Patent Publication Number: US-8111772-B2

Title: Method and apparatus for multi-antenna transmitting based on spatial-frequency encoding

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of International Application No. PCT/CN2007/000075, filed Jan. 9, 2007. This application claims the benefit and priority of Chinese Application No. 200610070854.2, filed Mar. 15, 2006. The entire disclosures of each of the above applications are incorporated herein by reference. 
    
    
     FIELD 
     The present disclosure relates to communication technologies, and in particular, to a method and apparatus for multi-antenna transmitting based on spatial-frequency encoding. 
     BACKGROUND 
     This section provides background information related to the present disclosure which is not necessarily prior art. 
     In recent years, the multiple input multiple output (MIMO) technology has become a major concern and has been applied in actual communication systems, owing to its ability of improving the transmit spectral efficiency and the reliability of wireless communication systems. In addition, the multi-carrier orthogonal frequency division multiplexing (OFDM) technology has become the focus of study, owing to its ability of overcoming the multipath considerations of wireless channels and achieving a higher spectral efficiency than single-carrier systems. MIMO and OFDM become the key technologies of mobile communication systems and have been widely applied in approaches including long term evolution (LTE) of third generation (3G) mobile communication systems and even fourth generation (4G) mobile communications systems. 
     Various transmit diversity and spatial multiplexing approaches can be implemented based on MIMO and OFDM technologies. Diversity gain can improve the performance of systems, and spatial multiplexing gain can improve the transmission rate. 
     A spatial-frequency encoding approach of the prior art, which is an extension of space-time encoding, replaces the time dimension of space-time encoding with frequency dimension for encoding. This approach is applied mainly in OFDM systems. As shown in  FIG. 1 , spatial-frequency encoding can obtain diversity gain or spatial multiplexing gain by encoding on multiple sub-carriers and antennas. At present, spatial-frequency encoding is categorized into space frequency block code (SFBC) and spatial multiplexing coding. When the encoding rate of SFBC is equal to or lower than 1, the transmitter performs orthogonal or non-orthogonal encoding on multiple antennas, and the receiver performs maximum likelihood decoding to obtain diversity gain. At present, 2-antenna transmitting based on orthogonal spatial-frequency encoding is applied most widely. Formula (1) shows the encoding matrix. 
     
       
         
           
             
               
                 
                   G 
                   = 
                   
                     ( 
                     
                       
                         
                           
                             S 
                             1 
                           
                         
                         
                           
                             - 
                             
                               S 
                               2 
                               * 
                             
                           
                         
                       
                       
                         
                           
                             S 
                             2 
                           
                         
                         
                           
                             S 
                             1 
                             * 
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     In formula (1), S 1  and S 2  are the symbols before spatial-frequency encoding. After 2-antenna transmitting based on orthogonal spatial-frequency encoding indicated by formula (1), transmit antenna  1  transmits S 1  on the sub-carrier k and −S 2 * on the sub-carrier k+1; transmit antenna  2  transmits S 2  on the sub-carrier k and S 1 * on the sub-carrier k+1. It is defined that the encoding rate is n/k, where n indicates the number of data symbols transmitted during one spatial-frequency encoding operation, and k indicates the number of the sub-carriers required for one spatial-frequency encoding operation. As seen from formula 1, the encoding rate for 2-antenna transmitting based on orthogonal spatial-frequency encoding is (1). The multiple sub-carriers occupied for one spatial-frequency encoding operation are hereinafter called a sub-carrier set. 
     It is supposed that the receiver has only one receive antenna, and that the channel fading factors for the data on two adjacent sub-carriers of the same transmit antenna are the same. The data received by the antenna on two sub-carriers can be expressed by formulas (2) and (3).
 
 r   1   =h   1   S   1   +h   2   S   2   +n   1   (2)
 
 r   2   =h   1 (− S   2 *)+ h   2   S   1   *+n   2   (3)
 
     h 1  and h 2  indicate the factors for channel fading from the two transmit antennas to the receive antenna. After channel estimation, the receiver can perform the maximum likelihood decoding, as expressed by formulas (4) and (5).
 
 Ŝ   1   =h   1   *r   1   +h   2   r   2 *=(| h   1 | 2   +|h   2 | 2 ) S   1   +h   1   *n   1   +h   2   n   2 *  (4)
 
 Ŝ   2   =h   2   *r   1   −h   1   r   2 *=(| h   1 | 2   +|h   2 | 2 ) S   2   −h   1   n   2   *+h   2   *n   1   (5)
 
     Ŝ 1  and Ŝ 2  indicate the estimation of the symbols S 1  and S 2 . 
     As seen from formulas (4) and (5), S 1  and S 2  each obtain second-order diversity after they are transmitted through the STBC transmit diversity. 
     When the number of transmit antennas is 3 or 4, only the orthogonal spatial-frequency encoding at rates of ½ and ¾ exists. 
     Formula (6) shows the matrix of 3-antenna transmitting based on orthogonal spatial-frequency encoding at a rate of ½: 
     
       
         
           
             
               
                 
                   
                     G 
                     
                       3 
                       , 
                       1 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               S 
                               1 
                             
                           
                           
                             
                               S 
                               2 
                             
                           
                           
                             
                               S 
                               3 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 2 
                               
                             
                           
                           
                             
                               S 
                               1 
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 4 
                               
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 3 
                               
                             
                           
                           
                             
                               S 
                               4 
                             
                           
                           
                             
                               S 
                               1 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 4 
                               
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 3 
                               
                             
                           
                           
                             
                               S 
                               2 
                             
                           
                         
                         
                           
                             
                               S 
                               1 
                               * 
                             
                           
                           
                             
                               S 
                               2 
                               * 
                             
                           
                           
                             
                               S 
                               3 
                               * 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 2 
                                 * 
                               
                             
                           
                           
                             
                               S 
                               1 
                               * 
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 4 
                                 * 
                               
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 3 
                                 * 
                               
                             
                           
                           
                             
                               S 
                               4 
                               * 
                             
                           
                           
                             
                               S 
                               1 
                               * 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 4 
                                 * 
                               
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 3 
                                 * 
                               
                             
                           
                           
                             
                               S 
                               2 
                               * 
                             
                           
                         
                       
                       ) 
                     
                     T 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Formula (7) shows the matrix of 4-antenna transmitting based on orthogonal spatial-frequency encoding at a rate of ½: 
     
       
         
           
             
               
                 
                   
                     G 
                     
                       4 
                       , 
                       1 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               S 
                               1 
                             
                           
                           
                             
                               S 
                               2 
                             
                           
                           
                             
                               S 
                               3 
                             
                           
                           
                             
                               S 
                               4 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 2 
                               
                             
                           
                           
                             
                               S 
                               1 
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 4 
                               
                             
                           
                           
                             
                               S 
                               3 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 3 
                               
                             
                           
                           
                             
                               S 
                               4 
                             
                           
                           
                             
                               S 
                               1 
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 4 
                               
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 3 
                               
                             
                           
                           
                             
                               S 
                               2 
                             
                           
                           
                             
                               S 
                               1 
                             
                           
                         
                         
                           
                             
                               S 
                               1 
                               * 
                             
                           
                           
                             
                               S 
                               2 
                               * 
                             
                           
                           
                             
                               S 
                               3 
                               * 
                             
                           
                           
                             
                               S 
                               4 
                               * 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 2 
                                 * 
                               
                             
                           
                           
                             
                               S 
                               1 
                               * 
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 4 
                                 * 
                               
                             
                           
                           
                             
                               S 
                               3 
                               * 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 3 
                                 * 
                               
                             
                           
                           
                             
                               S 
                               4 
                               * 
                             
                           
                           
                             
                               S 
                               1 
                               * 
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 2 
                                 * 
                               
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 4 
                                 * 
                               
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 3 
                                 * 
                               
                             
                           
                           
                             
                               S 
                               2 
                               * 
                             
                           
                           
                             
                               S 
                               1 
                               * 
                             
                           
                         
                       
                       ) 
                     
                     T 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Formula (8) shows the matrix of 3-antenna transmitting based on orthogonal spatial-frequency encoding at a rate of ¾: 
     
       
         
           
             
               
                 
                   
                     G 
                     
                       3 
                       , 
                       2 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               S 
                               1 
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 2 
                               
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 3 
                               
                             
                           
                         
                         
                           
                             
                               S 
                               2 
                               * 
                             
                           
                           
                             
                               S 
                               1 
                               * 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               S 
                               3 
                               * 
                             
                           
                           
                             0 
                           
                           
                             
                               S 
                               1 
                               * 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               - 
                               
                                 S 
                                 3 
                                 * 
                               
                             
                           
                           
                             
                               S 
                               2 
                               * 
                             
                           
                         
                       
                       ) 
                     
                     T 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Formula (9) shows the matrix of 4-antenna transmitting based on orthogonal spatial-frequency encoding at a rate of ¾: 
     
       
         
           
             
               
                 
                   
                     G 
                     
                       4 
                       , 
                       2 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               S 
                               1 
                             
                           
                           
                             
                               S 
                               2 
                             
                           
                           
                             
                               S 
                               3 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 2 
                                 * 
                               
                             
                           
                           
                             
                               S 
                               1 
                               * 
                             
                           
                           
                             0 
                           
                           
                             
                               - 
                               
                                 S 
                                 3 
                               
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 S 
                                 3 
                                 * 
                               
                             
                           
                           
                             0 
                           
                           
                             
                               S 
                               1 
                               * 
                             
                           
                           
                             
                               S 
                               2 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               S 
                               3 
                               * 
                             
                           
                           
                             
                               - 
                               
                                 S 
                                 2 
                                 * 
                               
                             
                           
                           
                             
                               S 
                               1 
                             
                           
                         
                       
                       ) 
                     
                     T 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     When the encoding rate of spatial multiplexing coding is higher than 1, different data is transmitted on the same sub-carrier of different antennas to improve the data transmission rate, that is, to obtain spatial multiplexing gain. Formulas (10) to (12) show the matrixes of spatial multiplexing coding when the number of transmit antennas is 2, 3, and 4. 
     
       
         
           
             
               
                 
                   
                     G 
                     2 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               S 
                               1 
                             
                           
                         
                         
                           
                             
                               S 
                               2 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     —Sending 
                     ⁢ 
                     
                       
                           
                       
                       ⁢ 
                       
                           
                       
                     
                     ⁢ 
                     two 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     data 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     streams 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     at 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     same 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     time 
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     G 
                     3 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               S 
                               1 
                             
                           
                         
                         
                           
                             
                               S 
                               2 
                             
                           
                         
                         
                           
                             
                               S 
                               3 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     —Sending 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     three 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     data 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     streams 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     at 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     same 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     time 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     G 
                     4 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               S 
                               1 
                             
                           
                         
                         
                           
                             
                               S 
                               2 
                             
                           
                         
                         
                           
                             
                               S 
                               3 
                             
                           
                         
                         
                           
                             
                               S 
                               4 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     —Sending 
                     ⁢ 
                     
                       
                           
                       
                       ⁢ 
                       
                           
                       
                     
                     ⁢ 
                     four 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     data 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     streams 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     at 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     same 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     time 
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     According to the definition of encoding rate, the encoding rates in formula (10), formula (11), and formula 12 are 2, 3, and 4 respectively. Compared with SFBC at a rate of 1, spatial multiplexing coding improves the data transmission rate dramatically. 
     Therefore, when only SFBC of the prior art is used, spatial multiplexing gain cannot be obtained, and the transmission rate of the system is decreased because the encoding rate of SFBC is lower than 1 when the number of transmit antennas is greater than 2. Alternatively, when only spatial multiplexing coding of the prior art is used, though spatial multiplexing gain can be obtained by concurrent transmission of multiple data streams, each data stream cannot obtain diversity gain, and the transmission reliability of each data stream is decreased. 
     Cyclic shift diversity (CSD) of the prior art is also a transmit diversity technology applied in OFDM systems. In this solution, frequency diversity gain is obtained in a way that the same OFDM symbols are cyclically shifted in different modes in the time domain and then transmitted by different antennas.  FIG. 2  shows the structure of the transmitter. 
     If a system has M transmit antennas, the OFDM symbols after IFFT processing are respectively input to M transmit antennas. The OFDM symbols on the first antenna are not shifted cyclically (cyclic shift=0), and those on the other antennas are shifted cyclically with different shift bits (δ m , m=1, 2, . . . M, where δ 1 =0). Supposing that the length of IFFT is N, the number of cyclic shift bits must meet the following condition: 0≦δ m ≦N−1. After cyclic shift, a cyclic prefix must be added to the OFDM symbols on each antenna before the symbols are transmitted by different antennas at the same time. 
     In fact, the OFDM symbols transmitted on different antennas are only different cyclic shifts of the same OFDM symbol in the time domain. It is supposed that the signal of the OFDM symbol in the time domain is x(n), (0≦n≦N−1), and that the signal corresponding to each sub-carrier in the frequency domain is X(k), k=0, . . . N−1. Because the CP lengths are the same, the orthogonality of sub-carriers does not change. As seen from FFT, cyclic shifts in the time domain are equivalent to the symbols in the frequency domain plus a phase rotation. Then, the signal obtained after the rotation is as follows:
 
 Z ( k )= X ( k ) e   −j2πδ/N   ,k= 0 , . . . N− 1  (13)
 
     In formula (13), δ indicates the number of cyclic shift bits in the time domain. According to the preceding relations of shift bits, the signal on each sub-carrier of each antenna in the frequency domain can be obtained:
 
 Z   m ( k )= X ( k ) e   −j2πδ     m     /N   ,k= 0 , . . . N− 1 ;m= 1 , . . . M   (14)
 
     Supposing that the number of the receive antennas on the receiver is 1, the signal received by the receiver in the frequency domain is as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             Y 
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           = 
                           
                             
                               
                                 ∑ 
                                 
                                   m 
                                   = 
                                   1 
                                 
                                 M 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   
                                     H 
                                     m 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     Z 
                                     m 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                             + 
                             
                               N 
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             = 
                             
                               
                                 
                                   X 
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     ∑ 
                                     
                                       m 
                                       = 
                                       1 
                                     
                                     M 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     
                                       
                                         H 
                                         m 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       ⅇ 
                                       
                                         
                                           - 
                                           j2π 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         k 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           
                                             δ 
                                             m 
                                           
                                           / 
                                           N 
                                         
                                       
                                     
                                   
                                 
                               
                               + 
                               
                                 N 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                           , 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       k 
                       = 
                       0 
                     
                     , 
                     
                       
                         … 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         N 
                       
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Y(k) indicates the signal received on sub-carrier k. H m (k) indicates the response from the frequency domain channel between transmit antenna m and the receive antenna on sub-carrier k. N(k) indicates additive white Gaussian noise (AWGN). 
     According to the result of formula (15), the multi-antenna system can be equivalent to a single-antenna system:
 
 Y ( k )= H   e ( k ) X ( k )+ N ( k ), k= 0 , . . . N− 1  (16)
 
     The equivalent channel is as follows: 
     
       
         
           
             
               
                 
                   
                     
                       H 
                       e 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         m 
                         = 
                         1 
                       
                       M 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           H 
                           m 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           
                             - 
                             j2π 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           k 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               δ 
                               m 
                             
                             / 
                             N 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     According to the final equivalent results, cyclic shift of different antennas in the time domain is equivalent to introduction of multipath in the time domain, which enhances frequency selection in the frequency domain. In this way, frequency diversity gain can be obtained through channel coding before OFDM modulation. In comparison with a single-antenna system, this cyclic shift method helps to obtain greater frequency diversity gain under the same channel coding and interleaving. 
     For details about CSD, refer to the  Multicarrier Delay Diversity Modulation for MIMO Systems.    
     When used alone to implement diversity, however, OFDM-based CSD has some inevitable defects: (i) the frequency diversity gain can be obtained only through channel coding; (ii) though CSD ensures that the encoding rate is 1, full-diversity gain is unavailable, and the diversity performance is inferior to orthogonal SFBC; (iii) improper delay values may lead to no frequency response on some sub-carriers, cause a puncturing effect, and affect the performance of decoders; and (iv) using CSD and SFBC together changes the responses of channels in the frequency domain, thus affecting the orthogonality of SFBC and decreasing the performance of SFBC. 
     SUMMARY 
     This section provides a general summary of the disclosure, and is not a comprehensive disclosure of its full scope or all of its features. 
     An embodiment provides a method and apparatus for multi-antenna transmitting based on spatial-frequency encoding to address considerations introduced by the prior art such as the inability of ensuring the encoding rate of 1 when the number of transmit antennas is greater than 2, the generation of a puncturing effect when improper delay values are used for CSD, and the inability of obtaining the transmit diversity gain when spatial multiplexing coding is used. 
     To address the above technical issues, an embodiment provides a method for multi-antenna transmitting based on spatial-frequency encoding. The method includes: 
     performing spatial-frequency encoding on input data and outputting multiple ways of encoded data; 
     mapping the encoded data to the same sub-carrier of each antenna in an antenna group; 
     adding a phase shift respectively to the encoded data on different sub-carriers of each antenna; 
     performing OFDM modulation on the phase-shifted encoded data on each antenna; and 
     transmitting the OFDM-modulated data through transmit antennas. 
     Further, an embodiment provides an apparatus for multi-antenna transmitting based on spatial-frequency encoding. The apparatus includes: 
     at least one spatial-frequency encoding unit, adapted to perform spatial-frequency encoding on input data and output at least two ways of encoded data; 
     at least two data mapping units, connected to the spatial-frequency encoding unit and adapted to map the encoded data to the same sub-carrier of each antenna in an antenna group; 
     at least two phase shifting units, connected to the two data mapping units respectively and adapted to add a phase shift to the encoded data on the sub-carriers of each antenna; 
     at least two OFDM modulating units, connected to phase shifting units and adapted to OFDM-modulate the encoded data after phase shifting and overlapping on antennas; and 
     at least two transmitting units, connected to two OFDM modulating units and adapted to transmit the OFDM-modulated data. 
     Therefore, an embodiment uses phase shifting in the frequency domain to replace cyclic shifting of CSD in the time domain, effectively avoiding the puncturing effect and preventing the combination of orthogonal SFBC and CSD from destroying the orthogonality of orthogonal SFBC. 
     An embodiment combines the spatial-frequency encoding and the phase shift transmit diversity to obtain the transmit diversity gain, spatial multiplexing gain, and frequency diversity gain; combines SFBC and phase shifting to solve the issue that the encoding rate is lower than 1 when the number of transmit antennas is greater than 2 in the case of using SFBC only; and combines spatial multiplexing coding and phase shifting to solve the inability of obtaining the diversity gain of each data stream if spatial multiplexing coding is used only. 
     Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure. 
    
    
     
       DRAWINGS 
       The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations, and are not intended to limit the scope of the present disclosure. 
         FIG. 1  shows the composition of a transmitter system that uses SFBC to implement transmit diversity in the prior art; 
         FIG. 2  shows the composition of a transmitter system that uses CSD to implement transmit diversity in the prior art; 
         FIG. 3  is a schematic diagram showing the mapping of data for multi-antenna transmitting based on SFBC and phase shifting in space and frequency dimensions according to an embodiment; 
         FIG. 4  is a schematic diagram showing the structure of an apparatus for multi-antenna transmitting based on SFBC and phase shifting according to an embodiment; 
         FIG. 5  is another schematic diagram showing the structure of the apparatus for multi-antenna transmitting based on SFBC and phase shifting according to an embodiment; 
         FIG. 6  is a schematic diagram showing the mapping of data for multi-antenna transmitting based on spatial multiplexing coding and phase shifting in time and frequency dimensions according to an embodiment; 
         FIG. 7  is a schematic diagram showing the structure of an apparatus for multi-antenna transmitting based on spatial multiplexing coding and phase shifting according to an embodiment; 
         FIG. 8  is another schematic diagram showing the structure of the apparatus for multi-antenna transmitting based on spatial multiplexing coding and phase shifting according to an embodiment; and 
         FIG. 9  is a flowchart of the method for multi-antenna transmitting based on SFBC and phase shifting according to an embodiment. 
     
    
    
     Corresponding reference numerals indicate corresponding parts throughout the several views of the drawings. 
     DETAILED DESCRIPTION 
     Example embodiments will now be described more fully with reference to the accompanying drawings. 
     Reference throughout this specification to “one embodiment,” “an embodiment,” “specific embodiment,” or the like in the singular or plural means that one or more particular features, structures, or characteristics described in connection with an embodiment is included in at least one embodiment of the present disclosure. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment,” “in a specific embodiment,” or the like in the singular or plural in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. 
     An embodiment combines SFBC and CSD to ensure the encoding rate of 1 when the number of transmit antennas is greater than 2. In this case, antennas are categorized into two groups, each containing at least one antenna. After SFBC is performed on input data according to the encoding matrix in formula (1), two ways of concurrent encoded data are output. Each way of data is mapped to a transmit antenna group. The data is OFDM modulated, cyclically shifted, and then transmitted on different antennas in the same antenna group. However, certain considerations arise when SFBC and CSD are directly used together. The reason is that the signals received on sub-carriers k and k+1 in the frequency domain can be expressed by formulas (18) and (19) (supposing that the receiver has only one antenna). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     Formula (20) must be met if data is encoded and second-order diversity gain is obtained according to formulas (4) and (5):
 
 H   1e ( k )= H   1e ′( k ), H   2e ( k )= H   2e ′( k )  (20)
 
     Because the spacing between sub-carriers k and k+1 is often smaller than the channel bandwidth, the following conditions are met: H 1 (k)=H 1 (k+1), H 2 (k)=H 2 (k+1), H 3 (k)=H 3 (k+1), H 4 (k)=H 4 (k+1). The following conditions must be met to make formula (20) valid: 
               ⅇ       -   j     ⁢       2   ⁢   π   ⁢           ⁢   k   ⁢           ⁢     τ   1       N         =     ⅇ       -   j     ⁢       2   ⁢     π   ⁡     (     k   +   1     )       ⁢     τ   1       N               
and
 
               ⅇ       -   j     ⁢       2   ⁢   π   ⁢           ⁢   k   ⁢           ⁢     τ   2       N         =       ⅇ       -   j     ⁢       2   ⁢     π   ⁡     (     k   +   1     )       ⁢     τ   2       N         .           
At this time, the condition of τ 1 =τ 2 =0 must be met. That means no CSD is performed. Therefore, CSD cannot be used to obtain the frequency diversity gain. To make formula 20 valid, that is, H 1e (k)=H 1e ′(k), H 2e (k)=H 2e ′(k), the frequency domain data transmitted on adjacent n sub-carriers of the same antenna based on SFBC must have the same phase shift, but this cannot be achieved if CSD is used alone. Further, the essence of obtaining diversity gain based on CSD is that the same frequency domain data transmitted on different antennas is multiplied by different phase shifts. Therefore, the present embodiment uses SFBC and CSD together and uses phase shifting in the frequency domain to replace cyclic shifting of CSD in the time domain. This phase shift meets the following conditions: the phase shift on the same transmit antenna changes every n sub-carrier sets, and the phase shifts on the same sub-carrier of different transmit antennas in the same antenna group are different. Those skilled in the art may understand that an embodiment may meet formula (20) and may also obtain frequency diversity gain similar to CSD.
 
     The present disclosure is hereinafter described in detail with reference to embodiments and accompanying drawings. In an embodiment, multi-antenna transmitting is based on, but is not limited to, SFBC and phase shifting, as well as spatial multiplexing coding and phase shifting. 
     As shown in  FIG. 3 , the data for multi-antenna transmitting based on SFBC and phase shifting is mapped respectively in time and frequency dimensions, where, sub-carriers k and k+1 are sub-carriers for one SFBC, antennas  1  and  2  are in antenna group  1 , the phase shift of sub-carriers k and k+1 on antenna  1  is θ 1 , and that on antenna  2  is θ 2 ; antennas  3  and  4  are in antenna group  2 , the phase shift of sub-carriers k and k+1 on antenna  3  is θ 3 , and that on antenna  4  is θ 4 . In addition, θ 1 ≠θ 2  and θ 3 ≠θ 4 . 
     When there is one receive antenna, the signals received by the receiver on sub-carriers k and k+1 in the frequency domain can be expressed by formulas (22) and (23). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     As can be known by those skilled in the art that, if decoding is performed according to formulas (4) and (5), formula (20) can be met and thus second-order diversity gain can be obtained. Moreover, because θ 1 ≠θ 2  and θ 3 ≠θ 4 , the diversity gain similar to CSD can be obtained. 
     The present disclosure is described below with reference to some exemplary embodiments. 
       FIG. 4  shows the structure of an apparatus for multi-antenna transmitting based on SFBC and phase shifting according to an embodiment. 
     The apparatus includes at least one spatial-frequency encoding unit, two data mapping units, two phase shifting units, two OFDM modulating units, and two transmit antennas. The spatial-frequency encoding unit is adapted to perform spatial-frequency encoding on the input data and output at least 2 ways of encoded data. The data mapping units are connected to the spatial-frequency encoding unit and adapted to map each way of the encoded data to the same sub-carrier of each antenna in an antenna group. The phase shifting units are adapted to add a phase shift respectively to the encoded data on each sub-carrier of an antenna. The OFDM modulating units are connected to the phase shifting units and adapted to OFDM-modulate the encoded data on each sub-carrier of an antenna. The transmit antennas are connected to the OFDM modulating units and adapted to transmit the OFDM-modulated data. For descriptive purposes, the embodiment provides an apparatus for 4-antenna transmitting. The apparatus includes, but is not limited to, one spatial-frequency encoding unit  10 , two data mapping units  20 - 1  and  20 - 2 , four phase shifting units  30 - 1 ,  30 - 2 ,  30 - 3 , and  30 - 4 , four OFDM modulating units  40 - 1 ,  40 - 2 ,  40 - 3 , and  40 - 4 , and four transmit antennas  50 - 1 ,  50 - 2 ,  50 - 3 , and  50 - 4 . The spatial-frequency encoding unit  10  outputs the frequency domain data of the first antenna group to the data mapping unit  20 - 1  and the frequency domain data of the second antenna group to the data mapping unit  20 - 2 . The data mapping unit  20 - 1  is connected to the phase shifting units  30 - 1  and  30 - 2 . The data mapping unit  20 - 2  is connected to the phase shifting units  30 - 3  and  30 - 4 . The four phase shifting units  30 - 1 ,  30 - 2 ,  30 - 3 , and  30 - 4 , four OFDM modulating units  40 - 1 ,  40 - 2 ,  40 - 3 , and  40 - 4 , and four transmit antennas  50 - 1 ,  50 - 2 ,  50 - 3 , and  50 - 4  correspond to each other and are connected in sequence. 
     At least four transmit antennas are typically employed in this embodiment because each antenna group has at least one transmit antenna and at least one antenna group has two transmit antennas. The number of transmit antennas typically ensures the implementation of antenna groups, but does not affect the essence of the disclosure. For ease of description, it is assumed that each antenna group contains two transmit antennas in a first embodiment.  FIG. 4  shows the groups of antennas in the first embodiment, where the transmit antennas marked in the same broken line frame belong to the same group. 
     The spatial-frequency encoding unit  10  is adapted to perform spatial-frequency encoding on input data. The spatial-frequency encoding unit  10  uses the following formula to ensure that the spatial-frequency encoding is completed within an OFDM symbol period. 
     
       
         
           
             
               
                 
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     Formula (1) is a second-order orthogonal encoding matrix. It may be understood that encoding in only space and frequency dimensions can be completed within one OFDM symbol period. The second-order orthogonal encoding is to ensure that the encoding rate is 1 and that the decoding method is simple. Theoretically, higher order or non-orthogonal encoding may be also used. 
     It is supposed that the input data is S 1  and S 2 . After the data is transmitted through the spatial-frequency encoding unit  10 , two ways of encoded data are output, namely, S 1  and −S 2 *, and S 2  and S 1 *. 
     The data mapping units  20 - 1  and  20 - 2  each copy one way of encoded data for the respective connected phase shifting units according to the input encoded data received and map the encoded data to each sub-carrier in turn. 
     The phase shifting unit is adapted to add the phase shifts of the other phase shifting units in the same antenna group to the input frequency domain data. The phase shifts are different. It may be understood that: the phase shifting unit adds the same phase shift to the encoded frequency domain data transmitted by the same transmit antenna on n adjacent sub-carrier pairs based on SFBC; the phase shifts of every n sub-carrier sets are different; and the phase shifts of the sub-carriers with the same frequency on different antennas in the same antenna group are different. For example, in the first embodiment, sub-carriers k and k+1 are sub-carriers for one SFBC, transmit antennas  50 - 1  and  50 - 2  are in antenna group  1 , the phase shift of sub-carriers k and k+1 on transmit antenna  50 - 1  is θ 1 , and that on antenna  50 - 2  is θ 2 ; transmit antennas  50 - 3  and  50 - 4  are in antenna group  2 , the phase shift of sub-carriers k and k+1 on antenna  50 - 3  is θ 3 , and that on antenna  50 - 4  is θ 4 , where, θ 1 ≠θ 2  and θ 3 ≠θ 4 . 
     The OFDM modulating unit modulates the phase-shifted encoded data that is output by the phase shifting units to the sub-carriers of OFDM. This unit may be implemented by IFFT. Those of ordinary skills in the art may already know the specific implementation process, so details are omitted. 
     The transmit antenna is adapted to transmit the output data of the OFDM modulating unit. 
     For ease of implementation, in a second embodiment, the phase shift of the encoded data on one antenna  50  of the same group may be set to 0, that is, θ 1 =0 and θ 3 =0 in the first embodiment. In addition, the phase shift sequences of different antenna groups may be set to the same for multiplexing of phase shifting units  30 , that is, θ 2 =θ 4  in the first embodiment. 
     In the third embodiment, time-varying phase sequences may be used to speed up channel changes, that is, enabling θ 1 , θ 2 , θ 3 , and θ 4  in the first embodiment to change in real time and differ between each or multiple OFDM symbols. 
       FIG. 5  shows another structure of the apparatus for multi-antenna transmitting, taking 3-antenna transmitting as an example, based on spatial-frequency encoding in an embodiment. The apparatus includes at least one spatial-frequency encoding unit  51 , three phase shifting units  52 - 1 ,  52 - 2 , and  52 - 3 , three OFDM modulating units  53 - 1 ,  53 - 2 , and  53 - 3 , and three transmitting units  54 - 1 ,  54 - 2 , and  54 - 3 . The spatial-frequency encoding unit  51  is adapted to perform spatial frequency encoding on input data and output two ways of encoded data through two antenna groups. The three phase shifting units are adapted to add a phase shift to the encoded data received from the spatial-frequency encoding unit. The three OFDM modulating units are connected to the three phase shifting units and adapted to OFDM-modulate the phase-shifted encoded data to corresponding sub-carriers. The three transmitting units are connected to the three OFDM modulating units and adapted to transmit the modulated data. 
     For functions of each unit of this apparatus, refer to related descriptions above. 
     Further, when spatial multiplexing coding is used, each data stream cannot obtain frequency diversity gain, which decreases the transmission quality. Therefore, in the fourth embodiment, spatial multiplexing coding and phase shifting are used together to obtain not only spatial multiplexing gain but also frequency diversity gain. 
       FIG. 6  shows the mapping of data for multi-antenna transmitting based on spatial multiplexing coding and phase shifting in time and frequency dimensions. It is supposed that the number of transmit antennas is 4. Formula (10) shows the spatial multiplexing coding at a rate of 2. As seen from formula (10), only one sub-carrier is needed for one spatial multiplexing coding operation.  FIG. 6  takes sub-carrier k as an example. Operations on other sub-carriers are similar. At this time, all transmit antennas belong to the same group, the input data is directly converted into two ways of concurrent data, and each way of data is mapped to all antennas for transmitting. On sub-carrier k, the phase shift of the encoded data S 1  is θ 1   1  on antenna  1 , θ 1   2  on antenna  2 , θ 1   3  on antenna  3 , and θ 1   4  on antenna  4 . The phase shift of the encoded data S 2  is θ 2   1  on antenna  1 , θ 2   2  on antenna  2 , θ 2   3  on antenna  3 , and θ 2   4  on antenna  4 . Then all the phase-shifted data is added up on each antenna. Data 
                 S   1     ⁢     ⅇ     jθ   1   1         +       S   2     ⁢     ⅇ     jθ   2   1               
is transmitted by antenna  1  on sub-carrier k,
 
                 S   1     ⁢     ⅇ     jθ   1   2         +       S   2     ⁢     ⅇ     jθ   2   2               
is transmitted by antenna  2 ,
 
                 S   1     ⁢     ⅇ     jθ   1   3         +       S   2     ⁢     ⅇ     jθ   2   3               
is transmitted by antenna  3 , and
 
                 S   1     ⁢     ⅇ     jθ   1   4         +       S   2     ⁢     ⅇ     jθ   2   4               
is transmitted by antenna  4 .
 
     For ease of implementation, in the fifth embodiment, the phase shift of the encoded data transmitted by one antenna in the same antenna group in the fourth embodiment may be set to 0, corresponding to θ 1   1 =0 and θ 2   1 =0 in the first embodiment. 
     In the sixth embodiment, time-varying phase sequences may be used in the fourth embodiment to speed up channel changes, that is, enabling θ 1   1 , θ 1   2 , θ 1   3 , θ 1   4 , θ 2   1 , θ 2   2 , θ 2   3 , and θ 2   4  to change in real time and differ between each or multiple OFDM symbols in the first embodiment. 
       FIG. 7  shows an apparatus for multi-antenna transmitting based on spatial multiplexing coding and phase shifting in an embodiment. Taking 4-antenna transmitting as an example, the apparatus includes at least one spatial-frequency encoding unit  71 , two data mapping units  72 - 1  and  72 - 2 , two phase shifting units, one additive unit, one OFDM modulating unit, and one transmit antenna. For descriptive purposes, this embodiment uses eight phase shifting units (expressed by  73 ), four additive units (expressed by  74 ), four OFDM modulating units (expressed by  75 ), and four transmit antennas (expressed by  76 ). The spatial-frequency encoding unit  71  is adapted to perform spatial-frequency encoding on the input data and output at least two ways of encoded data. The data mapping unit  72  is connected to the spatial-frequency encoding unit  71  and adapted to map the multiple ways of encoded data to the same sub-carrier of each antenna in an antenna group. The phase shifting unit  73  is adapted to add a phase shift respectively to the encoded data on each sub-carrier of an antenna. The additive unit  74  is connected to the phase shifting unit  73  and adapted to add up the phase-shifted encoded data. The OFDM modulating unit  75  is connected to the additive unit  74  and adapted to OFDM-modulate the encoded data added up on each sub-carrier of an antenna. The transmit antenna  76  is connected to the OFDM modulating unit  75  and adapted to transmit the OFDM-modulated data. 
     One difference between this embodiment and the preceding embodiments is as follows: When spatial multiplexing coding is used, after the phase shifting unit  73  adds a phase shift to the encoded data on the sub-carriers of each antenna, the additive unit  74  adds up the encoded data, and then transmits the encoded data to the OFDM modulating unit  75 . The subsequent processing is the same as that of the preceding embodiments. 
     For functions of each unit of this apparatus, refer to related descriptions above. 
       FIG. 8  shows another structure of the apparatus for multi-antenna transmitting based on spatial multiplexing coding and phase shifting in an embodiment. The apparatus includes at least one spatial-frequency encoding unit  81 , two data mapping units  821  and  822 , two phase shifting units  831  and  832 , two additive units  841  and  842 , two OFDM modulating units  851  and  852 , and two transmitting units  861  and  862 . The spatial-frequency encoding unit  81  is adapted to perform spatial-frequency encoding on the input data and output at least two ways of encoded data. The data mapping units  821  and  822  are connected to the spatial-frequency encoding unit  81  and adapted to map one way of the encoded data to the same sub-carrier of each antenna in an antenna group. The phase shifting units  831  and  832  are connected to the phase mapping units  821  and  822  and adapted to add a phase shift respectively to the encoded data on sub-carriers of each antenna. The additive units  841  and  842  are connected to the phase shifting units  831  and  832  and adapted to add up the phase-shifted encoded data on each sub-carrier of an antenna. The OFDM modulating units  851  and  852  are connected to the additive units  841  and  842  and adapted to OFDM-modulate the phase-shifted encoded data added up on antennas. The transmitting units  861  and  862  are connected to the OFDM modulating units  851  and  852  and adapted to transmit the modulated data. 
     One specific implementation process may be similar to that of preceding embodiments. 
     Further, an embodiment provides a method for multi-antenna transmitting based on spatial multiplexing coding and phase shifting.  FIG. 9  shows the specific process. The method includes: 
     S 10 : performing spatial-frequency encoding on input data and outputting multiple ways of encoded data; 
     S 20 : mapping the encoded data to the same sub-carrier of each antenna in an antenna group; 
     S 30 : adding a phase shift to the encoded data on different sub-carriers of each antenna; 
     S 40 : OFDM-modulating the phase-shifted encoded data on each antenna; and 
     S 50 : transmitting the OFDM-modulated data through transmit antennas. 
     When spatial-frequency multiplexing coding is used, this method also includes adding up the phase-shifted encoded data on each antenna before OFDM modulation. 
     In S 10 , spatial-frequency encoding is performed on the input data. The spatial-frequency encoding unit  10  uses the second-order orthogonal encoding matrix shown in formula 1 to ensure that spatial-frequency encoding is completed within an OFDM symbol period. It is supposed that the input data is S 1  and S 2 . After the data is transmitted to the spatial-frequency encoding unit  10 , two ways of encoded data are output, namely, S 1  and −S 2 *, and S 2  and S 1 *. 
     Then the process proceeds to S 20 . Multiple transmit antennas are grouped and the encoded data is mapped to the same sub-carrier of each antenna in the antenna group. 
     When SFBC is used, the number of antenna groups is equal to the number of ways of space frequency encoded data. When spatial multiplexing coding is used, the number of antenna groups is 1. 
     Then the process proceeds to S 30 . A phase shift is added respectively to the encoded data on different sub-carriers of each antenna. The phase shift meets the following conditions: the phase shifts of the encoded frequency domain data transmitted by the same transmit antenna on n adjacent sub-carrier pairs based on SFBC are the same; the phase shifts are different every n sub-carrier sets, and the phase shifts of the sub-carriers with the same frequency on different antennas in the same antenna group are different. 
     When SFBC is used, each way of data is mapped to different antenna groups. When spatial multiplexing coding is used, all data is mapped to the same antenna group. 
     Then the process proceeds to S 40 , where the phase-shifted encoded data on each antenna is OFDM-modulated, or the phase-shifted encoded data is added up and then OFDM-modulated. In this embodiment, OFDM may be implemented by IFFT. 
     Then the process proceeds to S 50 , where the OFDM-modulated data is transmitted by transmit antennas. In other words, the encoded data after mapping (namely, OFDM modulation) on sub-carriers is transmitted by antennas. 
     For the implementation of each process in this method, refer to descriptions of the functions of related units above. 
     In this embodiment, for ease of implementation, the phase shift of the encoded data on one of the transmit antennas in the same group may be set to 0, and the phase shifts of different antenna groups may be set to the same. Moreover, time-varying phase shifts may be used to adapt to channel changes better. 
     An embodiment not only uses spatial-frequency encoding to obtain space diversity gain and spatial multiplexing gain, but also introduces a phase shift to the frequency domain to obtain extra frequency diversity gain similar to CSD. The phase shift meets the following conditions: the phase shift of the encoded data on the same transmit antenna changes every n sub-carrier sets; the phase shifts of different ways of data on the same sub-carrier of the same transmit antenna are different; and the phase shifts on the same sub-carrier of different transmit antennas in the same antenna group are different. 
     Therefore, the present disclosure uses phase shifting in the frequency domain to replace CSD in the time domain, which effectively avoids the puncturing effect of CSD and prevents direct use of orthogonal SFBC and CSD from destroying the orthogonality of orthogonal SFBC. 
     Further, an embodiment combines spatial-frequency encoding and phase shift transmit diversity to obtain transmit diversity gain, spatial multiplexing gain, and frequency diversity gain. The combined use of SFBC and phase shifting can solve the issue that the encoding rate is lower than 1 when the number of transmit antennas is greater than 2 when SFBC is used. The combined use of spatial multiplexing coding and phase shifting solves the inability of obtaining the diversity gain of each data stream if only spatial multiplexing coding is used. 
     In addition, the phase shift is set to change every n sub-carrier sets, effectively ensuring that the channel change speed in n sub-carrier sets is not changed, and thus the interference estimation accuracy is not affected by the phase shift when a receiver capable of interference elimination is used. 
     The present disclosure has been described through some exemplary embodiments. It is apparent that those skilled in the art can make various modifications and variations to the disclosure without departing from the spirit and scope of the disclosure. The disclosure is intended to cover the modifications and variations provided that they fall in the scope of protection defined by the following claims or their equivalents. 
     The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.