Can someone explain OFDM to me?

[GreyWanderer]

Orthogonal Frequency Division Multiplexing

I understand that the signal is multiplexed into multiple channels, but I don’t quite understand this orthogonality that make the signals not interfere with eachother. Also, is this technology superior in every way to regular FDM?

[astro]

Orthogonal Frequency Division Multiplexing

In OFDM the subcarrier pulse used for transmission is chosen to be rectangular. This has the advantage that the task of pulse forming and modulation can be performed by a simple Inverse Discrete Fourier Transform (IDFT) which can be implemented very efficiently as a I Fast Fourier Transform (IFFT). Accordingly in the receiver we only need a FFT to reverse this operation. According to the theorems of the Fourier Transform the rectangular pulse shape will lead to a sin(x)/x type of spectrum of the subcarriers (see figure 0.5).

[GreyWanderer]

I think I saw that exact site when I googled for it. I may be stupid, but what I don’t understand is “By using an IFFT for modulation we implicitly chose the spacing of the subcarriers in such a way that at the frequency where we evaluate the received signal (indicated as arrows) all other signals are zero.”.

How is this archieved? And what exactly is orthogonality? Does it mean they are 90 degrees apart?

[mks57]

@GreyWanderer

And what exactly is orthogonality? Does it mean they are 90 degrees apart?

In a geometric coordinate system, the axes are orthogonal if they are perpendicular to each other, like with normal x/y and x/y/z coordinates. Yaw, pitch and roll are also orthogonal. A computer can have an orthogonal instruction set if the various fields of an instruction word are independent of each other.

[astro]

Orthogonality

In mathematics, orthogonal is synonymous with perpendicular when used as a simple adjective that is not part of any longer phrase with a standard definition. It means at right angles. It comes from the Greek “ortho”, meaning “right” and “gonia”, meaning “angle”. Two streets that cross each other at a right angle are orthogonal to each other. Two vectors in an inner product space are orthogonal if their inner product is zero. If the vectors are x and y this is written . The word normal is sometimes also used for this concept by mathematicians, although that word is rather overburdened.

In radio communications, multiple access schemes are orthogonal when a receiver can (theoretically) completely reject an arbitrarily strong unwanted signal. The orthogonal schemes are TDMA and FDMA. A non-orthogonal scheme is Code Division Multiple Access, CDMA.

[astro]

More specifically re signaling

Orthogonal (“composed of right angles”) is a technical term referring to a certain special characteristic of the long code, the short code and the Walsh codes. It refers to the fact that, for instance, if you take any two Walsh codes and XOR them together, the result will be 32 1’s and 32 0’s. But if you XOR a Walsh code with itself, the result is 64 0’s. The short code and long code are orthogonal to themselves at different offsets. What this means is that if two short codes are synchronized, then the XOR of them is all 0’s. If they are offset from each other, by any amount, then the XOR of them is about half 1’s and about half 0’s. The long code is also orthogonal to itself. This was done deliberately and without it CDMA wouldn’t work. This fundamental characteristic of the long code, short code and Walsh codes is what makes it possible for the rake receiver to separate out the chip sequence intended for this phone from the ones being sent to all the other