On Nov 11, 7:21 pm, Andrew FPGA <andrew.newsgr...@gmail.com> wrote:
> > No. T is the length of the OFDM symbol before the cyclic prefix has
> > been added.
>
> Umm, what part of what I wrote is no? I can define T how I like, and I
> defined it to include the cyclic prefix. If there is no window applied
> to the cyclic prefix, then the channel and the maths does not care
> about the relative size of the original OFDM symbol and cyclic prefix?
> A rect in the time domain is a sinc in the frequency domain. Where do
> you think my logic is wrong?

Whilst you're free to define T any way you like, the maths only works
(in the sense of retaining sub-carrier orthogonality) if T is defined
as the length excluding the CP.

>
> But, I suppose that in the receiver the cyclic prefix gets removed
> before the FFT demodulation. So as far as the FFT is concerned the
> cyclic prefix was never there, so now the sub-carriers are spaced
> closer together. Which raises the question, how does a
> shaped(windowed) cyclic prefix help reduce inter-carrier interference
> if it gets removed prior to the FFT demod? (I know the cyclic prefix
> is added to allow for a guard interval, to deal with spread from one
> OFDM symbol to the next. But I have also read papers describing how
> the CP is also windowed such that it brings an advantage to the shape
> of sub-carrier spectrum).

The shaping of the CP is irrelevant when it comes to eliminating ICI.
The standard explanation is along the lines of:

The CP effectively converts the linear convolution of the channel into
circular convolution over the non-CP section of the OFDM symbol. For
a DFT, the convolution theorem states that circular convolution in one
domain is equivalent to pointwise multiplication in the other domain.
In other words, after the FFT in the receiver, the original data may
be recovered simply by multiplying each sub-carrier symbol by a single
complex value. There is no interaction between the sub-carriers.


--
Oli