OFDM and oversampling

Started by May 3, 2006
```Hi !
I would like to know if in practice, it is useful to oversample the signal
at  IDFT output. The sampling rate at the IDFT output is the Nyquist rate
(2 times the frequency of the baseband signal) but I believe that it is
necessary to oversample in order to perform the Root Raised Cosine
Filtering. If I am right, what is the method to oversample :
- Interpolation (using an IDFT size 2 times the basic IDFT size) ?

It is difficult for me to find such informations.

Thanks a lot,

Sylvain

```
```Hi,
With the basic IDFT size, say that the sampling rate is fs, and
the largest baseband signal is fs/2. By doing zero padding to
interpolate twice (Adding alternate zeros), we will create image
frequencies ( fs/2 to fs). The Root Cosine filter will attenuate this
image though. Must simulate and check whether the resulting spectrum is

By doing IDFT at twice the rate (2fs), all the frequencies above fs/2
will be zeros since we force it to zeros at the input to the IDFT.

Computationally interpolating with zeros is better. We can decrease the
roll off factor (alpha) as much as possible (Compromises with increase
in number of taps of the filter) and make it meet the PSD Mask.

Anantan.

6.20 wrote:
> Hi !
> I would like to know if in practice, it is useful to oversample the signal
> at  IDFT output. The sampling rate at the IDFT output is the Nyquist rate
> (2 times the frequency of the baseband signal) but I believe that it is
> necessary to oversample in order to perform the Root Raised Cosine
> Filtering. If I am right, what is the method to oversample :
> - Interpolation (using an IDFT size 2 times the basic IDFT size) ?
>
> It is difficult for me to find such informations.
>
> Thanks a lot,
>
> Sylvain

```
```Why do you want to filter your OFMD isgnal with a RRC?

```
```@ Phil: RRCF is useful in order to supress ISI

>Why do you want to filter your OFMD isgnal with a RRC?
>
>

```
```For OFDM, the ISI is supressed via the cyclic prefix not RRF filtering.

```
```I think there are to kinds of symbols in OFDM systems:

- The symbols that are at the output of the (I)DFT. For example, at the
IDFT output, the space between 2 symbols is 1/(Bandwidth). In Hiperlan2 it
is 1/(20MHz)=50nsec=Ts.
- The OFDM symbol : The space between 2 OFDM symbols is N*Ts + Ncp*Ts. N
is the number of subcarriers and Ncp is the number of samples for the
Cyclic Prefix. For example in Hiperlan2 : Tofdm = Ts*64 + 16*Ts = 4usec.

So I speak about the first kind of symbols and YOU speak about ISI for
OFDM symbols, it is really different.

Sincerly,

sylvain

>For OFDM, the ISI is supressed via the cyclic prefix not RRF filtering.
>
>

```
```To go back to your original question, if you do not have sufficient
guard bands, i.e., if you are using almost all of your IFFT bins, then
oversampling may be required so that your reconstruction filter does
not have to be too sharp.

The oversampling can be done using a simple half-band filter.  What
would be the benefit of RRC?  Am I missing something?

```
```If i well understand your answer :
The Raised cosine Filter is not usefull in OFDM systems if I don't use all
the IFFT bins ?

>To go back to your original question, if you do not have sufficient
>guard bands, i.e., if you are using almost all of your IFFT bins, then
>oversampling may be required so that your reconstruction filter does
>not have to be too sharp.
>
>The oversampling can be done using a simple half-band filter.  What
>would be the benefit of RRC?  Am I missing something?
>
>

```
```When the samples go through the digital to analog converter (DAC), the
spectrum is replicated periodically, as you should now.  In order to
remove (suppress) the spectral replicas, a reconstruction filter is
required following the DAC.

If there are no high frequency bins left empty to create a large enough
gap between the spectral replicas, over sampling is required.  If you
oversample by a factor of 2, the spectral replicas are much further
apart and a reconstruction filter is much easier to design since the
roll-off can be much larger, i.e., a low order filter.  If this is the
solution that you are taking, the oversampling can be done using a
half-band filter for pure interpolation.  In my mind, the reason for
RRC filtering is pulse shaping.  Pulse shaping of this kind is not
usually done in OFDM.

If a high order reconstruction filter (remember, this is analog) is
practicable, then leaving some of the IFFTs high frequency bins empty
without oversampling is acceptable.

I hope that this was a little more clear and that it helps a little.  I
don't know your background, so just keep in mind that the above is not
the only reason to consider upsampling of OFDM.  Sometimes, the design
requires it for other reasons too.

```