# Patent

## Title
Method of determining an acquisition indicator bit in a communication system

## Abstract

A method of determining an acquisition indicator bit AIs at a receiver in a communication system which includes receiving multiplexed acquisition indicator bits y=B×AI+n, where B is the signature matrix known at both base station and the receiver, AI is all the acquisition indicator bits and n represents noise. Next, an estimated value of the acquisition indicator bit AÎML(s) as a function of 



  
    ∑
    j
    
       
    
  
  ⁢
  
     
  
  ⁢
  
    
      
        B
        T
      
      ⁡
      
        (
        
          s
          ,
          j
        
        )
      
    
    ×
    
      y
      ⁡
      
        (
        j
        )
      
    
  




is calculated, where BT(s,.) is the s-th row vector of the transposed matrix BT for acquisition indicator bit AIs. Finally, the acquisition indicator bit AIs is set as follows:

AIs=−1, if AÎML(s)<R

AIs=0, if R≦AÎML(s)<U

AIs=1, if AÎML(s)≧U,

where R and U are decision thresholds.

## Background
BACKGROUND AND SUMMARY OF THE INVENTION
The present invention relates generally to communication systems of coded data and, more specifically, to an improvement in determining an acquisition indicator bit at a receiver in a communication system.
Although the present invention will be described with respect to 3rd generation wideband code division multiple access (3G WCDMA) system, the same method can be used for determining an acquisition bit AIs at a receiver in other communication systems. General and specific references will also be made to the 3G WCDMA standard 3GPP TS 25.211, Physical channels and mapping of transport channels onto physical channels (FDD) (Release 4) and 3GPP TS 25.213, “Spreading and modulation (FDD)” (Release 4).
In 3rd generation CDMA systems, physical connections between UE (User Equipment) and base stations are established through the Physical Random Access Channel (PRACH) and Acquisition Indicator Channel (AICH). The UE transmits PRACH signal that carries the RACH preamble and message to a base station, to request a connection. When the base station recognizes a PRACH preamble, it responds with AICH to UE to indicate if the connection request is granted. An example of the AICH from 3GPP TS 25.211 is shown in FIG. 1.
Upon the AICH reception, the problem is to estimate the AIs based on the received real valued symbols a0, a1, . . . , a31 which are transmitted through AICH, where AIs, ∈{−1,0,1} and s=0,1, . . . , 15. An AIs of 0 indicates that the signature s is not a member of the set of available signatures. An AIs of 1 indicates a positive acknowledgement, and an AIs of −1 indicates a negative acknowledgement. At the base station, AIs is code multiplexed with others, {AIn:n≠s}, by the following formula: 



  
    
      
        
          
            a
            j
          
          =
          
            
              ∑
              
                s
                =
                0
              
              15
            
            ⁢
            
               
            
            ⁢
            
              
                AI
                s
              
              ⁢
              
                b
                
                  s
                  ,
                  j
                
              
            
          
        
        ,
        
          j
          =
          0
        
        ,
        1
        ,
        ...
        ⁢
        
           
        
        ,
        31
        ,
      
    
    
      
        (
        1
        )
      
    
  




where {bs,j:j=0,1, . . . 31} are given in Table 21 in 3GPP TS 25.211 and shown below in the example as BT.

The present invention is a method of determining an acquisition indicator bit AIs at a receiver in a communication system. The method includes receiving multiplexed acquisition indicator bits y=B×AI+n, where B is the signature matrix known at both base station and the receiver, AI is the set of all the acquisition indicator bits and n represents noise, for example, AWGN (additive white Gaussian noise). Next, an estimated value of the acquisition indicator bit AÎML(s) as a function of 



  
    ∑
    j
    
       
    
  
  ⁢
  
     
  
  ⁢
  
    
      
        B
        T
      
      ⁡
      
        (
        
          s
          ,
          j
        
        )
      
    
    ×
    
      y
      ⁡
      
        (
        j
        )
      
    
  




is calculated, where BT(s,.) is the s-th row vector of the transposed matrix BT for acquisition indicator bit AIs. Finally, the acquisition indicator bit AIs is set as follows:

AIs=−1, if AÎML(s)<R

AIs=0, if R≦AÎML(s)<U

AIs=1, if AÎML(s)≧U,

where R and U are decision thresholds.

The constants R and U may be equal absolute values, for example, −0.5 and 0.5, respectively. The estimated value AÎML(s) is calculated by 



  
    A
    ⁢
    
       
    
    ⁢
    
      
        
          I
          ^
        
        ML
      
      ⁡
      
        (
        s
        )
      
    
  
  =
  
    
      1
      32
    
    ⁢
    
      
        ∑
        
          j
          =
          0
        
        31
      
      ⁢
      
         
      
      ⁢
      
        
          
            B
            T
          
          ⁡
          
            (
            
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              ,
              j
            
            )
          
        
        ×
        
          
            y
            ⁡
            
              (
              j
              )
            
          
          .
        
      
    
  




The method is performed without forming a matrix B or BT and is performed in software.

These and other aspects of the present invention will become apparent from the following detailed description of the invention, when considered in conjunction with accompanying drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram of the structure of the acquisition indicator channel AICH of the 3G WCDMA system defined in 3GPP TS 25.211.
FIG. 2 is a flow chart of a method of determining an acquisition indicator bit AIs incorporating the principles of the present invention.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The method of the present invention, which is performed at the receiver of a communication system, is illustrated in FIG. 2. The input signal y is received at 10. An estimated acquisition indicator (AÎML(s)) is calculated from the input signal y. The resulting estimated acquisition indicator corresponding to a signature index s, AÎML(s) is then used for determining an acquisition indicator bit AIs having one of the values −1,0,1. The decided acquisition indicator bit is outputted at 16. The details of the method are described as follows:
In matrix form, equation (1) can be expressed as

a=B×AI,  (2)

where 



  
    
      
        
          a
          =
          
            
              [
              
                
                  a
                  0
                
                ,
                
                  a
                  1
                
                ,
                ...
                ⁢
                
                   
                
                ,
                
                  a
                  31
                
              
              ]
            
            T
          
        
        ,
      
    
  
  
    
      
        
          B
          =
          
            [
            
              
                
                  
                    b
                    
                      0
                      ,
                      0
                    
                  
                
                
                  
                    b
                    
                      1
                      ,
                      0
                    
                  
                
                
                  
                    b
                    
                      2
                      ,
                      0
                    
                  
                
                
                  ...
                
                
                  
                    b
                    
                      15
                      ,
                      0
                    
                  
                
              
              
                
                  
                    b
                    
                      0
                      ,
                      1
                    
                  
                
                
                  
                    b
                    
                      1
                      ,
                      1
                    
                  
                
                
                  
                    b
                    
                      2
                      ,
                      1
                    
                  
                
                
                  ...
                
                
                  
                    b
                    
                      15
                      ,
                      1
                    
                  
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋮
                
              
              
                
                  
                    b
                    
                      0
                      ,
                      31
                    
                  
                
                
                  
                    b
                    
                      1
                      ,
                      31
                    
                  
                
                
                  
                    b
                    
                      2
                      ,
                      31
                    
                  
                
                
                  ...
                
                
                  
                    b
                    
                      15
                      ,
                      31
                    
                  
                
              
            
            ]
          
        
        ,
      
    
  




and

AI=[AI0, AI1, . . . , AI15]T.

The received soft bits from a rake receiver can be modeled as

y=a+n

or

y=B×AI+n,  (3)

where n denotes noise, for example, the AWGN.

The maximum likelihood estimator for the unknown acquisition indicator, AÎML, in equation (3) is well known (see S. M. Kay, Fundamentals of Statistical Signal Processing (Estimation Theory), Prentice Hall) and is given by

AÎML=(BT×B)−1×BT×y.  (4)

Due to orthogonality (see Table 21 in 3GPP TS 25.211),

BT×B=32×I16×16,  (5)

where I16×16 is the identity matrix with dimension 16.

Thus, equation (4) can be reduced to 



  
    
      
        
          A
          ⁢
          
             
          
          ⁢
          
            
              I
              ^
            
            ML
          
        
        =
        
          
            1
            32
          
          ×
          
            B
            T
          
          ×
          
            y
            .
          
        
      
    
    
      
        (
        6
        )
      
    
  




It is assumed that the table index, s, for AICH signature patterns is equivalent to the one for the RACH preamble signatures from Table 3 in 3GPP TS 25.213. In other words, the index s is known at the user equipment UE so that only the portion corresponding to s of equation (6) is of interest.
Let Ts(y) be a statistic corresponding to an index s, given y 



  
    
      
        
          
            
              T
              s
            
            ⁡
            
              (
              y
              )
            
          
          =
          
            
              A
              ⁢
              
                 
              
              ⁢
              
                
                  
                    I
                    ^
                  
                  ML
                
                ⁡
                
                  (
                  s
                  )
                
              
            
            =
            
              
                1
                32
              
              ⁢
              
                
                  ∑
                  
                    j
                    =
                    0
                  
                  31
                
                ⁢
                
                   
                
                ⁢
                
                  
                    
                      B
                      T
                    
                    ⁡
                    
                      (
                      
                        s
                        ,
                        j
                      
                      )
                    
                  
                  ×
                  
                    y
                    ⁡
                    
                      (
                      j
                      )
                    
                  
                
              
            
          
        
        ,
      
    
    
      
        (
        7
        )
      
    
  




where BT(s,.) denotes the s-th row vector of the matrix BT.

Assuming uniform prior for the following hypotheses,

H−1: AIs=−1,

H0: AIs=0

H1: AIs=1, s=0,1, . . . , 15,

the 3-ary MAP decision rule (see S. M. Kay, Fundamentals of Statistical Signal Processing (Detection Theory), Prentice Hall) is to decide

AIs=−1, if Ts(y)<R

AIs=0, if R≦Ts(y)<U

AIs=1, if Ts(y)≧U,

where U and R are constants. The {Hi, i=−1,0,1} denote the hypotheses that the acquisition indicator bit is i. Assuming perfect channel, the constants R and U may be equal absolute values, for example, −0.5 and 0.5, respectively.

As an illustrative example, let AI0=−1, AI1=−1, AI2=1, AI3=−1, AI4=−1, AI5=−1, AI6=−1, AI7=−1, AI8=−1, AI9=−1, AI10=−0, AI11=−1, AI12=−1, AI13=−1, AI14=−1, and AI15=0.
Since AI is defined by

AI=[AI0AI1AI2AI3AI4AI5AI6AI7AI8AI9AI10AI11AI12AI13AI14AI15]^T,

where T denote the transpose, that is 



  
    
      
        AI
        =
        
        ⁢
        
          [
          
            -
            1
          
        
      
    
  
  
    
      
        
        ⁢
        
          -
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          -
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          ⁢
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          ]
        
        .
      
    
  




The matrix B (of size 32×16) in (2) is given by 


  
    
      
        
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            ,
          
        
        
          
            1
            ,
          
        
        
          
            1
            ,
          
        
        
          
            1
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            1
            ,
          
        
        
          1
        
      
    
  




  
    
       
    
    ⁢
    
      
        
          
            1
            ,
          
        
        
          
            1
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            1
            ,
          
        
        
          
            1
            ,
          
        
        
          
            1
            ,
          
        
        
          
            1
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            
              -
              1
            
            ,
          
        
        
          
            1
            ,
          
        
        
          1
        
      
    
  




  
    
       
    
    ⁢
    
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  -
                  1
                
              
            
          
        
      
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  -
                  1
                
              
            
          
        
      
    
  




  
    
       
    
    ⁢
    
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  -
                  1
                
              
            
          
        
      
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  -
                  1
                
              
            
          
        
      
    
  




  
    
       
    
    ⁢
    
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                1
              
            
          
        
      
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                1
              
            
          
        
      
    
  




  
    
       
    
    ⁢
    
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                1
              
            
          
        
      
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                1
              
            
          
        
      
    
  




  
    
       
    
    ⁢
    
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  -
                  1
                
              
            
          
        
      
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  -
                  1
                
              
            
          
        
      
    
  




  
    
       
    
    ⁢
    
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                1
              
            
          
        
      
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                1
              
            
          
        
      
    
  




  
    
       
    
    ⁢
    
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  -
                  1
                
              
            
          
        
      
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  -
                  1
                
              
            
          
        
      
    
  




  
    
       
    
    ⁢
    
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  -
                  1
                
              
            
          
        
      
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  -
                  1
                
              
            
          
        
      
    
  




  
    
       
    
    ⁢
    
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                1
              
            
          
        
      
      
        
          
            
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  1
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    -
                    1
                  
                  ,
                
              
              
                
                  
                    1
                    ]
                  
                  .
                
              
            
          
        
      
    
  



For instance, b0,0=1 and b2,1=−1.

The transposed B is then 



  
    
      B
      T
    
    =
    
      
        
          
            
              [
              
                1
                ,
              
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
        
      
      ⁢
      
         
      
      ⁢
      
        
          
            
              
                 
              
              ⁢
              
                1
                ,
              
            
          
          
            
              1
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
        
      
      ⁢
      
        
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              1
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
              ,
            
          
          
            
              
                -
                1
              
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      ⁢
      
        
          
            
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      ⁢
      
        
          
            
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      ⁢
      
        
          
            
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              ,
            
          
        
      
      ⁢
      
         
      
      ⁢
      1
    
  
  ,
  
    

  
  ⁢
  
    
      
        
           
        
      
      
        
          
            -
            1
          
          ,
        
      
      
        
          
            -
            1
          
          ,
        
      
      
        
          1
          ,
        
      
      
        
          1
          ,
        
      
      
        
          
            -
            1
          
          ,
        
      
      
        
          
            -
            1
          
          ,
        
      
      
        
          
            -
            1
          
          ,
        
      
      
        
          
            -
            1
          
          ,
        
      
      
        
          1
          ,
        
      
      
        
          1
          ]
        
      
    
  




From equation (3), a=B×AI.

Note that the size of y, a, B, and AI are 32×1, 32×1, 32×16, and 16×1, respectively.

The calculated a is then 



  
    
      
        a
        =
        
          [
          
            -
            
            ⁢
            12
          
        
      
    
  
  
    
      
        -
        
        ⁢
        12
      
    
  
  
    
      
        
        ⁢
        2
      
    
  
  
    
      
        
        ⁢
        2
      
    
  
  
    
      
        -
        
        ⁢
        4
      
    
  
  
    
      
        -
        
        ⁢
        4
      
    
  
  
    
      
        -
        
        ⁢
        2
      
    
  
  
    
      
        -
        
        ⁢
        2
      
    
  
  
    
      
        
        ⁢
        2
      
    
  
  
    
      
        
        ⁢
        2
      
    
  
  
    
      
        
        ⁢
        4
      
    
  
  
    
      
        
        ⁢
        4
      
    
  
  
    
      
        -
        
        ⁢
        2
      
    
  
  
    
      
        -
        
        ⁢
        2
      
    
  
  
    
      
        -
        
        ⁢
        4
      
    
  
  
    
      
        -
        
        ⁢
        4
      
    
  
  
    
      
        
        ⁢
        0
      
    
  
  
    
      
        
        ⁢
        0
      
    
  
  
    
      
        
        ⁢
        2
      
    
  
  
    
      
        
        ⁢
        2
      
    
  
  
    
      
        
        ⁢
        0
      
    
  
  
    
      
        
        ⁢
        0
      
    
  
  
    
      
        -
        
        ⁢
        2
      
    
  
  
    
      
        -
        
        ⁢
        2
      
    
  
  
    
      
        
        ⁢
        2
      
    
  
  
    
      
        
        ⁢
        2
      
    
  
  
    
      
        
        ⁢
        0
      
    
  
  
    
      
        
        ⁢
        0
      
    
  
  
    
      
        -
        
        ⁢
        2
      
    
  
  
    
      
        -
        
        ⁢
        2
      
    
  
  
    
      
        
        ⁢
        0
      
    
  
  
    
      
        
          
          ⁢
          0
          ]
        
        .
      
    
  




From equation (3), the noise is assumed as the additive white Gaussian. Suppose the noise values are given by 



  
    
      
        n
        =
        
        ⁢
        
          [
          0.1703
        
      
    
  
  
    
      
        
        ⁢
        0.3561
      
    
  
  
    
      
        
        ⁢
        0.2907
      
    
  
  
    
      
        
        ⁢
        0.2298
      
    
  
  
    
      
        
        ⁢
        0.0160
      
    
  
  
    
      
        
        ⁢
        0.2692
      
    
  
  
    
      
        
        ⁢
        0.2262
      
    
  
  
    
      
        -
        
        ⁢
        0.1017
      
    
  
  
    
      
        -
        
        ⁢
        0.1501
      
    
  
  
    
      
        -
        
        ⁢
        0.1177
      
    
  
  
    
      
        -
        
        ⁢
        0.5866
      
    
  
  
    
      
        -
        
        ⁢
        0.0930
      
    
  
  
    
      
        
        ⁢
        0.0471
      
    
  
  
    
      
        
        ⁢
        0.1252
      
    
  
  
    
      
        
        ⁢
        0.5740
      
    
  
  
    
      
        -
        
        ⁢
        0.1396
      
    
  
  
    
      
        
        ⁢
        0.2478
      
    
  
  
    
      
        
        ⁢
        0.3177
      
    
  
  
    
      
        
        ⁢
        0.3741
      
    
  
  
    
      
        -
        
        ⁢
        0.3945
      
    
  
  
    
      
        
        ⁢
        0.0843
      
    
  
  
    
      
        
        ⁢
        0.0946
      
    
  
  
    
      
        -
        
        ⁢
        0.4007
      
    
  
  
    
      
        -
        
        ⁢
        0.2951
      
    
  
  
    
      
        
        ⁢
        0.4304
      
    
  
  
    
      
        -
        
        ⁢
        0.0523
      
    
  
  
    
      
        
        ⁢
        0.1550
      
    
  
  
    
      
        
        ⁢
        0.0350
      
    
  
  
    
      
        -
        
        ⁢
        0.2527
      
    
  
  
    
      
        -
        
        ⁢
        0.2225
      
    
  
  
    
      
        
        ⁢
        0.1764
      
    
  
  
    
      
        
          
            -
            
            ⁢
            0.3777
          
          ]
        
        .
      
    
  




Then from equation (3), the observed samples, y, is 



  
    
      
        y
        =
        
          [
          
            -
            
            ⁢
            11.8297
          
        
      
    
  
  
    
      
        -
        
        ⁢
        11.6439
      
    
  
  
    
      
        
        ⁢
        2.2907
      
    
  
  
    
      
        
        ⁢
        2.2298
      
    
  
  
    
      
        -
        
        ⁢
        3.9840
      
    
  
  
    
      
        -
        
        ⁢
        3.7308
      
    
  
  
    
      
        -
        
        ⁢
        1.7738
      
    
  
  
    
      
        -
        
        ⁢
        2.1017
      
    
  
  
    
      
        
        ⁢
        1.8499
      
    
  
  
    
      
        
        ⁢
        1.8823
      
    
  
  
    
      
        
        ⁢
        3.4134
      
    
  
  
    
      
        
        ⁢
        3.9070
      
    
  
  
    
      
        -
        
        ⁢
        1.9529
      
    
  
  
    
      
        -
        
        ⁢
        1.8748
      
    
  
  
    
      
        -
        
        ⁢
        3.4260
      
    
  
  
    
      
        -
        
        ⁢
        4.1396
      
    
  
  
    
      
        
        ⁢
        0.2478
      
    
  
  
    
      
        
        ⁢
        0.3177
      
    
  
  
    
      
        
        ⁢
        2.3741
      
    
  
  
    
      
        
        ⁢
        1.6055
      
    
  
  
    
      
        
        ⁢
        0.0843
      
    
  
  
    
      
        
        ⁢
        0.0946
      
    
  
  
    
      
        -
        
        ⁢
        2.4007
      
    
  
  
    
      
        -
        
        ⁢
        2.2951
      
    
  
  
    
      
        
        ⁢
        2.4304
      
    
  
  
    
      
        
        ⁢
        1.9477
      
    
  
  
    
      
        
        ⁢
        0.1550
      
    
  
  
    
      
        
        ⁢
        0.0350
      
    
  
  
    
      
        -
        
        ⁢
        2.2527
      
    
  
  
    
      
        -
        
        ⁢
        2.2225
      
    
  
  
    
      
        
        ⁢
        0.1764
      
    
  
  
    
      
        
          
            -
            
            ⁢
            0.3777
          
          ]
        
        .
      
    
  




The y is the noisy version of the received acquisition indicator bits carried over AICH.
Assume that the signature index s is 2, then by equation (3), the AI2 can be estimated as 



  
    
      
        
          A
          ⁢
          
             
          
          ⁢
          
            
              
                I
                ^
              
              ML
            
            ⁡
            
              (
              2
              )
            
          
        
        =
        
        ⁢
        
          
            1
            32
          
          ⁢
          
            
              ∑
              
                j
                =
                0
              
              31
            
            ⁢
            
               
            
            ⁢
            
              
                
                  B
                  T
                
                ⁡
                
                  (
                  
                    2
                    ,
                    j
                  
                  )
                
              
              ×
              
                y
                ⁡
                
                  (
                  j
                  )
                
              
            
          
        
      
    
  
  
    
      
        =
        
        ⁢
        
          
            1
            /
            32
          
          *
          
            (
            
              
                1
                *
                
                  -
                  11.8297
                
              
              +
              
                1
                *
                
                  -
                  11.6439
                
              
              +
            
          
        
      
    
  
  
    
      
        
          
          ⁢
          
            
              1
              *
              2.2907
            
            +
            ...
            ⁢
            
               
            
            -
            
              1
              *
              0.1764
            
            +
            
              
                -
                1
              
              *
              
                -
                0.3777
              
            
          
          )
        
        =
        
          1.0434
          .
        
      
    
  




This is the multiplication of two vectors, the 3rd row of BT and y. Since AÎML(2) is greater than 0.5 using U=0.5, the decision can be made as AÎ(2)=1, which is matched with the initial setting, AI2=1.

Although the present invention has been described and illustrated in detail, it is to be clearly understood that the same is by way of illustration and example only, and is not to be taken by way of limitation. The scope of the present invention are to be limited only by the terms of the appended claims.

## Claims

1. A method of determining an acquisition indicator bit AIs at a receiver in a communication system, the method comprising:
receiving multiplexed acquisition bits y=B×AI+n, where B is the signature matrix known at both base station and the receiver, AI is all the acquisition indicator bits and n represents noise; 
calculating an estimated value of the AI bit of interest 

AÎML(s) as a function of 



  
    
      ∑
      j
    
    ⁢
    
      
        
          B
          T
        
        ⁡
        
          (
          
            s
            ,
            j
          
          )
        
      
      ×
      
        y
        ⁡
        
          (
          j
          )
        
      
    
  
  ,




where BT(s,.) is the s-th row vector of the transposed matrix BT for acquisition indicator bit AIs; and
setting the acquisition indicator bit AIs as follows: 


AIs=−1, if AÎML(s)<R 



AIs=0, if R≦AÎML(s)<U 



AIs=1, if AÎML(s)≧U 



where R and U are decision thresholds.

2. The method according to claim 1, wherein R and U are equal absolute values.

3. The method according to claim 1, wherein R and U are −0.5 and 0.5, respectively.

4. The method according to claim 1, wherein the estimated value AÎMMSE(s) is calculated by 



  
    A
    ⁢
    
       
    
    ⁢
    
      
        I
        ^
      
      MMSE
    
  
  =
  
    
      1
      
        (
        
          32
          +
          
            
              σ
              ^
            
            2
          
        
        )
      
    
    ⁢
    
      
        ∑
        
          j
          =
          0
        
        31
      
      ⁢
      
         
      
      ⁢
      
        
          
            B
            T
          
          ⁡
          
            (
            
              s
              ,
              j
            
            )
          
        
        ×
        
          
            y
            ⁡
            
              (
              j
              )
            
          
          .

5. The method of claim 1, wherein the method pre-stores matrix B or BT.

6. The method of claim 1, wherein the method is performed in software.