On Fri, Aug 23, 2013 at 10:10:13AM +0200, Bastian B. wrote:

I wonder why the OFDM Cyclic Prefixer uses the samples at the

beginning of the symbol to calculate the roll off. I would have

expected that the samples from the end of the previous symbol are

used. So something like this:

https://github.com/bastibl/gnuradio/commit/1a1f0f92cedac90ccadf5e42f4e09b3188b04352

But since also the unit test expects the samples from the start of

the symbol I might get the concept totally wrong.

First:

I’m not saying there’s definitely no bug in that code–checking that has

been high on my priority list. Just not high enough

That said, the samples can’t be from the end of the previous symbol, as

that would actually shorten the OFDM symbol duration. You’re copying the

last few samples of the OFDM symbol, right?

Think of it a bit like a filter. We start with rectangular pulse shapes,

and OFDM symbols have length T (or N samples), including the cyclic

prefix.

Now we want the same thing, but with pulse shaping. We cannot simply

change the duration of the OFDM symbol (well, we could, but we want a

fair comparison). If we’d be filtering the OFDM symbol in time domain,

we’d expect the delay line of the filter to trail the output, adding a

few samples to the OFDM symbol (but they would leak into the next

symbol, which means the OFDM symbol spacing is still T).

Only we’re not filtering–we’re adding a tapering window in time domain.

At the beginning of the symbol, we can simply multiply the samples with

the up-ramp of our tapering window (we use a raised cosine flank).

So what happens at the end? We could do the same: Multiply the last few

samples with the down-ramp. But then we’re simply throwing away energy.

It would be much nicer if the down-ramp came *after* the symbol, during

the up-ramp of the following symbol. This is achieved by adding samples

from the beginning of the symbol (think of it as a “cyclic postfix”) and

multiply those with the down-ramp of the tapering window.

In fact, this cyclic postfix is the *only* correct continuation of the

OFDM symbol, because of continuous phase. It looks like your solution

does not have continuous phase.

MB

PS: Do you have a copy of Nachrichtenübertragung (Kammeyer)? He explains

it quite well in Chapter 16.4.

–

Karlsruhe Institute of Technology (KIT)

Communications Engineering Lab (CEL)

Dipl.-Ing. Martin B.

Research Associate

Kaiserstraße 12

Building 05.01

76131 Karlsruhe

Phone: +49 721 608-43790

Fax: +49 721 608-46071

www.cel.kit.edu

KIT – University of the State of Baden-Württemberg and

National Laboratory of the Helmholtz Association