Patent Publication Number: US-11029389-B2

Title: FM-CW radar and method of generating FM-CW signal

Description:
FIELD 
     The present invention relates to an FM-CW radar that uses frequency modulation based on a frequency modulated continuous waves (FM-CW) scheme, and to a method of generating an FM-CW signal that is transmitted by the FM-CW radar. 
     BACKGROUND 
     An FM-CW radar has the ease of configuration and a relatively low frequency of the baseband that facilitates signal processing, and is thus used commonly these days as a millimeter wave band collision avoidance radar or the like with the aim of reducing cost. 
     An FM-CW scheme uses an up-chirp signal that varies a transmit frequency from a low frequency to a high frequency and a down-chirp signal that varies the frequency from a high frequency to a low frequency, and calculates the distance to a target as well as relative velocity with respect to the target on the basis of a sum of peak frequencies and a difference in the peak frequencies of beat signals respectively obtained from the chirp signals. 
     On the other hand, transmit/receive modules making up the FM-CW radar require adjustment work in a delivery inspection process due to individual differences and temperature characteristics of voltage control oscillators (hereinafter noted as a “VCO”), and thus hinder reduction of the inspection time in mass production. Because no feedback control performed after shipment, there is a problem in that the radar is unable to respond to a change in the characteristics of the VCO caused by aging or the like. 
     Note that Patent Literature 1 discloses the configuration including: a frequency divider that divides, by the number of divisions N, an output signal from the VCO an oscillating frequency of which varies according to an analog control voltage; a digital phase detector that detects phase information from an output signal of the frequency divider and outputs digital phase information; and a differentiator that differentiates the digital phase information output from the digital phase detector and converts the information into digital frequency information. 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Literature 1: Japanese Patent Application Laid-Open No. 2013-47617 
       
    
     SUMMARY 
     Technical Problem 
     Patent Literature 1 obtains the frequency information on the basis of the phase information included in the output of the VCO as described above, but does not disclose a specific method of generating the output of the VCO. A conventional technique has thus been unable to properly respond to the change in the characteristics of the VCO caused by aging or the like. 
     The present invention has been made in view of the aforementioned circumstances, where an object of the invention is to obtain an FM-CW radar capable of properly responding to a change in the characteristics of a VCO caused by aging or the like, and to obtain a method of generating an FM-CW signal. 
     Solution to Problem 
     There is provided an FM-CW radar using frequency modulation based on an FM-CW scheme. The FM-CW radar according to an aspect of the present invention includes: a high frequency circuit to receive a reflected wave from a target; and a signal processing unit to convert an analog signal generated by the high frequency circuit into a digital signal and detect at least a distance to the target and velocity of the target, wherein the high frequency circuit includes a voltage control oscillator to generate a frequency-modulated high frequency signal in response to receiving a modulation voltage from the signal processing unit, the signal processing unit includes a look up table to store default modulation control data, and the signal processing unit uses an initial frequency value and an initial voltage value calculated from a voltage-frequency characteristic manifested by application of a default chirp having a linear characteristic, and updates the data stored in the look up table with correction data that is generated by fixing a voltage increment and varying a time increment. 
     Advantageous Effects of Invention 
     According to the present invention, the FM-CW radar can properly respond to the change in the characteristics of the VCO caused by aging or the like. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram illustrating the configuration of an FM-CW radar according to a first embodiment. 
         FIG. 2  is a block diagram illustrating the configuration of the FM-CW radar according to the first embodiment, where some components are omitted. 
         FIG. 3  is a diagram provided for explaining parameters that make up modulation control data stored in an LUT. 
         FIG. 4  is a flowchart illustrating the flow of frequency information calculation processing performed by a microcomputer. 
         FIG. 5  is a block diagram illustrating the calculation flow of the processing illustrated in  FIG. 4  when the processing is performed by a dedicated processor. 
         FIG. 6  is a flowchart illustrating the flow of correction processing using a polynomial approximation. 
         FIG. 7  is a timing diagram provided for explaining an update of the LUT and transmission processing performed after the update. 
         FIG. 8  is a flowchart illustrating processing that calculates an initial frequency value and an initial voltage value using a cubic function. 
         FIG. 9  is a diagram illustrating the waveform of a default chirp. 
         FIG. 10  is a diagram illustrating the waveform of a V-f characteristic. 
         FIG. 11  is a diagram illustrating a desired t-f characteristic. 
         FIG. 12  is a diagram illustrating an applied voltage at the time of correction for obtaining the desired t-f characteristic. 
         FIG. 13  is a flowchart illustrating the flow of correction processing based on time error calculation performed by a microcomputer. 
         FIG. 14  is a diagram provided for explaining the concept of the correction processing based on the time error calculation. 
         FIG. 15  is a table illustrating an image of data stored in a non-volatile memory of the microcomputer. 
         FIG. 16  is a flowchart illustrating the flow of alarm processing according to a fourth embodiment. 
         FIG. 17  is a flowchart illustrating the flow of abnormality determination processing according to the fourth embodiment. 
         FIG. 18  is a flowchart illustrating the flow of singularity determination processing according to the fourth embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     An FM-CW radar and a method of generating an FM-CW signal according to an embodiment of the present invention will now be described in detail with reference to the drawings. Note that the present invention is not to be limited by the following embodiment. 
     First Embodiment 
       FIG. 1  is a block diagram illustrating the configuration of an FM-CW radar according to a first embodiment. The FM-CW radar according to the first embodiment is an FM-CW radar that uses frequency modulation based on an FM-CW scheme. As illustrated in  FIG. 1 , the FM-CW radar is made up of main components including: a high frequency circuit  13  that radiates a transmit signal as a radio wave into space via a transmitting antenna  1  (Tx) and receives, via a receiving antenna  2  (Rx), a reflected wave of the transmitted radio wave that is reflected from a target; a signal processing unit  14  that converts an analog signal output from the high frequency circuit  13  into a digital signal and detects the distance to the target as well as the velocity thereof and, if necessary, the bearing of the target; and a control circuit  12  that controls various control voltages supplied to the high frequency circuit  13 . 
     The high frequency circuit  13  includes, as basic components: a VCO  4  that receives, as a transmit command, a VCO modulation voltage being a triangular wave voltage signal from the signal processing unit  14  and generates a frequency-modulated high frequency signal; a power distributor  3  that supplies most of the high frequency signal output from the VCO  4  to the transmitting antenna  1  and supplies the rest as a local signal; and a mixer  5  that receives the local signal and uses it to convert the frequency of a received signal from the receiving antenna  2  or, to be specific, down-convert the received signal. The components of the high frequency circuit  13  are each formed of a microwave monolithic IC (MMIC). 
     A baseband amplifier circuit  6 , a prescaler  15 , a mixer  17 , and a reference frequency generator  18  are provided between the high frequency circuit  13  and the signal processing unit  14 . The functions of these components will be described later. Note that the transmitting antenna  1 , the receiving antenna  2 , the baseband amplifier circuit  6 , the control circuit  12 , the high frequency circuit  13 , the signal processing unit  14 , the prescaler  15 , the mixer  17 , and the reference frequency generator  18  make up a millimeter wave transceiver module. 
     The signal processing unit  14  includes: a microcomputer  10  that is a main circuit unit mainly performing transmission processing and measurement processing of the FM-CW radar; a digital-to-analog converter (hereinafter noted as “DAC” as appropriate)  7  that converts the triangular wave voltage signal being the transmit command from the microcomputer  10  into an analog signal and inputs the signal to the VCO  4  of the high frequency circuit  13 ; an analog-to-digital converter (hereinafter noted as “ADC” as appropriate)  8  that converts a received signal from the baseband amplifier circuit  6  into a digital signal and inputs the signal to the microcomputer  10 ; and an ADC  16 , the function of which will be described in detail later on. Note that the microcomputer  10  includes a look up table (hereinafter noted as “LUT” as appropriate)  9  that stores data of the triangular wave voltage signal being input to the VCO  4 . The FM-CW radar is further provided with an ambient temperature monitor  11  that monitors the ambient temperature, where a value detected by the ambient temperature monitor  11  is input to the microcomputer  10 . 
     Under the control of the microcomputer  10 , the control circuit  12  controls the various control voltages supplied to the MMICs in the high frequency circuit  13 . The microcomputer  10  is provided with a non-volatile memory  19 . The MMICs in the high frequency circuit  13  vary depending on a production lot. The non-volatile memory  19  in the microcomputer  10  thus stores a control voltage value that is individually adjusted and determined for each product of the millimeter wave transceiver module. In the actual operation, the control voltage value is read from the non-volatile memory  19  by the microcomputer  10  and supplied to the MMICs in the high frequency circuit  13  via the control circuit  12 . 
     The VCO  4  receives the VCO modulation voltage being the triangular wave voltage signal from the signal processing unit  14  and generates an FM-CW signal that is a high frequency signal including an up modulation signal which is shifted up in frequency within a certain period of time, and a down modulation signal which is shifted down in frequency within a certain period of time. Most of the FM-CW signal being generated is supplied from the power distributor  3  to the transmitting antenna  1 , and the transmitting antenna  1  radiates millimeter waves toward a target. The rest of the FM-CW signal, namely a portion not supplied to the transmitting antenna  1 , is supplied as a local signal to the mixer  5 . 
     A reflected wave reflected from the target that is captured by the receiving antenna  2  is input to the mixer  5  as a received signal. The mixer  5  mixes the received signal from the receiving antenna  2  and the local signal from the power distributor  3  to output a beat signal with a frequency corresponding to a difference in the frequencies of the two signals. The beat signal is amplified to an appropriate level in the baseband amplifier circuit  6  and then input to the microcomputer  10  via the ADC  8 . The microcomputer  10  obtains the distance to the target as well as the relative velocity with respect to the target and, if necessary, the bearing of the target on the basis of the frequency of the input beat signal during each of a period in which the frequency is shifted up and a period in which the frequency is shifted down. 
     Here, the frequency of a frequency-divided signal from the VCO  4  is decreased to a fraction of a certain integer by the prescaler  15  and then input to the mixer  17 . The mixer  17  mixes an output signal from the prescaler  15  and the local signal from the reference frequency generator  18  to output a signal with a frequency corresponding to a difference in the frequencies of the two signals. The output signal from the mixer  17  is input to the microcomputer  10  via the ADC  16  and is used to update the data on the triangular wave voltage signal stored in the LUT  9 . 
       FIG. 2  illustrates another possible configuration not using the mixer  17  or the reference frequency generator  18  used in  FIG. 1 .  FIG. 2  illustrates the configuration where the frequency band of a signal input to the ADC  16  is the frequency band of a signal output from the prescaler  15 . Although this requires a faster processing clock than the ADC  16  used in  FIG. 1 , the advantage of not using the mixer  17  or the reference frequency generator  18  can effectively reduce cost and improve reliability of the millimeter wave transceiver module. 
     Main parts of the FM-CW radar according to the first embodiment will now be described with reference to  FIGS. 1 and 3 to 7 .  FIG. 3  is a diagram provided for explaining parameters that make up modulation control data stored in the LUT  9 .  FIG. 4  is a flowchart illustrating the flow of frequency information calculation processing performed by the microcomputer  10 .  FIG. 5  is a block diagram illustrating the calculation flow of the processing illustrated in  FIG. 4  when the processing is performed by a dedicated processor.  FIG. 6  is a flowchart illustrating the flow of correction processing using a polynomial approximation.  FIG. 7  is a timing diagram provided for explaining an update of the LUT  9  and transmission processing performed after the update. 
     The modulation control data stored in the LUT  9  will be described first with reference to  FIG. 3 . The modulation control data is formed of a voltage step DV, a starting voltage BV, a time increment DC, and the number of pieces of time data DN. The diagram in  FIG. 3  has a horizontal axis representing time and a vertical axis representing a voltage value. The time increment DC and the number of pieces of time data DN are parameters along the time axis, whereas the starting voltage BV and the voltage step DV are parameters along the voltage axis. A more detailed description will now be provided. 
     (Voltage Step DV) 
     The voltage step DV is set to an integer multiple of the voltage resolution of the DAC  7  and is basically fixed. The DAC  7  with a reference voltage of 5 V and resolution of 10 bit has the voltage resolution of 5/1024≈0.00488 V, for example. 
     (Starting Voltage BV) 
     The starting voltage BV is a starting voltage of the modulation control data and is set to an integer multiple of the voltage resolution of the DAC  7 , as is the case with the voltage step DV. 
     (Time Increment DC) 
     The time increment DC is a duration of a certain voltage value and is set to an integer multiple of the minimum time resolution of the microcomputer  10 . The time increment DC essentially controls the waveform. Note that the time increment DC has a fixed value in default chirp data that is stored in the LUP  9  as a default. 
     (Number of Pieces of Time Data DN) 
     The number of pieces of time data DN is a cumulative value of the time increments DC in any single section and indicates the number of pieces of data in the single section. 
     Note that in order to increase the accuracy of correction, the present embodiment forms a desired waveform by fixing the value of the voltage step DV and varying the time increment DC. It is needless to say that the voltage step DV may be variable, not fixed. 
     The frequency information calculation processing will now be described with reference to  FIGS. 4 and 5 . 
     (Quadrature Demodulation) 
     Quadrature demodulation corresponds to processing in step S 101  of  FIG. 4  as well as processing by a sine function and cosine function generator  31  and multipliers  32   a ,  32   b  in  FIG. 5 . Specifically, a piece of data sampled from the ADC  16  is subjected to quadrature detection and separated into two signals including an in-phase (I) component and a quadrature (Q) component. These I component and Q component signals are expressed by the following expression.
 
[Expression 1]
 
 I ( n )= x ( n )·sin(ω·Δ t·n ) n= 1,2, . . . , k  
 
 Q ( n )= x ( n )·cos(ω·Δ t·n )  (1)
 
     x(n): Digital data acquired by sampling 
     k: The number of samples 
     Δt: Sampling interval 
     ω=2πf Lo  (f Lo : Lo frequency for quadrature demodulation) 
     (Filtering) 
     Filtering corresponds to processing in step S 102  of  FIG. 4  and processing by low pass filters (hereinafter noted as “LPF”)  33   a  and  33   b  in  FIG. 5 . Note that in the present embodiment, the filtering is performed to multiply the I signal and the Q signal acquired by the quadrature demodulation in step S 101  by corresponding weighting factors according to finite impulse response (FIR) filters, respectively. The FIR filtering can be expressed by the following expression. Not only the FIR filter but an infinite impulse response (IIR) filter may be used in the filtering. 
     
       
         
           
             
               
                 
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     (Phase Calculation) 
     Phase calculation corresponds to processing in step S 103  of  FIG. 4  and processing by an arctangent function calculator  34  in  FIG. 5 . The processing in step S 103  is performed to generate an instantaneous phase θ(n) expressed by the following expression. 
     
       
         
           
             
               
                 
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     (Frequency Calculation) 
     Frequency calculation corresponds to processing in step S 104  of  FIG. 4  and processing by a frequency calculator  35  in  FIG. 5 . The processing in step S 104  generates an instantaneous frequency f″(n) expressed by the following expression. 
     
       
         
           
             
               
                 
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     Those calculations yield a relationship between the time and the frequency. The acquired frequency is then converted into a value in the 76 to 77 GHz band by the following conversion expression.
 
[Expression 5]
 
 f ′( n )={ f ″( n )+ f   xo   }·N· 4  (5)
 
     f xo : Local oscillator frequency (generated by reference frequency generator) 
     N: Division number of prescaler 
     The above expression (5) applies to the case where a local oscillator signal frequency f xo  of the reference frequency generator  18  is 19 GHz, or where the frequency-divided signal from the VCO  4  is monitored in the 19 GHz band. 
     (Considering Delay Time Caused by Filter) 
     Consideration of a delay time caused by the filter corresponds to processing in step S 105  of  FIG. 4 . Regarding the relationship between the time and the frequency acquired through the processing in steps S 101  to S 104 , the processing in step S 105  is performed to shift the frequency data while taking into consideration the delay time caused by the FIR filter. Specifically, shift processing as expressed by the following expression is performed in step S 105 .
 
[Expression 6]
 
 f ( n )= f ′( n+t   d1 )  (6)
 
     Correction processing using a polynomial approximation will now be described. The frequency information calculated by the flow of the “frequency information calculation processing” illustrated in  FIG. 4  is stored as frequency data with respect to time into the non-volatile memory  19  of the microcomputer  10 . The modulation control data described with reference to  FIG. 3  is already stored in the LUT  9  of the microcomputer  10  as voltage data with respect to time. The correction processing using a polynomial approximation in this case uses a polynomial to approximate the relationship between the voltage and the frequency while referring to the “frequency data with respect to time” and the “voltage data with respect to time”. A piece of modulation data required to obtain linearity of the frequency is generated on the basis of an approximation function obtained by the polynomial approximation, and is applied to the LUT  9  as modulation control data to be output to a next period. That is, the approximation function obtained by the polynomial approximation is used to update the modulation control data stored in the LUT  9 . 
     Next, an example of the correction processing using a polynomial approximation will be described with reference to  FIG. 6 . Note that the example in  FIG. 6  uses, as preconditions, the 10-bit DAC  7  and a quadratic function as a function used in the polynomial approximation. 
     (Determining Voltage Range) 
     Determination of a voltage range corresponds to processing in step S 201  of  FIG. 6 . Specifically, the frequency is expressed as a quadratic function of the voltage as expressed by the following expression, where a center frequency fc corresponding to a center voltage Vc is obtained to then set a starting frequency fmin as well as a starting voltage Vmin for a required modulation width Δf. 
     
       
         
           
             
               
                 
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     (Setting Voltage Increment) 
     Setting of a voltage increment corresponds to processing in step S 202  of  FIG. 6 . Specifically, the voltage step DV is set to a fixed value. 
     (Setting Initial Voltage and Initial Frequency) 
     Setting of an initial voltage and an initial frequency corresponds to processing in step S 203  of  FIG. 6 . Specifically, an initial voltage V 0  is obtained by rounding the starting voltage Vmin obtained by expression (7) to a value that the DAC  7  can have for every voltage increment. Such value then serves as a starting voltage BV. An initial frequency f 0  is a frequency corresponding to V 0 . The initial frequency is obtained by the following expression.
 
[Expression 8]
 
 f   0   =aV   0   2   +bV   0   +c   (8)
 
     (Calculating Time Increment Data) 
     Calculation of time increment data corresponds to processing in step S 204  of  FIG. 6 . Note that a represents a theoretical slope of a frequency obtained from a modulation width and prescribed time.
 
[Expression 9]
 
 f=αt+f   0   (9)
 
     An expression for calculating time can be expressed by the following expression on the basis of expression (9) and the quadratic approximation (first expression) in expression (7).
 
[Expression 10]
 
 t =( aV   2   +bV+c−f   0 )/α  (10)
 
     Note that the voltage with the initial voltage of Vo is incremented by one step at a time. The time obtained is quantized by the minimum time resolution of the microcomputer  10  to be expressed. 
     (Calculating Final Voltage) 
     Calculation of a final voltage corresponds to processing in step S 205  of  FIG. 6 . Specifically, the final voltage is calculated up to where a cumulative time of the time increment data calculated in step S 204  does not exceed the prescribed time. The number of pieces of the time increments DC acquired is the number of pieces of time data DN. Note that with the initial voltage Vo, a final voltage Ve can be calculated by the following expression.
 
[Expression 11]
 
 Ve=Vo+DV×DN   (11)
 
     Next, an update of the LUT  9  and transmission processing performed after the update according to the first embodiment will be described with reference to a timing diagram in  FIG. 7 . The timing diagram in  FIG. 7  has a horizontal axis representing time and a vertical axis representing, from the top, an on state of a module power supply, a triangular wave modulation signal, a transmit frequency, a VCO control voltage, and a transmission system control voltage. 
     The LUT  9  stores predetermined data as a default of the modulation control data. The predetermined data is referred to as default chirp data.  FIG. 7  indicates the default chirp data by a waveform K 1  of the triangular wave modulation signal. When there is no change in the characteristics of the VCO  4 , the frequency of the FM-CW signal transmitted from the transmitting antenna  1  has a waveform as indicated by a waveform K 4  with linearity. On the other hand, when there occurs a change in the characteristics of the VCO  4  due to aging or the like, the frequency of the FM-CW signal transmitted from the transmitting antenna  1  has a waveform as indicated by a waveform K 2  without linearity. Because of the above, the first embodiment converts the frequency-divided signal from the VCO  4  into a digital signal to monitor the signal on a regular basis, and at the same time calculates the frequency information from the phase information of the frequency-divided signal from the VCO  4  (the processing flow in  FIG. 4 ). A result of the calculation is used to perform the correction processing and calculate voltage data that is required for ensuring the linearity of the transmit frequency (the processing flow in  FIG. 6 ). After the processing in  FIG. 6 , the data stored in the LUT  9  is updated to data as indicated by a waveform K 3 , which is then applied to the waveform K 2  to be able to generate the FM-CW signal that has the waveform with linearity as indicated by the waveform K 4 . 
     The FM-CW signal is not transmitted until a first round of the update of the LUT  9  is completed by calculating the frequency information and performing the correction processing. In this case, the frequency calculation and correction processing are performed after turning on the module power supply and then the VCO control voltage as illustrated in  FIG. 7 , whereas transmission of the FM-CW signal can be inhibited by keeping the transmission system control voltage off. The transmission system control voltage may be turned on in synchronization with the update of the LUT  9  to enable transmission of the FM-CW signal quickly after the update of the LUT  9 . 
     As described above, the first embodiment calculates the frequency information from the phase information of the frequency-divided signal output from the VCO  4 , and updates the data stored in the LUT  9  with correction data that is generated by using the result of the calculation, whereby the radar can properly respond to the change in the characteristics of the VCO caused by aging or the like. The ability to properly respond to the change in the characteristics of the VCO allows a reduction in the inspection time required in a delivery inspection process as well as construction of a mechanism of feedback control after the shipment, thereby allowing the VCO correction to be performed with higher accuracy. 
     Second Embodiment 
     The first embodiment has described the calculation processing in which the V-f curve is approximated by the quadratic function as the correction processing using the polynomial approximation. That is, the first embodiment has described the method of directly calculating the initial voltage value using the quadratic function. On the other hand, instead of directly calculating the initial voltage value, a second embodiment proposes a method in which the V-f curve can be approximated by a third-order or higher polynomial or another function including an exponential function by using a solution based on an iterative method with the use of an approximate solution. 
     The present embodiment will describe calculation processing using a cubic function as an example of a function other than the quadratic function with reference to  FIGS. 8 to 12 .  FIG. 8  is a flowchart illustrating processing that calculates the initial frequency value and the initial voltage value using a cubic function. The entire processing flow illustrated in  FIG. 8  corresponds to step S 203  illustrated in  FIG. 6 .  FIG. 9  is a diagram illustrating the waveform of a default chirp.  FIG. 10  is a diagram illustrating the waveform of a V-f characteristic.  FIG. 11  is a diagram illustrating a desired t-f characteristic.  FIG. 12  is a diagram illustrating an applied voltage at the time of correction for obtaining the desired t-f characteristic. Note that a basic configuration is identical or equivalent to the configuration of the first embodiment illustrated in  FIG. 1 or 2 , and thus a description of a specific configuration will be omitted. 
     First, the default chirp having a linear characteristic as illustrated in  FIG. 9  is applied (step S 301 ). Note that the default chirp data is stored in the LUT  9  as described above. The V-f characteristic as illustrated in  FIG. 10  is manifested by the application of the default chirp, whereby a curve representing the V-f characteristic, that is, the V-f curve, is obtained (step S 302 ). 
     Next, the V-f curve obtained in step S 302  is approximated by a cubic function as expressed below (step S 303 ).
 
[Expression 12]
 
 f=aV   3   +bV   2   +cV+d   (12)
 
     At this time, the differentiation of expression (12) as expressed below is also prepared.
 
[Expression 13]
 
 f′= 3 aV   2 +2 bV+c   (13)
 
     Next, an initial frequency value f min  is determined (step S 304 ). Specifically, the initial frequency value f min  can be determined with the voltage of 2.5V defined as the center frequency and ±200 MHz as the modulation bandwidth, for example. 
     The initial frequency value f min  obtained in step S 304  is substituted into expression (12) to set up a cubic equation as expressed below.
 
[Expression 14]
 
 aV   3   +bV   2   +cV+d−f   min =0  (14)
 
     Generally, when finding x that satisfies f (x)=0, a sequence converging to x can be obtained by a recursion formula as expressed below by taking an approximate solution x 0 . 
     
       
         
           
             
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     15 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     x 
                     
                       n 
                       + 
                       1 
                     
                   
                   = 
                   
                     
                       x 
                       n 
                     
                     - 
                     
                       
                         f 
                         ⁡ 
                         
                           ( 
                           
                             x 
                             n 
                           
                           ) 
                         
                       
                       
                         
                           f 
                           ′ 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             n 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Experience gives V 0 =1 as an approximate solution of an initial, voltage value V min . After that, the initial voltage value V min  is obtained by performing iterative calculation according to expression (14) above (step S 305 ). The initial voltage value V min  practically converges to a desired value by repeating the calculation about five times. 
     Finally, time increment data is calculated (step S 306 ). The idea of the processing in step S 306  is equivalent to the processing in step S 204  illustrated in  FIG. 6 . Although the description is redundant, the processing will be described below because the function is different from that in the description made with reference to  FIG. 6 . 
     First, target frequency data for obtaining linearity can be represented by a linear function as follows.
 
[Expression 16]
 
 f=αt+β   (16)
 
     The following expression can be obtained from expressions (12) and (16) above. 
                   [     Expression   ⁢           ⁢   17     ]                           t   =         aV   3     +     bV   2     +   cV   +   d   -   β     α             (   17   )               
α: slope of frequency (GHz/μs) determined by modulation width and modulation time
 
β: equal to initial frequency value (fmin)
 
     In expression (17) above, α is the slope of frequency (GHz/μs) and can be obtained from the modulation width and the modulation time. Moreover, the initial frequency value f min  may be substituted into β. The voltage increment is thereafter changed step by step starting from the initial voltage value V min  obtained in step S 305  above. At this time, time data corresponding to the voltage increment changed step by step, that is, the time increment data, is obtained. The time increment data obtained here is applied to the LUT  9  as modulation control data to be output in a next period. That is, the function approximated by the cubic function is used to update the modulation control data stored in the LUT  9 . The subsequent processing is the same as that described in the first embodiment and thus will not be described. 
     As described above, the second embodiment uses the initial frequency value and the initial voltage value calculated from the V-f characteristic manifested by the application of the default chirp having the linear characteristic and updates the data stored in the LUT  9  with the correction data generated by fixing the voltage increment and varying the time increment, thereby being able to properly respond to a change in the characteristics of the VCO caused by aging or the like. The ability to properly respond to the change in the characteristics of the VCO allows a reduction in the inspection time required in a delivery inspection process as well as construction of a feedback control mechanism after shipment, thereby allowing the VCO correction to be performed with high accuracy. 
     Third Embodiment 
     In the first embodiment, the LUT  9  is updated by the combination of the frequency calculation processing based on the phase calculation and the correction processing using the polynomial approximation. In a third embodiment, correction processing based on time error calculation is substituted for second and subsequent rounds of updating the LUT  9 . Note that a basic configuration is identical or equivalent to the configuration of the first embodiment illustrated in  FIG. 1 or 2 , and thus a description of a specific configuration will be omitted. 
     Main parts of an FM-CW radar according to the third embodiment will now be described with reference to  FIGS. 13 and 14 .  FIG. 13  is a flowchart illustrating the flow of the correction processing based on time error calculation performed by a microcomputer  10 .  FIG. 14  is a diagram provided for explaining the concept of the “correction processing based on time error calculation”. 
     (Calculating Error from Ideal Frequency Line) 
     Calculation of an error from an ideal frequency line corresponds to processing in step S 401  of  FIG. 13 . Specifically, “frequency data with respect to time” is calculated first according to the flow of “frequency information calculation processing” illustrated in  FIG. 4 . Then, an error δt (i) between the “frequency data with respect to time” and the ideal frequency line is calculated on the basis of the following expression. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     18 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       t 
                       ⁡ 
                       
                         ( 
                         i 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           f 
                           detect 
                         
                         ⁡ 
                         
                           ( 
                           i 
                           ) 
                         
                       
                       - 
                       
                         
                           f 
                           ideal 
                         
                         ⁡ 
                         
                           ( 
                           i 
                           ) 
                         
                       
                     
                     α 
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     In expression (18), f ideal  represents the ideal frequency line, and f detect  represents the frequency data calculated by the flow of  FIG. 4 . Moreover, α represents a theoretical slope value of the frequency obtained from a modulation width and prescribed time.  FIG. 14  illustrates an image of such calculation, where an arrow component between the waveform of the frequency data f detect  indicated by a solid waveform and the waveform of the ideal frequency line f ideal  is calculated as the error, the arrow component corresponding to a difference between the waveforms along a time axis. 
     (Correcting Time Increment Data) 
     Correction of time increment data corresponds to processing in step S 402  of  FIG. 13 . Specifically, a time increment DC is corrected by using the error from the ideal frequency line that is calculated by expression (18). Where the beginning of the data range is denoted as k-th, the time increment DC after correction can be obtained by the following expression.
 
[Expression 19]
 
 k - th  calculation:  DC ′( k )= DC ( k )+δ t ( k )
 
( k+ 1)- th  and subsequent calculations:  DC ′( k+ 1)= DC ( k+ 1)+δ t ( k+ 1)−δ t ( k )   (19)
 
     In expression (19), DC (k) represents k-th data before correction, δt (k) represents an error component obtained by using DC (k), and DC′ (k) represents k-th data after correction. Likewise, DC (k+1) represents (k+1)-th data before correction, δt (k+1) represents an error component obtained by using DC (k+1), and DC′ (k+1) represents (k+1)-th data after correction. 
     The LUT  9  of the third embodiment is updated as follows according to the flow of  FIG. 13 . In a first round of updating the LUT  9 , a frequency characteristic of default chirp data is subjected to a polynomial approximation (the quadratic approximation in the aforementioned example) and, from a result of the approximation, a voltage table required to secure linearity is calculated. In second and subsequent rounds of updating the LUT  9 , a time error with respect to the ideal frequency line is calculated according to the flow in  FIG. 13  instead of using the polynomial approximation, and then the time error is used to correct each time data. 
     The third embodiment as described above is adapted to calculate, as the error, the difference along the time axis between the calculated frequency information data and the waveform data of the ideal frequency line, and use the calculated error to perform the correction along the time axis to thus be able to obtain an effect similar to that of the first embodiment. 
     Fourth Embodiment 
     In a fourth embodiment, an indication of a change in characteristics of a VCO caused by a change in ambient temperature is perceived to result in an additional function of detecting an abnormality in a transmit frequency of an FM-CW radar and issuing an alarm and an error. A basic configuration is identical or equivalent to the configuration of the first embodiment illustrated in  FIG. 1 or 2 , and thus a description of a specific configuration will be omitted. 
     Main parts of the FM-CW radar according to the fourth embodiment will now be described with reference to  FIGS. 15 to 18 .  FIG. 15  is a table illustrating the image of data stored in a non-volatile memory  19  of a microcomputer  10 .  FIG. 16  is a flowchart illustrating the flow of “alarm processing” according to the fourth embodiment.  FIG. 17  is a flowchart illustrating the flow of “abnormality determination processing” according to the fourth embodiment.  FIG. 18  is a flowchart illustrating the flow of singularity determination processing according to the fourth embodiment. 
     An ambient temperature monitor  11  monitors the ambient temperature of a transceiver module on a regular basis. Temperature data obtained by the ambient temperature monitor  11  is stored in the non-volatile memory  19  along with the transmit frequency that is a frequency of a transmit signal of an FM-CW signal. 
     According to the flow of the alarm processing in  FIG. 16 , it is first determined whether or not the transmit frequency falls within a preset tolerance (step S 501 ). The transmit frequency falling outside the preset tolerance (No in step S 501 ) leads to a determination that there is an indication of deterioration, and an alarm is issued to a host control unit (step S 502 ). No alarm is issued if the transmit frequency falls within the present tolerance (Yes in step S 501 ). 
     The non-volatile memory  19  stores the transmit frequency information along with the ambient temperature data, thereby allowing one to check whether the transmit frequency deviates from a prescribed value and, in short, allowing one to issue the alarm to the host control unit. 
     Note that the non-volatile memory can store a limited number of data and may thus hold data at predetermined temperature intervals and, when not holding data on a temperature concerned, obtain a value of the temperature concerned by a linear approximation. 
     The processing flow in  FIG. 16  determines whether or not the frequency of the transmit signal falls within the tolerance, whereas a processing flow in  FIG. 17  may be executed to determine compliance with the Radio Act. Note that the processing flows in  FIGS. 16 and 17  can coexist. 
     In the execution of the processing flow in  FIG. 17 , a transmit frequency Max that is an upper limit of the transmit frequency stipulated by the Radio Act, a transmit frequency Min that is a lower limit of the transmit frequency being stipulated, and a modulation width of a transmit radar signal are stored in the non-volatile memory  19  together with the temperature data obtained by the ambient temperature monitor  11 , as illustrated in  FIG. 15 . 
     According to the flow of the abnormality determination processing in  FIG. 17 , it is first determined whether or not the transmit frequency falls within the range defined by the upper and lower limits (step S 601 ). The transmit frequency falling outside the range defined by the upper and lower limits (No in step S 601 ) leads to a determination that an abnormality is generated, and an error is issued to the host control unit (S 603 ). Even when the transmit frequency falls within the range defined by the upper and lower limits (Yes in S 601 ), it is further determined whether or not a modulation bandwidth of the FM-CW signal falls within a range defined by an upper limit (step S 602 ). Then if the modulation bandwidth falls outside the range defined by the upper limit (No in step S 602 ), an error is output to the host control unit (step S 603 ). 
     It is needless to say that an action such as stopping the output of transmission is taken when the error is issued to the host control unit. 
     The processing flow of  FIG. 18  may be executed in addition to the processing flows of  FIGS. 16 and 17 . Note that the processing flows of  FIGS. 16 to 18  can coexist. 
     In the flow of singularity determination processing illustrated in  FIG. 18 , it is first checked whether the transmit frequency Min has a temperature singularity (step S 701 ), and, if a singularity is found (Yes in step S 701 ), an alarm is issued to the host control unit (step S 703 ). Even if the transmit frequency Min has no temperature singularity (No in step S 701 ), it is further checked whether the transmit frequency Max has a temperature singularity (step S 702 ) so that an alarm is issued to the host control unit (step S 703 ) if a singularity is found (Yes in step S 702 ). Note that the purpose of the singularity here is to check whether or not the signal behaves differently at a specific temperature. Obtaining information on the singularity has an effect of facilitating a search for a failure when a problem occurs and contributing to improvement in reliability of the device. 
     Note that although the processing flow of  FIG. 18  performs the singularity determination processing for both the transmit frequency Min and the transmit frequency Max, the above effect can be obtained by performing the singularity determination processing for at least one of the frequencies. 
     In the fourth embodiment described above, the ambient temperature of the transceiver module including a high frequency circuit  13  is monitored and stored into the non-volatile memory  19  along with the transmit frequency of the FM-CW signal, whereby an effect that the alarm processing, the abnormality determination processing and the singularity determination processing can be performed is obtained in addition to the effect of the first embodiment. 
     The configuration illustrated in the aforementioned embodiment merely illustrates an example of the content of the present invention, and can thus be combined with another known technique or partially omitted and/or modified without departing from the gist of the present invention. 
     The processing in the first embodiment may be combined with the processing in the third embodiment, for example. Alternatively, the processing in the first embodiment may be combined with the processing in the fourth embodiment, or the processing in the third embodiment may be combined with the processing in the fourth embodiment. Still alternatively, the processing in the first to fourth embodiments may all be combined. 
     REFERENCE SIGNS LIST 
       1  transmitting antenna (Tx),  2  receiving antenna (Rx),  3  power distributor,  5 ,  17  mixer,  6  baseband amplifier circuit,  7  digital-to-analog converter (DAC),  8 ,  16  analog-to-digital converter (ADC),  9  look up table (LUT),  10  microcomputer,  11  ambient temperature monitor,  12  control circuit,  13  high frequency circuit,  14  signal processing unit,  15  prescaler,  18  reference frequency generator,  19  non-volatile memory,  31  sine function generator,  32   a ,  32   b  multiplier,  34  arctangent function calculator,  35  frequency calculator.