FDM and OFDM both have the same overlap!. In FDM the overlap is in the time domain. In OFDM the overlap is in the frequency domain.

First (you may already know this) the relationship between the rectangular pulse and the sin(x)/x (sinc) function:

A rectangular pulse in the time domain transforms to and from the sinc function in the frequency domain. A sinc function in the time domain transforms to and from a rectangular "brickwall" function in the frequency domain. In other words these two functions transform to each other by either FFT or IFFT.

In both FDM and OFDM we are taking multiple carrier frequencies, modulating them, then combining them for transmission.

For simplicity lets assume each carrier is on/off modulated. In idealized FDM, we modulate each carrier then

send each though a brickwall filter before combining to the antenna. Say the carriers are separated by 500KHz, (say at 1GHz + 500KHz, 1GHz + 1MHz ...)

Each carrier's 500KHz brickwall filter in the frequency domain cause a time domain spreading of its on/off pulses into time domain

sinc function with zero crossings every 1us.

Now, if we make the baud rate 1Mbps, each bit's ideal sampling point (center if eye) occurs at the zero crossing point of

all of the potentially interfering sinc functions from previously received bits. In other words there is lots of ISI, but none at the critical moment when the bits are sampled. This is called "signalling at the Nyquist rate" and is related to but not the same as

Nyquist sampling which you hear a lot about. (see en.wikipedia.org/wiki/Nyquist_ISI_criterion, apparently I am not allowed to include link because I am new to physicsforums).

Of course brick wall filters are hard to make, so we use things like raised cosine filters that create the same beneficial sinc zero crossings.

OFDM is analogous to FDM but with time and frequency domain reversed.

We on/off modulate our carriers, but they are combined as unfiltered rectangular pulses and sent straight to the antenna (simplification of course).

These time domain rectangular pulses become spread in the *frequency* domain as sinc functions.

If we on/off modulate each carrier at 1Mbps (1us symbol time), and simultaneously maintain 1MHz carrier spacing ("orthogonal"),

then the zero crossings of the sinc functions occur every 1MHz. Their positions are such that at each carrier frequency, all other carrier's smearing sinc functions have zero crossings. Thus each carrier frequency is free from interference.

Again there is plenty of interference between these signals, but none at the critical frequencies where the carriers are located.

Note the factor of 2 difference between the OFDM bandwidth and the FDM bandwith in my example. This is due to the convention of including negative frequency in the bandwidth in the OFDM case.

Naturally, there is much more to it than this, but this is the basics.

Hopefully you can figure out from this where the 50% comes from (look at the superimposed sinc functions).

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