how to calculate noise vector from Eb/No to plot a EbNo/BER graph (noise generation)

Hi,
I'm doing a final project in OFDM simulation and I would like to plot
a EbNo/BER graph. For a range of a specified EbNo, I I have to
generate a noise added to the signal. I have no idea how I could
generate a noise vector from this Eb/No.

supose that my signal is x = randint(1,N)
some people generate noise vector by  1/sqrt*(randn(N)+jrandn(N))
do I have to multiply this with a constealltion number? or do I have
to multiply this with any OFDM process too???

Thank you very much for your reply. I'm a bit stressful right now
because I don't have a lot of time to finish it.

Thank you very much
best regards,
Anna

Anna wrote:
> Hi,
> I'm doing a final project in OFDM simulation and I would like to plot
> a EbNo/BER graph. For a range of a specified EbNo, I I have to
> generate a noise added to the signal. I have no idea how I could
> generate a noise vector from this Eb/No.
> 
> supose that my signal is x = randint(1,N)
> some people generate noise vector by  1/sqrt*(randn(N)+jrandn(N))
> do I have to multiply this with a constealltion number? or do I have
> to multiply this with any OFDM process too???
> 
> Thank you very much for your reply. I'm a bit stressful right now
> because I don't have a lot of time to finish it.
> 
> Thank you very much
> best regards,
> Anna
> 

Here's an approach. Suppose your noiseless OFDM signal is 'z', the bit 
rate is 'Rb', sample rate is 'Fs', and target Eb/No is 'EbNo':

z = z./std(z);
n = (randn(length(z),1) + j*randn(length(z),1))/sqrt(2);
snr = 10.^(EbNo/10) * Rb / Fs;			
n = n./sqrt(snr);
z = z + n;

John

On Jul 27, 4:00 pm, John Sampson <jo...@3db-labs.com> wrote:
> Anna wrote:
> > Hi,
> > I'm doing a final project in OFDM simulation and I would like to plot
> > a EbNo/BER graph. For a range of a specified EbNo, I I have to
> > generate a noise added to the signal. I have no idea how I could
> > generate a noise vector from this Eb/No.
>
> > supose that my signal is x = randint(1,N)
> > some people generate noise vector by  1/sqrt*(randn(N)+jrandn(N))
> > do I have to multiply this with a constealltion number? or do I have
> > to multiply this with any OFDM process too???
>
> > Thank you very much for your reply. I'm a bit stressful right now
> > because I don't have a lot of time to finish it.
>
> > Thank you very much
> > best regards,
> > Anna
>
> Here's an approach. Suppose your noiseless OFDM signal is 'z', the bit
> rate is 'Rb', sample rate is 'Fs', and target Eb/No is 'EbNo':
>
> z = z./std(z);
> n = (randn(length(z),1) + j*randn(length(z),1))/sqrt(2);
> snr = 10.^(EbNo/10) * Rb / Fs;
> n = n./sqrt(snr);
> z = z + n;
>
> John


Thank you very much John, I've been searching for this solution for a
week. :-) Thank you so much

On Jul 27, 4:40 pm, Anna <petitmou...@gmail.com> wrote:
> On Jul 27, 4:00 pm, John Sampson <jo...@3db-labs.com> wrote:
>
>
>
> > Anna wrote:
> > > Hi,
> > > I'm doing a final project in OFDM simulation and I would like to plot
> > > a EbNo/BER graph. For a range of a specified EbNo, I I have to
> > > generate a noise added to the signal. I have no idea how I could
> > > generate a noise vector from this Eb/No.
>
> > > supose that my signal is x = randint(1,N)
> > > some people generate noise vector by  1/sqrt*(randn(N)+jrandn(N))
> > > do I have to multiply this with a constealltion number? or do I have
> > > to multiply this with any OFDM process too???
>
> > > Thank you very much for your reply. I'm a bit stressful right now
> > > because I don't have a lot of time to finish it.
>
> > > Thank you very much
> > > best regards,
> > > Anna
>
> > Here's an approach. Suppose your noiseless OFDM signal is 'z', the bit
> > rate is 'Rb', sample rate is 'Fs', and target Eb/No is 'EbNo':
>
> > z = z./std(z);
> > n = (randn(length(z),1) + j*randn(length(z),1))/sqrt(2);
> > snr = 10.^(EbNo/10) * Rb / Fs;
> > n = n./sqrt(snr);
> > z = z + n;
>
> > John

I still have one little question (I'm sorry, i know so little thing in
DSP) , why do we derive n by sqrt(snr) ,but not simply snr?

Anna wrote:
> On Jul 27, 4:40 pm, Anna <petitmou...@gmail.com> wrote:
> > On Jul 27, 4:00 pm, John Sampson <jo...@3db-labs.com> wrote:
> >
> >
> >
> > > Anna wrote:
> > > > Hi,
> > > > I'm doing a final project in OFDM simulation and I would like to plot
> > > > a EbNo/BER graph. For a range of a specified EbNo, I I have to
> > > > generate a noise added to the signal. I have no idea how I could
> > > > generate a noise vector from this Eb/No.
> >
> > > > supose that my signal is x = randint(1,N)
> > > > some people generate noise vector by  1/sqrt*(randn(N)+jrandn(N))
> > > > do I have to multiply this with a constealltion number? or do I have
> > > > to multiply this with any OFDM process too???
> >
> > > > Thank you very much for your reply. I'm a bit stressful right now
> > > > because I don't have a lot of time to finish it.
> >
> > > > Thank you very much
> > > > best regards,
> > > > Anna
> >
> > > Here's an approach. Suppose your noiseless OFDM signal is 'z', the bit
> > > rate is 'Rb', sample rate is 'Fs', and target Eb/No is 'EbNo':
> >
> > > z = z./std(z);
> > > n = (randn(length(z),1) + j*randn(length(z),1))/sqrt(2);
> > > snr = 10.^(EbNo/10) * Rb / Fs;
> > > n = n./sqrt(snr);
> > > z = z + n;
> >
> > > John
>
> I still have one little question (I'm sorry, i know so little thing in
> DSP) , why do we derive n by sqrt(snr) ,but not simply snr?

Hi Anna,

The snr is a ratio of powers.  Since n can be considered as a voltage,
we need the sqrt(snr) to have the proper ratio between the normalized
z vector and the n vector.

Phil

On 27 juil, 19:01, Phil <philguilleme...@alumni.uwaterloo.ca> wrote:
> Anna wrote:
> > On Jul 27, 4:40 pm, Anna <petitmou...@gmail.com> wrote:
> > > On Jul 27, 4:00 pm, John Sampson <jo...@3db-labs.com> wrote:
>
> > > > Anna wrote:
> > > > > Hi,
> > > > > I'm doing a final project in OFDM simulation and I would like to =
plot
> > > > > a EbNo/BER graph. For a range of a specified EbNo, I I have to
> > > > > generate a noise added to the signal. I have no idea how I could
> > > > > generate a noise vector from this Eb/No.
>
> > > > > supose that my signal is x =3D randint(1,N)
> > > > > some people generate noise vector by  1/sqrt*(randn(N)+jrandn(N))
> > > > > do I have to multiply this with a constealltion number? or do I h=
ave
> > > > > to multiply this with any OFDM process too???
>
> > > > > Thank you very much for your reply. I'm a bit stressful right now
> > > > > because I don't have a lot of time to finish it.
>
> > > > > Thank you very much
> > > > > best regards,
> > > > > Anna
>
> > > > Here's an approach. Suppose your noiseless OFDM signal is 'z', the =
bit
> > > > rate is 'Rb', sample rate is 'Fs', and target Eb/No is 'EbNo':
>
> > > > z =3D z./std(z);
> > > > n =3D (randn(length(z),1) + j*randn(length(z),1))/sqrt(2);
> > > > snr =3D 10.^(EbNo/10) * Rb / Fs;
> > > > n =3D n./sqrt(snr);
> > > > z =3D z + n;
>
> > > > John
>
> > I still have one little question (I'm sorry, i know so little thing in
> > DSP) , why do we derive n by sqrt(snr) ,but not simply snr?
>
> Hi Anna,
>
> The snr is a ratio of powers.  Since n can be considered as a voltage,
> we need the sqrt(snr) to have the proper ratio between the normalized
> z vector and the n vector.
>
> Phil- Masquer le texte des messages pr=E9c=E9dents -
>
> - Afficher le texte des messages pr=E9c=E9dents -

Ahhh I see. thank you very much Phil. have a nice day :-)
Anna

On Jul 27, 10:40 am, Anna <petitmou...@gmail.com> wrote:
> On Jul 27, 4:00 pm, John Sampson <jo...@3db-labs.com> wrote:
>
>
>
> > Anna wrote:
> > > Hi,
> > > I'm doing a final project in OFDM simulation and I would like to plot
> > > a EbNo/BER graph. For a range of a specified EbNo, I I have to
> > > generate a noise added to the signal. I have no idea how I could
> > > generate a noise vector from this Eb/No.
>
> > > supose that my signal is x = randint(1,N)
> > > some people generate noise vector by  1/sqrt*(randn(N)+jrandn(N))
> > > do I have to multiply this with a constealltion number? or do I have
> > > to multiply this with any OFDM process too???
>
> > > Thank you very much for your reply. I'm a bit stressful right now
> > > because I don't have a lot of time to finish it.
>
> > > Thank you very much
> > > best regards,
> > > Anna
>
> > Here's an approach. Suppose your noiseless OFDM signal is 'z', the bit
> > rate is 'Rb', sample rate is 'Fs', and target Eb/No is 'EbNo':
>
> > z = z./std(z);
> > n = (randn(length(z),1) + j*randn(length(z),1))/sqrt(2);
> > snr = 10.^(EbNo/10) * Rb / Fs;
> > n = n./sqrt(snr);
> > z = z + n;
>
> > John
>
> Thank you very much John, I've been searching for this solution for a
> week. :-) Thank you so much

You are welcome. I forgot to mention that EbNo is specified in dB.

John