Hello group, It is my pleasure to be posting queries to this group again. My understanding of the presence of the cyclic prefix (CP) in an OFDM symbol is to: 1. Prevent inter-symbol interference in a FIR channel if the length of the CP is larger than the delay spread of channel. 2. Makes linear convolution "appear" as circular convolution over the duration of the useful period in the OFDM symbol, thereby simplifying equalization at receiver. 3. My own advantage: Timing offset correction is simplified since any timing offset results in a progressive phase rotation, with sub-carriers closer to DC having much smaller phase rotation compared to sub-carriers closer to the nyquist frequency. My question is this: Advantage 3 holds only when the timing offset is such that the FFT input window starts before the ideal OFDM FFT start window i.e. the start of the FFT window includes a portion of the cyclic prefix, followed by the "useful portion" of the OFDM symbol. In such a case, the consequences outlined in (3) follow. What happens if the FFT input window starts with the first sample occuring AFTER the ideal FFT start window. In such a case, the last sample into the FFT input will be drawn from the cyclic prefix of the next OFDM symbol. In which case, the progressive phase rotation no longer occurs as the input to the FFT block is no longer circularly rotated. Should'nt practical OFDM symbols therefore include a cyclic postfix (drawn from the beginning of the OFDM symbol) to account for timing recovery if the timing offset is past the ideal timing instant. For example, the European DVB standard does not mention any cyclic post-fixes in their description of the OFDM transmit frame... Please clarify.. thank you regards Vikram

# OFDM cyclic extension related question

Started by ●February 11, 2005

Reply by ●February 13, 20052005-02-13

Sounds like you understand this well enough. Most systems don't apply a post-fix although sometimes it can make sense to do so if a window is applied to the symbols to control spectral sidelobes. You're right that most standards don't say anything about a post-fix, so it's important for a timing synchronization system to get it right for the reasons you've indicated. On 11 Feb 2005 17:09:37 -0800, cvikram@mac.com wrote:>Hello group, >It is my pleasure to be posting queries to this group again. > >My understanding of the presence of the cyclic prefix (CP) in an OFDM >symbol is to: > >1. Prevent inter-symbol interference in a FIR channel if the length of >the CP is larger than the delay spread of channel. >2. Makes linear convolution "appear" as circular convolution over the >duration of the useful period in the OFDM symbol, thereby simplifying >equalization at receiver. >3. My own advantage: Timing offset correction is simplified since any >timing offset results in a progressive phase rotation, with >sub-carriers closer to DC having much smaller phase rotation compared >to sub-carriers closer to the nyquist frequency. > >My question is this: Advantage 3 holds only when the timing offset is >such that the FFT input window starts before the ideal OFDM FFT start >window i.e. the start of the FFT window includes a portion of the >cyclic prefix, followed by the "useful portion" of the OFDM symbol. In >such a case, the consequences outlined in (3) follow. > >What happens if the FFT input window starts with the first sample >occuring AFTER the ideal FFT start window. In such a case, the last >sample into the FFT input will be drawn from the cyclic prefix of the >next OFDM symbol. In which case, the progressive phase rotation no >longer occurs as the input to the FFT block is no longer circularly >rotated. > >Should'nt practical OFDM symbols therefore include a cyclic postfix >(drawn from the beginning of the OFDM symbol) to account for timing >recovery if the timing offset is past the ideal timing instant. For >example, the European DVB standard does not mention any cyclic >post-fixes in their description of the OFDM transmit frame... > >Please clarify.. > >thank you >regards >Vikram >Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org

Reply by ●February 14, 20052005-02-14

Vikram, There are a couple of solutions to your problem. The first solution (to ensure your timing is correct) is to repeat the first OFDM symbol twice. This ensures that when you take the FFT over your window, you will capture a linear shifted version of your signal and can thus extract correct timing information. The second solution again assuming a repitition of the first OFDM symbol in a frame, then techniques are used to correlate the cyclic prefix to obtain a coarse estimate and then use further signal processing techniques to hone in on the correct timing. Incidentally, you can perform a similar estimate of the FFT window by extracting and correlating the scattered pilot symbols in a standard like DVB. Actually, as I stir the pot of my memory on OFDM, there are a number of techniques you can use to get the correct timing, because, after all, without that you'll end up with garbage coming out. Not sure if i answered your question because i'm not clear whether you want a feeling for the problem or want a specific technique used in the standards? col cvikram@mac.com wrote in message news:<1108170577.569244.117400@o13g2000cwo.googlegroups.com>...> Hello group, > It is my pleasure to be posting queries to this group again. > > My understanding of the presence of the cyclic prefix (CP) in an OFDM > symbol is to: > > 1. Prevent inter-symbol interference in a FIR channel if the length of > the CP is larger than the delay spread of channel. > 2. Makes linear convolution "appear" as circular convolution over the > duration of the useful period in the OFDM symbol, thereby simplifying > equalization at receiver. > 3. My own advantage: Timing offset correction is simplified since any > timing offset results in a progressive phase rotation, with > sub-carriers closer to DC having much smaller phase rotation compared > to sub-carriers closer to the nyquist frequency. > > My question is this: Advantage 3 holds only when the timing offset is > such that the FFT input window starts before the ideal OFDM FFT start > window i.e. the start of the FFT window includes a portion of the > cyclic prefix, followed by the "useful portion" of the OFDM symbol. In > such a case, the consequences outlined in (3) follow. > > What happens if the FFT input window starts with the first sample > occuring AFTER the ideal FFT start window. In such a case, the last > sample into the FFT input will be drawn from the cyclic prefix of the > next OFDM symbol. In which case, the progressive phase rotation no > longer occurs as the input to the FFT block is no longer circularly > rotated. > > Should'nt practical OFDM symbols therefore include a cyclic postfix > (drawn from the beginning of the OFDM symbol) to account for timing > recovery if the timing offset is past the ideal timing instant. For > example, the European DVB standard does not mention any cyclic > post-fixes in their description of the OFDM transmit frame... > > Please clarify.. > > thank you > regards > Vikram

Reply by ●February 15, 20052005-02-15

Col and Eric, Thank you very much for your prompt replies. Col, I liked your solution very much. The idea of repeating the OFDM symbol (since it is phase continuous) is a very appealing idea. It sounds like an idea that is easily implementable in practice. I am doing an design exploration of what it takes to build up a set of features for a OFDM modulator/demodulator. Hence the question... Regards Vikram Col Brown wrote:> Vikram, > > There are a couple of solutions to your problem. The first solution > (to ensure your timing is correct) is to repeat the first OFDM symbol > twice. This ensures that when you take the FFT over your window, you > will capture a linear shifted version of your signal and can thus > extract correct timing information. The second solution again > assuming a repitition of the first OFDM symbol in a frame, then > techniques are used to correlate the cyclic prefix to obtain a coarse > estimate and then use further signal processing techniques to hone in > on the correct timing. > > Incidentally, you can perform a similar estimate of the FFT window by > extracting and correlating the scattered pilot symbols in a standard > like DVB. Actually, as I stir the pot of my memory on OFDM, thereare> a number of techniques you can use to get the correct timing,because,> after all, without that you'll end up with garbage coming out. > > Not sure if i answered your question because i'm not clear whetheryou> want a feeling for the problem or want a specific technique used in > the standards? > > col > > > cvikram@mac.com wrote in messagenews:<1108170577.569244.117400@o13g2000cwo.googlegroups.com>...> > Hello group, > > It is my pleasure to be posting queries to this group again. > > > > My understanding of the presence of the cyclic prefix (CP) in anOFDM> > symbol is to: > > > > 1. Prevent inter-symbol interference in a FIR channel if the lengthof> > the CP is larger than the delay spread of channel. > > 2. Makes linear convolution "appear" as circular convolution overthe> > duration of the useful period in the OFDM symbol, therebysimplifying> > equalization at receiver. > > 3. My own advantage: Timing offset correction is simplified sinceany> > timing offset results in a progressive phase rotation, with > > sub-carriers closer to DC having much smaller phase rotationcompared> > to sub-carriers closer to the nyquist frequency. > > > > My question is this: Advantage 3 holds only when the timing offsetis> > such that the FFT input window starts before the ideal OFDM FFTstart> > window i.e. the start of the FFT window includes a portion of the > > cyclic prefix, followed by the "useful portion" of the OFDM symbol.In> > such a case, the consequences outlined in (3) follow. > > > > What happens if the FFT input window starts with the first sample > > occuring AFTER the ideal FFT start window. In such a case, the last > > sample into the FFT input will be drawn from the cyclic prefix ofthe> > next OFDM symbol. In which case, the progressive phase rotation no > > longer occurs as the input to the FFT block is no longer circularly > > rotated. > > > > Should'nt practical OFDM symbols therefore include a cyclic postfix > > (drawn from the beginning of the OFDM symbol) to account for timing > > recovery if the timing offset is past the ideal timing instant. For > > example, the European DVB standard does not mention any cyclic > > post-fixes in their description of the OFDM transmit frame... > > > > Please clarify.. > > > > thank you > > regards > > Vikram

Reply by ●July 22, 20062006-07-22

Hi Eric, Vikram, & Col, Are you aware of any technique by which one can achieve orthognality of the subcarriers (zero ICI) in an OFDM symbol duration without employing any cyclic prefix ? The channel is frequency selective and assume that sufficient guard interval is provided between adjacent OFDM symbols (zero ISI). Also, perfect time and frequency synchronization is assumed and is not an issue at present. I am exploring one such scheme and any reply from your side (whether you are aware of one or not) will be of great help to me. Thanks, John