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Asked: 2023-01-17T22:04:13+05:30 In:

5G PRACH zad-off chu sequence

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What is PRACH Zad-off Chu sequence in 5G? How do we generate multiple un-correlated sequences from it?

 

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    14 Answers

    1. This answer was edited.

      Zad-off Chu sequences are used to generate NR random-access preambles(PRACH)

      It has following unique properties for which it is used

      1.Constant amplitude before DFT and after DFT.

      2.Zero cyclic auto correlation.

      3.Low cross correlation

      Zad-off Chu sequence can be generated by using the formula as

          \[Xu(i)=e^{(\frac{-j \pi u i(i+1)} {L_R_A})} where\ i=1,2........L_R_A -1\]

      where

          \[ u \ be \ any \ value \ between \ 0 \ to L_R_A-1\]

          \[L_R_A =139 or 839\]

       If you create a sequence using this formula and create another sequence just by shifting the same sequence. And if you take the correlation of the two sequence, the result become zero.

      If you create two sequences using the formula shown just by changing ‘u'(the u value used in both sequence should be prime numbers) and take the correlation of the two sequences, the result will be 1/Sqrt(LRA).

       

       

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    2. For the generation of PRACH sequence in 5G we have two sequences

      1. PN
      2. Zad-off Chu

      Now a days we  prefer Zad-off Chu sequence over PN sequence because

      1. Close to zero auto correlation
      2. Zero cross correlation
      3. Constant amplitude

      Zadoff-Chu sequences have been used as synchronization sequences in modern wireless communication systems(LTE and 5G).

      Zad-off Chu sequence can be generated by using the formula as

        [Xu(i)=e^{(frac{-j pi u i(i+1)} {L_R_A})} where i=1,2........L_R_A -1],  [ u be any value between 0 to L_R_A-1]

        [L_R_A =139 or 839] (generally prime number)

      To create multiple uncorrelated sequences substitute i values in the above equation by keeping [L_R_A =139 or 839] .This generated sequence satisfies all the above properties .

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    3. This answer was edited.
      • PRACH Zadoff chu sequence: The Zadoff -Chu sequence have been used as synchronization sequences in modern wireless communication systems(LTE and 5G).

      Zad-off Chu sequence can be generated by using the formula as

          \[Xu(i)=e^{\frac{-j \pi u i(i+1)}{L_R_A}} where \ i=1,2........L_R_A -1\]

      ,

          \[ u\ be\ any \ value \ between \ 0 \to \ L_R_A-1\]

      The autocorrelation of the  sequence become zero.

      To create multiple uncorrelated sequences substitute i values in the above equation by keeping

          \[L_R_A =139\ or\ 839\]

      , generally a prime number.

       

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    4. Zad-off Chu sequence is mainly used in PRACH signal transmission in 5G communication. This sequence is mainly used rather than PN sequence because–

      • It has almost constant amplitude.
      • Almost zero auto correlation.
      • Almost zero cross correlation.

      Zad-off Chu sequence can be obtained from the following equation–

          \[X_u(i)=e^{-j*(\frac{\pi*u*i(i+1)}{L_{RA}})}\]

          \[Where, i=0, 1, 2, ..., L_{RA}\]

          \[L_{RA} is mainly a Prime number.\]

      By varying different values of u, we can generate different Zad-off Chu sequence signals.

       

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    5. This answer was edited.

      Zadoff Chu (ZC) sequences are the primary manifestation of the spread spectrum in modern cellular systems including LTE and 5G NR.

      ZC sequences are used for initial access in both the downlink (synchronization) and uplink (random access)

          \[X_u(i)=e^{(\frac{-j*\pi*u*i*(i+1)}{L_{RA}})}\]

          \[where \ i=0,1,..........,L_{RA}-1\]

          \[Generally \ L_{RA} = \ 139 \ or \ 839 \ , \ preferably \ prime \ number \]

       

      By using different ‘u’ values we can generate different Zad-off chu sequences

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    6. This answer was edited.

      Zad-off chu sequences are used to generate PRACH in 5G communication.

      It has following unique properties for which it is used.

      • constant amplitude before DFT and after DFT
      • zero cyclic auto-correlation
      • Low cross-correlation

      Zad-off chu sequence is generated by using following formula

          \[X_{u}(i) = e^{-j\frac{\Pi *u*i(i+1)}{L_{RA}}}\]

          \[ i = 0,1,....,L_{RA}-1\]

          \[Multiple\;uncorrelated\;sequences\;can\;be\;obtained\;by\;taking\]

          \[different\;u\;values\;from\;1\;to\;\L_{RA}-1\]

          \[Here\;\L_{RA}\;value\;should\;be\;taken\;as\;139\;or\;839\]

      .

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    7. This answer was edited.

      The Zad-off Chu sequence is a type of linear complex sequence that has low cross-correlation properties, which makes it well suited for use in the PRACH. The sequence is generated using a specific set of parameters, including the length of the sequence, the spreading factor, and the root sequence index. These parameters are used to determine the specific properties of the sequence, such as its autocorrelation and cross-correlation properties.

      we can generate Zad-off Chu sequence from this formula:

          \[X_u(i)=e^{(\frac{(-j)*\(pi*u*i)*(i+1)}{L_{RA}})}\]

       

          \[where \ i=0,1,..........,L_{RA}-1\]

      From this formula we can generate any uncorrelated signal by changing value of

      u . but it should be in between

          \[0 \; to \; L_{RA}-1\]

       

          \[Here \; i \;took\; L_{RA}\; as \;139 or 839\]

       

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    8. This answer was edited.

      PRACH is used in uplink of cellular systems for the initial access requests from the user.

      ZC sequences are complex sequences with unit amplitude and particular phase shifts. Zadoff Chu sequences are used to generate PRACH in  LTE snd 5G communication. Its due to the unique properties of the sequence that makes it well suited for use in PRACH.

      1. Zero cyclic auto-correlation
      2. Low cross-correlation
      3. Constant amplitude

          \[\text{The } q^{th} \text{ ZC sequence }s_{q}[n] \text{ is defined as}\]

          \[s_{q}[n] = e^{-j \pi q \frac{n(n+1)}{L_{RA}}} \]

          \[\text{where}, n = 0,1,2,.......,(L_{RA}-1) \]

      In the given figure that has been plotted for two different values of “q” we see the auto-correlation and the cross-correlation properties

       

      5G PRACH zad-off chu sequence
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    9. This answer was edited.

      Zadoff Chu sequence is used in the modern cellular systems i.e. LTE and 5G. The older cellular systems like 3G uses PN sequence. Zadoff Chu sequence. A Zadoff Chu sequence has two key parameters, (i) the root index u = 1, 2, …,LRA− 1 and (ii) the length of the sequence, LRA.

      Zad-off Chu sequence can be generated by using the formula as

       

        [Xu(i)=e^{(frac{-j pi u i(i+1)} {L_R_A})} where i=1,2........L_R_A -1]

      where,

        [ u be any value between 0 to L_R_A-1]

      LRA=139 or 839

      The correlation of the sequence generated by the above given formula and its shifted version will result into 0.

      If correlation of the two sequence generated by changing the u value will result in 1/√ LRA.

      ZC sequences have several highly desirable properties.

      Property 1: Constant unit Amplitude.

      Property 2: Zero Cyclic Autocorrelation.

      Property 3: Fixed Cyclic Cross-Correlation.

      Property 4: The DFT or IDFT of a ZC Sequence is a ZC Sequence.

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    10. This answer was edited.

      Zad off chu sequence is a complex valued sequence.When it is applied to a signal it gives a new signal of constant amplitude.

      • This sequences exhibit the useful property that cyclically shifted versions of themselves are orthogonal to one another.

      This sequence can be generated by using the formula :

          \[Z_u(i) = e^{\frac{-j*\pi*u*i*(i+1)}{L_{RA}}\]

          \[where \ i = \ 1,2.....L_{RA}-1\]

      So by varying the index i values in the above formula we can generate any uncorrelated sequences. 

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    11. This answer was edited.

      In 5G NR wireless system there are three sequences used. They are Zadoff chu sequence, gold sequence and m-sequence.

      • Gold sequence is used in CP-OFDM
      • Zadoff-chu sequence is used in DFT-s-OFDM (for SSS) and
      • m-sequence is used in PSS.

       

      Zadoff-Chu sequences are used to generate NR random-access preambles (PRACH). It has following unique properties for which it is used-
      -constant amplitude before DFT and after DFT
      -zero cyclic auto-correlation
      -low cross-correlation

       

      We can obtain the Zad-off Chu sequence from the following equation–

          \[X_u(i)=e^{-j*(\frac{\pi*u*i(i+1)}{L_{RA}})}\]

          \[Where, i=0, 1, 2, ..., L_{RA}\]

      We can vary different values of ‘u’ to generate different Zad-off Chu sequence signals. Multiple uncorrelated sequences can be obtained from different u values varying from 1 to LRA-1. Here LRA value should be taken as 139 or 839.

       

       

       

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    12. This answer was edited.

      For generating  PRACH sequence  we have two sequences. they are PN and Zad-off Chu

      we  prefer Zad-off Chu sequence over PN sequence because nearly zero auto and cross  correlation and Constant amplitude.

      Zad-off chu sequence is generated by using following formula

       

        [X_{u}(i) = e^{-jfrac{Pi *u*i(i+1)}{L_{RA}}}]

       

      where i ranges from   [ i = 0,1,....,L_{RA}-1]

       

      [Multiple;uncorrelated;sequences;can;be;obtained;by;taking] [different;u;values;from;1;to;L_{RA}-1]
      [Here;L_{RA};value;should;be;taken;as;139;or;839]

       

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    13. This answer was edited.

      PRACH Zadoff chu sequence in 5G is basically used for initial access process between the base station and the user equipment. It is the complex sequence uniquely generated by changing various parameters and possess extremely unique properties. There are totally 64 different types of Zadoff chu sequences used by the UEs of a cell.

      The sequence is generated as follows:

          \[x_{u}(i) = exp(\frac{-j*{\pi}u(i+1+2q)i}{L_{RA}})\]

      Multiple uncorrelated sequences are generated using the same above expression and by varying the values of u.

      When such sequences are generated, any cyclic shifted form of such sequences are also uncorrelated from each other. This is the primary feature of these sequences.

      This feature of Uncorrelatedness makes the receiver at the base station easier to detect the exact sequence sent by the corresponding UE.

       

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    14. This answer was edited.

      The RBs in which random access preamble is allowed to be transmitted is known as PRACH . Zadoff-chu(ZC)Sequences have been used as synchronization sequences in modern wireless communication systems , replacing the conventional pseudo-random noise (PN) sequences due to their perfect autocorrelation properties.

      Zadoff-chu sequence possess following features:

      • It has small variation in time hence it will add to good power amplification properties of the complex modulated signal of the LTE modem.
      • It has small variation in frequency hence channel estimation at receiver will be simple.
      • It has low cross correlation property hence it produces small inter cell interference.

      Zadoff-chu Sequence Properties:

      • It has zero circular auto-correlation.
      • It has constant amplitude.
      • It has flat frequency domain response.

      Zad-off Chu sequence can be generated by using the formula as:

                 

          \[Xu(i)=e^{(\frac{-j \pi u i(i+1)} {L_R_A})} where\ i=1,2........L_R_A -1\]


      where               

          \[ u \ be \ any \ value \ between \ 0 \ to L_R_A-1\]

                                         

          \[L_R_A =139 or 839\]

      (prime number)

      By varying different u values

          \[from\;1\;to\;\L_{RA}-1\]

      we can generate different uncorrelated  Zad-off Chu sequence signals.

       

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