PATENT ABSTRACT
A method and apparatus for implementing hybrid automatic repeat request (H-ARQ) in a multiple-input multiple-output (MIMO) wireless communication system are disclosed. A transmitter transmits at least two data packets via two or more antennas. If at least one of the data packets is not successfully transmitted, the transmitter retransmits the data packets while rearranging the data packets in an orthogonal spreading manner. Alternatively, the transmitter may retransmit only the unsuccessfully transmitted data packet along with a new data packet which replaces a successfully transmitted data packet. The unsuccessfully transmitted data packet may simply be repeated without changing its format. When only the unsuccessfully transmitted data packet is retransmitted along with the new data packet, the transmissions may be combined to recover the retransmitted data packet and the new data packet simultaneously.

PATENT DESCRIPTION
CROSS REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims the benefit of U.S. Provisional Application No. 60/792,765 filed Apr. 18, 2006, which is incorporated by reference as if fully set forth. 
     
     FIELD OF INVENTION 
       [0002]    The present invention is related to wireless communication systems. More particularly, the present invention is related to a method and apparatus for implementing hybrid automatic repeat request (H-ARQ) in a multiple-input multiple-output (MIMO) wireless communication system. 
       BACKGROUND 
       [0003]    H-ARQ is a transmission scheme that is widely used in many wireless communication systems to ensure successful data transmission. In H-ARQ, a receiver sends feedback to a transmitter, indicating successful or unsuccessful receipt of a data packet, so that the transmitter retransmits a failed data packet. 
         [0004]    MIMO is a technique used to increase data rate and system throughput. In a MIMO system, a transmitter and a receiver use multiple antennas for transmission and reception so that multiple data streams are transmitted simultaneously via multiple antennas. 
         [0005]    Different H-ARQ transmission schemes have been proposed for MIMO systems. In a conventional simple repetitive H-ARQ scheme for a MIMO system, symbols are simply repeated in a subsequent transmission if the initial transmission fails. Table 1 shows signal transmissions in accordance with the conventional simple repetitive H-ARQ for a 2×2 MIMO system. 
         [0000]    
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Antenna 1 
                 Antenna 2 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 first transmission 
                 x 1   
                 x 2   
               
               
                   
                 second transmission 
                 x 1   
                 x 2   
               
               
                   
                   
               
             
          
         
       
     
         [0006]    A space time block code (STBC)-based H-ARQ scheme for a MIMO system has been proposed for evolved universal terrestrial radio access (EUTRA). Table 2 shows signal transmissions in accordance with the STBC-based H-ARQ for a 2×2 MIMO system. 
         [0000]    
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Antenna 1 
                 Antenna 2 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 first transmission 
                 x 1   
                 x 2   
               
               
                   
                 second transmission 
                 x 2 * 
                 −x 1 * 
               
               
                   
                   
               
             
          
         
       
     
         [0007]    In a 2×2 MIMO system, as an exemplary MIMO system, a received signal may be expressed as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             
                               
                                 y 
                                 1 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 y 
                                 2 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     = 
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   
                                     h 
                                     11 
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     h 
                                     12 
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     h 
                                     21 
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     h 
                                     22 
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                          
                         
                           ( 
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   x 
                                   2 
                                 
                               
                             
                           
                           ) 
                         
                       
                       + 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                   ; 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    where t is an index in time, y i , i=1, 2, is received signals at receive antenna i, h ij , i,j=1, 2, is channel coefficients between receive antenna i and transmit antenna j, x j , j=1, 2, is transmitted signals at transmit antenna j, and n i , i=1, 2, is a noise at receive antenna i. It is assumed that the channel is quasi-static so that the channel coefficients are same during retransmission of the failed packet and the time index on the channel coefficients will be dropped hereinafter. 
         [0008]    At a high signal-to-noise ratio (SNR), the SNR for the two data streams after linear minimum mean square error (LMMSE) detection is written as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         SNR 
                          
                         
                           ( 
                           
                             x 
                             1 
                           
                           ) 
                         
                       
                       = 
                       
                         
                           ( 
                           
                             
                               d 
                               1 
                             
                             - 
                             
                               
                                 
                                    
                                   c 
                                    
                                 
                                 2 
                               
                               
                                 d 
                                 2 
                               
                             
                           
                           ) 
                         
                          
                         
                           
                             E 
                             s 
                           
                           
                             N 
                             0 
                           
                         
                       
                     
                     ; 
                   
                    
                   
                     
 
                   
                    
                   and 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     2 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           2 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ( 
                         
                           
                             d 
                             2 
                           
                           - 
                           
                             
                               
                                  
                                 c 
                                  
                               
                               2 
                             
                             
                               d 
                               1 
                             
                           
                         
                         ) 
                       
                        
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     3 
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    where E, is symbol energy, N 0  is noise power spectrum density, and 
         [0000]        d   1   =|h   11 | 2   +|h   21 | 2 ;  Equation (4) 
         [0000]        d   2   =|h   12 | 2   +|h   22 | 2 ;  and Equation (5) 
         [0000]        c=h   11   *h   12   +h   22   h   21 *.  Equation (6) 
         [0009]    An SNR ratio between two data streams is: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           1 
                         
                         ) 
                       
                     
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           2 
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         d 
                         1 
                       
                       
                         d 
                         2 
                       
                     
                     . 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     7 
                     ) 
                   
                 
               
             
           
         
       
     
       The SNR ratio in Equation (7) or its variation is used as criteria in assigning a modulation and coding scheme (MCS) for each of the data streams. 
       [0010]    For the conventional simple repetitive H-ARQ transmission, the received signal in the retransmission is written as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 h 
                                 11 
                               
                             
                             
                               
                                 h 
                                 12 
                               
                             
                           
                           
                             
                               
                                 h 
                                 21 
                               
                             
                             
                               
                                 h 
                                 22 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 1 
                               
                             
                           
                           
                             
                               
                                 x 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     8 
                     ) 
                   
                 
               
             
           
         
       
     
         [0011]    Combining Equation (1) and Equation (8) results in: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               1 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 h 
                                 11 
                               
                             
                             
                               
                                 h 
                                 12 
                               
                             
                           
                           
                             
                               
                                 h 
                                 21 
                               
                             
                             
                               
                                 h 
                                 22 
                               
                             
                           
                           
                             
                               
                                 h 
                                 11 
                               
                             
                             
                               
                                 h 
                                 12 
                               
                             
                           
                           
                             
                               
                                 h 
                                 21 
                               
                             
                             
                               
                                 h 
                                 22 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 1 
                               
                             
                           
                           
                             
                               
                                 x 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
           
         
       
     
         [0012]    At a high SNR, the SNRs for the two data streams, after LMMSE detection, are as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         SNR 
                          
                         
                           ( 
                           
                             x 
                             1 
                           
                           ) 
                         
                       
                       = 
                       
                         2 
                          
                         
                           ( 
                           
                             
                               d 
                               1 
                             
                             - 
                             
                               
                                 
                                    
                                   c 
                                    
                                 
                                 2 
                               
                               
                                 d 
                                 2 
                               
                             
                           
                           ) 
                         
                          
                         
                           
                             E 
                             s 
                           
                           
                             N 
                             0 
                           
                         
                       
                     
                     ; 
                   
                    
                   
                     
 
                   
                    
                   and 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     10 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     SNR 
                      
                     
                       ( 
                       
                         x 
                         2 
                       
                       ) 
                     
                   
                   = 
                   
                     2 
                      
                     
                       ( 
                       
                         
                           d 
                           2 
                         
                         - 
                         
                           
                             
                                
                               c 
                                
                             
                             2 
                           
                           
                             d 
                             1 
                           
                         
                       
                       ) 
                     
                      
                     
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     11 
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    The SNRs are 3 dB higher than initial transmission. The SNR ratio between the two data streams is the same as the initial transmission. 
         [0013]    For the STBC-based H-ARQ, the signal received for the retransmission is written as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 h 
                                 11 
                               
                             
                             
                               
                                 h 
                                 12 
                               
                             
                           
                           
                             
                               
                                 h 
                                 21 
                               
                             
                             
                               
                                 h 
                                 22 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 2 
                                 * 
                               
                             
                           
                           
                             
                               
                                 - 
                                 
                                   x 
                                   1 
                                   * 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     12 
                     ) 
                   
                 
               
             
           
         
       
     
         [0014]    Combining Equation (12) and Equation (1) results in: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               1 
                               * 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                               * 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 h 
                                 11 
                               
                             
                             
                               
                                 h 
                                 12 
                               
                             
                           
                           
                             
                               
                                 h 
                                 21 
                               
                             
                             
                               
                                 h 
                                 22 
                               
                             
                           
                           
                             
                               
                                 - 
                                 
                                   h 
                                   12 
                                   * 
                                 
                               
                             
                             
                               
                                 h 
                                 11 
                                 * 
                               
                             
                           
                           
                             
                               
                                 - 
                                 
                                   h 
                                   22 
                                   * 
                                 
                               
                             
                             
                               
                                 h 
                                 21 
                                 * 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 1 
                               
                             
                           
                           
                             
                               
                                 x 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   1 
                                   * 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                   * 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     13 
                     ) 
                   
                 
               
             
           
         
       
     
         [0015]    At high SNR, the SNRs after LMMSE detector for the two data streams are as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     SNR 
                      
                     
                       ( 
                       
                         x 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           2 
                         
                         ) 
                       
                     
                     ≈ 
                     
                       
                         ( 
                         
                           
                             d 
                             1 
                           
                           + 
                           
                             d 
                             2 
                           
                         
                         ) 
                       
                        
                       
                         
                           
                             E 
                             s 
                           
                           
                             N 
                             0 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     14 
                     ) 
                   
                 
               
             
           
         
       
     
       Comparing Equations (10), (11) and (14), it can be seen that STBC-based H-ARQ increases the total SNR across the two data streams compared to the simple repetitive H-ARQ when the cross term |c|≠0, which is generally true for a random MIMO channel. 
       [0016]    However, in many practical systems, to achieve the maximum capacity offered by the MIMO channel, a data rate assigned to each spatial data stream is controlled separately according to its own SNR. This scheme is often referred to as per-antenna rate control (PARC). At the initial transmission, the transmitter, (e.g., a Node-B), would allocate a higher modulation and coding scheme (MCS) to the antenna with a higher SNR and allocate a lower MCS to the antenna with a lower SNR. Since the MCS is often kept the same for each antenna when retransmission occurs, it is desirable to keep the same SNR ratio between the antennas after retransmissions. However, the STBC-based H-ARQ scheme equalizes the SNR across all data streams after packet combining as shown in Equation (14). Therefore, the STBC-based H-ARQ scheme is not suitable for systems that adaptively change data rate per spatial stream, (e.g., PARC). 
       SUMMARY 
       [0017]    The present invention is related to a method and apparatus for implementing H-ARQ in a MIMO wireless communication system. A transmitter transmits at least two data packets via two or more antennas. If at least one of the data packets is not successfully transmitted, the transmitter retransmits the data packets while rearranging the data packets in an orthogonal spreading manner. Alternatively, the transmitter may retransmit only the unsuccessfully transmitted data packet along with a new data packet while replacing a successfully transmitted data packet. The unsuccessfully transmitted data packet may simply be repeated without changing its format. When only the unsuccessfully transmitted data packet is retransmitted along with the new data packet, the transmissions may be combined to recover the retransmitted data packet and the new data packet simultaneously. 
     
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    A more detailed understanding of the invention may be had from the following description of a preferred embodiment, given by way of example and to be understood in conjunction with the accompanying drawings wherein: 
           [0019]      FIG. 1  is a block diagram of a transmitter configured in accordance with the present invention; and 
           [0020]      FIG. 2  is a block diagram of a receiver configured in accordance with the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0021]    The present invention may be implemented in any type of wireless communication systems including, but not limited to, wideband code division multiple access (WCDMA), frequency division duplex (FDD), time division duplex (TDD), long term evolution (LTE) of the third generation ( 3 G) system, orthogonal frequency division multiplexing (OFDM), or any other wireless communication system. 
         [0022]      FIGS. 1 and 2  are block diagrams of a transmitter  100  and a receiver  200  configured in accordance with the present invention. The transmitter  100  and the receiver  200  may be a wireless transmit/receive unit (WTRU) or a base station. The terminology “WTRU” includes but is not limited to a user equipment (UE), a mobile station, a fixed or mobile subscriber unit, a pager, a cellular telephone, a personal digital assistant (PDA), a computer, or any other type of user device capable of operating in a wireless environment. The terminology “base station” includes but is not limited to a Node-B, a site controller, an access point (AP), or any other type of interfacing device capable of operating in a wireless environment. 
         [0023]    The transmitter  100  includes at least two antennas  102 , an H-ARQ transmitter  104  and a controller  106 . The H-ARQ transmitter  104  transmits at least two data packets simultaneously via the antennas  102  by implementing an H-ARQ mechanism. The H-ARQ transmitter  104  retransmits data packets if at least one of the data packets is not successfully transmitted. The controller  106  arranges data packets for retransmission in accordance with an orthogonal spreading H-ARQ scheme, a modified repetitive H-ARQ scheme or a modified STBC-based H-ARQ scheme in accordance with the present invention, which will be explained in detail hereinafter. 
         [0024]    The receiver  200  includes at least two antennas  202 , an H-ARQ receiver  204  and a data processor  206 . The receiver  200  may optionally include a data combiner  208 . Data transmitted by the transmitter  100  is received by the antennas  202 . The H-ARQ receiver  204  receives the data by implementing an H-ARQ mechanism. The data processor  206  recovers data packets transmitted by the transmitter  100 . If the transmitter  100  retransmits an unsuccessfully transmitted data packet along with a new data packet which replaces a successfully transmitted data packet when at least one data packet is not successfully delivered to the receiver  200  at an initial transmission, the data combiner  208  may combine retransmitted data and the initially received data after subtracting the successfully received data packet from the initially received data. The data processor  206  then simultaneously processes the unsuccessfully transmitted data packet and the new data packet that are transmitted together in retransmission. The transmit and receive processing will be explained in detail hereinafter. 
         [0025]    An orthogonal spreading-based H-ARQ scheme in accordance with the present invention is explained. Table 3 shows signal transmissions in accordance with the orthogonal spreading-based H-ARQ scheme of the present invention for an exemplary 2×2 MIMO system. It should be noted that the 2×2 MIMO system is provided as an example, not as a limitation, and the present invention may be applied to a system employing more than two (2) antennas. 
         [0000]    
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 Antenna 1 
                 Antenna 2 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 first transmission 
                 x 1   
                 x 2   
               
               
                   
                 second transmission 
                 x 1   
                 −x 2   
               
               
                   
                   
               
             
          
         
       
     
         [0026]    A received signal for the retransmitted packet is written as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 h 
                                 11 
                               
                             
                             
                               
                                 h 
                                 12 
                               
                             
                           
                           
                             
                               
                                 h 
                                 21 
                               
                             
                             
                               
                                 h 
                                 22 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 1 
                               
                             
                           
                           
                             
                               
                                 - 
                                 
                                   x 
                                   2 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     15 
                     ) 
                   
                 
               
             
           
         
       
     
         [0027]    Combining Equation (15) and Equation (1) results in: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               1 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 h 
                                 11 
                               
                             
                             
                               
                                 h 
                                 12 
                               
                             
                           
                           
                             
                               
                                 h 
                                 21 
                               
                             
                             
                               
                                 h 
                                 22 
                               
                             
                           
                           
                             
                               
                                 h 
                                 11 
                               
                             
                             
                               
                                 - 
                                 
                                   h 
                                   12 
                                 
                               
                             
                           
                           
                             
                               
                                 h 
                                 21 
                               
                             
                             
                               
                                 - 
                                 
                                   h 
                                   22 
                                 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 1 
                               
                             
                           
                           
                             
                               
                                 x 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     16 
                     ) 
                   
                 
               
             
           
         
       
     
         [0028]    An LMMSE receiver to estimate x 1  and x 2  from Equation (16) is as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   x 
                                   ^ 
                                 
                                 1 
                               
                             
                           
                           
                             
                               
                                 
                                   x 
                                   ^ 
                                 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                       = 
                       
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     H 
                                     _ 
                                   
                                   H 
                                 
                                  
                                 
                                   H 
                                   _ 
                                 
                               
                               + 
                               
                                 
                                   
                                     N 
                                     0 
                                   
                                   
                                     E 
                                     s 
                                   
                                 
                                  
                                 I 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           
                             
                               H 
                               _ 
                             
                             H 
                           
                            
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       y 
                                       1 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       y 
                                       2 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       y 
                                       1 
                                     
                                      
                                     
                                       ( 
                                       
                                         t 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       y 
                                       2 
                                     
                                      
                                     
                                       ( 
                                       
                                         t 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                     ; 
                   
                    
                   
                     
 
                   
                    
                   where 
                    
                   
                     
 
                   
                    
                   
                     
                       H 
                       _ 
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               
                                 h 
                                 11 
                               
                             
                             
                               
                                 h 
                                 12 
                               
                             
                           
                           
                             
                               
                                 h 
                                 21 
                               
                             
                             
                               
                                 h 
                                 22 
                               
                             
                           
                           
                             
                               
                                 h 
                                 11 
                               
                             
                             
                               
                                 - 
                                 
                                   h 
                                   12 
                                 
                               
                             
                           
                           
                             
                               
                                 h 
                                 21 
                               
                             
                             
                               
                                 - 
                                 
                                   h 
                                   22 
                                 
                               
                             
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     17 
                     ) 
                   
                 
               
             
           
         
       
     
         [0029]    At a high SNR, the post-MMSE SNR for the two data streams are as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           1 
                         
                         ) 
                       
                     
                     = 
                     
                       2 
                        
                       
                         d 
                         1 
                       
                        
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     18 
                     ) 
                   
                 
               
             
             
               
                 and 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     SNR 
                      
                     
                       ( 
                       
                         x 
                         2 
                       
                       ) 
                     
                   
                   = 
                   
                     2 
                      
                     
                       d 
                       2 
                     
                      
                     
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     19 
                     ) 
                   
                 
               
             
           
         
       
     
         [0030]    The total SNR across all data streams is increased compared to the conventional simple repetitive H-ARQ scheme. The SNR after retransmission is shown in Equations (18) and (19). The SNR ratio between the two data streams is the same as the initial transmission, which is a desired feature for PARC-enabled MIMO systems. 
         [0031]    The orthogonal spreading-based H-ARQ scheme can be easily extended to more than two antenna systems. Assuming a symbol vector to be transmitted over N antennas is X 0 =(x 1 ,x 2 , . . . x N ). The orthogonal spreading-based H-ARQ transmission pattern is determined by: 
         [0000]        X=√{square root over (N)} Diag( X   0 ) U   N ;  Equation (20) 
         [0000]    where U N  is an N×N unitary matrix. The n-th column of the matrix X is transmitted during the n-th transmission. Table 4 shows signal transmissions in accordance with the present invention for an exemplary 4×4 MIMO system. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                 Antenna 1 
                 Antenna 2 
                 Antenna 3 
                 Antenna 4 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 first transmission 
                 x 1   
                 x 2   
                 x 3   
                 x 4   
               
               
                 second transmission 
                 x 1   
                 −x 2   
                 x 3   
                 −x 4   
               
               
                 third transmission 
                 x 1   
                 x 2   
                 −x 3   
                 −x 4   
               
               
                 fourth transmission 
                 x 1   
                 −x 2   
                 −x 3   
                 x 4   
               
               
                   
               
             
          
         
       
     
         [0032]    In accordance with another embodiment of the present invention, when one of the transmitted data packets is not successfully received, only the failed data packet is retransmitted along with a new data packet. The new data packet replaces the successfully transmitted data packet. For example, in a 2×2 MIMO system, data packets x 1  and x 2  are transmitted via two antennas, and data packet x 1  is successfully received, but data packet x 2  is not. In conventional systems, both packets x 1  and x 2  are retransmitted subsequently. In accordance with the present invention, only the failed packet x 2  is retransmitted and the successfully transmitted packet x 1  is not transmitted. Instead, a new data packet x 3  is transmitted along with the failed packet x 2 . 
         [0033]    Table 5 shows signal transmissions in accordance with the present invention and a conventional STBC-based H-ARQ scheme for an exemplary 2×2 MIMO system. In the conventional STBC-based H-ARQ, both packets x 1  and x 2  are retransmitted in different formats as shown in Table 5. In accordance with the present invention, a new data packet x 3  replaces the successfully received packet x 1  of the conventional STBC-based H-ARQ system, and the failed data packet x 2  and the new data packet x 3  are transmitted as in STBC-based H-ARQ scheme as shown in Table 5. It is assumed that no PARC type of rate adaptation is used in this case. To simplify receiver design, the format of the new packet x 3  may be identical to the data packet x 1  in the second transmission, (i.e., conjugated and inversed). Alternatively, the format for the new data packet x 3  may be different from data packet x 1 . 
         [0000]    
       
         
               
               
               
             
               
               
               
             
           
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 Antenna 1 
                 Antenna 2 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 first Transmission 
                 x 1  (success) 
                 x 2  (fail) 
               
               
                 second transmission 
                 x 2 * 
                 −x 1 * 
               
               
                 (conventional STBC-based H-ARQ) 
               
               
                 second transmission (present invention) 
                 x 2 * 
                 −x 3 * 
               
               
                   
               
             
          
         
       
     
         [0034]    At the receiver, since data packet x 1  is received successfully, the decoded bits of data packet x 1  are reconstructed and subtracted from received data for the first transmission. The modified received data is then combined with the received data for the second transmission. Spatial diversity is achieved in the retransmitted data packet, (i.e., data packet x 2 ). This arrangement improves an SNR of new data packet x 3  which will be explained hereinafter. 
         [0035]    The received signal of the first transmission is as in Equation (1). After subtracting the successfully received data packet x 1  from the received data, it becomes as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   
                                     
                                       y 
                                       ~ 
                                     
                                     1 
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       y 
                                       ~ 
                                     
                                     2 
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       y 
                                       1 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       y 
                                       2 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       
                                         h 
                                         11 
                                       
                                        
                                       
                                         ( 
                                         t 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         h 
                                         21 
                                       
                                        
                                       
                                         ( 
                                         t 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                              
                             
                               x 
                               1 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                             
                         
                          
                         
                           = 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       0 
                                     
                                     
                                       
                                         
                                           h 
                                           12 
                                         
                                          
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     
                                       0 
                                     
                                     
                                       
                                         
                                           h 
                                           22 
                                         
                                          
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         x 
                                         3 
                                       
                                     
                                   
                                   
                                     
                                       
                                         x 
                                         2 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         
                                           n 
                                           1 
                                         
                                          
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           n 
                                           2 
                                         
                                          
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                               . 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     21 
                     ) 
                   
                 
               
             
           
         
       
     
       Packet x 3  is added into Equation (21) to facilitate description hereafter. 
       [0036]    The received signal for the second transmission is written as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                       
                   
                    
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   h 
                                   11 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   12 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   h 
                                   21 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   22 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 2 
                                 * 
                               
                             
                           
                           
                             
                               
                                 - 
                                 
                                   x 
                                   3 
                                   * 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                         
                     
                      
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                           
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     22 
                     ) 
                   
                 
               
             
           
         
       
     
         [0037]    Combining Equations (21) and (22) results in: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               
                                 y 
                                 ~ 
                               
                               1 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 y 
                                 ~ 
                               
                               2 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               1 
                               * 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                               * 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   h 
                                   12 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   h 
                                   22 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 - 
                                 
                                   
                                     h 
                                     12 
                                     * 
                                   
                                    
                                   
                                     ( 
                                     
                                       t 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   11 
                                   * 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 - 
                                 
                                   
                                     h 
                                     22 
                                     * 
                                   
                                    
                                   
                                     ( 
                                     
                                       t 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   21 
                                   * 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 2 
                               
                             
                           
                           
                             
                               
                                 x 
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       N 
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     23 
                     ) 
                   
                 
               
             
           
         
       
     
         [0038]    Equation (23) converts two 2×2 system into a virtual 2×4 system. Conventional LMMSE may be applied to demodulate packets x 2  and x 3  as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   x 
                                   ^ 
                                 
                                 2 
                               
                             
                           
                           
                             
                               
                                 
                                   x 
                                   ^ 
                                 
                                 3 
                               
                             
                           
                         
                         ) 
                       
                       = 
                       
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     H 
                                     _ 
                                   
                                   H 
                                 
                                  
                                 
                                   H 
                                   _ 
                                 
                               
                               + 
                               
                                 
                                   
                                     N 
                                     0 
                                   
                                   
                                     E 
                                     s 
                                   
                                 
                                  
                                 I 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           
                             
                               H 
                               _ 
                             
                             H 
                           
                            
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       
                                         y 
                                         ~ 
                                       
                                       1 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         y 
                                         ~ 
                                       
                                       2 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       y 
                                       1 
                                       * 
                                     
                                      
                                     
                                       ( 
                                       
                                         t 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       y 
                                       2 
                                       * 
                                     
                                      
                                     
                                       ( 
                                       
                                         t 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     where 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       H 
                       _ 
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   h 
                                   12 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   h 
                                   22 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 - 
                                 
                                   
                                     h 
                                     12 
                                     * 
                                   
                                    
                                   
                                     ( 
                                     
                                       t 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   11 
                                   * 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 - 
                                 
                                   
                                     h 
                                     22 
                                     * 
                                   
                                    
                                   
                                     ( 
                                     
                                       t 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   21 
                                   * 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     24 
                     ) 
                   
                 
               
             
           
         
       
     
         [0039]    In quasi-static channel, spatial diversity is achieved on retransmitted data packet x 2  with reduced interference due to zero elements in the matrix above. Assuming quasi-static channel and dropping time index t, at high SNR, the SNRs of the data streams for the second transmission are written as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           2 
                         
                         ) 
                       
                     
                     ≈ 
                     
                       
                         ( 
                         
                           
                             d 
                             1 
                           
                           - 
                           
                             
                               
                                  
                                 c 
                                  
                               
                               2 
                             
                             
                               d 
                               2 
                             
                           
                         
                         ) 
                       
                        
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                     
                   
                   ; 
                   and 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     25 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           3 
                         
                         ) 
                       
                     
                     ≈ 
                     
                       
                         ( 
                         
                           
                             d 
                             2 
                           
                           - 
                           
                             
                               
                                  
                                 c 
                                  
                               
                               2 
                             
                             
                               d 
                               1 
                             
                           
                         
                         ) 
                       
                        
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     26 
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    where d 1 =|h 11 | 2 +|h 12 | 2 +|h 21 | 2 +|h 22 | 2 , d 2 =|h 12 | 2 +|h 22 | 2 , and c=−h 11 h 12 *−h 21 h 22 *. 
         [0040]    With respect to new data packet x 3 , a conventional detection technique may be used, where packet x 2  is detected independently from two transmissions followed by a maximum ratio combining (MRC), and packet x 3  is detected only using the second transmission. In other words, conventional technique solves Equations (21) and (22) separately, then perform combining. In Equation (21), since all effective channel coefficients corresponding to x 3  equal to zero (0), only information on x 2  can be derived from Equation (21). With this detection technique, the SNRs are as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           2 
                         
                         ) 
                       
                     
                     ≈ 
                     
                       
                         ( 
                         
                           
                             d 
                             1 
                           
                           - 
                           
                             
                               
                                  
                                 c 
                                  
                               
                               2 
                             
                             
                               d 
                               2 
                             
                           
                         
                         ) 
                       
                        
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                     
                   
                   ; 
                   and 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     27 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           3 
                         
                         ) 
                       
                     
                     ≈ 
                     
                       
                         ( 
                         
                           
                             d 
                             2 
                           
                           - 
                           
                             
                               
                                  
                                 c 
                                  
                               
                               2 
                             
                             
                               d 
                               1 
                               ′ 
                             
                           
                         
                         ) 
                       
                        
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     28 
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    where d 1 ′=|h 11 | 2 +|h 21 | 2 . The SNR of packet x 2  is identical in both techniques. However, a better SNR on x 3  is achieved in accordance with the present invention, when comparing Equations (26) and (28), and considering d 1 &gt;d 1 ′. 
         [0041]    The present invention may be extended to systems with more than two antennas. Tables 6 and 7 show examples of extension to a four antenna system. Table 6 shows conventional STBC-based H-ARQ scheme and Table 7 shows an STBD-based H-ARQ scheme with the successfully transmitted packet being replaced with a new packet in accordance with the present invention. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                 Antenna1 
                 Antenna 2 
                 Antenna 3 
                 Antenna 4 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Time 1 
                 x 1   
                 x 2   
                 x 3   
                 x 4   
               
               
                   
                 Time 2 
                 −x 2 * 
                 x 1 * 
                 −x 4 * 
                 x 3 * 
               
               
                   
                 Time 3 
                 −x 3 * 
                 −x 4 * 
                 x 1 * 
                 x 2 * 
               
               
                   
                 Time 4 
                 x 4   
                 −x 3   
                 −x 2   
                 x 1   
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 TABLE 7 
               
               
                   
                   
               
               
                   
                 Antenna1 
                 Antenna 2 
                 Antenna 3 
                 Antenna 4 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Time 1 
                 x 1  (fail) 
                 x 2  (fail) 
                 x 3   
                 x 4  (fail) 
               
               
                   
                 Time 2 
                 −x 2 * 
                 x 1 * (fail) 
                 −x 4 * (fail) 
                 x 5 * (fail) 
               
               
                   
                 Time 3 
                 −x 5 * 
                 −x 4 * 
                 x 1 * 
                 x 6 * (fail) 
               
               
                   
                 Time 4 
                 x 7   
                 −x 8   
                 −x 6   
                 x 9   
               
               
                   
                   
               
             
          
         
       
     
         [0042]    Alternatively, the failed packet x 2  may be simply repeated and a new packet x 3  is transmitted along with the packet x 2  simultaneously. Table 8 shows signal transmissions in accordance with the present invention and a conventional simple repetitive H-ARQ scheme for an exemplary 2×2 MIMO system. In the conventional simple repetitive H-ARQ scheme, the spatial stream that is successfully received is left blank for retransmission. In accordance with the present invention, a new data packet X 3  is transmitted in place of the blank packet. Therefore, higher spectral efficiency is achieved. 
         [0000]    
       
         
               
               
               
             
               
               
               
             
           
               
                   
                 TABLE 8 
               
               
                   
                   
               
               
                   
                 Antenna 1 
                 Antenna 2 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 first Transmission 
                 x 1  (success) 
                 x 2  (fail) 
               
               
                 second transmission 
                 0 
                 x 2   
               
               
                 (conventional simple repetitive H-ARQ) 
               
               
                 second transmission (Present invention) 
                 x 3   
                 x 2   
               
               
                   
               
             
          
         
       
     
         [0043]    The received signal of the first transmission is as in Equation (1). After subtracting data bits of the successfully received data packet x 1  from the initially received data, it becomes as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   
                                     
                                       y 
                                       ~ 
                                     
                                     1 
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       y 
                                       ~ 
                                     
                                     2 
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       y 
                                       1 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       y 
                                       2 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       
                                         h 
                                         11 
                                       
                                        
                                       
                                         ( 
                                         t 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         h 
                                         21 
                                       
                                        
                                       
                                         ( 
                                         t 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                              
                             
                               x 
                               1 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                             
                         
                          
                         
                           = 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       0 
                                     
                                     
                                       
                                         
                                           h 
                                           12 
                                         
                                          
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     
                                       0 
                                     
                                     
                                       
                                         
                                           h 
                                           22 
                                         
                                          
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         x 
                                         3 
                                       
                                     
                                   
                                   
                                     
                                       
                                         x 
                                         2 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         
                                           n 
                                           1 
                                         
                                          
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           n 
                                           2 
                                         
                                          
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                               . 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     29 
                     ) 
                   
                 
               
             
           
         
       
     
         [0044]    The received signal for the second transmission is written as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                              
                             
                               ( 
                               
                                 t 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                       
                   
                    
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   h 
                                   11 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   12 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   h 
                                   21 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   22 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 3 
                               
                             
                           
                           
                             
                               
                                 x 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                         
                     
                      
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   n 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                           
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     30 
                     ) 
                   
                 
               
             
           
         
       
     
         [0045]    Combining Equations (29) and (30) results in: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               
                                 y 
                                 ~ 
                               
                               1 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 y 
                                 ~ 
                               
                               2 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               1 
                             
                              
                             
                               ( 
                               
                                 t 
                                  
                                 
                                     
                                 
                                 + 
                                 
                                     
                                 
                                  
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                              
                             
                               ( 
                               
                                 t 
                                  
                                 
                                     
                                 
                                 + 
                                 
                                     
                                 
                                  
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   h 
                                   12 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   h 
                                   22 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   h 
                                   12 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   11 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   h 
                                   22 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   21 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 2 
                               
                             
                           
                           
                             
                               
                                 x 
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       N 
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     31 
                     ) 
                   
                 
               
             
           
         
       
     
         [0046]    Instead of solving Equations (29) and (30) followed by a combiner, the present invention applies LMMSE to solve Equation (31) as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   x 
                                   ^ 
                                 
                                 2 
                               
                             
                           
                           
                             
                               
                                 
                                   x 
                                   ^ 
                                 
                                 3 
                               
                             
                           
                         
                         ) 
                       
                       = 
                       
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     H 
                                     _ 
                                   
                                   H 
                                 
                                  
                                 
                                   H 
                                   _ 
                                 
                               
                               + 
                               
                                 
                                   
                                     N 
                                     0 
                                   
                                   
                                     E 
                                     s 
                                   
                                 
                                  
                                 I 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           
                             
                               H 
                               _ 
                             
                             H 
                           
                            
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       
                                         y 
                                         ~ 
                                       
                                       1 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         y 
                                         ~ 
                                       
                                       2 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       y 
                                       1 
                                     
                                      
                                     
                                       ( 
                                       
                                         t 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       y 
                                       2 
                                     
                                      
                                     
                                       ( 
                                       
                                         t 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                     ; 
                   
                    
                   
                     
 
                   
                    
                   where 
                    
                   
                     
 
                   
                    
                   
                     
                       H 
                       _ 
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   h 
                                   12 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   h 
                                   22 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   h 
                                   12 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   11 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   h 
                                   22 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   21 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     32 
                     ) 
                   
                 
               
             
           
         
       
     
         [0047]    At high SNR, the post-MMSE SNRs for x 2  and x 3  are as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           2 
                         
                         ) 
                       
                     
                     ≈ 
                     
                       
                         ( 
                         
                           
                             d 
                             1 
                           
                           - 
                           
                             
                               
                                  
                                 c 
                                  
                               
                               2 
                             
                             
                               d 
                               2 
                             
                           
                         
                         ) 
                       
                        
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                     
                   
                   ; 
                   and 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     33 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           3 
                         
                         ) 
                       
                     
                     ≈ 
                     
                       
                         ( 
                         
                           
                             d 
                             2 
                           
                           - 
                           
                             
                               
                                  
                                 c 
                                  
                               
                               2 
                             
                             
                               d 
                               1 
                             
                           
                         
                         ) 
                       
                        
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     34 
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    where d 1 =2(|h 12 | 2 +|h 22 | 2 ), d 2 =|h 11 | 2 +|h 21 | 2 , and c=h 11 h 12 *+h 21 h 22 *. 
         [0048]    For a conventional receiver, data is detected separately for each transmission before being combined. In other words, conventional detection solves Equations (29) and (30) separately, then combine post detected signal. Assuming LMMSE receiver is used to solve Equation (31), and a maximal ratio combining (MRC) is used to combine post-detection signal, the combined SNR for data x 2  and x 3  at high SNR can be written as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           2 
                         
                         ) 
                       
                     
                     ≈ 
                     
                       
                         ( 
                         
                           
                             d 
                             1 
                           
                           - 
                           
                             
                               
                                  
                                 c 
                                  
                               
                               2 
                             
                             
                               d 
                               2 
                             
                           
                         
                         ) 
                       
                        
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                     
                   
                   ; 
                   and 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     35 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       SNR 
                        
                       
                         ( 
                         
                           x 
                           3 
                         
                         ) 
                       
                     
                     ≈ 
                     
                       
                         ( 
                         
                           
                             d 
                             2 
                           
                           - 
                           
                             
                               
                                  
                                 c 
                                  
                               
                               2 
                             
                             
                               d 
                               1 
                               ′ 
                             
                           
                         
                         ) 
                       
                        
                       
                         
                           E 
                           s 
                         
                         
                           N 
                           0 
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     36 
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    where d 1 ′=(|h 12 | 2 +|h 22 | 2 ), d 2 =|h 11 | 2 +|h 21 | 2 , and c=h 11 h 12 *+h 21 h 22 *. 
         [0049]    By comparing Equations (33) and (35), it is shown that the SNR of the retransmitted data packet x 2  is identical for both the conventional scheme and the present invention. However, by comparing Equations (34) and (36), it is shown that the SNR of new data packet x 3  is improved using the present invention, since d 1 &gt;d 1 ′. 
         [0050]    Although the features and elements of the present invention are described in the preferred embodiments in particular combinations, each feature or element can be used alone without the other features and elements of the preferred embodiments or in various combinations with or without other features and elements of the present invention. The methods or flow charts provided in the present invention may be implemented in a computer program, software, or firmware tangibly embodied in a computer-readable storage medium for execution by a general purpose computer or a processor. Examples of computer-readable storage mediums include a read only memory (ROM), a random access memory (RAM), a register, cache memory, semiconductor memory devices, magnetic media such as internal hard disks and removable disks, magneto-optical media, and optical media such as CD-ROM disks, and digital versatile disks (DVDs). 
         [0051]    Suitable processors include, by way of example, a general purpose processor, a special purpose processor, a conventional processor, a digital signal processor (DSP), a plurality of microprocessors, one or more microprocessors in association with a DSP core, a controller, a microcontroller, Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) circuits, any other type of integrated circuit (IC), and/or a state machine. 
         [0052]    A processor in association with software may be used to implement a radio frequency transceiver for use in a wireless transmit receive unit (WTRU), user equipment (UE), terminal, base station, radio network controller (RNC), or any host computer. The WTRU may be used in conjunction with modules, implemented in hardware and/or software, such as a camera, a video camera module, a videophone, a speakerphone, a vibration device, a speaker, a microphone, a television transceiver, a hands free headset, a keyboard, a Bluetooth® module, a frequency modulated (FM) radio unit, a liquid crystal display (LCD) display unit, an organic light-emitting diode (OLED) display unit, a digital music player, a media player, a video game player module, an Internet browser, and/or any wireless local area network (WLAN) module.