Patent Publication Number: US-2021190903-A1

Title: Radar apparatus and signal processing method

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a Continuation of PCT International Application No. PCT/JP2018/040827, filed on Nov. 2, 2018, all of which is hereby expressly incorporated by reference into the present application. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a radar technique for detecting a target such as a mobile object, and more particularly to a radar technique for detecting a target by signal processing including coherent integration. 
     BACKGROUND ART 
     A general pulse Doppler radar can transmit a plurality of pulse waves on the basis of a pulse repetition interval (PRI), then receive a plurality of reflected waves corresponding to the plurality of pulse waves from a target to generate a plurality of received signals, and estimate relative velocity (target velocity) of the target on the basis of the plurality of received signals. 
     Among such pulse Doppler radars, there is known one that adopts a pulse-to-pulse stagger method in which transmission intervals of pulse waves are made unequal for the purpose of improving target detection performance. However, in the pulse-to-pulse stagger method, a pulse repetition interval is not constant. As a result, a phase change occurs in a received signal, and energy loss (integration loss) may occur during coherent integration. Patent Literature 1 (Japanese Unexamined Patent Publication No. 6-294864) discloses a pulse Doppler radar capable of avoiding occurrence of loss when coherent integration is performed on a received signal (received video signal), even if the radar is operated by the pulse-to-pulse stagger method. The pulse Doppler radar disclosed in Patent Literature 1 avoids occurrence of integration loss by predicting a phase change of the received signal from a value of a pulse repetition interval and a value of target velocity and correcting a phase of the received signal using a result of the prediction. 
     CITATION LIST 
     Patent Literature 
     Patent Literature 1: Japanese Unexamined Patent Publication No. 6-294864 (see, for example,  FIG. 1 ) 
     SUMMARY OF INVENTION 
     Technical Problem 
     As described above, the pulse Doppler radar disclosed in Patent Literature 1 requires the value of the target velocity in order to correct the phase of the received signal. Therefore, when detection of the target velocity fails, or when detection accuracy of the target velocity is low, there is a problem that integration loss occurs and target detection performance is deteriorated. 
     In view of the above, an object of the present invention is to provide a radar apparatus and a signal processing method for suppressing integration loss and improving target detection performance without requiring a value of target velocity. 
     Solution to Problem 
     A radar apparatus according to one aspect of the present invention including: processing circuitry to set a plurality of pairs of a pulse repetition interval longer than a predetermined reference interval and a pulse repetition interval shorter than the reference interval; continuously generate a plurality of transmission pulse signals at a timing based on the plurality of pairs of pulse repetition intervals; send out the plurality of transmission pulse signals to external space and receiving a plurality of reflected wave signals corresponding to the respective plurality of transmission pulse signals from the external space; generate a plurality of received signals corresponding to the respective plurality of transmission pulse signals by sampling each of the plurality of reflected wave signals having been received; generate a plurality of frequency domain signals by performing domain conversion processing from a time domain to a frequency domain on the plurality of received signals; and detect a target candidate on the basis of the plurality of frequency domain signals. 
     Advantageous Effects of Invention 
     According to the one aspect of the present invention, the plurality of pairs of the pulse repetition interval longer than the predetermined reference interval and the pulse repetition interval shorter than the reference interval is set, so that the signal conversion unit can suppress integration loss when performing the domain conversion processing without requiring a value of target velocity. Thus, it is possible to improve target detection performance. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram showing a schematic configuration of a radar apparatus according to a first embodiment of the present invention. 
         FIG. 2  is a block diagram schematically showing a configuration example of a signal generation circuit in the first embodiment. 
         FIG. 3  is a graph showing a setting example of a pulse repetition interval. 
         FIG. 4  is a graph showing another setting example of the pulse repetition interval. 
         FIG. 5  is a block diagram schematically showing a configuration example of a receiving circuit in the first embodiment. 
         FIG. 6  is a flowchart schematically showing an operation procedure of a radar signal processing circuit in the first embodiment. 
         FIG. 7A  is a diagram schematically showing an example of a phase state of pulse compression signals obtained when it is assumed that all pulse repetition intervals are set to the same value, and  FIG. 7B  is a diagram schematically showing an example of a phase state of pulse compression signals obtained when the pulse repetition intervals according to the first embodiment are set. 
         FIG. 8  is a graph schematically showing an example of spectra of three types of frequency domain signals. 
         FIG. 9  is a block diagram showing a hardware configuration example that implements functions of a PRI control unit and the radar signal processing circuit in the first embodiment. 
         FIG. 10  is a block diagram schematically showing a configuration of a radar apparatus according to a second embodiment of the present invention. 
         FIG. 11  is a diagram showing a relationship between a pulse compression signal and the pulse repetition interval in the first embodiment. 
         FIG. 12  is a diagram for explaining oversampling processing in the second embodiment. 
         FIG. 13  is a flowchart schematically showing an operation procedure of a radar signal processing circuit in the second embodiment. 
         FIG. 14A  is a diagram schematically showing an example of spectra of frequency domain signals generated in the first embodiment, and  FIG. 14B  is a diagram schematically showing an example of a spectrum of a frequency domain signal generated in the second embodiment. 
         FIG. 15  is a diagram schematically showing a configuration of a radar apparatus according to a third embodiment of the present invention. 
         FIG. 16  is a diagram schematically showing a configuration of a radar apparatus according to a fourth embodiment of the present invention. 
         FIG. 17  is a schematic configuration diagram of a signal generation circuit in the fourth embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, various embodiments of the present invention will be described in detail by referring to the drawings. It is to be noted that components denoted by the same reference numerals throughout the drawings have the same configuration and the same function. 
     First Embodiment 
       FIG. 1  is a block diagram showing a schematic configuration of a radar apparatus  1  according to a first embodiment of the present invention. As shown in  FIG. 1 , the radar apparatus  1  includes: a signal generation circuit  10  that generates a plurality of transmission pulse signals Tx(h,t) at a timing based on pulse repetition intervals (PRIs) T pri (h); a transmission and reception unit  11  that outputs the plurality of transmission pulse signals Tx(h,t) to an antenna (aerial)  12  and then receives a plurality of reflected wave signals Rx(h,t) corresponding to the respective plurality of transmission pulse signals Tx(h,t); a receiving circuit  13  that performs analog signal processing on the plurality of reflected wave signals Rx(h,t) to generate a plurality of received analog signals W 0 (h,t) and converts the respective plurality of analog signals W 0 (h,t) into a plurality of received digital signals (received video signals) V 0 (h,m); a radar signal processing circuit  30  that performs digital signal processing on the plurality of received digital signals V 0 (h,m) and detects a target candidate; and a display  60  that displays a result of the detection. 
     Further, the radar apparatus  1  includes a PRI control unit  14  that sets the pulse repetition interval T pri (h) used in the signal generation circuit  10 . As a frequency band used by the radar apparatus  1 , for example, a frequency band such as a millimeter wave band or a microwave band can be used. 
     For the transmission pulse signal Tx(h,t), the reflected wave signal Rx(h,t), and the received analog signal W 0 (h,t), a variable t represents time, a variable h is an integer in the range of 0 to H−1 representing a pulse hit number, and H is the number of pulse hits. Hereinafter, the pulse hit number h is referred to as a “hit number h”. Further, a variable m in the received digital signal V 0 (h,m) is an integer in the range of 0 to M(h)−1 representing a sampling number, and M(h) is a sampling point related to the hit number h. 
     The antenna  12  can radiate transmission waves Tw based on the transmission pulse signals Tx(0,t) to Tx(H−1,t) to external space, and then receives reflected waves Rw returned from the external space. The transmission and reception unit  11  outputs reflected wave signals Rx(0,t) to Rx(H−1,t) based on reception output of the antenna  12  to the receiving circuit  13 . 
       FIG. 2  is a block diagram schematically showing a configuration example of the signal generation circuit  10  in the first embodiment. As shown in  FIG. 2 , the signal generation circuit  10  includes a local oscillator  20 , a pulse generator  21 , an intra-pulse modulator  22 , and an output unit  23 . The local oscillator  20  generates a local oscillation signal L 0 (t) in an operating frequency band, and outputs the local oscillation signal L 0 (t) to the pulse generator  21  and the receiving circuit  13 . 
     Specifically, the local oscillator  20  can generate a local oscillation signal L 0 (t) having a constant transmission frequency f 0  within a certain observation period (period from time t=0 to time t=T obs ) as shown by the following equation (1). 
         L   0 ( t )= A   L  exp( j (2π f   0   t+ϕ   0 ))
 
       (0≤ t&lt;T   obs)    (1)
 
     Here, t is time, A L  is amplitude of the local oscillation signal L 0 (t), φ 0  is an initial phase of the local oscillation signal L 0 (t), T obs  is an upper limit of the observation period, and j is an imaginary unit. 
     The PRI control unit  14  shown in  FIG. 1  supplies a pulse width T 0  and a series of pulse repetition intervals T pri (0) to T pri (H−1) to the pulse generator  21 . The pulse generator  21  shown in  FIG. 2  can modulate the local oscillation signal L 0 (t) to continuously generate a plurality of pulse signals on the basis of the pulse width T 0  and the pulse repetition interval T pri (h). 
     For example, the PRI control unit  14  can calculate the pulse repetition interval T pri (h) as shown by an equation (2) for h=0,1, . . . , H−1, on the basis of a predetermined reference interval T pri,0  and a change amount ΔT pri (h) regarding the hit number h. 
         T   pri ( h )= T   pri,0   +ΔT   pri ( h ) 
       ( h= 0,1, . . . ,  H− 1)   (2)
 
     More specifically, the PRI control unit  14  sets a plurality of pairs of a pulse repetition interval longer than the reference interval T pri,0  and a pulse repetition interval shorter than the reference interval T pri,0 . By setting such a pulse repetition interval, it is possible to suppress radio wave interference with other radar systems. For example, the PRI control unit  14  can set a plurality of pairs of pulse repetition intervals each having symmetrical values about the reference interval T pri,0 , and match an average value of the pulse repetition intervals constituting each pair with the reference interval T pri,0 . The following equation (3) is an equation showing a setting example of the pulse repetition interval T pri (h). 
     
       
         
           
             
               
                 
                   
                     
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                                 ( 
                                 
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                                       K 
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                                      
                                     
                                       ( 
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                                      
                                     
                                       ( 
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                             = 
                             
                               
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                               + 
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                   ( 
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     In the equation (3), k indicates an integer equal to or more than 0, and K pri (h) is a coefficient for controlling the pulse repetition interval (PRI) regarding the hit number h (hereinafter sometimes referred to as “PRI coefficient”). According to the equation (3), it is set so that when the hit number h is an even number (h=2k), the pulse repetition interval T pri (h) takes a value of (1+K pri (h))T pri,0 , and when the hit number h is an odd number (h=2k+1), the pulse repetition interval T pri (h) takes a value of (1-K pri (h))T pri,0 . The PRI coefficient K pri (h) may be set to a constant value regardless of the value of the hit number h, or may be set to an individual value for each hit number h. 
       FIGS. 3 and 4  are graphs showing setting examples of the pulse repetition interval T pri (h). In the graphs of  FIGS. 3 and 4 , a horizontal axis represents the hit number h, a vertical axis represents the pulse repetition interval T pri (h), and a circle represents a value of the pulse repetition interval T pri (h). In the setting example of  FIG. 3 , the PRI coefficient K pri (h) in the equation (3) is set to a constant value regardless of the value of the hit number h. At this time, the change amount ΔT pri (h) in the equation (2) is constant. On the other hand, in the setting example of  FIG. 4 , the PRI coefficient K pri (h) in the equation (3) is set to a different value for each hit number h, and as the value of the hit number h is higher, the change amount ΔT pri (h)(=K pri (h)×T pri,0 ) is set to a higher value. From the viewpoint of preventing interference between received signals (for example, received analog signals), the pulse repetition interval T pri (h) shown in  FIG. 4  is preferable to the pulse repetition interval T pri (h) shown in  FIG. 3 . 
     The PRI control unit  14  in the present embodiment is a component different from the signal generation circuit  10 , but is not limited thereto. The PRI control unit  14  may be incorporated in the signal generation circuit  10  or the radar signal processing circuit  30 . 
     Next, the pulse generator  21  shown in  FIG. 2  can modulate the local oscillation signal L 0 (t) to generate a plurality of pulse signals L pls (h,t)(h=0,1, . . . ,H−1) on the basis of the pulse width T 0  and the series of pulse repetition intervals T pri (h)(h=0,1, . . . , H−1) set by the PRI control unit  14 . 
     Specifically, the pulse generator  21  can modulate the local oscillation signal L 0 (t) to generate the plurality of pulse signals L pls (h,t)(h=0,1, . . . , H−1) shown in the following equation (4) on the basis of the pulse width T 0  and the series of pulse repetition intervals T pri (h)(h=0,1, . . . , H−1). 
     
       
         
           
             
               
                 
                   
                     
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     In the equation (4), Ω[h] is a set of time t that satisfies the following equation (5) (where T pri (−1)=0). 
     
       
         
           
             
               
                 
                   
                     
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     Note that the PRI control unit  14  in the present embodiment is a component different from the signal generation circuit  10 , but is not limited to this. The PRI control unit  14  may be incorporated in the signal generation circuit  10  or the radar signal processing circuit  30 . 
     Next, the intra-pulse modulator  22  performs intra-pulse modulation on each of the plurality of pulse signals to generate a plurality of intra-pulse modulation signals as the transmission pulse signals Tx(h,t). The output unit  23  outputs these transmission pulse signals Tx(h,t) to the transmission and reception unit  11 . At this time, the output unit  23  may perform processing such as amplification on the transmission pulse signals Tx(h,t). Specifically, the intra-pulse modulator  22  first generates a modulation control signal L chp (h,t) for frequency-modulating the pulse signal L pls (h,t) using a modulation bandwidth B 0  according to the following equation (6). 
     
       
         
           
             
               
                 
                   
                     
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     Furthermore, as shown in the following equation (7), the intra-pulse modulator  22  can generate an intra-pulse modulation signal frequency-modulated using the modulation control signal L chp (h,t), that is, the transmission pulse signal Tx(h,t). 
     
       
         
           
             
               
                 
                   
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     The antenna  12  can radiate the plurality of transmission pulse signals Tx(h,t) to the external space as the transmission waves Tw, and then receive the reflected waves Rw returned from a target Tgt in the external space. The transmission and reception unit  11  can output the reflected wave signal Rx(h,t) as shown in the following equation (8). 
     
       
         
           
             
               
                 
                   
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                                 [ 
                                 h 
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                   ( 
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                         = 
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     In the equation (8), AR is amplitude of the reflected wave signal Rx(h,t) reflected on the target Tgt, R 0  is an initial target relative distance, v is target relative velocity, τ is time within one pulse, and c is light velocity. Further, Λ[h] is a set of time t satisfying the following equation (9). 
     
       
         
           
             
               
                 
                   
                     
                       
                         ∑ 
                         
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                           = 
                           
                             - 
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                   &lt; 
                   
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           
                             - 
                             1 
                           
                         
                         
                           h 
                           - 
                           1 
                         
                       
                        
                       
                         
                           T 
                           pri 
                         
                          
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         2 
                          
                         
                           R 
                           0 
                         
                       
                       c 
                     
                     + 
                     
                       T 
                       0 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Next, the configuration of the receiving circuit  13  will be described.  FIG. 5  is a block diagram schematically showing a configuration example of the receiving circuit  13 . As shown in  FIG. 5 , the receiving circuit  13  includes a down converter (mixer)  24 , a band filter  25 , an amplifier  26 , a phase detector  27 , and an A/D converter  28 . 
     The down converter  24  shown in  FIG. 5  converts the reflected wave signal Rx(h,t) into an analog signal in a lower frequency band (for example, an intermediate frequency band). The band filter  25  filters the analog signal and outputs a filter signal. The amplifier  26  amplifies the filter signal and outputs an amplified signal. Then, the phase detector  27  performs phase detection of the amplified signal and generates a detection signal composed of an in-phase component and an orthogonal component as the received analog signal W 0 (h,t). The following equation (10) is an equation representing the received analog signal W 0 (h,t). 
     
       
         
           
             
               
                 
                   
                     
                       W 
                       0 
                     
                      
                     
                       ( 
                       
                         h 
                         , 
                         t 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         Rx 
                          
                         
                           ( 
                           
                             h 
                             , 
                             t 
                           
                           ) 
                         
                       
                        
                       
                         
                           L 
                           0 
                           * 
                         
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                     
                     = 
                     
                       { 
                       
                         
                           
                             
                               
                                 
                                   A 
                                   V 
                                 
                                  
                                 
                                   exp 
                                    
                                   
                                     ( 
                                     
                                       j 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                        
                                       
                                           
                                       
                                        
                                       
                                         π 
                                          
                                         
                                           [ 
                                           
                                             
                                               
                                                 - 
                                                 
                                                   f 
                                                   0 
                                                 
                                               
                                                
                                               
                                                 
                                                   2 
                                                    
                                                   
                                                     ( 
                                                     
                                                       
                                                         R 
                                                         0 
                                                       
                                                       - 
                                                       vt 
                                                     
                                                     ) 
                                                   
                                                 
                                                 c 
                                               
                                             
                                             + 
                                             
                                               
                                                 
                                                   B 
                                                   0 
                                                 
                                                 
                                                   2 
                                                    
                                                   
                                                     T 
                                                     0 
                                                   
                                                 
                                               
                                                
                                               
                                                 
                                                   ( 
                                                   
                                                     τ 
                                                     - 
                                                     
                                                       
                                                         2 
                                                          
                                                         
                                                           ( 
                                                           
                                                             
                                                             R 
                                                             0 
                                                             
                                                             - 
                                                             vt 
                                                           
                                                           ) 
                                                         
                                                       
                                                       c 
                                                     
                                                   
                                                   ) 
                                                 
                                                 2 
                                               
                                             
                                           
                                           ] 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                               , 
                             
                           
                           
                             
                               t 
                               ∈ 
                               
                                 Λ 
                                  
                                 
                                   [ 
                                   h 
                                   ] 
                                 
                               
                             
                           
                         
                         
                           
                             
                               0 
                               , 
                             
                           
                           
                             
                               t 
                               ∉ 
                               
                                 Λ 
                                  
                                 
                                   [ 
                                   h 
                                   ] 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         h 
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         H 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Here, A V  indicates amplitude of the received analog signal W 0 (h,t), and an upper right superscript “*” indicates a complex conjugate. A local oscillation signal L 0 *(t) is a complex conjugate of the local oscillation signal L 0 (t). 
     The A/D converter  28  can generate the received digital signal (received video signal) V 0 (h,m) as shown in the following equation (11) by sampling the received analog signal W 0 (h,t) at a predetermined sampling interval Δt. 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       0 
                     
                      
                     
                       ( 
                       
                         h 
                         , 
                         m 
                       
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 
                                   A 
                                    
                                   
                                       
                                   
                                    
                                   
                                     exp 
                                      
                                     
                                       ( 
                                       
                                         
                                           - 
                                           j 
                                         
                                          
                                         
                                             
                                         
                                          
                                         2 
                                          
                                         
                                             
                                         
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           
                                             f 
                                             0 
                                           
                                           · 
                                           2 
                                         
                                          
                                         
                                           
                                             ( 
                                             
                                               
                                                 R 
                                                 0 
                                               
                                               - 
                                               
                                                 v 
                                                  
                                                 
                                                   ( 
                                                   
                                                     
                                                       
                                                         ∑ 
                                                         
                                                           n 
                                                           = 
                                                           
                                                             - 
                                                             1 
                                                           
                                                         
                                                         
                                                           h 
                                                           - 
                                                           1 
                                                         
                                                       
                                                        
                                                       
                                                         
                                                           T 
                                                           pri 
                                                         
                                                          
                                                         
                                                           ( 
                                                           n 
                                                           ) 
                                                         
                                                       
                                                     
                                                     + 
                                                     
                                                       m 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       Δ 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       t 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             ) 
                                           
                                           / 
                                           c 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     exp 
                                      
                                     
                                       ( 
                                       
                                         j 
                                          
                                         
                                             
                                         
                                          
                                         2 
                                          
                                         
                                             
                                         
                                          
                                         π 
                                          
                                         
                                           
                                             B 
                                             0 
                                           
                                           
                                             2 
                                              
                                             
                                               T 
                                               0 
                                             
                                           
                                         
                                          
                                         
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 Δ 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 t 
                                               
                                               - 
                                               
                                                 2 
                                                  
                                                 
                                                   
                                                     ( 
                                                     
                                                       
                                                         R 
                                                         0 
                                                       
                                                       - 
                                                       
                                                         v 
                                                          
                                                         
                                                           ( 
                                                           
                                                             
                                                             
                                                             ∑ 
                                                             
                                                             n 
                                                             = 
                                                             
                                                             - 
                                                             1 
                                                             
                                                             
                                                             
                                                             h 
                                                             - 
                                                             1 
                                                             
                                                             
                                                              
                                                             
                                                             
                                                             T 
                                                             pri 
                                                             
                                                              
                                                             
                                                             ( 
                                                             n 
                                                             ) 
                                                             
                                                             
                                                             
                                                             + 
                                                             
                                                             m 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             Δ 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             t 
                                                             
                                                           
                                                           ) 
                                                         
                                                       
                                                     
                                                     ) 
                                                   
                                                   / 
                                                   c 
                                                 
                                               
                                             
                                             ) 
                                           
                                           2 
                                         
                                       
                                       ) 
                                     
                                   
                                   , 
                                 
                               
                             
                           
                         
                         
                           
                             m 
                             ∈ 
                             
                               Ψ 
                                
                               
                                 [ 
                                 h 
                                 ] 
                               
                             
                           
                         
                       
                       
                         
                           
                             0 
                             , 
                           
                         
                         
                           
                             m 
                             ∉ 
                             
                               Ψ 
                                
                               
                                 [ 
                                 h 
                                 ] 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         m 
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         
                           M 
                            
                           
                             ( 
                             h 
                             ) 
                           
                         
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         h 
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         H 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     In the equation (11), m is an integer in the range of 0 to M(h)−1 representing a sampling number, and Ψ[h] is a set of sampling numbers m that satisfy a conditional expression of the following equation (12). 
     
       
         
           
             
               
                 
                   
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           
                             - 
                             1 
                           
                         
                         
                           h 
                           - 
                           1 
                         
                       
                        
                       
                         
                           T 
                           pri 
                         
                          
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         2 
                          
                         
                           R 
                           0 
                         
                       
                       c 
                     
                   
                   ≤ 
                   
                     m 
                      
                     
                         
                     
                      
                     Δ 
                      
                     
                         
                     
                      
                     t 
                   
                   &lt; 
                   
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           
                             - 
                             1 
                           
                         
                         
                           h 
                           - 
                           1 
                         
                       
                        
                       
                         
                           T 
                           pri 
                         
                          
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         2 
                          
                         
                           R 
                           0 
                         
                       
                       c 
                     
                     + 
                     
                       T 
                       0 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The radar signal processing circuit  30  can perform digital signal processing on the received digital signal V 0 (h,m) to detect a target candidate. Hereinafter, configuration and operation of the radar signal processing circuit  30  will be described by referring to  FIGS. 1 and 6 .  FIG. 6  is a flowchart schematically showing an operation procedure of the radar signal processing circuit  30  in the first embodiment. 
     As shown in  FIG. 1 , the radar signal processing circuit  30  includes a signal conversion unit  40  and a target detection unit  50 . The signal conversion unit  40  includes a correlation processing unit  42  that generates a pulse compression signal F V·Ex (h,m) by performing correlation processing using a reference signal on the received digital signal V 0 (h,m) and a domain conversion unit  44  that generates a plurality of frequency domain signals f d (h fft ,m)(h fft =0 to H−1) by performing, on a plurality of the pulse compression signals F V·Ex (h,m)(h=0 to H−1), a discrete Fourier transform in a pulse hit direction on the basis of a predetermined algorithm. Further, the target detection unit  50  includes a target candidate detection unit  51  that detects a target candidate on the basis of the frequency domain signal f d (h fft ,m) and a target candidate information calculating unit  52  that calculates target information related to the detected target candidate. 
     First, when received digital signals V 0 (h,m) are input, the correlation processing unit  42  generates pulse compression signals F V·Ex (h,m) by performing correlation processing using a reference signal Ex(m) on the received digital signals V 0 (h,m) (step ST 11 ). Specifically, the correlation processing unit  42  can generate the pulse compression signals F V·Ex (h,m) by performing a correlation calculation between the reference signal Ex(m) and the received digital signals V 0 (h,m). As the reference signal Ex(m), a reference signal having a modulation component B 0 /(2T 0 ) of the modulation control signal L chp (h,t) can be used as shown in the following equation (13). 
     
       
         
           
             
               
                 
                   
                     Ex 
                      
                     
                       ( 
                       m 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 A 
                                 E 
                               
                                
                               
                                 exp 
                                  
                                 
                                   ( 
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     π 
                                      
                                     
                                       
                                         B 
                                         0 
                                       
                                       
                                         2 
                                          
                                         
                                           T 
                                           0 
                                         
                                       
                                     
                                      
                                     
                                       m 
                                       2 
                                     
                                      
                                     Δ 
                                      
                                     
                                         
                                     
                                      
                                     
                                       t 
                                       2 
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               Δ 
                                
                               
                                   
                               
                                
                               t 
                             
                             ∈ 
                             
                               Φ 
                                
                               
                                 [ 
                                 m 
                                 ] 
                               
                             
                           
                         
                       
                       
                         
                           
                             0 
                             , 
                           
                         
                         
                           
                             
                               Δ 
                                
                               
                                   
                               
                                
                               t 
                             
                             ∉ 
                             
                               Φ 
                                
                               
                                 [ 
                                 m 
                                 ] 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     In the equation (13), A E  is amplitude of the reference signal Ex(m), and Φ[m] is a set of Δt satisfying a condition of the following equation (14). 
       0≤mΔt≤T 0    (14)
 
     For example, the correlation processing unit  42  may perform the correlation calculation by performing convolution operation as shown in the following equation (15). 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       
                         V 
                         · 
                         Ex 
                       
                     
                      
                     
                       ( 
                       
                         h 
                         , 
                         m 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         p 
                         = 
                         
                           
                             - 
                             
                               M 
                               p 
                             
                           
                           / 
                           2 
                         
                       
                       
                         
                           M 
                           p 
                         
                         / 
                         2 
                       
                     
                      
                     
                       
                         
                           V 
                           0 
                         
                          
                         
                           ( 
                           
                             h 
                             , 
                             
                               m 
                               + 
                               p 
                             
                           
                           ) 
                         
                       
                        
                       
                         
                           Ex 
                           * 
                         
                          
                         
                           ( 
                           p 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   ( 
                   
                     
                       m 
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       
                         M 
                          
                         
                           ( 
                           h 
                           ) 
                         
                       
                       - 
                       1 
                     
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   ( 
                   
                     
                       h 
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       H 
                       - 
                       1 
                     
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Here, M p  is a sampling point in the pulse. Note that, instead of the correlation calculation represented by the equation (15), a correlation calculation based on a known frequency domain convolution calculation may be performed. 
     Next, the domain conversion unit  44  performs a discrete Fourier transform based on a predetermined algorithm on the pulse compression signals F V·Ex (h,m) to generate frequency domain signals f d (h fft ,m) (step ST 13 ). The discrete Fourier transform is expressed by the following equation (16). 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       d 
                     
                      
                     
                       ( 
                       
                         
                           h 
                           fft 
                         
                         , 
                         m 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         h 
                         = 
                         0 
                       
                       
                         H 
                         - 
                         1 
                       
                     
                      
                     
                       
                         
                           F 
                           
                             V 
                             · 
                             Ex 
                           
                         
                          
                         
                           ( 
                           
                             h 
                             , 
                             m 
                           
                           ) 
                         
                       
                        
                       
                         exp 
                          
                         
                           ( 
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                               h 
                               H 
                             
                              
                             
                               h 
                               fft 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
             
               
                 
                   ( 
                   
                     
                       
                         h 
                         fft 
                       
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       H 
                       - 
                       1 
                     
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   ( 
                   
                     
                       m 
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       
                         M 
                          
                         
                           ( 
                           h 
                           ) 
                         
                       
                       - 
                       1 
                     
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Here, h fft  is a sampling number in the frequency domain, and H is a discrete Fourier transform point. 
     By deforming the equation (16) using the equations (11) to (15), the following equation (17) can be obtained. 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       d 
                     
                      
                     
                       ( 
                       
                         
                           h 
                           fft 
                         
                         , 
                         m 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         h 
                         = 
                         0 
                       
                       
                         H 
                         - 
                         1 
                       
                     
                      
                     
                       A 
                        
                       
                           
                       
                        
                       
                         exp 
                          
                         
                           ( 
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               
                                 f 
                                 0 
                               
                               · 
                               2 
                             
                              
                             
                               
                                 ( 
                                 
                                   
                                     R 
                                     0 
                                   
                                   - 
                                   
                                     v 
                                      
                                     
                                       ( 
                                       
                                         
                                           
                                             ∑ 
                                             
                                               n 
                                               = 
                                               
                                                 - 
                                                 1 
                                               
                                             
                                             
                                               h 
                                               - 
                                               1 
                                             
                                           
                                            
                                           
                                             
                                               T 
                                               pri 
                                             
                                              
                                             
                                               ( 
                                               n 
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           m 
                                            
                                           
                                               
                                           
                                            
                                           Δ 
                                            
                                           
                                               
                                           
                                            
                                           t 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                               / 
                               c 
                             
                           
                           ) 
                         
                       
                        
                       
                         exp 
                          
                         
                           ( 
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                               h 
                               H 
                             
                              
                             
                               h 
                               fft 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Here, A is amplitude of the frequency domain signal f d (h fft ,m). 
     By rearranging the equation (17), the following equation (18) can be obtained. 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       d 
                     
                      
                     
                       ( 
                       
                         
                           h 
                           fft 
                         
                         , 
                         m 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       exp 
                        
                       
                         ( 
                         
                           
                             - 
                             j 
                           
                            
                           
                               
                           
                            
                           2 
                            
                           
                               
                           
                            
                           π 
                            
                           
                               
                           
                            
                           
                             f 
                             0 
                           
                            
                           
                             
                               2 
                                
                               
                                 R 
                                 0 
                               
                             
                             c 
                           
                         
                         ) 
                       
                     
                      
                     
                       exp 
                        
                       
                         ( 
                         
                           j 
                            
                           
                               
                           
                            
                           2 
                            
                           
                               
                           
                            
                           π 
                            
                           
                               
                           
                            
                           
                             f 
                             0 
                           
                            
                           
                             
                               2 
                                
                               
                                   
                               
                                
                               vm 
                                
                               
                                   
                               
                                
                               Δ 
                                
                               
                                   
                               
                                
                               t 
                             
                             c 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                   
                     ∑ 
                     
                       h 
                       = 
                       0 
                     
                     
                       H 
                       - 
                       1 
                     
                   
                    
                   
                     A 
                      
                     
                         
                     
                      
                     
                       exp 
                        
                       
                         ( 
                         
                           j 
                            
                           
                               
                           
                            
                           2 
                            
                           
                               
                           
                            
                           
                             π 
                              
                             
                               ( 
                               
                                 
                                   
                                     
                                       f 
                                       0 
                                     
                                     · 
                                     2 
                                   
                                    
                                   v 
                                    
                                   
                                     
                                       ∑ 
                                       
                                         n 
                                         = 
                                         
                                           - 
                                           1 
                                         
                                       
                                       
                                         h 
                                         - 
                                         1 
                                       
                                     
                                      
                                     
                                       
                                         
                                           T 
                                           pri 
                                         
                                          
                                         
                                           ( 
                                           n 
                                           ) 
                                         
                                       
                                       / 
                                       c 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     h 
                                     H 
                                   
                                    
                                   
                                     h 
                                     fft 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     A right side of the equation (18) consists of a product of three terms. When magnitude of a value of a third term of the product on the right side is maximized, high integration efficiency can be obtained in the discrete Fourier transform. A condition that the magnitude of the value of the third term is almost maximized is as shown in the following equation (19). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           f 
                           0 
                         
                         · 
                         2 
                       
                        
                       v 
                        
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             
                               - 
                               1 
                             
                           
                           
                             h 
                             - 
                             1 
                           
                         
                          
                         
                           
                             
                               T 
                               pri 
                             
                              
                             
                               ( 
                               n 
                               ) 
                             
                           
                           / 
                           c 
                         
                       
                     
                     - 
                     
                       
                         h 
                         H 
                       
                        
                       
                         h 
                         fft 
                       
                     
                   
                   ≅ 
                   0 
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     When an average value of pulse repetition intervals T pri (h) on a left side of the equation (19) substantially matches the reference interval T pri,0 , the equation (19) is expressed by the following equation (20). 
     
       
         
           
             
               
                 
                   
                     
                       
                         f 
                         0 
                       
                        
                       
                         
                           2 
                            
                           
                             vT 
                             
                               pri 
                               , 
                               0 
                             
                           
                         
                         c 
                       
                     
                     - 
                     
                       
                         h 
                         fft 
                       
                       H 
                     
                   
                   ≅ 
                   0 
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     One condition that the average value of the pulse repetition intervals T pri (h) substantially matches the reference interval T pri,0  is, as described above, to set a plurality of pairs of pulse repetition intervals each having symmetrical values about the reference interval T pri,0 . The average value of the pulse repetition intervals forming each pair of the plurality of pairs matches the reference interval T pri,0 . As a more specific example, when the equation (3) is used, the average value of the pulse repetition intervals T pri (h) can be made to substantially match the reference interval T pri,0 . 
     Assuming that the sampling number h fft  satisfying a condition of the equation (20) is expressed as h fft,peak , the sampling number h fft,peak  is expressed as shown in the following equation (21). 
     
       
         
           
             
               
                 
                   
                     h 
                     
                       fft 
                       , 
                       peak 
                     
                   
                   ≅ 
                   
                     
                       f 
                       0 
                     
                      
                     
                       
                         2 
                          
                         
                           vT 
                           
                             pri 
                             , 
                             0 
                           
                         
                       
                       c 
                     
                      
                     H 
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     Thus, high integration efficiency can be obtained for the sampling number h fft,peak  in the frequency domain. At this time, a frequency range based on the reference interval T pri,0  can be calculated on the basis of a velocity value v amb,0  in the following equation (22). 
     
       
         
           
             
               
                 
                   
                     v 
                     
                       amb 
                       , 
                       0 
                     
                   
                   = 
                   
                     c 
                     
                       2 
                        
                       
                         f 
                         0 
                       
                        
                       
                         T 
                         
                           pri 
                           , 
                           0 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     Even if the pulse repetition intervals forming each pair do not have completely symmetrical values, when the plurality of pairs of the pulse repetition interval longer than the reference interval T pri,0  and the pulse repetition interval shorter than the reference interval T pri,0  is set so as to satisfy the condition that the average value of the pulse repetition intervals T pri (h) substantially matches the reference interval T pri,0  as shown in the following equation (23), it is possible to perform coherent integration based on the discrete Fourier transform with high efficiency. 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         0 
                       
                       
                         h 
                         - 
                         1 
                       
                     
                      
                     
                       
                         
                           T 
                           pri 
                         
                          
                         
                           ( 
                           n 
                           ) 
                         
                       
                       h 
                     
                   
                   ≅ 
                   
                     T 
                     
                       pri 
                       , 
                       0 
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     After the frequency domain signals f d (h fft ,m) are generated (step ST 13  in  FIG. 6 ), the target candidate detection unit  51  detects a target candidate on the basis of signal strength of the frequency domain signals f d (h fft ,m) (step ST 15 ). Specifically, for example, the target candidate detection unit  51  may detect the target candidate by using known CA-CFAR (Cell Average-Constant False Alarm Rate) processing. For example, in the CA-CFAR processing, since the maximum detection probability can be obtained so that a false alarm probability P fa  becomes a constant value, false detection can be controlled, and the target candidate can be detected on the basis of the signal strength of the frequency domain signals f d (h fft ,m) without detecting noise as much as possible. 
     The target candidate detection unit  51  can output, to the target candidate information calculating unit  52 , a target candidate number ntg assigned to the detected single or multiple target candidates, a sampling number m=m ntg  corresponding to the target candidate number ntg, and a sampling number h fft =h fft,ntg  of the frequency domain corresponding to the target candidate number ntg. For convenience of explanation, the target candidate number ntg takes an integer in the range of 1 to N tg . 
     Next, the target candidate information calculating unit  52  calculates a relative distance and relative velocity regarding the target candidate, and outputs data indicating the relative distance and the relative velocity to the display  60  (step ST 16  in  FIG. 6 ). Specifically, for example, the target candidate information calculating unit  52  can calculate a relative distance R 0,ntg  of an ntg-th target candidate on the basis of the target candidate number ntg and the sampling number m ntg  according to the following equation (24). 
     
       
         
           
             
               
                 
                   
                     R 
                     
                       0 
                       , 
                       ntg 
                     
                   
                   = 
                   
                     
                       
                         m 
                         ntg 
                       
                        
                       Δ 
                        
                       
                           
                       
                        
                       t 
                     
                     c 
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
             
               
                 
                   ( 
                   
                     
                       ntg 
                       = 
                       1 
                     
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       N 
                       tg 
                     
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Further, the target candidate information calculating unit  52  can calculate relative velocity V 0,ntg  of the ntg-th target candidate according to the following equation (25). 
       V 0,ntg =h fft,ntg Δv fft  
 
       ( n   tgt =1, . . . ,  N   tgt )   (25)
 
     In the equation (25), Δv fft  is a sampling interval of the relative velocity as shown in the following equation (26). 
     
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       v 
                       fft 
                     
                   
                   = 
                   
                     
                       c 
                       
                         2 
                          
                         
                             
                         
                          
                         
                           f 
                           0 
                         
                          
                         
                           T 
                           
                             pri 
                             , 
                             0 
                           
                         
                          
                         H 
                       
                     
                      
                     
                       h 
                       
                         fft 
                         , 
                         ntg 
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     The target candidate information calculating unit  52  can output a combination of the target candidate number ntg, the relative distance R 0,ntg , and the relative velocity V 0,ntg  to the display  60  as the target information. The display  60  can display the target information on a screen. 
     According to the first embodiment, the signal conversion unit  40  performs domain conversion processing using the discrete Fourier transform without using the relative velocity of the target candidate detected by the target detection unit  50 . Even in this case, the PRI control unit  14  sets the plurality of pairs of the pulse repetition interval longer than the reference interval T pri,0  and the pulse repetition interval shorter than the reference interval T pri,0 , so that the signal strength of the frequency domain signal f d (h fft ,m) can be increased, and integration loss when the domain conversion processing is performed can be suppressed. Thus, it is possible to improve target detection performance. 
     In particular, as illustrated in  FIGS. 3 and 4 , when the plurality of pairs of the even-numbered and odd-numbered pulse repetition intervals each having symmetrical values about the reference interval T pri,0  is set and the average value of the pulse repetition intervals constituting each pair matches the reference interval T pri,0 , the integration loss can be suppressed. 
       FIG. 7A  is a diagram schematically showing an example of a phase state of pulse compression signals F V·Ex (h,m)(h=0 to H−1) when all the pulse repetition intervals T pri (0) to T pri (H−1) are set to the same value. On the other hand,  FIG. 7B  is a diagram schematically showing an example of a phase state of pulse compression signals F V·Ex (h,m)(h=0 to H−1) when the pulse repetition intervals T pri (0) to T pri (H−1) are set in accordance with the equation (3) according to the present embodiment. In graphs of  FIGS. 7A and 7B , a horizontal axis represents a real part Re of the pulse compression signal F V·Ex (h,m), and a vertical axis represents an imaginary part Im of the pulse compression signal F V·Ex (h,m). As illustrated in  FIG. 7B , since phases of the pulse compression signals F V·Ex (h,m) are almost coherent in one or both of a case where the hit number h is even and a case where the hit number h is odd, it is possible to suppress a decrease in integration efficiency. 
       FIG. 8  is a graph schematically showing an example of spectra of three types of frequency domain signals. In the graph of  FIG. 8 , a horizontal axis represents velocity corresponding to frequency, and a vertical axis represents power. In  FIG. 8 , a solid line represents a spectrum of a frequency domain signal f d (h fft ,m) obtained when it is assumed that all the pulse repetition intervals T pri (0) to T pri (H−1) are set to the same value, and a broken line represents a spectrum of a frequency domain signal f d (h fft ,m) obtained when the pulse repetition intervals T pri (0) to T pri (H−1) are set in accordance with the equation (3) according to the present embodiment. Further, an alternate long and short dash line represents a spectrum of a frequency domain signal f d (h fft ,m) when it is assumed that the pulse repetition intervals T pri (0) to T pri (H−1) are randomly set. 
     When it is assumed that all the pulse repetition intervals are set to the same value, complete coherent integration is performed to obtain power P max , as shown in  FIG. 8 . When it is assumed that the pulse repetition intervals T pri (0) to T pri (H−1) are randomly set, power P rand  diffuses. On the other hand, when the pulse repetition intervals T pri (0) to T pri (H−1) are set in accordance with the equation (3), the power P max  cannot be obtained, but desired power P 0  equal to or larger than threshold power P th  can be ensured. 
     In this regard, the signal conversion unit  40  can set the change amount ΔT pri (h) in the equation (2) to a value that satisfies the following equations (27), (28), and (29) so that the PRI control unit  14  ensures the desired power P 0  equal to or larger than the threshold power P th  and a desired signal-to-noise power ratio SNR 0 . 
     
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       
                         T 
                         pri 
                       
                        
                       
                         ( 
                         h 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             0 
                           
                           
                             h 
                             - 
                             1 
                           
                         
                          
                         
                           
                             T 
                             pri 
                           
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                       - 
                       
                         
                           ( 
                           
                             h 
                             - 
                             1 
                           
                           ) 
                         
                          
                         
                           T 
                           
                             pri 
                             , 
                             0 
                           
                         
                       
                     
                     &lt; 
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         D 
                         pri 
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
             
               
                 
                   ( 
                   
                     
                       h 
                       = 
                       1 
                     
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       H 
                       - 
                       1 
                     
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     P 
                     rand 
                   
                   &lt; 
                   
                     P 
                     th 
                   
                   ≤ 
                   
                     P 
                     0 
                   
                   &lt; 
                   
                     P 
                     max 
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
             
               
                 
                   
                     SNR 
                     rnd 
                   
                   &lt; 
                   
                     SNR 
                     th 
                   
                   ≤ 
                   
                     SNR 
                     0 
                   
                   &lt; 
                   
                     SNR 
                     max 
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
     In the equation (27), ΔD pri  is an upper limit of the change amount ΔT pri (h). In the equation (29), SNR max  is a signal-to-noise power ratio obtained with the power P max  in  FIG. 8 , SNR rnd  is a signal-to-noise power ratio obtained with the power P rand  in  FIG. 8 , and SNR th  is a signal-to-noise power ratio obtained with the threshold power P th  in  FIG. 8 . 
     As described above, in the first embodiment, the integration loss during execution of the domain conversion processing using the discrete Fourier transform can be suppressed without requiring the value of the relative velocity of the target candidate detected by the target detection unit  50 . Thus, it is possible to improve target detection performance. Therefore, it is possible to provide the radar apparatus  1  that achieves the desired integration efficiency and the high SNR and has the improved target detection performance. 
     Note that a hardware configuration of the PRI control unit  14  and the radar signal processing circuit  30  may be implemented by an LSI (Large Scale Integrated circuit) such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field-Programmable Gate Array). 
       FIG. 9  is a block diagram showing a hardware configuration example that implements functions of the PRI control unit  14  and the radar signal processing circuit  30 . A signal processing circuit  70  shown in  FIG. 9  includes a processor  71  composed of an LSI, an input and output interface  74 , a memory  72 , a storage device  73 , and a signal path  75 . The signal path  75  is a bus for connecting the processor  71 , the input and output interface  74 , the memory  72 , and the storage device  73  to each other. The processor  71  is connected to the display  60  and the receiving circuit  13  via the input and output interface  74 . 
     The memory  72  includes, for example, a program memory for storing various program codes to be executed by the processor  71  to implement the functions of the PRI control unit  14  and the radar signal processing circuit  30 , a work memory used when the processor  71  executes digital signal processing, and a temporary storage memory in which data used in the digital signal processing is expanded. As the memory  72 , a plurality of semiconductor memories such as an ROM (Read Only Memory) and an SDRAM (Synchronous Dynamic Random Access Memory) may be used. 
     The processor  71  can access the storage device  73 . The storage device  73  is used to store various data such as setting data and signal data for the processor  71 . As the storage device  73 , for example, a volatile memory such as the SDRAM, an HDD (Hard Disk Drive), or an SSD (Solid State Drive) can be used. It should be noted that this storage device  73  can also store data to be stored in the memory  72 . 
     In the example of  FIG. 9 , the signal processing circuit  70  is implemented by using the single processor  71 , but is not limited thereto. The functions of the PRI control unit  14  and the radar signal processing circuit  30  may be implemented by using a plurality of processors that operate in cooperation with each other. Furthermore, any of the functions of the PRI control unit  14  and the radar signal processing circuit  30  may be implemented by dedicated hardware. 
     Second Embodiment 
       FIG. 10  is a block diagram schematically showing a configuration of a radar apparatus  2  according to a second embodiment of the present invention. As shown in  FIG. 10 , the radar apparatus  2  includes a signal generation circuit  10 , a transmission and reception unit  11 , a receiving circuit  13 , a radar signal processing circuit  31 , and a display  60 . The configuration of the radar apparatus  2  in the present embodiment is the same as the configuration of the radar apparatus  1  in the first embodiment, except that the radar signal processing circuit  31  in  FIG. 10  is provided instead of the radar signal processing circuit  30  in the first embodiment, and the PRI control unit  15  in  FIG. 10  is provided instead of the PRI control unit  14  in the first embodiment. 
     The PRI control unit  15  in the present embodiment has a PRI setting unit  15   a  and a GCD setting unit  15   b.  Similarly to the PRI control unit  14  in the first embodiment, the PRI setting unit  15   a  supplies a pulse width To and a series of pulse repetition intervals T pri (0) to T pri (H−1) to the signal generation circuit  10 . The PRI setting unit  15   a  sets a plurality of pairs of a pulse repetition interval longer than a reference interval T pri,0  and a pulse repetition interval shorter than the reference interval T pri,0 , and can supply the plurality of pairs of pulse repetition intervals to the signal generation circuit  10  as the series of pulse repetition intervals T pri (0) to T pri (H−1). 
     The GCD setting unit  15   b  sets a greatest common divisor ΔT GCD  of the series of pulse repetition intervals T pri (0) to T pri (H−1) set by the PRI setting unit  15   a,  and supplies the greatest common divisor ΔT GCD  to the signal conversion unit  41 . The greatest common divisor ΔT GCD  is expressed by the following equation (30). 
       Δ T   GCD =GCD( T   pri (0), . . . ,  T   pri ( H− 1))   (30)
 
     In the equation (30), GCD( ) is an operator that gives the greatest common divisor of H pulse repetition intervals T pri (0) to T pri (H−1). The GCD setting unit  15   b  may calculate a set value of the greatest common divisor ΔT GCD , or may use a data value stored in advance in the memory as the set value of the greatest common divisor ΔT GCD . The value of the greatest common divisor ΔT GCD  may be expressed as an integer or a decimal number. Further, the value of the greatest common divisor ΔT GCD  may be calculated with accuracy that can obtain a desired suppression amount of integration loss and a desired signal-to-noise ratio. 
     Similarly to the signal conversion unit  40  in the first embodiment, the signal conversion unit  41  in the present embodiment includes a correlation processing unit  42  that generates a pulse compression signal F V·Ex (h,m) by performing correlation processing using a reference signal on a received digital signal V 0 (h,m). 
     The signal conversion unit  41  in the present embodiment further includes an oversampling unit  43  and a domain conversion unit  45 . The oversampling unit  43  has a function of converting pulse compression signals F V·Ex (h,m)(h=0 to H−1) having H data points that are temporally unequally spaced regarding a hit number h into oversample signals F V·Ex·GCD (h GCD ,m)(h GCD =0 to Q−1) having Q data points that are temporally equally spaced. A sampling point Q is, for example, an integer given by the following equation (31). 
     
       
         
           
             
               
                 
                   Q 
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         0 
                       
                       
                         H 
                         - 
                         1 
                       
                     
                      
                     
                       
                         
                           
                             T 
                             pri 
                           
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                         / 
                         Δ 
                       
                        
                       
                           
                       
                        
                       
                         T 
                         GCD 
                       
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
           
         
       
     
     The domain conversion unit  45  generates frequency domain signals f d,GCD (h fft ,m)(h fft =0 to Q−1) having Q data points by performing a discrete Fourier transform in a pulse hit direction on the oversample signals F V·Ex·GCD (h GCD ,m)(h GCD =0 to Q−1) having the Q data points. 
     Since the PRI control unit  15  sets a pulse repetition interval T pri (h) that makes pulse wave transmission intervals unequal, H data points of the received digital signals V 0 (h,m)(h=0 to H−1) are data points that are temporally unequally spaced in the pulse hit direction. In the first embodiment, H data points of the pulse compression signals F V·Ex (h,m) generated from the received digital signals V 0 (h,m) are also temporally unequally spaced data points in the pulse hit direction. Since the domain conversion unit  44  in the first embodiment performs the discrete Fourier transform on the unequally spaced data points, there is a case where sufficient integration efficiency or sufficient calculation accuracy cannot be obtained. 
     Therefore, the oversampling unit  43  in the second embodiment uses the greatest common divisor ΔT GCD  and converts the pulse compression signals F V·Ex (h,m)(h=0 to H−1) having the H data points that are temporally unequally spaced in the pulse hit direction into the oversample signals F V·Ex·GCD (h GCD ,m)(h GCD =0 to Q−1) having the Q data points that are temporally equally spaced in the pulse hit direction. 
     As a result, the domain conversion unit  45  in the present embodiment can perform an accurate discrete Fourier transform on the oversample signal F V·Ex·GCD (h GCD ,m). In particular, when the discrete Fourier transform is performed on the basis of an algorithm of a Fast Fourier Transform (FFT), data points that are temporally equally spaced are required. In the present embodiment, the fast Fourier transform (FFT) can improve the integration efficiency with a small amount of calculation. 
     Specifically, the oversampling unit  43  performs oversampling at a ratio of T pri (h)/ΔT GCD  using the greatest common divisor ΔT GCD  given by the above equation (30) for each pulse repetition interval T pri (h). 
     Now, for the same sampling number m, it is assumed that a pulse compression signal F V·Ex (0,m) when the hit number h is zero matches an oversample signal F V·Ex·GCD (0,m) when a sampling number h GCD  is zero. For the non-zero hit number h, consider a case where the sampling number h GCD  is limited to a range shown by the following equation (32) (where, T pri (−1)=0). 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         
                           - 
                           1 
                         
                       
                       
                         
                           ( 
                           
                             h 
                             - 
                             1 
                           
                           ) 
                         
                         - 
                         1 
                       
                     
                      
                     
                       
                         
                           
                             T 
                             pri 
                           
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                         / 
                         Δ 
                       
                        
                       
                           
                       
                        
                       
                         T 
                         GCD 
                       
                     
                   
                   &lt; 
                   
                     h 
                     GCD 
                   
                   ≤ 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         
                           - 
                           1 
                         
                       
                       
                         h 
                         - 
                         1 
                       
                     
                      
                     
                       
                         
                           
                             T 
                             pri 
                           
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                         / 
                         Δ 
                       
                        
                       
                           
                       
                        
                       
                         T 
                         GCD 
                       
                     
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
             
               
                 
                   ( 
                   
                     
                       h 
                       = 
                       1 
                     
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       H 
                       - 
                       1 
                     
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Under a condition of the equation (32), the oversampling unit  43  can generate the oversample signal F V·Ex·GCD (h GCD ,m) for the same sampling number m in accordance with the following equation (33). 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       
                         V 
                         · 
                         Ex 
                         · 
                         GCD 
                       
                     
                      
                     
                       ( 
                       
                         
                           h 
                           GCD 
                         
                         , 
                         m 
                       
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 F 
                                 
                                   V 
                                   · 
                                   Ex 
                                 
                               
                                
                               
                                 ( 
                                 
                                   h 
                                   , 
                                   m 
                                 
                                 ) 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               mod 
                                
                               
                                   
                               
                                
                               
                                 ( 
                                 
                                   
                                     h 
                                     GCD 
                                   
                                   , 
                                   
                                     
                                       ∑ 
                                       
                                         n 
                                         = 
                                         
                                           - 
                                           1 
                                         
                                       
                                       
                                         h 
                                         - 
                                         1 
                                       
                                     
                                      
                                     
                                       
                                         
                                           
                                             T 
                                             pri 
                                           
                                            
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                         / 
                                         Δ 
                                       
                                        
                                       
                                           
                                       
                                        
                                       
                                         T 
                                         GCD 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                             = 
                             0 
                           
                         
                       
                       
                         
                           
                             0 
                             , 
                           
                         
                         
                           
                             
                               mod 
                                
                               
                                   
                               
                                
                               
                                 ( 
                                 
                                   
                                     h 
                                     GCD 
                                   
                                   , 
                                   
                                     
                                       ∑ 
                                       
                                         n 
                                         = 
                                         
                                           - 
                                           1 
                                         
                                       
                                       
                                         h 
                                         - 
                                         1 
                                       
                                     
                                      
                                     
                                       
                                         
                                           
                                             T 
                                             pri 
                                           
                                            
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                         / 
                                         Δ 
                                       
                                        
                                       
                                           
                                       
                                        
                                       
                                         T 
                                         GCD 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                             ≠ 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         h 
                         = 
                         1 
                       
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         H 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         m 
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         
                           M 
                            
                           
                             ( 
                             h 
                             ) 
                           
                         
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Here, mod(x,y) is a modulo operator that gives a remainder when an integer x is divided by an integer y. 
     According to the equations (32) and (33), when there is a sample of the pulse compression signal F V·Ex (h,m) corresponding to the sampling number h GCD  (when the modulo operator gives a zero value), the pulse compression signal F V·Ex (h,m) is output, and when there is no sample of the pulse compression signal F V·Ex (h,m) corresponding to the sampling number h GCD  (when the modulo operator gives a non-zero value), a zero value is output. 
       FIG. 11  is an explanatory diagram schematically showing a relationship between the hit number h, the pulse repetition interval T pri (h), and the pulse compression signal F V·Ex (h,m). The pulse compression signals F V·Ex (0,m),F V·Ex (1,m), . . . , F V·Ex (H−1,m) correspond to the unequally spaced pulse repetition intervals T pri (0), T pri (1), . . . , T pri (H−1), respectively.  FIG. 12  is an explanatory diagram schematically showing a relationship between the hit number h, the pulse repetition interval T pri (h), the sampling number h GCD , and the oversample signal F V·Ex·GCD (h GCD ,m). As shown in  FIG. 12 , an even-numbered pulse repetition interval T pri (h) has three times the length of the greatest common divisor ΔT GCD , and an odd-numbered pulse repetition interval T pri (h) has twice the length of the greatest common divisor ΔT GCD . For the even-numbered pulse repetition interval T pri (h), oversampling is performed at a rate of three times, so that output data points that are three times the input data points are generated. For the odd-numbered pulse repetition interval T pri (h), oversampling is performed at a double rate, so that output data points that are twice the input data points are generated. When the oversampling by the equations (32) and (33) is performed, oversample signals F V·Ex·GCD (0,m) to F V·Ex·GCD (4,m) are as follows. 
         F   V·Ex·GCD (0, m )= F   V·Ex (0, m ), 
         F   V·Ex·GCD (1, m )=0, 
         F   V·Ex·GCD (2, m )=0, 
         F   V·Ex·GCD (3, m )= F   V·Ex (1, m ), 
         F   V·Ex·GCD (4, m )=0. 
     Note that the oversampling unit  43  may output the oversample signal F V·Ex·GCD (h GCD ,m) obtained by the equation (33) to the domain conversion unit  45  as it is, but it is not limited thereto. By using a digital filter such as an FIR (Finite Impulse Response) filter, the oversampling unit  43  may filter the oversample signal F V·Ex·GCD (h GCD ,m) obtained by the equation (33) to calculate a filter signal, and output the filter signal to the domain conversion unit  45 . 
     Next,  FIG. 13  is a flowchart schematically showing an operation procedure of the radar signal processing circuit  31  in the second embodiment. Hereinafter, operation of the radar signal processing circuit  31  in the present embodiment will be described by referring to  FIG. 13 . 
     First, as in the case of the first embodiment, when received digital signals V 0 (h,m) are input, the correlation processing unit  42  generates pulse compression signals F V·Ex (h,m) by performing correlation processing using a reference signal Ex(m) on the received digital signals V 0 (h,m) (step ST 11 ). 
     Next, the oversampling unit  43  generates oversample signals F V·Ex·GCD (h GCD ,m)(h GCD =0 to Q−1) having data points that are temporally equally spaced in the pulse hit direction by oversampling the pulse compression signals F V·Ex (h,m) (step ST 12 ). 
     After that, the domain conversion unit  45  performs a discrete Fourier transform based on a predetermined algorithm such as a fast Fourier transform (FFT) or a Chirp Z-Transform (CZT) on the oversample signals F V·Ex·GCD (h GCD ,m) to generate frequency domain signals f d,GCD (h fft ,m) (step ST 14 ). As the algorithm of the chirp z-transform, an algorithm using FFT such as a Bluestein&#39;s FFT algorithm may be used. The discrete 
     Fourier transform is expressed by the following equation (34). 
     
       
         
           
             
               
                 
                   
                     
                       
                         f 
                         
                           d 
                           , 
                           GCD 
                         
                       
                        
                       
                         ( 
                         
                           
                             h 
                             fft 
                           
                           , 
                           m 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           
                             h 
                             GCD 
                           
                           = 
                           0 
                         
                         
                           Q 
                           - 
                           1 
                         
                       
                        
                       
                         
                           
                             F 
                             
                               
                                 V 
                                 · 
                                 Ex 
                               
                               , 
                               GCD 
                             
                           
                            
                           
                             ( 
                             
                               
                                 h 
                                 GCD 
                               
                               , 
                               m 
                             
                             ) 
                           
                         
                          
                         
                           exp 
                            
                           
                             ( 
                             
                               
                                 - 
                                 j 
                               
                                
                               
                                   
                               
                                
                               2 
                                
                               π 
                                
                               
                                 
                                   h 
                                   GCD 
                                 
                                 Q 
                               
                                
                               
                                 h 
                                 fft 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     ( 
                     
                       
                         
                           h 
                           fft 
                         
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         Q 
                         - 
                         1 
                       
                     
                     ) 
                   
                    
                   
                     
 
                   
                    
                   
                     ( 
                     
                       
                         m 
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         
                           M 
                            
                           
                             ( 
                             h 
                             ) 
                           
                         
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
           
         
       
     
     In the equation (34), h fft  is an integer in the range of 0 to Q−1 representing a sampling number in a frequency domain, and Q is a discrete Fourier transform point. 
     When the discussion for deriving the equation (20) according to the first embodiment is applied, the following equation (35) is established as a condition for obtaining high integration efficiency in the discrete Fourier transform. 
     
       
         
           
             
               
                 
                   
                     
                       
                         f 
                         0 
                       
                        
                       
                         
                           2 
                            
                           v 
                            
                           
                               
                           
                            
                           Δ 
                            
                           
                               
                           
                            
                           
                             T 
                             GCD 
                           
                         
                         c 
                       
                     
                     - 
                     
                       
                         h 
                         fft 
                       
                       Q 
                     
                   
                   ≅ 
                   0 
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
           
         
       
     
     Assuming that the sampling number h fft  satisfying the condition of the equation (35) is expressed as h fft,peak,GCD , the sampling number h fft,peak,GCD  is expressed as shown in the following equation (36). 
     
       
         
           
             
               
                 
                   
                     h 
                     
                       fft 
                       , 
                       peak 
                       , 
                       GCD 
                     
                   
                   ≅ 
                   
                     
                       f 
                       0 
                     
                      
                     
                       
                         2 
                          
                         v 
                          
                         
                             
                         
                          
                         Δ 
                          
                         
                             
                         
                          
                         
                           T 
                           GCD 
                         
                       
                       c 
                     
                      
                     Q 
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
           
         
       
     
     Therefore, high integration efficiency can be obtained for the sampling number h fft,peak,GCD  in the frequency domain. At this time, a frequency range based on the greatest common divisor ΔT GCD  can be calculated on the basis of a velocity value v amb,GCD  in the following equation (37). 
     
       
         
           
             
               
                 
                   
                     v 
                     
                       amb 
                       , 
                       GCD 
                     
                   
                   = 
                   
                     c 
                     
                       2 
                        
                       
                         f 
                         0 
                       
                        
                       Δ 
                        
                       
                           
                       
                        
                       
                         T 
                         GCD 
                       
                     
                   
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
           
         
       
     
     When the domain conversion unit  45  performs the discrete Fourier transform based on the known charp z-transform (CZT) algorithm using the FFT, the discrete Fourier transform can be performed only for a desired Doppler frequency range, so that a calculation amount can be reduced. For example, as shown in the following equation (38), the frequency domain signal f d,GCD (h fft ,m) may be generated by performing the discrete Fourier transform based on the CZT algorithm in a range between the minimum Doppler frequency corresponding to the velocity value −v amb,0 /2 and the maximum Doppler frequency corresponding to the velocity value +v amb,0 /2. 
     
       
         
           
             
               
                 
                   
                     
                       
                         f 
                         
                           d 
                           , 
                           GCD 
                         
                       
                        
                       
                         ( 
                         
                           
                             h 
                             fft 
                           
                           , 
                           m 
                         
                         ) 
                       
                     
                     = 
                     
                       CZT 
                        
                       
                         ( 
                         
                           
                             
                               F 
                               
                                 V 
                                 · 
                                 Ex 
                                 · 
                                 GCD 
                               
                             
                              
                             
                               ( 
                               
                                 
                                   h 
                                   GCD 
                                 
                                 , 
                                 m 
                               
                               ) 
                             
                           
                           , 
                           
                             - 
                             
                               
                                 v 
                                 
                                   amb 
                                   , 
                                   0 
                                 
                               
                               2 
                             
                           
                           , 
                           
                             
                               v 
                               
                                 amb 
                                 , 
                                 0 
                               
                             
                             2 
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     ( 
                     
                       
                         
                           h 
                           fft 
                         
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         Q 
                         - 
                         1 
                       
                     
                     ) 
                   
                    
                   
                     
 
                   
                    
                   
                     ( 
                     
                       
                         m 
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         
                           M 
                            
                           
                             ( 
                             h 
                             ) 
                           
                         
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
           
         
       
     
       FIG. 14A  is a diagram schematically showing an example of spectra of frequency domain signals f d (h fft ,m) generated in the first embodiment, and  FIG. 14B  is a diagram schematically showing an example of a spectrum of the frequency domain signal f d,GCD (h fft ,m) generated in the second embodiment. In graphs of  FIGS. 14A and 14B , a horizontal axis represents velocity corresponding to the Doppler frequency and a vertical axis represents power. In  FIG. 14A , a solid line represents the spectrum of the frequency domain signal obtained when there is no integration loss, and a broken line represents the spectrum of the frequency domain signal f d (h fft ,m) according to the first embodiment. Further, in  FIG. 14B , a solid line represents the spectrum of the frequency domain signal f d,GCD (h fft ,m) according to the second embodiment. In  FIG. 14A , it can be seen that the desired power P 0 , which is smaller than the maximum power P max  and larger than the threshold power P th , is obtained. In  FIG. 14B , the power obtained is almost equal to the maximum power P max . 
     Note that also in the first embodiment, the domain conversion unit  44  may perform the discrete Fourier transform based on the known algorithm of the chirp z-transform. 
     After the execution of step ST 14 , the target candidate detection unit  51  detects a target candidate on the basis of signal strength of the frequency domain signals f d,GCD (h fft ,m), as in the case of the first embodiment (step ST 15  in  FIG. 13 ). At this time, the target candidate detection unit  51  can output, to the target candidate information calculating unit  52 , a target candidate number ntg assigned to the detected single or plurality of target candidate(s), a sampling number m=m ntg  corresponding to the target candidate number ntg, and a sampling number h fft =h fft,ntg  of the frequency domain corresponding to the target candidate number ntg. 
     Next, as in the case of the first embodiment, the target candidate information calculating unit  52  calculates a relative distance and relative velocity regarding the target candidate, and outputs data indicating the relative distance and the relative velocity to the display  60  (step ST 16  in  FIG. 13 ). At this time, the target candidate information calculating unit  52  can calculate relative velocity V 0,ntg  of the ntg-th target candidate according to the following equation (39) using a sampling interval Δv fft  shown in the following equation (40). 
     
       
         
           
             
               
                 
                   
                     V 
                     
                       0 
                       , 
                       ntg 
                     
                   
                   = 
                   
                     
                       h 
                       
                         fft 
                         , 
                         ntg 
                       
                     
                      
                     Δ 
                      
                     
                         
                     
                      
                     
                       
                         v 
                         fft 
                       
                        
                       
                         
 
                       
                       ( 
                       
                         
                           
                             n 
                             tgt 
                           
                           = 
                           1 
                         
                         , 
                         … 
                          
                         
                             
                         
                         , 
                         
                           N 
                           tgt 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       v 
                       fft 
                     
                   
                   = 
                   
                     
                       c 
                       
                         2 
                          
                         
                           f 
                           0 
                         
                          
                         Δ 
                          
                         
                             
                         
                          
                         
                           T 
                           GCD 
                         
                          
                         Q 
                       
                     
                      
                     
                       h 
                       
                         fft 
                         , 
                         ntg 
                       
                     
                   
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
           
         
       
     
     Here, for convenience of explanation, the target candidate number ntg takes an integer in the range of 1 to N tgt . 
     As described above, in the second embodiment, the oversample signals F V·Ex·GCD (h GCD ,m) having the data points that are temporally equally spaced in the pulse hit direction are generated using the greatest common divisor ΔT GCD  of the pulse repetition intervals T pri (0) to T pri (H−1), and the discrete Fourier transform is performed on the oversample signals F V·Ex·GCD (h GCD ,m), so that compared with the first embodiment, it is possible to further suppress the integration loss. Therefore, it is possible to provide the radar apparatus  2  which achieves high integration efficiency and a high SNR and has improved target detection performance. 
     Note that a hardware configuration of the PRI control unit  15  and the radar signal processing circuit  31  in the second embodiment may be implemented by an LSI such as an ASIC or an FPGA. As in the case of the first embodiment, the hardware configuration of the PRI control unit  15  and the radar signal processing circuit  31  in the second embodiment may be implemented by the signal processing circuit  70  shown in  FIG. 9 . Further, the PRI control unit  15  is a component different from the signal generation circuit  10 , but is not limited to this. The PRI control unit  15  may be incorporated in the signal generation circuit  10  or the radar signal processing circuit  31 . 
     Third Embodiment 
       FIG. 15  is a block diagram schematically showing a configuration of a radar apparatus  3  according to a third embodiment of the present invention. The configuration of the radar apparatus  3  in the present embodiment is the same as the configuration of the radar apparatus  2  in the second embodiment, except that a PRI control unit  16  in  FIG. 15  is provided in place of the PRI control unit  15  in the second embodiment. 
     The PRI control unit  16  in the present embodiment includes a PRI setting unit  16   a  and a GCD setting unit  16   b.  The PRI setting unit  16   a  supplies a pulse width T 0  and a series of unequally spaced pulse repetition intervals T pri (0) to T pri (H−1) to a signal generation circuit  10 . The series of pulse repetition intervals T pri (0) to T pri (H−1) is not limited to a pair of a pulse repetition interval longer than a reference interval T pri,0  and a pulse repetition interval shorter than the reference interval T pri,0 . For example, the PRI setting unit  16   a  can set a random or pseudo-random value as a value of the pulse repetition intervals T pri (0) to T pri (H−1). Here, the GCD setting unit  16   b  may calculate a set value of the greatest common divisor ΔT GCD , or may use a data value stored in advance in a memory as the set value of the greatest common divisor ΔT GCD . The value of the greatest common divisor ΔT GCD  may be expressed as an integer or a decimal number. Further, the value of the greatest common divisor ΔT GCD  may be calculated with accuracy that can obtain a desired suppression amount of integration loss and a desired signal-to-noise ratio. 
     Similarly to the GCD setting unit  15   b  in the second embodiment, the GCD setting unit  16   b  sets the greatest common divisor ΔT GCD  of the series of pulse repetition intervals T pri (0) to T pri (H−1), and supplies the greatest common divisor ΔT GCD  to an oversampling unit  43  of a signal conversion unit  41 . 
     The oversampling unit  43  in the present embodiment uses the greatest common divisor ΔT GCD , and converts pulse compression signals F V·Ex (h,m)(h=0 to H−1) having H data points that are temporally unequally spaced in a pulse hit direction into oversample signals F V·Ex·GCD (h GCD ,m)(h GCD =0 to Q−1) having Q data points that are temporally equally spaced in the pulse hit direction. Similarly to the second embodiment, a domain conversion unit  45  in the present embodiment can perform a discrete Fourier transform based on an algorithm of a fast Fourier transform (FFT) or an algorithm of a charp z-transform (CZT) on the oversample signal F V·Ex·GCD (h GCD ,m) to generate a frequency domain signal f d,GCD (h fft ,m). As the algorithm of the chirp z-transform, an algorithm using FFT such as a Bluestein&#39;s FFT algorithm may be used. As a result, the domain conversion unit  45  can perform an accurate discrete Fourier transform on the oversample signal F V·Ex·GCD (h GCD ,m). 
     As described above, in the third embodiment, the oversample signals F V·Ex·GCD (h GCD ,m) having the data points that are temporally equally spaced in the pulse hit direction are generated using the greatest common divisor ΔT GCD  of the unequally spaced pulse repetition intervals T pri (0) to T pri (H−1), and the discrete Fourier transform is performed on the oversample signals F V·Ex·GCD (h GCD ,m), so that it is possible to suppress the integration loss. Therefore, it is possible to provide the radar apparatus  3  which achieves high integration efficiency and a high SNR and has improved target detection performance. 
     Note that a hardware configuration of the PRI control unit  16  and a radar signal processing circuit  31  in the third embodiment may be implemented by an LSI such as an ASIC or an FPGA. As in the case of the first embodiment, the hardware configuration of the PRI control unit  16  and the radar signal processing circuit  31  in the third embodiment may be implemented by the signal processing circuit  70  shown in  FIG. 9 . Further, the PRI control unit  16  is a component different from the signal generation circuit  10 , but is not limited thereto. The PRI control unit  16  may be incorporated in the signal generation circuit  10  or the radar signal processing circuit  31 . 
     Fourth Embodiment 
       FIG. 16  is a block diagram schematically showing a configuration of a radar apparatus  4  according to a fourth embodiment of the present invention. The configuration of the radar apparatus  4  in the present embodiment is the same as the configuration of the radar apparatus  1  in the first embodiment, except that a signal generation circuit  10 A is provided instead of the signal generation circuit  10  in the first embodiment.  FIG. 17  is a schematic configuration diagram of the signal generation circuit  10 A. The configuration of the signal generation circuit  10 A is the same as the configuration of the signal generation circuit  10  in the first embodiment, except that a local oscillator  20 A shown in  FIG. 17  is provided instead of the local oscillator  20  in the first embodiment. 
     In the present embodiment, the local oscillator  20 A shown in  FIG. 17  generates a local oscillation signal L 0 (t) whose oscillation frequency changes due to frequency hopping as shown in the following equation (41). 
         L   o ( t )= A   L  exp( j (2π( f   0   +hB   0 ) t+ϕ   0 ))
 
       (0≤ t&lt;T   obs )
 
       ( h= 0,1,  . . . , H− 1)   (41)
 
     Here, t is time, A L  is amplitude of the local oscillation signal L 0 (t), f 0  is center frequency, h is a hit number, B 0  is a modulation bandwidth, φ 0  is an initial phase of the local oscillation signal L 0 (t), T obs  is an upper limit of an observation period, and j is an imaginary unit. 
     At this time, a transmission and reception unit  11  outputs a reflected wave signal Rx(h,t) as shown in the following equation (42) instead of the above equation (8). 
     
       
         
           
             
               
                 
                   
                     Rx 
                      
                     
                       ( 
                       
                         h 
                         , 
                         t 
                       
                       ) 
                     
                   
                   = 
                   
                     
 
                   
                    
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 A 
                                 R 
                               
                                
                               
                                 exp 
                                  
                                 
                                   ( 
                                   
                                     j 
                                      
                                     
                                       { 
                                       
                                         
                                           2 
                                            
                                           
                                             π 
                                              
                                             
                                               [ 
                                               
                                                 
                                                   
                                                     ( 
                                                     
                                                       
                                                         f 
                                                         0 
                                                       
                                                       + 
                                                       
                                                         hB 
                                                         0 
                                                       
                                                     
                                                     ) 
                                                   
                                                    
                                                   
                                                     ( 
                                                     
                                                       τ 
                                                       - 
                                                       
                                                         
                                                           2 
                                                            
                                                           
                                                             ( 
                                                             
                                                             
                                                             R 
                                                             0 
                                                             
                                                             - 
                                                             vt 
                                                             
                                                             ) 
                                                           
                                                         
                                                         c 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     
                                                       B 
                                                       0 
                                                     
                                                     
                                                       2 
                                                        
                                                       
                                                         T 
                                                         0 
                                                       
                                                     
                                                   
                                                    
                                                   
                                                     
                                                       ( 
                                                       
                                                         τ 
                                                         - 
                                                         
                                                           
                                                             2 
                                                              
                                                             
                                                             ( 
                                                             
                                                             
                                                             R 
                                                             0 
                                                             
                                                             - 
                                                             vt 
                                                             
                                                             ) 
                                                             
                                                           
                                                           c 
                                                         
                                                       
                                                       ) 
                                                     
                                                     2 
                                                   
                                                 
                                               
                                               ] 
                                             
                                           
                                         
                                         + 
                                         
                                           φ 
                                           0 
                                         
                                       
                                       } 
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             t 
                             ∈ 
                             
                               Λ 
                                
                               
                                 [ 
                                 h 
                                 ] 
                               
                             
                           
                         
                       
                       
                         
                           
                             0 
                             , 
                           
                         
                         
                           
                             t 
                             ∉ 
                             
                               Λ 
                                
                               
                                 [ 
                                 h 
                                 ] 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   42 
                   ) 
                 
               
             
           
         
       
     
     A configuration of a receiving circuit  13  in the present embodiment is the same as that of the receiving circuit  13  ( FIG. 5 ) in the first embodiment. A phase detector  27  of the receiving circuit  13  in the present embodiment can generate a detection signal as shown in the following equation (43), instead of the above equation (10), as a received analog signal W 0 (h,t). 
     
       
         
           
             
               
                 W 
                 0 
               
                
               
                 ( 
                 
                   h 
                   , 
                   t 
                 
                 ) 
               
             
             = 
             
               
                 
                   Rx 
                    
                   
                     ( 
                     
                       h 
                       , 
                       t 
                     
                     ) 
                   
                 
                  
                 
                   
                     L 
                     0 
                     * 
                   
                    
                   
                     ( 
                     t 
                     ) 
                   
                 
               
               = 
               
                 
 
               
                
               
                 { 
                 
                   
                     
                       
                         
                           
                             
                               A 
                               V 
                             
                              
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   
                                     π 
                                      
                                     
                                       [ 
                                       
                                         
                                           
                                             - 
                                             
                                               ( 
                                               
                                                 
                                                   f 
                                                   0 
                                                 
                                                 + 
                                                 
                                                   hB 
                                                   0 
                                                 
                                               
                                               ) 
                                             
                                           
                                            
                                           
                                             
                                               2 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     R 
                                                     0 
                                                   
                                                   - 
                                                   vt 
                                                 
                                                 ) 
                                               
                                             
                                             c 
                                           
                                         
                                         + 
                                         
                                           
                                             
                                               B 
                                               0 
                                             
                                             
                                               2 
                                                
                                               
                                                 T 
                                                 0 
                                               
                                             
                                           
                                            
                                           
                                             
                                               ( 
                                               
                                                 τ 
                                                 - 
                                                 
                                                   
                                                     2 
                                                      
                                                     
                                                       ( 
                                                       
                                                         
                                                           R 
                                                           0 
                                                         
                                                         - 
                                                         vt 
                                                       
                                                       ) 
                                                     
                                                   
                                                   c 
                                                 
                                               
                                               ) 
                                             
                                             2 
                                           
                                         
                                       
                                       ] 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           , 
                         
                       
                       
                         
                           t 
                           ∈ 
                           
                             Λ 
                              
                             
                               [ 
                               h 
                               ] 
                             
                           
                         
                       
                     
                     
                       
                         
                           0 
                           , 
                         
                       
                       
                         
                           t 
                           ∉ 
                           
                             Λ 
                              
                             
                               [ 
                               h 
                               ] 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     ( 
                     
                       
                         h 
                         = 
                         0 
                       
                       , 
                       1 
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         H 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     Furthermore, an A/D converter  28  of the receiving circuit  13  in the present embodiment can generate a received digital signal (received video signal) V 0 (h,m) as shown in the following equation (44), instead of the above equation (11). 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       0 
                     
                      
                     
                       ( 
                       
                         h 
                         , 
                         m 
                       
                       ) 
                     
                   
                   = 
                   
                     
 
                   
                    
                   
                     { 
                     
                       
                         
                           
                             
                               A 
                                
                               
                                   
                               
                                
                               
                                 exp 
                                  
                                 
                                   ( 
                                   
                                     
                                       - 
                                       j 
                                     
                                      
                                     
                                         
                                     
                                      
                                     2 
                                      
                                     
                                       
                                         π 
                                          
                                         
                                           ( 
                                           
                                             
                                               f 
                                               0 
                                             
                                             + 
                                             
                                               hB 
                                               0 
                                             
                                           
                                           ) 
                                         
                                       
                                       · 
                                       2 
                                     
                                      
                                     
                                       
                                         ( 
                                         
                                           
                                             R 
                                             0 
                                           
                                           - 
                                           
                                             v 
                                              
                                             
                                               ( 
                                               
                                                 
                                                   
                                                     ∑ 
                                                     
                                                       n 
                                                       = 
                                                       
                                                         - 
                                                         1 
                                                       
                                                     
                                                     
                                                       h 
                                                       - 
                                                       1 
                                                     
                                                   
                                                    
                                                   
                                                     
                                                       T 
                                                       pri 
                                                     
                                                      
                                                     
                                                       ( 
                                                       n 
                                                       ) 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   m 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   Δ 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   t 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         ) 
                                       
                                       / 
                                       c 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                                 
                             
                           
                         
                         
                           
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   π 
                                    
                                   
                                     
                                       B 
                                       0 
                                     
                                     
                                       2 
                                        
                                       
                                         T 
                                         0 
                                       
                                     
                                   
                                    
                                   
                                     
                                       ( 
                                       
                                         
                                           m 
                                            
                                           
                                               
                                           
                                            
                                           Δ 
                                            
                                           
                                               
                                           
                                            
                                           t 
                                         
                                         - 
                                         
                                           2 
                                            
                                           
                                             
                                               ( 
                                               
                                                 
                                                   R 
                                                   0 
                                                 
                                                 - 
                                                 
                                                   v 
                                                    
                                                   
                                                     ( 
                                                     
                                                       
                                                         ∑ 
                                                         
                                                           n 
                                                           = 
                                                           
                                                             - 
                                                             1 
                                                           
                                                         
                                                         
                                                           h 
                                                           - 
                                                           1 
                                                         
                                                       
                                                        
                                                       
                                                         
                                                           
                                                             T 
                                                             pri 
                                                           
                                                            
                                                           
                                                             ( 
                                                             n 
                                                             ) 
                                                           
                                                         
                                                          
                                                         m 
                                                          
                                                         
                                                             
                                                         
                                                          
                                                         Δ 
                                                          
                                                         
                                                             
                                                         
                                                          
                                                         t 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               ) 
                                             
                                             / 
                                             c 
                                           
                                         
                                       
                                       ) 
                                     
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               m 
                               ∈ 
                               
                                 Ψ 
                                  
                                 
                                   [ 
                                   h 
                                   ] 
                                 
                               
                             
                           
                         
                         
                           
                             
                               0 
                               , 
                             
                           
                           
                             
                               
                                 m 
                                 ∉ 
                                 
                                   Ψ 
                                    
                                   
                                     [ 
                                     h 
                                     ] 
                                   
                                 
                               
                                
                               
                                   
                               
                             
                           
                         
                       
                        
                       
                         
 
                       
                        
                       
                         ( 
                         
                           
                             m 
                             = 
                             0 
                           
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           
                             
                               M 
                                
                               
                                 ( 
                                 h 
                                 ) 
                               
                             
                             - 
                             1 
                           
                         
                         ) 
                       
                        
                       
                         
 
                       
                        
                       
                         ( 
                         
                           
                             h 
                             = 
                             0 
                           
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           
                             H 
                             - 
                             1 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   44 
                   ) 
                 
               
             
           
         
       
     
     The equation (44) is an equation obtained when ascending frequency hopping is performed. A first term of a product on a right side of the equation (44) includes a parameter “hB 0 ” indicating a product of the modulation bandwidth B 0  and the hit number h. When descending frequency hopping is performed, the parameter “hB 0 ” is replaced with “−hB 0 ”. 
     At this time, a domain conversion unit  44  can generate a frequency domain signal f d (h fft ,m) as shown in the following equation (45) by performing a discrete Fourier transform on a pulse compression signal F V·Ex (h,m). 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       d 
                     
                      
                     
                       ( 
                       
                         
                           h 
                           fft 
                         
                         , 
                         m 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         h 
                         = 
                         0 
                       
                       
                         H 
                         - 
                         1 
                       
                     
                      
                     
                       A 
                        
                       
                           
                       
                        
                       
                         exp 
                          
                         
                           ( 
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                               
                                 π 
                                  
                                 
                                   ( 
                                   
                                     
                                       f 
                                       0 
                                     
                                     + 
                                     
                                       hB 
                                       0 
                                     
                                   
                                   ) 
                                 
                               
                               · 
                               2 
                             
                              
                             
                               
                                 ( 
                                 
                                   
                                     R 
                                     0 
                                   
                                   - 
                                   
                                     v 
                                      
                                     
                                       ( 
                                       
                                         
                                           
                                             ∑ 
                                             
                                               n 
                                               = 
                                               
                                                 - 
                                                 1 
                                               
                                             
                                             
                                               h 
                                               - 
                                               1 
                                             
                                           
                                            
                                           
                                             
                                               T 
                                               pri 
                                             
                                              
                                             
                                               ( 
                                               n 
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           m 
                                            
                                           
                                               
                                           
                                            
                                           Δ 
                                            
                                           
                                               
                                           
                                            
                                           t 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                               / 
                               c 
                             
                           
                           ) 
                         
                       
                        
                       
                         exp 
                          
                         
                           ( 
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                               h 
                               H 
                             
                              
                             
                               h 
                               fft 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   45 
                   ) 
                 
               
             
           
         
       
     
     As in the case of the first embodiment, the following equation (46) can be obtained by deforming the equation (45). 
     
       
         
           
             
               
                 
                   
                     
                       
                         f 
                         d 
                       
                        
                       
                         ( 
                         
                           
                             h 
                             fft 
                           
                           , 
                           m 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         exp 
                          
                         
                           ( 
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               f 
                               0 
                             
                              
                             
                               
                                 2 
                                  
                                 
                                   R 
                                   0 
                                 
                               
                               c 
                             
                           
                           ) 
                         
                       
                        
                       
                         exp 
                          
                         
                           ( 
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               f 
                               0 
                             
                              
                             
                               
                                 2 
                                  
                                 vm 
                                  
                                 
                                     
                                 
                                  
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                               c 
                             
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ∑ 
                       
                         h 
                         = 
                         0 
                       
                       
                         H 
                         - 
                         1 
                       
                     
                      
                     
                       A 
                        
                       
                           
                       
                        
                       
                         exp 
                          
                         
                           ( 
                           
                             j 
                              
                             
                                 
                             
                              
                             2 
                              
                             
                               π 
                                
                               
                                 ( 
                                 
                                   
                                     
                                       - 
                                       
                                         hB 
                                         0 
                                       
                                     
                                      
                                     
                                       
                                         2 
                                          
                                         
                                           R 
                                           0 
                                         
                                       
                                       c 
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         f 
                                         0 
                                       
                                       · 
                                       2 
                                     
                                      
                                     v 
                                      
                                     
                                       
                                         ∑ 
                                         
                                           n 
                                           = 
                                           
                                             - 
                                             1 
                                           
                                         
                                         
                                           h 
                                           - 
                                           1 
                                         
                                       
                                        
                                       
                                         
                                           
                                             T 
                                             pri 
                                           
                                            
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                         / 
                                         c 
                                       
                                     
                                   
                                   - 
                                   
                                     
                                       h 
                                       H 
                                     
                                      
                                     
                                       h 
                                       fft 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   46 
                   ) 
                 
               
             
           
         
       
     
     The right side of the equation (46) consists of a product of three terms. When magnitude of a value of a third term of the product on the right side is maximized, high integration efficiency can be obtained in the discrete Fourier transform. A condition that the magnitude of the value of the third term is almost maximized is as shown in the following equation (47). 
     
       
         
           
             
               
                 
                   
                     
                       
                         - 
                         
                           hB 
                           0 
                         
                       
                        
                       
                         
                           2 
                            
                           
                             R 
                             0 
                           
                         
                         c 
                       
                     
                     + 
                     
                       
                         
                           f 
                           0 
                         
                         · 
                         2 
                       
                        
                       v 
                        
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             
                               - 
                               1 
                             
                           
                           
                             h 
                             - 
                             1 
                           
                         
                          
                         
                           
                             T 
                             pri 
                           
                            
                           
                             
                               ( 
                               n 
                               ) 
                             
                             / 
                             c 
                           
                         
                       
                     
                     - 
                     
                       
                         h 
                         H 
                       
                        
                       
                         h 
                         fft 
                       
                     
                   
                   ≅ 
                   0 
                 
               
               
                 
                   ( 
                   47 
                   ) 
                 
               
             
           
         
       
     
     When an average value of the pulse repetition intervals T pri (h) on the left side of the equation (47) substantially matches a reference interval T pri,0 , the equation (47) is expressed by the following equation (48). 
     
       
         
           
             
               
                 
                   
                     
                       
                         - 
                         
                           B 
                           0 
                         
                       
                        
                       
                         
                           2 
                            
                           
                             R 
                             0 
                           
                         
                         c 
                       
                     
                     + 
                     
                       
                         f 
                         0 
                       
                        
                       
                         
                           2 
                            
                           
                             vT 
                             
                               pri 
                               , 
                               0 
                             
                           
                         
                         c 
                       
                     
                     - 
                     
                       
                         h 
                         fft 
                       
                       H 
                     
                   
                   ≅ 
                   0 
                 
               
               
                 
                   ( 
                   48 
                   ) 
                 
               
             
           
         
       
     
     Assuming that a sampling number h fft  satisfying a condition of the equation (48) is expressed as h fft,peak , the sampling number h fft,peak  is expressed as shown in the following equation (49). 
     
       
         
           
             
               
                 
                   
                     h 
                     
                       fft 
                       , 
                       peak 
                     
                   
                   ≅ 
                   
                     
                       ( 
                       
                         
                           
                             - 
                             
                               B 
                               0 
                             
                           
                            
                           
                             
                               2 
                                
                               
                                 R 
                                 0 
                               
                             
                             c 
                           
                         
                         + 
                         
                           
                             f 
                             0 
                           
                            
                           
                             
                               2 
                                
                               
                                 vT 
                                 
                                   pri 
                                   , 
                                   0 
                                 
                               
                             
                             c 
                           
                         
                       
                       ) 
                     
                      
                     H 
                   
                 
               
               
                 
                   ( 
                   49 
                   ) 
                 
               
             
           
         
       
     
     As described above, in the fourth embodiment, since the frequency hopping is used, it is possible to provide the radar apparatus  4  that further suppresses radio wave interference with other radar systems and lowers detected performance of the other radar systems. 
     Note that a hardware configuration of a PRI control unit  14  and a radar signal processing circuit  30  in the fourth embodiment may be implemented by an LSI such as an ASIC or an FPGA. As in the case of the first embodiment, the hardware configuration of the PRI control unit  14  and the radar signal processing circuit  30  in the fourth embodiment may be implemented by the signal processing circuit  70  shown in  FIG. 9 . 
     Although the first to fourth embodiments according to the present invention have been described above by referring to the drawings, the first to fourth embodiments are examples of the present invention, and there can be various other embodiments other than the first to fourth embodiments. The present invention can freely combine the first to fourth embodiments, modify arbitrary components in the first to fourth embodiments, or omit arbitrary components in the embodiments within the scope of the present invention. For example, in the configuration of the fourth embodiment, there can be a modified example in which the oversampling unit  43  in the second embodiment is incorporated, the PRI control unit  15  in the second embodiment or the PRI control unit  16  in the third embodiment is incorporated instead of the PRI control unit  14 , and the domain conversion unit  45  in the second embodiment is incorporated instead of the domain conversion unit  44 . 
     Further, in each of the first to fourth embodiments, there can be a modified example in which there is no intra-pulse modulation and correlation processing. In this case, the radar signal processing circuits  30  and  31  in the first to fourth embodiments are modified so as not to have the correlation processing unit  42 . Further, the domain conversion unit  44  in the first embodiment or the fourth embodiment may be modified so as to perform a discrete Fourier transform based on a predetermined algorithm on the received digital signal V 0 (h,m) to generate a frequency domain signal f d (h fft ,m). Furthermore, the oversampling unit  43  in the second embodiment or the third embodiment may convert received digital signals V 0 (h,m)(h=0 to H−1) having data points that are temporally unequally spaced regarding the hit number h into the oversample signals F V·Ex·GCD (h GCD ,m)(h GCD =0 to Q−1) having the data points that are temporally equally spaced. 
     INDUSTRIAL APPLICABILITY 
     The radar apparatus and the signal processing method according to the present invention can be used in a radar system that detects a relative position and relative velocity of a target such as a mobile target. Further, the radar apparatus according to the present invention can be used in a state of being installed on the ground or in a state of being mounted on a mobile object such as an aircraft, an artificial satellite, a vehicle, or a ship. 
     REFERENCE SIGNS LIST 
       1 ,  2 ,  3 ,  4 : radar apparatus,  10 ,  10 A: signal generation circuit,  11 : transmission and reception unit,  12 : antenna,  13 : receiving circuit,  14 ,  15 ,  16 : PRI control unit,  20 : local oscillator,  21 : pulse generator,  22 ,  22 A: intra-pulse modulator,  23 : output unit,  24 : down converter,  25 : band filter,  26 : amplifier,  27 : phase detector,  28 : A/D converter,  30 ,  31 : radar signal processing circuit,  40 ,  41 : signal conversion unit,  42 : correlation processing unit,  44 ,  45 : domain conversion unit,  50 : target detection unit,  51 : target candidate detection unit,  52 : target candidate information calculating unit,  60 : display,  70 : signal processing circuit,  71 : processor,  72 : memory,  73 : storage device,  74 : input and output interface,  75 : signal path, Tgt: target, Tw: transmission wave, Rw: reflected wave