# Patent

## Title
Method for generating a reference signal sequence using grouping

## Abstract

Method for generating reference signal sequence using grouping is explained. In this method, base sequences are grouped such that each group contains at least one base sequence of each length, so UE(s) can use various length sequences as a reference signal. And in this method, inter cell interference caused by using various length sequence as a reference signal sequence can be minimized by grouping sequences having the high cross correlation relation.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation of U.S. application Ser. No. 12/024,884, filed Feb. 1, 2008, currently pending, which pursuant to 35 U.S.C. §119 claims the benefit of Korean Patent Application Nos. 10-2007-0047494, filed on May 16, 2007, 10-2007-0099707, filed on Oct. 4, 2007, 10-2007-0108226, filed on Oct. 26, 2007 and 10-2007-0109089, filed on Oct. 29, 2007, and U.S. Provisional Application Ser. Nos. 60/888,065, filed on Feb. 2, 2007, 60/984,386, filed on Nov. 1, 2007 and 61/019,588, filed on Jan. 7, 2008, the contents of which are hereby incorporated by reference herein in their entirety.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to method for generating a reference signal sequence, and more particularly, to a method for grouping sequences having a variable length corresponding one or multiple of a resource block size, a method for generating a reference signal sequence and a method for generating a reference signal sequence using Zadoff-Chu (ZC) sequence.
2. Discussion of the Related Art
Following explanation is mainly discussed in view of 3GPP LTE system, but the present invention is not limited to this system, and exemplary 3GPP LTE system is only for making those skilled in the art clearly understand the present invention.
There are a lot of sequences used for transmitting signal, but in 3GPP LTE (3rd Generation Partnership Project Long Term Evolution) system, CAZAC (Constant Amplitude Zero Auto-Correlation) sequence forms the basis sequence for transmitting signals. CAZAC sequence can be used to various channels for extracting ID or control information, such as uplink/downlink synchronization channels (SCH) including P-SCH (primary SCH) and S-SCH (Secondary SCH), pilot channel for transmitting reference signal. And, the CAZAC sequence can be used in scrambling.
Two types of CAZAC sequences, i.e., GCL CAZAC sequence and Zadoff-Chu CAZAC sequence are mainly used as the CAZAC sequences. The two types of CAZAC sequences are associated with each other by a conjugate complex relation. That is, the GCL CAZAC sequence can be acquired by conjugate complex calculation for the Zadoff-Chu CAZAC sequence. The Zadoff-Chu CAZAC sequence is given as follows.




  
    
      
        
          c
          ⁡
          
            (
            
              
                k
                ;
                N
              
              ,
              M
            
            )
          
        
        =
        
          
            exp
            ⁡
            
              (
              
                
                  jπ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Mk
                    ⁡
                    
                      (
                      
                        K
                        +
                        1
                      
                      )
                    
                  
                
                N
              
              )
            
          
          ⁢
          
            
          
          ⁢
          
            (
            
              for
              ⁢
              
                
              
              ⁢
              odd
              ⁢
              
                
              
              ⁢
              N
            
            )
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          1
        
        ]
      
    
  
  
    
      
        
          c
          ⁡
          
            (
            
              
                k
                ;
                N
              
              ,
              M
            
            )
          
        
        =
        
          
            exp
            ⁡
            
              (
              
                
                  jπ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Mk
                    2
                  
                
                N
              
              )
            
          
          ⁢
          
            
          
          ⁢
          
            (
            
              for
              ⁢
              
                
              
              ⁢
              even
              ⁢
              
                
              
              ⁢
              N
            
            )
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          2
        
        ]
      
    
  




where k represents a sequence component index, N represents a length of CAZAC sequence to be generated, and M represents sequence ID or sequence index.

When the Zadoff-Chu CAZAC sequence given by the Equations 1 and 2 and the GCL CAZAC sequence which is a conjugate complex relation with the Zadoff-Chu CAZAC sequence are represented by c(k; N,M), these sequence can have three features as follows.

|C(k; N; M)|=1(for all k,N,M)  [Equation 3]





  
    
      
        
          
            R
            
              M
              :
              N
            
          
          ⁡
          
            (
            d
            )
          
        
        =
        
          {
          
            
              
                
                  1
                  ,
                
              
              
                
                  (
                  
                    
                      for
                      ⁢
                      
                        
                      
                      ⁢
                      d
                    
                    =
                    0
                  
                  )
                
              
            
            
              
                
                  0
                  ,
                
              
              
                
                  (
                  
                    
                      for
                      ⁢
                      
                        
                      
                      ⁢
                      d
                    
                    ≠
                    0
                  
                  )
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          4
        
        ]
      
    
  




RM1,M2; N(d)=p(for all M1,M2 and N)  [Equation 5]

The Equation 3 means that the CAZAC sequence always has a size of 1, and the Equation 4 shows that an auto-correlation function of the CAZAC sequence is expressed by a delta function. In this case, the auto-correlation is based on circular correlation. Also, the Equation 5 shows that a cross-correlation is always a constant.
Among these two kinds of CAZAC sequence, the following explanation is mainly focused on the Zadoff Chu sequence (hereinafter “ZC sequence”).
In the 3GPP LTE system, using this ZC sequence as reference signal sequence, the length of the ZC sequence should be equal to the resource block size. And, not only using one resource block size sequence, but the reference signal sequence having the length corresponding to multiples of resource block size can be used.
For a single-cell environment, the reference signals are transmitted by the localized FDM (Frequency Divisional Multiplexing) method for multiplexing signals from multiple user equipments (UEs). But, for the multi-cell environment, the reference signals are transmitted by the additional CDM (Code Divisional Multiplexing) method for distinguishing the signals from that of the neighboring cells. In this multiplexing, two type of method is possible. One is a CDM method using a ZC sequence having a different root indexes, and the other is a CDM method using a ZC sequence having the same root index (M) and but having differently applied cyclic shift.
When the length of the reference signals using these kinds of ZC sequences is same, the cross correlation values for both of the cases are not large. But, when the reference signals having a difference length came as interference from the neighboring cells and transmitted through the same frequency band or overlapped frequency band, the cross correlation value would be significant.
SUMMARY OF THE INVENTION
Accordingly, the present invention is directed to provide a method for generating reference signal sequence, which minimizes the interference caused by the signals having different length, came from the neighboring cells.
For this method, the present invention also provides a method for effectively grouping sequences such that each of the group is consisted of the sequences having high cross correlation value, and supports variable length sequences to be used as a reference signals.
Also, the present invention provides a method for generating reference signal sequence based on the above grouping.
To achieve these objects and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, a method for grouping sequences having a variable length corresponding one or multiple of a resource block size is provided. According to one embodiment, the method comprises: grouping the sequences into groups such that each of the groups contains at least one sequence of each length, wherein the grouped sequence is a base sequence which is used for applying a cyclic shift corresponding to variable cyclic shift value, and the base sequence with the cyclic shift is used as a reference signal sequence.
Preferably, a number of the groups is 30.
And, said grouping may be performed such that each of the groups contains one base sequence of each length corresponding to 1 to 5 times of the resource block size, and two base sequences of each length corresponding to 6 or more times of the resource block size.
And, preferably, the base sequence having a length corresponding to 3 or more times of the resource block size is defined by using a Zadoff-Chu (ZC) sequence, and the base sequence having a length corresponding to 1 or 2 times of the resource block size is defined by using other sequence other than the ZC sequence.
In another aspect of the present invention, a method for generating a reference signal sequence is provided. In one embodiment for this aspect, the method comprises: defining one or more base sequences having a variable length corresponding to one or multiple of a resource block size; and applying a cyclic shift corresponding to variable cyclic shift value to the defined base sequence, wherein the base sequences are divided into groups, and each of the group comprises at least one base sequence of each length.
In this case, the base sequence may be defined by cyclic extension of the ZC sequence having a length (NzcRS) given by a largest prime number which is less than a corresponding reference signal sequence size. Also the base sequence may be defined by truncation of the ZC sequence having a length (NzcRS) given by the smallest prime number which is larger than a corresponding reference signal sequence size.
Also in this embodiment, preferably, a number of the groups is 30.
And, each of the groups may contain one base sequence of each length corresponding to 1 to 5 times of the resource block size, and two base sequences of each length corresponding to 6 or more times of the resource block size.
And, the base sequence having a length corresponding to 3 or more times of the resource block size may be defined by using a Zadoff-Chu (ZC) sequence with specific ZC sequence index (q), and the base sequence having a length corresponding to 1 or 2 times of the resource block size may be defined by using other sequence other than the ZC sequence.
And, preferably, the specific ZC sequence index (q) is a function of a group index (u) and a base sequence number index (v) within the group.
And, the defined base sequence with cyclic shift may be used for uplink reference signal sequence.
Also for above embodiments, the resource block size may correspond to a size of 12 subcarriers in a frequency domain.
In another aspect of the present invention, a method for generating a reference signal sequence using Zadoff-Chu (ZC) sequence is provided. In on embodiment for this aspect, the method comprises: defining a specific base sequence using q-th root ZC sequence, wherein the base sequences are divided into groups, and the “q” is a function of a group index (u) and a base sequence number index (v) within the group; and applying a cyclic shift corresponding to variable cyclic shift value to the defined base sequence to generate the reference signal sequence.
In one case, the specific ZC sequence index (q) may be determined by one of equations of,




  
    
      
        
          q
          =
          
            
              round
              ⁡
              
                (
                y
                )
              
            
            +
            
              
                floor
                ⁡
                
                  (
                  
                    
                      v
                      +
                      1
                    
                    2
                  
                  )
                
              
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  
                    floor
                    ⁡
                    
                      (
                      
                        
                          round
                          ⁡
                          
                            (
                            y
                            )
                          
                        
                        -
                        y
                      
                      )
                    
                  
                  +
                  v
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          y
          =
          
            
              
                N
                zc
                RS
              
              ·
              
                (
                
                  u
                  +
                  1
                
                )
              
            
            
              N
              
                reference
                ,
                zc
              
              RS
            
          
        
        ,
        
          

        
        ⁢
        
          u
          ∈
          
            {
            
              0
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              29
            
            }
          
        
        ,
        
          

        
        ⁢
        
          v
          ∈
          
            {
            
              0
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              
                
                  floor
                  ⁡
                  
                    (
                    
                      
                        N
                        ZC
                        RS
                      
                      /
                      30
                    
                    )
                  
                
                -
                1
              
            
            }
          
        
        ,
      
    
    
      
        (
        1
        )
      
    
  
  
    
      
        
          q
          =
          
            
              round
              ⁡
              
                (
                y
                )
              
            
            +
            
              
                floor
                ⁡
                
                  (
                  
                    
                      v
                      +
                      1
                    
                    2
                  
                  )
                
              
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  
                    floor
                    ⁡
                    
                      (
                      
                        
                          round
                          ⁡
                          
                            (
                            y
                            )
                          
                        
                        -
                        y
                      
                      )
                    
                  
                  +
                  v
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          y
          =
          
            
              
                (
                
                  
                    N
                    zc
                    RS
                  
                  -
                  1
                
                )
              
              ·
              
                (
                
                  u
                  +
                  1
                
                )
              
            
            
              
                N
                
                  reference
                  ,
                  zc
                
                RS
              
              -
              1
            
          
        
        ,
        
          

        
        ⁢
        
          u
          ∈
          
            {
            
              0
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              29
            
            }
          
        
        ,
        
          

        
        ⁢
        
          v
          ∈
          
            {
            
              0
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              
                
                  floor
                  ⁡
                  
                    (
                    
                      
                        N
                        ZC
                        RS
                      
                      /
                      30
                    
                    )
                  
                
                -
                1
              
            
            }
          
        
        ,
        or
      
    
    
      
        (
        2
        )
      
    
  
  
    
      
        
          q
          =
          
            
              round
              ⁡
              
                (
                y
                )
              
            
            +
            
              
                floor
                ⁡
                
                  (
                  
                    
                      v
                      +
                      1
                    
                    2
                  
                  )
                
              
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  
                    floor
                    ⁡
                    
                      (
                      
                        
                          round
                          ⁡
                          
                            (
                            y
                            )
                          
                        
                        -
                        y
                      
                      )
                    
                  
                  +
                  v
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          y
          =
          
            
              round
              ⁡
              
                (
                
                  
                    N
                    zc
                    RS
                  
                  
                    N
                    
                      reference
                      ,
                      zc
                    
                    RS
                  
                
                )
              
            
            ·
            
              (
              
                u
                +
                1
              
              )
            
          
        
        ,
        
          

        
        ⁢
        
          u
          ∈
          
            {
            
              0
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              29
            
            }
          
        
        ,
        
          

        
        ⁢
        
          v
          ∈
          
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                
                  
                    floor
                    ⁡
                    
                      (
                      
                        
                          N
                          ZC
                          RS
                        
                        /
                        30
                      
                      )
                    
                  
                  -
                  1
                
              
              }
            
            .
          
        
      
    
    
      
        (
        3
        )
      
    
  




wherein NzcRS is the length given by the largest prime number which is less than the corresponding reference signal sequence size, Nreference,zcRS is the corresponding reference signal sequence size, the “round (z)” is a function of rounding off to a nearest integer nearest to z, and the “floor (z)” is a function of making a greatest integer not greater than z. But, NzcRS can be the length given by the smallest prime number which is greater than the corresponding reference signal sequence, for another embodiment of this invention.

In the other case, the specific ZC sequence index (q) may be determined by one of equations of,




  
    
      
        
          q
          =
          
            
              floor
              (
              
                y
                +
                
                  0
                  ⁢
                  .5
                
              
              )
            
            +
            
              
                floor
                ⁡
                
                  (
                  
                    
                      v
                      +
                      1
                    
                    2
                  
                  )
                
              
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  
                    floor
                    ⁡
                    
                      (
                      
                        
                          floor
                          ⁡
                          
                            (
                            
                              y
                              +
                              0.5
                            
                            )
                          
                        
                        -
                        y
                      
                      )
                    
                  
                  +
                  v
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          y
          =
          
            
              
                N
                zc
                RS
              
              ·
              
                (
                
                  u
                  +
                  1
                
                )
              
            
            
              N
              
                reference
                ,
                zc
              
              RS
            
          
        
        ,
        
          

        
        ⁢
        
          u
          ∈
          
            {
            
              0
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              29
            
            }
          
        
        ,
        
          

        
        ⁢
        
          v
          ∈
          
            {
            
              0
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              
                
                  floor
                  ⁡
                  
                    (
                    
                      
                        N
                        ZC
                        RS
                      
                      /
                      30
                    
                    )
                  
                
                -
                1
              
            
            }
          
        
      
    
    
      
        (
        1
        )
      
    
  
  
    
      
        
          q
          =
          
            
              floor
              (
              
                y
                +
                
                  0
                  ⁢
                  .5
                
              
              )
            
            +
            
              
                floor
                ⁡
                
                  (
                  
                    
                      v
                      +
                      1
                    
                    2
                  
                  )
                
              
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  
                    floor
                    ⁡
                    
                      (
                      
                        
                          floor
                          ⁡
                          
                            (
                            
                              y
                              +
                              0.5
                            
                            )
                          
                        
                        -
                        y
                      
                      )
                    
                  
                  +
                  v
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          y
          =
          
            
              
                (
                
                  
                    N
                    zc
                    RS
                  
                  -
                  1
                
                )
              
              ·
              
                (
                
                  u
                  +
                  1
                
                )
              
            
            
              
                N
                
                  reference
                  ,
                  zc
                
                RS
              
              -
              1
            
          
        
        ,
        
          

        
        ⁢
        
          u
          ∈
          
            {
            
              0
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              29
            
            }
          
        
        ,
        
          

        
        ⁢
        
          v
          ∈
          
            {
            
              0
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              
                
                  floor
                  ⁡
                  
                    (
                    
                      
                        N
                        ZC
                        RS
                      
                      /
                      30
                    
                    )
                  
                
                -
                1
              
            
            }
          
        
        ,
        or
      
    
    
      
        (
        2
        )
      
    
  
  
    
      
        
          q
          =
          
            
              floor
              (
              
                y
                +
                
                  0
                  ⁢
                  .5
                
              
              )
            
            +
            
              
                floor
                ⁡
                
                  (
                  
                    
                      v
                      +
                      1
                    
                    2
                  
                  )
                
              
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  
                    floor
                    ⁡
                    
                      (
                      
                        
                          floor
                          ⁡
                          
                            (
                            
                              y
                              +
                              0.5
                            
                            )
                          
                        
                        -
                        y
                      
                      )
                    
                  
                  +
                  v
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          y
          =
          
            
              floor
              ⁡
              
                (
                
                  
                    
                      N
                      zc
                      RS
                    
                    
                      N
                      
                        reference
                        ,
                        zc
                      
                      RS
                    
                  
                  +
                  0.5
                
                )
              
            
            ·
            
              (
              
                u
                +
                1
              
              )
            
          
        
        ,
        
          

        
        ⁢
        
          u
          ∈
          
            {
            
              0
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              29
            
            }
          
        
        ,
        
          

        
        ⁢
        
          v
          ∈
          
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                
                  
                    floor
                    ⁡
                    
                      (
                      
                        
                          N
                          ZC
                          RS
                        
                        /
                        30
                      
                      )
                    
                  
                  -
                  1
                
              
              }
            
            .
          
        
      
    
    
      
        (
        3
        )
      
    
  




wherein NzcRS is the length given by the largest prime number which is less than the corresponding reference signal sequence size, Nreference,zcRS is the corresponding reference signal sequence size, the “round (z)” is a function of rounding off to a nearest integer nearest to z, and the “floor (z)” is a function of making a greatest integer not greater than z. But, NzcRS can be the length given by the smallest prime number which is greater than the corresponding reference signal sequence, for another embodiment of this invention.

In one specific embodiment of this invention, the maximum number of the base sequence number index (v) within each group may be set to is 2, and then the specific ZC sequence index (q) can be determined by one of equations of,




  
    
      
        
          q
          =
          
            
              round
              ⁡
              
                (
                y
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                
                  N
                  zc
                  RS
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
              
                N
                
                  reference
                  ,
                  zc
                
                RS
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            

          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
      
    
    
      
        (
        1
        )
      
    
  
  
    
      
        
          q
          =
          
            
              round
              ⁡
              
                (
                y
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                
                  (
                  
                    
                      N
                      zc
                      RS
                    
                    -
                    1
                  
                  )
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
              
                
                  N
                  
                    reference
                    ,
                    zc
                  
                  RS
                
                -
                1
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            

          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
          ,
          or
        
      
    
    
      
        (
        2
        )
      
    
  
  
    
      
        
          q
          =
          
            
              round
              ⁡
              
                (
                y
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                round
                ⁡
                
                  (
                  
                    
                      N
                      zc
                      RS
                    
                    
                      N
                      
                        reference
                        ,
                        zc
                      
                      RS
                    
                  
                  )
                
              
              ·
              
                (
                
                  u
                  +
                  1
                
                )
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            

          
          ⁢
          
            v
            ∈
            
              
                {
                
                  0
                  ,
                  1
                
                }
              
              .
            
          
        
      
    
    
      
        (
        3
        )
      
    
  




rr by one of equations of,




  
    
      
        
          q
          =
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  y
                  +
                  0.5
                
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                
                  N
                  zc
                  RS
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
              
                N
                
                  reference
                  ,
                  
                    
                  
                  ⁢
                  zc
                
                RS
              
            
          
          ,
          
            
          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
      
    
    
      
        (
        1
        )
      
    
  
  
    
      
        
          q
          =
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  y
                  +
                  0.5
                
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                
                  (
                  
                    
                      N
                      zc
                      RS
                    
                    -
                    1
                  
                  )
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
              
                
                  N
                  
                    reference
                    ,
                    
                      
                    
                    ⁢
                    zc
                  
                  RS
                
                -
                1
              
            
          
          ,
          
            
          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
        ⁢
        
          

        
        ⁢
        or
      
    
    
      
        (
        2
        )
      
    
  
  
    
      
        
          q
          =
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  y
                  +
                  0.5
                
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              floor
              ⁢
              
                
              
              ⁢
              
                
                  (
                  
                    
                      
                        N
                        zc
                        RS
                      
                      
                        N
                        
                          reference
                          ,
                          
                            
                          
                          ⁢
                          zc
                        
                        RS
                      
                    
                    +
                    0.5
                  
                  )
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
      
    
    
      
        (
        3
        )
      
    
  




Preferably, Nreference,zcRS can be set to 31 or 37, but Nreference,zcRS can be set to other values as well.
According to these embodiments of this invention, because the base sequence for applying cyclic shift is grouped, and each group contains at least one base sequence of each length, UE(s) can use various length sequences as a reference signal sequence when specific group is allocated to one cell or Node B.
Additionally, because each group contains base sequences having high cross correlation relation, if each group is allocated to one cell or Node B, inter cell interference can be minimized.



BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are included to provide a further understanding of the invention, illustrate embodiments of the invention and together with the description serve to explain the principle of the invention.
In the drawings:
FIG. 1 shows a conceptual diagram for explaining the truncated sequence generation method.
FIG. 2 shows a conceptual diagram for explaining the generation method using padding part.
FIGS. 3 to 5 show conceptual diagrams of grouping sequences according to one embodiment of this invention.
FIG. 8 is a flowchart depicting a method according to an embodiment of the present invention.
FIG. 9 is a block diagram of mobile terminal according to an embodiment of the present invention.



DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, the preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. It is to be understood that the detailed description which will be disclosed along with the accompanying drawings is intended to describe the exemplary embodiments of the present invention, and is not intended to describe a unique embodiment which the present invention can be carried out.
Hereinafter, the detailed description includes detailed matters to provide full understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention can be carried out without the detailed matters. To prevent the concept of the present invention from being ambiguous, structures and apparatuses of the known art will be omitted, or will be shown in the form of a block diagram based on main functions of each structure and apparatus. Also, wherever possible, the same reference numbers will be used throughout the drawings and the specification to refer to the same or like parts.
As stated above, the present invention is directed to provide a method for generating reference signal sequence, which minimizes the interference caused by the signals having different length, came from the neighboring cells.
To this end, the length of the CAZAC sequence is explained.
Presently, in the 3GPP LTE system, the resource block (RB) size for transmitting all kind of the OFDM symbol including reference signal symbol corresponds to the size of 12 subcarriers. So, when ZC is generated for uplink reference signal sequence, the size of ZC sequence would correspond to 12 subcarriers size.
For the case of CAZAC sequence, the number of CAZAC sequence indexes (M) which could be distinguished from each other is decided by the number of relative prime number relative prime to the sequence length (N). So, when the ZC sequence is generated to have the length of 12, the number of ZC sequences having a different sequence index is 4. But, if the ZC sequence is generated based on the prime number length (N), the number of ZC sequence having a different sequence index can be N−1, which maximizes the number of ZC sequence. Therefore, various methods for generating CAZAC sequence based on the prime number length are provided.
First, a truncated sequence generation method is explained.
FIG. 1 shows a conceptual diagram for explaining the truncated sequence generation method.
As shown in the FIG. 1, when the required CAZAC sequence length is “L”, CAZAC sequence having the prime number length of “X” (where X>L) is generated. And, the generated CAZAC sequence having the length “X” is truncated to have the length “L”, that is, part of the sequence having the length of “X−L” is truncated.
By this method, the number of CAZAC sequence is maximized. But because part of the generated sequence is truncated, the auto/cross correlation properties of CAZAC sequence explained with the equations 4 and 5 are somewhat deteriorated. And, when the sequences having poor correlation properties are eliminated, the actual number of sequence is diminished. Moreover, because of the truncation, good PAPR property of CAZAC sequence can also be deteriorated.
So, another type of methods for generating CAZAC sequence based on the prime number is presented. One of these method is that the CAZAC sequence is generated to have the prime number length “X” (where X<L), and components having the length of “L−X” is added to the generated CAZAC sequence. This components added to the generated sequence can be called as padding part, so this method can be called as generation method using padding part.
FIG. 2 shows a conceptual diagram for explaining the generation method using padding part.
As shown in the FIG. 2, when the required CAZAC sequence length is “L”, the CAZAC sequence is generated to have the length “X”, which is a maximum prime number smaller than “L”. And, the padding part having the length of “L−X” is added to the generated sequence.
In one method for this kind of methods, the padding part can be consisted of zeros. By this method, the number of CAZAC sequence can be maximized. Moreover, the auto/cross correlation properties of the CAZAC sequence can be maintained when distinction of the sequences is done with regard to the length of “C1” in FIG. 2.
And, preferably, the padding part can be a cyclic extension of the CAZAC sequence. That is, the padding part (C2) can be generated by cyclic copying of the first part of the generated CAZAC sequence, and be added to the generated sequence. By doing so, the resultant sequence can have a good auto-cross correlation propertied even when the distinction of the sequence is done with regard to the entire sequence length (L). So, this method has further advantage than the above method using the padding part as zeros.
The present invention for generating reference signal sequence using CAZAC sequence is mainly based on the generation method using padding part generated by the above mentioned cyclic extension. But, limitation to this generation method is not necessary, that is, present invention can be based on the truncated sequence generation method and the generation method using padding part consisted of zeros.
Based on this, the inter cell interference caused by using sequences having difference length is explained.
When CAZAC sequence is used for reference signal sequence, the inter cell interference is proportional to the cross correlation value between two sequence. So, in the following examples, the cross correlation value, caused by the overlapping between the original reference signal transmitted through certain resource region and the incoming sequence came from the neighboring cells, having difference length from that of the original reference signal, and transmitted through the same resource region, is considered with regard to the index of the ZC sequences.
More specifically, in the following examples, the sequences having the length of 1 RB, 2 RB and 3 RB is considered. And, let us presume that the sequences having the length of 1 RB and 2 RB are generated by the cyclic extension of the ZC sequence having the length given by the largest prime number which is less than a corresponding resource block size. And, let us presume that the sequence having the length of 3 RB is generated by the truncated sequence generation method. That is, the sequences can be generated to have the corresponding resource block size based on the prime number length by one of the above 3 generation methods.
First, consider the case when the sequence having 1 RB length and the sequence having 2 RB length is overlapped in the same resource region. The sequence having 1 RB length and the sequence having 2 RB length can be expressed as follows.




  
    
      
        
          
            
              
                g
                
                  1
                  ⁢
                  
                    
                  
                  ⁢
                  RB
                
              
              ⁡
              
                (
                
                  k
                  ;
                  
                    s
                    1
                  
                
                )
              
            
            =
            
              e
              
                
                  -
                  j
                
                ⁢
                
                  π
                  
                    N
                    1
                  
                
                ⁢
                
                  s
                  1
                
                ⁢
                
                  k
                  ⁡
                  
                    (
                    
                      k
                      +
                      1
                    
                    )
                  
                
              
            
          
          ,
          
            
          
          ⁢
          
            k
            =
            0
          
          ,
          ...
          ⁢
          
            
          
          ,
          
            N
            -
            1
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              
                g
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  RB
                
              
              ⁡
              
                (
                
                  k
                  ;
                  
                    s
                    2
                  
                
                )
              
            
            =
            
              e
              
                
                  -
                  j
                
                ⁢
                
                  π
                  
                    N
                    2
                  
                
                ⁢
                
                  s
                  2
                
                ⁢
                
                  k
                  ⁡
                  
                    (
                    
                      k
                      +
                      1
                    
                    )
                  
                
              
            
          
          ,
          
            
          
          ⁢
          
            k
            =
            0
          
          ,
          ...
          ⁢
          
            
          
          ,
          
            
              2
              ⁢
              N
            
            -
            1
          
        
      
    
    
      
        
          [
          
            Equation
            ⁢
            
              
            
            ⁢
            6
          
          ]
        
        ⁢
        
          
        
      
    
  




Here, s1 and s2 indicate the indexes which are relative prime to the sequence length (N or 2N). In this example, for the sequences having 1 RB length and 2 RB length are generated using the cyclic extension method, s1 can be 1, 2, . . . , 10 and s2 can be 1, 2, . . . , 22. And, N1 may be 11, and N2 may be 23.
Based on this, the cross correlation value (c(d; s1,s2)) generated when the sequence with 1 RB length is overlapped with the sequence with 2 RB length in the first 12 subcarriers region of the sequence with 2 RB length can be expressed as follows.




  
    
      
        
          
            c
            ⁡
            
              (
              
                
                  d
                  ;
                  
                    s
                    1
                  
                
                ,
                
                  s
                  2
                
              
              )
            
          
          =
          
            
              ∑
              
                k
                =
                0
              
              
                N
                -
                1
              
            
            ⁢
            
              
            
            ⁢
            
              
                
                  g
                  
                    1
                    ⁢
                    RB
                  
                
                ⁡
                
                  (
                  
                    k
                    ;
                    
                      s
                      1
                    
                  
                  )
                
              
              ⁢
              
                
                  g
                  
                    2
                    ⁢
                    RB
                  
                  *
                
                ⁡
                
                  (
                  
                    
                      k
                      +
                      d
                    
                    ;
                    
                      s
                      2
                    
                  
                  )
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              For
              ⁢
              
                
              
              ⁢
              d
            
            =
            0
          
          ,
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          7
        
        ]
      
    
  
  
    
      
        
          
            
              
                c
                ⁢
                
                  (
                  
                    
                      0
                      ;
                      
                        s
                        1
                      
                    
                    ,
                    
                      s
                      2
                    
                  
                  )
                
              
              =
              
              ⁢
              
                
                  ∑
                  
                    k
                    =
                    0
                  
                  
                    N
                    -
                    1
                  
                
                ⁢
                
                  
                
                ⁢
                
                  exp
                  (
                  
                    
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            π
                            
                              N
                              1
                            
                          
                          ⁢
                          
                            s
                            1
                          
                          ⁢
                          
                            mod
                            (
                            
                              k
                              ,
                              
                                N
                                -
                                1
                              
                            
                            )
                          
                        
                      
                    
                    
                      
                        
                          (
                          
                            
                              mod
                              (
                              
                                k
                                ,
                                
                                  N
                                  -
                                  1
                                
                              
                              )
                            
                            +
                            1
                          
                          )
                        
                      
                    
                  
                  )
                
              
            
          
        
        
          
            
              
              ⁢
              
                exp
                (
                
                  
                
                ⁢
                
                  
                    
                      
                        j
                        ⁢
                        
                          π
                          
                            N
                            2
                          
                        
                        ⁢
                        
                          s
                          2
                        
                        ⁢
                        
                          mod
                          (
                          
                            k
                            ,
                            
                              
                                2
                                ⁢
                                N
                              
                              -
                              1
                            
                          
                          )
                        
                      
                    
                  
                  
                    
                      
                        (
                        
                          
                            mod
                            (
                            
                              k
                              ,
                              
                                
                                  2
                                  ⁢
                                  N
                                
                                -
                                1
                              
                            
                            )
                          
                          +
                          1
                        
                        )
                      
                    
                  
                
                )
              
              ⁢
              
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  [
                  
                    
                  
                  ⁢
                  
                    
                      ∑
                      
                        k
                        =
                        0
                      
                      10
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      exp
                      ⁢
                      
                        
                      
                      ⁢
                      
                        {
                        
                          
                        
                        ⁢
                        
                          
                            
                              
                                π
                                ⁢
                                
                                  
                                
                                ⁢
                                
                                  k
                                  ⁡
                                  
                                    (
                                    
                                      k
                                      +
                                      1
                                    
                                    )
                                  
                                
                              
                            
                          
                          
                            
                              
                                j
                                ⁡
                                
                                  (
                                  
                                    
                                      
                                        s
                                        2
                                      
                                      23
                                    
                                    -
                                    
                                      
                                        s
                                        1
                                      
                                      11
                                    
                                  
                                  )
                                
                              
                            
                          
                        
                        ⁢
                        
                          
                        
                        }
                      
                    
                  
                  ⁢
                  
                    
                  
                  ]
                
                +
              
            
          
        
        
          
            
              
              ⁢
              
                exp
                ⁡
                
                  (
                  
                    j
                    ⁢
                    
                      π
                      23
                    
                    ⁢
                    
                      
                        s
                        2
                      
                      ·
                      11
                      ·
                      12
                    
                  
                  )
                
              
            
          
        
      
    
    
      
        
      
    
  




According to the equation 7, it can be understood that if the combination of sequence indexes (s1 and s2) meet the condition that the term of




  (
  
    
      
        s
        2
      
      23
    
    -
    
      
        s
        1
      
      11
    
  
  )




becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation.

Therefore, one embodiment of the present invention proposes to perform grouping the sequences into groups such that the sequences contained in each group have the high cross correlation relation with each other. And, if 1 RB length sequence and 2 RB length sequence are considered, grouping the combination of sequence indexes which meets the condition that the term of




  (
  
    
      
        s
        2
      
      23
    
    -
    
      
        s
        1
      
      11
    
  
  )




becomes close to zero is proposed.

But, to determine more general condition for the grouping sequences, let us consider some other examples.
When 1 RB sequence is overlapped in the last 12 subcarriers region of the 2 RB sequence, the cross correlation value (c(d; s1,s2)) of the two sequences can be expressed as follows.




  
    
      
        
          
            c
            ⁡
            
              (
              
                
                  d
                  ;
                  
                    s
                    1
                  
                
                ,
                
                  s
                  2
                
              
              )
            
          
          =
          
            
              ∑
              
                k
                =
                0
              
              
                N
                -
                1
              
            
            ⁢
            
              
            
            ⁢
            
              
                
                  g
                  
                    1
                    ⁢
                    RB
                  
                
                ⁡
                
                  (
                  
                    k
                    ;
                    
                      s
                      1
                    
                  
                  )
                
              
              ⁢
              
                
                  g
                  
                    2
                    ⁢
                    RB
                  
                  *
                
                ⁡
                
                  (
                  
                    
                      k
                      +
                      12
                      +
                      d
                    
                    ;
                    
                      s
                      2
                    
                  
                  )
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              For
              ⁢
              
                
              
              ⁢
              d
            
            =
            0
          
          ,
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          8
        
        ]
      
    
  
  
    
      
        
          
            
              
                c
                ⁢
                
                  (
                  
                    
                      d
                      ;
                      
                        s
                        1
                      
                    
                    ,
                    
                      s
                      2
                    
                  
                  )
                
              
              =
              
              ⁢
              
                
                  ∑
                  
                    k
                    =
                    0
                  
                  
                    N
                    -
                    1
                  
                
                ⁢
                
                  
                
                ⁢
                
                  exp
                  (
                  
                    
                  
                  ⁢
                  
                    
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            π
                            
                              N
                              1
                            
                          
                          ⁢
                          
                            s
                            1
                          
                          ⁢
                          
                            mod
                            (
                            
                              k
                              ,
                              
                                N
                                -
                                1
                              
                            
                            )
                          
                        
                      
                    
                    
                      
                        
                          (
                          
                            
                              mod
                              (
                              
                                k
                                ,
                                
                                  N
                                  -
                                  1
                                
                              
                              )
                            
                            +
                            1
                          
                          )
                        
                      
                    
                  
                  )
                
              
            
          
        
        
          
            
              
              ⁢
              
                exp
                (
                
                  
                
                ⁢
                
                  
                    
                      
                        j
                        ⁢
                        
                          π
                          
                            N
                            2
                          
                        
                        ⁢
                        
                          s
                          2
                        
                        ⁢
                        
                          mod
                          (
                          
                            
                              k
                              +
                              12
                            
                            ,
                            
                              
                                2
                                ⁢
                                N
                              
                              -
                              1
                            
                          
                          )
                        
                      
                    
                  
                  
                    
                      
                        (
                        
                          
                            mod
                            (
                            
                              
                                k
                                +
                                12
                              
                              ,
                              
                                
                                  2
                                  ⁢
                                  N
                                
                                -
                                1
                              
                            
                            )
                          
                          +
                          1
                        
                        )
                      
                    
                  
                
                ⁢
                
                  
                
                )
              
            
          
        
        
          
            
              =
              
              ⁢
              
                 
                
                  
                    [
                    
                      
                    
                    ⁢
                    
                      
                        ∑
                        
                          k
                          =
                          0
                        
                        10
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        exp
                        ⁢
                        
                          
                        
                        ⁢
                        
                          {
                          
                            
                          
                          ⁢
                          
                            
                              
                                
                                  jπ
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  
                                    k
                                    ⁡
                                    
                                      (
                                      
                                        k
                                        +
                                        1
                                      
                                      )
                                    
                                  
                                
                              
                            
                            
                              
                                
                                  
                                    (
                                    
                                      
                                        
                                          s
                                          2
                                        
                                        23
                                      
                                      -
                                      
                                        
                                          s
                                          1
                                        
                                        11
                                      
                                    
                                    )
                                  
                                  +
                                
                              
                            
                            
                              
                                
                                  
                                    
                                      s
                                      2
                                    
                                    23
                                  
                                  ·
                                  12
                                  ·
                                  
                                    (
                                    
                                      
                                        2
                                        ⁢
                                        
                                          
                                        
                                        ⁢
                                        k
                                      
                                      +
                                      13
                                    
                                    )
                                  
                                
                              
                            
                          
                          ⁢
                          
                            
                          
                          }
                        
                      
                    
                    ⁢
                    
                      
                    
                    ]
                  
                  ⁢
                  
                    
                  
                  +
                  
                    
                  
                  ⁢
                  1
                
              
            
          
        
      
    
    
      
        
      
    
  




According to the equation 8, it can also concluded that if the combination of sequence indexes (s1 and s2) meet the condition that the term of




  (
  
    
      
        s
        2
      
      23
    
    -
    
      
        s
        1
      
      11
    
  
  )




becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation. So, if 1 RB length sequence and 2 RB length sequence are considered, the position where the overlapping is occurred is not change the grouping condition.

Next, let us consider the case when the 1 RB length sequence and the 3 RB length sequence are overlapped in the same resource region.
First of all, the 1 RB length sequence and the 3 RB length sequence can be expressed as follows.




  
    
      
        
          
            
              
                g
                
                  1
                  ⁢
                  
                    
                  
                  ⁢
                  RB
                
              
              ⁡
              
                (
                
                  k
                  ;
                  
                    s
                    1
                  
                
                )
              
            
            =
            
              e
              
                
                  -
                  j
                
                ⁢
                
                  π
                  
                    N
                    1
                  
                
                ⁢
                
                  s
                  1
                
                ⁢
                
                  k
                  ⁡
                  
                    (
                    
                      k
                      +
                      1
                    
                    )
                  
                
              
            
          
          ,
          
            
          
          ⁢
          
            k
            =
            0
          
          ,
          ...
          ⁢
          
            
          
          ,
          
            N
            -
            1
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              
                g
                
                  3
                  ⁢
                  
                    
                  
                  ⁢
                  RB
                
              
              ⁡
              
                (
                
                  k
                  ;
                  
                    s
                    3
                  
                
                )
              
            
            =
            
              e
              
                
                  -
                  j
                
                ⁢
                
                  π
                  
                    N
                    3
                  
                
                ⁢
                
                  s
                  3
                
                ⁢
                
                  k
                  ⁡
                  
                    (
                    
                      k
                      +
                      1
                    
                    )
                  
                
              
            
          
          ,
          
            
          
          ⁢
          
            k
            =
            0
          
          ,
          ...
          ⁢
          
            
          
          ,
          
            
              3
              ⁢
              N
            
            -
            1
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          9
        
        ]
      
    
  




Here, s1 and s3 indicate the indexes which are relative prime to the sequence length (N or 3N). In this example, for the 1 RB length sequences is generated using the cyclic extension method and the 3 RB length sequence is generated using the truncated sequence generation method, s1 can be 1, 2, . . . , 10 and s2 can be 1, 2, . . . , 36. And, N1 may be 11, and N2 may be 37.
Based on this, if the 1 RB length sequence is overlapped in the first 12 subcarriers region of the 3 RB length sequence, the cross correlation value between the two sequences can be expressed as follows.




  
    
      
        
          
            c
            ⁡
            
              (
              
                
                  d
                  ;
                  
                    s
                    1
                  
                
                ,
                
                  s
                  3
                
              
              )
            
          
          =
          
            
              ∑
              
                k
                =
                0
              
              
                N
                -
                1
              
            
            ⁢
            
              
            
            ⁢
            
              
                
                  g
                  
                    1
                    ⁢
                    RB
                  
                
                ⁡
                
                  (
                  
                    k
                    ;
                    
                      s
                      1
                    
                  
                  )
                
              
              ⁢
              
                
                  g
                  
                    3
                    ⁢
                    RB
                  
                  *
                
                ⁡
                
                  (
                  
                    
                      k
                      +
                      d
                    
                    ;
                    
                      s
                      3
                    
                  
                  )
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              For
              ⁢
              
                
              
              ⁢
              d
            
            =
            0
          
          ,
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          10
        
        ]
      
    
  
  
    
      
        
          
            
              
                c
                ⁢
                
                  (
                  
                    
                      0
                      ;
                      
                        s
                        1
                      
                    
                    ,
                    
                      s
                      3
                    
                  
                  )
                
              
              =
              
              ⁢
              
                
                  ∑
                  
                    k
                    =
                    0
                  
                  
                    N
                    -
                    1
                  
                
                ⁢
                
                  
                
                ⁢
                
                  exp
                  (
                  
                    
                  
                  ⁢
                  
                    
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            π
                            
                              N
                              1
                            
                          
                          ⁢
                          
                            s
                            1
                          
                          ⁢
                          
                            mod
                            (
                            
                              k
                              ,
                              
                                N
                                -
                                1
                              
                            
                            )
                          
                        
                      
                    
                    
                      
                        
                          (
                          
                            
                              mod
                              (
                              
                                k
                                ,
                                
                                  N
                                  -
                                  1
                                
                              
                              )
                            
                            +
                            1
                          
                          )
                        
                      
                    
                  
                  )
                
              
            
          
        
        
          
            
              
              ⁢
              
                exp
                ⁢
                
                  (
                  
                    
                  
                  ⁢
                  
                    j
                    ⁢
                    
                      π
                      
                        N
                        3
                      
                    
                    ⁢
                    
                      s
                      3
                    
                    ⁢
                    
                      k
                      (
                      
                        k
                        +
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    
                  
                  )
                
                 
              
            
          
        
        
          
            
              
                =
                
                ⁢
                
                  
                    [
                    
                      
                    
                    ⁢
                    
                      
                        ∑
                        
                          k
                          =
                          0
                        
                        10
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        exp
                        ⁢
                        
                          
                        
                        ⁢
                        
                          {
                          
                            
                          
                          ⁢
                          
                            
                              
                                
                                  jπ
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  
                                    k
                                    ⁡
                                    
                                      (
                                      
                                        k
                                        +
                                        1
                                      
                                      )
                                    
                                  
                                
                              
                            
                            
                              
                                
                                  (
                                  
                                    
                                      
                                        s
                                        3
                                      
                                      37
                                    
                                    -
                                    
                                      
                                        s
                                        1
                                      
                                      11
                                    
                                  
                                  )
                                
                              
                            
                          
                          ⁢
                          
                            
                          
                          }
                        
                      
                    
                    ⁢
                    
                      
                    
                    ]
                  
                  ⁢
                  
                    
                  
                  +
                
              
              ⁢
              
                
              
            
          
        
        
          
            
              
              ⁢
              
                exp
                (
                
                  
                
                ⁢
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  
                    π
                    37
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      s
                      3
                    
                    ·
                    
                      
                    
                    ⁢
                    11
                    ⁢
                    
                      
                    
                    ·
                    
                      
                    
                    ⁢
                    12
                  
                
                ⁢
                
                  
                
                )
              
            
          
        
      
    
    
      
        
      
    
  




According to the equation 10, it can be understood that if the combination of sequence indexes (s1 and s3) meet the condition that the term of




  (
  
    
      
        s
        3
      
      37
    
    -
    
      
        s
        1
      
      11
    
  
  )




becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation. Therefore, if 1 RB length sequence and 3 RB length sequence are considered, grouping the combination of sequence indexes which meets the condition that the term of





  (
  
    
      
        s
        3
      
      37
    
    -
    
      
        s
        1
      
      11
    
  
  )




becomes close to zero is proposed.

And, to certify the relation with the position where the overlapping is occurred, let us consider the case when the 1 RB length sequence is overlapped in the second 12 subcarriers region of the 3 RB length sequence. In this case, the cross correlation value between these two sequences can be expressed as follows.




  
    
      
        
          
            c
            ⁡
            
              (
              
                
                  d
                  ;
                  
                    s
                    1
                  
                
                ,
                
                  s
                  3
                
              
              )
            
          
          =
          
            
              ∑
              
                k
                =
                0
              
              
                N
                -
                1
              
            
            ⁢
            
              
            
            ⁢
            
              
                
                  g
                  
                    1
                    ⁢
                    RB
                  
                
                ⁡
                
                  (
                  
                    k
                    ;
                    
                      s
                      1
                    
                  
                  )
                
              
              ⁢
              
                
                  g
                  
                    3
                    ⁢
                    RB
                  
                  *
                
                ⁡
                
                  (
                  
                    
                      k
                      +
                      12
                      +
                      d
                    
                    ;
                    
                      s
                      3
                    
                  
                  )
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              For
              ⁢
              
                
              
              ⁢
              d
            
            =
            0
          
          ,
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          11
        
        ]
      
    
  
  
    
      
        
          
            
              
                (
                
                  
                    0
                    ;
                    
                      s
                      1
                    
                  
                  ,
                  
                    s
                    3
                  
                
                )
              
              =
              
              ⁢
              
                
                  ∑
                  
                    k
                    =
                    0
                  
                  
                    N
                    -
                    1
                  
                
                ⁢
                
                  
                
                ⁢
                
                  exp
                  (
                  
                    
                  
                  ⁢
                  
                    
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            π
                            
                              N
                              1
                            
                          
                          ⁢
                          
                            s
                            1
                          
                          ⁢
                          
                            mod
                            (
                            
                              k
                              ,
                              
                                N
                                -
                                1
                              
                            
                            )
                          
                        
                      
                    
                    
                      
                        
                          (
                          
                            
                              mod
                              (
                              
                                k
                                ,
                                
                                  N
                                  -
                                  1
                                
                              
                              )
                            
                            +
                            1
                          
                          )
                        
                      
                    
                  
                  )
                
              
            
          
        
        
          
            
              
              ⁢
              
                
                   
                   
                
                ⁢
                
                  exp
                  (
                  
                    
                  
                  ⁢
                  
                    j
                    ⁢
                    
                      π
                      
                        N
                        3
                      
                    
                    ⁢
                    
                      
                        s
                        3
                      
                      ⁡
                      
                        (
                        
                          k
                          +
                          
                            1
                            ⁢
                            2
                          
                        
                        )
                      
                    
                    ⁢
                    
                      (
                      
                        k
                        +
                        13
                      
                      )
                    
                  
                  ⁢
                  
                    
                  
                  )
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  [
                  
                    
                      ∑
                      
                        k
                        =
                        0
                      
                      10
                    
                    ⁢
                    
                      exp
                      ⁡
                      
                        [
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          π
                          ⁢
                          
                            {
                            
                              
                                
                                  
                                    
                                      
                                        
                                          k
                                          ⁡
                                          
                                            (
                                            
                                              k
                                              +
                                              1
                                            
                                            )
                                          
                                        
                                      
                                    
                                    
                                      
                                        
                                          (
                                          
                                            
                                              
                                                s
                                                3
                                              
                                              37
                                            
                                            -
                                            
                                              
                                                s
                                                1
                                              
                                              11
                                            
                                          
                                          )
                                        
                                      
                                    
                                  
                                
                              
                              
                                
                                  
                                    
                                      
                                        s
                                        2
                                      
                                      37
                                    
                                    ·
                                    12
                                    ·
                                    
                                      (
                                      
                                        
                                          2
                                          ⁢
                                          k
                                        
                                        +
                                        13
                                      
                                      )
                                    
                                  
                                
                              
                            
                            }
                          
                        
                        ]
                      
                    
                  
                  ]
                
                +
              
            
          
        
        
          
            
              
              ⁢
              
                exp
                ⁡
                
                  (
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    
                      π
                      37
                    
                    ⁢
                    
                      
                        s
                        3
                      
                      ·
                      23
                      ·
                      24
                    
                  
                  )
                
              
            
          
        
      
    
    
      
        
      
    
  




And, when the 1 RB length sequence overlapped in the last 12 subcarrier region of the 3 RB length sequence, the cross correlation value can be expressed as follows.




  
    
      
        
          
            c
            ⁡
            
              (
              
                
                  d
                  ;
                  
                    s
                    1
                  
                
                ,
                
                  s
                  3
                
              
              )
            
          
          =
          
            
              ∑
              
                k
                =
                0
              
              
                N
                -
                1
              
            
            ⁢
            
              
            
            ⁢
            
              
                
                  g
                  
                    1
                    ⁢
                    RB
                  
                
                ⁡
                
                  (
                  
                    k
                    ;
                    
                      s
                      1
                    
                  
                  )
                
              
              ⁢
              
                
                  g
                  
                    3
                    ⁢
                    RB
                  
                  *
                
                ⁡
                
                  (
                  
                    
                      k
                      +
                      24
                      +
                      d
                    
                    ;
                    
                      s
                      3
                    
                  
                  )
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              For
              ⁢
              
                
              
              ⁢
              d
            
            =
            0
          
          ,
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          12
        
        ]
      
    
  
  
    
      
        
          
            
              
                c
                ⁢
                
                  (
                  
                    
                      0
                      ;
                      
                        s
                        1
                      
                    
                    ,
                    
                      s
                      3
                    
                  
                  )
                
              
              =
              
              ⁢
              
                
                  ∑
                  
                    k
                    =
                    0
                  
                  
                    N
                    -
                    1
                  
                
                ⁢
                
                  
                
                ⁢
                
                  exp
                  (
                  
                    
                  
                  ⁢
                  
                    
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            π
                            
                              N
                              1
                            
                          
                          ⁢
                          
                            s
                            1
                          
                          ⁢
                          
                            mod
                            (
                            
                              k
                              ,
                              
                                N
                                -
                                1
                              
                            
                            )
                          
                        
                      
                    
                    
                      
                        
                          (
                          
                            
                              mod
                              (
                              
                                k
                                ,
                                
                                  N
                                  -
                                  1
                                
                              
                              )
                            
                            +
                            1
                          
                          )
                        
                      
                    
                  
                  )
                
              
            
          
        
        
          
            
              
              ⁢
              
                exp
                (
                
                  
                
                ⁢
                
                  j
                  ⁢
                  
                    π
                    
                      N
                      3
                    
                  
                  ⁢
                  
                    
                      s
                      3
                    
                    ⁡
                    
                      (
                      
                        k
                        +
                        24
                      
                      )
                    
                  
                  ⁢
                  
                    (
                    
                      k
                      +
                      
                        
                      
                      ⁢
                      25
                    
                    )
                  
                
                )
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                     
                     
                  
                  [
                  
                    
                  
                  ⁢
                  
                    
                      ∑
                      
                        k
                        =
                        0
                      
                      10
                    
                    ⁢
                    
                      exp
                      [
                      
                        
                      
                      ⁢
                      
                        jπ
                        ⁢
                        
                          
                        
                        ⁢
                        
                          {
                          
                            
                          
                          ⁢
                          
                            
                              
                                
                                  
                                    
                                  
                                  ⁢
                                  
                                    k
                                    ⁡
                                    
                                      (
                                      
                                        k
                                        +
                                        1
                                      
                                      )
                                    
                                  
                                
                              
                            
                            
                              
                                
                                  
                                    (
                                    
                                      
                                        
                                          s
                                          3
                                        
                                        37
                                      
                                      -
                                      
                                        
                                          s
                                          1
                                        
                                        11
                                      
                                    
                                    )
                                  
                                  +
                                
                              
                            
                            
                              
                                
                                  
                                    
                                      s
                                      2
                                    
                                    37
                                  
                                  ·
                                  12
                                  ·
                                  
                                    (
                                    
                                      
                                        2
                                        ⁢
                                        
                                          
                                        
                                        ⁢
                                        k
                                      
                                      +
                                      13
                                    
                                    )
                                  
                                
                              
                            
                          
                          ⁢
                          
                            
                          
                          }
                        
                      
                      ⁢
                      
                        
                      
                      ]
                    
                  
                  ⁢
                  
                    
                  
                  ]
                
                +
              
            
          
        
        
          
            
              
              ⁢
              
                exp
                ⁡
                
                  (
                  
                    j
                    ⁢
                    
                      π
                      37
                    
                    ⁢
                    
                      
                        s
                        3
                      
                      ·
                      35
                      ·
                      36
                    
                  
                  )
                
              
            
          
        
      
    
    
      
        
      
    
  




According to the equations 11 and 12, it can also concluded that if the combination of sequence indexes (s1 and s3) meet the condition that the term of




  (
  
    
      
        s
        3
      
      37
    
    -
    
      
        s
        1
      
      11
    
  
  )




becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation. So, if 1 RB length sequence and 3 RB length sequence are considered, the position where the overlapping is occurred is not change the grouping condition.

According to the above examples, the present embodiment proposes to perform grouping sequences such that two sequence indexes among all the sequence indexes grouped into the same group meet the condition that the term (s2/N2−s1/N1) becomes close to zero, when the two sequences having the length of N1 and N2 are considered. Here, N1 and N2 can be maximum relative prime numbers which are less than the resultant reference signal sequence. And, s1 and s2 mean the root indexes of the ZC sequences, and can be selected among the ranges of 1 ̃(N1−1) and 1 ̃(N2−1) respectively.
Based on this concept, let's consider more general grouping method considering various length sequences.
FIGS. 3 to 5 show conceptual diagrams of grouping sequences according to one embodiment of this invention.
According to this embodiment, among various length sequences such as 1 RB, 2 RB, 3 RB . . . as shown in the FIG. 3, the sequences whose indexes meet the high cross correlation condition as stated above may be grouped into the same group. And, each of the sequence groups can be allocated to the same cell or node B.
Generally, FDM is done with the unit of cell or Node B, so the inference caused by using the sequences having difference length can be minimized within one cell or Node B. So, by allocating the sequences having the high cross correlation relation to the same cell or Node B, the inter cell interference caused by using the different length sequences can be minimized.
And, another embodiment of this invention proposes to perform grouping such that each of the groups contains at least one sequence of each length. By doing so, if the sequence group is allocated to the same cell or Node B, UE(s) located in that cell or Node B can be supported to use various length reference signal sequence. But specific grouping method can be variously defined.
First, the number of sequences allocated to one group can be proportional to the number of RBs which corresponds to the reference signal sequence length. In FIG. 3, one sequence for 1 RB length sequence, two sequences for 2 RB length sequence, 3 sequences for 3 RB length sequence, and so on, are grouped.
Second, the number of sequences allocated to one group can be a constant number. In FIG. 4, one sequence for each RB length sequence is grouped to the same group.
And, the present embodiment can be defined to perform grouping such that the number of sequences allocated to one group is neither proportional to the sequence length nor remain constant. FIG. 5 shows an example of grouping sequence such that one sequence for 1 RB length sequence, 2 sequences for 2 RB length sequence, 2 sequences for 3 RB length sequence, and 3 sequences for 4 RB length sequence, and so on, are grouped into one group.
As like the above, if each group contains at least one sequence of each RB length, the maximum number of sequence per group can be defined. When the maximum number of sequence per group is defined, a method for selecting root index of the ZC sequence within the sequence number limit can be defined as follows.
If one sequence is selected per each RB length sequence, and if one specific sequence with the index of s1 and the length of N1 is already selected for that group, one sequence per (having index of s2) each RB length can be selected, of which index make the term of (s2/N2−s1/N1) to be closest to zero, where N2 is the sequence length corresponding to the considered RB length. And, if 2 sequences are selected per certain RB length sequence, and if one specific sequence with the index of s1 and the length of N1 is already selected for that group, two sequences per that RB length can be selected to make the term of (s2/N2−s1/N1) to be close to zero. This can be more generalized to the maximum sequence number of “x” per each RB length.
And, another grouping method can be defined as follows. If one sequence is selected per each RB length sequence, and if one specific sequence with the index of s1 and the length of N1 is already selected for that group, first, select certain number (y) of sequences among sequences which make the term (s2/N2−s1/N1) to be close to certain value, and then, select one sequence among the y sequences which has high cross correlation relation with the sequence having the index of s1. And, if 2 sequences are selected per certain RB length sequence, and if one specific sequence with the index of s1 and the length of N1 is already selected for that group, first, select certain number (y) of sequences among sequences which make the term (s2/N2−s1/N1) to be close to certain value, and then, select two sequences among the y sequences which have high cross correlation relation with the sequence having the index of s1. This can be more generalized to the maximum sequence number of “x” per each RB length.
In the above examples, one specific sequence with the index of s1 and the length of N1 is firstly selected and becomes the reference for selecting rest of the sequence. This reference sequence can be defined to be 1 RB length sequence, 2 RB length sequence, 3 RB length sequence, and so on. But In the following explanation, let us presume that the reference sequence is the 3 RB length sequence. And, because the number of sequence indexes per 3 RB length is 30, the number of groups for grouping sequence according to this embodiment of the invention can be 30.
Considering that the number of root indexes for 3 RB length sequence is 30, the number of root index selected for certain group can be determined as follows.

round(the number of root index for certain RB length sequence/30)  [Equation 13]

Here, “round (z)” is a function of rounding off to a nearest integer nearest to z.
By the equation 13, for 3 RB and 4 RB lengths, 1 sequence can be selected. And, for 5 RB ̃6 RB lengths, 2 sequence can be selected. Further, for the length greater than the 6 RB length, 3 or more sequence can be selected, respectively. And, according to one embodiment of this invention, sequence with the length less than 3 RB length can be differently defined, such as not using ZC sequence. By doing so, the number of sequences selected for 1 RB length and 2 RB length can be determined to 1.
To summarize, according to this embodiment, the number of sequence per groups can be defined as follows.

{1 RB,2 RB,3 RB,4 RB,5 RB,6 RB,8 RB,9 RB,10 RB,12 RB,15 RB,16 RB,18 RB,20 RB,24 RB,25 RB, . . . }={1,1,1,1,2,2,3,3,4,5,6,6,7,8,9,9, . . . }  [Equation 14]

Based on this, the following tables 1-5 show an example of sequence grouping such that each group contains the number of sequences according to the equation 14, and the sequences selected per each group satisfy the high cross correlation relation as stated above.



















TABLE 1





Groupindex














based on 3RBs
3RB
4RB
5RB

6RB

8RB


9RB



























1
1
2
2
1
2
3
3
2
4
3
4
2


2
2
3
4
3
5
4
6
5
7
7
6
8


3
3
5
6
5
7
6
9
8

10
11
9


4
4
6
8
7
9
10
11
12

14
13
15


5
5
8
10
9
11
12
14
15
13
17
18
16


6
6
9
11
12
14
13
17
18
16
21
20
22


7
7
11
13
14
16
17
20
21
19
24
25
23


8
8
12
15
16
18
19
23
22
24
28
27
29


9
9
14
17
18
21
20
26
25
27
31
32
30


10
10
15
19

23
22
29
28
30
35
34
36


11
11
17
21

25
26
32
31

38
37
39


12
12
18
23
22
27
28
34
35

41
42
40


13
13
20
25
24
30
29
37
38
36
45
44
46


14
14
21
27
26
32
33
40
41
39
48
49
47


15
15
23
29
28
34
35
43
44
42
52
51
53


16
16
24
30
31
37
36
46
45
47
55
56
54


17
17
26
32
33
39
38
49
48
50
59
58
60


18
18
27
34
35
41
42
52
51
53
62
63
61


19
19
29
36
37
44
43
55
54

66
65
67


20
20
30
38

46
45
57
58

69
70
68


21
21
32
40

48
49
60
61
59
72
73
71


22
22
33
42
41
50
51
63
64
62
76
75
77


23
23
35
44
43
53
52
66
67
65
79
80
78


24
24
36
46
45
55
54
69
68
70
83
82
84


25
25
38
48
47
57
58
72
71
73
86
87
85


26
26
39
49
50
60
59
75
74
76
90
89
91


27
27
41
51
52
62
61
78
77

93
94
92


28
28
42
53
54
64
65
80
81

97
96
98


29
29
44
55
56
66
67
83
84
82
100
101
99


30
30
45
57
58
69
68
86
87
85
104
103
105































TABLE 2





Groupindex

















based on 3RBs
10RB



12RB




15RB






























1
4
3
5
2
4
5
3
6
2
6
5
7
4
8
3


2
7
8
6

9
8
10
7

12
11
13
10
14
9


3
11
10
12

13
14
12
15

17
18
16
19
15
20


4
15
14
16
13
18
17
19
16

23
24
22
25
21


5
18
19
17

22
23
21
24

29
28
30
27
31


6
22
21
23

27
26
28
25

35
34
36
33
37
32


7
26
25
27
24
31
32
30
33

40
41
39
42
38
43


8
29
30
28

36
35
37
34

46
47
45
48
44


9
33
32
34

40
41
39
42

52
51
53
50
54


10
36
37
35
38
45
44
46
43

58
57
59
56
60
55


11
40
41
39

49
50
48
51

64
63
65
62
66
61


12
44
43
45

54
53
55
52

69
70
68
71
67
72


13
47
48
46
49
58
59
57
60

75
76
74
77
73


14
51
52
50

63
62
64
61

81
80
82
79
83


15
55
54
56

67
68
66
69

87
86
88
85
89
84


16
58
59
57

72
71
73
70

92
93
91
94
90
95


17
62
61
63

76
77
75
78

98
99
97
100
96


18
66
65
67
64
81
80
82
79

104
103
105
102
106


19
69
70
68

85
86
84
87

110
109
111
108
112
107


20
73
72
74

90
89
91
88

115
116
114
117
113
118


21
77
76
78
75
94
95
93
96

121
122
120
123
119
124


22
80
81
79

99
98
100
97

127
128
126
129
125


23
84
83
85

103
104
102
105

133
132
134
131
135


24
87
88
86
89
108
107
109
106

139
138
140
137
141
136


25
91
92
90

112
113
111
114

144
145
143
146
142
147


26
95
94
96

117
116
118
115

150
151
149
152
148


27
98
99
97
100
121
122
120
123

156
155
157
154
158


28
102
103
101

126
125
127
124

162
161
163
160
164
159


29
106
105
107

130
131
129
132

167
168
166
169
165
170


30
109
110
108
111
135
134
136
133
137
173
174
172
175
171
176





























TABLE 3





Groupindex















based on 3RBs
16RB





18RB




























1
6
7
5
8
4
9
7
6
8
5
9
4
10


2
12
13
11
14
10
15
14
13
15
12
16
11
17


3
18
19
17
20
16
21
20
21
19
22
18
23
17


4
25
24
26
23
27
22
27
28
26
29
25
30
24


5
31
30
32
29
33
28
34
35
33
36
32
37
31


6
37
36
38
35
39
34
41
40
42
39
43
38
44


7
43
44
42
45
41
46
48
47
49
46
50
45
51


8
49
50
48
51
47
52
54
55
53
56
52
57
51


9
55
56
54
57
53
58
61
62
60
63
59
64
58


10
62
61
63
60
64
59
68
69
67
70
66
71
65


11
68
67
69
66
70
65
75
74
76
73
77
72
78


12
74
73
75
72
76
71
82
81
83
80
84
79
85


13
80
81
79
82
78
83
88
89
87
90
86
91
85


14
86
87
85
88
84
89
95
96
94
97
93
98
92


15
92
93
91
94
90
95
102
103
101
104
100
105
99


16
99
98
100
97
101
96
109
108
110
107
111
106
112


17
105
104
106
103
107
102
116
115
117
114
118
113
119


18
111
110
112
109
113
108
123
122
124
121
125
120
126


19
117
118
116
119
115
120
129
130
128
131
127
132
126


20
123
124
122
125
121
126
136
137
135
138
134
139
133


21
129
130
128
131
127
132
143
142
144
141
145
140
146


22
136
135
137
134
138
133
150
149
151
148
152
147
153


23
142
141
143
140
144
139
157
156
158
155
159
154
160


24
148
147
149
146
150
145
163
164
162
165
161
166
160


25
154
155
153
156
152
157
170
171
169
172
168
173
167


26
160
161
159
162
158
163
177
176
178
175
179
174
180


27
166
167
165
168
164
169
184
183
185
182
186
181
187


28
173
172
174
171
175
170
191
190
192
189
193
188
194


29
179
178
180
177
181
176
197
198
196
199
195
200
194


30
185
184
186
183
187
182
204
205
203
206
202
207
201


























TABLE 4





Group index












based on 3RBs
20RB







24RB
































1
8
7
9
6
10
5
11
4
9
10
8
11
7
12
6
13
5


2
15
16
14
17
13
18
12
19
18
19
17
20
16
21
15
22
14


3
23
24
22
25
21
26
20

27
28
26
29
25
30
24
31
23


4
31
30
32
29
33
28
34

37
36
38
35
39
34
40
33
41


5
39
38
40
37
41
36
42
35
46
45
47
44
48
43
49
42
50


6
46
47
45
48
44
49
43

55
54
56
53
57
52
58
51
59


7
54
53
55
52
56
51
57

64
63
65
62
66
61
67
60
68


8
62
61
63
60
64
59
65
58
73
74
72
75
71
76
70
77
69


9
69
70
68
71
67
72
66
73
82
83
81
84
80
85
79
86
78


10
77
78
76
79
75
80
74

91
92
90
93
89
94
88
95
87


11
85
84
86
83
87
82
88

100
101
99
102
98
103
97
104
96


12
93
92
94
91
95
90
96
89
110
109
111
108
112
107
113
106
114


13
100
101
99
102
98
103
97

119
118
120
117
121
116
122
115
123


14
108
107
109
106
110
105
111

128
127
129
126
130
125
131
124
132


15
116
115
117
114
118
113
119
112
137
136
138
135
139
134
140
133
141


16
123
124
122
125
121
126
120
127
146
147
145
148
144
149
143
150
142


17
131
132
130
133
129
134
128

155
156
154
157
153
158
152
159
151


18
139
138
140
137
141
136
142

164
165
163
166
162
167
161
168
160


19
146
147
145
148
144
149
143
150
173
174
172
175
171
176
170
177
169


20
154
155
153
156
152
157
151

183
182
184
181
185
180
186
179
187


21
162
161
163
160
164
159
165

192
191
193
190
194
189
195
188
196


22
170
169
171
168
172
167
173
166
201
200
202
199
203
198
204
197
205


23
177
178
176
179
175
180
174
181
210
209
211
208
212
207
213
206
214


24
185
188
184
187
183
188
182

219
220
218
221
217
222
216
223
215


25
193
192
194
191
195
190
196

228
229
227
230
226
231
225
232
224


26
200
201
199
202
198
203
197
204
237
238
236
239
235
240
234
241
233


27
208
209
207
210
206
211
205

246
247
245
248
244
249
243
250
242


28
216
215
217
214
218
213
219

256
255
257
254
258
253
259
252
260


29
224
223
225
222
226
221
227
220
265
264
266
263
267
262
268
261
269


30
231
232
230
233
229
234
228
235
274
273
275
272
276
271
277
270
278


















TABLE 5





Group




index


based


on


3RBs
25RBs
























1
9
10
8
11
7
12
6
13
5


2
19
18
20
17
21
16
22
15
23


3
28
29
27
30
26
31
25
32
24


4
38
37
39
36
40
35
41
34
42


5
47
48
46
49
45
50
44
51
43


6
57
56
58
55
59
54
60
53
61


7
66
67
65
68
64
69
63
70
62


8
76
75
77
74
78
73
79
72
80


9
85
86
84
87
83
88
82
89
81


10
95
94
96
93
97
92
98
91
99


11
104
103
105
102
106
101
107
100
108


12
113
114
112
115
111
116
110
117
109


13
123
122
124
121
125
120
126
119
127


14
132
133
131
134
130
135
129
136
128


15
142
141
143
140
144
139
145
138
146


16
151
152
150
153
149
154
148
155
147


17
161
160
162
159
163
158
164
157
165


18
170
171
169
172
168
173
167
174
166


19
180
179
181
178
182
177
183
176
184


20
189
190
188
191
187
192
186
193
185


21
198
199
197
200
196
201
195
202
194


22
208
207
209
206
210
205
211
204
212


23
217
218
216
219
215
220
214
221
213


24
227
226
228
225
229
224
230
223
231


25
236
237
235
238
234
239
233
240
232


26
246
245
247
244
248
243
249
242
250


27
255
256
254
257
253
258
252
259
251


28
265
264
266
263
267
262
268
261
269


29
274
275
273
276
272
277
271
278
270


30
284
283
285
282
286
281
287
280
288









In the tables 1 ̃5, 1 RB and 2 RB length sequence are not shown because 1 RB and 2 RB length sequence are differently defined.
And, in another example, considering that the number of root indexes for 3 RB length sequence is 30, the number of root index selected for certain group can be determined as follows.

floor(the number of root index for certain RB length sequence/30)  [Equation 15]

Here, floor (z) is a function of making the greatest integer not greater than z.
By the equation 15, for 3 ̃5 RB lengths, 1 sequence can be selected. And, for 6 ̃8 RB lengths, 2 sequence can be selected. Further, for the length greater than the 9 RB length, 3 or more sequence can be selected, respectively. And, according to one embodiment of this invention, sequence with the length less than 3 RB length can be differently defined, such as not using ZC sequence. By doing so, the number of sequences selected for 1 RB length and 2 RB length can be determined to 1.
To summarize, according to this embodiment, the number of sequence per groups can be defined as follows.

{1 RB,2 RB,3 RB,4 RB,5 RB,6 RB,8 RB,9 RB,10 RB,12 RB,15 RB,16 RB,18 RB,20 RB,24 RB,25 RB, . . . }={1,1,1,1,1,2,2,3,3,4,5,6,7,7,9,9, . . . }  [Equation 16]

Based on this, the following tables 6-8 show an example of sequence grouping such that each group contains the number of sequences according to the equation 16, and the sequences selected per each group satisfy the high cross correlation relation as stated above.


















TABLE 6







Gr. Idx













3RBs
3RB
4RB
5RB
6RB

8RB

9RB


10RB






















1
1
2
2
2
3
3
2
3
4
2
4
3


2
2
3
4
5
4
6
5
7
6
8
7
8


3
3
5
6
7
6
9
8
10
11
9
11
10


4
4
6
8
9
10
11
12
14
13
15
15
14


5
5
8
10
11
12
14
15
17
18
16
18
19


6
6
9
11
14
13
17
18
21
20
22
22
21


7
7
11
13
16
17
20
21
24
25
23
26
25


8
8
12
15
18
19
23
22
28
27
29
29
30


9
9
14
17
21
20
26
25
31
32
30
33
32


10
10
15
19
23
22
29
28
35
34
36
36
37


11
11
17
21
25
26
32
31
38
37
39
40
41


12
12
18
23
27
28
34
35
41
42
40
44
43


13
13
20
25
30
29
37
38
45
44
46
47
48


14
14
21
27
32
33
40
41
48
49
47
51
52


15
15
23
29
34
35
43
44
52
51
53
55
54


16
16
24
30
37
36
46
45
55
56
54
58
59


17
17
26
32
39
38
49
48
59
58
60
62
61


18
18
27
34
41
42
52
51
62
63
61
66
65


19
19
29
36
44
43
55
54
66
65
67
69
70


20
20
30
38
46
45
57
58
69
70
68
73
72


21
21
32
40
48
49
60
61
72
73
71
77
76


22
22
33
42
50
51
63
64
76
75
77
80
81


23
23
35
44
53
52
66
67
79
80
78
84
83


24
24
36
46
55
54
69
68
83
82
84
87
88


25
25
38
48
57
58
72
71
86
87
85
91
92


26
26
39
49
60
59
75
74
90
89
91
95
94


27
27
41
51
62
61
78
77
93
94
92
98
99


28
28
42
53
64
65
80
81
97
96
98
102
103


29
29
44
55
66
67
83
84
100
101
99
106
105


30
30
45
57
69
68
86
87
104
103
105
109
110

















Gr. Idx








3RBs

12RB

15RB























1
5
4
5
3
6
6
5
7
4
8



2
6
9
8
10
7
12
11
13
10
14



3
12
13
14
12
15
17
18
16
19
15



4
16
18
17
19
16
23
24
22
25
21



5
17
22
23
21
24
29
28
30
27
31



6
23
27
26
28
25
35
34
36
33
37



7
27
31
32
30
33
40
41
39
42
38



8
28
36
35
37
34
46
47
45
48
44



9
34
40
41
39
42
52
51
53
50
54



10
35
45
44
46
43
58
57
59
56
60



11
39
49
50
48
51
64
63
65
62
66



12
45
54
53
55
52
69
70
68
71
67



13
46
58
59
57
60
75
76
74
77
73



14
50
63
62
64
61
81
80
82
79
83



15
56
67
68
66
69
87
86
88
85
89



16
57
72
71
73
70
92
93
91
94
90



17
63
76
77
75
78
98
99
97
100
96



18
67
81
80
82
79
104
103
105
102
106



19
68
85
86
84
87
110
109
111
108
112



20
74
90
89
91
88
115
116
114
117
113



21
78
94
95
93
96
121
122
120
123
119



22
79
99
98
100
97
127
128
126
129
125



23
85
103
104
102
105
133
132
134
131
135



24
86
108
107
109
106
139
138
140
137
141



25
90
112
113
111
114
144
145
143
146
142



26
96
117
116
118
115
150
151
149
152
148



27
97
121
122
120
123
156
155
157
154
158



28
101
126
125
127
124
162
161
163
160
164



29
107
130
131
129
132
167
168
166
169
165



30
108
135
134
136
133
173
174
172
175
171























TABLE 7





Gr.








Idx


3RBs
16RB

18RB

20RB



































1
6
7
5
8
4
9
7
6
8
5
9
4
10
8
7
9
6
10
5
11


2
12
13
11
14
10
15
14
13
15
12
16
11
17
15
16
14
17
13
18
12


3
18
19
17
20
16
21
20
21
19
22
18
23
17
23
24
22
25
21
26
20


4
25
24
26
23
27
22
27
28
26
29
25
30
24
31
30
32
29
33
28
34


5
31
30
32
29
33
28
34
35
33
36
32
37
31
39
38
40
37
41
36
42


6
37
36
38
35
39
34
41
40
42
39
43
38
44
46
47
45
48
44
49
43


7
43
44
42
45
41
46
48
47
49
46
50
45
51
54
53
55
52
56
51
57


8
49
50
48
51
47
52
54
55
53
56
52
57
51
62
61
63
60
64
59
65


9
55
56
54
57
53
58
61
62
60
63
59
64
58
69
70
68
71
67
72
66


10
62
61
63
60
64
59
68
69
67
70
66
71
65
77
78
76
79
75
80
74


11
68
67
69
66
70
65
75
74
76
73
77
72
78
85
84
86
83
87
82
88


12
74
73
75
72
76
71
82
81
83
80
84
79
85
93
92
94
91
95
90
96


13
80
81
79
82
78
83
88
89
87
90
86
91
85
100
101
99
102
98
103
97


14
86
87
85
88
84
89
95
96
94
97
93
98
92
108
107
109
106
110
105
111


15
92
93
91
94
90
95
102
103
101
104
100
105
99
116
115
117
114
118
113
119


16
99
98
100
97
101
96
109
108
110
107
111
106
112
123
124
122
125
121
126
120


17
105
104
106
103
107
102
116
115
117
114
118
113
119
131
132
130
133
129
134
128


18
111
110
112
109
113
108
123
122
124
121
125
120
126
139
138
140
137
141
136
142


19
117
118
116
119
115
120
129
130
128
131
127
132
126
146
147
145
148
144
149
143


20
123
124
122
125
121
126
136
137
135
138
134
139
133
154
155
153
156
152
157
151


21
129
130
128
131
127
132
143
142
144
141
145
140
146
162
161
163
160
164
159
165


22
136
135
137
134
138
133
150
149
151
148
152
147
153
170
169
171
168
172
167
173


23
142
141
143
140
144
139
157
156
158
155
159
154
160
177
178
176
179
175
180
174


24
148
147
149
146
150
145
163
164
162
165
161
166
160
185
186
184
187
183
188
182


25
154
155
153
156
152
157
170
171
169
172
168
173
167
193
192
194
191
195
190
196


26
160
161
159
162
158
163
177
176
178
175
179
174
180
200
201
199
202
198
203
197


27
166
167
165
168
164
169
184
183
185
182
186
181
187
208
209
207
210
206
211
205


28
173
172
174
171
175
170
191
190
192
189
193
188
194
216
215
217
214
218
213
219


29
179
178
180
177
181
176
197
198
196
199
195
200
194
224
223
225
222
226
221
227


30
185
184
186
183
187
182
204
205
203
206
202
207
201
231
232
230
233
229
234
228




















TABLE 8





Gr. Idx






3RBs
24RB

25RBs

































1
9
10
8
11
7
12
6
13
5
9
10
8
11
7
12
6
13
5


2
18
19
17
20
16
21
15
22
14
19
18
20
17
21
16
22
15
23


3
27
28
26
29
25
30
24
31
23
28
29
27
30
26
31
25
32
24


4
37
36
38
35
39
34
40
33
41
38
37
39
36
40
35
41
34
42


5
46
45
47
44
48
43
49
42
50
47
48
46
49
45
50
44
51
43


6
55
54
56
53
57
52
58
51
59
57
56
58
55
59
54
60
53
61


7
64
63
65
62
66
61
67
60
68
66
67
65
68
64
69
63
70
62


8
73
74
72
75
71
76
70
77
69
76
75
77
74
78
73
79
72
80


9
82
83
81
84
80
85
79
86
78
85
86
84
87
83
88
82
89
81


10
91
92
90
93
89
94
88
95
87
95
94
96
93
97
92
98
91
99


11
100
101
99
102
98
103
97
104
96
104
103
105
102
106
101
107
100
108


12
110
109
111
108
112
107
113
106
114
113
114
112
115
111
116
110
117
109


13
119
118
120
117
121
116
122
115
123
123
122
124
121
125
120
126
119
127


14
128
127
129
126
130
125
131
124
132
132
133
131
134
130
135
129
136
128


15
137
136
138
135
139
134
140
133
141
142
141
143
140
144
139
145
138
146


16
146
147
145
148
144
149
143
150
142
151
152
150
153
149
154
148
155
147


17
155
156
154
157
153
158
152
159
151
161
160
162
159
163
158
164
157
165


18
164
165
163
166
162
167
161
168
160
170
171
169
172
168
173
167
174
166


19
173
174
172
175
171
176
170
177
169
180
179
181
178
182
177
183
176
184


20
183
182
184
181
185
180
186
179
187
189
190
188
191
187
192
186
193
185


21
192
191
193
190
194
189
195
188
196
198
199
197
200
196
201
195
202
194


22
201
200
202
199
203
198
204
197
205
208
207
209
206
210
205
211
204
212


23
210
209
211
208
212
207
213
206
214
217
218
216
219
215
220
214
221
213


24
219
220
218
221
217
222
216
223
215
227
226
228
225
229
224
230
223
231


25
228
229
227
230
226
231
225
232
224
236
237
235
238
234
239
233
240
232


26
237
238
236
239
235
240
234
241
233
246
245
247
244
248
243
249
242
250


27
246
247
245
248
244
249
243
250
242
255
256
254
257
253
258
252
259
251


28
256
255
257
254
258
253
259
252
260
265
264
266
263
267
262
268
261
269


29
265
264
266
263
267
262
268
261
269
274
275
273
276
272
277
271
278
270


30
274
273
275
272
276
271
277
270
278
284
283
285
282
286
281
287
280
288









As like the tables 1 ̃5, in the tables 6 ̃8, 1 RB and 2 RB length sequence are not shown because 1 RB and 2 RB length sequence are differently defined.
In another embodiment of this invention, the maximum number of sequences per each group can be predetermined for various reasons. The following tables 9 and 10 show the example of the case when the maximum number of sequences per group is limited to 5 sequences.


















TABLE 9







Gr. Idx













3RBs
3RB
4RB
5RB
6RB

8RB

9RB


10RB






















1
1
2
2
2
3
3
2
3
4
2
4
3


2
2
3
4
5
4
6
5
7
6
8
7
8


3
3
5
6
7
6
9
8
10
11
9
11
10


4
4
6
8
9
10
11
12
14
13
15
15
14


5
5
8
10
11
12
14
15
17
18
16
18
19


6
6
9
11
14
13
17
18
21
20
22
22
21


7
7
11
13
16
17
20
21
24
25
23
26
25


8
8
12
15
18
19
23
22
28
27
29
29
30


9
9
14
17
21
20
26
25
31
32
30
33
32


10
10
15
19
23
22
29
28
35
34
36
36
37


11
11
17
21
25
26
32
31
38
37
39
40
41


12
12
18
23
27
28
34
35
41
42
40
44
43


13
13
20
25
30
29
37
38
45
44
46
47
48


14
14
21
27
32
33
40
41
48
49
47
51
52


15
15
23
29
34
35
43
44
52
51
53
55
54


16
16
24
30
37
36
46
45
55
56
54
58
59


17
17
26
32
39
38
49
48
59
58
60
62
61


18
18
27
34
41
42
52
51
62
63
61
66
65


19
19
29
36
44
43
55
54
66
65
67
69
70


20
20
30
38
46
45
57
58
69
70
68
73
72


21
21
32
40
48
49
60
61
72
73
71
77
76


22
22
33
42
50
51
63
64
76
75
77
80
81


23
23
35
44
53
52
66
67
79
80
78
84
83


24
24
36
46
55
54
69
68
83
82
84
87
88


25
25
38
48
57
58
72
71
86
87
85
91
92


26
26
39
49
60
59
75
74
90
89
91
95
94


27
27
41
51
62
61
78
77
93
94
92
98
99


28
28
42
53
64
65
80
81
97
96
98
102
103


29
29
44
55
66
67
83
84
100
101
99
106
105


30
30
45
57
69
68
86
87
104
103
105
109
110

















Gr. Idx








3RBs

12RB

15RB























1
5
4
5
3
6
6
5
7
4
8



2
6
9
8
10
7
12
11
13
10
14



3
12
13
14
12
15
17
18
16
19
15



4
16
18
17
19
16
23
24
22
25
21



5
17
22
23
21
24
29
28
30
27
31



6
23
27
26
28
25
35
34
36
33
37



7
27
31
32
30
33
40
41
39
42
38



8
28
36
35
37
34
46
47
45
48
44



9
34
40
41
39
42
52
51
53
50
54



10
35
45
44
46
43
58
57
59
56
60



11
39
49
50
48
51
64
63
65
62
66



12
45
54
53
55
52
69
70
68
71
67



13
46
58
59
57
60
75
76
74
77
73



14
50
63
62
64
61
81
80
82
79
83



15
56
67
68
66
69
87
86
88
85
89



16
57
72
71
73
70
92
93
91
94
90



17
63
76
77
75
78
98
99
97
100
96



18
67
81
80
82
79
104
103
105
102
106



19
68
85
86
84
87
110
109
111
108
112



20
74
90
89
91
88
115
116
114
117
113



21
78
94
95
93
96
121
122
120
123
119



22
79
99
98
100
97
127
128
126
129
125



23
85
103
104
102
105
133
132
134
131
135



24
86
108
107
109
106
139
138
140
137
141



25
90
112
113
111
114
144
145
143
146
142



26
96
117
116
118
115
150
151
149
152
148



27
97
121
122
120
123
156
155
157
154
158



28
101
126
125
127
124
162
161
163
160
164



29
107
130
131
129
132
167
168
166
169
165



30
108
135
134
136
133
173
174
172
175
171























TABLE 10





Gr. Idx








3RBs
16RB

18RB

20RB




























1
6
7
5
8
4
7
6
8
5
9
8
7
9


2
12
13
11
14
10
14
13
15
12
16
15
16
14


3
18
19
17
20
16
20
21
19
22
18
23
24
22


4
25
24
26
23
27
27
28
26
29
25
31
30
32


5
31
30
32
29
33
34
35
33
36
32
39
38
40


6
37
36
38
35
39
41
40
42
39
43
46
47
45


7
43
44
42
45
41
48
47
49
46
50
54
53
55


8
49
50
48
51
47
54
55
53
56
52
62
61
63


9
55
56
54
57
53
61
62
60
63
59
69
70
68


10
62
61
63
60
64
68
69
67
70
66
77
78
76


11
68
67
69
66
70
75
74
76
73
77
85
84
86


12
74
73
75
72
76
82
81
83
80
84
93
92
94


13
80
81
79
82
78
88
89
87
90
86
100
101
99


14
86
87
85
88
84
95
96
94
97
93
108
107
109


15
92
93
91
94
90
102
103
101
104
100
116
115
117


16
99
98
100
97
101
109
108
110
107
111
123
124
122


17
105
104
106
103
107
116
115
117
114
118
131
132
130


18
111
110
112
109
113
123
122
124
121
125
139
138
140


19
117
118
116
119
115
129
130
128
131
127
146
147
145


20
123
124
122
125
121
136
137
135
138
134
154
155
153


21
129
130
128
131
127
143
142
144
141
145
162
161
163


22
136
135
137
134
138
150
149
151
148
152
170
169
171


23
142
141
143
140
144
157
156
158
155
159
177
178
176


24
148
147
149
146
150
163
164
162
165
161
185
186
184


25
154
155
153
156
152
170
171
169
172
168
193
192
194


26
160
161
159
162
158
177
176
178
175
179
200
201
199


27
166
167
165
168
164
184
183
185
182
186
208
209
207


28
173
172
174
171
175
191
190
192
189
193
216
215
217


29
179
178
180
177
181
197
198
196
199
195
224
223
225


30
185
184
186
183
187
204
205
203
206
202
231
232
230

















Gr. Idx








3RBs

24RB

25RBs

























1
6
10
9
10
8
11
7
9
10
8
11
7



2
17
13
18
19
17
20
16
19
18
20
17
21



3
25
21
27
28
26
29
25
28
29
27
30
26



4
29
33
37
36
38
35
39
38
37
39
36
40



5
37
41
46
45
47
44
48
47
48
46
49
45



6
48
44
55
54
56
53
57
57
56
58
55
59



7
52
56
64
63
65
62
66
66
67
65
68
64



8
60
64
73
74
72
75
71
76
75
77
74
78



9
71
67
82
83
81
84
80
85
86
84
87
83



10
79
75
91
92
90
93
89
95
94
96
93
97



11
83
87
100
101
99
102
98
104
103
105
102
106



12
91
95
110
109
111
108
112
113
114
112
115
111



13
102
98
119
118
120
117
121
123
122
124
121
125



14
106
110
128
127
129
126
130
132
133
131
134
130



15
114
118
137
136
138
135
139
142
141
143
140
144



16
125
121
146
147
145
148
144
151
152
150
153
149



17
133
129
155
156
154
157
153
161
160
162
159
163



18
137
141
164
165
163
166
162
170
171
169
172
168



19
148
144
173
174
172
175
171
180
179
181
178
182



20
156
152
183
182
184
181
185
189
190
188
191
187



21
160
164
192
191
193
190
194
198
199
197
200
196



22
168
172
201
200
202
199
203
208
207
209
206
210



23
179
175
210
209
211
208
212
217
218
216
219
215



24
187
183
219
220
218
221
217
227
226
228
225
229



25
191
195
228
229
227
230
226
236
237
235
238
234



26
202
198
237
238
236
239
235
246
245
247
244
248



27
210
206
246
247
245
248
244
255
256
254
257
253



28
214
218
256
255
257
254
258
265
264
266
263
267



29
222
226
265
264
266
263
267
274
275
273
276
272



30
233
229
274
273
275
272
276
284
283
285
282
286










And, in another example, the maximum number of sequences can be predetermined to 4. The following tables 11 and 12 show this case.






















TABLE 11





Gr.

















Idx


3RBs
3RB
4RB
5RB
6RB

8RB
9RB


10RB

12RB


15RB




































1
1
2
2
2
3
3
2
3
4
2
4
3
5
4
5
3
6
6
5
7
4


2
2
3
4
5
4
6
5
7
6
8
7
8
6
9
8
10
7
12
11
13
10


3
3
5
6
7
6
9
8
10
11
9
11
10
12
13
14
12
15
17
18
16
19


4
4
6
8
9
10
11
12
14
13
15
15
14
16
18
17
19
16
23
24
22
25


5
5
8
10
11
12
14
15
17
18
16
18
19
17
22
23
21
24
29
28
30
27


6
6
9
11
14
13
17
18
21
20
22
22
21
23
27
26
28
25
35
34
36
33


7
7
11
13
16
17
20
21
24
25
23
26
25
27
31
32
30
33
40
41
39
42


8
8
12
15
18
19
23
22
28
27
29
29
30
28
36
35
37
34
46
47
45
48


9
9
14
17
21
20
26
25
31
32
30
33
32
34
40
41
39
42
52
51
53
50


10
10
15
19
23
22
29
28
35
34
36
36
37
35
45
44
46
43
58
57
59
56


11
11
17
21
25
26
32
31
38
37
39
40
41
39
49
50
48
51
64
63
65
62


12
12
18
23
27
28
34
35
41
42
40
44
43
45
54
53
55
52
69
70
68
71


13
13
20
25
30
29
37
38
45
44
46
47
48
46
58
59
57
60
75
76
74
77


14
14
21
27
32
33
40
41
48
49
47
51
52
50
63
62
64
61
81
80
82
79


15
15
23
29
34
35
43
44
52
51
53
55
54
56
67
68
66
69
87
86
88
85


16
16
24
30
37
36
46
45
55
56
54
58
59
57
72
71
73
70
92
93
91
94


17
17
26
32
39
38
49
48
59
58
60
62
61
63
76
77
75
78
98
99
97
100


18
18
27
34
41
42
52
51
62
63
61
66
65
67
81
80
82
79
104
103
105
102


19
19
29
36
44
43
55
54
66
65
67
69
70
68
85
86
84
87
110
109
111
108


20
20
30
38
46
45
57
58
69
70
68
73
72
74
90
89
91
88
115
116
114
117


21
21
32
40
48
49
60
61
72
73
71
77
76
78
94
95
93
96
121
122
120
123


22
22
33
42
50
51
63
64
76
75
77
80
81
79
99
98
100
97
127
128
126
129


23
23
35
44
53
52
66
67
79
80
78
84
83
85
103
104
102
105
133
132
134
131


24
24
36
46
55
54
69
68
83
82
84
87
88
86
108
107
109
106
139
138
140
137


25
25
38
48
57
58
72
71
86
87
85
91
92
90
112
113
111
114
144
145
143
146


26
26
39
49
60
59
75
74
90
89
91
95
94
96
117
116
118
115
150
151
149
152


27
27
41
51
62
61
78
77
93
94
92
98
99
97
121
122
120
123
156
155
157
154


28
28
42
53
64
65
80
81
97
96
98
102
103
101
126
125
127
124
162
161
163
160


29
29
44
55
66
67
83
84
100
101
99
106
105
107
130
131
129
132
167
168
166
169


30
30
45
57
69
68
86
87
104
103
105
109
110
108
135
134
136
133
173
174
172
175






















TABLE 12







Gr. Idx








3RBs
16RB

18RB

20RB





















1
6
7
5
8
7
6
8
5
8
7
9


2
12
13
11
14
14
13
15
12
15
16
14


3
18
19
17
20
20
21
19
22
23
24
22


4
25
24
26
23
27
28
26
29
31
30
32


5
31
30
32
29
34
35
33
36
39
38
40


6
37
36
38
35
41
40
42
39
46
47
45


7
43
44
42
45
48
47
49
46
54
53
55


8
49
50
48
51
54
55
53
56
62
61
63


9
55
56
54
57
61
62
60
63
69
70
68


10
62
61
63
60
68
69
67
70
77
78
76


11
68
67
69
66
75
74
76
73
85
84
86


12
74
73
75
72
82
81
83
80
93
92
94


13
80
81
79
82
88
89
87
90
100
101
99


14
86
87
85
88
95
96
94
97
108
107
109


15
92
93
91
94
102
103
101
104
116
115
117


16
99
98
100
97
109
108
110
107
123
124
122


17
105
104
106
103
116
115
117
114
131
132
130


18
111
110
112
109
123
122
124
121
139
138
140


19
117
118
116
119
129
130
128
131
146
147
145


20
123
124
122
125
136
137
135
138
154
155
153


21
129
130
128
131
143
142
144
141
162
161
163


22
136
135
137
134
150
149
151
148
170
169
171


23
142
141
143
140
157
156
158
155
177
178
176


24
148
147
149
146
163
164
162
165
185
186
184


25
154
155
153
156
170
171
169
172
193
192
194


26
160
161
159
162
177
176
178
175
200
201
199


27
166
167
165
168
184
183
185
182
208
209
207


28
173
172
174
171
191
190
192
189
216
215
217


29
179
178
180
177
197
198
196
199
224
223
225


30
185
184
186
183
204
205
203
206
231
232
230

















Gr. Idx








3RBs

24RB

25RBs






















1
6
9
10
8
11
9
10
8
11



2
17
18
19
17
20
19
18
20
17



3
25
27
28
26
29
28
29
27
30



4
29
37
36
38
35
38
37
39
36



5
37
46
45
47
44
47
48
46
49



6
48
55
54
56
53
57
56
58
55



7
52
64
63
65
62
66
67
65
68



8
60
73
74
72
75
76
75
77
74



9
71
82
83
81
84
85
86
84
87



10
79
91
92
90
93
95
94
96
93



11
83
100
101
99
102
104
103
105
102



12
91
110
109
111
108
113
114
112
115



13
102
119
118
120
117
123
122
124
121



14
106
128
127
129
126
132
133
131
134



15
114
137
136
138
135
142
141
143
140



16
125
146
147
145
148
151
152
150
153



17
133
155
156
154
157
161
160
162
159



18
137
164
165
163
166
170
171
169
172



19
148
173
174
172
175
180
179
181
178



20
156
183
182
184
181
189
190
188
191



21
160
192
191
193
190
198
199
197
200



22
168
201
200
202
199
208
207
209
206



23
179
210
209
211
208
217
218
216
219



24
187
219
220
218
221
227
226
228
225



25
191
228
229
227
230
236
237
235
238



26
202
237
238
236
239
246
245
247
244



27
210
246
247
245
248
255
256
254
257



28
214
256
255
257
254
265
264
266
263



29
222
265
264
266
263
274
275
273
276



30
233
274
273
275
272
284
283
285
282










And, in another example, the maximum number of sequences can be predetermined to 3. The following tables 13 and 14 show this case.



















TABLE 13







Gr. Idx














3RBs
3RB
4RB
5RB
6RB

8RB

9RB


10RB























1
1
2
2
2
3
3
2
3
4
2
4
3
5


2
2
3
4
5
4
6
5
7
6
8
7
8
6


3
3
5
6
7
6
9
8
10
11
9
11
10
12


4
4
6
8
9
10
11
12
14
13
15
15
14
16


5
5
8
10
11
12
14
15
17
18
16
18
19
17


6
6
9
11
14
13
17
18
21
20
22
22
21
23


7
7
11
13
16
17
20
21
24
25
23
26
25
27


8
8
12
15
18
19
23
22
28
27
29
29
30
28


9
9
14
17
21
20
26
25
31
32
30
33
32
34


10
10
15
19
23
22
29
28
35
34
36
36
37
35


11
11
17
21
25
26
32
31
38
37
39
40
41
39


12
12
18
23
27
28
34
35
41
42
40
44
43
45


13
13
20
25
30
29
37
38
45
44
46
47
48
46


14
14
21
27
32
33
40
41
48
49
47
51
52
50


15
15
23
29
34
35
43
44
52
51
53
55
54
56


16
16
24
30
37
36
46
45
55
56
54
58
59
57


17
17
26
32
39
38
49
48
59
58
60
62
61
63


18
18
27
34
41
42
52
51
62
63
61
66
65
67


19
19
29
36
44
43
55
54
66
65
67
69
70
68


20
20
30
38
46
45
57
58
69
70
68
73
72
74


21
21
32
40
48
49
60
61
72
73
71
77
76
78


22
22
33
42
50
51
63
64
76
75
77
80
81
79


23
23
35
44
53
52
66
67
79
80
78
84
83
85


24
24
36
46
55
54
69
68
83
82
84
87
88
86


25
25
38
48
57
58
72
71
86
87
85
91
92
90


26
26
39
49
60
59
75
74
90
89
91
95
94
96


27
27
41
51
62
61
78
77
93
94
92
98
99
97


28
28
42
53
64
65
80
81
97
96
98
102
103
101


29
29
44
55
66
67
83
84
100
101
99
106
105
107


30
30
45
57
69
68
86
87
104
103
105
109
110
108


















Gr. Idx










3RBs
12RB

15RB

16RB

18RB






















1
4
5
3
6
5
7
6
7
5
7
6
8


2
9
8
10
12
11
13
12
13
11
14
13
15


3
13
14
12
17
18
16
18
19
17
20
21
19


4
18
17
19
23
24
22
25
24
26
27
28
26


5
22
23
21
29
28
30
31
30
32
34
35
33


6
27
26
28
35
34
36
37
36
38
41
40
42


7
31
32
30
40
41
39
43
44
42
48
47
49


8
36
35
37
46
47
45
49
50
48
54
55
53


9
40
41
39
52
51
53
55
56
54
61
62
60


10
45
44
46
58
57
59
62
61
63
68
69
67


11
49
50
48
64
63
65
68
67
69
75
74
76


12
54
53
55
69
70
68
74
73
75
82
81
83


13
58
59
57
75
76
74
80
81
79
88
89
87


14
63
62
64
81
80
82
86
87
85
95
96
94


15
67
68
66
87
86
88
92
93
91
102
103
101


16
72
71
73
92
93
91
99
98
100
109
108
110


17
76
77
75
98
99
97
105
104
106
116
115
117


18
81
80
82
104
103
105
111
110
112
123
122
124


19
85
86
84
110
109
111
117
118
116
129
130
128


20
90
89
91
115
116
114
123
124
122
136
137
135


21
94
95
93
121
122
120
129
130
128
143
142
144


22
99
98
100
127
128
126
136
135
137
150
149
151


23
103
104
102
133
132
134
142
141
143
157
156
158


24
108
107
109
139
138
140
148
147
149
163
164
162


25
112
113
111
144
145
143
154
155
153
170
171
169


26
117
116
118
150
151
149
160
161
159
177
176
178


27
121
122
120
156
155
157
166
167
165
184
183
185


28
126
125
127
162
161
163
173
172
174
191
190
192


29
130
131
129
167
168
166
179
178
180
197
198
196


30
135
134
136
173
174
172
185
184
186
204
205
203






















TABLE 14





Gr. Idx








3RBs
20RB

24RB

25RBs
























1
8
7
9
9
10
8
9
10
8


2
15
16
14
18
19
17
19
18
20


3
23
24
22
27
28
26
28
29
27


4
31
30
32
37
36
38
38
37
39


5
39
38
40
46
45
47
47
48
46


6
46
47
45
55
54
56
57
56
58


7
54
53
55
64
63
65
66
67
65


8
62
61
63
73
74
72
76
75
77


9
69
70
68
82
83
81
85
86
84


10
77
78
76
91
92
90
95
94
96


11
85
84
86
100
101
99
104
103
105


12
93
92
94
110
109
111
113
114
112


13
100
101
99
119
118
120
123
122
124


14
108
107
109
128
127
129
132
133
131


15
116
115
117
137
136
138
142
141
143


16
123
124
122
146
147
145
151
152
150


17
131
132
130
155
156
154
161
160
162


18
139
138
140
164
165
163
170
171
169


19
146
147
145
173
174
172
180
179
181


20
154
155
153
183
182
184
189
190
188


21
162
161
163
192
191
193
198
199
197


22
170
169
171
201
200
202
208
207
209


23
177
178
176
210
209
211
217
218
216


24
185
186
184
219
220
218
227
226
228


25
193
192
194
228
229
227
236
237
235


26
200
201
199
237
238
236
246
245
247


27
208
209
207
246
247
245
255
256
254


28
216
215
217
256
255
257
265
264
266


29
224
223
225
265
264
266
274
275
273


30
231
232
230
274
273
275
284
283
285









And, in another example, the maximum number of sequences can be predetermined to 2. The following tables 15 and 16 show this case.



















TABLE 15





Gr. Idx














3RBs
3RB
4RB
5RB
6RB

8RB

9RB

10RB
12RB
15RB






























1
1
2
2
2
3
3
2
3
4
4
3
4
5
6
5


2
2
3
4
5
4
6
5
7
6
7
8
9
8
12
11


3
3
5
6
7
6
9
8
10
11
11
10
13
14
17
18


4
4
6
8
9
10
11
12
14
13
15
14
18
17
23
24


5
5
8
10
11
12
14
15
17
18
18
19
22
23
29
28


6
6
9
11
14
13
17
18
21
20
22
21
27
26
35
34


7
7
11
13
16
17
20
21
24
25
26
25
31
32
40
41


8
8
12
15
18
19
23
22
28
27
29
30
36
35
46
47


9
9
14
17
21
20
26
25
31
32
33
32
40
41
52
51


10
10
15
19
23
22
29
28
35
34
36
37
45
44
58
57


11
11
17
21
25
26
32
31
38
37
40
41
49
50
64
63


12
12
18
23
27
28
34
35
41
42
44
43
54
53
69
70


13
13
20
25
30
29
37
38
45
44
47
48
58
59
75
76


14
14
21
27
32
33
40
41
48
49
51
52
63
62
81
80


15
15
23
29
34
35
43
44
52
51
55
54
67
68
87
86


16
16
24
30
37
36
46
45
55
56
58
49
72
71
92
93


17
17
26
32
39
38
49
48
59
58
62
61
76
77
98
99


18
18
27
34
41
42
52
51
62
63
66
65
81
80
104
103


19
19
29
36
44
43
55
54
66
65
69
70
85
86
110
109


20
20
30
38
46
45
57
58
69
70
73
72
90
89
115
116


21
21
32
40
48
49
60
61
72
73
77
76
94
95
121
122


22
22
33
42
50
51
63
64
76
75
80
81
99
98
127
128


23
23
35
44
53
52
66
67
79
80
84
83
103
104
133
132


24
24
36
46
55
54
69
68
83
82
87
88
108
107
139
138


25
25
38
48
57
58
72
71
86
87
91
92
112
113
144
145


26
26
39
49
60
59
75
74
90
89
95
94
117
116
150
151


27
27
41
51
62
61
78
77
93
94
98
99
121
122
156
155


28
28
42
53
64
65
80
81
97
96
102
103
126
125
162
161


29
29
44
55
66
67
83
84
100
101
106
105
130
131
167
168


30
30
45
57
69
68
86
87
104
103
109
110
135
134
173
174





















TABLE 16





Gr. Idx 3RBs
16RB
18RB
20RB
24RB
25RB

























1
6
7
7
6
8
7
9
10
9
10


2
12
13
14
13
15
16
18
19
19
18


3
18
19
20
21
23
24
27
28
28
29


4
25
24
27
28
31
30
37
36
38
37


5
31
30
34
35
39
38
46
45
47
48


6
37
36
41
40
46
47
55
54
57
56


7
43
44
48
47
54
53
64
63
66
67


8
49
50
54
55
62
61
73
74
76
75


9
55
56
61
62
69
70
82
83
85
86


10
62
61
68
69
77
78
91
92
95
94


11
68
67
75
74
85
84
100
101
104
103


12
74
73
82
81
93
92
110
109
113
114


13
80
81
88
89
100
101
119
118
123
122


14
86
87
95
96
108
107
128
127
132
133


15
92
93
102
103
116
115
137
136
142
141


16
99
98
109
108
123
124
146
147
151
152


17
105
104
116
115
131
132
155
156
161
160


18
111
110
123
122
139
138
164
165
170
171


19
117
118
129
130
146
147
173
174
180
179


20
123
124
136
137
154
155
183
182
189
190


21
129
130
143
142
162
161
192
191
198
199


22
136
135
150
149
170
169
201
200
208
207


23
142
141
157
156
177
178
210
209
217
218


24
148
147
163
164
185
186
219
220
227
226


25
154
155
170
171
193
192
228
229
236
237


26
160
161
177
176
200
201
237
238
246
245


27
166
167
184
183
208
209
246
247
255
256


28
173
172
191
190
216
215
256
255
265
264


29
179
178
197
198
224
223
265
264
274
275


30
185
184
204
205
231
232
274
273
284
283









And, in another example, the maximum number of sequences can be predetermined to 1. The following table 17 shows this case.





















TABLE 17





Gr. Idx 3RBs
3RB
4RB
5RB
6RB
8RB
9RB
10RB
12RB
15RB
16RB
18RB
20RB
24RB
25RB





























1
1
2
2
2
3
3
4
4
6
6
7
8
9
9


2
2
3
4
5
6
7
7
9
12
12
14
15
18
19


3
3
5
6
7
9
10
11
13
17
18
20
23
27
28


4
4
6
8
9
11
14
15
18
23
25
27
31
37
38


5
5
8
10
11
14
17
18
22
29
31
34
39
46
47


6
6
9
11
14
17
21
22
27
35
37
41
46
55
57


7
7
11
13
16
20
24
26
31
40
43
48
54
64
66


8
8
12
15
18
23
28
29
36
46
49
54
62
73
76


9
9
14
17
21
26
31
33
40
52
55
61
69
82
85


10
10
15
19
23
29
35
36
45
58
62
68
77
91
95


11
11
17
21
25
32
38
40
49
64
68
75
85
100
104


12
12
18
23
27
34
41
44
54
69
74
82
93
110
113


13
13
20
25
30
37
45
47
58
75
80
88
100
119
123


14
14
21
27
32
40
48
51
63
81
86
95
108
128
132


15
15
23
29
34
43
52
55
67
87
92
102
116
137
142


16
16
24
30
37
46
55
58
72
92
99
109
123
146
151


17
17
26
32
39
49
59
62
76
98
105
116
131
155
161


18
18
27
34
41
52
62
66
81
104
111
123
139
164
170


19
19
29
36
44
55
66
69
85
110
117
129
146
173
180


20
20
30
38
46
57
69
73
90
115
123
136
154
183
189


21
21
32
40
48
60
72
77
94
121
129
143
162
192
198


22
22
33
42
50
63
76
80
99
127
136
150
170
201
208


23
23
35
44
53
66
79
84
103
133
142
157
177
210
217


24
24
36
46
55
69
83
87
108
139
148
163
185
219
227


25
25
38
48
57
72
86
91
112
144
154
170
193
228
236


26
26
39
49
60
75
90
95
117
150
160
177
200
237
246


27
27
41
51
62
78
93
98
121
156
166
184
208
246
255


28
28
42
53
64
80
97
102
126
162
173
191
216
256
265


29
29
44
55
66
83
100
106
130
167
179
197
224
265
274


30
30
45
57
69
86
104
109
135
173
185
204
231
274
284









Considering the complexity of configuration and the flexibility for supporting UE(s) to use variable length reference signal sequence, one embodiment of this invention proposes to perform grouping such that each of the groups contains one base sequence of each length corresponding to 1 to 5 RB length, and two base sequences of each length corresponding to 6 RB or more length. This corresponds to the tables 15 and 16.
Here, base sequence means the ZC sequence indicated by the root index, and is used for applying the cyclic shift corresponding to various cyclic shift values. And, the base sequence with cyclic shift can be used as a reference signal sequence.
The above tables 1 ̃17 is the case when the root index(es) is selected by using the term of (s1/N1−s2/N2). But in another embodiment of this invention, the root index(es) can be selected by actual cross correlation value calculation. The following tables 18 ̃20 correspond to the tables 6 ̃8, but the root indexes are selected by actual cross correlation value calculation.

















TABLE 18







Gr. Idx












3RBs
3RB
4RB
5RB
6RB

8RB

9RB

10RB






















1
1
25
2
20
2
3
25
57
4
75
60
79


2
2
3
4
40
33
65
28
7
71
96
64
45


3
3
14
6
7
21
53
9
46
10
37
11
39


4
4
6
47
9
66
56
41
14
85
78
15
71


5
5
39
39
47
54
44
50
71
44
60
56
75


6
6
9
31
61
14
17
84
21
92
85
97
50


7
7
42
33
16
28
20
87
24
51
60
82
63


8
8
12
30
42
54
23
5
28
99
49
67
86


9
9
45
17
68
21
48
85
31
74
58
61
89


10
10
15
19
23
5
73
29
106
70
34
93
112


11
11
1
21
11
25
32
2
38
102
11
40
78


12
12
37
23
51
63
79
64
96
77
41
72
44


13
13
4
5
6
30
67
37
45
9
18
104
47


14
14
21
7
32
22
40
58
102
84
48
51
6


15
15
23
58
58
34
43
61
105
16
25
17
111


16
16
24
1
13
65
46
28
91
2
82
96
2


17
17
26
52
39
49
31
49
23
59
16
62
107


18
18
43
54
65
41
22
52
62
98
89
9
66


19
19
29
36
8
20
10
25
30
12
87
41
24


20
20
46
38
46
60
87
57
69
5
96
73
35


21
21
32
40
48
66
16
60
1
37
73
20
1


22
22
2
42
3
50
41
78
76
49
33
52
24


23
23
35
29
29
17
66
55
79
8
58
46
27


24
24
5
26
55
43
69
2
83
56
47
31
12


25
25
38
28
10
57
72
27
15
65
86
63
46


26
26
8
20
24
17
45
75
63
54
90
95
57


27
27
41
22
62
44
33
48
93
22
29
23
98


28
28
33
53
64
50
36
80
61
97
70
102
57


29
29
44
8
31
38
24
39
100
36
11
49
68


30
30
22
55
69
51
86
64
50
103
18
34
109

















Gr. Idx








3RBs

12RB

15RB























1
4
74
51
4
5
6
95
140
125
5



2
75
9
120
44
8
101
71
131
12
11



3
86
83
13
14
48
17
107
77
18
62



4
14
18
122
87
129
23
83
113
68
24



5
103
92
23
115
78
29
118
148
28
163



6
67
27
96
131
73
35
154
124
34
94



7
26
101
124
32
66
40
130
160
41
100



8
1
36
105
8
89
46
136
106
47
91



9
78
133
110
41
75
52
141
171
142
7



10
36
45
114
91
17
58
147
57
177
13



11
12
119
3
50
77
64
153
4
63
19



12
100
54
100
123
26
69
159
129
114
10



13
85
12
58
128
114
75
165
153
120
76



14
23
63
132
7
35
81
21
170
36
80



15
83
67
137
21
68
86
27
176
146
42



16
30
2
118
71
16
93
152
3
33
137



17
90
7
76
77
132
158
98
9
143
134



18
28
11
127
81
25
104
14
44
59
103



19
70
85
39
16
113
20
50
110
65
169



20
101
136
20
89
43
115
26
175
116
71



21
39
94
48
25
129
121
32
122
2
166



22
35
6
64
52
99
127
38
8
172
67



23
112
103
34
131
80
133
73
132
88
43



24
88
38
15
73
108
139
49
19
138
79



25
16
112
66
43
113
144
25
55
145
85



26
38
47
116
24
61
150
61
31
151
16



27
42
121
75
52
17
156
96
155
66
111



28
74
56
79
126
125
162
72
102
42
161



29
106
130
95
19
131
78
48
108
167
168



30
81
65
135
134
100
173
54
84
39
174























TABLE 19





Gr.








Idx


3RBs
16RB

18RB

20RB



































1
6
102
70
54
7
159
112
7
6
165
49
147
8
8
7
167
127
87
9
187


2
76
12
108
140
60
13
119
14
84
154
98
56
13
15
135
95
175
75
16
111


3
18
114
19
82
66
146
20
126
91
161
21
73
147
23
143
103
24
142
22
71


4
25
152
120
24
88
168
133
28
168
98
196
80
154
31
150
190
30
32
210
111


5
30
158
174
69
31
107
34
175
139
33
35
87
203
39
38
158
118
218
198
98


6
37
132
101
133
180
38
41
146
40
199
182
181
83
46
126
47
45
106
94
206


7
43
139
107
91
44
170
48
153
118
188
206
47
174
54
174
173
134
53
55
213


8
49
113
145
50
97
177
54
195
139
181
2
55
53
62
181
221
61
2
141
63


9
151
103
56
132
183
8
61
202
62
132
114
19
167
69
189
70
149
129
229
10


10
62
157
189
61
14
125
68
174
209
173
138
121
69
77
197
157
196
76
236
137


11
68
67
163
20
106
4
75
74
76
5
181
180
159
85
204
5
84
164
25
86


12
74
169
10
138
170
75
187
152
81
82
166
29
208
92
13
172
33
152
236
212


13
80
176
81
144
79
16
194
36
141
159
18
89
173
220
180
101
21
100
160
148


14
86
150
182
87
10
48
95
201
25
96
11
166
180
108
107
109
188
228
48
168


15
188
93
29
156
92
140
102
208
32
103
172
101
207
116
36
235
115
195
56
68


16
3
98
162
35
99
51
109
3
179
56
110
39
4
123
203
4
124
44
183
171


17
105
41
9
104
181
143
116
10
186
115
200
31
45
131
132
130
51
11
191
71


18
111
47
15
110
175
149
17
175
70
52
193
122
38
19
59
138
139
218
140
79


19
117
22
181
21
116
53
24
59
130
182
129
45
3
27
147
146
226
206
87
67


20
28
123
124
171
85
187
136
31
137
135
206
52
66
35
154
234
155
214
75
153


21
129
34
2
66
130
177
143
37
2
73
142
196
185
162
42
82
43
163
3
102


22
135
136
59
8
183
21
150
9
149
44
79
97
192
170
169
50
90
110
10
74


23
142
78
46
94
141
14
16
30
209
157
72
156
158
58
177
18
178
237
98
176


24
148
52
84
100
147
21
163
93
23
5
58
164
111
185
65
66
105
186
184
26


25
154
59
90
155
58
11
170
65
171
12
64
128
86
193
113
192
33
194
133
97


26
33
161
17
122
160
84
177
72
176
178
36
8
71
200
81
121
41
21
201
141


27
166
39
71
167
103
23
78
183
43
113
15
131
185
208
89
49
209
207
29
128


28
173
77
45
172
109
125
85
50
138
190
191
64
32
216
96
97
215
217
136
56


29
115
179
51
131
178
83
92
197
127
57
113
155
198
224
223
104
144
64
164
128


30
185
89
121
137
184
70
46
99
204
205
162
64
98
232
231
72
112
152
230
52




















TABLE 20





Gr.






Idx


3RBs
24RB

25RBs

































1
9
151
150
103
80
198
10
8
221
9
10
156
107
205
229
8
68
83


2
19
207
18
17
159
89
188
75
231
19
165
18
214
92
166
20
239
136


3
28
27
169
216
122
240
26
98
84
28
175
126
27
248
29
224
102
87


4
36
37
178
225
35
131
93
249
263
38
184
135
39
136
233
37
111
155


5
140
45
234
46
187
47
272
188
258
194
48
145
47
243
193
267
242
106


6
55
196
149
197
243
56
267
54
244
56
203
252
154
130
58
155
174
57


7
64
205
158
206
253
63
65
252
135
66
213
212
164
262
261
67
286
139


8
73
214
262
74
72
168
144
215
243
76
222
75
271
173
149
77
2
17


9
82
223
81
271
177
83
176
153
224
85
231
183
12
86
280
84
281
158


10
91
280
92
90
186
232
233
21
185
95
241
192
94
168
96
21
290
93


11
242
195
6
101
99
100
30
44
102
104
250
251
6
202
103
105
31
201


12
109
110
204
39
15
251
111
180
166
113
260
211
16
112
40
114
115
187


13
119
213
260
24
120
48
118
261
232
123
269
25
270
221
196
220
122
124


14
128
33
270
34
222
269
127
129
71
132
230
133
131
279
278
34
191
35


15
137
136
138
278
66
43
231
42
208
288
142
44
239
289
240
143
83
259


16
146
147
4
145
5
217
240
52
75
5
151
249
54
4
53
34
210
150


17
155
13
249
61
14
156
154
250
212
161
63
160
162
15
14
102
259
258


18
164
70
23
259
163
165
22
51
108
170
24
268
23
72
97
73
171
169


19
174
173
32
79
172
244
268
103
117
180
33
179
82
277
181
253
178
106


20
41
183
277
182
88
184
253
239
181
189
43
42
287
91
190
188
262
92


21
192
50
3
191
193
97
262
135
98
198
52
101
199
125
200
197
3
272


22
201
60
202
12
106
59
200
107
130
208
62
110
281
207
13
209
12
135


23
210
69
21
209
211
139
68
40
97
218
71
22
120
217
144
216
291
276


24
219
78
125
77
30
220
31
218
148
227
80
81
129
228
31
32
226
7


25
87
228
134
86
40
227
39
229
16
237
90
41
139
163
235
138
236
119


26
96
143
49
237
25
238
236
11
124
99
245
148
246
50
247
100
26
51


27
247
246
105
58
248
152
190
34
20
255
109
254
158
157
60
256
182
108


28
256
114
67
161
255
185
257
43
199
265
118
167
266
45
264
69
119
191


29
264
76
265
123
266
194
124
95
208
274
128
275
127
79
273
201
157
54


30
274
132
180
85
273
275
133
104
62
284
283
137
186
88
64
282
285
210









In this case, if the maximum number of sequences per each group is predetermined to 5, the grouping can be performed as shown in the following tables 21 and 22. The tables 21 and 22 are also the case when the base sequences are selected by actual cross correlation calculation.















TABLE 21







Gr. Idx 3RBs
3RB
4RB
5RB
6RB
8RB
9RB

10RB






















1
1
25
2
20
2
3
25
57
4
75
60
79


2
2
3
4
40
33
65
28
7
71
96
64
45


3
3
14
6
7
21
53
9
46
10
37
11
39


4
4
6
47
9
66
56
41
14
85
78
15
71


5
5
39
39
47
54
44
50
71
44
60
56
75


6
6
9
31
61
14
17
84
21
92
85
97
50


7
7
42
33
16
28
20
87
24
51
60
82
63


8
8
12
30
42
54
23
5
28
99
49
67
86


9
9
45
17
68
21
48
85
31
74
58
61
89


10
10
15
19
23
5
73
29
106
70
34
93
112


11
11
1
21
11
25
32
2
38
102
11
40
78


12
12
37
23
51
63
79
64
95
77
41
72
44


13
13
4
5
6
30
67
37
45
9
18
104
47


14
14
21
7
32
22
40
58
102
84
48
51
6


15
15
23
58
58
34
43
61
105
16
25
17
111


16
16
24
1
13
65
46
28
91
2
82
96
2


17
17
26
52
39
49
31
49
23
59
16
62
107


18
18
43
54
65
41
22
52
62
98
89
9
66


19
19
29
36
8
20
10
25
30
12
87
41
24


20
20
46
38
46
60
87
57
69
5
96
73
35


21
21
32
40
48
66
16
60
1
37
73
20
1


22
22
2
42
3
50
41
78
76
49
33
52
24


23
23
35
29
29
17
66
55
79
8
58
46
27


24
24
5
26
55
43
69
2
83
56
47
31
12


25
25
38
28
10
57
72
27
15
65
86
63
46


26
26
8
20
24
17
45
75
63
54
90
95
57


27
27
41
22
62
44
33
48
93
22
29
23
98


28
28
33
53
64
50
36
80
61
97
70
102
57


29
29
44
8
31
38
24
39
100
39
11
49
68


30
30
22
55
69
51
86
64
50
103
18
34
109















Gr. Idx 3RBs

12RB

15RB




















1
4
74
51
4
5
6
95
140
125
5


2
75
9
120
44
8
101
71
131
12
11


3
86
83
13
14
48
17
107
77
18
62


4
14
18
122
87
129
23
83
113
68
24


5
103
92
23
115
78
29
118
148
28
163


6
67
27
96
131
73
35
154
124
34
94


7
26
101
124
32
66
40
130
160
41
100


8
1
36
105
8
59
46
136
106
47
91


9
78
133
110
41
75
52
141
171
142
7


10
36
45
114
91
17
58
147
57
177
13


11
12
119
3
50
77
64
153
4
63
19


12
100
54
100
123
26
69
159
129
114
10


13
85
12
58
128
114
75
165
135
120
76


14
23
63
132
7
35
81
21
170
36
80


15
83
67
137
21
68
86
27
176
146
42


16
30
2
118
71
16
93
152
3
33
137


17
90
7
76
77
132
158
98
9
143
134


18
28
11
127
81
25
104
14
44
59
103


19
70
85
39
16
113
20
50
110
65
169


20
101
136
20
89
43
115
26
175
116
71


21
39
94
48
25
129
121
32
122
2
166


22
35
6
64
52
99
127
38
8
172
67


23
112
103
34
131
80
133
73
132
88
43


24
88
38
15
73
108
139
49
19
138
79


25
16
112
66
43
113
144
25
55
145
85


26
38
47
116
24
61
150
61
31
151
16


27
42
121
75
52
17
156
96
155
66
111


28
74
56
79
126
125
162
72
102
42
161


29
106
130
95
19
131
78
48
108
167
168


30
81
65
135
134
100
173
54
84
39
174






















TABLE 22







Gr. Idx








3RBs
16RB

18RB

20RB























1
6
102
70
54
7
112
7
6
165
49
8
7
167


2
76
12
108
140
60
119
14
84
154
98
15
135
95


3
81
114
19
82
66
20
126
91
161
21
23
143
103


4
25
152
120
24
88
133
28
168
98
196
31
150
190


5
30
158
174
69
31
34
175
139
33
35
39
38
158


6
37
132
101
133
180
41
146
40
199
182
46
126
47


7
43
139
107
91
44
48
153
118
188
206
54
174
173


8
49
113
145
50
97
54
195
139
181
2
62
181
221


9
151
103
56
132
183
61
202
62
132
114
69
189
70


10
62
157
189
61
14
68
174
209
173
138
77
197
157


11
68
67
163
20
106
75
74
76
5
181
85
204
5


12
74
169
10
138
170
187
152
81
82
166
92
13
172


13
80
176
81
144
79
194
36
141
159
18
220
180
101


14
86
150
182
87
10
95
201
25
96
11
108
107
109


15
188
93
29
156
92
102
208
32
103
172
116
36
235


16
3
98
162
35
99
109
3
179
56
110
123
203
4


17
105
41
9
104
181
116
10
186
115
200
131
132
130


18
111
47
15
110
175
17
175
70
52
193
19
59
138


19
117
22
181
21
116
24
59
130
182
129
27
147
146


20
28
123
124
171
85
136
31
137
135
206
35
154
234


21
129
34
2
66
130
143
37
2
73
142
162
42
82


22
135
136
59
8
183
150
9
149
44
79
170
169
50


23
142
78
46
94
141
16
30
209
157
72
58
177
18


24
148
52
84
100
147
163
93
23
5
58
185
65
66


25
154
59
90
155
58
170
65
171
12
64
193
113
192


26
33
161
17
122
160
177
72
176
178
36
200
81
121


27
166
39
71
167
103
78
183
43
113
15
208
89
49


28
173
77
45
172
109
85
50
138
190
191
216
96
97


29
115
179
51
131
178
92
197
127
57
113
224
223
104


30
185
89
121
137
184
46
99
204
205
162
232
231
72

















Gr. Idx








3RBs

24RB

25RB

























1
127
87
9
151
150
103
80
9
10
156
107
205



2
175
75
19
207
18
17
159
19
165
18
214
92



3
24
142
28
27
169
216
122
28
175
126
27
248



4
30
32
36
37
178
225
35
38
184
135
39
136



5
118
218
140
45
234
46
187
194
48
145
47
243



6
45
106
55
196
149
197
243
56
203
252
154
130



7
134
53
64
205
158
206
253
66
213
212
164
262



8
61
2
73
214
262
74
72
76
222
75
271
173



9
149
129
82
223
81
271
177
85
231
183
12
86



10
196
76
91
280
92
90
186
95
241
192
94
168



11
84
164
242
195
6
101
99
104
250
251
6
202



12
33
152
109
110
204
39
15
113
260
211
16
112



13
21
100
119
213
260
24
120
123
269
25
270
221



14
188
228
128
33
270
34
222
132
230
133
131
279



15
115
195
137
136
138
278
66
288
142
44
239
289



16
124
44
146
147
4
145
5
5
151
249
54
4



17
51
11
155
13
249
61
14
161
63
160
162
15



18
139
218
164
70
23
259
163
170
24
268
23
72



19
226
206
174
173
32
79
172
180
33
179
82
277



20
155
214
41
183
277
182
88
189
43
42
287
91



21
43
163
192
50
3
191
193
198
52
101
199
125



22
90
110
201
60
202
12
106
208
62
110
281
207



23
178
237
210
69
21
209
211
218
71
22
120
217



24
105
186
219
78
125
77
30
227
80
81
129
228



25
33
194
87
228
134
86
40
237
90
41
139
163



26
41
21
96
143
49
237
25
99
245
148
246
50



27
209
207
247
246
105
58
248
255
109
254
158
157



28
215
217
256
114
67
161
255
265
118
167
266
45



29
144
64
264
76
265
123
266
274
128
275
127
79



30
112
152
274
132
180
85
273
284
283
137
186
88










In another example, if the maximum number of sequences per each group is predetermined to 4, the grouping can be performed as shown in the following tables 23 and 24. The tables 23 and 24 are also the case when the base sequences are selected by actual cross correlation calculation.





















TABLE 23





Gr.
















Idx


3RBs
3RB
4RB
5RB
6RB

8RB

9RB

10RB
12RB

15RB




































1
1
25
2
20
2
3
25
57
4
75
60
79
4
74
51
4
5
6
95
140
125


2
2
3
4
40
33
65
28
7
71
96
64
45
75
9
120
44
8
101
71
131
12


3
3
14
6
7
21
53
9
46
10
37
11
39
86
83
13
14
48
17
107
77
18


4
4
6
47
9
66
56
41
14
85
78
15
71
14
18
122
87
129
23
83
113
68


5
5
39
39
47
54
44
50
71
44
60
56
75
103
92
23
115
78
29
118
148
28


6
6
9
31
61
14
17
84
21
92
85
97
50
67
27
96
131
73
35
154
124
34


7
7
42
33
16
28
20
87
24
51
60
82
63
26
101
124
32
66
40
130
160
41


8
8
12
30
42
54
23
5
28
99
49
67
86
1
36
105
8
59
46
136
106
47


9
9
45
17
68
21
48
85
31
74
58
61
89
78
133
110
41
75
52
141
171
142


10
10
15
19
23
5
73
29
106
70
34
93
112
36
45
114
91
17
58
147
57
177


11
11
1
21
11
25
32
2
38
102
11
40
78
12
119
3
50
77
64
153
4
63


12
12
37
23
51
63
79
64
95
77
41
72
44
100
54
100
123
26
69
159
129
114


13
13
4
5
6
30
67
37
45
9
18
104
47
85
12
58
128
114
75
165
135
120


14
14
21
7
32
22
40
58
102
84
48
51
6
23
63
132
7
35
81
21
170
36


15
15
23
58
58
34
43
61
105
16
25
17
111
83
67
137
21
68
86
27
176
146


16
16
24
1
13
65
46
28
91
2
82
96
2
30
2
118
71
16
93
152
3
33


17
17
26
52
39
49
31
49
23
59
16
62
107
90
7
76
77
132
158
98
9
143


18
18
43
54
65
41
22
52
62
98
89
9
66
28
11
127
81
25
104
14
44
59


19
19
29
36
8
20
10
25
30
12
87
41
24
70
85
39
16
113
20
50
110
65


20
20
46
38
46
60
87
57
69
5
96
73
35
101
136
20
89
43
115
26
175
116


21
21
32
40
48
66
16
60
1
37
73
20
1
39
94
48
25
129
121
32
122
2


22
22
2
42
3
50
41
78
76
49
33
52
24
35
6
64
52
99
127
38
8
172


23
23
35
29
29
17
66
55
79
8
58
46
27
112
103
34
131
80
133
73
132
88


24
24
5
26
55
43
69
2
83
56
47
31
12
88
38
15
73
108
139
49
19
138


25
25
38
28
10
57
72
27
15
65
86
63
46
16
112
66
43
113
144
25
55
145


26
26
8
20
24
17
45
75
63
54
90
95
57
38
47
116
24
61
150
61
31
151


27
27
41
22
62
44
33
48
93
22
29
23
98
42
121
75
52
17
156
96
155
66


28
28
33
53
64
50
36
80
61
97
70
102
57
74
56
79
126
125
162
72
102
42


29
29
44
8
31
38
24
39
100
36
11
49
68
106
130
95
19
131
78
48
108
167


30
30
22
55
69
51
86
64
50
103
18
34
109
81
65
135
134
100
173
54
84
39


























TABLE 24





Gr.












Idx


3RBs
16RB

18RB

20RB

24RB

25RBs



































1
6
102
70
54
112
7
6
165
8
7
167
127
9
151
150
103
9
10
156
107


2
76
12
108
140
119
14
84
154
15
135
95
175
19
207
18
17
19
165
18
214


3
18
114
19
82
20
126
91
161
23
143
103
24
28
27
169
216
28
175
126
27


4
25
152
120
24
133
28
168
98
31
150
190
30
36
37
178
225
38
184
135
39


5
30
158
174
69
34
175
139
33
39
38
158
118
140
45
234
46
194
48
145
47


6
37
132
101
133
41
146
40
199
46
126
47
45
55
196
149
197
56
203
252
154


7
43
139
107
91
48
153
118
188
54
174
173
134
64
205
158
206
66
213
212
164


8
49
113
145
50
54
195
139
181
62
181
221
61
73
214
262
74
76
222
75
271


9
151
103
56
132
61
202
62
132
69
189
70
149
82
223
81
271
85
231
183
12


10
62
157
189
61
68
174
209
173
77
197
157
196
91
280
92
90
95
241
192
94


11
68
67
163
20
75
74
76
5
85
204
5
84
242
195
6
101
104
250
251
6


12
74
169
10
138
187
152
81
82
92
13
172
33
109
110
204
39
113
260
211
16


13
80
176
81
144
194
36
141
159
220
180
101
21
119
213
260
24
123
269
25
270


14
86
150
182
87
95
201
25
96
108
107
109
188
128
33
270
34
132
230
133
131


15
188
93
29
156
102
208
32
103
116
36
235
115
137
136
138
278
288
142
44
239


16
3
98
162
35
109
3
179
56
123
203
4
124
146
147
4
145
5
151
249
54


17
105
41
9
104
116
10
186
115
131
132
130
51
155
13
249
61
161
63
160
162


18
111
47
15
110
17
175
70
52
19
59
138
139
164
70
23
259
170
24
268
23


19
117
22
181
21
24
59
130
182
27
147
146
226
174
173
32
79
180
33
179
82


20
28
123
124
171
136
31
137
135
35
154
234
155
41
183
277
182
189
43
42
287


21
129
34
2
66
143
37
2
73
162
42
82
43
192
50
3
191
198
52
101
199


22
135
136
59
8
150
9
149
44
170
169
50
90
201
60
202
12
208
62
110
281


23
142
78
46
94
16
30
209
157
58
177
18
178
210
69
21
209
218
71
22
120


24
148
52
84
100
163
93
23
5
185
65
66
105
219
78
125
77
227
80
81
129


25
154
59
90
155
170
65
171
12
193
113
192
33
87
228
134
86
237
90
41
139


26
33
161
17
122
177
72
176
178
200
81
121
41
96
143
49
237
99
245
148
246


27
166
39
71
167
78
183
43
113
208
89
49
209
247
246
105
58
255
109
254
158


28
173
77
45
172
85
50
138
190
216
96
97
215
256
114
67
161
265
118
167
266


29
115
179
51
131
92
197
127
57
224
223
104
144
264
76
265
123
274
128
275
127


30
185
89
121
137
46
99
204
205
232
231
72
112
274
132
180
85
284
283
137
186









In another example, if the maximum number of sequences per each group is predetermined to 3, the grouping can be performed as shown in the following tables 25 and 26. The tables 25 and 26 are also the case when the base sequences are selected by actual cross correlation calculation.

















TABLE 25







Gr. Idx 3RBs
3RB
4RB
5RB
6RB

8RB
9RB

10RB






















1
1
25
2
20
2
3
25
57
4
75
60
79


2
2
3
4
40
33
65
28
7
71
96
64
45


3
3
14
6
7
21
53
9
46
10
37
11
39


4
4
6
47
9
66
56
41
14
85
78
15
71


5
5
39
39
47
54
44
50
71
44
60
56
75


6
6
9
31
61
14
17
84
21
92
85
97
50


7
7
42
33
16
28
20
87
24
51
60
82
63


8
8
12
30
42
54
23
5
28
99
49
67
86


9
9
45
17
68
21
48
85
31
74
58
61
89


10
10
15
19
23
5
73
29
106
70
34
93
112


11
11
1
21
11
25
32
2
38
102
11
40
78


12
12
37
23
51
63
79
64
95
77
41
72
44


13
13
4
5
6
30
67
37
45
9
18
104
47


14
14
21
7
32
22
40
58
102
84
48
51
6


15
15
23
58
58
34
43
61
105
16
25
17
111


16
16
24
1
13
65
46
28
91
2
82
96
2


17
17
26
52
39
49
31
49
23
59
16
62
107


18
18
43
54
65
41
22
52
62
98
89
9
66


19
19
29
36
8
20
10
25
30
12
87
41
24


20
20
46
38
46
60
87
57
69
5
96
73
35


21
21
32
40
48
66
16
60
1
37
73
20
1


22
22
2
42
3
50
41
78
76
49
33
52
24


23
23
35
29
29
17
66
55
79
8
58
46
27


24
24
5
26
55
43
69
2
83
56
47
31
12


25
25
38
28
10
57
72
27
15
65
86
63
46


26
26
8
20
24
17
45
75
63
54
90
95
57


27
27
41
22
62
44
33
48
93
22
29
23
98


28
28
33
53
64
50
36
80
61
97
70
102
57


29
29
44
8
31
38
24
39
100
36
11
49
68


30
30
22
55
69
51
86
64
50
103
18
34
109

















Gr. Idx 3RBs

12RB

15RB

16RB




















1
4
74
51
4
6
95
140
6
102
70


2
75
9
120
44
101
71
131
76
12
108


3
86
83
13
14
17
107
77
18
114
19


4
14
18
122
87
23
83
113
25
152
120


5
103
92
23
115
29
118
148
30
158
174


6
67
27
96
131
35
154
124
37
132
101


7
26
101
124
32
40
130
160
43
139
107


8
1
36
105
8
46
136
106
49
113
145


9
78
133
110
41
52
141
171
151
103
56


10
36
45
114
91
58
147
57
62
157
189


11
12
119
3
50
64
153
4
68
67
163


12
100
54
100
123
69
159
129
74
169
10


13
85
12
58
128
75
165
135
80
176
81


14
23
63
132
7
81
21
170
86
150
182


15
83
67
137
21
86
27
176
188
93
29


16
30
2
118
71
93
152
3
3
98
162


17
90
7
76
77
158
98
9
105
41
9


18
28
11
127
81
104
14
44
111
47
15


19
70
85
39
16
20
50
110
117
22
181


20
101
136
20
89
115
26
175
28
123
124


21
39
94
48
25
121
32
122
129
34
2


22
35
6
64
52
127
38
8
135
136
59


23
112
103
34
131
133
73
132
142
78
46


24
88
38
15
73
139
49
19
148
52
84


25
16
112
66
43
144
25
55
154
59
90


26
38
47
116
24
150
61
31
33
161
17


27
42
121
75
52
156
96
155
166
39
71


28
74
56
79
126
162
72
102
173
77
45


29
106
130
95
19
78
48
180
115
179
51


30
81
65
135
134
173
54
84
185
89
121
























TABLE 26





Gr. Idx










3RBs
18RB

20RB

24RB

25RBs



























1
112
7
6
8
7
167
9
151
150
9
10
156


2
119
14
84
15
135
95
19
207
18
19
165
18


3
20
126
91
23
143
103
28
27
169
28
175
126


4
133
28
168
31
150
190
36
37
178
38
184
135


5
34
175
139
39
38
158
140
45
234
194
48
145


6
41
146
40
46
126
47
55
196
149
56
203
252


7
48
153
118
54
174
173
64
205
158
66
213
212


8
54
195
139
62
181
221
73
214
262
76
222
75


9
61
202
62
69
189
70
82
223
81
85
231
183


10
68
174
209
77
197
157
91
280
92
95
241
192


11
75
74
76
85
204
5
242
195
6
104
250
251


12
187
152
81
92
13
172
109
110
204
113
260
211


13
194
36
141
220
180
101
119
213
260
123
269
25


14
95
201
25
108
107
109
128
33
270
132
230
133


15
102
208
32
116
36
235
137
136
138
288
142
44


16
109
3
179
123
203
4
146
147
4
5
151
249


17
116
10
186
131
132
130
155
13
249
161
63
160


18
17
175
70
19
59
138
164
70
23
170
24
268


19
24
59
130
27
147
146
174
173
32
180
33
179


20
136
31
137
35
154
234
41
183
277
189
43
42


21
143
37
2
162
42
82
192
50
3
198
52
101


22
150
9
149
170
169
50
201
60
202
208
62
110


23
16
30
209
58
177
18
210
69
21
218
71
22


24
163
93
23
185
65
66
219
78
125
227
80
81


25
170
65
171
193
113
192
87
228
134
237
90
41


26
177
72
176
200
81
121
96
143
49
99
245
148


27
78
183
43
208
89
49
247
246
105
255
109
254


28
85
50
138
216
96
97
256
114
67
265
118
167


29
92
197
127
224
223
104
264
76
265
274
128
275


30
46
99
204
232
231
72
274
132
180
284
283
137









In another example, if the maximum number of sequences per each group is predetermined to 2, the grouping can be performed as shown in the following table 27. The table 27 is also the case when the base sequences are selected by actual cross correlation calculation.

















TABLE 27







Gr. Idx












3RBs
3RB
4RB
5RB
6RB

8RB
9RB

10RB
12RB























1
1
25
2
20
2
3
25
57
4
60
79
74
51


2
2
3
4
40
33
65
28
7
71
64
45
9
120


3
3
14
6
7
21
53
9
46
10
11
39
83
13


4
4
6
47
9
66
56
41
14
85
15
71
18
122


5
5
39
39
47
54
44
50
71
44
56
75
92
23


6
6
9
31
61
14
17
84
21
92
97
50
27
96


7
7
42
33
16
28
20
87
24
51
82
63
101
124


8
8
12
30
42
54
23
5
28
99
67
86
36
105


9
9
45
17
68
21
48
85
31
74
61
89
133
110


10
10
15
19
23
5
73
29
106
70
93
112
45
114


11
11
1
21
11
25
32
2
38
102
40
78
119
3


12
12
37
23
51
63
79
64
95
77
72
44
54
100


13
13
4
5
6
30
67
37
45
9
104
47
12
58


14
14
21
7
32
22
40
58
102
84
51
6
63
132


15
15
23
58
58
34
43
61
105
16
17
111
67
137


16
16
24
1
13
65
46
28
91
2
96
2
2
118


17
17
26
52
39
49
31
49
23
59
62
107
7
76


18
18
43
54
65
41
22
52
62
98
9
66
11
127


19
19
29
36
8
20
10
25
30
12
41
24
85
39


20
20
46
38
46
60
87
57
69
5
73
35
136
20


21
21
32
40
48
66
16
60
1
37
20
1
94
48


22
22
2
42
3
50
41
78
76
49
52
24
6
64


23
23
35
29
29
17
66
55
79
8
46
27
103
34


24
24
5
26
55
43
69
2
83
56
31
12
38
15


25
25
38
28
10
57
72
27
15
65
63
46
112
66


26
26
8
20
24
17
45
75
63
54
95
57
47
116


27
27
41
22
62
44
33
48
93
22
23
98
121
75


28
28
33
53
64
50
36
80
61
97
102
57
56
79


29
29
44
8
31
38
24
39
100
36
49
68
130
95


30
30
22
55
69
51
86
64
50
103
34
109
65
135
















Gr. Idx
15RB
16RB
18RB
20RB
24RB
25RBs






















1
6
95
6
102
112
7
8
7
9
151
9
10


2
101
71
76
12
119
14
15
135
19
207
19
165


3
17
107
18
114
20
126
23
143
28
27
28
175


4
23
83
25
152
133
28
31
150
36
37
38
184


5
29
118
30
158
34
175
39
38
140
45
194
48


6
35
154
37
132
41
146
46
126
55
196
56
203


7
40
130
43
139
48
153
54
174
64
205
66
213


8
46
136
49
113
54
195
62
181
73
214
76
222


9
52
141
151
103
61
202
69
189
82
223
85
231


10
58
147
62
157
68
174
77
197
91
280
95
241


11
64
153
68
67
75
74
85
204
242
195
104
250


12
69
159
74
169
187
152
92
13
109
110
113
260


13
75
165
80
176
194
36
220
180
119
213
123
269


14
81
21
86
150
95
201
108
107
128
33
132
230


15
86
27
188
93
102
208
116
36
137
136
288
142


16
93
152
3
98
109
3
123
203
146
147
5
151


17
158
98
105
41
116
10
131
132
155
13
161
63


18
104
14
111
47
17
175
19
59
164
70
170
24


19
20
50
117
22
24
59
27
147
174
173
180
33


20
115
26
28
123
136
31
35
154
41
183
189
43


21
121
32
129
34
143
37
162
42
192
50
198
52


22
127
38
135
136
150
9
170
169
201
60
208
62


23
133
73
142
78
16
30
58
177
210
69
218
71


24
139
49
148
52
163
93
185
65
219
78
227
80


25
144
25
154
59
170
65
193
113
87
228
237
90


26
150
61
33
161
177
72
200
81
96
143
99
245


27
156
96
166
39
78
183
208
89
247
246
255
109


28
162
72
173
77
85
50
216
96
256
114
265
118


29
78
48
115
179
92
197
224
223
264
76
274
128


30
173
54
185
89
46
99
232
231
274
132
284
283









In another example, if the maximum number of sequences per each group is predetermined to 1, the grouping can be performed as shown in the following table 28. The table 28 is also the case when the base sequences are selected by actual cross correlation calculation.





















TABLE 28





Gr. Idx
















3RBs
3RB
4RB
5RB
6RB
8RB
9RB
10RB
12RB
15RB
16RB
18RB
20RB
24RB
25RBs





























1
1
25
2
20
3
57
60
74
6
6
112
8
9
9


2
2
3
4
40
65
7
64
9
101
76
119
15
19
19


3
3
14
6
7
53
46
11
83
17
18
20
23
28
28


4
4
6
47
9
56
14
15
18
23
25
133
31
36
38


5
5
39
39
47
44
71
56
92
29
30
34
39
140
194


6
6
9
31
61
17
21
97
27
35
37
41
46
55
56


7
7
42
33
16
20
24
82
101
40
43
48
54
64
66


8
8
12
30
42
23
28
67
36
46
49
54
62
73
76


9
9
45
17
68
48
31
61
133
52
151
61
69
82
85


10
10
15
19
23
73
106
93
45
58
62
68
77
91
95


11
11
1
21
11
32
38
40
119
64
68
75
85
242
104


12
12
37
23
51
79
95
72
54
69
74
187
92
109
113


13
13
4
5
6
67
45
104
12
75
80
194
220
119
123


14
14
21
7
32
40
102
51
63
81
86
95
108
128
132


15
15
23
58
58
43
105
17
67
86
188
102
116
137
288


16
16
24
1
13
46
91
96
2
93
3
109
123
146
5


17
17
26
52
39
31
23
62
7
158
105
116
131
155
161


18
18
43
54
65
22
62
9
11
104
111
17
19
164
170


19
19
29
36
8
10
30
41
85
20
117
24
27
174
180


20
20
46
38
46
87
69
73
136
115
28
136
35
41
189


21
21
32
40
48
16
1
20
94
121
129
143
162
192
198


22
22
2
42
3
41
76
52
6
127
135
150
170
201
208


23
23
35
29
29
66
79
46
103
133
142
16
58
210
218


24
24
5
26
55
69
83
31
38
139
148
163
185
219
227


25
25
38
28
10
72
15
63
112
144
154
170
193
87
237


26
26
8
20
24
45
63
95
47
150
33
177
200
96
99


27
27
41
22
62
33
93
23
121
156
166
78
208
247
255


28
28
33
53
64
36
61
102
56
162
173
85
216
256
265


29
29
44
8
31
24
100
49
130
78
115
92
224
264
274


30
30
22
55
69
86
50
34
65
173
185
46
232
274
284









For the above cases, the tables can be reorganized according to the allocated number of sequence per each group and each length.
For another example of this invention, the above tables can be extended to 100 RB length, and following tables show this example. In this example, the maximum number of the root index number (v) for 5 RB length or less is set to 1, and maximum number of the root index number (v) for the length longer than 5 RB is set to 2.









TABLE 29









RB

















3
4
5
6
8
9
10
12
15









Nzc

















31
47
59
71
89
107
113
139
179









Max root per RB

















1
1
1
2
2
2
2
2
2








Gr.
v






















Idx
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1

























0
1
2
2
2
3
3
2
3
4
4
3
4
5
6
5


1
2
3
4
5
4
6
5
7
6
7
8
9
8
12
11


2
3
5
6
7
6
9
8
10
11
11
10
13
14
17
18


3
4
6
8
9
10
11
12
14
13
15
14
18
17
23
24


4
5
8
10
11
12
14
15
17
18
18
19
22
23
29
28


5
6
9
11
14
13
17
18
21
20
22
21
27
26
35
34


6
7
11
13
16
17
20
21
24
25
26
25
31
32
40
41


7
8
12
15
18
19
23
22
28
27
29
30
36
35
46
47


8
9
14
17
21
20
26
25
31
32
33
32
40
41
52
51


9
10
15
19
23
22
29
28
35
34
36
37
45
44
58
57


10
11
17
21
25
26
32
31
38
37
40
41
49
50
64
63


11
12
18
23
27
28
34
35
41
42
44
43
54
53
69
70


12
13
20
25
30
29
37
38
45
44
47
48
58
59
75
76


13
14
21
27
32
33
40
41
48
49
51
52
63
62
81
80


14
15
23
29
34
35
43
44
52
51
55
54
67
68
87
86


15
16
24
30
37
36
46
45
55
56
58
59
72
71
92
93


16
17
26
32
39
38
49
48
59
58
62
61
76
77
98
99


17
18
27
34
41
42
52
51
62
63
66
65
81
80
104
103


18
19
29
36
44
43
55
54
66
65
69
70
85
86
110
109


19
20
30
38
46
45
57
58
69
70
73
72
90
89
115
116


20
21
32
40
48
49
60
61
72
73
77
76
94
95
121
122


21
22
33
42
50
51
63
64
76
75
80
81
99
98
127
128


22
23
35
44
53
52
66
67
79
80
84
83
103
104
133
132


23
24
36
46
55
54
69
68
83
82
87
88
108
107
139
138


24
25
38
48
57
58
72
71
86
87
91
92
112
113
144
145


25
26
39
49
60
59
75
74
90
89
95
94
117
116
150
151


26
27
41
51
62
61
78
77
93
94
98
99
121
122
156
155


27
28
42
53
64
65
80
81
97
96
102
103
126
125
162
161


28
29
44
55
66
67
83
84
100
101
106
105
130
131
167
168


29
30
45
57
69
68
86
87
104
103
109
110
135
134
173
174


















TABLE 30









RB
















16
18
20
24
25
27
30
32









Nzc
















191
211
239
283
293
317
359
383









Max root per RB
















2
2
2
2
2
2
2
2








Gr.
v























Idx
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1


























0
6
7
7
6
8
7
9
10
9
10
10
11
12
11
12
13


1
12
13
14
13
15
16
18
19
19
18
20
21
23
24
25
24


2
18
19
20
21
23
24
27
28
28
29
31
30
35
34
37
38


3
25
24
27
28
31
30
37
36
38
37
41
40
46
47
49
50


4
31
30
34
35
39
38
46
45
47
48
51
52
58
57
62
61


5
37
36
41
40
46
47
55
54
57
56
61
62
69
70
74
75


6
43
44
48
47
54
53
64
63
66
67
72
71
81
82
86
87


7
49
50
54
55
62
61
73
74
76
75
82
81
93
92
99
98


8
55
56
61
62
69
70
82
83
85
86
92
93
104
105
111
112


9
62
61
68
69
77
78
91
92
95
94
102
103
116
115
124
123


10
68
67
75
74
85
84
100
101
104
103
112
113
127
128
136
135


11
74
73
82
81
93
92
110
109
113
114
123
122
139
138
148
149


12
80
81
88
89
100
101
119
118
123
122
133
132
151
150
161
160


13
86
87
95
96
108
107
128
127
132
133
143
144
162
163
173
172


14
92
93
102
103
116
115
137
136
142
141
153
154
174
173
185
186


15
99
98
109
108
123
124
146
147
151
152
164
163
185
186
198
197


16
105
104
116
115
131
132
155
156
161
160
174
173
197
196
210
211


17
111
110
123
122
139
138
164
165
170
171
184
185
208
209
222
223


18
117
118
129
130
146
147
173
174
180
179
194
195
220
221
235
234


19
123
124
136
137
154
155
183
182
189
190
205
204
232
231
247
248


20
129
130
143
142
162
161
192
191
198
199
215
214
243
244
259
260


21
136
135
150
149
170
169
201
200
208
207
225
224
255
254
272
271


22
142
141
157
156
177
178
210
209
217
218
235
236
266
267
284
285


23
148
147
163
164
185
186
219
220
227
226
245
246
278
277
297
296


24
154
155
170
171
193
192
228
229
236
237
256
255
290
289
309
308


25
160
161
177
176
200
201
237
238
246
245
266
265
301
302
321
322


26
166
167
184
183
208
209
246
247
255
256
276
277
313
312
334
333


27
173
172
191
190
216
215
256
255
265
264
286
287
324
325
346
345


28
179
178
197
198
224
223
265
264
274
275
297
296
336
335
358
359


29
185
184
204
205
231
232
274
273
284
283
307
306
347
348
371
370


















TABLE 31









RB
















36
40
45
48
50
54
60
64









Nzc
















431
479
523
571
599
647
719
761









Max root per RB
















2
2
2
2
2
2
2
2








Gr.
v























Idx
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1


























0
14
13
15
16
17
16
18
19
19
20
21
20
23
24
25
24


1
28
27
31
30
34
33
37
36
39
38
42
41
46
47
49
50


2
42
41
46
47
51
50
55
56
58
57
63
62
70
69
74
73


3
56
55
62
61
67
68
74
73
77
78
83
84
93
92
98
99


4
70
69
77
78
84
85
92
93
97
96
104
105
116
115
123
122


5
83
84
93
92
101
102
111
110
116
115
125
126
139
140
147
148


6
97
98
108
109
118
119
129
128
135
136
146
147
162
163
172
171


7
111
112
124
123
135
134
147
148
155
154
167
166
186
185
196
197


8
125
126
139
140
152
151
166
165
174
173
188
187
209
208
221
220


9
139
140
155
154
169
168
184
185
193
194
209
208
232
231
245
246


10
153
152
170
169
186
185
203
202
213
212
230
229
255
256
270
271


11
167
166
185
186
202
203
221
222
232
231
250
251
278
279
295
294


12
181
180
201
200
219
220
239
240
251
252
271
272
302
301
319
320


13
195
194
216
217
236
237
258
257
271
270
292
293
325
324
344
343


14
209
208
232
231
253
254
276
277
290
289
313
314
348
347
368
369


15
222
223
247
248
270
269
295
294
309
310
334
333
371
372
393
392


16
236
237
263
262
287
286
313
314
328
329
355
354
394
395
417
418


17
250
251
278
279
304
303
332
331
348
347
376
375
417
418
442
441


18
264
265
294
293
321
320
350
349
367
368
397
396
441
440
466
467


19
278
279
309
310
337
338
368
369
386
387
417
418
464
463
491
490


20
292
291
324
325
354
355
387
386
406
405
438
439
487
488
516
515


21
306
305
340
339
371
372
405
406
425
426
459
460
510
511
540
541


22
320
319
355
356
388
389
424
423
444
445
480
481
533
534
565
564


23
334
333
371
370
405
404
442
443
464
463
501
500
557
556
589
590


24
348
347
386
387
422
421
460
461
483
484
522
521
580
579
614
613


25
361
362
402
401
439
438
479
478
502
503
543
542
603
604
638
639


26
375
376
417
418
456
455
497
498
522
521
564
563
626
627
663
662


27
389
390
433
432
472
473
516
515
541
542
584
585
649
650
687
688


28
403
404
448
449
489
490
534
535
560
561
605
606
673
672
712
711


29
417
418
464
463
506
507
553
552
580
579
626
627
696
695
736
737


















TABLE 32









RB















72
76
80
81
90
96
100









Nzc















863
887
953
971
1069
1151
1193









Max root per RB















2
2
2
2
2
2
2








Gr.
v





















Idx
0
1
0
1
0
1
0
1
0
1
0
1
0
1
























0
28
27
29
28
31
30
31
32
34
35
37
38
38
39


1
56
55
57
58
61
62
63
62
69
68
74
75
77
76


2
84
83
86
85
92
93
94
93
103
104
111
112
115
116


3
111
112
114
115
123
122
125
126
138
137
149
148
154
153


4
139
140
143
144
154
153
157
156
172
173
186
185
192
193


5
167
168
172
171
184
185
188
187
207
206
223
222
231
230


6
195
194
200
201
215
216
219
220
241
242
260
259
269
270


7
223
222
229
228
246
245
251
250
276
275
297
298
308
307


8
251
250
258
257
277
276
282
281
310
311
334
335
346
347


9
278
279
286
287
307
308
313
314
345
344
371
372
385
384


10
306
307
315
314
338
339
345
344
379
380
408
409
423
424


11
334
335
343
344
369
368
376
375
414
413
446
445
462
461


12
362
361
372
371
400
399
407
408
448
449
483
482
500
501


13
390
389
401
400
430
431
439
438
483
482
520
519
539
538


14
418
417
429
430
461
462
470
469
517
518
557
556
577
578


15
445
446
458
457
492
491
501
502
552
551
594
595
616
615


16
473
474
486
487
523
522
532
533
586
587
631
632
654
655


17
501
502
515
516
553
554
564
563
621
620
668
669
693
692


18
529
528
544
543
584
585
595
596
655
656
705
706
731
732


19
557
556
572
573
615
614
626
627
690
689
743
742
770
769


20
585
584
601
600
646
645
658
657
724
725
780
779
808
809


21
612
613
629
630
676
677
689
690
759
758
817
816
847
846


22
640
641
658
659
707
708
720
721
793
794
854
853
885
886


23
668
669
687
686
738
737
752
751
828
827
891
892
924
923


24
696
695
715
716
769
768
783
784
862
863
928
929
962
963


25
724
723
744
743
799
800
814
815
897
896
965
966
1001
1000


26
752
751
773
772
830
831
846
845
931
932
1002
1003
1039
1040


27
779
780
801
802
861
860
877
878
966
965
1040
1039
1078
1077


28
807
808
830
829
892
891
908
909
1000
1001
1077
1076
1116
1117


29
835
836
858
859
922
923
940
939
1035
1034
1114
1113
1155
1164









Based on these concepts, the present invention provides a method for generating reference signal sequence using ZC sequence as follows.
To generate reference signal sequence, one embodiment of the present invention defines a specific base sequence for allying cyclic shift. In this embodiment, the base sequence is defined using ZC sequence with certain root index (hereinafter “q”). And, the specific base sequence is selected from the base sequence groups, and each of the base sequence group contains base sequences having a high cross correlation relation as stated above. So, if one wants to select the specific base sequence with index of “q”, the “q” should be selected considering the group index (hereinafter “u”) and the base sequence number index within each group (hereinafter “v”). That is, “q” should be a function of “u” and “v”.
And, after the specific base sequence with root index “q” is selected, then the cyclic shift corresponding to various cyclic shift values can be applied to the selected base sequence.
If the relation between the “q”, “u” and “v” is more specifically considered, “q” can be acquired by the following equations. The following equations 17 and 18 are for selecting the index “q” to meet the condition that the term (s1/N1−s2/N2) becomes close to zero.




  
    
      
        
          q
          =
          
            
              round
              ⁢
              
                
              
              ⁢
              
                (
                y
                )
              
            
            +
            
              floor
              ⁢
              
                
              
              ⁢
              
                
                  (
                  
                    
                      v
                      +
                      1
                    
                    2
                  
                  )
                
                ·
                
                  
                    (
                    
                      -
                      1
                    
                    )
                  
                  
                    
                      floor
                      ⁡
                      
                        (
                        
                          
                            round
                            ⁡
                            
                              (
                              y
                              )
                            
                          
                          -
                          y
                        
                        )
                      
                    
                    +
                    v
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                
                  N
                  zc
                  RS
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
              
                N
                
                  reference
                  ,
                  
                    
                  
                  ⁢
                  zc
                
                RS
              
            
          
          ,
          
            
          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            

          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                
                  
                    floor
                    ⁢
                    
                      
                    
                    ⁢
                    
                      (
                      
                        
                          N
                          ZC
                          RS
                        
                        /
                        30
                      
                      )
                    
                  
                  -
                  1
                
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          17
        
        ]
      
    
  
  
    
      
        
          q
          =
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  y
                  +
                  0.5
                
                )
              
            
            +
            
              floor
              ⁢
              
                
              
              ⁢
              
                
                  (
                  
                    
                      v
                      +
                      1
                    
                    2
                  
                  )
                
                ·
                
                  
                    (
                    
                      -
                      1
                    
                    )
                  
                  
                    
                      floor
                      ⁡
                      
                        (
                        
                          
                            floor
                            ⁡
                            
                              (
                              
                                y
                                +
                                0.5
                              
                              )
                            
                          
                          -
                          y
                        
                        )
                      
                    
                    +
                    v
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                
                  N
                  zc
                  RS
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
              
                N
                
                  reference
                  ,
                  
                    
                  
                  ⁢
                  zc
                
                RS
              
            
          
          ,
          
            
          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            

          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                
                  
                    floor
                    ⁢
                    
                      
                    
                    ⁢
                    
                      (
                      
                        
                          N
                          ZC
                          RS
                        
                        /
                        30
                      
                      )
                    
                  
                  -
                  1
                
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          18
        
        ]
      
    
  




Here, NzcRS is the target ZC sequence generation length used in generating the q-th root ZC sequence, and NzcRS is given by the largest prime number which is less than the corresponding reference signal sequence size. That is, the base sequence is generated by cyclic extension method.
And, Nreference,zcRS is the length given by the largest prime number which is less than the reference sequence size, for example, 3 RB length. If the grouping is based on the 3 RB length, then Nreference,zcRS is 31. The “round (z)” is a function of rounding off to a nearest integer nearest to z, and the “floor (z)” is a function of making a greatest integer not greater than z.
And, according to another embodiment of this invention, if the ZC sequence is generated based on the truncation method, then NzcRS can be given by the smallest prime number which is greater than the corresponding reference signal sequence size. And, in this case, Nreference,zcRS can be the length given by the smallest prime number which is greater than the reference sequence size, for example, 3 RB length. If the grouping is based on the 3 RB length, then Nreference,zcRS can be 37.
And, according to equations 17 and 18, “m”-th element of the “q”-th ZC sequence (xq(m)) can be expressed as follows.




  
    
      
        
          
            
              x
              q
            
            ⁡
            
              (
              m
              )
            
          
          =
          
            e
            
              
                -
                j
              
              ⁢
              
                
                  π
                  ⁢
                  
                    
                  
                  ⁢
                  
                    qm
                    ⁡
                    
                      (
                      
                        m
                        +
                        1
                      
                      )
                    
                  
                
                
                  N
                  ZC
                  RS
                
              
            
          
        
        ,
        
          
        
        ⁢
        
          0
          ≤
          m
          ≤
          
            
              N
              ZC
              RS
            
            -
            1
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          19
        
        ]
      
    
  




Because “round (y)” and “floor (y+0.5)” are actually equivalent, the equations 17 and 18 have the same meaning. In the equations 17 and 18, the term (−1)floor(round(y)−y) means that if “y” has 0.5 or greater value in its decimal place, (−1)floor(round(y)−y) can be calculated as “1”, and if “y” has the value less than 0.5 in its decimal place, (−1)floor(round(y)−y) can be calculated as “−1”. So, (−1)floor(round(y)−y) can be replaced with (−1)floor(y−round(y))+1 or any other equivalent terms having the same meaning.
In the above examples, when the grouping is performed for the length greater than the 3 RB length based on the 3 RB length, and when the ZC sequence is generated based on the cyclic extension method, Nreference,zcRS can be 31. Also, when the ZC sequence is generated based on the truncation method, Nreference,zcRS can be 37. And, when the grouping is performed for the length greater than the 4 RB length based on the 4 RB length, and when the ZC sequence is generated based on the cyclic extension method, Nreference,zcRS can be 47. Also, when the ZC sequence is generated based on the truncation method, Nreference,zcRS can be 49. And, this can be easily employed to other length based grouping.
Above mentioned tables can be acquired by the equations 17 and 18. The following examples are part of selecting root index according to the equations 17 and 18.
First, if the Nreference,zc=31, the method for selecting first group (“u”=0) when 1) Nzc=47, 2) Nzc=71/31) Nzc=211 is as follows. In the following examples, the equation 18 is used.
1) Nreference,zc=31, NzcRS=47, u=0, v=0; y=47/31,




  q
  =
  
    
      
        ⌊
        
          
            47
            31
          
          +
          0.5
        
        ⌋
      
      +
      
        
          ⌊
          
            
              0
              +
              1
            
            2
          
          ⌋
        
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            
              ⌊
              
                
                  ⌊
                  
                    
                      47
                      31
                    
                    +
                    0.5
                  
                  ⌋
                
                -
                
                  47
                  31
                
              
              ⌋
            
            +
            0
          
        
      
    
    =
    2
  




So, for 4 RB length, the first base sequence number (v=0) in the first group (u=0) is 2 (q=2).
2) Nreference,zc=31, NzcRS=71, u=0, v=0; y=71/31,




  q
  =
  
    
      
        ⌊
        
          
            71
            31
          
          +
          0.5
        
        ⌋
      
      +
      
        
          ⌊
          
            
              0
              +
              1
            
            2
          
          ⌋
        
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            
              ⌊
              
                
                  ⌊
                  
                    
                      71
                      31
                    
                    +
                    0.5
                  
                  ⌋
                
                -
                
                  71
                  31
                
              
              ⌋
            
            +
            0
          
        
      
    
    =
    2
  




So, for 6 RB length, the first base sequence number (v=0) in the first group (u=0) is 2 (q=2).
3) Nreference,zc=31, NZCRS=211, u=0, v=0; y=211/31,




  q
  =
  
    
      
        ⌊
        
          
            211
            31
          
          +
          0.5
        
        ⌋
      
      +
      
        
          ⌊
          
            
              0
              +
              1
            
            2
          
          ⌋
        
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            
              ⌊
              
                
                  ⌊
                  
                    
                      211
                      31
                    
                    +
                    0.5
                  
                  ⌋
                
                -
                
                  211
                  31
                
              
              ⌋
            
            +
            0
          
        
      
    
    =
    7
  




So, for 18 RB length, the first base sequence number (v=0) in the first group (u=0) is 7 (q=7).
For the above cases, the selected root indexes (q) correspond to the data in tables 6 ̃8 which are generated based on 3 RB length.
In another example, if the Nreference,zc=47 (based on 4 RB length), the method for selecting the second group (“u”=1) when 1) Nzc=59, 2) Nzc=107 3) Nzc=139 is as follows. In the following examples, the equation 18 is used.
1) Nreference,zc=47, NzcRS=59, u=1, v=0; y=59/47*2,




  q
  =
  
    
      
        ⌊
        
          
            
              59
              ·
              2
            
            47
          
          +
          0.5
        
        ⌋
      
      +
      
        
          ⌊
          
            
              0
              +
              1
            
            2
          
          ⌋
        
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            
              ⌊
              
                
                  ⌊
                  
                    
                      
                        59
                        ·
                        2
                      
                      47
                    
                    +
                    
                      0.5
                      *
                    
                  
                  ⌋
                
                -
                
                  
                    59
                    ·
                    2
                  
                  47
                
              
              ⌋
            
            +
            0
          
        
      
    
    =
    3
  




So, for 5 RB length, the first base sequence number (v=0) in the second group (u=1) is 3 (q=3).
2) Nreference,zc=47, NzcRS=107, u=1, v=0; y=107/47*2,




  q
  =
  
    
      
        ⌊
        
          
            
              107
              ·
              2
            
            47
          
          +
          0.5
        
        ⌋
      
      +
      
        
          ⌊
          
            
              0
              +
              1
            
            2
          
          ⌋
        
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            
              ⌊
              
                
                  ⌊
                  
                    
                      
                        107
                        ·
                        2
                      
                      47
                    
                    +
                    0.5
                  
                  ⌋
                
                -
                
                  
                    107
                    ·
                    2
                  
                  47
                
              
              ⌋
            
            +
            0
          
        
      
    
    =
    5
  




So, for 9 RB length, the first base sequence number (v=0) in the second group (u=1) is 5 (q=5).
3) Nreference,zc=47, NzcRS=139, u=1, v=0; y=139/47*2,




  q
  =
  
    
      
        ⌊
        
          
            
              139
              ·
              2
            
            47
          
          +
          0.5
        
        ⌋
      
      +
      
        
          ⌊
          
            
              0
              +
              1
            
            2
          
          ⌋
        
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            
              ⌊
              
                
                  ⌊
                  
                    
                      
                        139
                        ·
                        2
                      
                      47
                    
                    +
                    0.5
                  
                  ⌋
                
                -
                
                  
                    139
                    ·
                    2
                  
                  47
                
              
              ⌋
            
            +
            0
          
        
      
    
    =
    6
  




So, for 12 RB length, the first base sequence number (v=0) in the second group (u=1) is 6 (q=6).
In another embodiment of the present invention, the equations 17 and 18 can be replaced as follows.




  
    
      
        
          
            
              q
              =
              
                
                  round
                  ⁢
                  
                    
                  
                  ⁢
                  
                    (
                    y
                    )
                  
                
                +
                
                  floor
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      (
                      
                        
                          v
                          +
                          1
                        
                        2
                      
                      )
                    
                    ·
                    
                      
                        (
                        
                          -
                          1
                        
                        )
                      
                      
                        
                          floor
                          ⁡
                          
                            (
                            
                              
                                round
                                ⁡
                                
                                  (
                                  y
                                  )
                                
                              
                              -
                              y
                            
                            )
                          
                        
                        +
                        v
                      
                    
                  
                
              
            
            ⁢
            
              

            
            ⁢
            where
          
          ⁢
          
            

          
          ⁢
          
            
              y
              =
              
                
                  
                    (
                    
                      
                        N
                        zc
                        RS
                      
                      -
                      1
                    
                    )
                  
                  ·
                  
                    (
                    
                      u
                      +
                      1
                    
                    )
                  
                
                
                  
                    N
                    
                      reference
                      ,
                      
                        
                      
                      ⁢
                      zc
                    
                    RS
                  
                  -
                  1
                
              
            
            ,
            
              

            
            ⁢
            
              u
              ∈
              
                {
                
                  0
                  ,
                  1
                  ,
                  ...
                  ⁢
                  
                    
                  
                  ,
                  29
                
                }
              
            
            ,
            
              

            
            ⁢
            
              v
              ∈
              
                {
                
                  0
                  ,
                  1
                  ,
                  ...
                  ⁢
                  
                    
                  
                  ,
                  
                    
                      floor
                      ⁢
                      
                        
                      
                      ⁢
                      
                        (
                        
                          
                            N
                            ZC
                            RS
                          
                          /
                          30
                        
                        )
                      
                    
                    -
                    1
                  
                
                }
              
            
          
        
        ⁢
        
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          20
        
        ]
      
    
  
  
    
      
        
          
            q
            =
            
              
            
            ⁢
            
              
                floor
                ⁢
                
                  
                
                ⁢
                
                  (
                  
                    y
                    +
                    0.5
                  
                  )
                
              
              +
              
                floor
                ⁢
                
                  
                
                ⁢
                
                  
                    (
                    
                      
                        v
                        +
                        1
                      
                      2
                    
                    )
                  
                  ·
                  
                    
                      (
                      
                        -
                        1
                      
                      )
                    
                    
                      
                        floor
                        ⁡
                        
                          (
                          
                            
                              floor
                              ⁡
                              
                                (
                                
                                  y
                                  +
                                  0.5
                                
                                )
                              
                            
                            -
                            y
                          
                          )
                        
                      
                      +
                      v
                    
                  
                
              
            
          
          ⁢
          
            
          
          ⁢
          
            

          
          ⁢
          where
          ⁢
          
            

          
          ⁢
          
            
              y
              =
              
                
                  
                    (
                    
                      
                        N
                        zc
                        RS
                      
                      -
                      1
                    
                    )
                  
                  ·
                  
                    (
                    
                      u
                      +
                      1
                    
                    )
                  
                
                
                  
                    N
                    
                      reference
                      ,
                      
                        
                      
                      ⁢
                      zc
                    
                    RS
                  
                  -
                  1
                
              
            
            ,
            
              

            
            ⁢
            
              u
              ∈
              
                {
                
                  0
                  ,
                  1
                  ,
                  ...
                  ⁢
                  
                    
                  
                  ,
                  29
                
                }
              
            
            ,
            
              

            
            ⁢
            
              v
              ∈
              
                {
                
                  0
                  ,
                  1
                  ,
                  ...
                  ⁢
                  
                    
                  
                  ,
                  
                    
                      floor
                      ⁢
                      
                        
                      
                      ⁢
                      
                        (
                        
                          
                            N
                            ZC
                            RS
                          
                          /
                          30
                        
                        )
                      
                    
                    -
                    1
                  
                
                }
              
            
          
        
        ⁢
        
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          21
        
        ]
      
    
  




Because “round (y)” and “floor (y+0.5)” are actually equivalent, the equations 20 and 21 have the same meaning.
In another embodiment of the present invention, the equations 17 and 18 can be replaced as follows.




  
    
      
        
          
            q
            =
            
              
                round
                ⁢
                
                  
                
                ⁢
                
                  (
                  y
                  )
                
              
              +
              
                floor
                ⁢
                
                  
                
                ⁢
                
                  
                    (
                    
                      
                        v
                        +
                        1
                      
                      2
                    
                    )
                  
                  ·
                  
                    
                      (
                      
                        -
                        1
                      
                      )
                    
                    
                      
                        floor
                        ⁡
                        
                          (
                          
                            
                              round
                              ⁡
                              
                                (
                                y
                                )
                              
                            
                            -
                            y
                          
                          )
                        
                      
                      +
                      v
                    
                  
                
              
            
          
          ⁢
          
            

          
          ⁢
          where
          ⁢
          
            
          
          ⁢
          
            
              y
              =
              
                round
                ⁢
                
                  
                
                ⁢
                
                  
                    (
                    
                      
                        N
                        zc
                        RS
                      
                      
                        N
                        
                          reference
                          ,
                          
                            
                          
                          ⁢
                          zc
                        
                        RS
                      
                    
                    )
                  
                  ·
                  
                    (
                    
                      u
                      +
                      1
                    
                    )
                  
                
              
            
            ,
            
              

            
            ⁢
            
              u
              ∈
              
                {
                
                  0
                  ,
                  1
                  ,
                  ...
                  ⁢
                  
                    
                  
                  ,
                  29
                
                }
              
            
            ,
            
              

            
            ⁢
            
              v
              ∈
              
                {
                
                  0
                  ,
                  1
                  ,
                  ...
                  ⁢
                  
                    
                  
                  ,
                  
                    
                      floor
                      ⁢
                      
                        
                      
                      ⁢
                      
                        (
                        
                          
                            N
                            ZC
                            RS
                          
                          /
                          30
                        
                        )
                      
                    
                    -
                    1
                  
                
                }
              
            
          
        
        ⁢
        
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          22
        
        ]
      
    
  
  
    
      
        
          q
          =
          
            
          
          ⁢
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  y
                  +
                  0.5
                
                )
              
            
            +
            
              floor
              ⁢
              
                
              
              ⁢
              
                
                  (
                  
                    
                      v
                      +
                      1
                    
                    2
                  
                  )
                
                ·
                
                  
                    (
                    
                      -
                      1
                    
                    )
                  
                  
                    
                      floor
                      ⁡
                      
                        (
                        
                          
                            floor
                            ⁡
                            
                              (
                              
                                y
                                +
                                0.5
                              
                              )
                            
                          
                          -
                          y
                        
                        )
                      
                    
                    +
                    v
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              floor
              ⁢
              
                
              
              ⁢
              
                
                  (
                  
                    
                      
                        N
                        zc
                        RS
                      
                      
                        N
                        
                          reference
                          ,
                          
                            
                          
                          ⁢
                          zc
                        
                        RS
                      
                    
                    +
                    0.5
                  
                  )
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            

          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                
                  
                    floor
                    ⁢
                    
                      
                    
                    ⁢
                    
                      (
                      
                        
                          N
                          ZC
                          RS
                        
                        /
                        30
                      
                      )
                    
                  
                  -
                  1
                
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          23
        
        ]
      
    
  




These equations correspond to various grouping method explained with regard to the above mentioned tables.
If the maximum number of sequences, which can be grouped in one group, are predetermined to 2, the equations 17-18, 20-21 and 22-23 can be simplified as follows, respectively.




  
    
      
        
          q
          =
          
            
              round
              ⁢
              
                
              
              ⁢
              
                (
                y
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      
                        
                      
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                
                  N
                  zc
                  RS
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
              
                N
                
                  reference
                  ,
                  
                    
                  
                  ⁢
                  zc
                
                RS
              
            
          
          ,
          
            
          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          24
        
        ]
      
    
  
  
    
      
        
          q
          =
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  y
                  +
                  0.5
                
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      
                        
                      
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                
                  N
                  zc
                  RS
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
              
                N
                
                  reference
                  ,
                  
                    
                  
                  ⁢
                  zc
                
                RS
              
            
          
          ,
          
            
          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          25
        
        ]
      
    
  
  
    
      
        
          q
          =
          
            
              round
              ⁢
              
                
              
              ⁢
              
                (
                y
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                
                  (
                  
                    
                      N
                      zc
                      RS
                    
                    -
                    1
                  
                  )
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
              
                
                  N
                  
                    reference
                    ,
                    
                      
                    
                    ⁢
                    zc
                  
                  RS
                
                -
                1
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          26
        
        ]
      
    
  
  
    
      
        
          q
          =
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  y
                  +
                  0.5
                
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                
                  (
                  
                    
                      N
                      zc
                      RS
                    
                    -
                    1
                  
                  )
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
              
                
                  N
                  
                    reference
                    ,
                    
                      
                    
                    ⁢
                    zc
                  
                  RS
                
                -
                1
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          27
        
        ]
      
    
  
  
    
      
        
          q
          =
          
            
              round
              ⁢
              
                
              
              ⁢
              
                (
                y
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              round
              ⁢
              
                
              
              ⁢
              
                
                  (
                  
                    
                      N
                      zc
                      RS
                    
                    
                      N
                      
                        reference
                        ,
                        
                          
                        
                        ⁢
                        zc
                      
                      RS
                    
                  
                  )
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          28
        
        ]
      
    
  
  
    
      
        
          q
          =
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  y
                  +
                  0.5
                
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          
        
        ⁢
        
          
            y
            =
            
              floor
              ⁢
              
                
              
              ⁢
              
                
                  (
                  
                    
                      
                        N
                        zc
                        RS
                      
                      
                        N
                        
                          reference
                          ,
                          
                            
                          
                          ⁢
                          zc
                        
                        RS
                      
                    
                    +
                    0.5
                  
                  )
                
                ·
                
                  (
                  
                    u
                    +
                    1
                  
                  )
                
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          29
        
        ]
      
    
  




The equations 17-18, 20-21 and 22-23 are for selecting ZC root index to meet the condition that the term (s1/N1−s2/N2) become close to zero. And, the equations 24-29 are for selecting root index ZC root index when the maximum number of sequences per groups of each length is limited to 2.
But if we make these equations to be more generalized such that the term (s1/N1−s2/N2) become close to a specific value (T), the following equations can be acquired. In this case, the value “T” can be 0, 1⁄2 . . . , −1⁄2, 1⁄3, −1⁄3. But value “T” can have other value.
In the following equations, the equations 30 and 31 are for selecting ZC root index when the maximum number of sequence per group of each length can have the maximum value. And, the equations 32 and 33 are for selecting ZC root index when the maximum number of sequence per group of each length is limited to 2.




  
    
      
        
          q
          =
          
            
              round
              ⁢
              
                
              
              ⁢
              
                (
                y
                )
              
            
            +
            
              floor
              ⁢
              
                
              
              ⁢
              
                
                  (
                  
                    
                      v
                      +
                      1
                    
                    2
                  
                  )
                
                ·
                
                  
                    (
                    
                      -
                      1
                    
                    )
                  
                  
                    
                      floor
                      ⁡
                      
                        (
                        
                          
                            round
                            ⁡
                            
                              (
                              y
                              )
                            
                          
                          -
                          y
                        
                        )
                      
                    
                    +
                    v
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                N
                zc
                RS
              
              ·
              
                (
                
                  T
                  +
                  
                    
                      (
                      
                        u
                        +
                        1
                      
                      )
                    
                    
                      N
                      
                        reference
                        ,
                        
                          
                        
                        ⁢
                        zc
                      
                      RS
                    
                  
                
                )
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            

          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                
                  
                    floor
                    ⁢
                    
                      
                    
                    ⁢
                    
                      (
                      
                        
                          N
                          ZC
                          RS
                        
                        /
                        30
                      
                      )
                    
                  
                  -
                  1
                
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          30
        
        ]
      
    
  
  
    
      
        
          q
          =
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  y
                  +
                  0.5
                
                )
              
            
            +
            
              floor
              ⁢
              
                
              
              ⁢
              
                
                  (
                  
                    
                      v
                      +
                      1
                    
                    2
                  
                  )
                
                ·
                
                  
                    (
                    
                      -
                      1
                    
                    )
                  
                  
                    
                      floor
                      ⁡
                      
                        (
                        
                          
                            floor
                            ⁡
                            
                              (
                              
                                y
                                +
                                0.5
                              
                              )
                            
                          
                          -
                          y
                        
                        )
                      
                    
                    +
                    v
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                N
                zc
                RS
              
              ·
              
                (
                
                  T
                  +
                  
                    
                      (
                      
                        u
                        +
                        1
                      
                      )
                    
                    
                      N
                      
                        reference
                        ,
                        
                          
                        
                        ⁢
                        zc
                      
                      RS
                    
                  
                
                )
              
            
          
          ,
          
            
          
          ⁢
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                
                  
                    floor
                    ⁢
                    
                      
                    
                    ⁢
                    
                      (
                      
                        
                          N
                          ZC
                          RS
                        
                        /
                        30
                      
                      )
                    
                  
                  -
                  1
                
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          31
        
        ]
      
    
  
  
    
      
        
          q
          =
          
            
              round
              ⁢
              
                
              
              ⁢
              
                (
                y
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                N
                zc
                RS
              
              ·
              
                (
                
                  T
                  +
                  
                    
                      (
                      
                        u
                        +
                        1
                      
                      )
                    
                    
                      N
                      
                        reference
                        ,
                        
                          
                        
                        ⁢
                        zc
                      
                      RS
                    
                  
                
                )
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          32
        
        ]
      
    
  
  
    
      
        
          q
          =
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  y
                  +
                  0.5
                
                )
              
            
            +
            
              v
              ·
              
                
                  (
                  
                    -
                    1
                  
                  )
                
                
                  floor
                  ⁡
                  
                    (
                    
                      2
                      ⁢
                      y
                    
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
        ⁢
        
          

        
        ⁢
        
          
            y
            =
            
              
                N
                zc
                RS
              
              ·
              
                (
                
                  T
                  +
                  
                    
                      (
                      
                        u
                        +
                        1
                      
                      )
                    
                    
                      N
                      
                        reference
                        ,
                        
                          
                        
                        ⁢
                        zc
                      
                      RS
                    
                  
                
                )
              
            
          
          ,
          
            

          
          ⁢
          
            u
            ∈
            
              {
              
                0
                ,
                1
                ,
                ...
                ⁢
                
                  
                
                ,
                29
              
              }
            
          
          ,
          
            
          
          ⁢
          
            v
            ∈
            
              {
              
                0
                ,
                1
              
              }
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          33
        
        ]
      
    
  




It will be apparent to those skilled in the art that the present invention can be embodied in other specific forms without departing from the spirit and essential characteristics of the invention. Thus, the above embodiments are to be considered in all respects as illustrative and not restrictive. The scope of the invention should be determined by reasonable interpretation of the appended claims and all change which comes within the equivalent scope of the invention are included in the scope of the invention.
According to the embodiments of the present invention, inter cell interference caused by using variable length sequences can be minimized. And, if each grouped base sequence is allocated to specific cell or Node B, UE(s) can use variable length sequence as reference signal.
These methods are appropriate to be employed in 3GPP LTE (3rd Generation Partnership Project Long Term Evolution) system. But, those skilled in the art can easily understand that these methods can be employed to any wireless communication system using various length sequences as a reference signal sequences.
FIG. 8 is a flowchart depicting a method for transmitting a reference signal sequence and includes acquiring the reference signal sequence which has been obtained by applying a cyclic shift to a base sequence of a plurality of base sequences using a Zadoff-Chu (ZC) sequence having a q-th root index, wherein the cyclic shift corresponds to a cyclic shift value (block 810). Block 820 includes transmitting the acquired reference signal sequence to a receiving party, such that the plurality of base sequences form sequence groups and the “q” is a function of a group index (u) of the sequence groups and a base sequence number index (v) within a sequence group of the sequence groups.
FIG. 9 is a block diagram of mobile terminal 910 for transmitting a reference signal sequence. The mobile terminal includes transceiver 920, which may be configured to transmit signals, and processor 930. The processor may be configured to acquire the reference signal sequence which has been obtained by applying a cyclic shift to a base sequence of a plurality of base sequences using a Zadoff-Chu (ZC) sequence having a q-th root index. In general, the cyclic shift corresponds to a cyclic shift value. The processor may also be configured to cause the transceiver to transmit the acquired reference signal sequence to a receiving party, such that the plurality of base sequences form sequence groups and the “q” is a function of a group index (u) of the sequence groups and a base sequence number index (v) within a sequence group of the sequence groups.
Although the preferred embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the invention as disclosed in the accompanying claims.

## Claims

1. A method for transmitting a reference signal sequence, the method comprising:
acquiring the reference signal sequence which has been obtained by applying a cyclic shift to a base sequence of a plurality of base sequences using a Zadoff-Chu (ZC) sequence having a q-th root index, wherein the cyclic shift corresponds to a cyclic shift value; and
transmitting the acquired reference signal sequence to a receiving party,
wherein the plurality of base sequences form sequence groups and the “q” is a function of a group index (u) of the sequence groups and a base sequence number index (v) within a sequence group of the sequence groups.

2. The method according to claim 1, wherein a number of “u” is 30 and a number of “v” is based on a length of the base sequence.

3. The method according to claim 1, wherein the “q” is determined by the equation:



  
    
      
    
    ⁢
    
      q
      =
      
        
          floor
          ⁢
          
            
          
          ⁢
          
            (
            
              y
              +
              0.5
            
            )
          
        
        +
        
          floor
          ⁢
          
            
          
          ⁢
          
            
              (
              
                
                  v
                  +
                  1
                
                2
              
              )
            
            ·
            
              
                (
                
                  -
                  1
                
                )
              
              
                
                  floor
                  ⁡
                  
                    (
                    
                      
                        floor
                        ⁡
                        
                          (
                          
                            y
                            +
                            0.5
                          
                          )
                        
                      
                      -
                      y
                    
                    )
                  
                
                +
                v
              
            
          
        
      
    
  




  where




  
    
      y
      =
      
        
          
            N
            zc
            RS
          
          ·
          
            (
            
              u
              +
              1
            
            )
          
        
        
          N
          
            reference
            ,
            
              
            
            ⁢
            zc
          
          RS
        
      
    
    ,
    
      u
      ∈
      
        {
        
          0
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          29
        
        }
      
    
    ,
    
      
    
    ⁢
    
      

    
    ⁢
    
      v
      ∈
      
        {
        
          0
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  
                    N
                    ZC
                    RS
                  
                  /
                  30
                
                )
              
            
            -
            1
          
        
        }
      
    
    ,
  


wherein NzcRS is a ZC sequence generation length used in generating the ZC sequence having the q-th root index, NzcRS is the largest prime number which is less than the length of the base sequence using the ZC sequence having the q-th root index, Nreference,zcRS is a specific reference prime number, and “floor (z)” is a function that generates a greatest integer not greater than z.

4. The method according to claim 1, wherein the “q” is determined by the equation:



  
    
      
    
    ⁢
    
      q
      =
      
        
          floor
          ⁢
          
            
          
          ⁢
          
            (
            
              y
              +
              0.5
            
            )
          
        
        +
        
          floor
          ⁢
          
            
          
          ⁢
          
            
              (
              
                
                  v
                  +
                  1
                
                2
              
              )
            
            ·
            
              
                (
                
                  -
                  1
                
                )
              
              
                
                  floor
                  ⁡
                  
                    (
                    
                      
                        floor
                        ⁡
                        
                          (
                          
                            y
                            +
                            0.5
                          
                          )
                        
                      
                      -
                      y
                    
                    )
                  
                
                +
                v
              
            
          
        
      
    
  




  where




  
    
      y
      =
      
        
          
            N
            zc
            RS
          
          ·
          
            (
            
              u
              +
              1
            
            )
          
        
        
          N
          
            reference
            ,
            
              
            
            ⁢
            zc
          
          RS
        
      
    
    ,
    
      u
      ∈
      
        {
        
          0
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          29
        
        }
      
    
    ,
    
      
    
    ⁢
    
      

    
    ⁢
    
      v
      ∈
      
        {
        
          0
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          
            
              floor
              ⁢
              
                
              
              ⁢
              
                (
                
                  
                    N
                    ZC
                    RS
                  
                  /
                  30
                
                )
              
            
            -
            1
          
        
        }
      
    
    ,
  


wherein NzcRS is a ZC sequence generation length used in generating the ZC sequence having the q-th root index, NzcRS is the smallest prime number which is greater than the length of the base sequence using the ZC sequence having the q-th root index, Nreference,zcRS is a specific reference prime number, and “floor (z)” is a function that generates a greatest integer not greater than z.

5. The method according to claim 1, wherein a maximum number of the base sequences within each sequence group is 2, and
wherein the “q” is determined by the equation:




  
    q
    =
    
      
        floor
        ⁢
        
          
        
        ⁢
        
          (
          
            y
            +
            0.5
          
          )
        
      
      +
      
        v
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            floor
            ⁡
            
              (
              
                2
                ⁢
                y
              
              )
            
          
        
      
    
  




  where




  
    
      y
      =
      
        
          
            N
            zc
            RS
          
          ·
          
            (
            
              u
              +
              1
            
            )
          
        
        
          N
          
            reference
            ,
            
              
            
            ⁢
            zc
          
          RS
        
      
    
    ,
    
      

    
    ⁢
    
      u
      ∈
      
        {
        
          0
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          29
        
        }
      
    
    ,
    
      
    
    ⁢
    
      v
      ∈
      
        {
        
          0
          ,
          1
        
        }
      
    
    ,
  


wherein NzcRS is a ZC sequence generation length used in generating the ZC sequence having the q-th root index, NzcRS is the largest prime number which is less than the length of the base sequence using the ZC sequence having the q-th root index, Nreference,zcRS is a specific reference prime number, and “floor (z)” is a function that generates a greatest integer not greater than z.

6. The method according to claim 1, wherein a maximum number of the base sequences within each sequence group is 2 and the “q” is determined by the equation:



  
    q
    =
    
      
        floor
        ⁢
        
          
        
        ⁢
        
          (
          
            y
            +
            0.5
          
          )
        
      
      +
      
        v
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            floor
            ⁡
            
              (
              
                2
                ⁢
                y
              
              )
            
          
        
      
    
  




  where




  
    
      y
      =
      
        
          
            N
            zc
            RS
          
          ·
          
            (
            
              u
              +
              1
            
            )
          
        
        
          N
          
            reference
            ,
            
              
            
            ⁢
            zc
          
          RS
        
      
    
    ,
    
      

    
    ⁢
    
      u
      ∈
      
        {
        
          0
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          29
        
        }
      
    
    ,
    
      
    
    ⁢
    
      v
      ∈
      
        {
        
          0
          ,
          1
        
        }
      
    
    ,
  


wherein NzcRS is a ZC sequence generation length used in generating the ZC sequence having the q-th root index, NzcRS is the smallest prime number which is greater than the length of the base sequence using the ZC sequence having the q-th root index, Nreference,zcRS is a specific reference prime number, and “floor (z)” is a function that generates a greatest integer not greater than z).

7. The method according to claim 3, wherein the specific reference prime number is 31.

8. The method according to claims 5, wherein the specific reference prime number is 31.

9. A mobile terminal for transmitting a reference signal sequence, the mobile terminal comprising:
a transceiver configured to transmit signals; and
a processor configured to:
acquire the reference signal sequence which has been obtained by applying a cyclic shift to a base sequence of a plurality of base sequences using a Zadoff-Chu (ZC) sequence having a q-th root index, wherein the cyclic shift corresponds to a cyclic shift value; and
cause the transceiver to transmit the acquired reference signal sequence to a receiving party, wherein the plurality of base sequences form sequence groups and the “q” is a function of a group index (u) of the sequence groups and a base sequence number index (v) within a sequence group of the sequence groups.

10. The mobile terminal of claim 9, wherein a number of “u” is 30 and a number of “v” is given based on a length of the base sequence.

11. The mobile terminal of claim 9, wherein the “q” is determined by



  
    q
    =
    
      
        floor
        ⁡
        
          (
          
            y
            +
            0.5
          
          )
        
      
      +
      
        
          floor
          ⁡
          
            (
            
              
                v
                +
                1
              
              2
            
            )
          
        
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            
              floor
              ⁡
              
                (
                
                  
                    floor
                    ⁡
                    
                      (
                      
                        y
                        +
                        0.5
                      
                      )
                    
                  
                  -
                  y
                
                )
              
            
            +
            v
          
        
      
    
  




  
    
      
        where
        ⁢
        
          
        
        ⁢
        y
      
      =
      
        
          
            N
            x
            RS
          
          ·
          
            (
            
              u
              +
              1
            
            )
          
        
        
          N
          
            reference
            ,
            x
          
          RS
        
      
    
    ,
    
      u
      ∈
      
        {
        
          0
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          29
        
        }
      
    
    ,
    
      

    
    ⁢
    
      v
      ∈
      
        {
        
          0
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          
            
              floor
              ⁡
              
                (
                
                  
                    N
                    ZC
                    RS
                  
                  /
                  30
                
                )
              
            
            -
            1
          
        
        }
      
    
  


wherein NzcRS is a ZC sequence generation length used in generating the ZC sequence having the q-th root index, NzcRS is given by the largest prime number which is less than the length of the base sequence using the ZC sequence having the q-th root index, Nreference,zcRS is a specific reference prime number, and the “floor (z)” is a function of making a greatest integer not greater than z.

12. The mobile terminal according to claim 9, wherein the “q” is determined by



  
    q
    =
    
      
        floor
        ⁡
        
          (
          
            y
            +
            0.5
          
          )
        
      
      +
      
        
          floor
          ⁡
          
            (
            
              
                v
                +
                1
              
              2
            
            )
          
        
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            
              floor
              ⁡
              
                (
                
                  
                    floor
                    ⁡
                    
                      (
                      
                        y
                        +
                        0.5
                      
                      )
                    
                  
                  -
                  y
                
                )
              
            
            +
            v
          
        
      
    
  




  
    
      
        where
        ⁢
        
          
        
        ⁢
        y
      
      =
      
        
          
            N
            x
            RS
          
          ·
          
            (
            
              u
              +
              1
            
            )
          
        
        
          N
          
            reference
            ,
            x
          
          RS
        
      
    
    ,
    
      u
      ∈
      
        {
        
          0
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          29
        
        }
      
    
    ,
    
      

    
    ⁢
    
      v
      ∈
      
        {
        
          0
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          
            
              floor
              ⁡
              
                (
                
                  
                    N
                    ZC
                    RS
                  
                  /
                  30
                
                )
              
            
            -
            1
          
        
        }
      
    
  


wherein NzcRS is a ZC sequence generation length used in generating the ZC sequence having the q-th root index, NzcRS is given by the smallest prime number which is greater than the length of the base sequence using the ZC sequence having the q-th root index, Nreference,zcRS is a specific reference prime number, and the “floor (z)” is a function of making a greatest integer not greater than z.

13. The mobile terminal according to claim 9, wherein a maximum number of the base sequences within each sequence group is 2, and
wherein the “q” is determined by




  
    q
    =
    
      
        floor
        ⁡
        
          (
          
            y
            +
            0.5
          
          )
        
      
      +
      
        v
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            floor
            ⁡
            
              (
              
                2
                ⁢
                y
              
              )
            
          
        
      
    
  




  
    
      
        
          where
          ⁢
          
            
          
          ⁢
          y
        
        =
        
          
            
              N
              zc
              RS
            
            ·
            
              (
              
                u
                +
                1
              
              )
            
          
          
            N
            
              reference
              ,
              zc
            
            RS
          
        
      
      ,
      
        u
        ∈
        
          {
          
            0
            ,
            1
            ,
            ...
            ⁢
            
              
            
            ,
            29
          
          }
        
      
      ,
      
        v
        ∈
        
          {
          
            0
            ,
            1
          
          }
        
      
    
    ⁢
    
      
    
  


wherein NzcRS is a ZC sequence generation length used in generating the ZC sequence having the q-th root index, NzcRS is given by the largest prime number which is less than the length of the base sequence using the ZC sequence having the q-th root index, Nreference,zcRS is a specific reference prime number, and the “floor (z)” is a function of making a greatest integer not greater than z.

14. The mobile terminal according to claim 9, wherein a maximum number of the base sequences within each sequence group is 2, and
wherein the “q” is determined by




  
    q
    =
    
      
        floor
        ⁡
        
          (
          
            y
            +
            0.5
          
          )
        
      
      +
      
        v
        ·
        
          
            (
            
              -
              1
            
            )
          
          
            floor
            ⁡
            
              (
              
                2
                ⁢
                y
              
              )
            
          
        
      
    
  




  
    
      
        
          where
          ⁢
          
            
          
          ⁢
          y
        
        =
        
          
            
              N
              zc
              RS
            
            ·
            
              (
              
                u
                +
                1
              
              )
            
          
          
            N
            
              reference
              ,
              zc
            
            RS
          
        
      
      ,
      
        u
        ∈
        
          {
          
            0
            ,
            1
            ,
            ...
            ⁢
            
              
            
            ,
            29
          
          }
        
      
      ,
      
        v
        ∈
        
          {
          
            0
            ,
            1
          
          }
        
      
    
    ⁢
    
      
    
  


wherein NzcRS is a ZC sequence generation length used in generating the ZC sequence having the q-th root index, NzcRS is given by the smallest prime number which is greater than the length the base sequence using the ZC sequence having the q-th root index, Nreference,zcRS is a specific reference prime number, and the “floor (z)” is a function of making a greatest integer not greater than z).

15. The mobile terminal according to claim 11, wherein the specific reference prime number is 31.

16. The mobile terminal according to claim 13, wherein the specific reference prime number is 31.