Patent Publication Number: US-7215656-B1

Title: Transmission and receiving using spreading modulation for spread spectrum communications and thereof apparatus

Description:
TECHNICAL FIELD 
   This invention is concerned with spreading modulation methods for orthogonal multiple channel transmitters in CDMA (code division multiple access) communication systems. More particularly it is related to orthogonal complex-domain spreading modulation methods for CDMA communication systems when there are channels with statistically higher transmitting power. 
   BACKGROUND ART 
   In description of the prior art, the same reference number is used for a component having the same function as that of the present invention.  FIG. 1  shows a schematic diagram for a conventional CDMA transmitter with orthogonal multiple channels. The transmitter in  FIG. 1  is based on the cdma2000 system, which is one of the candidates for IMT-2000 (International Mobile Telecommunications-2000) system as a third generation mobile communication systems. The transmitter has 5 orthogonal channels: A Pilot CHannel (PiCH) used for coherent demodulation; a Dedicated Control CHannel (DCCH) for transmitting control information; a Fundamental CHannel (FCH) for transmitting low speed data such as voice; and two Supplementary CHannels (SCH; SCH 1 , SCH 2 ) for high-speed data services. Each channel passes through a channel encoder and/or an interleaver (not shown in  FIG. 1 ) according to the required quality of the channel. 
   Each channel performs the signal conversion process by changing a binary data {0, 1} into {+1, −1}. Even though it is explained with the changed {+1, −1}, our method can be equally applied to the information represented by several bits, for example, { 00 ,  01 ,  11 ,  10 } is changed into {+3, +1, −1, −3}. The gain for each channel is controlled based on the required quality and transmitting data rate by using the gain controllers G P ( 110 ), G D ( 112 ), G S2 ( 114 ), G S1 ( 116 ), and G F ( 118 ). The gain for each channel is determined by a specific reference gain, and the amplifiers ( 170 ,  172 ) control the overall gain. For example, with G P =1, other gain G D , G S2 , G S1 , or G F  can be controlled. Gain controlled signal for each channel is spread at the spreader ( 120 ,  122 ,  124 ,  126 ,  128 ) with orthogonal Hadamard code W PiCH [n], W DCCH [n], W SCH2 [n], W SCH1 [n], or W FCH [n], and is delivered to the adder ( 130 ,  132 ). 
   Hadamard matrix, H (p) , comprising the orthogonal Hadamard codes has the following four properties: 
   (1) The orthogonality is guaranteed between the columns and the rows of an Hadamard matrix. When 
                   H     (   p   )       =               H     p   ×   p       =     [           h     0   ,   0             h     0   ,   1           ⋯         h     0   ,     p   -   1                   h     1   ,   0             h     1   ,   1           ⋯         h     1   ,     p   -   1                 ⋮       ⋮       ⋰       ⋮             h       p   -   1     ,   0             h       p   -   1     ,   1           ⋯         h       p   -   1     ,     p   -   1               ]                   [             h   0     _                 h   1     _             ⋮               h     p   -   1       _           ]     =     [           h   0     _     T     ⁢           ⁢         h   1     _     T     ⁢   ⋯   ⁢           ⁢         h     p   -   1       _     T       ]             =             [     EQUATION   ⁢           ⁢   1     ]               
and,  h     i,j     ∈{+1, −1}; i,j∈{0, 1, 2, . . . , p−1}   
matrix H (p)  is a p×p Hadamard matrix if the following equations hold.
   H   p×p   H   T   p×p   =pI   (p)   [EQUATION 2]     h i       ·  h j       =p·δ   i,j    
Where I (p)  is a p×p identity matrix,
 
and  δ     i,j    is the Kronecker Delta symbol, which becomes 1 of i=j, and 0 for i≠j.
 
   (2) It is still an Hadamard matrix H (p)  even if the order of the columns and the rows of an Hadamard matrix is changed. 
   (3) The order of Hadamard matrix H (p) , p, is 1, 2, or a multiple number of 4. In other words,  p−{1,2}∪{4n|n∈Z     +     } , where Z +  is a set of integers which are greater than 0. 
   (4) The mn×mn matrix H (mn)  produced by the Kronecker product (as in EQUATION 3) from a m×m Hadamard matrix A (m)  and a n×n Hadamard matrix B (n)  is also an Hadamard matrix. 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         H 
                         
                           mn 
                           × 
                           mn 
                         
                       
                       = 
                       
                         
                           A 
                           
                             m 
                             × 
                             m 
                           
                         
                         ⊗ 
                         
                           B 
                           
                             n 
                             × 
                             n 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 
                                   a 
                                   
                                     0 
                                     , 
                                     0 
                                   
                                 
                               
                               
                                 
                                   a 
                                   
                                     0 
                                     , 
                                     1 
                                   
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   a 
                                   
                                     0 
                                     , 
                                     
                                       m 
                                       - 
                                       1 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   a 
                                   
                                     1 
                                     , 
                                     0 
                                   
                                 
                               
                               
                                 
                                   a 
                                   
                                     1 
                                     , 
                                     1 
                                   
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   a 
                                   
                                     1 
                                     , 
                                     
                                       m 
                                       - 
                                       1 
                                     
                                   
                                 
                               
                             
                             
                               
                                 ⋮ 
                               
                               
                                 ⋮ 
                               
                               
                                 ⋰ 
                               
                               
                                 ⋮ 
                               
                             
                             
                               
                                 
                                   a 
                                   
                                     
                                       m 
                                       - 
                                       1 
                                     
                                     , 
                                     0 
                                   
                                 
                               
                               
                                 
                                   a 
                                   
                                     
                                       m 
                                       - 
                                       1 
                                     
                                     , 
                                     1 
                                   
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   a 
                                   
                                     
                                       m 
                                       - 
                                       1 
                                     
                                     , 
                                     
                                       m 
                                       - 
                                       1 
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                         ⊗ 
                         
                           [ 
                           
                             
                               
                                 
                                   b 
                                   
                                     0 
                                     , 
                                     0 
                                   
                                 
                               
                               
                                 
                                   b 
                                   
                                     0 
                                     , 
                                     1 
                                   
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   b 
                                   
                                     0 
                                     , 
                                     
                                       n 
                                       - 
                                       1 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   b 
                                   
                                     1 
                                     , 
                                     0 
                                   
                                 
                               
                               
                                 
                                   b 
                                   
                                     1 
                                     , 
                                     1 
                                   
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   b 
                                   
                                     1 
                                     , 
                                     
                                       n 
                                       - 
                                       1 
                                     
                                   
                                 
                               
                             
                             
                               
                                 ⋮ 
                               
                               
                                 ⋮ 
                               
                               
                                 ⋰ 
                               
                               
                                 ⋮ 
                               
                             
                             
                               
                                 
                                   b 
                                   
                                     
                                       n 
                                       - 
                                       1 
                                     
                                     , 
                                     0 
                                   
                                 
                               
                               
                                 
                                   b 
                                   
                                     
                                       n 
                                       - 
                                       1 
                                     
                                     , 
                                     1 
                                   
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   b 
                                   
                                     
                                       n 
                                       - 
                                       1 
                                     
                                     , 
                                     
                                       n 
                                       - 
                                       1 
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     b 
                                     
                                       0 
                                       , 
                                       0 
                                     
                                   
                                   ⁢ 
                                   A 
                                 
                               
                               
                                 
                                   
                                     b 
                                     
                                       0 
                                       , 
                                       1 
                                     
                                   
                                   ⁢ 
                                   A 
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   
                                     b 
                                     
                                       0 
                                       , 
                                       
                                         n 
                                         - 
                                         1 
                                       
                                     
                                   
                                   ⁢ 
                                   A 
                                 
                               
                             
                             
                               
                                 
                                   
                                     b 
                                     
                                       1 
                                       , 
                                       0 
                                     
                                   
                                   ⁢ 
                                   A 
                                 
                               
                               
                                 
                                   
                                     b 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                   ⁢ 
                                   A 
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   
                                     b 
                                     
                                       1 
                                       , 
                                       
                                         n 
                                         - 
                                         1 
                                       
                                     
                                   
                                   ⁢ 
                                   A 
                                 
                               
                             
                             
                               
                                 ⋮ 
                               
                               
                                 ⋮ 
                               
                               
                                 ⋰ 
                               
                               
                                 ⋮ 
                               
                             
                             
                               
                                 
                                   
                                     b 
                                     
                                       
                                         n 
                                         - 
                                         1 
                                       
                                       , 
                                       0 
                                     
                                   
                                   ⁢ 
                                   A 
                                 
                               
                               
                                 
                                   
                                     b 
                                     
                                       
                                         n 
                                         - 
                                         1 
                                       
                                       , 
                                       1 
                                     
                                   
                                   ⁢ 
                                   A 
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   
                                     b 
                                     
                                       
                                         n 
                                         - 
                                         1 
                                       
                                       , 
                                       
                                         n 
                                         - 
                                         1 
                                       
                                     
                                   
                                   ⁢ 
                                   A 
                                 
                               
                             
                           
                           ] 
                         
                         = 
                         
                           [ 
                           
                             
                               
                                 
                                   h 
                                   
                                     0 
                                     , 
                                     0 
                                   
                                 
                               
                               
                                 
                                   h 
                                   
                                     0 
                                     , 
                                     1 
                                   
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   h 
                                   
                                     0 
                                     , 
                                     
                                       mn 
                                       - 
                                       1 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   
                                     1 
                                     , 
                                     0 
                                   
                                 
                               
                               
                                 
                                   h 
                                   
                                     1 
                                     , 
                                     1 
                                   
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   h 
                                   
                                     1 
                                     , 
                                     
                                       mn 
                                       - 
                                       1 
                                     
                                   
                                 
                               
                             
                             
                               
                                 ⋮ 
                               
                               
                                 ⋮ 
                               
                               
                                 ⋰ 
                               
                               
                                 ⋮ 
                               
                             
                             
                               
                                 
                                   h 
                                   
                                     
                                       mn 
                                       - 
                                       1 
                                     
                                     , 
                                     0 
                                   
                                 
                               
                               
                                 
                                   h 
                                   
                                     
                                       mn 
                                       - 
                                       1 
                                     
                                     , 
                                     1 
                                   
                                 
                               
                               
                                 ⋯ 
                               
                               
                                 
                                   h 
                                   
                                     
                                       mn 
                                       - 
                                       1 
                                     
                                     , 
                                     
                                       mn 
                                       - 
                                       1 
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
             
             
               
                 [ 
                 
                   EQUATION 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
                 ] 
               
             
           
         
       
     
   
   The present invention describes CDMA systems using the column vectors or row vectors of a 2 n ×2 n  Hadamard matrix  H     (2″)    as orthogonal codes, where the 2 n ×2 n  Hadamard matrix  H     (2″)    is generated from a 2×2 Hadamard matrix as shown in EQUATION 4 (n=1, 2, 3, . . . , 8). In particular, the set of the column vectors or the row vectors of the produced Hadamard matrix is 2 n  dimensional Walsh codes. 
                         ⁢         H     (   2   )       =       H     2   ×   2       =       [           +   1           +   1               +   1           -   1           ]     =     [           W   0     (   2   )                 W   1     (   2   )             ]           ⁢     
     ⁢       H     (   4   )       =           ⁢       H     4   ×   4       =           ⁢         H     2   ×   2       ⊗     H     2   ×   2         =             [           +   1           +   1           +   1           +   1               +   1           -   1           +   1           -   1               +   1           +   1           -   1           -   1               +   1           -   1           -   1           +   1           ]     =         [           W   0     (   4   )                 W   1     (   4   )                 W   2     (   4   )                 W   3     (   4   )             ]     ⁢     
     ⁢     H     (   8   )         =       H     8   ×   8       =       H     2   ×   2       ⊗             H     4   ×   4       =             [           ⁢           +   1           +   1           +   1           +   1           +   1           +   1           +   1           +   1               +   1           -   1           +   1           -   1           +   1           -   1           +   1           -   1               +   1           +   1           -   1           -   1           +   1           +   1           -   1           -   1               +   1           -   1           -   1           +   1           +   1           -   1           -   1           +   1               +   1           +   1           +   1           +   1           -   1           -   1           -   1           -   1               +   1           -   1           +   1           -   1           -   1           +   1           -   1           +   1               +   1           +   1           -   1           -   1           -   1           -   1           +   1           +   1               +   1           -   1           -   1           +   1           -   1           +   1           +   1           -   1           ⁢           ]     ⁢           =           ⁢     [           ⁢           W   0     (   8   )                 W   1     (   8   )                 W   2     (   8   )                 W   3     (   8   )                 W   4     (   8   )                 W   5     (   8   )                 W   6     (   8   )                 W   7     (   8   )             ⁢           ]                                       [     EQUATION   ⁢           ⁢   4     ]               
The orthogonal Walsh codes of the above mentioned Hadamard matrix H (p)  have the following property (p=2 n ).
 
                           W   i     (   p   )       ⊙     W   j     (   p   )         ≡       ⁢       (       w     i   ,   0       (   p   )       ,     w     i   ,   1       (   p   )       ,   …   ⁢           ,     w     i   ,     p   -   1         (   p   )         )     ⊙     (       w     j   ,   0       (   p   )       ,     w     j   ,   1       (   p   )       ,   …   ⁢           ,     w     j   ,     p   -   1         (   p   )         )                   =       ⁢     (         w     i   ,   0       (   p   )       ⁢     w     j   ,   0       (   p   )         ,       w     i   ,   1       (   p   )       ⁢     w     j   ,   1       (   p   )         ,   ⋯   ⁢           ,       w     i   ,     p   -   1         (   p   )       ⁢     w     j   ,     p   -   1         (   p   )           )                 =       ⁢     (       w     k   ,   0       (   p   )       ,     w     k   ,   1       (   p   )       ,   …   ⁢           ,     w     k   ,     p   -   1         (   p   )         )                 =       ⁢     W   k     (   p   )                     [     EQUATION   ⁢           ⁢   5     ]               
Where {i, j, k}⊂{0, 2, 3, . . . , 2 n −2}. If i, j, k are represented by binary numbers as in EQUATION 6,
 i=(i n−1 , i n−2 , i n−3 , . . . , i 1 , i 0 ) 2 , j=(j n−1 , j n−2 , j n−3 , . . . , j 1 , j 0 ) 2 , k=(k n−1 , k n−2 , k n−3 , . . . , k 1 , k 0 ) 2   [EQUATION 6] 
the following relation holds among i, j, k:
 (k n−1 , k n−2 , k n−3 , . . . , k 1 , k 0 ) 2 =(i n−1 ⊕j n−1 , i n−2 ⊕j n−2 , j n−3 ⊕j n−3 , . . . , i 1 ⊕j 1 , i 0 ⊕j 0 ) Z    [EQUATION 7] 
Here ⊕ represents the eXclusive OR (XOR) operator. Therefore,  W     i       (p)     [n]=W     i       (p)     [n]W     0       (p)     [n]  for i∈{0, 1, 2, . . . , 2 n −1}, and  W     2k+1       (p)     [n]=W     2k       (p)     [n]W     1       (p)     [n]  for k∈{0, 1, 2, . . . , 2 n−1 −1}.
 
   In order to distinguish the orthogonal multiple channels, the Hadamard matrix H (p)  is used, and the order of the Hadamard matrix H (p) , p(=2 n ) is the Spreading Factor (SF). In direct sequence spread spectrum communication systems, the spreading bandwidth is fixed, so the transmission chip rate is also fixed. When there are several channels having different data transmission rates with a fixed transmission chip rate, the tree-structured Orthogonal Variable Spreading Factor (OVSF) codes are used (as shown in EQUATION 8) in order to recover the desired channels at the receiving terminal using the orthogonal property of the channels. 
   The OVSF codes with conversion (“0” “+1” and “1” “−1”) and orthogonal Walsh functions are shown in EQUATION 8 and EQUATION 9, respectively. An allocation method of the tree-structured OVSF codes with the orthogonal property is shown in the following references: (1) F. Adachi, M. Sawahashi and K. Okawa, “Tree-structured generation of orthogonal spreading codes with different lengths for forward link of DS-CDMA mobile radio, “Electronics Letters, Vol. 33, January 1997, pp27–28. (2) U.S. Pat. No. 5,751,761, “System and method for orthogonal spread spectrum sequence generation in variable data rate systems”. 
                       
The above equation shows the OVSF codes.
 
                       
The above equation shows the relation between the OVSF codes and orthogonal Walsh codes.
 
   The outputs (x T [n], y T [n]) of the adder ( 130 ,  132 ) in  FIG. 1  can be written as the following equations: 
   
     
       
         
           
             
               
                 
                   
                     
                       x 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       n 
                       ] 
                     
                   
                   = 
                     
                   ⁢ 
                   
                     
                       
                         G 
                         P 
                       
                       ⁢ 
                       
                         
                           W 
                           HCH 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           D 
                           HCH 
                         
                         ⁡ 
                         
                           [ 
                           
                             ⌊ 
                             
                               n 
                               
                                 SF 
                                 DCH 
                               
                             
                             ⌋ 
                           
                           ] 
                         
                       
                     
                     + 
                     
                       
                         G 
                         D 
                       
                       ⁢ 
                       
                         
                           W 
                           DCCH 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           D 
                           DCCH 
                         
                         ⁡ 
                         
                           [ 
                           
                             ⌊ 
                             
                               n 
                               
                                 SF 
                                 DCCH 
                               
                             
                             ⌋ 
                           
                           ] 
                         
                       
                     
                     + 
                     
                       
                         G 
                         S2 
                       
                       ⁢ 
                       
                         
                           W 
                           SCH2 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           D 
                           SCH2 
                         
                         ⁡ 
                         
                           [ 
                           
                             ⌊ 
                             
                               n 
                               
                                 SF 
                                 SCH2 
                               
                             
                             ⌋ 
                           
                           ] 
                         
                       
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       y 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       n 
                       ] 
                     
                   
                   = 
                   
                     
                       
                         G 
                         F 
                       
                       ⁢ 
                       
                         
                           W 
                           FCH 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           D 
                           FCH 
                         
                         ⁡ 
                         
                           [ 
                           
                             ⌊ 
                             
                               n 
                               
                                 SF 
                                 FCH 
                               
                             
                             ⌋ 
                           
                           ] 
                         
                       
                     
                     + 
                     
                       
                         G 
                         S1 
                       
                       ⁢ 
                       
                         
                           W 
                           SCH1 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           D 
                           SCH1 
                         
                         ⁡ 
                         
                           [ 
                           
                             ⌊ 
                             
                               n 
                               
                                 SF 
                                 SCH1 
                               
                             
                             ⌋ 
                           
                           ] 
                         
                       
                     
                   
                 
               
             
             
               
                 [ 
                 
                   EQUATION 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   10 
                 
                 ] 
               
             
           
         
       
     
   
   Here └x┘ is a largest integer not greater than x. 
   The above mentioned Walsh code W PiCH [n], W DCCH [n], W SCH2 [n], W SCH1 [n], and W FCH [n] are orthogonal Walsh functions selected from H (SF     PiCH     ) , H (SF     DCCH     ) , H (SF     SCH2     ) , H (SF     SCH1     ) , H (SF     PCH     ) . An allocation method of the orthogonal Walsh functions to each channel with the orthogonal property follows the allocation method of the OVSF codes. SF PiCH , SF DCCH , SF SCH2 , SF SCH1 , and SF FCH  are spreading factors for the corresponding channels. 
   For simple explanation, assume the transmitting power of SCH 1  and SCH 2  is assumed to be statistically greater than the power of PiCH, DCCH, and FCH. (This assumption does not change the present invention.) In other words, it is assumed the relation G S1 &gt;G P +G D +G F , and G S2 &gt;G P +G D +G F , holds statistically. The above assumptions hold in two cases: In the first case, the transmission data rate for the supplementary channel (SCH 1 , SCH 2 ) is greater than that of other channels (PiCH, DCCH, FCH), and the required quality such as the signal-to-noise ratio (SNR) for each channel is comparable. In the second case, the transmission data rates are comparable, and the required quality is more restricted. If there are only two channels available in a transmitter, the assumptions hold, and the two channels are allocated to SCH 1  and SCH 2 . When the assumptions hold, EQUATION 10 can be approximated as EQUATION 11. 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           x 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       ≃ 
                         
                       ⁢ 
                       
                         
                           G 
                           S2 
                         
                         ⁢ 
                         
                           
                             W 
                             SCH2 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         ⁢ 
                         
                           
                             D 
                             SCH2 
                           
                           ⁡ 
                           
                             [ 
                             
                               ⌊ 
                               
                                 n 
                                 
                                   SF 
                                   SCH2 
                                 
                               
                               ⌋ 
                             
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           y 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       ≃ 
                         
                       ⁢ 
                       
                         
                           G 
                           S1 
                         
                         ⁢ 
                         
                           
                             W 
                             SCH1 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         ⁢ 
                         
                           
                             D 
                             SCH1 
                           
                           ⁡ 
                           
                             [ 
                             
                               ⌊ 
                               
                                 n 
                                 
                                   SF 
                                   SCH1 
                                 
                               
                               ⌋ 
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 [ 
                 
                   EQUATION 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   11 
                 
                 ] 
               
             
           
         
       
     
   
   The spreading modulation takes place at the Spreading Modulator ( 140 ) with the first inputs (x T [n], y T [n]) and the second inputs, PN (Pseudo-Noise) sequences (C 1 [n], C 2 [n]), and the outputs (I T [n], Q T [n]) are produced. The peak transmission power to the average power ratio (PAR: Peak-to-Average Ratio) can be improved according to the structure of the Spreading Modulator ( 140 ) and the method how to generate the scrambling codes (C scramble ,  i [n], C scramble ,  Q [n]) from the inputs of the two PN sequences (C 1 [n], C 2 [n]). Conventional embodiments for the Spreading Modulator ( 140 ) are shown in  FIG. 3   a ˜ 3   d.  The outputs (I T [n], Q T [n]) of the Spreading Modulator ( 140 ) pass through the low-pass-filters ( 160 ,  162 ) and the power amplifiers ( 170 ,  172 ). Then the amplified outputs are delivered to the modulators ( 180 ,  182 ) which modulate the signals into the desired frequency band using carrier. And the modulator signals are added by the adder ( 190 ), and delivered to an antenna. 
     FIG. 2  shows a schematic diagram for a receiver according to the transmitter of  FIG. 1 . The received signals passed through an antenna are demodulated at the demodulators ( 280 ,  282 ) with the same carrier used at the transmitter, and I R [n] and Q R [n] are generated after passing through the low-pas filters ( 260 ,  262 ). Then, the spreading demodulator ( 240 ) generates the signals (x R [n], y R [n]) with two PN sequences (C 1 [n], C 2 [n]). 
   In order to pick up the desired channels, i.e., DCCH, FCH, SCH# 1 , SCH# 2 , among the received code division multiplexed signals (x R [n], y R [n]), the signals are multiplied by the same orthogonal code W xxCH [n] (where, xxCH=DCCH or FCH) or W yyCH [n] (where, yyCH=SCH 1  or SCH 2 ) used at the transmitter, at the de-spreaders ( 224 ,  226 ,  225 ,  227 ). Now, the signals are integrated during the symbol period (T 2x  or T 2y ) proportional to the data rate of the corresponding channel. Since the signals at the receiver are distorted, PiCH is used to correct the distorted signal phase. Therefore, the signals (x R [n], y R [n]) are multiplied by the corresponding orthogonal code W PiCH [n], and are integrated during the period of T 1  at the integrators ( 210 ,  212 ). 
   When the PiCH includes additional information such as a control command to control the transmitting power at the receiver, besides the pilot signals for the phase correction, the additional information is extracted by the de-multiplexer, and the phase is estimate and corrected using the part of the pilot signals with the known phase. However, it is assumed that the PiCH does not include any additional information for simplicity. The phase corrections are performed at the second (kind) complex-domain multipliers ( 242 ,  246 ) using the estimated phase information through the integrators ( 210 ,  212 ). After selecting the output port according to the desired channel (DCCH, FCH, SCH 1 , or SCH 2 ) at the second complex-domain multipliers ( 242 ,  246 ), the receiver recovers the transmitted data through the de-interleaver and/or the channel decoder (not shown in  FIG. 2 ). 
   The first ( 143 ) and the second complex-domain multiplier ( 243  or  246 ) execute the following function. 
   [EQUATION 12] 
   Operations for the first complex-domain multipliers ( 143 ,  145 ):
 
 O   I   [n]+jO   Q   [n]= ( x   I   [n]+jx   Q   [n] )( y   I   [n]+jy   Q   [n] )
 
 O   I   [n]=x   I   [n]y   I   [n]−x   Q   [n]y   Q   [n] 
 
 O   Q   [n]=x   I   [n]y   Q   ]n]+x   Q   ]n]y   I   [n] 
 
Operations for the second complex-domain multipliers ( 242 ,  243 ,  245 ,  246 ):
 
 O   I   [n]+jO   Q   [n]= ( x   I   [n]+jx   Q   [n] )( y   I   [n]+jy   Q   [n] )
 
 O   I   [n]=x   I   [n]y   I   [n]+x   Q   [n]y   Q   [n] 
 
 O   Q   [n]=−x   I   [n]y   Q   ]n]+x   Q   ]n]y   I   [n] 
 
     FIG. 7   a  and  FIG. 7   b  show signal constellation diagrams. In  FIG. 7   a,  a square represents the input (x I [n]+jx Q [n]) of the first complex-domain multiplier, and a circle shows a normalized output (O I [n]+jO Q [n]) of the first complex-domain multiplier.  FIG. 7   b  shows four transitions (0, +π/2, −π/2, π) of the first complex-domain multiplier input (x I [n]+jx Q [n]) according to the time flow. The PAR characteristic becomes worse at the origin crossing transition (or π-transition) in  FIG. 7   b.    
     FIG. 3   a  shows the schematic diagram for a conventional spreading modulator. This spreading modulation method is used in the forward link (from a base station to its mobile station) for a CDMA system of IS-95 method. This spreading modulation is called the QPSK (Quadrature Phase Shift Keying) spreading modulation.
   I   T   [n]=x   T   [n]C   scramble,I   [n]   [EQUATION 13]   Q   T   [n]=y   T   [n]C   scramble,Q   [n]   
   The outputs (C scramble, I [n], C scramble, Q [n]) of the secondary scrambling code generator shown in  FIG. 4   a  are given by EQUATION 14. In other words, the secondary scrambling codes are the same as the primary scrambling codes.
 
C scramble, I   [n]=C   1   [n]   [EQUATION 14]
 
C scramble, Q   [n]=C   2   [n] 
 
In the IS-95 system, x T [n]=y T [n], but generally x T [n]≠y T [n] in the QPSK spreading modulation. For |I T [n]|=|Q T [n]|=1 based on the normalization, the possible transitions of the signal constellation point occurring in the QPSK spreading modulation are shown in EQUATION 15. The probability for {0, +π/2, −π/2, π) transition is equally 1/4 for each transition.
 
   
     
       
         
           
             arg 
             ⁡ 
             
               ( 
               
                 
                   
                     
                       I 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       
                         n 
                         + 
                         1 
                       
                       ] 
                     
                   
                   + 
                   
                     
                       jQ 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       
                         n 
                         + 
                         1 
                       
                       ] 
                     
                   
                 
                 
                   
                     
                       I 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       n 
                       ] 
                     
                   
                   + 
                   
                     
                       jQ 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       n 
                       ] 
                     
                   
                 
               
               ) 
             
           
           ∈ 
           
             { 
             
               0 
               , 
               
                 + 
                 
                   π 
                   2 
                 
               
               , 
               
                 - 
                 
                   π 
                   2 
                 
               
               , 
               π 
             
             } 
           
         
       
     
   
     FIG. 8   a  shows the transitions of the signal constellation point for the QPSK spreading modulation when I T [n]=±1, Q T [n]=±1, and SF=4. For n≡0 mod SF, (I T [n], Q T [n]) becomes one of (+1, +1), (+1, −1), (−1, −1), (−1, +1) with an equal probability of 1/4. The transition is assumed to start at (+1, +1). There is no change in the signal constellation diagram at a chip time of n+1/2. At a chip time of n+1, (I T [n], Q T [n]) transits to one of (+1, +1), (+1, −1), (−1, −1), (−1, +1) with an equal probability of 1/4.  FIG. 8   a  shows the case of (+1, −1) transition. 
   There is no change in the signal constellation diagram at a chip time of n+3/2. At a chip time of n+2, (I T [n], Q T [n]) transits to one of (+1, +1), (+1, −1), (−1, −1), (−1, +1) with an equal probability of 1/4.  FIG. 8   a  shows the case of (−1, +1) transition. The PAR characteristic becomes worse in this case due to an origin crossing transition (π-transition). 
   There is no change in the signal constellation diagram at a chip time of n+5/2. At a chip time of n+3, (I T [n], Q T [n]) transits to one of (+1, +1), (+1, −1), (−1, −1), (−1, +1) with an equal probability of 1/4.  FIG. 8   a  shows the case of (−1, −1) transition. 
   There is no change in the signal constellation diagram at a chip time of n+7/2. At a chip time of n+4, (I T [n], Q T [n]) transits to one of (+1, +1), (+1, −1), (−1, −1), (−1, +1) with an equal probability of 1/4. The above transition process is repeated according to the probability. 
     FIG. 3   b  shows a schematic diagram for another conventional spreading modulator. This spreading modulation method is used in the reverse link (from a mobile station to its base station) for the IS-95 CDMA system. This spreading modulation is called the OQPSK (Offset QPSK) spreading modulation, and the output signals are governed by EQUATION 16. 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           I 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         
                           
                             x 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         ⁢ 
                         
                           
                             C 
                             
                               scramble 
                               . 
                               I 
                             
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           Q 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         
                           
                             y 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             
                               n 
                               - 
                               
                                 1 
                                 2 
                               
                             
                             ] 
                           
                         
                         ⁢ 
                         
                           
                             C 
                             
                               scramble 
                               . 
                               Q 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               n 
                               - 
                               
                                 1 
                                 2 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 [ 
                 
                   EQUATION 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   16 
                 
                 ] 
               
             
           
         
       
     
   
   The outputs (C scramble, I [n], C scramble, Q [n]) of the secondary scrambling code generator in  FIG. 4   a  are given by EQUATION 17. In other words, the secondary scrambling codes are the same as the primary scrambling codes, as in the previous QPSK spreading modulation.
 
C scramble, I [n]=C 1 [n]  [EQUATION 17]
 
C scramble, Q [n]=C 2 [n]
 
Generally x T [n]≠y T [n] in OQPSK spreading modulation. For |I T [n]|=|Q T [n]|=1 based on the normalization, the possible transitions of the signal constellation point occurring in the QPSK spreading modulation are shown in EQUATION 18. The probabilities for {0, +π/2, −π/2, π} transitions are 1/2, 1/4, 1/4, 0, respectively.
 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         arg 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 
                                   I 
                                   T 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     n 
                                     + 
                                     
                                       1 
                                       / 
                                       2 
                                     
                                   
                                   ] 
                                 
                               
                               + 
                               
                                 
                                   jQ 
                                   T 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     n 
                                     + 
                                     
                                       1 
                                       / 
                                       2 
                                     
                                   
                                   ] 
                                 
                               
                             
                             
                               
                                 
                                   I 
                                   T 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   n 
                                   ] 
                                 
                               
                               + 
                               
                                 
                                   jQ 
                                   T 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   n 
                                   ] 
                                 
                               
                             
                           
                           ) 
                         
                       
                       ∈ 
                         
                       ⁢ 
                       
                         { 
                         
                           0 
                           , 
                           
                             + 
                             
                               π 
                               2 
                             
                           
                           , 
                           
                             - 
                             
                               π 
                               2 
                             
                           
                         
                         } 
                       
                     
                   
                 
                 
                   
                     
                       
                         arg 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 
                                   I 
                                   T 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     n 
                                     + 
                                     1 
                                   
                                   ] 
                                 
                               
                               + 
                               
                                 
                                   jQ 
                                   T 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     n 
                                     + 
                                     1 
                                   
                                   ] 
                                 
                               
                             
                             
                               
                                 
                                   I 
                                   T 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     n 
                                     + 
                                     
                                       1 
                                       / 
                                       2 
                                     
                                   
                                   ] 
                                 
                               
                               + 
                               
                                 
                                   jQ 
                                   T 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     n 
                                     + 
                                     
                                       1 
                                       / 
                                       2 
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                           ) 
                         
                       
                       ∈ 
                         
                       ⁢ 
                       
                         { 
                         
                           0 
                           , 
                           
                             + 
                             
                               π 
                               2 
                             
                           
                           , 
                           
                             - 
                             
                               π 
                               2 
                             
                           
                         
                         } 
                       
                     
                   
                 
               
             
             
               
                 [ 
                 
                   EQUATION 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   18 
                 
                 ] 
               
             
           
         
       
     
   
   In OQPSK spreading modulation shown in  FIG. 3   b,  the signal of the orthogonal phase channel (Q-channel) is delayed by a half cup (Tc/2) relative to the signal of the in-phase channel (I-channel) in order to improve the PAR characteristic of QPSK spreading modulation in  FIG. 3   a.  Due to a half chip (Tc/2) delay, the codes of the I-channel and Q-channel signals cannot be changed simultaneously. Thus, the π-transition crossing the origin is prohibited, and the PAR characteristic is improved. 
     FIG. 8   b  shows the transitions of the signal constellation point for the OQPSK spreading modulation when I T [n]=±1, Q T [n]=±1, and SF=4. For n≡0 mod SF, (I t [n], Q T [n]) becomes one of (+1, +1), (+1, −1), (−1, −1), (−1, +1) with an equal probability of 1/4. The transition is assumed to start at (+1, +1). At a chip time of n+1/2, (I T [n], Q T [n]) transits to either (+1, +1) or (+1, −1) with an equal probability of 1/2.  FIG. 8   b  shows the case of (+1, +1) transition: At a chip time of n+1, (I T [n], Q T [n]) transits to either (+1, +1) or (−1, +1) with an equal probability of 1/2.  FIG. 8   b  shows the case of (+1, +1) transition: At a chip time of n+3/2, (I T [n], Q T [n]) transits to either (+1, +1) or (+1, −1) with an equal probability of 1/2.  FIG. 8   b  shows the case of (+1, −1) transition: At a chip time of n+2, (I T [n], Q T [n]) transits to either (+1, −1) or (−1, −1) with an equal probability of 1/2.  FIG. 8   b  shows the case of (−1, −1) transition: At a chip time of n+5/2, (I T [n], Q T [n]) transits to either (−1, −1) or (−1, +1) with an equal probability of 1/2.  FIG. 8   b  shows the case of (−1, +1) transition: At a chip time of n+3, (I T [n], Q T [n]) transits to either (+1, +1) or (−1, +1) with an equal probability of 1/2.  FIG. 8   b  shows the case of (−1, +1) transition: At a chip time of n+7/2, (I T [n], Q T [n]) transits to either (−1, +1) or (−1, −1) with an equal probability of 1/2.  FIG. 8   b  shows the case of (−1, −1) transition: At a chip time of n+4, (I T [n], Q T [n]) transits to either (+1, −1) or (−1, −1) with an equal probability of 1/2. The above transition process is repeated according to the probability. 
     FIG. 3   c  shows a schematic diagram for another conventional spreading modulator. This spreading modulation method is subdivided into three methods according to the scrambling code generator ( 150 ). The first method is used in the forward link (from a base station to its mobile station) for a W-CDMA (Wideband CDMA) system as another candidate for cdma2000 or IMT-2000 system. This spreading modulation is called the CQPSK (Complex QPSK) spreading modulation, and the output signals are governed by EQUATION 19. 
                         I   T     ⁡     [   n   ]       +       jQ   T     ⁡     [   n   ]         =       ⁢       (         x   T     ⁡     [   n   ]       +       jy   T     ⁡     [   n   ]         )     ⁢     {       1     2       ⁢     (         C     scramble   ,   I       ⁡     [   n   ]       +       jC     scramble   ,   Q       ⁡     [   n   ]         )       }         ⁢     
     ⁢         I   T     ⁡     [   n   ]       =       ⁢         1     2       ⁢       x   T     ⁡     [   n   ]       ⁢       C     scramble   ,   I       ⁡     [   n   ]         -       1     2       ⁢       y   T     ⁡     [   n   ]       ⁢       C     scramble   ,   Q       ⁡     [   n   ]             ⁢     
     ⁢         Q   T     ⁡     [   n   ]       =       ⁢         1     2       ⁢       x   T     ⁡     [   n   ]       ⁢       C     scramble   ,   Q       ⁡     [   n   ]         -       1     2       ⁢       y   T     ⁡     [   n   ]       ⁢       C     scramble   ,   I       ⁡     [   n   ]                     [     EQUATION   ⁢           ⁢   19     ]               
The outputs (C scramble, I [n], C scramble, Q [n]) of the secondary scrambling code generator in  FIG. 4   a  are given by EQUATION 20. In other words, the secondary scrambling codes are the same as the primary scrambling codes, as described in the previous QPSK and OQPSK spreading modulation.
 C scramble, I [n]=C 1 [n]  [EQUATION 20] C scramble, Q [n]=C 2 [n] 
Generally x T [n]≠y T [n] in CQPSK spreading modulation. For |I T [n]|=|Q T [n]|=1 based on the normalization, the possible transitions of the signal constellation point occurring in the CQPSK spreading modulation are shown in EQUATION 21. The probability for {0, +π/2, −π/2, π) transition is equally 1/4 for each transition.
 
   
     
       
         
           
             
               
                 
                   arg 
                   ⁡ 
                   
                     ( 
                     
                       
                         
                           
                             I 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             
                               n 
                               + 
                               1 
                             
                             ] 
                           
                         
                         + 
                         
                           
                             jQ 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             
                               n 
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                       
                         
                           
                             I 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         + 
                         
                           
                             jQ 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                       
                     
                     ) 
                   
                 
                 ∈ 
                   
                 ⁢ 
                 
                   { 
                   
                     0 
                     , 
                     
                       + 
                       
                         π 
                         2 
                       
                     
                     , 
                     
                       - 
                       
                         π 
                         2 
                       
                     
                     , 
                     π 
                   
                   } 
                 
               
             
             
               
                 [ 
                 
                   EQUATION 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   21 
                 
                 ] 
               
             
           
         
       
     
   
   The previous OQPSK method is effective when the I-channel and Q-channel powers are the same as in IS-95 reverse link channels. But the Q-channel signal should be delayed by a half chip, and the amplitude of the transmitting power for I-channel is different from that for Q-channel in the case of  FIG. 1  when several channels with different transmitting powers are using orthogonal channels. The linear range of the amplifier should be selected based upon the largest transmitting signal power in order to reduce the neighboring channel interference from the signal distortion and the inter-modulation. 
   On the other hand, in CQPSK spreading modulation, I-channel signal (x T [n]) and Q-channel signal (y T [n]) are multiplied in complex-domain by the secondary scrambling codes, C scramble, I [n] and C scramble, Q [n] of the same amplitude. Therefore, the smaller of signal power level of the two (I and Q) become large, and the larger of signal power level of the two becomes small; the two signal power levels are equalized statistically. The CQPSK spreading modulation is more effective to improve the PAR characteristic when there are multiple channels with different power levels. In the CQPSK spreading modulation, x T [n]+jy T [n] makes an origin crossing transition (π-transition) with a probability of 1/4. 
     FIG. 8   c  shows the transitions of the signal constellation point for the CQPSK spreading modulation when x T [n]=±1, y T [n]=±1, I T [n]=±1, Q T [n]=±1, and SF=4. For n≡0 mod SF, x T [n]+jy T [n] and C scramble, I [n]+jC scramble, Q [n] become one of 1+j, 1−j, −1−j, −1+j with an equal probability of 1/4, and it is assumed that x T [n]+jy T [n]=1+j and C scramble, I [n]+jC scramble, Q [n]=1+j; in other words, in this case, I T [n]+jQ T [n]=0+j√{square root over (2)}. And this equation becomes I T [n]+jQ T [n]=0+jl due to the normalization. There is no change in the signal constellation diagram at a chip time of n+1/2. At a chip time of n+1, x T [n]+jy T [n] transits to one of 1+j, 1−j, −1−j, and −1+j, and C scramble, I [n]+jC scramble, Q [n] also transits to one of 1+j, 1−j, −1−j, and −1+j. 
   The second method is used in the reverse link (from a mobile station to its base station) for a G-CDMA (Global-CDMA) I and II systems as another candidate for IMT-2000 system proposed at International Telecommunications Union (ITU, http://www.itu.int) in June 1998. This spreading modulation is called the OCQPSK (Orthogonal Complex QPSK) spreading modulation referring to Korean Patent NO. 10-269593-0000. The following relations hold when only an even number is assigned to the subscript of the orthogonal Walsh code for each channel. 
   
     
       
         
           
             
               
                 
                   
                     
                       x 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       
                         2 
                         ⁢ 
                         n 
                       
                       ] 
                     
                   
                   ≃ 
                   
                     
                       x 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           2 
                           ⁢ 
                           n 
                         
                         + 
                         1 
                       
                       ] 
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       y 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       
                         2 
                         ⁢ 
                         n 
                       
                       ] 
                     
                   
                   ≃ 
                   
                     
                       y 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           2 
                           ⁢ 
                           n 
                         
                         + 
                         1 
                       
                       ] 
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       
                         I 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         n 
                         ] 
                       
                     
                     + 
                     
                       
                         jQ 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         n 
                         ] 
                       
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             x 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         + 
                         
                           
                             jy 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       { 
                       
                         
                           1 
                           
                             2 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 C 
                                 
                                   scramble 
                                   , 
                                   I 
                                 
                               
                               ⁡ 
                               
                                 [ 
                                 n 
                                 ] 
                               
                             
                             + 
                             
                               
                                 jC 
                                 
                                   scramble 
                                   , 
                                   Q 
                                 
                               
                               ⁡ 
                               
                                 [ 
                                 n 
                                 ] 
                               
                             
                           
                           ) 
                         
                       
                       } 
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       I 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       n 
                       ] 
                     
                   
                   = 
                   
                     
                       
                         1 
                         
                           2 
                         
                       
                       ⁢ 
                       
                         
                           x 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           C 
                           
                             scramble 
                             , 
                             I 
                           
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                     
                     - 
                     
                       
                         1 
                         
                           2 
                         
                       
                       ⁢ 
                       
                         
                           y 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           C 
                           
                             scramble 
                             . 
                             Q 
                           
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       Q 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       n 
                       ] 
                     
                   
                   = 
                   
                     
                       
                         1 
                         
                           2 
                         
                       
                       ⁢ 
                       
                         
                           x 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           C 
                           
                             scramble 
                             , 
                             Q 
                           
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                     
                     + 
                     
                       
                         1 
                         
                           2 
                         
                       
                       ⁢ 
                       
                         
                           y 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           C 
                           
                             scramble 
                             . 
                             I 
                           
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                     
                   
                 
               
             
             
               
                 [ 
                 
                   EQUATION 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   22 
                 
                 ] 
               
             
           
         
       
     
   
   The outputs (C scramble, I [n], C scramble, Q [n]) of the secondary scrambling code generator in  FIG. 4   b  are given by EQUATION 23. Since W 0   (p) [n]=1, the secondary scrambling code generators in  FIG. 4   b  and  FIG. 4   c  are the same for k=0.
 
 C   scramble,I   [n]+jC   scramble,Q   [n]=C   1   [n] ( W   2k   (p)   [n]+jW   2k+1   (p)   [n] )   [EQUATION 23]
 
 C   scramble,I   [n]=C   1   [n]W   2k   (p)   [n] 
 
 C   scramble,Q   [n]=C   1   [n]W   2k+1   (p)   [n] 
 
Where p is a power of 2 (i.e., p=2 n ), and
 
   
     
       
         
           k 
           ∈ 
           
             { 
             
               0 
               , 
               1 
               , 
               2 
               , 
               ⋯ 
               ⁢ 
               
                   
               
               , 
               
                 
                   p 
                   2 
                 
                 - 
                 1 
               
             
             } 
           
         
       
     
   
   Generally x T [n]≠y T [n] in OCQPSK spreading modulation. For |I T [n]|=|Q T [n]|=1 based on the normalization, the possible transitions of the signal constellation point occurring in the OCQPSK spreading modulation are shown in EQUATION 24. The probabilities for {0, +π/2, −π/2, π} transitions are 0, 1/2, 1/2, and 0 for n=2t+1 (odd number), and 1/4, 1/4, 1/4, and 1/4 in case of n=2t (even number) for each transition, respectively. 
                           I   T     ⁡     [     n   +   1     ]       +       jQ   T     [     n   +   1     }             I   T     ⁡     [   n   ]       +       jQ   T     ⁡     [   n   ]           =           (         x   T     ⁡     [     n   +   1     ]       +       jy   T     ⁡     [     n   +   1     ]         )     ⁢     (         C     scramble   ,   I       ⁡     [     n   +   1     ]       +       jC     scramble   ,   Q       ⁡     [     n   +   1     ]         )           (         x   T     ⁡     [   n   ]       +       jy   T     ⁡     [   n   ]         )     ⁢     (         C     scramble   ,   I       ⁡     [   n   ]       +       jC     scramble   ,   Q       ⁡     [   n   ]         )         ⁢     
     ⁢           =             x   T     ⁡     [     n   +   1     ]       +       jy   T     ⁡     [     n   +   1     ]               x   T     ⁡     [   n   ]       +       jy   T     ⁡     [   n   ]           ·           C   1     ⁡     [     n   +   1     ]       ⁢     (         W     2   ⁢   k       (   p   )       ⁡     [     n   +   1     ]       +       jW       2   ⁢   k     +   1       (   p   )       ⁡     [     n   +   1     ]         )             C   1     ⁡     [   n   ]       ⁢     (         W     2   ⁢   k       (   p   )       ⁡     [   n   ]       +       jW       2   ⁢   k     +   1       (   p   )       ⁡     [   n   ]         )               ⁢          ⁢       arg   ⁢     {           ⁢           I   T     ⁡     [       2   ⁢   t     +   1     ]       +       jQ   T     ⁡     [       2   ⁢   t     +   1     ]               I   T     ⁡     [     2   ⁢   t     ]       +       jQ   T     ⁡     [     2   ⁢   t     ]           ⁢           }       ⁢           ∈     {       +     π   2       ,     -     π   2         }       ⁢     
     ⁢       arg   ⁢     {           I   T     ⁡     [       2   ⁢   t     +   2     ]       +       jQ   T     ⁡     [       2   ⁢   t     +   2     ]               I   T     ⁡     [       2   ⁢   t     +   1     ]       +       jQ   T     ⁡     [       2   ⁢   t     +   1     ]           }       ∈     {     0   ,     +     π   2       ,     -     π   2       ,   π     }               [     EQUATION   ⁢           ⁢   24     ]               
In the OCQPSK spreading modulation, the following properties are used:
 
For W 2k   (p) [n],
 
             k   ∈     {     0   ,   1   ,   2   ,   …   ⁢           ,       P   2     -   1       }       ;         
W 2k   (p) [2t]=W 2k   (p) [2t+1], t∈{0, 1, 2, . . . }.
 
And for W 2k+1   (p) [n],
 
             k   ∈     {     0   ,   1   ,   2   ,   …   ⁢           ,       P   2     -   1       }       ;         
W 2k+1   (p) [2t]=−W 2k+1   (p) [2t+1], t∈{0, 1, 2, . . . }.
 
   The orthogonal Walsh codes with even number subscripts are used for the channel identification except for the case when the orthogonal Walsh codes with odd number subscripts must be used for the channel identification due to the high transmitting data rate. Because x T [2t]=x T [2t+1], y T [2t]=y T [2t+1], t∈{0, 1, 2, . . . }, the following approximation holds as described in EQUATION 25. 
   
     
       
         
           
             
               
                 
                   
                     
                       x 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       n 
                       ] 
                     
                   
                   + 
                   
                     
                       jy 
                       T 
                     
                     ⁡ 
                     
                       [ 
                       n 
                       ] 
                     
                   
                 
                 ≃ 
                 
                   
                     
                       G 
                       S2 
                     
                     ⁢ 
                     
                       
                         W 
                         SCH2 
                       
                       ⁡ 
                       
                         [ 
                         n 
                         ] 
                       
                     
                     ⁢ 
                     
                       
                         D 
                         SCH2 
                       
                       ⁡ 
                       
                         [ 
                         
                           ⌊ 
                           
                             n 
                             
                               SF 
                               SCH2 
                             
                           
                           ⌋ 
                         
                         ] 
                       
                     
                   
                   + 
                   
                     
                       jG 
                       S1 
                     
                     ⁢ 
                     
                       
                         W 
                         SCH1 
                       
                       ⁡ 
                       
                         [ 
                         n 
                         ] 
                       
                     
                     ⁢ 
                     
                       
                         D 
                         SCH1 
                       
                       ⁡ 
                       
                         [ 
                         
                           ⌊ 
                           
                             n 
                             
                               SF 
                               SCH1 
                             
                           
                           ⌋ 
                         
                         ] 
                       
                     
                   
                 
               
             
             
               
                 [ 
                 
                   EQUATION 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   25 
                 
                 ] 
               
             
           
         
       
     
   
   In the OCQPSK spreading modulation, avoiding the origin crossing transition (π-transition) which makes worse the PAR characteristic for n=2t+1, the PAR characteristic of the spreading signals is improved compared to the CQPSK spreading modulation. At n=2t, x T [n]+jy T [n] makes an origin crossing transition (π-transition) with a probability of 1/4 as in the CQPSK spreading modulation, while, at n=2t+1, the corresponding probability is zero. Therefore, the average probability for the origin crossing transition (π-transition) decreases to 1/8 from 1/4. C 1 [n] for the scrambling in  FIG. 4   b  is also used in identifying the transmitter. 
   The third method is used in the reverse link (from a mobile station to its base station) for a W-CDMA system as another candidate for cdma2000 and IMT-2000 system. This spreading modulation is POCQPSK (Permuted Orthogonal Complex QPSK) spreading modulation referring to Korean Patent NO. 10-269593-0000. The following relations hold when only an even number is assigned to the subscript of the orthogonal Walsh code for each channel. 
                       x   T     ⁡     [     2   ⁢           ⁢   n     ]       ≃       x   T     ⁡     [       2   ⁢           ⁢   n     +   1     ]         ⁢           ⁢         y   T     ⁡     [     2   ⁢           ⁢   n     ]       ≃       y   T     ⁡     [       2   ⁢           ⁢   n     +   1     ]         ⁢     
     ⁢                 I   T     ⁡     [   n   ]       +       jQ   T     ⁡     [   n   ]         =       (         x   T     ⁡     [   n   ]       +       jy   T     ⁡     [   n   ]         )     ⁢     {       1     2       ⁢     (         C     scramble   ,   I       ⁡     [   n   ]       +       jC     scramble   ,   Q       ⁡     [   n   ]         )       }                       I   T     ⁡     [   n   ]       =         1     2       ⁢       x   T     ⁡     [   n   ]       ⁢       C     scramble   ,   I       ⁡     [   n   ]         -       1     2       ⁢       y   T     ⁡     [   n   ]       ⁢       C     scramble   ,   Q       ⁡     [   n   ]                           Q   T     ⁡     [   n   ]       =         1     2       ⁢       x   T     ⁡     [   n   ]       ⁢       C     scramble   ,   Q       ⁡     [   n   ]         +       1     2       ⁢       y   T     ⁡     [   n   ]       ⁢       C     scramble   ,   I       ⁡     [   n   ]                           [     EQUATION   ⁢           ⁢   26     ]               
The outputs (C scramble, I [n], C scramble, Q [n]) of the secondary scrambling code generator in  FIG. 4   d  are given by EQUATION 27.
   C   scramble,I   [n]+jC   scramble,Q   [n]=C   1   [n] ( W   2k   (p)   [n]+jC′   2   [n]W   2k+1   (p)   [n] )   [EQUATION 27]   C   scramble,I   [n]=C   1   [n]W   2k   (p)   [n]     C   scramble,Q   [n]=C   1   [n]C′   2   [n]W   2k+1   (p)   [n]     C′   2 [2 t]=C′   2 [2 t+ 1]= C   2 [2 t],  t∈{0, 1, 2, . . . } 
   Generally x T [n]≠y T [n] in POCQPSK spreading modulation. For |I T [n]|=|Q T [n]|=1 based on the normalization, the possible transitions of the signal constellation point occurring in the POCQPSK spreading modulation are shown in EQUATION 28. The probabilities for {0, +π/2, −π/2, π} transition is 0, 1/2, 1/2, and 0 for n=2t+1 (odd number), and 1/4, 1/4, 1/4, and 1/4 in case of n=2t (even number) for each transition, respectively. 
   
     
       
         
           
             
               
                 
                   
                     I 
                     T 
                   
                   ⁡ 
                   
                     [ 
                     
                       
                         2 
                         ⁢ 
                         t 
                       
                       + 
                       2 
                     
                     ] 
                   
                 
                 + 
                 
                   
                     jQ 
                     T 
                   
                   ⁡ 
                   
                     [ 
                     
                       
                         2 
                         ⁢ 
                         t 
                       
                       + 
                       2 
                     
                     ] 
                   
                 
               
               
                 
                   
                     I 
                     T 
                   
                   ⁡ 
                   
                     [ 
                     
                       
                         2 
                         ⁢ 
                         t 
                       
                       + 
                       1 
                     
                     ] 
                   
                 
                 + 
                 
                   
                     jQ 
                     T 
                   
                   ⁡ 
                   
                     [ 
                     
                       
                         2 
                         ⁢ 
                         t 
                       
                       + 
                       1 
                     
                     ] 
                   
                 
               
             
             = 
             
               
                 
                   
                     ( 
                     
                       
                         
                           x 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             2 
                           
                           ] 
                         
                       
                       + 
                       
                         
                           jy 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             2 
                           
                           ] 
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           C 
                           
                             scramble 
                             , 
                             I 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             2 
                           
                           ] 
                         
                       
                       + 
                       
                         
                           jC 
                           
                             scramble 
                             , 
                             Q 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             2 
                           
                           ] 
                         
                       
                     
                     ) 
                   
                 
                 
                   
                     ( 
                     
                       
                         
                           x 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                       + 
                       
                         
                           jy 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           C 
                           
                             scramble 
                             , 
                             I 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                       + 
                       
                         
                           jC 
                           
                             scramble 
                             , 
                             Q 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                     
                     ) 
                   
                 
               
               ⁢ 
               
                   
               
               = 
               
                 
                   
                     
                       
                         x 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             2 
                             ⁢ 
                             t 
                           
                           + 
                           2 
                         
                         ] 
                       
                     
                     + 
                     
                       
                         jy 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             2 
                             ⁢ 
                             t 
                           
                           + 
                           2 
                         
                         ] 
                       
                     
                   
                   
                     
                       
                         x 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             2 
                             ⁢ 
                             t 
                           
                           + 
                           1 
                         
                         ] 
                       
                     
                     + 
                     
                       
                         jy 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             2 
                             ⁢ 
                             t 
                           
                           + 
                           1 
                         
                         ] 
                       
                     
                   
                 
                 · 
                 
                   
                     
                       W 
                       
                         2 
                         ⁢ 
                         k 
                       
                       
                         ( 
                         p 
                         ) 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           2 
                           ⁢ 
                           t 
                         
                         + 
                         2 
                       
                       ] 
                     
                   
                   
                     
                       W 
                       
                         2 
                         ⁢ 
                         k 
                       
                       
                         ( 
                         p 
                         ) 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           2 
                           ⁢ 
                           t 
                         
                         + 
                         1 
                       
                       ] 
                     
                   
                 
                 · 
                 
                   
                     
                       C 
                       1 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           2 
                           ⁢ 
                           t 
                         
                         + 
                         2 
                       
                       ] 
                     
                   
                   
                     
                       C 
                       1 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           2 
                           ⁢ 
                           t 
                         
                         + 
                         1 
                       
                       ] 
                     
                   
                 
                 · 
                 
                   
                     1 
                     + 
                     
                       
                         
                           
                             jC 
                             ′ 
                           
                           2 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             2 
                           
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           W 
                           1 
                           
                             ( 
                             p 
                             ) 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             2 
                           
                           ] 
                         
                       
                     
                   
                   
                     1 
                     + 
                     
                       
                         
                           
                             jC 
                             ′ 
                           
                           2 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           W 
                           1 
                           
                             ( 
                             p 
                             ) 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                     
                   
                 
               
             
           
           ⁢ 
           
               
           
         
       
     
     
       
         
           
               
           
           ⁢ 
           
             
               arg 
               ⁢ 
               
                   
               
               ⁢ 
               
                 { 
                 
                   
                     
                       
                         I 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             2 
                             ⁢ 
                             t 
                           
                           + 
                           2 
                         
                         ] 
                       
                     
                     + 
                     
                       
                         jQ 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             2 
                             ⁢ 
                             t 
                           
                           + 
                           2 
                         
                         ] 
                       
                     
                   
                   
                     
                       
                         I 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             2 
                             ⁢ 
                             t 
                           
                           + 
                           1 
                         
                         ] 
                       
                     
                     + 
                     
                       
                         jQ 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             2 
                             ⁢ 
                             t 
                           
                           + 
                           1 
                         
                         ] 
                       
                     
                   
                 
                 } 
               
             
             ∈ 
             
               { 
               
                 0 
                 , 
                 
                   + 
                   
                     π 
                     2 
                   
                 
                 , 
                 
                   - 
                   
                     π 
                     2 
                   
                 
                 , 
                 π 
               
               } 
             
           
         
       
     
     
       
         
           
             
               
                 
                   
                     
                       
                         I 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             2 
                             ⁢ 
                             t 
                           
                           + 
                           1 
                         
                         ] 
                       
                     
                     + 
                     
                       
                         jQ 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             2 
                             ⁢ 
                             t 
                           
                           + 
                           1 
                         
                         ] 
                       
                     
                   
                   
                     
                       
                         I 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           2 
                           ⁢ 
                           t 
                         
                         ] 
                       
                     
                     + 
                     
                       
                         jQ 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           2 
                           ⁢ 
                           t 
                         
                         ] 
                       
                     
                   
                 
                 = 
                 
                   
                     
                       
                         
                           x 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                       + 
                       
                         
                           jy 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                     
                     
                       
                         
                           x 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           
                             2 
                             ⁢ 
                             t 
                           
                           ] 
                         
                       
                       + 
                       
                         
                           jy 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           
                             2 
                             ⁢ 
                             t 
                           
                           ] 
                         
                       
                     
                   
                   · 
                   
                     
                       
                         
                           C 
                           
                             scramble 
                             , 
                             I 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                       + 
                       
                         
                           jC 
                           
                             scramble 
                             , 
                             Q 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                     
                     
                       
                         
                           C 
                           
                             scramble 
                             , 
                             I 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             2 
                             ⁢ 
                             t 
                           
                           ] 
                         
                       
                       + 
                       
                         
                           jC 
                           
                             scramble 
                             , 
                             Q 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             2 
                             ⁢ 
                             t 
                           
                           ] 
                         
                       
                     
                   
                 
               
             
           
           
             
               
                 = 
                 
                   
                     
                       
                         C 
                         1 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             2 
                             ⁢ 
                             t 
                           
                           + 
                           1 
                         
                         ] 
                       
                     
                     
                       
                         C 
                         1 
                       
                       ⁡ 
                       
                         [ 
                         
                           2 
                           ⁢ 
                           t 
                         
                         ] 
                       
                     
                   
                   · 
                   
                     
                       
                         
                           W 
                           
                             2 
                             ⁢ 
                             k 
                           
                           
                             ( 
                             p 
                             ) 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                       + 
                       
                         
                           
                             
                               jC 
                               ′ 
                             
                             2 
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 2 
                                 ⁢ 
                                 t 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                         ⁢ 
                         
                           
                             W 
                             
                               
                                 2 
                                 ⁢ 
                                 k 
                               
                               + 
                               1 
                             
                             
                               ( 
                               p 
                               ) 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 2 
                                 ⁢ 
                                 t 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                     
                       
                         
                           W 
                           
                             2 
                             ⁢ 
                             k 
                           
                           
                             ( 
                             p 
                             ) 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             2 
                             ⁢ 
                             t 
                           
                           ] 
                         
                       
                       + 
                       
                         
                           
                             
                               jC 
                               ′ 
                             
                             2 
                           
                           ⁡ 
                           
                             [ 
                             
                               2 
                               ⁢ 
                               t 
                             
                             ] 
                           
                         
                         ⁢ 
                         
                           
                             W 
                             
                               
                                 2 
                                 ⁢ 
                                 k 
                               
                               + 
                               1 
                             
                             
                               ( 
                               p 
                               ) 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               2 
                               ⁢ 
                               t 
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
             
           
           
             
               
                 
                   = 
                   
                     
                       
                         
                           C 
                           1 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               2 
                               ⁢ 
                               t 
                             
                             + 
                             1 
                           
                           ] 
                         
                       
                       
                         
                           C 
                           1 
                         
                         ⁡ 
                         
                           [ 
                           
                             2 
                             ⁢ 
                             t 
                           
                           ] 
                         
                       
                     
                     · 
                     
                       
                         1 
                         - 
                         
                           
                             
                               
                                 jC 
                                 ′ 
                               
                               2 
                             
                             ⁡ 
                             
                               [ 
                               
                                 2 
                                 ⁢ 
                                 t 
                               
                               ] 
                             
                           
                           ⁢ 
                           
                             
                               W 
                               1 
                               
                                 ( 
                                 p 
                                 ) 
                               
                             
                             ⁡ 
                             
                               [ 
                               
                                 2 
                                 ⁢ 
                                 t 
                               
                               ] 
                             
                           
                         
                       
                       
                         1 
                         + 
                         
                           
                             
                               
                                 jC 
                                 ′ 
                               
                               2 
                             
                             ⁡ 
                             
                               [ 
                               
                                 2 
                                 ⁢ 
                                 t 
                               
                               ] 
                             
                           
                           ⁢ 
                           
                             
                               W 
                               1 
                               
                                 ( 
                                 p 
                                 ) 
                               
                             
                             ⁡ 
                             
                               [ 
                               
                                 2 
                                 ⁢ 
                                 t 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     arg 
                     ⁢ 
                     
                       { 
                       
                         
                           
                             
                               I 
                               T 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   2 
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 1 
                               
                               ] 
                             
                           
                           + 
                           
                             
                               jQ 
                               T 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   2 
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 1 
                               
                               ] 
                             
                           
                         
                         
                           
                             
                               I 
                               T 
                             
                             ⁡ 
                             
                               [ 
                               
                                 2 
                                 ⁢ 
                                 t 
                               
                               ] 
                             
                           
                           + 
                           
                             
                               jQ 
                               T 
                             
                             ⁡ 
                             
                               [ 
                               
                                 2 
                                 ⁢ 
                                 t 
                               
                               ] 
                             
                           
                         
                       
                       } 
                     
                   
                   ∈ 
                   
                     { 
                     
                       
                         + 
                         
                           π 
                           2 
                         
                       
                       , 
                       
                         - 
                         
                           π 
                           2 
                         
                       
                     
                     } 
                   
                 
               
             
           
         
       
     
   
   The POCQPSK spreading modulation is basically the same as the OCQPSK spreading modulation. Therefore, at n=2t, x T [n]+jy T [n] makes an origin crossing transition (π-transition) with a probability of 1/4 as described in the CQPSK spreading modulation, while, at n=2t+1, the corresponding probability is zero. C′ 2 [n] decimated from C 2 [n] is used in order to compensate for the lack of the randomness due to a periodic repetition of the orthogonal Walsh functions. The decimation should be made with the following properties: For t∈{0, 1, 2, . . . } and 
             k   ∈     {     0   ,   1   ,   2   ,   …   ⁢           ,       P   2     -   1       }       ,         
W 2k+1   (p) [2t]=−W 2k+1   (p) [2t+1], and C′ 2 [2t]W 2k+1   (p) [2t]=−C′ 2 [2t+1]W 2k+1   (p) [2t+1].
 
Even though C 2 [n] is decimated to 2:1 in the above case, 2 d :1 decimation for d∈{1, 2, 3, . . . } is also possible. When 2 d =max{SF PiCH , SF DCCH , SF SCH2 , SF SCH1 , SF FCD }, the randomness of the POCQPSK is the same as that of the OCQPSK, and the randomness becomes high for 2:1 decimation with d=1. C 1 [n] and C 2 [n] for the scrambling to obtain the better spectrum characteristic are also used to identify the transmitter through the auto-correlation and the cross-correlation. The number of identifiable transmitters increases when both of C 2 [n] and C 2 [n] are used as the scrambling codes.
 
     FIG. 9  and  FIG. 10  show schematic diagrams for a transmitter and a receiver using the POCQPSK spreading modulation.  FIG. 9  shows a schematic diagram for the transmitter based on the cdma2000 system, which is one of the candidates for IMT-2000 system as a third generation mobile communication system. The transmitter has five orthogonal channels: PiCH, DCCH, FCH, SCH 1 , and SCH 2 . Each channel performs the signal conversion process by changing a binary data {0, 1} into {+1, −1}. 
   The gain controlled signal for each channel is spread at the spreader ( 120 ,  122 ,  124 ,  126 ,  128 ) with the orthogonal OVSF code W PiCH [n], W DCCH [n], W SCH2 [n], W SCH1 [n], or W FCH [n], and is delivered to the adder ( 130 ,  132 ). The spreading modulation takes place at the Spreading Modulator ( 140 ) with the first inputs (x T [n], y T [n]) and the second inputs (the primary scrambling codes; C 1 [n] and C 2 [n]), and the outputs (I T [n], Q T [n]) are generated. The spreading modulator ( 140 ) comprises the scrambling code generator ( 510 ) and the first complex-domain multiplier ( 143 ). The scrambling code generator ( 510 ) produces the secondary scrambling codes (C scramble, I [n], C scramble, Q [n]) with the primary scrambling codes (C 1 [n], C 2 [n]) as the inputs to improve the PAR characteristic. The first complex-domain multiplier ( 143 ) takes x T [n] and y T [n] as inputs and the secondary scrambling codes (C scramble, I [n], C scramble, Q [n]) as another inputs. 
   The primary scrambling codes (C 1 [n], C 2 [n]) in the cdma2000 system is produced by the primary scrambling code generator ( 550 ) using three PN sequences (PN I [n], PN Q [n], PN long [n]) as shown in  FIG. 5   a  with the following equation:
 
 C   1   [n]=PN   I   [n]PN   long   [n]   [EQUATION 29]
 
 C   2   [n]=PN   Q   [n]PN   long   [n− 1]
 
The secondary scrambling codes (C scramble, I [n], C scramble, Q [n]) are given by the following equation:
 
 C   scramble,I   [n]=C   1   [n]W   0   (p)   [n]=C   1   [n]   [EQUATION 30]
 
 C   scramble,Q   [n]=C   1   [n]C′   2   [n]W   1   (p)   [n] 
 
 C′   2 [2 t]=C′   2 [2 t+ 1]= C   2 [2 t],  t∈{0, 1, 2, . . .}
 
The outputs (I T [n], Q T [n]) of the Spreading Modulator ( 140 ) pass through the low-pass filters ( 160 ,  162 ) and power amplifiers ( 170 ,  172 ). Then the amplified outputs are delivered to the modulators ( 180 ,  182 ) which modulate the signals into the desired frequency band using a carrier. And the modulated signals are added by the adder ( 190 ), and delivered to an antenna.
 
     FIG. 10  shows a schematic diagram for a receiver according to the transmission of  FIG. 9 . The received signals through an antenna are demodulated at the demodulators ( 280 ,  282 ) with the same carrier used at the transmitter, and I R [n] and Q R [n] are generated after the signals pass through the low-pass filters ( 260 ,  262 ). Then, the spreading demodulator ( 240 ) produces the signals (x R [n], y R [n]) with the primary scrambling codes (C 1 [n], C 2 [n]). The spreading demodulator ( 240 ) comprises the scrambling code generator ( 510 ) and the second complex-domain multiplier ( 243 ). The scrambling code generator ( 510 ) produces the secondary scrambling codes (C scramble, I[n], C   scramble, Q [n]) with the primary scrambling codes (C 1 [n], C 2 [n]) as the inputs to improve the PAR characteristic. The second complex-domain multiplier ( 243 ) in the spreading demodulator ( 240 ) takes the I R [n], Q R [n] as the first inputs and the secondary scrambling codes (C scramble, I [n], C scramble, Q [n]) as the second inputs. The first and secondary scrambling codes are generated by the same method as in the transmitter. 
   In order to select the desired channels among the outputs (x R [n], y R [n]) of the spreading demodulator ( 240 ), the signals are multiplied by the same orthogonal code W xxCH [n] (where, xxCH=DCCH or FCH) or W yyCH [n] (where, yyCH=SCH 1  or SCH 2 ) used at the transmitter, at the despreaders ( 224 ,  226 ,  225 ,  227 ). Then, the signals are integrated during the symbol period T 2x  or T 2y . Since the signals at the receiver are distorted, PiCH is used to correct the distorted signal phase. Therefore, the signals (x R [n], y R [n]) are multiplied by the corresponding orthogonal code W PiCH [n], and are integrated during the period of T 1  at the integrators ( 210 ,  212 ). 
   The reverse link PiCH in the cdma2000 system may include additional information such as a control command to control the transmitting power at the receiver, besides the pilot signals for the phase correction. In this case, the additional information is extracted by the de-multiplexer, and the phase is estimated using the part of the pilot signals having the known phase. The phase corrections are performed at the second (kind) complex-domain multipliers ( 242 ,  246 ) shown in the left of  FIG. 10  using the estimated phase information through the integrators ( 210 ,  212 ). 
   However, the conventional CDMA systems have two problems: The first problem is that the strict condition for the linearity of the power amplifier is required. The second problem is when there are several transmitting channels, the signal distortion and the neighboring frequency interference should be reduced. Therefore, the expensive power amplifiers with the better linear characteristic are required. 
   DISCLOSURE OF THE INVENTION  
   The object of this invention is to provide a method and an apparatus for the spreading modulation method in CDMA spread spectrum communication systems to solve the above mentioned problems. In the spreading modulation method according to this invention, the probability for the spread signals (x T [n]+jy T [n]) to make the origin crossing transition (π-transition) becomes zero not only at n=2t+1, t∈{0, 1, 2, . . . } as in cases of the OCQPSK and POCQPSK spreading modulation but also at n=2t only except for the time n≡0 (mod min{SF PiCH , SF DCCH , SF SCH2 , SF SCF1 , SF FCH }) when the spreading transmitting data vary. Therefore, the PAR characteristic is improved by using the proposed spreading modulation scheme. In other words, this invention provides a method and an apparatus for the spreading modulation method with improved PAR characteristic in CDMA spread spectrum communication systems. 
   In accordance with an aspect of this invention an apparatus and a method for spreading modulation are invented in CDMA systems with a transmitter and receivers. 
   The transmitter according to the proposed invention has several channels with different information. Each channel spreads with the orthogonal codes using a complex-domain multiplier in addition to the conventional spreaders, and the spread signals are added. Then the signals are scrambled with the PN sequences, are modulated with a carrier, and are delivered to an antenna. 
   The receiver according to the invention demodulates the received signals with the same carrier used in the transmitter. The demodulated mixed signals are de-scrambled with the same synchronized PN sequences, and the de-scrambled signals are de-spread with the same synchronized orthogonal codes using a complex-domain multiplier in addition to the conventional de-spreaders. Then the desired information is recovered at the receiver with the conventional signal processing. 
   In a preferred embodiment, the transmitter according to the invention has an additional complex-domain multiplier and a special scrambling code generator. The probability for the spread signals (x T [n]+jy T [n]) to make the origin crossing transition (π-transition) becomes zero not only for n=2t+1, t∈{0, 1, 2, . . . } but also for n=2t only except for the time n≡0 (mod min {SF PiCH , SF DCCH , SF SCH2 , SF SCH1 , SF FCH} ) when the spread transmitting data vary. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Exemplary embodiments of the present invention will be described in conjunction with the drawings in which: 
       FIG. 1  shows a schematic diagram for a conventional CDMA transmitter with orthogonal multiple channels; 
       FIG. 2  shows a schematic diagram for a receiver according to the transmitter of  FIG. 1 ; 
       FIG. 3   a  shows a schematic diagram for a conventional QPSK spreading modulator; 
       FIG. 3   b  shows a schematic diagram for a conventional OQPSK spreading modulator; 
       FIG. 3   c  shows a schematic diagram for a conventional CQPSK, OCQPSK, POCQPSK spreading modulator and for a spreading modulator according to the present invention; 
       FIG. 3   d  shows another schematic diagram for a conventional OCQPSK, POCQPSK spreading modulator; 
       FIG. 4   a  shows a schematic diagram for the scrambling code generator in the QPSK, OQPSK, CQPSK spreading modulation; 
       FIG. 4   b  shows a schematic diagram for the scrambling code generator in the OCQPSK spreading modulation; 
       FIG. 4   c  shows another schematic diagram for the scrambling code generator in the OCQPSK spreading modulation; 
       FIG. 4   d  shows a schematic diagram for the scrambling code generator in the POCQPSK spreading modulation; 
       FIG. 5   a  shows schematic diagrams for the first and secondary scrambling code generators in the cdma2000 modulation; 
       FIG. 5   b  shows a general diagram for the secondary scrambling code generator in  FIG. 5   a;    
       FIG. 6   a  shows a schematic diagram for a conventional CQPSK, OCQPSK, POCQPSK spreading demodulator and for a spreading demodulator according to the present invention; 
       FIG. 6   b  shows a schematic diagram for a conventional OCQPSK, POCQPSK spreading demodulator; 
       FIG. 7   a  shows a signal constellation diagram and transitions; 
       FIG. 7   b  shows four possible transitions of a signal constellation point; 
       FIG. 8   a  shows the transition of a signal constellation point for the QPSK spreading modulation; 
       FIG. 8   b  shows the transitions of a signal constellation point for the OQPSK spreading modulation; 
       FIG. 8   c  shows the transitions of a signal constellation point for the CQPSK spreading modulation; 
       FIG. 9  shows a schematic diagram for a cdma2000 transmitter; 
       FIG. 10  shows a schematic diagram for a cdma2000 receiver according to the transmitter of  FIG. 9 ; 
       FIG. 11   a  shows a schematic diagram for a transmitter according to the present invention; 
       FIG. 11   b  shows a schematic diagram for the scrambling code generator in the DCQPSK spreading modulation according to the present invention; and 
       FIG. 12  shows a schematic diagram for a receiver according to the transmitter of  FIG. 11   a.    
   

   &lt;Explanations for main symbols in the drawings&gt;
       110 ,  112 ,  114 ,  116 ,  118 : gain controller     120 ,  122 ,  124 ,  126 ,  128 : spreader     130 ,  132 : adder     140 ,  141 : spreading modulator     143 ,  145 : first (kind) complex(-domain) multiplier     150 ,  151 : scrambling code generator     160 ,  162 : low-pass filter (LPF)     170 ,  172 : power amplifier     180 ,  182 : modulator     190 : adder     210 ,  212 ,  214 ,  215 ,  216 ,  217 : integrator     220 ,  222 ,  224 ,  226 ,  225 ,  227 : de-spreader     240 ,  241 : spreading demodulator     242 ,  243 ,  245 ,  246 : second (kind) complex(-domain) multiplier     260 ,  262 : low-pass filter     280 ,  282 : demodulator     510 ,  520 ,  530 ,  550 : scrambling code generator     1220 ,  1222 ,  1224 ,  1226 : de-spreader   

   BEST MODE FOR CARRYING OUT THE INVENTION  
   The present invention will be better understood with regard to the following description, appended claims, and accompanying figures. In this application, similar reference numbers are used for components similar to the prior art and the modified or added components in comparison with the prior art are described for the present invention in detail. 
     FIG. 11  and  FIG. 12  show schematic diagram for a transmitter and a receiver according to the present invention, respectively. The transmitter in  FIG. 11   a  and the receiver in  FIG. 12  are modified from the transmitter and the receiver with the POCQPSK spreading modulator shown in  FIG. 9  and  FIG. 10 . The transmitter according to the invention has 5 orthogonal channels: PiCH, DCCH, FCH, SCH 1 , and SCH 2 . 
   Unlike the previous transmitter as in  FIG. 9 , the transmitter according to the invention has an additional complex-domain multiplier ( 145 ) shown in the left of  FIG. 11   a.  The complex-domain multiplier ( 145 ) takes the transmitting data 
           (         D     SCH   ⁢           ⁢   1       ⁡     [     [     n     SF     SCH   ⁢           ⁢   1         ]     ]       ,           ⁢       D     SCH   ⁢           ⁢   2       ⁡     [     [     n     SF     SCH   ⁢           ⁢   2         ]     ]         )         
of SCH 1  and SCH 2  of statistically high transmitting power as the first inputs and takes the orthogonal OVSF codes (H SCH1 [n], H SCH2 [n]) as the second inputs. And the first orthogonal complex-domain spreading occurs at the complex-domain multiplier ( 145 ). Other gain-controlled signals for PiCH, DCCH and FCH spread at the spreaders ( 1120 ,  1122 ,  1128 ) with orthogonal OVSF codes (H PiCH [n], H DCCH [n], H FCH [n]), and are delivered to the adders ( 130 ,  132 ) with the outputs (S I [n], S Q [n]) of the complex-domain multiplier ( 145 ). The outputs (x T [n], y T [n]) of the adder ( 130 ,  132 ) are given in EQUATION 31.
 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           x 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         
                           
                             G 
                             p 
                           
                           ⁢ 
                           
                             
                               H 
                               
                                 Π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 CH 
                               
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                           ⁢ 
                           
                             
                               D 
                               
                                 Π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 CH 
                               
                             
                             ⁡ 
                             
                               [ 
                               
                                 ⌊ 
                                 
                                   n 
                                   
                                     SF 
                                     
                                       Π 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       CH 
                                     
                                   
                                 
                                 ⌋ 
                               
                               ] 
                             
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             G 
                             D 
                           
                           ⁢ 
                           
                             
                               H 
                               DCCH 
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                           ⁢ 
                           
                             
                               D 
                               DCCH 
                             
                             ⁡ 
                             
                               [ 
                               
                                 ⌊ 
                                 
                                   n 
                                   
                                     SF 
                                     DCCH 
                                   
                                 
                                 ⌋ 
                               
                               ] 
                             
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             1 
                             
                               2 
                             
                           
                           ⁢ 
                           
                             G 
                             
                               S 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               H 
                               
                                 SCH 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             [ 
                             n 
                             } 
                           
                           ⁢ 
                           
                             
                               D 
                               
                                 SCH 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁡ 
                             
                               [ 
                               
                                 ⌊ 
                                 
                                   n 
                                   
                                     SF 
                                     
                                       SCH 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                 
                                 ⌋ 
                               
                               ] 
                             
                           
                         
                         - 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           1 
                           
                             2 
                           
                         
                         ⁢ 
                         
                           G 
                           
                             S 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ⁢ 
                         
                           
                             H 
                             
                               SCH 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         ⁢ 
                         
                           
                             D 
                             
                               SCH 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               ⌊ 
                               
                                 n 
                                 
                                   SF 
                                   
                                     SCH 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                               ⌋ 
                             
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       ≃ 
                         
                       ⁢ 
                       
                         
                           
                             1 
                             
                               2 
                             
                           
                           ⁢ 
                           
                             G 
                             
                               S 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               H 
                               
                                 SCH 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                           ⁢ 
                           
                             
                               D 
                               
                                 SCH 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁡ 
                             
                               [ 
                               
                                 ⌊ 
                                 
                                   n 
                                   
                                     SF 
                                     
                                       SCH 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                 
                                 ⌋ 
                               
                               ] 
                             
                           
                         
                         - 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           1 
                           
                             2 
                           
                         
                         ⁢ 
                         
                           G 
                           
                             S 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ⁢ 
                         
                           
                             H 
                             
                               SCH 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         ⁢ 
                         
                           
                             D 
                             
                               SCH 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               ⌊ 
                               
                                 2 
                                 
                                   SF 
                                   
                                     SCH 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                               ⌋ 
                             
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           y 
                           T 
                         
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         
                           
                             G 
                             F 
                           
                           ⁢ 
                           
                             
                               H 
                               FCH 
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                           ⁢ 
                           
                             
                               D 
                               FCH 
                             
                             ⁡ 
                             
                               [ 
                               
                                 ⌊ 
                                 
                                   n 
                                   
                                     SF 
                                     FCH 
                                   
                                 
                                 ⌋ 
                               
                               ] 
                             
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             1 
                             
                               2 
                             
                           
                           ⁢ 
                           
                             G 
                             
                               S 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁢ 
                           
                             
                               H 
                               
                                 SCH 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                           ⁢ 
                           
                             
                               D 
                               
                                 SCH 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             ⁡ 
                             
                               [ 
                               
                                 ⌊ 
                                 
                                   n 
                                   
                                     SF 
                                     
                                       SCH 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                   
                                 
                                 ⌋ 
                               
                               ] 
                             
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           1 
                           
                             2 
                           
                         
                         ⁢ 
                         
                           G 
                           
                             S 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         ⁢ 
                         
                           
                             H 
                             
                               SCH 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         ⁢ 
                         
                           
                             D 
                             
                               SCH 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               ⌊ 
                               
                                 n 
                                 
                                   SF 
                                   
                                     SCH 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                 
                               
                               ⌋ 
                             
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       ≃ 
                         
                       ⁢ 
                       
                         
                           
                             1 
                             
                               2 
                             
                           
                           ⁢ 
                           
                             G 
                             
                               S 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁢ 
                           
                             
                               H 
                               
                                 SCH 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                           ⁢ 
                           
                             
                               D 
                               
                                 SCH 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             ⁡ 
                             
                               [ 
                               
                                 ⌊ 
                                 
                                   n 
                                   
                                     SF 
                                     
                                       SCH 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                   
                                 
                                 ⌋ 
                               
                               ] 
                             
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           1 
                           
                             2 
                           
                         
                         ⁢ 
                         
                           G 
                           
                             S 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         ⁢ 
                         
                           
                             H 
                             
                               SCH 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         ⁢ 
                         
                           
                             D 
                             
                               SCH 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               ⌊ 
                               
                                 n 
                                 
                                   SF 
                                   
                                     SCH 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                 
                               
                               ⌋ 
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 [ 
                 
                   EQUATION 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   31 
                 
                 ] 
               
             
           
         
       
     
   
   The spreading modulation takes place at the Spreading Modulator ( 141 ) with the first inputs (x T [n], y T [n]) and the second inputs (the primary scrambling codes; C 1 [n] and C 2 [n]), and the outputs (I T [n], Q T [n]) are generated. The spreading modulator ( 141 ) comprises the scrambling code generator ( 530 ) and the complex-domain multiplier ( 143 ). The scrambling code generator ( 530 ) according to the present invention shown in  FIG. 11   b  generates the secondary scrambling codes (C scramble, I [n], C scramble, Q [n]) with the primary scrambling codes (C 1 [n], C 2 [n]) as the inputs to improve the PAR characteristic. The complex-domain multiplier ( 143 ) takes the x T [n], y T [n] as inputs and the secondary scrambling codes (C scramble, I [n], C scramble, Q [n]) as another inputs. The primary scrambling codes (C 1 [n], C 2 [n]) in the cdma2000 system are generated by the primary scrambling code generator ( 550 ) using three PN sequences (PN I [n], PN Q [n], PN long [n]) as shown in  FIG. 5   a  with the following equation:
 
 C   1   [n]=PN   I   [n]PN   long   [n]   [EQUATION 32]
 
 C   2   [n]=PN   Q   [n]PN   long   [n− 1]
 
The secondary scrambling codes (C scramble, I [n], C scramble, Q [n]) shown in  FIG. 11   b  are given by the following equations.
 
   (1) For n≡0 mod min{SF PiCH , SF DCCH , SF SCH2 , SF SCH1 , SF FCH ) 
   
     
       
         
           
             
               
                 
                   
                     C 
                     
                       scramble 
                       . 
                       I 
                     
                   
                   ⁡ 
                   
                     [ 
                     n 
                     ] 
                   
                 
                 = 
                 
                   
                     C 
                     1 
                   
                   ⁡ 
                   
                     [ 
                     n 
                     ] 
                   
                 
               
             
             
               
                 [ 
                 
                   EQUATION 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   33 
                 
                 ] 
               
             
           
           
             
               
                 
                   
                     C 
                     
                       scramble 
                       . 
                       Q 
                     
                   
                   ⁡ 
                   
                     [ 
                     n 
                     ] 
                   
                 
                 = 
                 
                   
                     C 
                     2 
                   
                   ⁡ 
                   
                     [ 
                     n 
                     ] 
                   
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   arg 
                   ⁢ 
                   
                     { 
                     
                       
                         
                           
                             I 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         + 
                         
                           
                             jQ 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                       
                       
                         
                           
                             I 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             
                               n 
                               - 
                               1 
                             
                             ] 
                           
                         
                         + 
                         
                           
                             jQ 
                             T 
                           
                           ⁡ 
                           
                             [ 
                             
                               n 
                               - 
                               1 
                             
                             ] 
                           
                         
                       
                     
                     } 
                   
                 
                 ∈ 
                 
                   { 
                   
                     0 
                     , 
                     
                       + 
                       
                         π 
                         2 
                       
                     
                     , 
                     
                       - 
                       
                         π 
                         2 
                       
                     
                     , 
                     π 
                   
                   } 
                 
               
             
             
               
                   
               
             
           
         
       
     
   
   (2) For n≢0 mod min{SF PiCH , SF DCCH , SF SCH2 , SF SCH1 , SF FCH }
 
 C   scramble,I   [n]+jC   scramble,Q   [n]=jC   2   [n]{C   scramble,I   [n− 1] H   SCH1   [n− 1] H   SCH1   [n]+jC   scramble,Q   [n− 1] H   SCH2   [n− 1] H   SCH2   [n]}   [EQUATION 34]
 
 C   scramble,I   [n]=−C   2   [n]C   scramble,Q   [n− 1] H   SCH2   [n− 1] H   SCH2   [n] 
 
 C   scramble,Q   [n]=−C   2   [n]C   scramble,I   [n− 1] H   SCH1   [n− 1] H   SCH1   [n] 
 
   The spreading modulation according to the present invention is called the PCQPSK (Double Complex QPSK) spreading modulation. For |I T [n]|=|Q T [n]|=1 based on the normalization, the possible transitions of the signal constellation point occurring in the DCQPSK spreading modulation are shown in EQUATION 35 and EQUATION 36. The probabilities for {0, +π/2, −π/2, π} transitions are 1/4, 1/4, 1/4, and 1/4 for n≡0 mod SF min , and 0, 1/2, 1/2, and 0 when n≢0 mod SF min  for each transition, respectively. Here, SF min =min{SF PiCH , SF DCCH , SF SCH2 , SF SCH1 , SF FCH }. 
   (1) For n≡0 mod SF min   
   
     
       
         
           
             
               
                 
                   
                     
                       
                         I 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         n 
                         ] 
                       
                     
                     + 
                     
                       
                         jQ 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         n 
                         ] 
                       
                     
                   
                   
                     
                       
                         I 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           n 
                           - 
                           1 
                         
                         ] 
                       
                     
                     + 
                     
                       
                         jQ 
                         T 
                       
                       ⁡ 
                       
                         [ 
                         
                           n 
                           - 
                           1 
                         
                         ] 
                       
                     
                   
                 
                 = 
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 D 
                                 
                                   SCH 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                               
                               ⁡ 
                               
                                 [ 
                                 
                                   ⌊ 
                                   
                                     n 
                                     
                                       SF 
                                       min 
                                     
                                   
                                   ⌋ 
                                 
                                 ] 
                               
                             
                             + 
                             
                               
                                 jD 
                                 
                                   SCH 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ⁡ 
                               
                                 [ 
                                 
                                   ⌊ 
                                   
                                     n 
                                     
                                       SF 
                                       min 
                                     
                                   
                                   ⌋ 
                                 
                                 ] 
                               
                             
                           
                           
                             
                               
                                 D 
                                 
                                   SCH 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                               
                               ⁡ 
                               
                                 [ 
                                 
                                   ⌊ 
                                   
                                     
                                       n 
                                       - 
                                       1 
                                     
                                     
                                       SF 
                                       min 
                                     
                                   
                                   ⌋ 
                                 
                                 ] 
                               
                             
                             + 
                             
                               
                                 jD 
                                 
                                   SCH 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ⁡ 
                               
                                 [ 
                                 
                                   ⌊ 
                                   
                                     
                                       n 
                                       - 
                                       1 
                                     
                                     
                                       SF 
                                       min 
                                     
                                   
                                   ⌋ 
                                 
                                 ] 
                               
                             
                           
                         
                         ) 
                       
                       · 
                       
                         
                           
                             
                               H 
                               
                                 SCH 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                           + 
                           
                             
                               jH 
                               
                                 SCH 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     H 
                                     
                                       SCH 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                   ⁡ 
                                   
                                     [ 
                                     
                                       n 
                                       - 
                                       1 
                                     
                                     ] 
                                   
                                 
                                 + 
                               
                             
                           
                           
                             
                               
                                 
                                   jH 
                                   
                                     SCH 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     n 
                                     - 
                                     1 
                                   
                                   ] 
                                 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           
                             C 
                             1 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         + 
                         
                           
                             jC 
                             2 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   C 
                                   
                                     scramble 
                                     . 
                                     I 
                                   
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     n 
                                     - 
                                     1 
                                   
                                   ] 
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 jC 
                                 
                                   scramble 
                                   . 
                                   Q 
                                 
                               
                               [ 
                               
                                 n 
                                 - 
                                 1 
                               
                               } 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     arg 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       { 
                       
                           
                       
                       ⁢ 
                       
                         
                           
                             
                               I 
                               T 
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                           + 
                           
                             
                               jQ 
                               T 
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                         
                         
                           
                             
                               I 
                               T 
                             
                             ⁡ 
                             
                               [ 
                               
                                 n 
                                 - 
                                 1 
                               
                               ] 
                             
                           
                           + 
                           
                             
                               jQ 
                               T 
                             
                             ⁡ 
                             
                               [ 
                               
                                 n 
                                 - 
                                 1 
                               
                               ] 
                             
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       } 
                     
                   
                   ∈ 
                   
                     { 
                     
                       0 
                       , 
                       
                         + 
                         
                           π 
                           2 
                         
                       
                       , 
                       
                         - 
                         
                           π 
                           2 
                         
                       
                       , 
                       π 
                     
                     } 
                   
                 
               
             
             
               
                 [ 
                 
                   EQUATION 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   35 
                 
                 ] 
               
             
           
         
       
     
   
   (2) For n≢mod SF min   
                                       I   T     ⁡     [   n   ]       +       jQ   T     ⁡     [   n   ]               I   T     ⁡     [     n   -   1     ]       +       jQ   T     ⁡     [     n   -   1     ]           =       ⁢         jC   2     ⁡     [     n   -   1     ]       ⁢       H   SCH1     ⁡     [   n   ]       ⁢       H   SCH2     ⁡     [   n   ]       ⁢       H   SCH1     ⁡     [     n   -   1     ]       ⁢       H   SCH2     ⁡     [     n   -   1     ]       ⁢       NUM   ⁡     [     n   -   1     ]         DEN   ⁡     [     n   -   1     ]                       =       ⁢         jC   2     ⁡     [     n   -   1     ]       ⁢       H   a     ⁡     [   n   ]       ⁢       H   a     ⁡     [     n   -   1     ]       ⁢       NUM   ⁡     [     n   -   1     ]         DEN   ⁡     [     n   -   1     ]                         NUM   ⁡     [     n   -   1     ]       =       ⁢       (           C   I     ⁡     [     n   -   2     ]       ⁢       H   SCH1     ⁡     [     n   -   2     ]         -         C   Q     ⁡     [     n   -   2     ]       ⁢       H   2     ⁡     [     n   -   2     ]           )     +                     ⁢         jH   a     ⁡     [   n   ]       ⁢     (           C   I     ⁡     [     n   -   2     ]       ⁢       H   SCH1     ⁡     [     n   -   2     ]         +         C   Q     ⁡     [     n   -   2     ]       ⁢       H   2     ⁡     [     n   -   2     ]           )                   =       ⁢     {           (           C   I     ⁡     [     n   -   2     ]       ⁢       H   SCH1     ⁡     [     n   -   2     ]         -         C   Q     ⁡     [     n   -   2     ]       ⁢       H   2     ⁡     [     n   -   2     ]           )                   jH   a     ⁡     [   n   ]       ⁢     (           C   I     ⁡     [     n   -   2     ]       ⁢       H   SCH1     ⁡     [     n   -   2     ]         +         C   Q     ⁡     [     n   -   2     ]       ⁢       H   2     ⁡     [     n   -   2     ]           )                       ⁢                   DEN   ⁡     [     n   -   1     ]       =           C   I     ⁡     [     n   -   2     ]       ⁢       H   SCH1     ⁡     [     n   -   2     ]         -         C   Q     ⁡     [     n   -   2     ]       ⁢       H   2     ⁡     [     n   -   2     ]             )     +         jH   o     ⁡     [     n   -   1     ]       ⁢     (     C   I                     =     {           (           C   I     ⁡     [     n   -   2     ]       ⁢       H   SCH1     ⁡     [     n   -   2     ]         -         C   Q     ⁡     [     n   -   2     ]       ⁢       H   2     ⁡     [     n   -   2     ]           )                   jH   o     ⁡     [     n   -   1     ]       ⁢     (           C   I     ⁡     [     n   -   2     ]       ⁢       H   SCH1     ⁡     [     n   -   2     ]         +         C   Q     ⁡     [     n   -   2     ]       ⁢       H   2     ⁡     [     n   -   2     ]           )                       ⁡     [     n   -   2     ]       ⁢       H   SCH1     ⁡     [     n   -   2     ]         +         C   Q     ⁡     [     n   -   2     ]       ⁢       H   2     ⁡     [     n   -   2     ]           ⁢           )     ⁢             arg   ⁢     {           I   T     ⁡     [   n   ]       +       jQ   T     ⁡     [   n   ]               I   T     ⁡     [     n   -   1     ]       +       jQ   T     ⁡     [     n   -   1     ]           }       =       ⁢           C   2     ⁡     [     n   -   1     ]       ⁢     H   a     ⁢     {   n   }     ⁢       H   a     ⁡     [     n   -   1     ]       ⁢     π   2       +     arg   ⁢     {             H   a     ⁡     [   n   ]                   H   a     ⁡     [     n   -   1     ]             }                     =       ⁢       ±     π   2       +     arg   ⁢     {         H   a     ⁡     [   n   ]           H   a     ⁡     [     n   -   1     ]         }                     ∈       ⁢     {       +     π   2       ,     -     π   2         }                     [     EQUATION   ⁢           ⁢   36     ]               
Where H α [n]=H SCH1 [n]H SCH2 [n]. With the bit-wise XOR (eXculisive OR) operation in EQUATION 6, (α) 2 =(SCH 1 ) 2 ⊕(SCH 2 ) 2 ).
 
   In the OCQPSK or POCQPSK spreading modulation, as mentioned earlier, the orthogonal Walsh codes with even number subscripts are used except for the inevitable cases such as the case with the high transmitting data rate for a certain channel of spreading factor (SF) of 2. However, the DCQPSK spreading modulation supports the variable spreading factor keeping the orthogonal channel property with any orthogonal codes as shown in the previous equations. Thus the orthogonal code is represented by “H” instead of “W” representing the orthogonal Walsh code. The spreading factor (SF) or size of the orthogonal code need not be the power of 2. 
   The outputs (I T [n], Q T [n]) of the Spreading Modulator ( 141 ) pass through the low-pass filters ( 160 ,  162 ) and the amplifiers ( 170 ,  172 ). Then the amplified outputs are delivered to the modulators ( 180 ,  182 ) which modulate the signals into the desired frequency band using a carrier. And the modulated signals are added by the adder ( 190 ), and delivered to an antenna. 
     FIG. 12  shows a schematic diagram for a receiver according to the transmitter of  FIG. 11   a.  The received signals through the antenna are demodulated at the demodulators ( 280 ,  282 ) with the same carrier used at the transmitter, and I R [n] and Q R [n] are generated after the signals pass through the low-pas filters ( 260 ,  262 ). Then, the spreading demodulator ( 241 ) produces the signals (x R [n], y R [n]) with the primary scrambling codes (C 1 [n], C 2 [n]). The spreading demodulator ( 241 ) comprises the scrambling code generator ( 530 ) and the complex-domain multiplier ( 243 ). The scrambling code generator ( 520 ) produces the secondary scrambling codes (C scramble, I [n], C scramble, Q [n]) with the primary scrambling codes (C 1 [n], C 2 [n]) as the inputs to improve the PAR characteristic. The complex-domain multiplier ( 243 ) takes I R [n] and Q R [n] as the first inputs and the secondary scrambling codes (C scramble, I [n], C scramble, Q [n]) as the second inputs. The first and secondary scrambling codes are generated by the same method as in the transmitter. 
   In order to pick up the desired channels among the ourputs (x R [n], y R [n]) of the spreading demodulator ( 241 ), the signals are multiplied by the same orthogonal code H xxCH [n] (where, xxCH=DCCH or FCH) used in the transmitter, at the de-spreaders ( 1224 ,  1226 ) or the signal are multiplied in complex-domain at the complex-domain multiplier ( 245 ) in  FIG. 12  with the same orthogonal code H xxCH [n] (where, xxCH=SCH 1  or SCH 2 ) used in the transmitter. Now, the signals are integrated during the symbol period T 2x  or T 2y . Since the signals at the receiver are distorted, PiCH is used to correct the distorted signal phase. Accordingly, the signals (x R [n], y R [n]) are multiplied by the corresponding orthogonal code H PiCH [n], and are integrated during the period of T 1  at the integrators ( 210 ,  212 ). 
   The reverse link PiCH in the cdma2000 system may include additional information such as a control command to control the transmitting power at the receiver, besides the pilot signals for the phase correction. In this case, the additional information is extracted by the de-multiplexer, and the phase is estimated using the part of the pilot signals having the known phase. The phase corrections are performed at the complex-domain multipliers ( 242 ,  246 ) using the estimated phase information through the integrators ( 210 ,  212 ). 
   The DCQPSK spreading modulation according to the present invention yields the following effects: First, the PAR characteristic is improved because the probability of the origin crossing transition (□-transition) becomes zero only except for the time when the spread transmitting data vary. Second, the flexibility for the channel allocation becomes better because the DCQPSK can use all orthogonal codes while the OCQPSK or POCQPSK should use the orthogonal Walsh codes with even number subscripts. 
   While the foregoing invention has been described in terms of the embodiments discussed above, numerous variations are also possible. Accordingly, modifications and changes such as those suggested above, but not limited thereto, are considered to be within the scope of the following claims.