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ZADOFF-CHU SEQUENCES (in LTE)

Started by Manolete July 23, 2009
Hello,

I'm studying Zadoff-Chu sequences properties.
If you take a look into
"http://en.wikipedia.org/wiki/Zadoff%E2%80%93Chu_sequence" you can see the
generation of the sequence. Well, in LTE (in P-SS) we  use 3 sequences of
length 63 (N=63) and roots u=25,29,34.
All books say that these sequences have an ideal periodic autocorrelation
function and a constant periodic cross-correlation equal to 1/sqrt(N)

Let's take the Circular Cross Correlation function of
"http://www.mathworks.com/matlabcentral/fileexchange/4810" and check all
this:

I get an ideal periodic autocorrelation for all sequences and a constant
periodic cross-correlation equal to (1/sqrt(N))=(0.126) for the pair of
roots 25-29 and 29-34. But for the pair 25-34 the cross-correlation is not
constant and its maximum value is three times 0.126.
Can you find the problem? I'm getting crazy!
Thank you very much!


PS: This is my code to generate the sequences:

function seq = zadoff(root)    
for n=0:62
    seq(n+1)=exp(-j*(pi*root*n*(n+1))/63);
end







On Jul 23, 9:51&#2013266080;pm, "Manolete" <jmaz5...@gmail.com> wrote:
> Hello, > > I'm studying Zadoff-Chu sequences properties. > If you take a look into > "http://en.wikipedia.org/wiki/Zadoff%E2%80%93Chu_sequence" you can see the > generation of the sequence. Well, in LTE (in P-SS) we &#2013266080;use 3 sequences of > length 63 (N=63) and roots u=25,29,34. > All books say that these sequences have an ideal periodic autocorrelation > function and a constant periodic cross-correlation equal to 1/sqrt(N) > > Let's take the Circular Cross Correlation function of > "http://www.mathworks.com/matlabcentral/fileexchange/4810" and check all > this: > > I get an ideal periodic autocorrelation for all sequences and a constant > periodic cross-correlation equal to (1/sqrt(N))=(0.126) for the pair of > roots 25-29 and 29-34. But for the pair 25-34 the cross-correlation is not > constant and its maximum value is three times 0.126. > Can you find the problem? I'm getting crazy! > Thank you very much!
The different result is likely due to the fact that the difference between 25 and 34 (that is, 9) is not relatively prime to the period (63) of the sequences whereas the other two differences (4 and 5 respectively) *are* relatively prime to 63. For a related phenomenon, see the paper (http://www.ifp.uiuc.edu/~sarwate/pubs/Sarwate79Bounds.pdf) (Note, the last time I checked, the version of this paper that is provided by IEEExplore is missing a page; now let the semi-annual flame war about IEEExplore start!) --Dilip Sarwate
dvsarwate@yahoo.com <dvsarwate@gmail.com> wrote:

>The different result is likely due to the fact that the difference >between 25 and 34 (that is, 9) is not relatively prime to the >period (63) of the sequences whereas the other two differences >(4 and 5 respectively) *are* relatively prime to 63.
Good catch. Steve