So lets discuss orthogonality.

In Euclidean geometry (the normal geometry you got in high school) orthogonality is the relation of two lines at right angles to one another. In other words... they are perpendicular. But that is a strictly 2 dimensional understanding. Radio waves are not lines, they radiate outward and can be polarized in any orientation. So successive waves can overlap and not even intersect and share the same frequency. Try to imagine it like a series of overlapping slinkys. But each slinky is carrying redundant data so while this increases it's resistance to interference, is has the downside of reducing the load of data it can carry. If that sounds a lot like FDMA that's because they are similar.

COFDM is coded orthogonal frequency-division multiplexing. COFDM and OFDM only differ in that with COFDM forward error correction is applied to the signal before transmission. (Remember the transmission can be occurring on 1,000 narrow-band frequencies.) In this manner COFDM reduces the number of errors caused by lost carriers from shadow fading, frequency selective fading, channel noise and other propagation effects.

Forward error correction improved it's redundancy by encoding an error-correcting code. This was the receiver can correct a certain number of errors without retransmission. This idea was comes form a single American mathematician, Richard Hamming. In 1950 he created the first error-correcting algorithm: the Hamming (7,4) code. It was such a good idea we even use it in modems. He was a damn genius and died in 1997 after a long and accomplished career.