Zadoff-Chu sequence concept

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ahmed youssef 2024-4-18

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https://ww2.mathworks.cn/matlabcentral/answers/2108471-zadoff-chu-sequence-concept

评论： ahmed youssef 2024-4-18

Zaddoff-Chu sequence has two main propoerties: 1- constant modulus 2- good correlation characteristics. Most of the papers claim that the autocorrelation of sequence has zero values for all shifted version of sequence except the lag=0. However, if you try to use the matlab code zadoffChuSeq(u,N) to varify this propoerties, you will find the small peaks at time axis. This means it is not perfrectely sequqnce as they calimed. Did I miss somthing?

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Manikanta Aditya 2024-4-18

As, you’re observing very large peaks around the zero-lag peak with zadoffChuSeq(3,67), it might be worth double-checking the implementation of the function for any potential errors or deviations from the theoretical formula. Additionally, ensure that the parameters used (such as u and N) satisfy the necessary conditions for a Zadoff-Chu sequence.

If after verification everything seems correct, then these large peaks might be an artifact of how MATLAB handles computations and displays plots rather than an issue with the sequence itself.

The image you attached indeed shows a prominent peak near x=60 and several smaller peaks throughout the plot. These peaks could be due to the reasons mentioned above.

ahmed youssef 2024-4-18

编辑：ahmed youssef 2024-4-18

Thank you again! I tried using Python with the same parameters (67,3). Here is the output using the same parameters. Note that the output of autocorrelation has been produced using Python code as well as manual implementation of autocorrelation. It gives the same result in each case.

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AH 2024-4-18

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The Zadoff-Chu sequences have the useful property of having zero cyclic autocorrelation at all nonzero lags. One fast way to check this property is shown below

N = 67;

x = zadoffChuSeq(3,N);

X = fft(x);

cR = fftshift(ifft(X.*conj(X))); % circular correlation

figure

plot((-(N-1)/2:(N-1)/2),abs(cR))

xlabel("Lag")

ylabel("Autocorreleation")