Abstract:
A relaying method and system in a communication system having a Base Station (BS), a Mobile Station (MS) for communicating with the BS, and a Relay Station (RS) for relaying signals between the BS and the MS are provided. In the relaying method and system, the BS generates a BS pilot sequence and transmits the generated BS pilot sequence to the RS. wherein a partial cross correlation between the BS pilot sequence and an RS pilot sequence, being the BS pilot sequence relayed by the RS is always ‘0’. Accordingly, system capacity is more efficiently utilized.

Description:
PRIORITY 
       [0001]    This application claims priority under 35 U.S.C. § 119(a) to a Korean Patent Application filed in the Korean Intellectual Property Office on Sep. 6, 2006 and assigned Serial No. 2006-85752, the entire disclosure of which is incorporated herein by reference. 
       BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention generally relates to a relay communication system. More particularly, the present invention relates to a relay system and method for providing a pilot sequence that optimizes channel estimation performance in a relay communication system. 
         [0004]    2. Description of the Related Art 
         [0005]    Signal transmission and reception typically take place via a direction link between a Base Station (BS) and a Mobile Station (MS) in a communication system. Relative to the fixedness of BSs, however, a wireless network is not flexibly configured, shadowing area exists, and provisioning of an efficient communication service is difficult in a radio environment experiencing fluctuating change in channel status. To overcome these shortcomings, the use of Relay Stations (RSs) was proposed. 
         [0006]    These relay communication systems increase system capacity and expand cell coverage. When the channel status between a BS and an MS is poor, an RS is positioned between them to thereby providing a better radio channel to the MS via an RS-based relay link. Signal relaying enables an MS at a cell boundary having a poor channel status to use a higher-rate data channel and expands cell coverage. The configuration of a conventional relay communication system will be described with reference to  FIG. 1 . 
         [0007]      FIG. 1  illustrates the configuration of a conventional relay communication system. 
         [0008]    Referring to  FIG. 1 , the relay communication system includes, for example, a BS  111 , an RS  113  and an MS  115 . The RS  113  provides a relay path between the BS  111  and the MS  115 . 
         [0009]    Although the MS  115  and the BS  111  can communicate directly with each other, it is assumed herein that the MS  115  communicates with the BS  111  with the aid of the RS  113 . The RS  113  relays signals between the BS  111  and the MS  115 , and the MS  115  exchanges signals with the BS  111  via the RS  113 . 
         [0010]    Let a channel between the BS  111  and the RS  113  be denoted by h BR , a channel between the RS  113  and the MS  115  be denoted by h RM , and a channel between the BS  111  and the MS  115  be denoted by h BM . If the BS  111  transmits a signal x B , a signal received at the RS  113  and a signal to be forwarded by the RS  113  are given as Equation (1); 
         [0000]        Y   R   =h   BR   x   B   +n   R   (1) 
         [0000]        x   R =α( h   BR   x   B   +n   R ) 
         [0000]    where y R  denotes the signal received at the RS  113  from the BS  111 , x R  denotes the signal forwarded by the RS  113 , n R  denotes noise received at the RS  113 , and α denotes an amplifier gain constant of the RS  113 . 
         [0011]    Meanwhile, the MS  115  receives the signal from the BS  111  via the RS  113 . The received signal is expressed as Equation (2); 
         [0000]        Y   M   =αh   RM   h   BR   x   B   +αn   R   +n   M   (2) 
         [0000]    where y M  denotes the signal received at the MS  115  from the BS  111  via the RS  113  and n M  denotes noise received at the MS  115 . 
         [0012]    The communication system uses a half duplex relay scheme. For one time period, one transmitter, for example, the BS  111  or the RS  113  transmits a signal. With reference to  FIG. 2 , the half duplex relay scheme will be described below. 
         [0013]      FIG. 2  illustrates a conventional half duplex relay scheme. 
         [0014]    Referring to  FIG. 2 , an RS relays a signal received from a BS to an MS in a relay communication system. Two time periods, T 1  and T 2  are defined for signal transmission/reception. 
         [0015]    At T 1 , the BS transmits a signal ‘x 1 ’, and the RS receives the signal ‘x 1 ’ without any signal transmission. At T 2 , the BS discontinues signal transmission, while the RS amplifies and forwards the received signal ‘x 1 ’ to the MS. The half duplex relay scheme is characterized in that each transmitter, for example, the BS or the RS transmits a signal during a different time period. 
         [0016]    In the half duplex relay communication system, only one transmitter operates during one time period. Therefore, overall system capacity is not efficiently utilized. 
       SUMMARY OF THE INVENTION 
       [0017]    An aspect of the present invention is to address at least the above mentioned problems and/or disadvantages and to provide at least the advantages described below. Accordingly, an aspect the present invention is to provide a relay system and method in a communication system. 
         [0018]    Another aspect of the present invention is to provide a full duplex relay system and method in a communication system. 
         [0019]    A further aspect of the present invention is to provide a full duplex relay system and method for enabling at least two transmitters to transmit signals during one time period in a communication system using an RS that amplifies a signal for relaying. 
         [0020]    Still another aspect of the present invention is to provide a relay system and method for generating a pilot sequence that enables a full duplex relay in a communication system using relay station adapted to a Decode-and-Forward (DF) strategy. 
         [0021]    In accordance with an aspect of the present invention, a relaying method in a communication system having a BS, a MS for communicating with the BS, and an RS for relaying signals between the BS and the MS is provided. In the relaying method, the BS generates a BS pilot sequence and transmits the generated BS pilot sequence to the RS wherein a partial cross correlation between the BS pilot sequence and an RS pilot sequence being the BS pilot sequence relayed by the RS is always ‘0’. 
         [0022]    In accordance with another aspect of the present invention, a relay system in a communication system having a BS, a MS for communicating with the BS, and an RS for relaying signals between the BS and the MS is provided. In the relay system, the BS generates a BS pilot sequence and transmits the generated BS pilot sequence to the RS, and the RS receives the BS pilot sequence from the BS and relays the received BS pilot sequence as an RS pilot sequence to the MS. Here, a partial cross correlation between the BS pilot sequence and the RS pilot sequence is always ‘0’. 
     
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0023]    The above and other objects, features and advantages of certain exemplary embodiments of the present invention will be more apparent from the following detailed description taken in conjunction with the accompanying drawings, in which: 
           [0024]      FIG. 1  illustrates the configuration of a conventional relay communication system; 
           [0025]      FIG. 2  illustrates a conventional half duplex relay scheme; 
           [0026]      FIG. 3  illustrates the configuration of a relay communication system according to the present invention; 
           [0027]      FIG. 4  illustrates a full duplex relay system according to the present invention; 
           [0028]      FIG. 5  is a block diagram of a BS according to the present invention; 
           [0029]      FIG. 6  is a diagram illustrating transmission time periods of pilot sequences according to the present invention; and 
           [0030]      FIG. 7  is a block diagram of an RS according to the present invention. 
       
    
    
       [0031]    Throughout the drawings, the same drawing reference numerals will be understood to refer to the same elements, features and structures. 
       DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0032]    The following description with reference to the accompanying drawings is provided to assist in a comprehensive understanding of exemplary embodiments of the invention as defined by the claims and their equivalents. It includes various specific details to assist in that understanding but these are to be regarded as merely exemplary. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the invention. Also, descriptions of well-known functions and constructions are omitted for clarity and conciseness. 
         [0033]    Exemplary embodiments of the present invention provide a system and method for transmitting signals using a full duplex relay scheme, for example, in a communication system. 
         [0034]    The communication system includes a BS, a MS for communicating with the BS, and an RS for relaying signals between the BS and the at least one MS. The BS generates a pilot sequence and transmits a signal with the pilot sequence to the RS. Simultaneously with receiving the signal from the BS, the RS amplifies a signal received from the BS in a previous time period and transmits the amplified signal to the MS. 
         [0035]    Notably, the pilot sequence is generated such that the product between the pilot sequence and its Hermitian is a real number multiple of a unitary matrix. In other words, the BS generates a pilot sequence such that the partial cross correlation between the pilot sequence and a delayed version of the pilot sequence forwarded by the RS is ‘0’, and the RS relays the pilot sequence to the MS. Thus, a full duplex relaying is performed. The partial cross correlation is multiplication of pilot sequences with each other. 
         [0036]      FIG. 3  illustrates the configuration of a relay communication system according to the present invention. 
         [0037]    Referring to  FIG. 3 , the relay communication system includes a BS  311 , an RS  313  and an MS  315 . 
         [0038]    To increase data rate and expand service coverage, the RS  313  provides a relay path between the BS  311  and the MS  315 . The RS  313  can be a fixed RS, a mobile RS, or a general MS. 
         [0039]    It is assumed that the communication system operates in Orthogonal Frequency Division Multiplexing (OFDM)/Orthogonal Frequency Division Multiple Access (OFDMA). The RS  313  relays signals between the BS  311  and the MS  315 . Thus, the MS  315  can transmit and receive signals to and from the BS  311  via the RS  313 . 
         [0040]    Assuming that an i th  subcarrier is a pilot subcarrier in the OFDMA system, let a channel between the BS  311  and the RS  313  on the i th  subcarrier in a t th  symbol interval be denoted by H i,br,t , a channel between the RS  313  and the MS  315  on the i th  subcarrier in the t th  symbol interval be denoted by H i,RM,t , and a channel between the BS  311  and the MS  315  on the i th  subcarrier in the t th  symbol interval be denoted by H i,BM,t . 
         [0041]    The relay communication system adopts a full duplex relay scheme in which at least two transmitters, for example, the BS  311  and the RS  313  transmit signals simultaneously during a given time period. 
         [0042]    With reference to  FIG. 4 , the full duplex relay scheme according to an exemplary embodiment of the present invention will be described. 
         [0043]      FIG. 4  illustrates a full duplex relay scheme according to the present invention. 
         [0044]    Referring to  FIG. 4 , an RS relays a signal received from a BS to an MS in a relay communication system. Two signal transmission/reception time periods T 1  and T 2  are identified. 
         [0045]    At T 1 , the BS transmits a signal ‘x 1 ’ and at the same time, the RS amplifies and transmits a previously received signal ‘x 0 ’ to the MS. At T 2 , the BS transmits a signal ‘x 2 ’ and at the same time, the RS amplifies and forwards the previously received signal ‘x 1 ’ to the MS. 
         [0046]    Compared to the conventional half duplex relay scheme, the full duplex relay scheme leads to efficient utilization of system capacity. In the full duplex relay scheme, during a given time period, one or more transmitters transmit signals, which interfere with each other. Accordingly, exemplary embodiments of the present invention propose a pilot sequence that optimizes channel estimation performance when the full duplex relay scheme is used. 
         [0047]    With reference to  FIG. 5 , the configuration of an exemplary BS apparatus for generating and transmitting a pilot sequence will be described. 
         [0048]      FIG. 5  is a block diagram of a BS according to the present invention. 
         [0049]    Referring to  FIG. 5 , the BS includes encoders  511 , modulators  513 , a Multiple Input Multiple output (MIMO) processor  515 , a pilot sequence generator  517 , subcarrier mappers  519  and transmitters  521 . 
         [0050]    The encoders  511  encode received information bits. The modulators  513  modulate the code symbols received from the encoders  511 . The MIMO processor  515  MIMO-processes the modulated signals so that they can be transmitted through multiple antennas. 
         [0051]    If the BS transmits signals using a single antenna system, for instance, a Single Input Single Output (SISO) scheme, the MIMO processor  515  is not used, and a single subcarrier mapper  519  and a single transmitter  521  exist, which are connected to a single antenna. 
         [0052]    The pilot sequence generator  517  generates pilot sequences according to information about the number M of antennas in current use in the BS and a relaying delay. M can be preset in the BS and information about the relaying delay is received from the RS or the MS. The pilot sequence generation will be detailed later. 
         [0053]    The subcarrier mappers  519  map the outputs of the MIMO processor  515  and the pilot sequences received from the pilot sequence generator  517  to subcarriers. 
         [0054]    The transmitters  521  process the outputs of the subcarrier mappers  519  by Inverse Fast Fourier Transform (IFFT), Cyclic prefix/Postfix (CP) insertion, windowing, and RF upconversion and transmit the resulting RF signals through the antennas. 
         [0055]    The product of a pilot sequence generated in the pilot sequence generator  517  and its Hermitian sequence is a real number multiple of a unitary matrix. This pilot sequence generation condition is given as Equation (3); 
         [0000]      P t   H P t =λI  (3) 
         [0000]    where P t  is a pilot sequence matrix having a pilot sequence transmitted from a t−(2×M+1) th  symbol interval to a t th  symbol interval and its delayed version as column vectors. Here, M is the number of transmit antennas. H denotes a Hermitian operation, I denotes the unitary matrix, and λ denotes a real number multiplied by the unitary matrix. How P t  is formed under different transmit antenna situations will be described later. 
         [0056]    In an exemplary embodiment of the present invention, an optimal pilot sequence is acquired on the assumption that a channel is kept unchanged during 2×M symbol intervals. 
         [0057]      FIG. 6  is a diagram illustrating transmission time periods of pilot sequences in a communication system according to the present invention. 
         [0058]    Referring to  FIG. 6 , pilot sequences transmitted by the BS and the RS are shown. One symbol of pilot sequence transmission delay occurs between the BS and the RS. The BS and the RS each transmit a pilot sequence P t  with pilot symbols P i1  to P iN  in symbol intervals. Let a pilot symbol of the pilot sequence P t  transmitted on an i th  subcarrier at time t be denoted by P it . 
         [0059]    A pilot sequence transmitted by the BS and a relayed version of the pilot sequence transmitted by the RS have a time offset of one symbol between them. 
         [0060]    The RS receives a signal from the BS and relays the received signal with a delay of one symbol. Thus, the RS transmits a pilot symbol P it−1  in a t th  symbol interval. 
         [0061]    In the case where the BS operates using a single antenna, for example, in SISO, a pilot sequence that the BS generates for a full duplex relay satisfies Equation (3). Here, P t  takes the form of a matrix 
         [0000]    
       
         
           
             
               [ 
               
                 
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           t 
                           - 
                           1 
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           t 
                           - 
                           2 
                         
                       
                     
                   
                 
                 
                   
                     
                       P 
                       
                         i 
                         , 
                         t 
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           t 
                           - 
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               ] 
             
             . 
           
         
       
     
         [0062]    In SISO, received signals at the MS are modeled as Equation (4); 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             Y 
                             
                               i 
                               , 
                               1 
                             
                           
                         
                       
                       
                         
                           
                             Y 
                             
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                           ⋮ 
                         
                       
                       
                         
                           
                             Y 
                             
                               i 
                               , 
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                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 H 
                                 
                                   iBM 
                                   , 
                                   1 
                                 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 α 
                                  
                                 
                                     
                                 
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                                     , 
                                     1 
                                   
                                 
                                  
                                 
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                                     , 
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                                 H 
                                 
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                                   2 
                                 
                               
                             
                             
                               0 
                             
                             
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                               0 
                             
                             
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                               0 
                             
                             
                               
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                                     , 
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                                   H 
                                   
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                                     , 
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                                   iBM 
                                   , 
                                   3 
                                 
                               
                             
                             
                               0 
                             
                             
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                               ⋮ 
                             
                             
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                                 α 
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                                     , 
                                     
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                                   H 
                                   
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                                     , 
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                         ] 
                       
                        
                       
                         [ 
                         
                           
                             
                               
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                                   , 
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                                   , 
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                                   i 
                                   , 
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                               ⋮ 
                             
                           
                           
                             
                               
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                                   i 
                                   , 
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                         ] 
                       
                     
                     + 
                     
                       [ 
                       
                         
                           
                             
                               W 
                               
                                 i 
                                 , 
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               W 
                               
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                                 , 
                                 2 
                               
                             
                           
                         
                         
                           
                             
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                                 , 
                                 3 
                               
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               W 
                               
                                 i 
                                 , 
                                 N 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Y i,t  denotes a received signal on the i th  subcarrier at time t, H iBM,t , H iBR,t  and H iRM,t  denote the channel between the BS and the MS, the channel between the BS and the RS, and the channel between the RS and the MS on the i th  subcarrier at time t, P i,t  denotes a pilot symbol transmitted on the i th  subcarrier at time t, a denotes an amplifier gain constant of the RS, and W i,t  denotes noise received on the i th  subcarrier at time t. 
         [0063]    Any two of the received signals can be expressed as Equation (5); 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               Y 
                               
                                 i 
                                 , 
                                 
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                                   - 
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                       ] 
                     
                     = 
                     
                       
                         
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                       + 
                       
                         [ 
                         
                           
                             
                               
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                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       H 
                       
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                         , 
                         t 
                       
                     
                     ≡ 
                     
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                        
                       
                           
                       
                        
                       
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                           , 
                           t 
                         
                         
                           ≡ 
                           
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                             t 
                           
                         
                       
                        
                       
                         H 
                         
                           iRM 
                           , 
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0064]    The pilot sequence P t  can be expressed as a pilot matrix of the received signals, that is, 
         [0000]    
       
         
           
             
               [ 
               
                 
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           t 
                           - 
                           1 
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
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                           - 
                           2 
                         
                       
                     
                   
                 
                 
                   
                     
                       P 
                       
                         i 
                         , 
                         t 
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           t 
                           - 
                           1 
                         
                       
                     
                   
                 
               
               ] 
             
             . 
           
         
       
     
       When receiving the signals from the BS, the MS performs channel estimation using P t . If the MS uses a Minimum Mean Square Error (MMSE) channel estimator, the channel estimation is given as Equation (6); 
       [0065]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               H 
                               ^ 
                             
                             
                               iBM 
                               , 
                               t 
                             
                           
                         
                       
                       
                         
                           
                             
                               H 
                               ^ 
                             
                             
                               iBRM 
                               , 
                               t 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               P 
                               t 
                               H 
                             
                              
                             
                               P 
                               t 
                             
                           
                           + 
                           I 
                         
                         ) 
                       
                       
                         - 
                         1 
                       
                     
                      
                     
                       
                         P 
                         t 
                         H 
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 Y 
                                 
                                   t 
                                   - 
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                                 Y 
                                 t 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0066]    If the MS uses a Zero Forcing (ZF) channel estimator, the channel estimation is given as Equation (7); 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               H 
                               ^ 
                             
                             
                               iBM 
                               , 
                               t 
                             
                           
                         
                       
                       
                         
                           
                             
                               H 
                               ^ 
                             
                             
                               iBRM 
                               , 
                               t 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             P 
                             t 
                             H 
                           
                            
                           
                             P 
                             t 
                           
                         
                         ) 
                       
                       
                         - 
                         1 
                       
                     
                      
                     
                       
                         P 
                         t 
                         H 
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 Y 
                                 
                                   t 
                                   - 
                                   1 
                                 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 t 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0067]    The use of the pilot sequence P t  satisfying Equation (3) in the BS and the RS minimizes channel estimation errors. When the BS and the RS transmit signals in SISO according to Equation (3), their pilot sequences satisfy the following Equation (8). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           P 
                           
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                               t 
                               - 
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                     0 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         
                            
                           
                             P 
                             
                               i 
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                               t 
                             
                           
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                         2 
                       
                       + 
                       
                         
                            
                           
                             P 
                             
                               i 
                               , 
                               
                                 t 
                                 - 
                                 1 
                               
                             
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       
                         
                            
                           
                             P 
                             
                               i 
                               , 
                               
                                 t 
                                 - 
                                 1 
                               
                             
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             P 
                             
                               i 
                               , 
                               
                                 t 
                                 - 
                                 2 
                               
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0068]    where P i,t−1  and P i,t  denote a pilot sequence from the BS and P i,t−2  and P i,t−1  denote a pilot sequence from the RS. 
         [0069]    In SISO, the following exemplary pilot sequences are available. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           1 
                            
                           
                               
                           
                            
                           1 
                         
                          
                         
                             
                         
                         - 
                         1 
                          
                         
                             
                         
                         - 
                         
                           1 
                            
                           
                               
                           
                            
                           1 
                            
                           
                               
                           
                            
                           1 
                         
                          
                         
                             
                         
                         - 
                         
                           1 
                            
                           
                               
                           
                            
                           … 
                         
                       
                       ] 
                     
                      
                     
                       
 
                     
                     [ 
                     
                       
                         2 
                       
                        
                       
                           
                       
                        
                       0 
                        
                       
                           
                       
                        
                       
                         2 
                       
                        
                       
                           
                       
                        
                       0 
                        
                       
                           
                       
                        
                       
                         2 
                       
                        
                       
                           
                       
                        
                       0 
                        
                       
                           
                       
                        
                       
                         2 
                       
                        
                       
                           
                       
                        
                       0 
                        
                       
                           
                       
                        
                       
                         2 
                       
                        
                       
                           
                       
                        
                       0 
                        
                       
                           
                       
                        
                       … 
                     
                     ] 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       1 
                       
                         2 
                       
                     
                      
                     
                       [ 
                       
                         1 
                         + 
                         
                           j 
                            
                           
                               
                           
                            
                           1 
                         
                         + 
                         j 
                          
                         
                             
                         
                         - 
                         1 
                         - 
                         j 
                          
                         
                             
                         
                         - 
                         1 
                         - 
                         
                           j 
                            
                           
                               
                           
                            
                           1 
                         
                         + 
                         
                           j 
                            
                           
                               
                           
                            
                           1 
                         
                         + 
                         j 
                          
                         
                             
                         
                         - 
                         1 
                         - 
                         j 
                          
                         
                             
                         
                         - 
                         1 
                         - 
                         
                           j 
                            
                           
                               
                           
                            
                           1 
                         
                         + 
                         
                           j 
                            
                           
                               
                           
                            
                           1 
                         
                         + 
                         
                           j 
                            
                           
                               
                           
                            
                           … 
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0070]    In the case where the BS operates in MIMO, pilot sequences that the BS generates for a full duplex relay also satisfy Equation (3), i.e. P t   H P t =λI. How the matrix P t  is configured for different numbers of transmit antennas will be described below. 
         [0071]    Assuming that the BS and the RS each use two antennas (M=2) for signal transmission and reception, pilot sequences are generated as follows. 
         [0072]    In MIMO, received signals at the MS are modeled as Equation (10); 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   Y 
                                   
                                     i 
                                     , 
                                     
                                       n 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   Y 
                                   
                                     i 
                                     , 
                                     
                                       n 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   Y 
                                   
                                     i 
                                     , 
                                     
                                       n 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                 
                               
                             
                             
                               
                                 ⋮ 
                               
                             
                             
                               
                                 
                                   Y 
                                   
                                     i 
                                     , 
                                     
                                       n 
                                        
                                       
                                           
                                       
                                        
                                       N 
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                         = 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       H 
                                       
                                         iBM 
                                         , 
                                         
                                           11 
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     
                                       H 
                                       
                                         iBM 
                                         , 
                                         
                                           1 
                                            
                                           
                                               
                                           
                                            
                                           2 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     ⋯ 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     
                                         
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         H 
                                         _ 
                                       
                                       
                                         iBM 
                                         , 
                                         
                                           21 
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         H 
                                         _ 
                                       
                                       
                                         iBM 
                                         , 
                                         
                                           22 
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     
                                       H 
                                       
                                         iBM 
                                         , 
                                         
                                           2 
                                            
                                           
                                               
                                           
                                            
                                           1 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     
                                       H 
                                       
                                         iBM 
                                         , 
                                         
                                           22 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     ⋯ 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     
                                         
                                     
                                   
                                 
                                 
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     
                                       
                                         H 
                                         _ 
                                       
                                       
                                         iBRM 
                                         , 
                                         
                                           31 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         H 
                                         _ 
                                       
                                       
                                         iBRM 
                                         , 
                                         
                                           32 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     
                                       H 
                                       
                                         iBM 
                                         , 
                                         
                                           2 
                                            
                                           
                                               
                                           
                                            
                                           1 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     
                                       H 
                                       
                                         iBM 
                                         , 
                                         
                                           22 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     ⋯ 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     
                                         
                                     
                                   
                                   
                                     0 
                                   
                                 
                                 
                                   
                                     ⋮ 
                                   
                                   
                                     ⋮ 
                                   
                                   
                                     ⋮ 
                                   
                                   
                                     ⋮ 
                                   
                                   
                                     ⋮ 
                                   
                                   
                                     ⋮ 
                                   
                                   
                                     ⋰ 
                                   
                                   
                                     ⋮ 
                                   
                                   
                                     ⋮ 
                                   
                                   
                                     ⋮ 
                                   
                                   
                                     ⋮ 
                                   
                                   
                                     
                                         
                                     
                                   
                                 
                                 
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     0 
                                   
                                   
                                     ⋯ 
                                   
                                   
                                     
                                       
                                         H 
                                         _ 
                                       
                                       
                                         iBRM 
                                         , 
                                         
                                           N 
                                            
                                           
                                               
                                           
                                            
                                           1 
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         H 
                                         _ 
                                       
                                       
                                         iBRM 
                                         , 
                                         
                                           N 
                                            
                                           
                                               
                                           
                                            
                                           2 
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     
                                       H 
                                       
                                         iBM 
                                         , 
                                         
                                           N 
                                            
                                           
                                               
                                           
                                            
                                           1 
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     
                                       H 
                                       
                                         iBM 
                                         , 
                                         
                                           N 
                                            
                                           
                                               
                                           
                                            
                                           2 
                                            
                                           n 
                                         
                                       
                                     
                                   
                                   
                                     
                                         
                                     
                                   
                                 
                               
                               ] 
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     
                                       P 
                                       
                                         i 
                                         , 
                                         11 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       P 
                                       
                                         i 
                                         , 
                                         21 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       P 
                                       
                                         i 
                                         , 
                                         12 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       P 
                                       
                                         i 
                                         , 
                                         22 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       P 
                                       
                                         i 
                                         , 
                                         23 
                                       
                                     
                                   
                                 
                                 
                                   
                                     ⋮ 
                                   
                                 
                                 
                                   
                                     
                                       P 
                                       
                                         i 
                                         , 
                                         
                                           1 
                                            
                                           
                                             ( 
                                             
                                               N 
                                               - 
                                               1 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       P 
                                       
                                         i 
                                         , 
                                         
                                           2 
                                            
                                           
                                             ( 
                                             
                                               N 
                                               - 
                                               1 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       P 
                                       
                                         i 
                                         , 
                                         
                                           1 
                                            
                                           
                                               
                                           
                                            
                                           N 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       P 
                                       
                                         i 
                                         , 
                                         
                                           2 
                                            
                                           
                                               
                                           
                                            
                                           N 
                                         
                                       
                                     
                                   
                                 
                               
                               ] 
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 W 
                                 
                                   i 
                                   , 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 W 
                                 
                                   i 
                                   , 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 W 
                                 
                                   i 
                                   , 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     3 
                                   
                                 
                               
                             
                           
                           
                             
                               ⋮ 
                             
                           
                           
                             
                               
                                 W 
                                 
                                   i 
                                   , 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     N 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where H iBM,tmn  denotes the channel of an i th  subcarrier at time t from an m th  transmit antenna of the BS to an n th  receive antenna of the MS,  H   iBRM, tmn  denotes the effective channel of the i th  subcarrier transmitted at time t from the m th  transmit antenna of the BS to the n th  receive antenna of the MS via the RS, P i,mt  denotes a pilot symbol transmitted on the i th  subcarrier at time t from the m th  transmit antenna of the BS, and Y i,mt  denotes a signal received on the i th  subcarrier at time t at the n th  receive antenna of the MS. 
         [0073]    Any four of the received signals are expressed as Equation (11) 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             Y 
                             
                               i 
                               , 
                               
                                 n 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             Y 
                             
                               i 
                               , 
                               
                                 n 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             Y 
                             
                               i 
                               , 
                               
                                 n 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             Y 
                             
                               i 
                               , 
                               
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                             
                         
                          
                         
                           
                             
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       1 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           3 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       2 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           3 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       1 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           4 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       2 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           4 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       1 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           2 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       2 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           2 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       1 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           3 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       2 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           3 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       1 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       2 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       1 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           2 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       2 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           2 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       1 
                                        
                                       
                                           
                                       
                                        
                                       t 
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       2 
                                        
                                       
                                           
                                       
                                        
                                       t 
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       1 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       2 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                           
                           
                             ≡ 
                             
                               P 
                               t 
                             
                           
                         
                         ] 
                       
                       [ 
                       
                           
                       
                        
                       
                         
                           
                             
                               H 
                               
                                 iBM 
                                 , 
                                 
                                   t 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                           
                         
                         
                           
                             
                               H 
                               
                                 iBM 
                                 , 
                                 
                                   t 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 H 
                                 _ 
                               
                               
                                 iBRM 
                                 , 
                                 
                                   t 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 H 
                                 _ 
                               
                               
                                 iBRM 
                                 , 
                                 
                                   t 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                     + 
                     
                       [ 
                       
                           
                       
                        
                       
                         
                           
                             
                               W 
                               
                                 i 
                                 , 
                                 
                                   n 
                                    
                                   
                                     ( 
                                     
                                       t 
                                       - 
                                       3 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               W 
                               
                                 i 
                                 , 
                                 
                                   n 
                                    
                                   
                                     ( 
                                     
                                       t 
                                       - 
                                       2 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               W 
                               
                                 i 
                                 , 
                                 
                                   n 
                                    
                                   
                                     ( 
                                     
                                       t 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               W 
                               
                                 i 
                                 , 
                                 
                                   n 
                                    
                                   
                                       
                                   
                                    
                                   t 
                                 
                               
                             
                           
                         
                       
                        
                       
                           
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where P t  can be expressed as a pilot matrix of the received signals, i.e. 
         [0000]    
       
         
           
             
               [ 
               
                 
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           1 
                            
                           
                             ( 
                             
                               t 
                               - 
                               3 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           2 
                            
                           
                             ( 
                             
                               t 
                               - 
                               3 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           1 
                            
                           
                             ( 
                             
                               t 
                               - 
                               4 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           2 
                            
                           
                             ( 
                             
                               t 
                               - 
                               4 
                             
                             ) 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           1 
                            
                           
                             ( 
                             
                               t 
                               - 
                               2 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           2 
                            
                           
                             ( 
                             
                               t 
                               - 
                               2 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           1 
                            
                           
                             ( 
                             
                               t 
                               - 
                               3 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           2 
                            
                           
                             ( 
                             
                               t 
                               - 
                               3 
                             
                             ) 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           1 
                            
                           
                             ( 
                             
                               t 
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           2 
                            
                           
                             ( 
                             
                               t 
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           1 
                            
                           
                             ( 
                             
                               t 
                               - 
                               2 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           2 
                            
                           
                             ( 
                             
                               t 
                               - 
                               2 
                             
                             ) 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           1 
                            
                           
                               
                           
                            
                           t 
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           2 
                            
                           
                               
                           
                            
                           t 
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           1 
                            
                           
                             ( 
                             
                               t 
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           2 
                            
                           
                             ( 
                             
                               t 
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               ] 
             
             . 
           
         
       
     
       When the MS receives the signals from the BS, it performs channel estimation using P t . If the MS uses an MMSE channel estimator, the channel estimation is 
       [0074]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               H 
                               ^ 
                             
                             
                               iBM 
                               , 
                               
                                 t 
                                  
                                 
                                     
                                 
                                  
                                 1 
                                  
                                 n 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               H 
                               ^ 
                             
                             
                               iBM 
                               , 
                               
                                 t 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 n 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               H 
                               ^ 
                             
                             
                               iBRM 
                               , 
                               
                                 t 
                                  
                                 
                                     
                                 
                                  
                                 1 
                                  
                                 n 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               H 
                               ^ 
                             
                             
                               iBRM 
                               , 
                               t2n 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               P 
                               t 
                               H 
                             
                              
                             
                               P 
                               t 
                             
                           
                           + 
                           I 
                         
                         ) 
                       
                       
                         - 
                         1 
                       
                     
                      
                     
                       
                         P 
                         t 
                         H 
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 Y 
                                 
                                   i 
                                   , 
                                   
                                     n 
                                      
                                     
                                       ( 
                                       
                                         t 
                                         - 
                                         3 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 
                                   i 
                                   , 
                                   
                                     n 
                                      
                                     
                                       ( 
                                       
                                         t 
                                         - 
                                         2 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 
                                   i 
                                   , 
                                   
                                     n 
                                      
                                     
                                       ( 
                                       
                                         t 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 
                                   i 
                                   , 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     t 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0075]    The use of P t  satisfying Equation (3) in the BS and the RS minimizes channel estimation errors in the MS and the RS. When the BS and the RS transmit signals in MIMO according to Equation (3), their pilot sequences satisfy the following Equation (13); 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               ∑ 
                               
                                 l 
                                 = 
                                 0 
                               
                               
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   M 
                                 
                                 - 
                                 1 
                               
                             
                              
                             
                                 
                             
                              
                             
                               
                                 P 
                                 
                                   i 
                                   , 
                                   
                                     j 
                                      
                                     
                                       ( 
                                       
                                         t 
                                         - 
                                         l 
                                       
                                       ) 
                                     
                                   
                                 
                                 * 
                               
                                
                               
                                 P 
                                 
                                   i 
                                   , 
                                   
                                     k 
                                      
                                     
                                       ( 
                                       
                                         t 
                                         - 
                                         l 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           = 
                             
                            
                           0 
                         
                         , 
                         
                           
                             for 
                              
                             
                                 
                             
                              
                             j 
                           
                           ≠ 
                           k 
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               ∑ 
                               
                                 l 
                                 = 
                                 0 
                               
                               
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   M 
                                 
                                 - 
                                 1 
                               
                             
                              
                             
                                 
                             
                              
                             
                               
                                 P 
                                 
                                   i 
                                   , 
                                   
                                     j 
                                      
                                     
                                       ( 
                                       
                                         t 
                                         - 
                                         l 
                                       
                                       ) 
                                     
                                   
                                 
                                 * 
                               
                                
                               
                                 P 
                                 
                                   i 
                                   , 
                                   
                                     k 
                                      
                                     
                                       ( 
                                       
                                         t 
                                         - 
                                         l 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           = 
                             
                            
                           0 
                         
                         , 
                         
                           
                             for 
                              
                             
                                 
                             
                              
                             j 
                           
                           ≠ 
                           k 
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               ∑ 
                               
                                 l 
                                 = 
                                 0 
                               
                               
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   M 
                                 
                                 - 
                                 1 
                               
                             
                              
                             
                                 
                             
                              
                             
                               
                                  
                                 
                                   P 
                                   
                                     i 
                                     , 
                                     
                                       j 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           l 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                  
                               
                               2 
                             
                           
                           = 
                             
                            
                           
                             
                               
                                 ∑ 
                                 
                                   l 
                                   = 
                                   0 
                                 
                                 
                                   
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     M 
                                   
                                   - 
                                   1 
                                 
                               
                                
                               
                                   
                               
                                
                               
                                 
                                    
                                   
                                     P 
                                     
                                       i 
                                       , 
                                       
                                         j 
                                          
                                         
                                           ( 
                                           
                                             t 
                                             - 
                                             l 
                                             - 
                                             1 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                    
                                 
                                 2 
                               
                             
                             = 
                             λ 
                           
                         
                         , 
                         
                           for 
                            
                           
                               
                           
                            
                           all 
                            
                           
                               
                           
                            
                           i 
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           j 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where, P i,j(t−1)  is a BS sequence, P i,k(t−1−1)  is an RS sequence, and P i,j(t−1)  and P i,k(t−1)  are pilot sequences from the BS. 
         [0076]    For two antennas, the following pilot sequences are available as the pilot sequences transmitted by the BS. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                         
                     
                      
                     
                       
                         time 
                          
                         
                             
                         
                          
                         shift 
                       
                        
                       
                         
 
                       
                        
                       
                         
                           
                             
                               
                                 - 
                                 
                                   P 
                                   
                                     i 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                               
                               = 
                                 
                                
                               
                                 [ 
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                    
                                   
                                       
                                   
                                    
                                   ⋯ 
                                 
                                 ] 
                               
                             
                           
                         
                         
                           
                             
                               
                                   
                               
                                
                               
                                 
                                   P 
                                   
                                     i 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                                 = 
                                   
                                  
                                 
                                   [ 
                                   
                                     0 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                      
                                     
                                         
                                     
                                      
                                     ⋯ 
                                   
                                   ] 
                                 
                               
                             
                           
                         
                       
                     
                     } 
                   
                    
                   2 
                    
                   
                       
                   
                    
                   symbol 
                    
                   
                       
                   
                    
                   time 
                    
                   
                       
                   
                    
                   shift 
                 
                  
                 
                   
 
                 
                  
                 
                   
                     
                       
                         
                           - 
                           
                             P 
                             
                               i 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         = 
                           
                          
                         
                           [ 
                           
                             
                               1 
                                
                               
                                   
                               
                                
                               
                                 
                                   1 
                                   + 
                                   j 
                                 
                                 
                                   2 
                                 
                               
                             
                              
                             
                                 
                             
                             - 
                             
                               1 
                                
                               
                                   
                               
                                
                               
                                 
                                   1 
                                   + 
                                   j 
                                 
                                 
                                   2 
                                 
                               
                                
                               
                                   
                               
                                
                               1 
                                
                               
                                   
                               
                                
                               
                                 
                                   1 
                                   + 
                                   j 
                                 
                                 
                                   2 
                                 
                               
                             
                              
                             
                                 
                             
                             - 
                             
                               1 
                                
                               
                                   
                               
                                
                               
                                 
                                   1 
                                   + 
                                   j 
                                 
                                 
                                   2 
                                 
                               
                                
                               
                                   
                               
                                
                               1 
                                
                               
                                   
                               
                                
                               
                                 
                                   1 
                                   + 
                                   j 
                                 
                                 
                                   2 
                                 
                               
                             
                              
                             
                                 
                             
                             - 
                             
                               1 
                                
                               
                                   
                               
                                
                               
                                 
                                   1 
                                   + 
                                   j 
                                 
                                 
                                   2 
                                 
                               
                                
                               
                                   
                               
                                
                               ⋯ 
                             
                           
                           ] 
                         
                       
                     
                   
                   
                     
                       
                         
                           P 
                           
                             i 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         = 
                         
                           [ 
                             
                            
                           
                             
                               
                                 
                                   
                                     
                                       
                                         - 
                                         1 
                                       
                                        
                                       
                                           
                                       
                                        
                                       
                                         
                                           1 
                                           + 
                                           j 
                                         
                                         
                                           2 
                                         
                                       
                                        
                                       
                                           
                                       
                                        
                                       1 
                                        
                                       
                                           
                                       
                                        
                                       
                                         
                                           1 
                                           + 
                                           j 
                                         
                                         
                                           2 
                                         
                                       
                                     
                                     
                                        
                                       
                                         CAZAC 
                                          
                                         
                                             
                                         
                                          
                                         sequence 
                                          
                                         
                                             
                                         
                                          
                                         of 
                                          
                                         
                                             
                                         
                                          
                                         period 
                                          
                                         
                                             
                                         
                                          
                                         4 
                                       
                                     
                                   
                                    
                                   
                                       
                                   
                                   - 
                                   
                                       
                                   
                                    
                                   
                                     1 
                                      
                                     
                                         
                                     
                                      
                                     
                                       
                                         1 
                                         + 
                                         j 
                                       
                                       
                                         2 
                                       
                                     
                                      
                                     
                                         
                                     
                                      
                                     1 
                                      
                                     
                                         
                                     
                                      
                                     
                                       
                                         1 
                                         + 
                                         j 
                                       
                                       
                                         2 
                                       
                                     
                                   
                                    
                                   
                                       
                                   
                                   - 
                                   
                                       
                                   
                                    
                                   
                                     1 
                                      
                                     
                                         
                                     
                                      
                                     
                                       
                                         1 
                                         + 
                                         j 
                                       
                                       
                                         2 
                                       
                                     
                                      
                                     
                                         
                                     
                                      
                                     1 
                                      
                                     
                                         
                                     
                                      
                                     
                                       
                                         1 
                                         + 
                                         j 
                                       
                                       
                                         2 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                     
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               } 
             
              
             
                 
             
              
             2 
              
             
                 
             
              
             symbol 
              
             
                 
             
              
             time 
              
             
                 
             
              
             shift 
           
         
       
     
         [0077]    As noted from Equation (14), the pilot sequences can be a Constant Amplitude and Zero Autocorrelation (CAZAC) sequence of period  4  and its two symbol-shifted sequence, or a sequence with a value every four symbols and its two symbol-shifted sequence. Here, P im  denotes a pilot sequence vector from an m th  transmit antenna. 
         [0078]    For three transmit antennas in each of the BS and the RS, P t  can be expressed as a pilot matrix of received signals, i.e. 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               1 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     6 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     6 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     6 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             p 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 t 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                   . 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
         [0079]    The use of P t  satisfying Equation (3) in the BS and the RS minimizes channel estimation errors. The following pilot sequences are available. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         P 
                         
                           i 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       = 
                       
                         ⌊ 
                         
                           
                             6 
                           
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           
                             6 
                           
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           
                             6 
                           
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           0 
                            
                           
                               
                           
                            
                           ⋯ 
                         
                         ⌋ 
                       
                     
                      
                     
                       
 
                     
                      
                     
                       
                         P 
                         
                           i 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       = 
                       
                         
                           [ 
                           
                             0 
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             
                               6 
                             
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             
                               6 
                             
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             
                               6 
                             
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             0 
                              
                             
                                 
                             
                              
                             ⋯ 
                           
                           ] 
                         
                          
                         
                             
                         
                          
                         2 
                          
                         
                             
                         
                          
                         symbol 
                          
                         
                             
                         
                          
                         time 
                          
                         
                             
                         
                          
                         shift 
                       
                     
                      
                     
                       
 
                     
                      
                     
                       
                         P 
                         
                           i 
                            
                           
                               
                           
                            
                           3 
                         
                       
                       = 
                       
                         
                           
                             
                               [ 
                               
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 
                                   6 
                                 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 
                                   6 
                                 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 
                                   6 
                                 
                                  
                                 
                                     
                                 
                                  
                                 0 
                                  
                                 
                                     
                                 
                                  
                                 ⋯ 
                               
                               ] 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             symbol 
                              
                             
                                 
                             
                              
                             time 
                              
                             
                                 
                             
                              
                             shift 
                           
                            
                           
                              
                           
                            
                           
                             P 
                             
                               i 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         = 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             1 
                                              
                                             
                                                 
                                             
                                              
                                             
                                               
                                                 
                                                   3 
                                                 
                                                 + 
                                                 j 
                                               
                                               2 
                                             
                                              
                                             
                                                 
                                             
                                              
                                             
                                               
                                                 
                                                   - 
                                                   1 
                                                 
                                                 + 
                                                 
                                                   
                                                     3 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     j 
                                                   
                                                 
                                               
                                               2 
                                             
                                           
                                            
                                           
                                               
                                           
                                           - 
                                           
                                             1 
                                              
                                             
                                                 
                                             
                                              
                                             
                                               
                                                 
                                                   - 
                                                   1 
                                                 
                                                 + 
                                                 
                                                   
                                                     3 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     j 
                                                   
                                                 
                                               
                                               2 
                                             
                                              
                                             
                                                 
                                             
                                              
                                             
                                               
                                                 
                                                   3 
                                                 
                                                 + 
                                                 j 
                                               
                                               2 
                                             
                                           
                                         
                                          
                                         
                                             
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                             
                                         
                                          
                                         
                                           
                                             1 
                                              
                                             
                                                 
                                             
                                              
                                             
                                               
                                                 
                                                   3 
                                                 
                                                 + 
                                                 j 
                                               
                                               2 
                                             
                                              
                                             
                                                 
                                             
                                              
                                             
                                               
                                                 
                                                   - 
                                                   1 
                                                 
                                                 + 
                                                 
                                                   
                                                     3 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     j 
                                                   
                                                 
                                               
                                               2 
                                             
                                           
                                            
                                           
                                               
                                           
                                           - 
                                           
                                             1 
                                              
                                             
                                                 
                                             
                                              
                                             
                                               
                                                 
                                                   - 
                                                   1 
                                                 
                                                 + 
                                                 
                                                   
                                                     3 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     j 
                                                   
                                                 
                                               
                                               2 
                                             
                                              
                                             
                                                 
                                             
                                              
                                             
                                               
                                                 
                                                   3 
                                                 
                                                 + 
                                                 j 
                                               
                                               2 
                                             
                                           
                                         
                                          
                                         
                                             
                                         
                                       
                                     
                                   
                                 
                                  
                                 ⋯ 
                               
                               ] 
                             
                              
                             
                               
 
                             
                              
                             
                               P 
                               
                                 i 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                           = 
                           
                             
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           
                                               
                                           
                                            
                                           
                                             
                                               
                                                 
                                                   
                                                     - 
                                                     1 
                                                   
                                                   + 
                                                   
                                                     
                                                       3 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       j 
                                                     
                                                   
                                                 
                                                 2 
                                               
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     3 
                                                   
                                                   + 
                                                   j 
                                                 
                                                 2 
                                               
                                                
                                               
                                                   
                                               
                                                
                                               1 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     3 
                                                   
                                                   + 
                                                   j 
                                                 
                                                 2 
                                               
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     - 
                                                     1 
                                                   
                                                   + 
                                                   
                                                     
                                                       3 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       j 
                                                     
                                                   
                                                 
                                                 2 
                                               
                                             
                                              
                                             
                                                 
                                             
                                             - 
                                             1 
                                           
                                            
                                           
                                               
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                               
                                           
                                            
                                           
                                             
                                               
                                                 
                                                   
                                                     - 
                                                     1 
                                                   
                                                   + 
                                                   
                                                     
                                                       3 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       j 
                                                     
                                                   
                                                 
                                                 2 
                                               
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     3 
                                                   
                                                   + 
                                                   j 
                                                 
                                                 2 
                                               
                                                
                                               
                                                   
                                               
                                                
                                               1 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     3 
                                                   
                                                   + 
                                                   j 
                                                 
                                                 2 
                                               
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     - 
                                                     1 
                                                   
                                                   + 
                                                   
                                                     
                                                       3 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       j 
                                                     
                                                   
                                                 
                                                 2 
                                               
                                             
                                              
                                             
                                                 
                                             
                                             - 
                                             1 
                                           
                                            
                                           
                                               
                                           
                                         
                                       
                                     
                                   
                                    
                                   ⋯ 
                                 
                                  
                                 
                                     
                                 
                                 ] 
                               
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               symbol 
                                
                               
                                   
                               
                                
                               time 
                                
                               
                                   
                               
                                
                               shift 
                                
                               
                                 
 
                               
                                
                               
                                 P 
                                 
                                   i 
                                    
                                   
                                       
                                   
                                    
                                   3 
                                 
                               
                             
                             = 
                             
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   - 
                                                   1 
                                                 
                                                 + 
                                                 
                                                   
                                                     3 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     j 
                                                   
                                                 
                                               
                                               2 
                                             
                                              
                                             
                                                 
                                             
                                             - 
                                             
                                               1 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     - 
                                                     1 
                                                   
                                                   + 
                                                   
                                                     
                                                       3 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       j 
                                                     
                                                   
                                                 
                                                 2 
                                               
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     3 
                                                   
                                                   + 
                                                   j 
                                                 
                                                 2 
                                               
                                                
                                               
                                                   
                                               
                                                
                                               1 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     3 
                                                   
                                                   + 
                                                   j 
                                                 
                                                 2 
                                               
                                             
                                           
                                           
                                              
                                             
                                               CAZAC 
                                                
                                               
                                                   
                                               
                                                
                                               sequence 
                                                
                                               
                                                   
                                               
                                                
                                               of 
                                                
                                               
                                                   
                                               
                                                
                                               period 
                                                
                                               
                                                   
                                               
                                                
                                               6 
                                             
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                               
                                           
                                            
                                           
                                             
                                               
                                                 
                                                   - 
                                                   1 
                                                 
                                                 + 
                                                 
                                                   
                                                     3 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     j 
                                                   
                                                 
                                               
                                               2 
                                             
                                              
                                             
                                                 
                                             
                                             - 
                                             
                                               1 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     - 
                                                     1 
                                                   
                                                   + 
                                                   
                                                     
                                                       3 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       j 
                                                     
                                                   
                                                 
                                                 2 
                                               
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     3 
                                                   
                                                   + 
                                                   j 
                                                 
                                                 2 
                                               
                                                
                                               
                                                   
                                               
                                                
                                               1 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   
                                                     3 
                                                   
                                                   + 
                                                   j 
                                                 
                                                 2 
                                               
                                             
                                           
                                            
                                           
                                               
                                           
                                         
                                       
                                     
                                   
                                    
                                   
                                       
                                   
                                    
                                   ⋯ 
                                 
                                  
                                 
                                     
                                 
                                 ] 
                               
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               symbol 
                                
                               
                                   
                               
                                
                               time 
                                
                               
                                   
                               
                                
                               shift 
                             
                           
                         
                       
                     
                   
                    
                   
                       
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
         [0080]    Referring to Equation (15), the pilot sequences of the BS and the RS each using three transmit antennas are CAZAC sequences of period  6 , for example. 
         [0081]    For four transmit antennas in each of the BS and the RS, P t  can be expressed as a pilot matrix of received signals, i.e. 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     7 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     7 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     7 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     7 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     8 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     8 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     8 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     8 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     6 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     6 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     6 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     6 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     7 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     7 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     7 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     7 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     6 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     6 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     6 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     6 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             p 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     5 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     4 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 t 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 1 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 3 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             P 
                             
                               i 
                               , 
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                   . 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
         [0082]    The use of P t  satisfying Equation (3) in the BS and the RS minimizes channel estimation errors. Examples of pilot sequences for this case are given as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                     P 
                     
                       i 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               
                                 1 
                                  
                                 
                                     
                                 
                                  
                                 1 
                                  
                                 
                                     
                                 
                                  
                                 j 
                               
                                
                               
                                   
                               
                               - 
                               
                                 1 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                                
                               
                                   
                               
                               - 
                               
                                 1 
                                  
                                 
                                     
                                 
                                  
                                 j 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               
                                   
                               
                                
                               
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   j 
                                 
                                  
                                 
                                     
                                 
                                 - 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                                  
                                 
                                     
                                 
                                 - 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                           
                         
                       
                        
                       
                           
                       
                        
                       ⋯ 
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
             
               
                 
                   
                     P 
                     
                       i 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   j 
                                 
                                  
                                 
                                     
                                 
                                 - 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                                  
                                 
                                     
                                 
                                 - 
                                 1 
                               
                             
                           
                           
                             
                               
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   j 
                                 
                                  
                                 
                                     
                                 
                                 - 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                                  
                                 
                                     
                                 
                                 - 
                                 1 
                               
                             
                           
                         
                          
                         
                             
                         
                          
                         ⋯ 
                       
                       ] 
                     
                      
                     
                         
                     
                      
                     2 
                      
                     
                         
                     
                      
                     symbol 
                      
                     
                         
                     
                      
                     time 
                      
                     
                         
                     
                      
                     shift 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     P 
                     
                       i 
                        
                       
                           
                       
                        
                       3 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 1 
                                  
                                 
                                     
                                 
                                 - 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   j 
                                 
                                  
                                 
                                     
                                 
                                 - 
                                 1 
                               
                             
                           
                           
                             
                               
                                 1 
                                  
                                 
                                     
                                 
                                 - 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   j 
                                 
                                  
                                 
                                     
                                 
                                 - 
                                 1 
                               
                             
                           
                         
                          
                         
                             
                         
                          
                         ⋯ 
                       
                       ] 
                     
                      
                     
                         
                     
                      
                     2 
                      
                     
                         
                     
                      
                     symbol 
                      
                     
                         
                     
                      
                     time 
                      
                     
                         
                     
                      
                     shift 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     P 
                     
                       i 
                        
                       
                           
                       
                        
                       4 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   j 
                                    
                                   
                                       
                                   
                                   - 
                                   
                                     1 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                    
                                   
                                       
                                   
                                   - 
                                   
                                     1 
                                      
                                     
                                         
                                     
                                      
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 
                                    
                                   
                                     CAZAC 
                                      
                                     
                                         
                                     
                                      
                                     sequence 
                                      
                                     
                                         
                                     
                                      
                                     of 
                                      
                                     
                                         
                                     
                                      
                                     period 
                                      
                                     
                                         
                                     
                                      
                                     8 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 j 
                                  
                                 
                                     
                                 
                                 - 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                                  
                                 
                                     
                                 
                                 - 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                           
                         
                          
                         
                             
                         
                          
                         ⋯ 
                       
                       ] 
                     
                      
                     2 
                      
                     
                         
                     
                      
                     symbol 
                      
                     
                         
                     
                      
                     time 
                      
                     
                         
                     
                      
                     shift 
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
         [0083]    As noted from Equation (16), the pilot sequences can be CAZAC sequences of period  8 . 
         [0084]    Now a description will be made of a pilot sequence, in the case where the pilot sequence is delayed by ‘a’ symbol interval at the RS. Also, in this case, the BS generates a pilot sequence satisfying Equation (3). 
         [0085]    While a pilot sequence for SISO is described below, pilot sequences for MIMO can be generated by extending the pilot sequence for SISO and thus will not be described separately. Any two signals received from the BS are expressed as Equation (17); 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               Y 
                               
                                 i 
                                 , 
                                 
                                   t 
                                   - 
                                   1 
                                 
                               
                             
                           
                         
                         
                           
                             
                               Y 
                               
                                 i 
                                 , 
                                 t 
                               
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     P 
                                     
                                       i 
                                       , 
                                       
                                         t 
                                         - 
                                         1 
                                       
                                     
                                   
                                 
                                 
                                   
                                     P 
                                     
                                       i 
                                       , 
                                       
                                         t 
                                         - 
                                         a 
                                         - 
                                         1 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     P 
                                     
                                       i 
                                       , 
                                       t 
                                     
                                   
                                 
                                 
                                   
                                     P 
                                     
                                       i 
                                       , 
                                       
                                         t 
                                         - 
                                         a 
                                       
                                     
                                   
                                 
                               
                             
                             ] 
                           
                           
                             ≡ 
                             
                               P 
                               t 
                             
                           
                         
                          
                         
                           [ 
                           
                             
                               
                                 
                                   H 
                                   
                                     iBM 
                                     , 
                                     t 
                                   
                                 
                               
                             
                             
                               
                                 
                                   α 
                                    
                                   
                                       
                                   
                                    
                                   
                                     H 
                                     
                                       iBR 
                                       , 
                                       t 
                                     
                                   
                                    
                                   
                                     H 
                                     
                                       iRM 
                                       , 
                                       t 
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                       + 
                       
                         [ 
                         
                           
                             
                               
                                 W 
                                 
                                   i 
                                   , 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 W 
                                 
                                   i 
                                   , 
                                   t 
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       H 
                       
                         iBRM 
                         , 
                         t 
                       
                     
                     ≡ 
                     
                       α 
                        
                       
                           
                       
                        
                       
                         H 
                         
                           iBR 
                           , 
                           t 
                         
                       
                        
                       
                         H 
                         
                           iRM 
                           , 
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0086]    The pilot sequence P t  can be expressed as a pilot matrix of the received signals, that is, 
         [0000]    
       
         
           
             
               [ 
               
                 
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           t 
                           - 
                           1 
                         
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           t 
                           - 
                           a 
                           - 
                           1 
                         
                       
                     
                   
                 
                 
                   
                     
                       P 
                       
                         i 
                         , 
                         t 
                       
                     
                   
                   
                     
                       P 
                       
                         i 
                         , 
                         
                           t 
                           - 
                           a 
                         
                       
                     
                   
                 
               
               ] 
             
             . 
           
         
       
     
         [0087]    The use of the pilot sequence P t  satisfying Equation (3) in the BS minimizes channel estimation errors. When the BS transmits a pilot sequence in SISO according to Equation (3), the pilot sequence satisfies the following Equation (18); 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           P 
                           
                             t 
                             - 
                             1 
                           
                           * 
                         
                          
                         
                           P 
                           
                             t 
                             - 
                             a 
                             - 
                             1 
                           
                         
                       
                       + 
                       
                         
                           P 
                           t 
                           * 
                         
                          
                         
                           P 
                           
                             t 
                             - 
                             a 
                           
                         
                       
                     
                     = 
                     0 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         
                            
                           
                             P 
                             t 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             P 
                             
                               t 
                               - 
                               1 
                             
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       
                         
                            
                           
                             P 
                             
                               t 
                               - 
                               a 
                               - 
                               1 
                             
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             P 
                             
                               t 
                               - 
                               a 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
         [0088]    For a=2, for example, the following examples of pilot sequences are available. The ‘a’ is symbol interval 
         [0000]    
       
         
           
             
               
                 
                   
                     - 
                     
                       ⌊ 
                       
                         
                           2 
                         
                          
                         
                             
                         
                          
                         
                           2 
                         
                          
                         
                             
                         
                          
                         0 
                          
                         
                             
                         
                          
                         0 
                          
                         
                             
                         
                          
                         
                           2 
                         
                          
                         
                             
                         
                          
                         
                           2 
                         
                          
                         
                             
                         
                          
                         0 
                          
                         
                             
                         
                          
                         0 
                          
                         
                             
                         
                          
                         
                           2 
                         
                          
                         
                             
                         
                          
                         
                           2 
                         
                          
                         
                             
                         
                          
                         ⋯ 
                       
                       ⌋ 
                     
                   
                    
                   
                     
 
                   
                   - 
                   
                     [ 
                     
                       
                         1 
                          
                         
                             
                         
                          
                         1 
                          
                         
                             
                         
                          
                         1 
                       
                        
                       
                           
                       
                       - 
                       
                         1 
                          
                         
                             
                         
                          
                         1 
                          
                         
                             
                         
                          
                         1 
                          
                         
                             
                         
                          
                         1 
                       
                        
                       
                           
                       
                       - 
                       
                         1 
                          
                         
                             
                         
                          
                         1 
                          
                         
                             
                         
                          
                         1 
                          
                         
                             
                         
                          
                         1 
                       
                        
                       
                           
                       
                       - 
                       
                         1 
                          
                         
                             
                         
                          
                         ⋯ 
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
         [0089]    When multiple antennas are used, for example, in MIMO, pilot sequences are generated by the above SISO pilot sequence generation method using changed antenna indexes or time indexes. 
         [0090]    Now a description will be made of the configuration of an exemplary RS for receiving the pilot sequence from the BS with reference to  FIG. 7 . 
         [0091]      FIG. 7  is a block diagram of an RS for performing a relay function according to the present invention. 
         [0092]    Referring to  FIG. 7 , the RS includes receivers  711 , delays  713 , amplifiers  715  and transmitters  717 . 
         [0093]    The receivers  711  receive signals from the BS and process the received signals. 
         [0094]    The delays  713  delay the signals received from the receivers  711  by a predetermined time period. 
         [0095]    The amplifiers  715  amplify the delayed signals to a power level high enough for the MS to receive the signals. 
         [0096]    The transmitters  717  process the amplified signals and transmit them to the MS. 
         [0097]    As a transmitter, for example, the BS generates a pilot sequence and transmits a signal using the pilot sequence so as to minimize channel estimation errors in the MS. Since the RS uses the pilot sequence received from the BS, interference between signals transmitted using the pilot sequence is minimized in the relay communication system. 
         [0098]    As is apparent from the above description, at least two transmitters can transmit signals simultaneously during one time interval in a full duplex relay scheme in a relay communication system. A pilot sequence proposed to suit the full duplex relay reduces channel estimation errors in an MS and enables full duplex relaying. 
         [0099]    While the invention has been shown and described with reference to certain exemplary embodiments of the present invention thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention as defined by the appended claims and their equivalents.