Abstract:
Provided is an array signal processing device capable of, when a spatial averaging method is applied to array signal processing, reducing the number of antennas constituting an array antenna while making use of the spatial averaging method. In the array signal processing device ( 300 ), an array antenna ( 310 ) comprises four antennas ( 311 - 1  to  311 - 4 ) disposed at the four vertices of a parallelogram. Correlation calculation units ( 341 - 1, 2 ) calculate, based on a received signal, spatial correlation matrices for respective sub-array antenna ( 312 - 1 ) and sub-array antenna ( 312 - 2 ), the sub-array antenna ( 312 - 1 ) comprising the antennas ( 311 - 1, 3 ) disposed at the opposing two vertices and the antenna ( 311 - 2 ), the sub-array antenna ( 312 - 2 ) comprising the antennas ( 311 - 1, 3 ) and the antenna ( 311 - 4 ). An array rotation unit ( 342 ) converts a first spatial matrix of the calculated two spatial matrices to the complex conjugate thereof. A spatial averaging unit ( 343 ) averages the complex conjugate of the first spatial matrix and a second spatial matrix.

Description:
TECHNICAL FIELD  
       [0001]    The present invention relates to an array signal processing apparatus. 
       BACKGROUND ART  
       [0002]    The arrival direction (φ, θ) of a wave can be estimated using an array antenna arranged in a planar manner, such as an circular array. Here, φ represents the azimuth in the same plane (xy plane) as the plane of an array antenna, and θ represents the elevation when the perpendicular direction to that plane is the z axis. 
         [0003]    Further, when detecting each arriving wave component by demultiplexing a plurality of arriving waves having high correlation (coherent) into each arriving wave component, the spatial smoothing technique using a plurality of subarray antennas provided in positions that shift horizontally in space, is effective. 
         [0004]    This method realizes suppression of correlation between arriving waves by determining the arithmetic mean of correlation matrices obtained in each subarray antenna. 
         [0005]    Patent Literature 1 and Non-Patent Literature 1 disclose a method of estimating the arrival direction of a wave while suppressing correlation between coherent waves by applying the spatial smoothing technique to the above-described planar array. 
         [0006]      FIG. 1  shows an array antenna disclosed in Patent Literature 1. In  FIG. 1 , array antenna  10  is formed with five antennas  100 - 1  to  100 - 5  that are arranged on a plane. Further, array antenna  10  is configured with subarray antenna  101 - 1  formed with antennas  100 - 1  to  3 , and subarray antenna  101 - 2  formed with antennas  100 - 3  to  5 . That is, subarray antenna  101 - 1  and subarray antenna  101 - 2  share antenna  100 - 3 . 
         [0007]    As is clear from  FIG. 1 , when being shifted horizontally, subarray antenna  101 - 1  coincides with subarray antenna  101 - 2 . Therefore, it is possible to employ the spatial smoothing technique for array antenna  10 , and it is possible to suppress correlation between arriving waves as described above, by calculating correlation matrices for a reception signal in each of two subarray antennas  101  and determining the arithmetic mean of the obtained two correlation matrices. As a result of this, it is possible to accurately detect respective arrival directions of a plurality of arriving waves having high correlation. 
       CITATION LIST  
     Patent Literature 
       [0000]    
       
         PTL 1 
         Japanese Patent Application Laid-Open No.2004-361377 
       
     
       Non-Patent Literature 
       [0000]    
       
         NPL 1 
         “Adaptive Signal Processing by Array Antenna,” Nobuyoshi 
       
     
         [0012]    Kikuma, Kagaku Gijutsu Shuppan, Inc. 
       SUMMARY OF INVENTION  
     Technical Problem 
       [0013]    By the way, basically, an array signal processing apparatus that processes a signal received from an array antenna is provided with the same number of processing circuits as the number of antennas forming the array antenna. For this reason, by reducing the number of antennas, it is possible to reduce the circuit size and power consumption. 
         [0014]    Therefore, although there is a demand for reduction of circuit size and power consumption for an array signal processing apparatus to which the above-described spatial smoothing technique is applied, it is difficult to use the spatial smoothing technique simply by reducing the number of antennas. 
         [0015]    It is therefore an object of the present invention to provide an array signal processing apparatus that can use the spatial smoothing technique and reduce the number of constituent antennas of an array antenna at the same time, when applying the spatial smoothing technique to array signal processing. 
       Solution to Problem 
       [0016]    An array signal processing apparatus according to the present invention employs a configuration to include: an array antenna formed with four antennas that are arranged on four vertexes of a parallelogram, respectively; a correlation calculation section that calculates spatial correlation matrices for each of a first subarray antenna formed with two antennas arranged on two vertexes facing each other out of the four vertexes and one of the antennas other than the two antennas, and a second subarray antenna formed with the two antennas and the other one of the antennas other than the two antennas, based on reception signals; a conversion section that converts a first spatial matrix out of the calculated two spatial matrices into a complex conjugate; and a spatial smoothing section that determines the arithmetic mean of the complex conjugate of the first spatial matrix and a second spatial matrix. 
       Advantageous Effects of Invention 
       [0017]    According to the present invention, it is possible to provide an array signal processing apparatus that can use the spatial smoothing technique and reduce the number of constituent antennas of an array antenna at the same time, when applying the spatial smoothing technique to array signal processing. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0018]      FIG. 1  shows an array antenna disclosed in Patent Literature 1; 
           [0019]      FIG. 2  shows a direction manifold; 
           [0020]      FIG. 3  is a block diagram showing a configuration of an array signal processing apparatus according to Embodiment 1 of the present invention; 
           [0021]      FIG. 4  shows an example of a configuration of an array antenna; 
           [0022]      FIG. 5  is a block diagram showing a configuration of a signal processing section; 
           [0023]      FIG. 6  shows a configuration of an array antenna for which the conventional spatial smoothing technique can be used; 
           [0024]      FIG. 7  shows a configuration of an array antenna when subarray antennas are not regular triangles; 
           [0025]      FIG. 8  shows an example of the result of computer simulation for estimating the arrival direction that supports the effects of suppressing correlation between coherent waves shown in the array signal processing apparatus; and 
           [0026]      FIG. 9  is a block diagram showing a configuration of a radio communication system according to Embodiment 2 of the present invention. 
       
    
    
     DESCRIPTION OF EMBODIMENTS  
       [0027]    [Theory about Array Reception Signal and Spatial Correlation] 
         [0028]    &lt;Direction Manifold of Circular Array&gt; 
         [0029]    As described above, it is possible to estimate the arrival direction (φ, θ) of a wave with respect to a hemispherical plane by using an array antenna arranged in a planar manner, such as a circular array. φ represents the azimuth in the same plane (xy plane) as the plane of an array antenna, and θ represents the elevation when the perpendicular direction to that plane is the z axis. 
         [0030]    The minimum configuration of a planar array that can estimate the arrival direction (φ, θ) is equilateral triangular array  20  formed with three antennas  200 - 1  to  200 - 3  as shown in  FIG. 2 . 
         [0031]    Here, when each antenna  200  has ideal omni directivity (having the even complex radiation pattern), antenna  200  is arranged on each vertex of a equilateral triangle having a side of length of d 0 , and the center of that equilateral triangle is the phase center of an arriving wave, two dimensional direction manifold a 3  (φ, θ) for equilateral triangular array  201  can be represented by equation 1. Here, φ 0  is a parameter indicating a rotational angle of azimuth of equilateral triangular array  20  with respect to the y axis. 
         [0000]    
       
         
           
             
               
                 
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         [0032]    Generally, an array manifold indicates a complex response vector with respect to the incoming direction of an arriving wave. Each element of this complex response vector corresponds to each constituent antenna of an array antenna. Here, because an ideal antenna is assumed, in equation 1, the arrival direction is a variable and the relative phase relationship depending on the antenna arrangement is expressed. 
         [0033]    Here, when generalizing equation 1 with respect to an equidistant circular array having natural number M antennas, following equation 2 can be obtained. 
         [0000]    
       
         
           
             
               
                 
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         [0034]    &lt;Array Reception Signal and Spatial Correlation Matrix&gt; 
         [0035]    (1) First, a case will be described where waves arriving at an array antenna become two plane waves having no correlation (uncorrelated) between each other. 
         [0036]    When two incoming signals to an array antenna are s 1  (t) and s 2  (t), an array manifold is a (φ, θ), and noise vectors of a plurality of reception processing sequences corresponding to each constituent antenna are N (t), array reception signal vector X (t) can be modelized as shown in equation 3. 
         [0000]      [3] 
         [0000]        X ( t )= s   1 ( t )· a (φ 1 , θ 1 )+ s   2 ( t )· a (φ 2 , θ 2 )+ N ( t )   (Equation 3)
 
         [0037]    Here, equation 3 is a formularization of continuous time domain t, and when this is expressed in discrete time domain i, equation 4 can be obtained. However, in equation 4, L represents the number of samples of discrete time, and X(t) and N(t) represent both complex vectors having the same number of dimensions as the number of antennas forming an array antenna. 
         [0000]      [4] 
         [0000]        X ( i )= s   1 ( i )· a (φ 1 , θ 1 )+ s   2 ( i )· a (φ 2 , θ 2 )+ N ( i )   (Equation 4)
 
         [0000]      i=1,2 . . . , L 
         [0038]    Then, correlation matrix R xx  in a spatial domain in an array antenna can be estimated by following equation 5, using reception signal vector X (i) represented by discrete time i. 
         [0000]    
       
         
           
             
               
                 
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                      
                     
                         
                     
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                        
                       
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         [0039]    In this R xx , diagonal terms indicate autocorrelation in each antenna, and non-diagonal terms indicate cross correlation between antennas. Here, when the number of samples L is large enough, a noise component remains only in the terms representing autocorrelation (i.e. in diagonal terms). 
         [0040]    Therefore, when an array antenna subject to determination of correlation matrices is a equilateral triangular array, which is a manifold indicated by equation 1, and when the number of samples L is large enough, correlation matrix R xx  can be formulated as shown in following equation 6. 
         [0000]      [6] 
         [0000]        R   xx   =A·S·A   H +σ 2   I    (Equation 6)
 
         [0041]    Here, S is represented by following equation 7. 
         [0000]    
       
         
           
             
               
                 
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                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
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                   = 
                   
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                             1 
                           
                         
                         
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         [0042]    Further, I represents an unit matrix of 3×3, σ represents the standard deviation of a noise in a receiving sequence, and three sequences of noise components are even. 
         [0043]    Further, A is represented by following equation 8. 
         [0000]      [8] 
         [0000]        A=[a   3 (φ 1 , θ 1 )  a   3 (φ 2 , θ 2 )]  (Equation 8)
 
         [0044]    Further, P 1  and P 2  in equation 7 represent average power of incoming signal s i (t) and average power of s 2 (t), respectively, which are represented by following equations 9 and 10. 
         [0000]      [9] 
         [0000]        P   1   =E└s   1 ( t )· s   i ( t )*┘  (Equation 9)
 
         [0000]      [10] 
         [0000]        P   2   =E└s   2 ( t )· s   2 ( t )*┘  (Equation 10)
 
         [0045]    As described above, when it is possible to consider that incoming signals s 1 (t) and s 2 (t) are uncorrelated, diagonal elements indicating a correlation matrix of an incoming signal are P 1 , P 2 , and 0. For example, with the MUSIC method or the ESPRIT method, which are known as partial spatial algorithms, arrival directions of two waves having no correlation are estimated using an orthogonality of an eigen space, which is a partial space of this R xx . 
         [0046]    (2) When waves arriving at an array antenna becomes two plane waves having correlation between each other. 
         [0047]    On the other hand, when arriving waves are two waves with coherence (high correlation), the rank of correlation matrix R xx  decreases to one. Under this condition of decrease, only one independent eigenvector is calculated by R xx . Therefore, under this condition of decrease, it is difficult to demultiplex two waves to detect the arrival directions. 
         [0048]    To take measures against this kind of problem, there is a method of recovering the rank of correlation matrix R xx  to “2,” that is, there is the spatial smoothing technique for determining the arithmetic mean of correlation matrices of a plurality of subarray antennas, as a technique of demultiplexing a reception signal into each arriving wave component to detect each arriving wave component by suppressing a plurality of coherent arriving waves. See Non-Patent Literature 1 for the detailed description of this spatial smoothing technique. Further, the MUSIC method and the ESPRIT method are also described in detail in Non-Patent Literature 1. 
         [0049]    Now, embodiments of the present invention will be described in detail with reference to the accompanying drawings. In embodiments, the same parts will be assigned the same reference numerals and overlapping explanations will be omitted. 
       Embodiment 1 
       [0050]    [Configuration of Array Signal Processing Apparatus] 
         [0051]      FIG. 3  is a block diagram showing a configuration of array signal processing apparatus  300  according to Embodiment 1 of the present invention. In  FIG. 3 , array signal processing apparatus  300  includes array antenna  310 , RF reception section  320 , A/D conversion section  330 , and signal processing section  340 . 
         [0052]    Array antenna  310  includes four antennas  311 - 1  to  4 . In array antenna  310 , four antennas  311 - 1  to  4  are arranged on four vertexes of a parallelogram, respectively. 
         [0053]      FIG. 4  shows an example of a configuration of array antenna  310 . In  FIG. 4 , four antennas  311 - 1  to  4  are arranged on four vertexes of a parallelogram, respectively. In  FIG. 4 , a triangle formed by the arrangement position of antennas  311 - 1  to  3  and a triangle formed by the arrangement position of antennas  311 - 1 ,  3 , and  4  are each regular triangle. Antennas  311 - 1  to  3  and antennas  311 - 1 ,  3 , and  4  form subarray antenna  312 - 1  and subarray antenna  312 - 2 , respectively. 
         [0054]    Array antenna  310  outputs reception signals received from antennas  311 - 1  to  4  to RF reception section  320 . 
         [0055]    RF reception section  320  contains a down converter circuit. RF reception section  320  receives as input four sequences of RF reception signals received by four antennas  311 - 1  to  4 , and performs radio reception processing, such as down-conversion and amplification, on each RF reception signal. RF reception section  320  outputs the reception signals obtained by radio reception processing to A/D conversion section  330 . The reception signals output to A/D conversion section  330  are four sequences of IF signals or eight sequences of IQ baseband signals. 
         [0056]    A/D conversion section  330  receives as input the reception signals output from RF reception section  320  (i.e. four sequences of IF signals or eight sequences of IQ baseband signals), performs discrete time sampling on the input reception signals, and obtains a digital signal by quantizing each sample value. These digital signals can be obtained for each of the four sequences or eight sequences that are associated with antennas  311 - 1  to  4 . 
         [0057]    Signal processing section  340  receives as input the digital signal group corresponding to antennas  311 - 1  to  4  and applies the spatial smoothing technique to this digital signal group, to obtain correlation matrices in which correlation between a plurality of arriving waves arriving at antennas  311 - 1  to  4  is suppressed. Then, signal processing section  340  calculates the arrival direction of a wave with respect to array antenna  310 , based on the correlation matrices in which correlation between arriving waves is suppressed. 
         [0058]    Specifically, signal processing section  340  calculates spatial correlation matrices for each of the first subarray antenna formed with two antennas arranged on two vertexes facing each other out of the four vertexes and one of the antennas other than those two antennas, and the second subarray antenna formed with those two antennas and the other one of the antennas, based on reception signals. Here, the first subarray antenna is subarray antenna  312 - 1  and the second subarray antenna is subarray antenna  312 - 2 . 
         [0059]    Then, signal processing section  340  converts the first spatial correlation matrix out of the calculated two spatial correlation matrices into a complex conjugate, and determines the arithmetic mean of the obtained complex conjugate and the second spatial correlation matrix. By this means, an arithmetic mean determination correlation matrix, in which correlation between arriving waves is suppressed, can be obtained. 
         [0060]    Then, signal processing section  340  calculates the arrival direction of the reception signal based on the obtained arithmetic mean determination correlation matrix. 
         [0061]    Specifically, as shown in  FIG. 5 , signal processing section  340  includes correlation calculation sections  341 - 1  and  2 , array rotation section  342 , spatial smoothing section  343 , and direction calculation section  344 . 
         [0062]    Correlation calculation section  341 - 1  calculates correlation matrix R xx     —     1  for subarray antenna  312 - 1 , based on the reception signal of each antenna  311  forming that subarray antenna  312 - 1 . 
         [0063]    Correlation calculation section  341 - 2  calculates correlation matrix R xx     —     2  for subarray antenna  312 - 2 , based on the reception signal of each antenna  311  forming that subarray antenna  312 - 2 . 
         [0064]    Array rotation section  342  calculates R* xx     —     1 , which is the complex conjugate of R xx     —     1 . 
         [0065]    Spatial smoothing section  343  calculates mean correlation matrix R xx     —     ss  by determining the arithmetic mean of R* xx     —     1  and R xx     —     2 . 
         [0066]    Direction calculation section  344  calculates the arrival direction of a reception wave with respect to array antenna  310 , based on mean correlation matrix R xx     —     ss . Here, processing related to eigenvalue decomposition of a matrix and to the inner product of an array manifold that are required for the MUSIC method or the like is performed. 
         [0067]    [Operation of Array Signal Processing Apparatus] 
         [0068]    An operation of array signal processing apparatus  300  having the above configuration will be described below. 
         [0069]    In array signal processing apparatus  300 , correlation calculation section  341 - 1  calculates correlation matrix R xx     —     1  related to subarray antenna  312 - 1 . Further, correlation calculation section  341 - 2  calculates correlation matrix R xx     —     2  related to subarray antenna  312 - 2 . 
         [0070]    Here, as is clear from  FIG. 4 , there is a positional relationship in which subarray antenna  312 - 1  and subarray antenna  312 - 2  do not coincide even when being simply shifted horizontally. Therefore, it is difficult to apply the conventional spatial smoothing technique as is. 
         [0071]    If this conventional spatial smoothing technique is used, in the case of an antenna array containing two equilateral triangle subarray antennas, as is the case with array antenna  310 , such an antenna needs to have the configuration represented by array antenna  610  shown in  FIG. 6 . Array antenna  610  includes subarray antenna  612 - 1  formed with antennas  611 - 1  to  3  and subarray antenna  612 - 2  formed with antennas  611 - 4  to  6 . Then, by shifting subarray antenna  612 - 1  horizontally, subarray antenna  612 - 1  can lay over subarray antenna  612 - 2 . Therefore, with array antenna  610 , it is possible to expect correlation suppression effects by determining the arithmetic mean of correlation matrix R xx     —     3  related to subarray antenna  612 - 1  and correlation matrix R xx     —     4  related to subarray antenna  612 - 2 . 
         [0072]    Here, the forms of array antenna  310  and array antenna  610  will be compared. When comparing the form of array antenna  310  with the form of array antenna  610  in the condition where subarray antenna  312 - 2  and subarray antenna  612 - 2  are superposed, subarray antenna  312 - 1  coincides with subarray antenna  612 - 1  when being rotated by 180° (i.e. being reversed). This center of rotation matches the center of the circle that passes arrangement positions of all constituent antennas of subarray antenna  312 - 1 . 
         [0073]    That is, because it is possible to use correlation matrix R xx     —     2  for correlation matrix R xx     —     4 , if it is possible to derive correlation matrix R xx     —     3  from correlation matrix R xx     —     1 , it is possible to use the spatial smoothing technique for array antenna  310  as well. 
         [0074]    Therefore, the relationship between correlation matrix R xx     —     1  and correlation matrix R xx     —     3  will be discussed below. 
         [0075]    First, correlation matrix R xx     —     3  is formularized. Subarray antenna  612 - 1  and subarray antenna  612 - 2  are each regular triangular array antenna, as described above. Therefore, it is possible to apply the array manifold shown in equation 1 to either subarray antenna  612 - 1  or subarray antenna  612 - 2 . However, the antenna arrangement of  FIG. 6  corresponds to a case where the rotation of the azimuth of equilateral triangular array  20  shown in  FIG. 2  is φ 0 =−30°. 
         [0076]    That is, equation 1 shows that array manifolds related to two subarray antennas which coincides when one of the subarray antennas is reversed, are the complex conjugates each other. That is, a*(θ, φ), which is the complex conjugate of a(θ, φ), is an array manifold when reverse (e.g. 180° rotation) is performed. 
         [0077]    Further, a reception signal of an array antenna can be modelized as shown in equation 3. With this reason, a reception signal of a reversed equilateral triangular array is represented using a*(θ, φ), which is an array manifold representing the complex conjugate. 
         [0078]    That is, correlation matrix R xx     —     3  is represented by following equation 11. 
         [0000]    
       
         
           
             
               
                 
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                                   σ 
                                   2 
                                 
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                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 A 
                                 · 
                                 S 
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                               + 
                               
                                 
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                                   2 
                                 
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                         = 
                           
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                           R 
                           
                             XX 
                              
                             
                                 
                             
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                             _ 
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                             1 
                           
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                   [ 
                   11 
                   ] 
                 
               
             
           
         
       
     
         [0079]    As is clear from  FIG. 11 , as a result, correlation matrix R xx     —     3  becomes the complex conjugate of correlation matrix R xx     —     1 . 
         [0080]    Using this relationship, array rotation section  342  calculates R* xx     —     1  (i.e. R xx     —     3 ), which is the complex conjugate of R xx     —     1 . This processing of calculating the complex conjugate of a correlation matrix in array rotation section  342  is the signal processing that is newly added to the conventional method. 
         [0081]    By the way, the correlation matrix used here has features of the Hermitian matrix. Therefore, in this correlation matrix, all diagonal terms are real numbers, and for non-diagonal terms, elements that are located in symmetric positions are the complex conjugates each other. For example, element r 12  of the first row, second column of correlation matrix R and element r 21  of the second row, first column are the complex conjugates each other. Therefore, to determine R* xx     —     1 , which is the complex conjugate of R xx     —     1 , it is necessary to reconfigure R* xx     —     1  simply by reading each matrix element configuring R xx     —     1  in a lateral direction and writing each of the matrix element in a longitudinal direction. In other words, R* xx     —     1 , which is the complex conjugate of Hermitian matrix R xx     —     1  can be regarded as R T   xx     —     1 , which is the transpose matrix of R xx     —     1 . This indicates that it is possible to realize processing of array rotation section  342 , which constitutes the feature of the present invention, by associating the reading position with the position in which writing is started, from the memory domain storing correlation matrix R xx     —     1 . 
         [0082]    Then, spatial smoothing section  343  calculates mean correlation matrix R xx     —     ss  by determining the arithmetic mean of R* xx     —     1  and R xx     —     2 . By this means, it is possible to calculate mean correlation signal R xx     —     ss  using array antenna  310 , which, conventionally, can only be calculated using array antenna  10  or array antenna  610 . 
         [0083]    Further, when taking into account features of the above-described Hermitian matrix, mean correlation signal R xx     —     ss  can be expressed as shown in following equation 12. 
         [0000]    
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
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                     12 
                   
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                           2 
                         
                       
                     
                   
                   
                     
                       
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                   [ 
                   12 
                   ] 
                 
               
             
           
         
       
     
         [0084]    Further, compared to the numbers of antennas forming each of array antenna  10  and array antenna  610 , the number of antennas forming array antenna  310  is small. 
         [0085]    That is, when array antenna  10 , which is a conventional method, is used instead of array antenna  310 , RF reception section  320  converts an RF signal received from each of five antennas  100 - 1  to  100 - 5  into an IF signal or a baseband signal. This means that five sequences of down converter circuits are required in RF reception section  320 . 
         [0086]    At this time, in order to accurately estimate correlation matrices used to calculate the direction of an arriving radio wave, it is necessary to use the same local signal source or reference clock source of the above-described five sequences of down converter circuits. At this time, for example, a local signal output from one synthesis section is distributed to five sequences. The circuit realizing this distribution into five sequences not only requires high costs of components but also requires more complex circuit configuration compared to four sequences of distribution circuits, and therefore is not preferred from the viewpoint of practicality. 
         [0087]    In addition, A/D conversion section  330  receives as input reception signals output from RF reception section  320  (i.e. five sequences of IF signals or ten sequences of IQ baseband signals), performs discrete time sampling on the input reception signals, and obtains a digital signal by quantizing each sample value. Likewise, it is necessary to obtain a digital signal for each of five sequences or ten sequences of signals that are associated with antennas  100 - 1  to  100 - 5  while securing synchronization of sample timing for five sequences of analog inputs. 
         [0088]    Here, a general-purpose A/D conversion apparatus has two sequences or four sequences of input terminals and is often provided in the form of one substrate. 
         [0089]    In this way, by reducing the number of required processing sequences from five to four, hardware for processing a reception signal of an array antenna can not only reduce the number of components, but also can have an advantage in development costs in that it is easy to design the circuit or select the substrate. 
         [0090]    As described above, according to the present embodiment, it is possible to realize an array antenna processing apparatus that can use the spatial smoothing technique and reduce the number of constituent antennas of an array antenna at the same time, when applying the spatial smoothing technique to array signal processing. 
         [0091]    Although a case has been described with the above embodiment where each subarray antenna is a regular triangle, the present invention is not limited to this, and it is also possible to apply the present invention to an array antenna in which four antennas are arranged on vertexes of an arbitrary parallelogram, respectively. 
         [0092]      FIG. 7  shows an array antenna when subarray antennas are not regular triangles. In  FIG. 7A , array antenna  710  includes subarray antenna  712 - 1  and subarray antenna  712 - 2 . In  FIG. 7B , array antenna  720  includes subarray antenna  722 - 1  and subarray antenna  722 - 2 . Then, subarray antenna  712 - 1 , subarray antenna  712 - 2 , subarray antenna  722 - 1 , and subarray antenna  722 - 2  are all congruences. Subarray antenna  712 - 1  and subarray antenna  722 - 1  are reversed from each other. 
         [0093]    That is, even for subarray antenna  712 - 1  and subarray antenna  722 - 1 , which are not longitudinal triangles (i.e. constituent antenna arrangement having lower symmetry than the arrangement of a longitudinal triangle), by performing operations performed for the above-described regular triangular subarray antenna  312 - 1  and subarray antenna  612 - 1 , it is possible to determine the mean correlation matrix using array antenna  710 . 
         [0094]    Further,  FIG. 8  shows an example of the result of computer simulation for estimating the arrival direction that supports the effects of suppressing correlation between coherent waves shown in array signal processing apparatus  300 . In  FIG. 8 , the horizontal axis indicates 360° direction in the horizontal plane (azimuth) on which array antenna  720  is arranged and the vertical axis indicates an angular spectrum estimated by the MUSIC method. Then, the vertical axis is normalized by the maximum value of the spectrum. The conditions of simulation are as follows. Two coherent (here, perfectly correlated) waves arrive from the azimuth of 150° and 210°, and the reception SNR with respect to the arriving wave in the direction of 150° is ten dBs and the reception SNR with respect to the arriving wave in the direction of 210° is four dBs. However, for either of two arriving waves of the azimuth of 150° and 210°, the elevation in the arrival direction is 90°. 
         [0095]    In  FIG. 8 , curve  800  is an angular spectrum calculated when the arrival direction is estimated using subarray antenna  712 - 2  only. In contrast to this, curve  801  is an angular spectrum calculated when the spatial smoothing processing is performed using both subarray antenna  712 - 1  and subarray antenna  712 - 2 . In curve  801 , pointed peaks appear in the direction of 150° and the direction of 210°. That is, by detecting two peaks appearing in curve  801 , it is possible to estimate the arrival direction by demultiplexing a coherent wave. 
         [0096]    As described above, when an array antenna containing two subarray antennas is adopted, it is possible to determine an mean correlation matrix by one time of determination of the arithmetic mean. Therefore, in this case, the largest number of arriving waves in which correlation can be suppressed is two. Further, when estimating the arrival direction using the MUSIC method, it is possible to demultiplex the arriving waves of the number obtained by subtracting one from the number of antennas forming the subarray antenna. From the above, it is possible to regard the array antenna that is formed with four antennas and contains two congruent subarray antennas as shown in  FIG. 7A , as the minimum configuration of a planar array with which two-dimensional estimation of arrival directions for two coherent waves is possible. 
         [0097]    Generally, a monopole antenna or a microstrip antenna is used for an antenna forming an planar array. For example, a monopole antenna shows an even directivity of vertical polarization with respect to the azimuth, but is null in the direction of the z axis. Further, a microstrip antenna is null with respect to the azimuth, but shows the maximum directivity gain in the direction of the z axis. Therefore, which antenna to adopt is determined based on the environment in which the array antenna is mounted or based on the requirements of the system. 
       Embodiment 2 
       [0098]    An specific case where array signal processing apparatus  300  according to Embodiment 1 is applied will be described with Embodiment 2. 
         [0099]      FIG. 9  is a block diagram showing a configuration of radio communication system  900 . In  FIG. 9 , radio communication system  900  includes radio apparatus  910  and tag  920 . 
         [0100]    In radio communication system  900 , radio apparatus  910  transmits an impulse radio-ultra wideband (IR-UWB) pulse signal from a radio transmission section (not shown). Tag  920  transmits a response UWB pulse signal to radio apparatus  910  according to a received UWB pulse signal. It is possible to apply either of the following three methods to this tag  920 . The first method is an active method, the second method is a passive method, and the third method is a semi-passive method. The third semi-passive method is a non-synchronous method in which the reference clock of the transmission side of an UWB pulse signal and the reference clock of the reception side do not synchronize. Further, in the third semi-passive method, the reception side transmits a response UWB signal after amplifying a reception UWB signal. 
         [0101]    Then, radio apparatus  910  includes a function section corresponding to array signal processing apparatus  300 , and estimates the arrival direction of a signal transmitted from tag  920 . 
         [0102]    In  FIG. 9 , radio apparatus  910  includes bandpass filters (BPFs)  911 - 1  to  4  and down converters  912 - 1  to  4  that correspond to antennas  311 - 1  to  4 . 
         [0103]    In radio apparatus  910 , antennas  311 - 1  to  4  are narrow-band antennas that receive a partial band of the IR-UWB band. 
         [0104]    Here, when estimating the arrival direction of a radio wave, as a fundamental principle, a phase error between antenna sequences is an error of estimation result in estimation of the arrival direction. Therefore, it is necessary to manage the phase error between antenna sequences within a desired error range, by calibration, for example. For this reason, when estimating the arrival direction of a wide band signal such as an UWB pulse, it is necessary to manage the accuracy of a phase for an overall wide band, which, in reality, is difficult. With this reason, in reality, a signal in the narrowest possible band, will be used. The simplest example of a narrow band signal is a single continuous wave (hereinafter referred to as continuous wave, CW) signal contained in an IR-UWB signal. An UWB signal in the IR-UWB method is generated by passing an edge signal of frequency oscillated in the crystal oscillation circuit of the transmission side through a bandpass filter. When, the frequency of a crystal oscillator is 10 MHz, for example, it is expected that an IR-UWB signal is a signal in which CWs are arranged at the interval of 10 MHz, in the band of 3.4 to 4.8 GHz, which is below the UWB, or the band of 7.25 to 10.6 GHz, which is above the UWB. Therefore, in the present embodiment, for example, an IR-UWB signal is treated as a CW of 4 GHz or 9 GHz, and the center frequency of antennas  311 - 1  to  4  forming array antenna  310  is set at a frequency of 4 GHz or 9 GHz. 
         [0105]    Signals received by antennas  311 - 1  to  4  pass bandpass filters  911 - 1  to  4 , where interference is removed, and then are converted into an IF signal or an IQ baseband signal in down converters  912 - 1  to  4 . In the case of an IF signal, for example, a signal is converted into an IF signal of 10 MHz. In this case, a local signal is a signal that is 10 MHz apart above or below 4 GHz or 9 GHz. Then, it is preferable to use an image rejection mixer as down converter  912  to remove a neighboring image. Further, in the case of an IQ baseband signal, because there is no image signal, a neighboring CW signal is cut by a baseband filter having a cutoff frequency of about 5 MHz in bandpass filter  911 . 
         [0106]    The IF signal or IQ baseband signal that is generated in down converters  912 - 1  to  4  is converted into a digital signal in A/D conversion section  330  and is input to correlation calculation sections  341 - 1  and  2 . 
         [0107]    Correlation calculation section  341 - 1  calculates correlation matrix R xx     —     1  for subarray antenna  312 - 1 , based on the reception signal of each antenna  311  forming subarray antenna  312 - 1 . Correlation calculation section  341 - 2  calculates correlation matrix R xx     —     2  for subarray antenna  312 - 2 , based on the reception signal of each antenna  311  forming subarray antenna  312 - 2 . 
         [0108]    In the case of a UWB pulse signal modulated with the on-off-keying (OOK) scheme, because a UWB pulse signal contains a DC component, generally, covariance is calculated by subtracting the average component of a signal from a correlation matrix. Further, in the case of a UWB pulse signal modulated with the bi-phase scheme, because a UWB pulse signal does not contain a DC component, generally, a correlation matrix is used. A correlation matrix or a covariance matrix is accumulated in a memory in correlation calculation section  341 . 
         [0109]    Array rotation section  342  calculates R* xx     —     1 , which is the complex conjugate of R xx     —     1 . 
         [0110]    Spatial smoothing section  343  calculates mean correlation matrix R xx     —     ss  by determining the arithmetic mean of R* xx     —     1  and R xx     —     2 . 
         [0111]    Direction calculation section  344  calculates the arrival direction of a reception wave with respect to array antenna  310 , based on mean correlation matrix R xx     —     ss . Here, processing related to eigenvalue decomposition of a matrix and to the inner product of an array manifold that are required for the MUSIC method or the like is performed. 
         [0112]    Also, although cases have been described with the above embodiment as examples where the present invention is configured by hardware, the present invention can also be realized by software. 
         [0113]    Each function block employed in the description of each of the aforementioned embodiments may typically be implemented as an LSI constituted by an integrated circuit. These may be individual chips or partially or totally contained on a single chip. “LSI” is adopted here but this may also be referred to as “IC,” “system LSI,” “super LSI,” or “ultra LSI” depending on differing extents of integration. 
         [0114]    Further, the method of circuit integration is not limited to LSI&#39;s, and implementation using dedicated circuitry or general purpose processors is also possible. After LSI manufacture, utilization of a programmable FPGA (Field Programmable Gate Array) or a reconfigurable processor where connections and settings of circuit cells within an LSI can be reconfigured is also possible. 
         [0115]    Further, if integrated circuit technology comes out to replace LSI&#39;s as a result of the advancement of semiconductor technology or a derivative other technology, it is naturally also possible to carry out function block integration using this technology. Application of biotechnology is also possible. 
       INDUSTRIAL APPLICABILITY  
       [0116]    The disclosure of Japanese Patent Application No. 2009-109478, filed on Apr. 28, 2009, including the specification, drawings and abstract, is incorporated herein by reference in its entirety. 
         [0117]    An array signal processing apparatus according to the present invention is useful for using the spatial smoothing technique and reducing the number of constituent antennas of an array antenna at the same time, when applying the spatial smoothing technique to array signal processing. 
       REFERENCE SIGNS LIST  
       [0000]    
       
           300  Array signal processing apparatus 
           310 ,  610 ,  710 ,  720  Array antenna 
           311 ,  611  Antenna 
           312 ,  612 ,  712 ,  722  Subarray antenna 
           320  RF reception section 
           330  A/D conversion section 
           340  Signal processing section 
           341  Correlation calculation section 
           342  Array rotation section 
           343  Spatial smoothing section 
           344  Direction calculation section 
           900  Radio communication system 
           910  Radio apparatus 
           911  Bandpass filter 
           912  Down converter 
           920  Tag