Abstract:
A module and a method for estimating signal direction of arrival are disclosed. The module consists of a processing unit and a direction finder. Using spatial signatures at different carrier frequencies, the processing unit generates a generating set of a subspace. Based on the generating set, the signal subspace is extended. Then, the direction finder estimates signal direction of arrival according to the signal subspace. The module for estimating signal direction of arrival of the present invention effectively reduces wrong estimation of the signal direction of arrival caused by loss of rank.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    The present invention relates to a module and method for estimating direction of arrival (DOA), especially to a module and a method for estimating signal direction of arrival applied to a multicarrier modulation system. 
         [0002]    Two techniques for a beamforming algorithm for a smart antenna system are beamforming algorithms respectively based on the signal direction of arrival and based on the spatial signature. In order to give correct beam pattern, the beamforming algorithm based on the signal direction of arrival needs to get the signal angle of arrival. As to algorithms for estimating signal direction of arrival such as multiple signal classification (MUSIC) or estimating signal parameter via rotational invariance techniques (ESPRIT), they estimate the direction of arrival by means of subspaces so as to give a beam pattern. 
         [0003]    However, during transmission over wireless channels, direct path and multipath signals may interfere with one another and have high correlation due to reflection, diffraction or scattering. Owing to high correlation of the received signals, loss of rank may happen in the signal subspace. Thus the estimation algorithm for signal direction of arrival can&#39;t extend subspaces for estimating correct signal angle of arrival. 
         [0004]    In order to solve problems of loss of rank in subspaces cause by signal correlation, a plurality of spatial smoothing algorithm is revealed such as forward-backward spatial smoothing (FBSS). While by the forward-backward spatial smoothing, the number of signal angle of arrival being estimated is 2M/3 and the M is number of antennas. On the restriction of the number of the antennas, the number of signal direction of arrival being estimated is not enough. 
       SUMMARY OF THE INVENTION 
       [0005]    It is therefore a primary object of the present invention to provide a module and a method for estimating signal direction of arrival that generate a spanning set of a subspace by means of multicarrier transmission for reducing signal relevance caused by multipath signal transmission and improving accuracy of the estimation. 
         [0006]    It is another object of the present invention to provide a module and a method for estimating signal direction of arrival that generate a generating set of a subspace by spatial signature matrix formed from spatial signature vector at different subcarrier frequencies. Then a whole signal subspace is given by the generating set so as to improve wrong estimation of signal direction of arrival resulted from loss of rank in the subspace. 
         [0007]    In order to achieve above objects, the present invention provides a module for estimating signal direction of arrival applied to estimate direction of arrival of the signal received by a smart antenna system. The signal includes a plurality of subcarrier frequencies while the module consists of a processing unit and a direction finder. According to different subcarrier frequencies and signal transmission paths, a plurality of spatial signature vectors corresponding to different subcarriers are obtained by the processing unit. By extension of the spatial signature matrix from the spatial signature vector corresponding to various subcarrier frequencies, a subspace is given. The column vector of the spatial signature matrix is from the spatial signature vector at different subcarrier frequencies. According to the above subspace, the direction finder estimates the direction of arrival of the signal received by the smart antenna system. 
         [0008]    The above-mentioned smart antenna system includes an array antenna module that consists of a number of M receiving end antennas while M is a positive integer. Thus the spatial signature matrix is a generating set of the signal subspace with dimension of M and M is the rank of the generating set. Therefore, by means of the signal subspace extended from the spatial signature matrix, the above direction finder estimates angle of arrival of a number of M−1 signals. 
         [0009]    In an embodiment, the way that the direction finder estimates the direction of arrival includes at least one of the multiple signal classification (MUSIC) or the estimating signal parameter via rotational invariance techniques (ESPRIT). 
         [0010]    Furthermore, a method for estimating signal direction of arrival according to the present invention is applied to estimate direction of arrival of the signal received by a smart antenna system. The signal includes a plurality of subcarrier frequencies. The method including following steps: obtaining a spatial signature vector corresponding to the received signal according to the subcarrier frequency firstly while these spatial signature vectors correspond to different subcarrier frequencies; then extend to give a subspace of the received signal according to the spatial signature vectors corresponding to different subcarrier frequencies; estimate the signal direction of arrival when the signal is transmitted to the smart antenna system through direct path or multipath. 
         [0011]    In summary, the signal subspace is extended by the spatial signature matrix so that the problem of loss of rank of the subspace caused by signal correlation can be avoided. Furthermore, the direction finder that operates based on the signal subspace estimates the signal direction of arrival more accurately. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]    The structure and the technical means adopted by the present invention to achieve the above and other objects can be best understood by referring to the following detailed description of the preferred embodiments and the accompanying drawings, wherein 
           [0013]      FIG. 1  is a block diagram of an embodiment of a module for estimating signal direction of arrival according to the present invention; 
           [0014]      FIG. 2  is a block diagram of another embodiment of a simulation system for estimating signal direction of arrival according to the present invention; 
           [0015]      FIG. 3  is a flow chart of an embodiment of a method for estimating signal direction of arrival according to the present invention. 
           [0016]      FIG. 4  shows simulation results of the embodiment in  FIG. 2 . 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0017]    In communication systems, correct estimation of signal direction of arrival is beneficial to beam pattern synthesis. Take a smart antenna applied to an Orthogonal Frequency Division Multiplexing (OFDM) system as an example, correct beam pattern is generated by accurate estimation of signal direction of arrival. The more number of angles of arrival the smart antenna system recognizes, the more correct the beam pattern given is when signals are transmitted to the smart antenna system through different pathways. 
         [0018]    Refer to  FIG. 1 , an array antenna module  110  is coupled to a radio frequency/intermediate frequency (RF/IF) module  120  and DOA module  130  is coupled between the RF/IF module  120  and a beamforming module  140 . The DOA module  130  consists of a processing unit  132  and a direction finder  134  that connect with each other. And the processing unit  132  is coupled to the RF/IF module  120  while the direction finder  134  is coupled to the beamforming module  140 . Moreover, the array antenna module  110  includes a plurality of receiving end antennas ranging from ANT 01  to ANT 0 M. The antennas can be omnidirectional, sector, or directional antenna, arranged linearly or circularly. 
         [0019]    The array antenna module  110  is used to receive signal  r (t). Take OFDM system as an example, the signal  r (t) includes a plurality of subcarrier frequencies. After the array antenna module  110  receiving the signal  r (t), the signal  r (t) is sent to the processing unit  132  through the RF/IF module  120 . Transmission of the signal  r (t) through different pathways at various subcarrier frequencies generates different spatial signature vectors. By spectral-spatial smoothing algorithm, processing unit  132  obtains a spatial signature matrix formed from spatial signature vector at different subcarrier frequencies. In other words, column vector of the spatial signature matrix is from spatial signature vector at different subcarrier frequencies. By this spatial signature matrix, a subspace SP of the signal  r (t) is extended and sent to the direction finder  134 . 
         [0020]    After receiving the subspace SP, the direction finder  134  uses algorithm for estimating signal angle of arrival such as multiple signal classification (MUSIC) or estimating signal parameter via rotational invariance techniques (ESPRIT) to estimate the angle of arrival of the signal  r (t) and sends an output signal OUT to the beamforming module  140 . The output signal OUT includes direction of arrival information related to the signal  r (t). Then the beamforming module  140  produces a beam pattern of the signal  r (t) according to the angle of arrival information related to the signal  r (t). The more accurate the angle of arrival information is, the more correct the beam pattern produced by the beamforming module  140  is. In this embodiment, if the array antenna module  110  includes a number of M receiving end antennas, M is a positive integer, the number of angle of arrival that the direction finder  134  can estimate is M−1. 
         [0021]    Next, spectral-spatial smoothing algorithm used in the processing unit  132  is described. In an embodiment, a smart antenna system applied to an Orthogonal Frequency Division Multiplexing system is taken as an example. It is assumed that signal is transmitted by a number of P subcarrier frequencies, P is a positive integer. The number of receiving end antennas ANT 01 ˜ANT 0 M in the array antenna module  110  is M and M is a positive integer. The receiving end antennas ANT 01 ˜ANT 0 M are arranged in a uniform linear fashion. Then the signal  r (t) received by the array antenna module  110  having a spatial signature matrix A of a M×P matrix. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         A 
                         = 
                           
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                   ( 
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         [0000]    
       
         
           
             
               
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         [0000]    is the spatial signature of the ith subcarrier frequency 
         [0000]    
       
         
           
             
               
                 
                   a 
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                 i 
               
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                 ( 
                 
                   
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         [0000]    is a M×1 vector 
       P is the number of subcarrier frequency, 
     N m  is the number of paths, 
     C is light speed 
     D is the distance between two of the receiving end antennas ANT 01 ˜ANT 0 M, 
       [0022]    θ l  is an angle of arrival of the lth path,
 
α l   i  is the amplitude and phase difference of the ith subcarrier&#39;s lth path,
 
       M is the number of the receiving end antenna, 
     P must be larger than the number of antenna and the number of multipath signal 
       [0023]    l, i is a positive integer 
         [0024]    The above spatial signature matrix A can be converted into the following form: 
         [0000]    
       
         
           
             
               
                 
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                           ⋯ 
                         
                         
                           
                             
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                                 l 
                                 = 
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                                 m 
                               
                             
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                                 α 
                                 l 
                                 P 
                               
                                
                               
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                                    
                                   
                                       
                                   
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                                   2 
                                    
                                   
                                       
                                   
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                                   π 
                                    
                                   
                                       
                                   
                                    
                                   
                                     f 
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                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     
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                                       l 
                                     
                                      
                                     
                                       ( 
                                       
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                                         - 
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                                       ) 
                                     
                                   
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                     ] 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0025]    In equation (2), the rank of the spatial signature matrix A is between 1 and M, that is 
         [0000]      1≦r≦M  (3) 
         [0000]    wherein r is the rank of A, and r is a positive integer. In order to prove that the rank of the spatial signature matrix A is M and it is a generating set of the subspace with dimension, the spatial signature matrix A in equation (2) can be expressed as the sum of the antenna array response matrix A 1 , . . . , A N     m   . Thus the spatial signature matrix A can be converted into another form: 
         [0000]        A=A   1   +A   2   + . . . +A   N     m     (3) 
         [0026]    The antenna array response matrix A l  of the lth multipath signal is 
         [0000]    
       
         
           
             
               
                 
                   
                     A 
                     l 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
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                               l 
                               1 
                             
                           
                           
                             
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                                   2 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                    
                                   
                                       
                                   
                                    
                                   
                                     f 
                                     P 
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     
                                       θ 
                                       l 
                                     
                                      
                                     
                                       ( 
                                       
                                         D 
                                         C 
                                       
                                       ) 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       M 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0027]    In the equation (4), the antenna array response matrix A l  is composed of antenna array response vector, thus it can be converted to: 
         [0000]        A   l =[ ā   l   1 (θ l , ƒ 1 )  ā   1   2 (θ l , ƒ 2 ) . . .  ā   l   P (θ l , ƒ P )]  (5) 
         [0000]    while 
         [0000]    
       
         
           
             
               
                 
                   a 
                   ⇀ 
                 
                 l 
                 i 
               
                
               
                 ( 
                 
                   
                     θ 
                     l 
                   
                   , 
                   
                     f 
                     i 
                   
                 
                 ) 
               
             
              
             
                 
             
              
             
               is 
                
               
                 [ 
                 
                   
                     α 
                     l 
                     i 
                   
                   , 
                   
                     
                       α 
                       l 
                       i 
                     
                      
                     
                        
                       
                         j 
                          
                         
                             
                         
                          
                         2 
                          
                         
                             
                         
                          
                         π 
                          
                         
                             
                         
                          
                         
                           f 
                           i 
                         
                          
                         sin 
                          
                         
                             
                         
                          
                         
                           θ 
                           l 
                         
                          
                         
                           D 
                           C 
                         
                       
                     
                   
                   , 
                   … 
                    
                   
                       
                   
                   , 
                   
                     
                       α 
                       l 
                       i 
                     
                      
                     
                        
                       
                         j 
                          
                         
                             
                         
                          
                         2 
                          
                         
                             
                         
                          
                         π 
                          
                         
                             
                         
                          
                         
                           f 
                           i 
                         
                          
                         sin 
                          
                         
                             
                         
                          
                         
                           θ 
                           l 
                         
                          
                         
                           D 
                           C 
                         
                          
                         
                           ( 
                           
                             M 
                             - 
                             1 
                           
                           ) 
                         
                       
                     
                   
                 
                 ] 
               
             
           
         
       
     
         [0000]    and  ā   l   i (θ l , ƒ i ) is converted into 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         a 
                         ⇀ 
                       
                       l 
                       i 
                     
                      
                     
                       ( 
                       
                         
                           θ 
                           l 
                         
                         , 
                         
                           f 
                           i 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         α 
                         l 
                         i 
                       
                        
                       
                         [ 
                         
                           1 
                            
                           
                               
                           
                            
                           
                              
                             
                               j 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 f 
                                 i 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 
                                   θ 
                                   l 
                                 
                                  
                                 
                                   ( 
                                   
                                     D 
                                     c 
                                   
                                   ) 
                                 
                               
                             
                           
                            
                           
                               
                           
                            
                           ⋯ 
                            
                           
                               
                           
                            
                           
                              
                             
                               j 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 
                                   f 
                                   i 
                                 
                                  
                                 
                                   ( 
                                   
                                     M 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 
                                   θ 
                                   l 
                                 
                                  
                                 
                                   ( 
                                   
                                     D 
                                     c 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                     T 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0028]    In consideration of the following matrix 
         [0000]    
       
         
           
             
               
                 
                   
                     Z 
                     l 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           1 
                         
                         
                           1 
                         
                         
                           ⋯ 
                         
                         
                           1 
                         
                       
                       
                         
                           
                              
                             
                               j 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 f 
                                 1 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 
                                   θ 
                                   l 
                                 
                                  
                                 
                                   ( 
                                   
                                     D 
                                     C 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                              
                             
                               j 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 f 
                                 2 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 
                                   θ 
                                   l 
                                 
                                  
                                 
                                   ( 
                                   
                                     D 
                                     C 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           ⋯ 
                         
                         
                           
                              
                             
                               j 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 f 
                                 P 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 
                                   θ 
                                   l 
                                 
                                  
                                 
                                   ( 
                                   
                                     D 
                                     C 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           ⋮ 
                         
                         
                           ⋮ 
                         
                         
                           ⋰ 
                         
                         
                           ⋮ 
                         
                       
                       
                         
                           
                              
                             
                               j 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 
                                   f 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     M 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 
                                   θ 
                                   l 
                                 
                                  
                                 
                                   ( 
                                   
                                     D 
                                     C 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                              
                             
                               j 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 
                                   f 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     M 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 
                                   θ 
                                   l 
                                 
                                  
                                 
                                   ( 
                                   
                                     D 
                                     C 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           ⋯ 
                         
                         
                           
                              
                             
                               j 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 f 
                                 P 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 
                                   θ 
                                   l 
                                 
                                  
                                 
                                   ( 
                                   
                                     D 
                                     C 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0029]    In the equation (7), the matrix Z l  is an M×P Vandermonde matrix and the Z l -dimension is M. 
         [0030]    The matrix Z l  includes a number of M independent column vector and the column vector of Z l  multiplies a constant will not change independence and ranks of the column vectors. Thus rank of the matrix A l  is also M. In equation (3), the column vector of the spatial signature matrix A is a linear combination of the column vector corresponding to the antenna array response matrix A 1 , . . . , A N     m    because the spatial signature matrix A is the sum of the matrix A 1 , . . . , A N     m   . 
         [0031]    Thus the ith column vector is converted to 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             a 
                             ⇀ 
                           
                           i 
                         
                         = 
                         
                           
                             ∑ 
                             
                               l 
                               = 
                               1 
                             
                             
                               N 
                               m 
                             
                           
                            
                           
                             
                               
                                 a 
                                 ⇀ 
                               
                               l 
                               i 
                             
                              
                             
                               ( 
                               
                                 
                                   θ 
                                   l 
                                 
                                 , 
                                 
                                   f 
                                   i 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               
                                 a 
                                 ⇀ 
                               
                               1 
                               i 
                             
                              
                             
                               ( 
                               
                                 
                                   θ 
                                   1 
                                 
                                 , 
                                 
                                   f 
                                   i 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               
                                 a 
                                 ⇀ 
                               
                               2 
                               i 
                             
                              
                             
                               ( 
                               
                                 
                                   θ 
                                   2 
                                 
                                 , 
                                 
                                   f 
                                   i 
                                 
                               
                               ) 
                             
                           
                           + 
                           … 
                           + 
                           
                             
                               
                                 a 
                                 ⇀ 
                               
                               
                                 N 
                                 m 
                               
                               i 
                             
                              
                             
                               ( 
                               
                                 
                                   θ 
                                   
                                     N 
                                     m 
                                   
                                 
                                 , 
                                 
                                   f 
                                   i 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0032]    In above description, the rank of the antenna array response matrix A 1 , . . . , A N     m    is M so that the dimension of the column vector of the spatial signature matrix A is M. According to above demonstration, the  ā   i  in the equation (4) can be expressed as 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       
                         a 
                         ⇀ 
                       
                       i 
                     
                     = 
                     
                       
                         
                           ∑ 
                           
                             l 
                             = 
                             1 
                           
                           
                             N 
                             m 
                           
                         
                          
                         
                           
                             α 
                             l 
                             i 
                           
                            
                           
                             
                               b 
                               ⇀ 
                             
                             1 
                           
                         
                       
                       + 
                       
                         
                           ∑ 
                           
                             l 
                             = 
                             1 
                           
                           
                             N 
                             m 
                           
                         
                          
                         
                           
                             α 
                             l 
                             i 
                           
                            
                           
                              
                             
                               j 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 f 
                                 i 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 θ 
                                 t 
                               
                                
                               
                                 D 
                                 C 
                               
                             
                           
                            
                           
                             
                               b 
                               ⇀ 
                             
                             2 
                           
                         
                       
                       + 
                       … 
                       + 
                       
                         
                           ∑ 
                           
                             l 
                             = 
                             1 
                           
                           
                             N 
                             m 
                           
                         
                          
                         
                           
                             α 
                             l 
                             i 
                           
                            
                           
                              
                             
                               j 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 f 
                                 i 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 θ 
                                 t 
                               
                                
                               
                                 D 
                                 C 
                               
                                
                               
                                 ( 
                                 
                                   M 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                            
                           
                             
                               b 
                               ⇀ 
                             
                             M 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0000]    while  b   i =[00 . . . 1 . . . 0] T , the ith element is 1 while the rest element is 0.
       A basis of B={  b   1   b   2  . . .  b   M } represents all sets.       
 
         [0034]    The basis of B represents all column vectors of the spatial signature matrix A from the equation (9). If a vector  ν  is any one of vector in a vector space V with dimension M, the vector  ν  is a linear combination of column vectors of the spatial signature matrix A and is expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                             
                         
                          
                         
                           
                             v 
                             ⇀ 
                           
                           = 
                             
                            
                           
                             
                               
                                 β 
                                 1 
                               
                                
                               
                                 
                                   a 
                                   ⇀ 
                                 
                                 1 
                               
                             
                             + 
                             
                               
                                 β 
                                 2 
                               
                                
                               
                                 
                                   a 
                                   ⇀ 
                                 
                                 2 
                               
                             
                             + 
                             … 
                             + 
                             
                               
                                 β 
                                 P 
                               
                                
                               
                                 
                                   a 
                                   ⇀ 
                                 
                                 P 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             β 
                             1 
                           
                           [ 
                           
                             
                               
                                 ( 
                                 
                                   
                                     ∑ 
                                     
                                       l 
                                       = 
                                       1 
                                     
                                     
                                       N 
                                       m 
                                     
                                   
                                    
                                   
                                     α 
                                     l 
                                     1 
                                   
                                 
                                 ) 
                               
                                
                               
                                 
                                   b 
                                   ⇀ 
                                 
                                 1 
                               
                             
                             + 
                             
                               
                                 ( 
                                 
                                   
                                     ∑ 
                                     
                                       l 
                                       = 
                                       1 
                                     
                                     
                                       N 
                                       m 
                                     
                                   
                                    
                                   
                                     
                                       α 
                                       l 
                                       1 
                                     
                                      
                                     
                                        
                                       
                                         j 
                                          
                                         
                                             
                                         
                                          
                                         2 
                                          
                                         
                                             
                                         
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           f 
                                           1 
                                         
                                          
                                         sin 
                                          
                                         
                                             
                                         
                                          
                                         
                                           θ 
                                           t 
                                         
                                          
                                         
                                           D 
                                           C 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 
                                   b 
                                   ⇀ 
                                 
                                 2 
                               
                             
                             + 
                             … 
                             + 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                             
                            
                           
                             
                               ∑ 
                               
                                 l 
                                 = 
                                 1 
                               
                               
                                 N 
                                 m 
                               
                             
                              
                             
                               
                                 α 
                                 l 
                                 1 
                               
                                
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                    
                                   
                                       
                                   
                                    
                                   
                                     f 
                                     1 
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     t 
                                   
                                    
                                   
                                     D 
                                     C 
                                   
                                    
                                   
                                     ( 
                                     
                                       M 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                                
                               
                                 
                                   b 
                                   ⇀ 
                                 
                                 M 
                               
                             
                           
                           ] 
                         
                         + 
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             β 
                             2 
                           
                           [ 
                           
                             
                               
                                 ( 
                                 
                                   
                                     ∑ 
                                     
                                       l 
                                       = 
                                       1 
                                     
                                     
                                       N 
                                       m 
                                     
                                   
                                    
                                   
                                     α 
                                     l 
                                     2 
                                   
                                 
                                 ) 
                               
                                
                               
                                 
                                   b 
                                   ⇀ 
                                 
                                 1 
                               
                             
                             + 
                             
                               
                                 ( 
                                 
                                   
                                     ∑ 
                                     
                                       l 
                                       = 
                                       1 
                                     
                                     
                                       N 
                                       m 
                                     
                                   
                                    
                                   
                                     
                                       α 
                                       l 
                                       2 
                                     
                                      
                                     
                                        
                                       
                                         j 
                                          
                                         
                                             
                                         
                                          
                                         2 
                                          
                                         
                                             
                                         
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           f 
                                           2 
                                         
                                          
                                         sin 
                                          
                                         
                                             
                                         
                                          
                                         
                                           θ 
                                           t 
                                         
                                          
                                         
                                           D 
                                           C 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 
                                   b 
                                   ⇀ 
                                 
                                 2 
                               
                             
                             + 
                             … 
                             + 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                             
                            
                           
                             
                               ∑ 
                               
                                 l 
                                 = 
                                 1 
                               
                               
                                 N 
                                 m 
                               
                             
                              
                             
                               
                                 α 
                                 l 
                                 2 
                               
                                
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                    
                                   
                                       
                                   
                                    
                                   
                                     f 
                                     2 
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     t 
                                   
                                    
                                   
                                     D 
                                     C 
                                   
                                    
                                   
                                     ( 
                                     
                                       M 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                                
                               
                                 
                                   b 
                                   ⇀ 
                                 
                                 M 
                               
                             
                           
                           ] 
                         
                         + 
                         … 
                         + 
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             β 
                             P 
                           
                           [ 
                           
                             
                               
                                 ( 
                                 
                                   
                                     ∑ 
                                     
                                       l 
                                       = 
                                       1 
                                     
                                     
                                       N 
                                       m 
                                     
                                   
                                    
                                   
                                     α 
                                     l 
                                     P 
                                   
                                 
                                 ) 
                               
                                
                               
                                 
                                   b 
                                   ⇀ 
                                 
                                 1 
                               
                             
                             + 
                             
                               
                                 ( 
                                 
                                   
                                     ∑ 
                                     
                                       l 
                                       = 
                                       1 
                                     
                                     
                                       N 
                                       m 
                                     
                                   
                                    
                                   
                                     
                                       α 
                                       l 
                                       P 
                                     
                                      
                                     
                                        
                                       
                                         j 
                                          
                                         
                                             
                                         
                                          
                                         2 
                                          
                                         
                                             
                                         
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           f 
                                           P 
                                         
                                          
                                         sin 
                                          
                                         
                                             
                                         
                                          
                                         
                                           θ 
                                           t 
                                         
                                          
                                         
                                           D 
                                           C 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 
                                   b 
                                   ⇀ 
                                 
                                 2 
                               
                             
                             + 
                             … 
                             + 
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             ( 
                             
                               
                                 ∑ 
                                 
                                   l 
                                   = 
                                   1 
                                 
                                 
                                   N 
                                   m 
                                 
                               
                                
                               
                                 
                                   α 
                                   l 
                                   P 
                                 
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                                     2 
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                                       θ 
                                       t 
                                     
                                      
                                     
                                       D 
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                                      
                                     
                                       ( 
                                       
                                         M 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
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                               b 
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                             M 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
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         [0000]    In equation (10), the vector  ν  is converted into a linear combination of the basis B. Obviously, by selecting proper number β 1  . . . β P  any vector in the vector space V with dimension M can be given by linear combination of the column vectors of the spatial signature matrix A. Thus the equation (10) can be converted to 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
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                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0035]    Therefore, a set of column vectors of the spatial signature matrix A is a generating set of the vector space V with dimension M while M is the rank of this generating set. The processing unit  132  uses the column vector of the spatial signature matrix A to extend the subspace SP so as to solve problems of loss of rank of the subspace SP caused by multipath transmission. After receiving the subspace SP extended from the column vector of the spatial signature matrix A, the direction finder  134  estimates the direction of arrival. 
         [0036]    The accuracy of the method for estimating signal direction of arrival is proved by simulation. As shown in  FIG. 2 , the system for estimating signal direction of arrival includes 3 parts—an emitting unit  210 , a channel unit  220  and a receiving unit  230 . The emitting unit  210  is composed of a modulator  211 , a multiplexer  212  and a transmitting antenna  213 . The multiplexer  212  is disposed between the modulator  211  and the transmitting antenna  213 . The channel unit  220  consists of an additive white Gaussian noise unit  222  and multipath channels  221 . The receiving unit  230  includes an array antenna module  110 , a radio frequency/intermediate frequency (RF/IF) module  120  and a DOA module  130 . The array antenna module  110  is coupled to the RF/IF module  120  while the DOA module  130  is coupled between the RF/IF module  120  and a beamforming module  140 . The DOA module  130  is composed of a processing unit  132  and a direction finder  134  that connect with each other. And the processing unit  132  is coupled to the RF/IF module  120  while the direction finder  134  is coupled to the beamforming module  140 . Furthermore, the array antenna module  110  includes a plurality of receiving end antennas from ANT 01  to ANT 0 M. The receiving unit  230  has similar parts as embodiment in  FIG. 1  and the way of signal transmission and connecting components are also the same. 
         [0037]    A transmitted signal  y (t) with multiple subcarriers is generated by an input signal s(t) passing through the modulator  211  and the multiplexer  212  and is transmitted by the transmitting antenna  213 . Then the transmitted signal  y (t) is added with white noise  n (t) by the additive white Gaussian noise unit  222  for simulating influence of environmental noises on the signal  y (t). Next through the multipath channels  221 , channel effects of the signal  y (t) transmitted through multiple paths are simulated. Thus the signal  r (t) received by the array antenna module  110  is expressed as: 
         [0000]        r ( t )= A   y ( t )+  n ( t ) 
         [0000]    wherein the column vector of the spatial signature matrix A respectively is spatial signature vector formed by transmission of the signal  y (t) through multiple path at various subcarriers. Then by the processing unit  132 , the signal  r (t) is sent to the processing unit  132  through the RF/IF module  120 . The processing unit  132  is in charge to process the signal  r (t) to get the spatial signature matrix A and outputs subspace SP of the signal  r (t) to the direction finder  134 . according to the spatial signature matrix A. By means of an algorithm for estimating signal direction of arrival such as Total Least Squares ESPRIT (TLS ESPRIT), the direction finder  134  estimates angle of arrival of the signal  r (t) according to the subspace SP. The angle of arrival of the signal  r (t) is generated by a source of randomness. Take Laplacian distribution as an example, in this embodiment, the angle of arrival respectively are 40.2423°, 23.8428° and 18.3726°. 
         [0038]      FIG. 4  shows simulation results of the embodiment. In this Figure, the actual received angle is angle of arrival of the signal  r (t), respectively are 40.2423°, 23.8428° and 18.3726° while angle of arrival of the signal  r (t) obtained by the module for estimating signal direction of arrival of the present invention are 40.2431°, 23.8434° and 18.3715°. Without the module of the present invention, the estimated results of the angle of arrival of the signal  r (t) only by the algorithm of the direction finder  134  such as TLS ESPRIT are respectively 22.4713°, −46.8703° and −7.1790. Therefore, by means of the present invention, the accuracy of the direction of arrival of the signal  r (t) is improved and the error is less than 0.1%. 
         [0039]    Refer to  FIG. 3 , a method for estimating signal direction of arrival according to the present invention is applied to detect the direction of arrival of signal  r (t) received by a smart antenna system. The signal  r (t) includes a plurality of subcarriers. First, refer to step  310 , the array antenna module  110  receives a signal  r (t). Then in step S 320 , the processing unit  132  obtains a spatial signature matrix composed of a plurality of spatial signature vectors corresponding to the subcarriers according to various subcarriers and signal transmission paths. In other words, the column vector of the spatial signature matrix is formed by the plurality of spatial signature vectors and each spatial signature vector corresponds to a subcarrier. Next, in step S 330 , according to the obtained spatial signature matrix, the processing unit  132  extends a subspace of the signal  r (t) for estimating direction of arrival of the signal  r (t). The directional of arrival includes at least one of the angle of arrival of the signal  r (t) or signal strength. 
         [0040]    The above smart antenna system includes an array antenna module that consists of a number of M receiving end antennas, M is a positive integer. If the dimension of the subspace is M, a set of column vectors of the spatial signature matrix is a generating set of the above signal subspace and M is the rank of the generating set. 
         [0041]    In another embodiment, the method for extending the subspace in the step  330  includes a spectral-spatial smoothing algorithm. While in the step  340 , the method for estimating signal direction of arrival includes at least one of the multiple signal classification (MUSIC) or the estimating signal parameter via rotational invariance techniques. 
         [0042]    Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details, and representative devices shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.