I'm currently trying to simulate Frequency Domain Equalization, and the effect that over sampling in the frequency domain has on the affect of the equalization. If I understand things correctly this is the process that's supposed to happen using a single Carrier when transmitting
- Modulate and transmit the symbols to create $x(n)$, each symbol being $N$ samples.
- add noise, $z(n)$, and channel effects, $h(n)$, for the receiver, $ y(n) = h(n)\star x(n) + z(n)$
- Zero pad, where $ZP$ is the number of added zeros, in the time domain to over sample in the frequency domain. $FFT(y(n),N+ZP)$. Note that increasing the order of the FFT should be the same as zero padding in the time domain
- Do Equalization in the frequency domain
- Go back to the time domain
- Demodulate the symbols
The part I'm not sure about is step 5, where we go back to the time domain. In order for my number of samples per symbol to be correct, I need N samples, but I have $N+ZP$ samples if I take the same size $IFFT$. Doing the Zero padding and taking the $FFT$ should be interpolation... but i'm not sure how to do the decimation so that I have the correct number of samples. Does anyone have any idea about this? Thanks!