Patent Publication Number: US-10320083-B2

Title: Waveguide device and antenna device including the waveguide device

Description:
BACKGROUND 
     1. Technical Field 
     The present disclosure relates to a waveguide device, and an antenna device including the waveguide device. 
     2. Description of the Related Art 
     Examples of waveguiding structures including an artificial magnetic conductor are disclosed in Patent Documents 1 to 3 and Non-Patent Documents 1 and 2 as follows.
     Patent Document 1: International Publication No. 2010/050122   Patent Document 2: the specification of U.S. Pat. No. 8,803,638   Patent Document 3: the specification of European Patent Application Publication No. 1331688   Non-Patent Document 1: H. Kirino and K. Ogawa, “A 76 GHz Multi-Layered Phased Array Antenna using a Non-Metal Contact Metamaterial Waveguide”, IEEE Transaction on Antenna and Propagation, Vol. 60, No. 2, pp. 840-853, February, 2012   Non-Patent Document 2: A. Uz. Zaman and P.-S. Kildal, “Ku Band Linear Slot-Array in Ridge Gapwaveguide Technology, EUCAP 2013, 7th European Conference on Antenna and Propagation   

     An artificial magnetic conductor is a structure which artificially realizes the properties of a perfect magnetic conductor (PMC), which does not exist in nature. One property of a perfect magnetic conductor is that “a magnetic field on its surface has zero tangential component”. This property is the opposite of the property of a perfect electric conductor (PEC), i.e., “an electric field on its surface has zero tangential component”. Although no perfect magnetic conductor exists in nature, it can be embodied by an artificial periodic structure. An artificial magnetic conductor functions as a perfect magnetic conductor in a specific frequency band which is defined by its periodic structure. An artificial magnetic conductor restrains or prevents an electromagnetic wave of any frequency that is contained in the specific frequency band (propagation-restricted band) from propagating along the surface of the artificial magnetic conductor. For this reason, the surface of an artificial magnetic conductor may be referred to as a high impedance surface. 
     In the waveguide devices disclosed in Patent Documents 1 to 3 and Non-Patent Documents 1 and 2, an artificial magnetic conductor is realized by a plurality of electrically conductive rods which are arrayed along row and column directions. Such rods are projections which may also be referred to as posts or pins. Each of these waveguide devices includes, as a whole, a pair of opposing electrically conductive plates. One conductive plate has a ridge protruding toward the other conductive plate, and stretches of an artificial magnetic conductor extending on both sides of the ridge. An upper face (i.e., its electrically conductive face) of the ridge opposes, via a gap, a conductive surface of the other conductive plate. An electromagnetic wave of a wavelength which is contained in the propagation-restricted band of the artificial magnetic conductor propagates along the ridge, in the space (gap) between this conductive surface and the upper face of the ridge. 
     SUMMARY 
     In a waveguide such as an antenna feeding network, a waveguide member may have a bend(s) and/or a branching portion(s). At a bend or a branching portion, a change occurs in the direction that the waveguide member extends. At such a portion of change in the direction that the waveguide member extends, unless remedied, an impedance mismatching would occur, thus causing unwanted reflection of a propagating electromagnetic wave. Such reflection would not only cause a propagation loss in the signal, but also induce unwanted noises. 
     Non-Patent Document 1 discloses varying the height of the ridge at a position near a bend or a branching portion in order to enhance impedance matching at the bend or the branching portion. In a waveguide which is disclosed in Non-Patent Document 2, the ridge width varies at a portion near a branching portion of the waveguide member. 
     Various embodiments of the present disclosure provide a waveguide device with an enhanced degree of impedance matching at a bend or a branching portion of a waveguide member. 
     A waveguide device according to one aspect of the present disclosure includes: a first electrically conductive member having an electrically conductive surface which is shaped as a plane or a curved surface; a second electrically conductive member having a plurality of electrically conductive rods arrayed thereon, each conductive rod having a leading end opposing the conductive surface of the first conductive member; and a waveguide member having an electrically conductive waveguide face opposing the conductive surface of the first conductive member, the waveguide member being disposed among the plurality of conductive rods and extending along the conductive surface. The waveguide member includes at least one of a bend at which the direction that the waveguide member extends changes and a branching portion at which the direction that the waveguide member extends ramifies into two or more directions. A measure of an outer shape of a cross section of at least one of the plurality of conductive rods that is adjacent to the bend or the branching portion, taken perpendicular to an axial direction of the at least one conductive rod, monotonically decreases from a root that is in contact with the second conductive member toward the leading end. 
     Hereinafter, any reference to a “conductive member” is intended to mean an “electrically conductive member”; any reference to a “conductive rod” is intended to mean an “electrically conductive rod”; any reference to a “conductive surface” is intended to mean an “electrically conductive surface”; and so on. 
     In accordance with an embodiment of the present disclosure, a novel construction for rods that constitute an artificial magnetic conductor can enhance the degree of impedance matching at any bend or branching portion of a waveguide member. 
     These general and specific aspects may be implemented using a system, a method, and a computer program, and any combination of systems, methods, and computer programs. 
     Additional benefits and advantages of the disclosed embodiments will be apparent from the specification and Figures. The benefits and/or advantages may be individually provided by the various embodiments and features of the specification and drawings disclosure, and need not all be provided in order to obtain one or more of the same. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view schematically showing an exemplary schematic construction for an example of a waveguide device  100  according to the present disclosure. 
         FIG. 2A  is a diagram schematically showing a construction for the waveguide device  100  in  FIG. 1 , in a cross section parallel to the XZ plane. 
         FIG. 2B  is a diagram schematically showing another construction for the waveguide device  100  in  FIG. 1 , in a cross section parallel to the XZ plane. 
         FIG. 3  is another perspective view schematically illustrating the construction of the waveguide device  100 . 
         FIG. 4  is a diagram showing an exemplary range of dimension of each member in the structure shown in  FIG. 2A . 
         FIG. 5A  is a cross-sectional view schematically showing electromagnetic waves propagating in the waveguide device  100 . 
         FIG. 5B  is a cross-sectional view schematically showing the construction of a known hollow waveguide  130 . 
         FIG. 5C  is a cross-sectional view showing an implementation in which two waveguide members  122  are provided on a second conductive member  120 . 
         FIG. 5D  is a cross-sectional view schematically showing the construction of a waveguide device in which two hollow waveguides  130  are placed side-by-side. 
         FIG. 6  is a perspective view schematically showing an exemplary construction for a waveguide device according to an embodiment of the present disclosure. 
         FIG. 7  is a diagram schematically showing the construction of a cross section of the waveguide device  100  taken parallel to the XZ plane. 
         FIG. 8A  is a cross-sectional view of a conductive rod  124  in a plane containing the axial direction (Z direction). 
         FIG. 8B  is an upper plan view of the conductive rod  124  of  FIG. 8A  as viewed in the axial direction (Z direction). 
         FIG. 9A  is a perspective view schematically showing a conventional construction where the side faces of each conductive rod  124  are not tilted, in a construction including a branching portion. 
         FIG. 9B  is an upper plan view of the waveguide device shown in  FIG. 9A . 
         FIG. 9C  is a perspective view schematically showing a construction according to the present embodiment where the side faces of each conductive rod  124  are tilted, in a construction including a branching portion. 
         FIG. 9D  is an upper plan view of the waveguide device shown in  FIG. 9C . 
         FIG. 10  is a graph showing an input reflection coefficient S for an input wave at frequencies of 0.967 Fo, 1.000 Fo and 1.033 Fo, in the respective cases where the angle of tilt θ is 0°, 1°, 2°, 3°, 4° and 5°, in a construction including a branching portion. 
         FIG. 11  is a perspective view schematically showing another exemplary construction for a waveguide device according to another embodiment of the present disclosure. 
         FIG. 12A  is a perspective view schematically showing a conventional construction in which the side faces of each conductive rod  124  are not tilted, in a construction including a bend. 
         FIG. 12B  is an upper plan view of the waveguide device shown in  FIG. 12A . 
         FIG. 12C  is a perspective view schematically showing a construction according to the present embodiment where the side faces of each conductive rod  124  are tilted, in a construction including a bend. 
         FIG. 12D  is an upper plan view of the waveguide device shown in  FIG. 12C . 
         FIG. 13  is a graph showing an input reflection coefficient S for an input wave at frequencies of 0.967 Fo, 1.000 Fo and 1.033 Fo, in the respective cases where the angle of tilt θ is 0°, 1°, 2°, 3°, 4° and 5°, in a construction including a bend. 
         FIG. 14A  is a graph showing an example of expressing a measure D of the outer shape of a cross section of a conductive rod  124  taken perpendicular to the axial direction (Z direction), as a function D(z) of distance z of the conductive rod  124  from its root  124   b.    
         FIG. 14B  is a graph representing an example where, within a specific range of z, D(z) does not change in magnitude even if z increases. 
         FIG. 15A  is a cross-sectional view of a conductive rod  124  in a plane containing the axial direction (Z direction) in another example. 
         FIG. 15B  is an upper plan view of the conductive rod  124  of  FIG. 15A  as viewed in the axial direction (Z direction). 
         FIG. 16A  is a cross-sectional view of a conductive rod  124  in a plane containing the axial direction (Z direction) in still another example. 
         FIG. 16B  is an upper plan view of the conductive rod  124  of  FIG. 16A  as viewed in the axial direction (Z direction). 
         FIG. 17A  is a diagram showing a cross section of a conductive rod  124  taken parallel to the XZ plane in still another example. 
         FIG. 17B  is a diagram showing a cross section of the conductive rod  124  of  FIG. 17A  taken parallel to the YZ plane. 
         FIG. 17C  is a diagram showing a cross section of the conductive rod  124  of  FIG. 17A  taken parallel to the XY plane. 
         FIG. 18A  is a cross-sectional view of a conductive rod  124  in a plane containing the axial direction (Z direction) in still another example. 
         FIG. 18B  is an upper plan view of the conductive rod  124  of  FIG. 18A  as viewed in the axial direction (Z direction). 
         FIG. 19  is a cross-sectional view showing an exemplary construction in which an earlier-described characteristic shape is imparted to only those conductive rods  124  which are adjacent to a waveguide member  122 . 
         FIG. 20A  is an upper plan view of an array antenna according to an embodiment of the present disclosure as viewed in the Z direction. 
         FIG. 20B  is a cross-sectional view taken along line B-B in  FIG. 20A . 
         FIG. 21  is a diagram showing a planar layout of waveguide members  122  in a first waveguide device  100   a.    
         FIG. 22  is a diagram showing a planar layout of a waveguide member  122  in a second waveguide device  100   b.    
         FIG. 23A  is a cross-sectional view showing an exemplary structure where only a waveguide face  122   a , defining an upper face of the waveguide member  122 , is electrically conductive, while any portion of the waveguide member  122  other than the waveguide face  122   a  is not electrically conductive. 
         FIG. 23B  is a diagram showing a variant in which the waveguide member  122  is not formed on the second conductive member  120 . 
         FIG. 23C  is a diagram showing an exemplary structure where the second conductive member  120 , the waveguide member  122 , and each of the plurality of conductive rods  124  are composed of a dielectric surface that is coated with an electrically conductive material such as a metal. 
         FIG. 23D  is a diagram showing an exemplary structure in which dielectric layers  110   b  and  120   b  are respectively provided on the outermost surfaces of conductive members  110  and  120 , a waveguide member  122 , and conductive rods  124 . 
         FIG. 23E  is a diagram showing another exemplary structure in which dielectric layers  110   b  and  120   b  are respectively provided on the outermost surfaces of conductive members  110  and  120 , a waveguide member  122 , and conductive rods  124 . 
         FIG. 23F  is a diagram showing an example where the height of the waveguide member  122  is lower than the height of the conductive rods  124  and a conductive surface  110   a  of the first conductive member  110  protrudes toward the waveguide member  122 . 
         FIG. 24A  is a diagram showing an example where a conductive surface  110   a  of the first conductive member  110  is shaped as a curved surface. 
         FIG. 24B  is a diagram showing an example where also a conductive surface  120   a  of the second conductive member  120  is shaped as a curved surface. 
         FIG. 25  is a diagram showing a driver&#39;s vehicle  500 , and a preceding vehicle  502  that is traveling in the same lane as the driver&#39;s vehicle  500 . 
         FIG. 26  is a diagram showing an onboard radar system  510  of the driver&#39;s vehicle  500 . 
         FIG. 27A  is a diagram showing a relationship between an array antenna AA of the onboard radar system  510  and plural arriving waves k. 
         FIG. 27B  is a diagram showing the array antenna AA receiving the k th  arriving wave. 
         FIG. 28  is a block diagram showing an exemplary fundamental construction of a vehicle travel controlling apparatus  600  according to the present disclosure. 
         FIG. 29  is a block diagram showing another exemplary construction for the vehicle travel controlling apparatus  600 . 
         FIG. 30  is a block diagram showing an example of a more specific construction of the vehicle travel controlling apparatus  600 . 
         FIG. 31  is a block diagram showing a more detailed exemplary construction of the radar system  510  according to this Application Example. 
         FIG. 32  is a diagram showing change in frequency of a transmission signal which is modulated based on the signal that is generated by a triangular wave generation circuit  581 . 
         FIG. 33  is a diagram showing a beat frequency fu in an “ascent” period and a beat frequency fd in a “descent” period. 
         FIG. 34  is a diagram showing an exemplary implementation in which a signal processing circuit  560  is implemented in hardware including a processor PR and a memory device MD. 
         FIG. 35  is a diagram showing a relationship between three frequencies f1, f2 and f3. 
         FIG. 36  is a diagram showing a relationship between synthetic spectra F1 to F3 on a complex plane. 
         FIG. 37  is a flowchart showing the procedure of a process of determining relative velocity and distance according to a variant. 
     
    
    
     DETAILED DESCRIPTION 
     Prior to describing embodiments of the present disclosure, an exemplary fundamental construction and operation of a waveguide device which includes a plurality of conductive rods (artificial magnetic conductor) in a two-dimensional array will be described. 
       FIG. 1  is a perspective view schematically showing a non-limiting example of a fundamental construction of such a waveguide device.  FIG. 1  shows XYZ coordinates along X, Y and Z directions which are orthogonal to one another. The waveguide device  100  shown in the figure includes a plate-like first conductive member  110  and a plate-like second conductive member  120 , which are in opposing and parallel positions to each other. A plurality of conductive rods  124  are arrayed on the second conductive member  120 . 
     Note that any structure appearing in a figure of the present application is shown in an orientation that is selected for ease of explanation, which in no way should limit its orientation when an embodiment of the present disclosure is actually practiced. Moreover, the shape and size of a whole or a part of any structure that is shown in a figure should not limit its actual shape and size. 
       FIG. 2A  is a diagram schematically showing the construction of a cross section of the waveguide device  100  in  FIG. 1 , taken parallel to the XZ plane. As shown in  FIG. 2A , the first conductive member  110  has a conductive surface  110   a  on the side facing the second conductive member  120 . The conductive surface  110   a  has a two-dimensional expanse along a plane which is orthogonal to the axial direction (Z direction) of the conductive rods  124  (i.e., a plane which is parallel to the XY plane). Although the conductive surface  110   a  is shown to be a smooth plane in this example, the conductive surface  110   a  does not need to be a plane, as will be described later. 
       FIG. 3  is a perspective view schematically showing the waveguide device  100 , illustrated so that the spacing between the first conductive member  110  and the second conductive member  120  is exaggerated for ease of understanding. In an actual waveguide device  100 , as shown in  FIG. 1  and  FIG. 2A , the spacing between the first conductive member  110  and the second conductive member  120  is narrow, with the first conductive member  110  covering over all of the conductive rods  124  on the second conductive member  120 . 
     See  FIG. 2A  again. The plurality of conductive rods  124  arrayed on the second conductive member  120  each have a leading end  124   a  opposing the conductive surface  110   a . In the example shown in the figure, the leading ends  124   a  of the plurality of conductive rods  124  are on the same plane. This plane defines the surface  125  of an artificial magnetic conductor. Each conductive rod  124  does not need to be entirely electrically conductive; instead, at least the surface (the upper face and the side face) of the rod-like structure may be electrically conductive. Moreover, each second conductive member  120  does not need to be entirely electrically conductive, so long as it can support the plurality of conductive rods  124  to constitute an artificial magnetic conductor. Of the surfaces of the second conductive member  120 , a face  120   a  carrying the plurality of conductive rods  124  may be electrically conductive, such that the conductor interconnects the surfaces of adjacent ones of the plurality of conductive rods  124 . In other words, the entire combination of the second conductive member  120  and the plurality of conductive rods  124  may at least present a conductive surface with rises and falls opposing the conductive surface  110   a  of the first conductive member  110 . 
     On the second conductive member  120 , a ridge-like waveguide member  122  is provided among the plurality of conductive rods  124 . More specifically, stretches of an artificial magnetic conductor are present on both sides of the waveguide member  122 , such that the waveguide member  122  is sandwiched between the stretches of artificial magnetic conductor on both sides. As can be seen from  FIG. 3 , the waveguide member  122  in this example is supported on the second conductive member  120 , and extends linearly along the Y direction. In the example shown in the figure, the waveguide member  122  has the same height and width as those of the conductive rods  124 . As will be described later, however, the height and width of the waveguide member  122  may have different values from those of the conductive rod  124 . Unlike the conductive rods  124 , the waveguide member  122  extends along a direction (which in this example is the Y direction) in which to guide electromagnetic waves along the conductive surface  110   a . Similarly, the waveguide member  122  does not need to be entirely electrically conductive, but may at least include an electrically conductive waveguide face  122   a  opposing the conductive surface  110   a  of the first conductive member  110 . The second conductive member  120 , the plurality of conductive rods  124 , and the waveguide member  122  may be parts of a continuous single-piece body. Furthermore, the first conductive member  110  may also be a part of such a single-piece body. 
     On both sides of the waveguide member  122 , the space between the surface  125  of each stretch of artificial magnetic conductor and the conductive surface  110   a  of the first conductive member  110  does not allow an electromagnetic wave of any frequency that is within a specific frequency band to propagate. This frequency band is called a “prohibited band”. The artificial magnetic conductor is designed so that the frequency of a signal wave to propagate in the waveguide device  100  (which may hereinafter be referred to as the “operating frequency”) is contained in the prohibited band. The prohibited band may be adjusted based on the following: the height of the conductive rods  124 , i.e., the depth of each groove formed between adjacent conductive rods  124 ; the width of each conductive rod  124 ; the interval between conductive rods  124 ; and the size of the gap between the leading end  124   a  and the conductive surface  110   a  of each conductive rod  124 . 
     With the above structure, a signal wave can be propagated along a waveguide (ridge waveguide) extending between the conductive surface  110   a  of the first conductive member  110  and the waveguide face  122   a . Such a ridge waveguide may be referred to as a WRG (Waffle-iron Ridge waveGuide). 
     Next, with reference to  FIG. 4 , the dimensions, shape, positioning, and the like of each member will be described. 
       FIG. 4  is a diagram showing an exemplary range of dimension of each member in the structure shown in  FIG. 2A . The waveguide device is used for at least one of the transmission and the reception of an electromagnetic wave of a predetermined band (referred to as the operating frequency band). In the present specification, λo denotes a representative value of wavelengths in free space (e.g., a central wavelength corresponding to a center frequency in the operating frequency band) of an electromagnetic wave (signal wave) propagating in a waveguide extending between the conductive surface  110   a  of the first conductive member  110  and the waveguide face  122   a  of the waveguide member  122 . Moreover, λm denotes a wavelength, in free space, of an electromagnetic wave of the highest frequency in the operating frequency band. The end of each conductive rod  124  that is in contact with the second conductive member  120  is referred to as the “root”. As shown in  FIG. 4 , each conductive rod  124  has the leading end  124   a  and the root  124   b . Examples of dimensions, shapes, positioning, and the like of the respective members are as follows. 
     (1) Width of the Conductive Rod 
     The width (i.e., the size along the X direction and the Y direction) of the conductive rod  124  may be set to less than λm/2. Within this range, resonance of the lowest order can be prevented from occurring along the X direction and the Y direction. Since resonance may possibly occur not only in the X and Y directions but also in any diagonal direction in an X-Y cross section, the diagonal length of an X-Y cross section of the conductive rod  124  is also preferably less than λm/2. The lower limit values for the rod width and diagonal length will conform to the minimum lengths that are producible under the given manufacturing method, but is not particularly limited. 
     (2) Distance from the Root of the Conductive Rod to the Conductive Surface of the First Conductive Member 
     The distance from the root  124   b  of each conductive rod  124  to the conductive surface  110   a  of the first conductive member  110  may be longer than the height of the conductive rods  124 , while also being less than λm/2. When the distance is λm/2 or more, resonance may occur between the root  124   b  of each conductive rod  124  and the conductive surface  110   a , thus reducing the effect of signal wave containment. 
     The distance from the root  124   b  of each conductive rod  124  to the conductive surface  110   a  of the first conductive members  110  corresponds to the spacing between the first conductive member  110  and the second conductive member  120 . For example, when a signal wave of 76.5±0.5 GHz (which belongs to the millimeter band or the extremely high frequency band) propagates in the waveguide, the wavelength of the signal wave is in the range from 3.8934 mm to 3.9446 mm. Therefore, λm equals 3.8934 mm in this case, so that the spacing between the first conductive member  110  and the second conductive member  120  is set to less than a half of 3.8934 mm. So long as the first conductive member  110  and the second conductive member  120  realize such a narrow spacing while being disposed opposite from each other, the first conductive member  110  and the second conductive member  120  do not need to be strictly parallel. Moreover, when the spacing between the first conductive member  110  and the second conductive member  120  is less than λm/2, a whole or a part of the first conductive member  110  and/or the second conductive member  120  may be shaped as a curved surface. On the other hand, the first and second conductive members  110  and  120  each have a planar shape (i.e., the shape of their region as perpendicularly projected onto the XY plane) and a planar size (i.e., the size of their region as perpendicularly projected onto the XY plane) which may be arbitrarily designed depending on the purpose. 
     Although the conductive surface  120   a  is illustrated as a plane in the example shown in  FIG. 2A , embodiments of the present disclosure are not limited thereto. For example, as shown in  FIG. 2B , the conductive surface  120   a  may be the bottom parts of faces each of which has a cross section similar to a U-shape or a V-shape. The conductive surface  120   a  will have such a structure when each conductive rod  124  or the waveguide member  122  is shaped with a width which increases toward the root. Even with such a structure, the device shown in  FIG. 2B  can function as the waveguide device according to an embodiment of the present disclosure so long as the distance between the conductive surface  110   a  and the conductive surface  120   a  is less than a half of the wavelength λm. 
     (3) Distance L2 from the Leading End of the Conductive Rod to the Conductive Surface 
     The distance L2 from the leading end  124   a  of each conductive rod  124  to the conductive surface  110   a  is set to less than λm/2. When the distance is λm/2 or more, a propagation mode that reciprocates between the leading end  124   a  of each conductive rod  124  and the conductive surface  110   a  may occur, thus no longer being able to contain an electromagnetic wave. 
     (4) Arrangement and Shape of Conductive Rods 
     The interspace between two adjacent conductive rods  124  among the plurality of conductive rods  124  has a width of less than λm/2, for example. The width of the interspace between any two adjacent conductive rods  124  is defined by the shortest distance from the surface (side face) of one of the two conductive rods  124  to the surface (side face) of the other. This width of the interspace between rods is to be determined so that resonance of the lowest order will not occur in the regions between rods. The conditions under which resonance will occur are determined based by a combination of: the height of the conductive rods  124 ; the distance between any two adjacent conductive rods; and the capacitance of the air gap between the leading end  124   a  of each conductive rod  124  and the conductive surface  110   a . Therefore, the width of the interspace between rods may be appropriately determined depending on other design parameters. Although there is no clear lower limit to the width of the interspace between rods, for manufacturing ease, it may be e.g. λm/16 or more when an electromagnetic wave in the extremely high frequency band is to be propagated. Note that the interspace does not need to have a constant width. So long as it remains less than λm/2, the interspace between conductive rods  124  may vary. 
     The arrangement of the plurality of conductive rods  124  is not limited to the illustrated example, so long as it exhibits a function of an artificial magnetic conductor. The plurality of conductive rods  124  do not need to be arranged in orthogonal rows and columns; the rows and columns may be intersecting at angles other than 90 degrees. The plurality of conductive rods  124  do not need to form a linear array along rows or columns, but may be in a dispersed arrangement which does not present any straightforward regularity. The conductive rods  124  may also vary in shape and size depending on the position on the second conductive member  120 . 
     The surface  125  of the artificial magnetic conductor that are constituted by the leading ends  124   a  of the plurality of conductive rods  124  does not need to be a strict plane, but may be a plane with minute rises and falls, or even a curved surface. In other words, the conductive rods  124  do not need to be of uniform height, but rather the conductive rods  124  may be diverse so long as the array of conductive rods  124  is able to function as an artificial magnetic conductor. 
     Furthermore, each conductive rod  124  does not need to have a prismatic shape as shown in the figure, but may have a cylindrical shape, for example. Furthermore, each conductive rod  124  does not need to have a simple columnar shape. The artificial magnetic conductor may also be realized by any structure other than an array of conductive rods  124 , and various artificial magnetic conductors are applicable to the waveguide device of the present disclosure. Note that, when the leading end  124   a  of each conductive rod  124  has a prismatic shape, its diagonal length is preferably less than λm/2. When the leading end  124   a  of each conductive rod  124  is shaped as an ellipse, the length of its major axis is preferably less than λm/2. Even when the leading end  124   a  has any other shape, the dimension across it is preferably less than λm/2 even at the longest position. 
     (5) Width of the Waveguide Face 
     The width of the waveguide face  122   a  of the waveguide member  122 , i.e., the size of the waveguide face  122   a  along a direction which is orthogonal to the direction that the waveguide member  122  extends, may be set to less than λm/2 (e.g. λo/8). If the width of the waveguide face  122   a  is λm/2 or more, resonance will occur along the width direction, which will prevent any WRG from operating as a simple transmission line. 
     (6) Height of the Waveguide Member 
     The height (i.e., the size along the Z direction in the example shown in the figure) of the waveguide member  122  is set to less than λm/2. The reason is that, if the distance is λm/2 or more, the distance between the root  124   b  of each conductive rod  124  and the conductive surface  110   a  will be λm/2 or more. Similarly, the height of the conductive rods  124  (especially those conductive rods  124  which are adjacent to the waveguide member  122 ) is set to less than λm/2. 
     (7) Distance L1 Between the Waveguide Face and the Conductive Surface 
     The distance L1 between the waveguide face  122   a  of the waveguide member  122  and the conductive surface  110   a  is set to less than λm/2. If the distance is λm/2 or more, resonance will occur between the waveguide face  122   a  and the conductive surface  110   a , which will prevent functionality as a waveguide. In one example, the distance is λm/4 or less. In order to ensure manufacturing ease, when an electromagnetic wave in the extremely high frequency band is to propagate, it is preferably λm/16 or more, for example. 
     The lower limit of the distance L1 between the conductive surface  110   a  and the waveguide face  122   a  and the lower limit of the distance L2 between the conductive surface  110   a  and the leading end  124   a  of each rod  124  depends on the machining precision, and also on the precision when assembling the two upper/lower conductive members  110  and  120  so as to be apart by a constant distance. When a pressing technique or an injection technique is used, the practical lower limit of the aforementioned distance is about 50 micrometers (μm). In the case of using an MEMS (Micro-Electro-Mechanical System) technique to make a product in e.g. the terahertz range, the lower limit of the aforementioned distance is about 2 to about 3 μm. 
     In the waveguide device  100  of the above-described construction, a signal wave of the operating frequency is unable to propagate in the space between the surface  125  of the artificial magnetic conductor and the conductive surface  110   a  of the first conductive member  110 , but propagates in the space between the waveguide face  122   a  of the waveguide member  122  and the conductive surface  110   a  of the first conductive member  110 . Unlike in a hollow waveguide, the width of the waveguide member  122  in such a waveguide structure does not need to be equal to or greater than a half of the wavelength of the electromagnetic wave to propagate. Moreover, the first conductive member  110  and the second conductive member  120  do not need to be interconnected by a metal wall that extends along the thickness direction (i.e., in parallel to the YZ plane). 
       FIG. 5A  schematically shows an electromagnetic wave that propagates in a narrow space, i.e., a gap between the waveguide face  122   a  of the waveguide member  122  and the conductive surface  110   a  of the first conductive member  110 . Three arrows in  FIG. 5A  schematically indicate the orientation of an electric field of the propagating electromagnetic wave. The electric field of the propagating electromagnetic wave is perpendicular to the conductive surface  110   a  of the first conductive member  110  and to the waveguide face  122   a.    
     On both sides of the waveguide member  122 , stretches of artificial magnetic conductor that are created by the plurality of conductive rods  124  are present. An electromagnetic wave propagates in the gap between the waveguide face  122   a  of the waveguide member  122  and the conductive surface  110   a  of the first conductive member  110 .  FIG. 5A  is schematic, and does not accurately represent the magnitude of an electromagnetic field to be actually created by the electromagnetic wave. A part of the electromagnetic wave (electromagnetic field) propagating in the space over the waveguide face  122   a  may have a lateral expanse, to the outside (i.e., toward where the artificial magnetic conductor exists) of the space that is delineated by the width of the waveguide face  122   a . In this example, the electromagnetic wave propagates in a direction (Y direction) which is perpendicular to the plane of  FIG. 5A . As such, the waveguide member  122  does not need to extend linearly along the Y direction, but may include a bend(s) and/or a branching portion(s) not shown. Since the electromagnetic wave propagates along the waveguide face  122   a  of the waveguide member  122 , the direction of propagation would change at a bend, whereas the direction of propagation would ramify into plural directions at a branching portion. 
     In the waveguide structure of  FIG. 5A , no metal wall (electric wall), which would be indispensable to a hollow waveguide, exists on both sides of the propagating electromagnetic wave. Therefore, in the waveguide structure of this example, “a constraint due to a metal wall (electric wall)” is not included in the boundary conditions for the electromagnetic field mode to be created by the propagating electromagnetic wave, and the width (size along the X direction) of the waveguide face  122   a  is less than a half of the wavelength of the electromagnetic wave. 
     For reference,  FIG. 5B  schematically shows a cross section of a hollow waveguide  130 . With arrows,  FIG. 5B  schematically shows the orientation of an electric field of an electromagnetic field mode (TE 10 ) that is created in the internal space  132  of the hollow waveguide  130 . The lengths of the arrows correspond to electric field intensities. The width of the internal space  132  of the hollow waveguide  130  needs to be set to be broader than a half of the wavelength. In other words, the width of the internal space  132  of the hollow waveguide  130  cannot be set to be smaller than a half of the wavelength of the propagating electromagnetic wave. 
       FIG. 5C  is a cross-sectional view showing an implementation where two waveguide members  122  are proved on the second conductive member  120 . Thus, an artificial magnetic conductor that is created by the plurality of conductive rods  124  exists between the two adjacent waveguide members  122 . More accurately, stretches of artificial magnetic conductor created by the plurality of conductive rods  124  are present on both sides of each waveguide member  122 , such that each waveguide member  122  is able to independently propagate an electromagnetic wave. 
     For reference&#39;s sake,  FIG. 5D  schematically shows a cross section of a waveguide device in which two hollow waveguides  130  are placed side-by-side. The two hollow waveguides  130  are electrically insulated from each other. Each space in which an electromagnetic wave is to propagate needs to be surrounded by a metal wall that defines the respective hollow waveguide  130 . Therefore, the interval between the internal spaces  132  in which electromagnetic waves are to propagate cannot be made smaller than a total of the thicknesses of two metal walls. Usually, a total of the thicknesses of two metal walls is longer than a half of the wavelength of a propagating electromagnetic wave. Therefore, it is difficult for the interval between the hollow waveguides  130  (i.e., interval between their centers) to be shorter than the wavelength of a propagating electromagnetic wave. Particularly for electromagnetic waves of wavelengths in the extremely high frequency band (i.e., electromagnetic wave wavelength: 10 mm or less) or even shorter wavelengths, a metal wall which is sufficiently thin relative to the wavelength is difficult to be formed. This presents a cost problem in commercially practical implementation. 
     On the other hand, a waveguide device  100  including an artificial magnetic conductor can easily realize a structure in which waveguide members  122  are placed close to one another. Thus, such a waveguide device  100  can be suitably used in an array antenna that includes plural antenna elements in a close arrangement. 
     In order to enhance the degree of impedance matching at a bend(s) and a branching portion(s) of a waveguide member  122 , the inventors have paid attention to the conductive rods  124  constituting an artificial magnetic conductor. Then, as will be described below in detail, the inventors have succeeded in enhancing the degree of impedance matching at a bend(s) and a branching portion(s) of a waveguide member  122  by improving the shape of the conductive rods  124 . With an enhanced degree of impedance matching, a waveguide device having an improved propagation efficiency and less noise can be provided. It also allows to enhance the performance of an antenna device that includes such a waveguide device. More specifically, signal wave reflection is reduced through impedance matching, whereby power loss can be reduced, and in an antenna device, disorder in the phase of the electromagnetic wave to be transmitted or received can be reduced. Therefore, in communications, deteriorations in a communication signal can be suppressed; in a radar, precision of distance or azimuth-of-arrival estimation can be improved. 
     Hereinafter, a non-limiting and illustrative embodiment of a waveguide device according to the present disclosure will be described. 
     &lt;Fundamental Construction of the Waveguide Device&gt; 
     First, see  FIGS. 6 and 7 .  FIG. 6  is a perspective view schematically showing an exemplary construction for a waveguide device according to the present embodiment. For ease of understanding,  FIG. 6  exaggerates the spacing between the first electrically conductive member  110  and the second electrically conductive member  120 .  FIG. 7  is a diagram schematically showing the construction of the waveguide device  100  in a cross section taken parallel to the XZ plane. 
     As shown in  FIGS. 6 and 7 , the waveguide device  100  of the present embodiment includes: a first electrically conductive member  110  having an electrically conductive surface  110   a  which is shaped as a plane; a second electrically conductive member  120  having a plurality of electrically conductive rods  124  arrayed thereon, each having a leading end  124   a  opposing the conductive surface  110   a ; and a waveguide member  122  having an electrically conductive waveguide face  122   a  opposing the conductive surface  110   a  of the first conductive member  110 . The waveguide member  122 , which extends along the conductive surface  110   a , is provided among the plurality of conductive rods  124 . Stretches of an artificial magnetic conductor composed of the plurality of conductive rods  124  are present on both sides of the waveguide member  122 , such that the waveguide member  122  is sandwiched between the stretches of artificial magnetic conductor on both sides. In the present embodiment, the waveguide member  122  includes a branching portion  136  at which the direction that the waveguide member  122  extends ramifies into two or more directions. At the branching portion  136  in this example, the two branched waveguide members constitute an angle of 180 degrees, thus resulting in a shape resembling the letter “T”; hence, it may also be called a “T-branching”. Another example of the branching portion  136  is a “Y-branching”, where the two branched waveguide members extend in directions which are apart by an angle smaller than 180 degrees. 
     As described earlier, the plurality of conductive rods  124  arrayed on the second conductive member  120  each have a leading end  124   a  opposing the conductive surface  110   a . In the example shown in the figure, the leading ends  124   a  of the conductive rods  124  are on substantially the same plane, thus defining the surface  125  of the artificial magnetic conductor. 
     &lt;Fundamental Structure of Conductive Rods&gt; 
     Branching Portion 
     In the present embodiment, as shown in  FIG. 7 , the side faces of each conductive rod  124  are tilted so that a measure of the outer shape of a cross section of each conductive rod  124  taken perpendicular to the axial direction (Z direction) monotonically decreases from the root  124   b  toward the leading end  124   a . This enhances the degree of impedance matching at the branching portion  136  of the waveguide member  122 , as has been made clear by an electromagnetic field simulation. 
       FIG. 8A  is a cross-sectional view of a conductive rod  124  in a plane containing the axial direction (Z direction).  FIG. 8B  is an upper plan view of the conductive rod  124  of  FIG. 8A  as viewed in the axial direction (Z direction). In this example, each conductive rod  124  has a frustum shape with square cross sections perpendicular to the axial direction (Z direction), such that the four side faces  124   s  of the conductive rod  124  are tilted with respect to the axial direction (Z direction). As shown in  FIG. 8A , the angle of tilt of each side face  124   s  of each conductive rod is defined by an angle  9 , which the normal  124   n  of the side face  124   s  constitutes with an arbitrary plane Pz that is orthogonal to the axial direction (Z direction). 
     The “measure of the outer shape of a cross section of the conductive rod taken perpendicular to the axial direction” is defined by the diameter of a smallest circle that is capable of containing the “outer shape of a cross section” inside. Such a circle will be a circumcircle in the case where the outer shape of a cross section is a triangle, a rectangle (including a square), or a regular polygon. In the case where the “outer shape of a cross section” is a circle or an ellipse, the “measure of the outer shape of a cross section” is the diameter of the circle or the length of the major axis of the ellipse. In the present disclosure, the “outer shape of a cross section” of a conductive rod is not limited to a shape for which a circumcircle exists. In the example shown in  FIGS. 8A and 8B , the measure of the outer shape of a cross section of each conductive rod  124  taken perpendicular to the axial direction decreases from the root  124   b  of the conductive rod  124  toward the leading end  124   a.    
     In the example shown in  FIGS. 8A and 8B , the area of a cross section taken perpendicular to the axial direction of the conductive rod  124  is smaller at the leading end  124   a  than at the root  124   b . As described earlier, each conductive rod  124  does not need to be entirely electrically conductive, but only the surface may be electrically conductive. Therefore, the conductive rod  124  may have a hollow structure, or include a dielectric core inside. The “area of a cross section of the conductive rod taken perpendicular to the axial direction” means the area of a region which is delineated from the exterior by the contour line of the “outer shape” of a cross section of the conductive rod taken perpendicular to the axial direction. Even if a non-electrically conductive portion is included within that region, it is irrelevant to the “area of the cross section”. 
     Hereinafter, it will be described how use of such conductive rods  124  improves the degree of impedance matching. 
     The inventors have made it clear through a simulation that the construction according to the present embodiment provides an improved degree of impedance matching over the conventional construction in which the side faces of each conductive rod  124  are not tilted. Herein, the degree of impedance matching is represented by an input reflection coefficient. The lower the input reflection coefficient is, the higher the degree of impedance matching is. The input reflection coefficient is a coefficient which represents a ratio of the intensity of a reflected wave to the intensity of an input wave which is incoming to a radio frequency line or an element. 
       FIGS. 9A through 9D  are diagrams showing the construction of a waveguide device used in this simulation.  FIG. 9A  is a perspective view schematically showing a conventional construction in which the side faces of each conductive rod  124  are not tilted.  FIG. 9B  is an upper plan view of the waveguide device shown in  FIG. 9A .  FIG. 9C  is a perspective view schematically showing a construction according to the present embodiment where the side faces of each conductive rod  124  are tilted.  FIG. 9D  is an upper plan view of the waveguide device shown in  FIG. 9C . 
     In this simulation, an input reflection coefficient S of the branching portion was measured with respect to a number of constructions in which the four side faces of each conductive rod  124  had different angles of tilt. In this simulation, given a frequency Fo of 74.9475 GHz, an electromagnetic wave (also referred to as an “input wave”) in a frequency band centered around Fo was measured. Given a wavelength λo in free space that corresponds to Fo, an average width of each conductive rod, an average width of interspaces between rods, and the width of the waveguide member (ridge) were λo/8, while the height of each rod and the ridge was λo/4. The input wave was allowed to be incident in the orientation of an arrow shown in  FIG. 9D  and  FIG. 9B . 
       FIG. 10  is a graph showing results of this simulation. The graph of  FIG. 10  shows an input reflection coefficient S (dB) for an input wave at frequencies of 0.967 Fo, 1.000 Fo and 1.033 Fo, in the respective cases where the angle of tilt θ is 0°, 1°, 2°, 3°, 4° and 5°. 
     It can be seen from  FIG. 10  that, irrespective of the frequency of the input wave, the input reflection coefficient S becomes lower as the side faces of each conductive rod  124  are tilted. In other words, it was confirmed that the construction of the present embodiment improves the degree of impedance matching. 
     Bend 
     The aforementioned effect is also achieved in the case where the waveguide member  122  includes a bend(s). A bend is a portion where a change occurs in the direction that the waveguide member  122  extends. A bend is inclusive of any portion where the direction that the waveguide member  122  extends undergoes a drastic change, a gentle change, or meanders. 
     See  FIG. 11 .  FIG. 11  is a perspective view schematically showing another exemplary construction of a waveguide device according to the present embodiment. For ease of understanding, the first conductive member  110  is omitted from illustration in  FIG. 11 . 
     The waveguide device shown in the figure includes two waveguide members  122 , where one of the waveguide member  122  includes a bend  138 . 
     By using conductive rods  124  with tilted side faces, the degree of impedance matching can also be improved at the bend  138 . This will be described below. 
     The inventors have conducted a simulation, through which it has been made clear that a construction including a bend also improves the degree of impedance matching over that of the conventional construction in which the side faces of each conductive rod  124  are not tilted. Hereinafter, results of this simulation will be described. 
       FIGS. 12A through 12D  are diagrams showing the construction of a waveguide device used in this simulation.  FIG. 12A  is a perspective view schematically showing a conventional construction in which the side faces of each conductive rod  124  are not tilted.  FIG. 12B  is an upper plan view of the waveguide device shown in  FIG. 12A .  FIG. 12C  is a perspective view schematically showing a construction according to the present embodiment where the side faces of each conductive rod  124  are tilted.  FIG. 12D  is an upper plan view of the waveguide device shown in  FIG. 12C . In this simulation, the input wave is allowed to be incident in the orientation of an arrow shown in  FIG. 12B  and  FIG. 12D , and an input reflection coefficient at the bend was measured. Otherwise, the simulation conditions were similar to the conditions in the earlier-mentioned simulation. 
       FIG. 13  is a graph showing results of this simulation. The graph of  FIG. 13  shows an input reflection coefficient S (dB) for an input wave at frequencies of 0.967 Fo, 1.000 Fo and 1.033 Fo, in the respective cases where the angle of tilt θ is 0°, 1°, 2°, 3°, 4° and 5°. 
     It can be seen from  FIG. 13  that, irrespective of the frequency of the input wave, the input reflection coefficient S becomes lower as the side faces of each conductive rod  124  are tilted. In other words, it was confirmed that the construction of the present embodiment improves the degree of impedance matching. 
     Note that a branching portion and a bend may both be included in one waveguide member  122 . For example, the waveguide member  122  may feature a structure combining a branching portion and a bend. Moreover, the shape (e.g., height or width) of the waveguide member  122  may undergo a local change(s) in a conventional manner, at a position near a branching portion or a bend. By thus introducing local changes in the shape of the waveguide member  122 , a further improvement in the degree of impedance matching can be attained, in combination with the effect of the conductive rods  124  of the waveguide device according to the present disclosure. 
     &lt;Other Structures for Conductive Rods&gt; 
     Next, examples of other shapes for the conductive rods that can provide the effect according to the present disclosure will be described. 
     First, see  FIGS. 14A and 14B .  FIG. 14A  is a graph showing an example of expressing a measure D of the outer shape of a cross section of a conductive rod  124  taken perpendicular to the axial direction (Z direction), as a function D(z) of distance z of the conductive rod  124  from its root  124   b . The distance z is to be measured from the root  124   b  of each conductive rod  124 , in parallel to the axial direction (Z direction) of the conductive rod  124 . 
       FIG. 14A  shows an example of a function D(z) concerning the conductive rods  124  as mentioned above. In  FIG. 14A , the letter “h” means the height (i.e., size along the axial direction) of the conductive rod. D(z) has a gradient corresponding to the tilt of a side face  124   s  of each conductive rod  124 . While the gradient of D(z) in the earlier-described embodiment was uniform in each conductive rod  124 , the waveguide device according to the present disclosure is not limited to such an example. The aforementioned effect will be obtained so long as D(z) monotonically decreases in response to increasing z. 
     In the present application, the feature that “a measure of the outer shape of a cross section of a conductive rod taken perpendicular to the axial direction monotonically decreases from its root that is in contact with the second conductive member toward its leading end” means that D(z1)≥D(z2) and D(0)&gt;D(h) hold true for any arbitrary z1 and z2 that satisfies 0&lt;z1&lt;z2&lt;h. As indicated by the sign “≥” consisting of an inequality sign and an equality sign, the conductive rod may have a portion whose D(z) does not change in magnitude even if z increases.  FIG. 14B  represents an example where, within a specific range of z, D(z) does not change in magnitude even if z increases. The aforementioned effect can also be obtained with a conductive rod having such outer dimensions. 
       FIG. 15A  is a cross-sectional view of a conductive rod  124  in a plane containing the axial direction (Z direction) in another example.  FIG. 15B  is an upper plan view of the conductive rod  124  of  FIG. 15A  as viewed in the axial direction (Z direction). In this example, the outer shape of a cross section of the conductive rod  124  taken perpendicular to the axial direction is a circle. The “outer shape of a cross section” may also be an ellipse. In the case where the outer shape of a cross section is a circle, the “measure of the outer shape of a cross section of the conductive rod taken perpendicular to the axial direction” is equal to the diameter of the circle. In the case where the outer shape of a cross section is an ellipse, the “measure of the outer shape of a cross section of the conductive rod taken perpendicular to the axial direction” is equal to the length of the major axis of ellipse. 
     Thus, even when “a cross section of the conductive rod taken perpendicular to the axial direction” has a shape other than a square, the degree of impedance matching at a branching portion(s) and a bend(s) can be enhanced by tilting its side faces. 
     Note that the leading end  124   a  of each conductive rod  124  does not need to be a plane; as in the example shown in  FIGS. 16A and 16B , it may also be a curved surface. 
       FIGS. 17A, 17B and 17C  are diagrams showing another exemplary shape of a conductive rod  124 .  FIG. 17A  shows a cross section of a conductive rod  124  taken parallel to the XZ plane;  FIG. 17B  shows a cross section of the conductive rod  124  taken parallel to the YZ plane; and  FIG. 17C  shows a cross section of the conductive rod  124  taken parallel to the XY plane. In this example, the outer shape of a cross section of the conductive rod  124  taken perpendicular to the axial direction is a rectangle, as shown in  FIG. 17C . As shown in  FIGS. 17A and 17B , among the four side faces  124   sa ,  124   sb ,  124   sc  and  124   sd  of the conductive rod  124  in this example, only the faces  124   sc  and  124   sd  are tilted; the other side faces  124   sa  and  124   sb  are not tilted. 
       FIG. 18A  is a cross-sectional view of a conductive rod  124  in a plane containing the axial direction (Z direction) in still another example.  FIG. 18B  is an upper plan view of the conductive rod  124  of  FIG. 18A  as viewed in the axial direction (Z direction). The conductive rod  124  in this example has a stepped shape. A measure of “a cross section of the conductive rod taken perpendicular to the axial direction” undergoes drastic changes locally. In the meaning of the present application, such a shape also satisfies the feature that “a measure of the outer shape of a cross section of a conductive rod taken perpendicular to the axial direction monotonically decreases from its root that is in contact with the second conductive member toward its leading end”. 
     In the above embodiment, the plurality of conductive rods  124  that are arrayed on the second conductive member  120  are of an identical shape. However, the waveguide device according to the present disclosure is not limited to such examples. The plurality of conductive rods  124  composing an artificial magnetic conductor may be of different shapes and/or sizes from one another. Moreover, as shown in  FIG. 19 , the earlier-described characteristic shape may be imparted to only those conductive rods  124  which are adjacent to the waveguide member  122 . Moreover, a shape which is identical to that of a conventional conductive rod may be imparted to those conductive rods which are in any position that does not affect the degree of impedance matching at a branching portion or a bend of the waveguide member  122 , while the earlier-described characteristic shape may be imparted only to those conductive rods which are in any position that affects the degree of impedance matching at a branching portion or a bend. Specifically, it suffices so long as a measure of the outer shape of a cross section of “a conductive rod that is adjacent to a branching portion or a bend” of the waveguide member  122 , taken perpendicular to the axial direction, monotonically decreases from its root toward its leading end. As used herein, “a conductive rod that is adjacent to a branching portion or a bend” is defined, when there is no other intervening conductive rod between a conductive rod of interest and “a branching portion or a bend”, to be that “conductive rod of interest”. 
     &lt;Antenna Device&gt; 
     Hereinafter, a non-limiting and illustrative embodiment of an antenna device including a waveguide device according to the present disclosure will be described. 
       FIG. 20A  is an upper plan view of an antenna device (array antenna) including 16 slots (openings)  112  in an array of 4 rows and 4 columns, as viewed in the Z direction.  FIG. 20B  is a cross-sectional view taken along line B-B in  FIG. 20A . In the antenna device shown in the figures, a first waveguide device  100   a  and a second waveguide device  100   b  are layered. The first waveguide device  100   a  includes waveguide members  122 U that directly couple to slots  112  functioning as radiation elements (antenna elements). The second waveguide device  100   b  includes further waveguide members  122 L that couple to the waveguide members  122 U of the first waveguide device  100   a . The waveguide members  122 L and the conductive rods  124 L of the second waveguide device  100   b  are arranged on a third conductive member  140 . The second waveguide device  100   b  is basically similar in construction to the first waveguide device  100   a.    
     On the first conductive member  110  in the first waveguide device  100   a , side walls  114  surrounding each slot  112  are provided. The side walls  114  form a horn that adjusts directivity of the slot  112 . The number and arrangement of slots  112  in this example are only illustrative. The orientations and shapes of the slots  112  are not limited to those of the example shown in the figures, either. It is not intended that the example shown in the figures provides any limitation as to whether the side walls  114  of each horn are tilted or not, the angles thereof, or the shape of each horn. 
       FIG. 21  is a diagram showing a planar layout of waveguide members  122 U in the first waveguide device  100   a .  FIG. 22  is a diagram showing a planar layout of a waveguide member  122 L in the second waveguide device  100   b . As is clear from these figures, the waveguide members  122 U of the first waveguide device  100   a  extend linearly, and include no branching portions or bends; on the other hand, the waveguide members  122 L of the second waveguide device  100   b  include both branching portions and bends. In terms of fundamental construction of the waveguide device, the combination of the “second conductive member  120 ” and the “third conductive member  140 ” in the second waveguide device  100   b  corresponds to the combination in the first waveguide device  100   a  of the “first conductive member  110 ” and the “second conductive member  120 ”. 
     What is characteristic in the array antenna shown in the figures is that each conductive rod  124 L has a shape as shown in  FIGS. 8A and 8B . As a result, the degree of impedance matching is improved at the branching portions and the bends of the waveguide members  122 L. 
     Note that the shape of the conductive rods  124 L is not limited to the example shown in  FIGS. 8A and 8B . As mentioned earlier, the shapes, sizes, and array patterns of the conductive rods  124 L may be various. 
     See  FIGS. 21 and 22  again. The waveguide members  122 U of the first waveguide device  100   a  couple to the waveguide member  122 L of the second waveguide device  100   b , through ports (openings)  145 U that are provided in the second conductive member  120 . Stated otherwise, an electromagnetic wave which has propagated through the waveguide member  122 L of the second waveguide device  100   b  passes through a port  145 U to reach a waveguide member  122 U of the first waveguide device  100   a , and propagates through the waveguide member  122 U of the first waveguide device  100   a . In this case, each slot  112  functions as an antenna element to allow an electromagnetic wave which has propagated through the waveguide to be emitted into space. Conversely, when an electromagnetic wave which has propagated in space impinges on a slot  112 , the electromagnetic wave couples to the waveguide member  122 U of the first waveguide device  100   a  that lies directly under that slot  112 , and propagates through the waveguide member  122 U of the first waveguide device  100   a . An electromagnetic wave which has propagated through a waveguide member  122 U of the first waveguide device  100   a  may also pass through a port  145 U to reach the waveguide member  122 L of the second waveguide device  100   b , and propagates through the waveguide member  122 L of the second waveguide device  100   b . Via a port  145 L of the third conductive member  140 , the waveguide member  122 L of the second waveguide device  100   b  may couple to an external waveguide device or radio frequency circuit (electronic circuit). As one example,  FIG. 22  illustrates an electronic circuit  200  which is connected to the port  145 L. Without being limited to a specific position, the electronic circuit  200  may be provided at any arbitrary position. The electronic circuit  200  may be provided on a circuit board which is on the rear surface side (i.e., the lower side in  FIG. 20B ) of the third conductive member  140 , for example. Such an electronic circuit may be an MMIC (Monolithic Microwave Integrated Circuit) that generates millimeter waves, for example. 
     The first conductive member  110  shown in  FIG. 20A  may be called an “emission layer”. Moreover, the entirety of the second conductive member  120 , the waveguide members  122 U, and the conductive rods  124 U shown in  FIG. 21  may be called an “excitation layer”, whereas the entirety of the third conductive member  140 , the waveguide member  122 L, and the conductive rods  124 L shown in  FIG. 22  may be called a “distribution layer”. Moreover, the “excitation layer” and the “distribution layer” may be collectively called a “feeding layer”. Each of the “emission layer”, the “excitation layer”, and the “distribution layer” can be mass-produced by processing a single metal plate. 
     In the array antenna of this example, as can be seen from  FIG. 20B , an emission layer, an excitation layer, and a distribution layer are layered, which are in plate form; therefore, a flat and low-profile flat panel antenna is realized as a whole. For example, the height (thickness) of a multilayer structure having a cross-sectional construction as shown in  FIG. 20B  can be set to 10 mm or less. 
     With the waveguide member  122 L shown in  FIG. 22 , the distances from the port  145 L of the third conductive member  140  to the respective ports  145 U (see  FIG. 21 ) of the second conductive member  120  measured along the waveguide member  122 L are all set to an identical value. Therefore, a signal wave which is input to the waveguide member  122 L reaches the four ports  145 U of the second conductive member  120  all in the same phase, from the port  145 L of the third conductive member  140 . As a result, the four waveguide members  122 U on the second conductive member  120  can be excited in the same phase. 
     It is not necessary for all slots  112  functioning as antenna elements to emit electromagnetic waves in the same phase. The network patterns of the waveguide members  122 U and  122 L in the excitation layer and the distribution layer may be arbitrary, and they may be arranged so that the respective waveguide members  122 U and  122 L independently propagate different signals. 
     Although the waveguide members  122 U of the first waveguide device  100   a  in this example include neither a branching portion nor a bend, the waveguide device functioning as an excitation layer may also include a waveguide member having at least one of a branching portion and a bend. As mentioned earlier, it is not necessary for all conductive rods in the waveguide device to be similar in shape. 
     &lt;Other Variants&gt; 
     Next, variants of the waveguide member  122 , the conductive members  110  and  120 , and the conductive rods  124  will be described. 
       FIG. 23A  is a cross-sectional view showing an exemplary structure where only a waveguide face  122   a , defining an upper face of the waveguide member  122 , is electrically conductive, while any portion of the waveguide member  122  other than the waveguide face  122   a  is not electrically conductive. Similarly, the first conductive member  110  and the second conductive member  120  are electrically conductive only at their surface (conductive surface  110   a ,  120   a ) that carries or faces the waveguide member  122 , but not in any other portion. Thus, each of the waveguide member  122 , the first conductive member  110 , and the second conductive member  120  does not need to be entirely electrically conductive. 
       FIG. 23B  is a diagram showing a variant in which the waveguide member  122  is not formed on the second conductive member  120 . In this example, the waveguide member  122  is fixed to a supporting member (e.g., a wall in the outer periphery of the housing) that supports the first conductive member  110  and the second conductive member  120 . A gap exists between the waveguide member  122  and the second conductive member  120 . Thus, the waveguide member  122  does not need to be connected to the second conductive member  120 . 
       FIG. 23C  is a diagram showing an exemplary structure where the second conductive member  120 , the waveguide member  122 , and each of the plurality of conductive rods  124  are composed of a dielectric surface that is coated with an electrically conductive material such as a metal. The second conductive member  120 , the waveguide member  122 , and the plurality of conductive rods  124  are connected to one another via a conductor. On the other hand, the first conductive member  110  is composed of an electrically conductive material such as a metal. 
       FIGS. 23D and 23E  are diagrams showing example structures in which dielectric layers  110   b  and  120   b  are respectively provided on the outermost surfaces of conductive members  110  and  120 , a waveguide member  122 , and conductive rods  124 .  FIG. 23D  shows an example structure where the surface of metal conductive members, which are conductors, are covered with a dielectric layer.  FIG. 23E  shows an example where the conductive member  120  is structured so that the surface of members which are composed of a dielectric, e.g., resin, is covered with a conductor such as a metal, this metal layer being further covered with a dielectric layer. The dielectric layer that covers the metal surface may be a coating of resin or the like, or an oxide film of passivation coating or the like which is generated as the metal becomes oxidized. 
     The dielectric layer on the outermost surface will allow losses to be increased in the electromagnetic wave propagating through the WRG waveguide, but is able to protect the conductive surfaces  110   a  and  120   a  (which are electrically conductive) from corrosion. Moreover, even if a conductor line to carry a DC voltage, or an AC voltage of such a low frequency that it is not capable of propagation on certain WRG waveguides, may exist in places that may come in contact with the conductive rods  124 , short-circuiting can be prevented. 
       FIG. 23F  is a diagram showing an example where the height of the waveguide member  122  is lower than the height of the conductive rods  124  and the conductive surface  110   a  of the first conductive member  110  protrudes toward the waveguide member  122 . Even such a structure will operate in a similar manner to the above-described embodiment, so long as the ranges of dimensions depicted in  FIG. 4  are satisfied. 
       FIG. 24A  is a diagram showing an example where the conductive surface  110   a  of the first conductive member  110  is shaped as a curved surface.  FIG. 24B  is a diagram showing an example where also a conductive surface  120   a  of the second conductive member  120  is shaped as a curved surface. As demonstrated by these examples, the conductive surface(s)  110   a ,  120   a  may not be shaped as a plane(s), but may shaped as a curved surface(s). 
     Application Example: Onboard Radar System 
     Next, as an Application Example of utilizing the above-described array antenna, an instance of an onboard radar system including an array antenna will be described. A transmission wave used in an onboard radar system may have a frequency of e.g. 76 gigahertz (GHz) band, which will have a wavelength λo of about 4 mm in free space. 
     In safety technology of automobiles, e.g., collision avoidance systems or automated driving, it is particularly essential to identify one or more vehicles (targets) that are traveling ahead of the driver&#39;s vehicle. As a method of identifying vehicles, techniques of estimating the directions of arriving waves by using a radar system have been under development. 
       FIG. 25  shows a driver&#39;s vehicle  500 , and a preceding vehicle  502  that is traveling in the same lane as the driver&#39;s vehicle  500 . The driver&#39;s vehicle  500  includes an onboard radar system which incorporates an array antenna according to the above-described embodiment. When the onboard radar system of the driver&#39;s vehicle  500  emits a radio frequency transmission signal, the transmission signal reaches the preceding vehicle  502  and is reflected therefrom, so that a part of the signal returns to the driver&#39;s vehicle  500 . The onboard radar system receives this signal to calculate a position of the preceding vehicle  502 , a distance (“range”) to the preceding vehicle  502 , velocity, etc. 
       FIG. 26  shows the onboard radar system  510  of the driver&#39;s vehicle  500 . The onboard radar system  510  is provided within the vehicle. More specifically, the onboard radar system  510  is disposed on a face of the rearview mirror that is opposite to its specular surface. From within the vehicle, the onboard radar system  510  emits a radio frequency transmission signal in the direction of travel of the vehicle  500 , and receives a signal(s) which arrives from the direction of travel. 
     The onboard radar system  510  of this Application Example includes an array antenna according to the above embodiment. In the Application Example, it is arranged so that the direction that each of the plurality of waveguide members extends coincides with the vertical direction, and that the direction in which the plurality of waveguide members are arrayed coincides with the horizontal direction. As a result, the lateral dimension of the plurality of slots as viewed from the front can be reduced. Exemplary dimensions of an antenna device including the above array antenna may be 60 mm (wide)×30 mm (long)×10 mm (deep). It will be appreciated that this is a very small size for a millimeter wave radar system of the 76 GHz band. 
     Note that many a conventional onboard radar system is provided outside the vehicle, e.g., at the tip of the front nose. The reason is that the onboard radar system is relatively large in size, and thus is difficult to be provided within the vehicle as in the present disclosure. Note that the onboard radar system  510  of this Application Example may be mounted at the tip of the front nose. Since the footprint of the onboard radar system on the front nose is reduced, other parts can be more easily placed. 
     The Application Example allows the interval between a plurality of waveguide members (ridges) that are used in the transmission antenna to be narrow, which also narrows the interval between a plurality of slots to be provided opposite from a number of adjacent waveguide members. This reduces the influences of grating lobes. For example, when the interval between the centers of two laterally adjacent slots is less than the wavelength λo of the transmission wave (i.e., less than about 4 mm), no grating lobes will occur frontward. As a result, influences of grating lobes are reduced. Note that grating lobes will occur when the interval at which the antenna elements are arrayed is greater than a half of the wavelength of an electromagnetic wave. If the interval at which the antenna elements are arrayed is less than the wavelength, no grating lobes will occur frontward. Therefore, in the case where each antenna element composing an array antenna is only frontward-sensitive, as in the Application Example, grating lobes will exert substantially no influences so long as the interval at which the antenna elements are arrayed is smaller than the wavelength. By adjusting the array factor of the transmission antenna, the directivity of the transmission antenna can be adjusted. A phase shifter may be provided so as to be able to individually adjust the phases of electromagnetic waves that are transmitted on plural waveguide members. By providing a phase shifter, the directivity of the transmission antenna can be changed in any desired direction. Since the construction of a phase shifter is well-known, description thereof will be omitted. 
     A reception antenna according to the Application Example is able to reduce unwanted reception of reflected waves associated with grating lobes, thereby being able to improve the precision of the below-described processing. Hereinafter, an example of a reception process will be described. 
       FIG. 27A  shows a relationship between an array antenna AA of the onboard radar system  510  and plural arriving waves k (k: an integer from 1 to K; the same will always apply below. K is the number of targets that are present in different azimuths). The array antenna AA includes M antenna elements in a linear array. Principlewise, an antenna can be used for both transmission and reception, and therefore the array antenna AA can be used for both a transmission antenna and a reception antenna. Hereinafter, an example method of processing an arriving wave which is received by the reception antenna will be described. 
     The array antenna AA receives plural arriving waves that simultaneously impinge at various angles. Some of the plural arriving waves may be arriving waves which have been emitted from the transmission antenna of the same onboard radar system  510  and reflected by a target(s). Furthermore, some of the plural arriving waves may be direct or indirect arriving waves that have been emitted from other vehicles. 
     The incident angle of each arriving wave (i.e., an angle representing its direction of arrival) is an angle with respect to the broadside B of the array antenna AA. The incident angle of an arriving wave represents an angle with respect to a direction which is perpendicular to the direction of the line along which antenna elements are arrayed. 
     Now, consider a k th  arriving wave. Where K arriving waves are impinging on the array antenna from K targets existing at different azimuths, a “k th  arriving wave” means an arriving wave which is identified by an incident angle θ k . 
       FIG. 27B  shows the array antenna AA receiving the k th  arriving wave. The signals received by the array antenna AA can be expressed as a “vector” having M elements, by eq. 1.
 
 S =[ s   1   ,s   2   , . . . ,s   M ] T   (eq. 1)
 
     In the above, s m  (where m is an integer from 1 to M; the same will also be true hereinbelow) is the value of a signal which is received by an m th  antenna element. The superscript  T  means transposition. S is a column vector. The column vector S is defined by a product of multiplication between a direction vector (referred to as a steering vector or a mode vector) as determined by the construction of the array antenna and a complex vector representing a signal from each target (also referred to as a wave source or a signal source). When the number of wave sources is K, the waves of signals arriving at each individual antenna element from the respective K wave sources are linearly superposed. In this state, s m  can be expressed by eq. 2. 
     
       
         
           
             
               
                 
                   
                     s 
                     m 
                   
                   = 
                   
                     
                       ∑ 
                       
                         k 
                         = 
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                   [ 
                   
                     eq 
                     . 
                     
                         
                     
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                     2 
                   
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     In eq. 2, a k , θ k  and ϕ k  respectively denote the amplitude, incident angle, and initial phase of the k th  arriving wave. Moreover, λ denotes the wavelength of an arriving wave, and j is an imaginary unit. 
     As will be understood from eq. 2, s m  is expressed as a complex number consisting of a real part (Re) and an imaginary part (Im). 
     When this is further generalized by taking noise (internal noise or thermal noise) into consideration, the array reception signal X can be expressed as eq. 3.
 
 X=S+N   (eq. 3)
 
     N is a vector expression of noise. 
     The signal processing circuit generates a spatial covariance matrix Rxx (eq. 4) of arriving waves by using the array reception signal X expressed by eq. 3, and further determines eigenvalues of the spatial covariance matrix Rxx. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           R 
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                                   Rxx 
                                   11 
                                 
                               
                               
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     In the above, the superscript  H  means complex conjugate transposition (Hermitian conjugate). 
     Among the eigenvalues, the number of eigenvalues which have values equal to or greater than a predetermined value that is defined based on thermal noise (signal space eigenvalues) corresponds to the number of arriving waves. Then, angles that produce the highest likelihood as to the directions of arrival of reflected waves (i.e. maximum likelihood) are calculated, whereby the number of targets and the angles at which the respective targets are present can be identified. This process is known as a maximum likelihood estimation technique. 
     Next, see  FIG. 28 .  FIG. 28  is a block diagram showing an exemplary fundamental construction of a vehicle travel controlling apparatus  600  according to the present disclosure. The vehicle travel controlling apparatus  600  shown in  FIG. 28  includes a radar system  510  which is mounted in a vehicle, and a travel assistance electronic control apparatus  520  which is connected to the radar system  510 . The radar system  510  includes an array antenna AA and a radar signal processing apparatus  530 . 
     The array antenna AA includes a plurality of antenna elements, each of which outputs a reception signal in response to one or plural arriving waves. As mentioned earlier, the array antenna AA is capable of emitting a millimeter wave of a high frequency. 
     In the radar system  510 , the array antenna AA needs to be attached to the vehicle, while at least some of the functions of the radar signal processing apparatus  530  may be implemented by a computer  550  and a database  552  which are provided externally to the vehicle travel controlling apparatus  600  (e.g., outside of the driver&#39;s vehicle). In that case, the portions of the radar signal processing apparatus  530  that are located within the vehicle may be perpetually or occasionally connected to the computer  550  and database  552  external to the vehicle so that bidirectional communications of signal or data are possible. The communications are to be performed via a communication device  540  of the vehicle and a commonly-available communications network. 
     The database  552  may store a program which defines various signal processing algorithms. The content of the data and program needed for the operation of the radar system  510  may be externally updated via the communication device  540 . Thus, at least some of the functions of the radar system  510  can be realized externally to the driver&#39;s vehicle (which is inclusive of the interior of another vehicle), by a cloud computing technique. Therefore, an “onboard” radar system in the meaning of the present disclosure does not require that all of its constituent elements be mounted within the (driver&#39;s) vehicle. However, for simplicity, the present application will describe an implementation in which all constituent elements according to the present disclosure are mounted in a single vehicle (i.e., the driver&#39;s vehicle), unless otherwise specified. 
     The radar signal processing apparatus  530  includes a signal processing circuit  560 . The signal processing circuit  560  directly or indirectly receives reception signals from the array antenna AA, and inputs the reception signals, or a secondary signal(s) which has been generated from the reception signals, to an arriving wave estimation unit AU. A part or a whole of the circuit (not shown) which generates a secondary signal(s) from the reception signals does not need to be provided inside of the signal processing circuit  560 . A part or a whole of such a circuit (preprocessing circuit) may be provided between the array antenna AA and the radar signal processing apparatus  530 . 
     The signal processing circuit  560  is configured to perform computation by using the reception signals or secondary signal(s), and output a signal indicating the number of arriving waves. As used herein, a “signal indicating the number of arriving waves” can be said to be a signal indicating the number of preceding vehicles (which may be one preceding vehicle or plural preceding vehicles) ahead of the driver&#39;s vehicle. 
     The signal processing circuit  560  may be configured to execute various signal processing which is executable by known radar signal processing apparatuses. For example, the signal processing circuit  560  may be configured to execute “super-resolution algorithms” such as the MUSIC method, the ESPRIT method, or the SAGE method, or other algorithms for direction-of-arrival estimation of relatively low resolution. 
     The arriving wave estimation unit AU shown in  FIG. 28  estimates an angle representing the azimuth of each arriving wave by an arbitrary algorithm for direction-of-arrival estimation, and outputs a signal indicating the estimation result. The signal processing circuit  560  estimates the distance to each target as a wave source of an arriving wave, the relative velocity of the target, and the azimuth of the target by using a known algorithm which is executed by the arriving wave estimation unit AU, and output a signal indicating the estimation result. 
     In the present disclosure, the term “signal processing circuit” is not limited to a single circuit, but encompasses any implementation in which a combination of plural circuits is conceptually regarded as a single functional part. The signal processing circuit  560  may be realized by one or more System-on-Chips (SoCs). For example, a part or a whole of the signal processing circuit  560  may be an FPGA (Field-Programmable Gate Array), which is a programmable logic device (PLD). In that case, the signal processing circuit  560  includes a plurality of computation elements (e.g., general-purpose logics and multipliers) and a plurality of memory elements (e.g., look-up tables or memory blocks). Alternatively, the signal processing circuit  560  may be a set of a general-purpose processor(s) and a main memory device(s). The signal processing circuit  560  may be a circuit which includes a processor core(s) and a memory device(s). These may function as the signal processing circuit  560 . 
     The travel assistance electronic control apparatus  520  is configured to provide travel assistance for the vehicle based on various signals which are output from the radar signal processing apparatus  530 . The travel assistance electronic control apparatus  520  instructs various electronic control units to fulfill predetermined functions, e.g., a function of issuing an alarm to prompt the driver to make a braking operation when the distance to a preceding vehicle (vehicular gap) has become shorter than a predefined value; a function of controlling the brakes; and a function of controlling the accelerator. For example, in the case of an operation mode which performs adaptive cruise control of the driver&#39;s vehicle, the travel assistance electronic control apparatus  520  sends predetermined signals to various electronic control units (not shown) and actuators, to maintain the distance of the driver&#39;s vehicle to a preceding vehicle at a predefined value, or maintain the traveling velocity of the driver&#39;s vehicle at a predefined value. 
     In the case of the MUSIC method, the signal processing circuit  560  determines eigenvalues of the spatial covariance matrix, and, as a signal indicating the number of arriving waves, outputs a signal indicating the number of those eigenvalues (“signal space eigenvalues”) which are greater than a predetermined value (thermal noise power) that is defined based on thermal noise. 
     Next, see  FIG. 29 .  FIG. 29  is a block diagram showing another exemplary construction for the vehicle travel controlling apparatus  600 . The radar system  510  in the vehicle travel controlling apparatus  600  of  FIG. 29  includes an array antenna AA, which includes an array antenna that is dedicated to reception only (also referred to as a reception antenna) Rx and an array antenna that is dedicated to transmission only (also referred to as a transmission antenna) Tx; and an object detection apparatus  570 . 
     At least one of the transmission antenna Tx and the reception antenna Rx has the aforementioned waveguide structure. The transmission antenna Tx emits a transmission wave, which may be a millimeter wave, for example. The reception antenna Rx that is dedicated to reception only outputs a reception signal in response to one or plural arriving waves (e.g., a millimeter wave(s)). 
     A transmission/reception circuit  580  sends a transmission signal for a transmission wave to the transmission antenna Tx, and performs “preprocessing” for reception signals of reception waves received at the reception antenna Rx. A part or a whole of the preprocessing may be performed by the signal processing circuit  560  in the radar signal processing apparatus  530 . A typical example of preprocessing to be performed by the transmission/reception circuit  580  may be generating a beat signal from a reception signal, and converting a reception signal of analog format into a reception signal of digital format. 
     Note that the radar system according to the present disclosure may, without being limited to the implementation where it is mounted in the driver&#39;s vehicle, be used while being fixed on the road or a building. 
     Next, an example of a more specific construction of the vehicle travel controlling apparatus  600  will be described. 
       FIG. 30  is a block diagram showing an example of a more specific construction of the vehicle travel controlling apparatus  600 . The vehicle travel controlling apparatus  600  shown in  FIG. 30  includes a radar system  510  and an onboard camera system  700 . The radar system  510  includes an array antenna AA, a transmission/reception circuit  580  which is connected to the array antenna AA, and a signal processing circuit  560 . 
     The onboard camera system  700  includes an onboard camera  710  which is mounted in a vehicle, and an image processing circuit  720  which processes an image or video that is acquired by the onboard camera  710 . 
     The vehicle travel controlling apparatus  600  of this Application Example includes an object detection apparatus  570  which is connected to the array antenna AA and the onboard camera  710 , and a travel assistance electronic control apparatus  520  which is connected to the object detection apparatus  570 . The object detection apparatus  570  includes a transmission/reception circuit  580  and an image processing circuit  720 , in addition to the above-described radar signal processing apparatus  530  (including the signal processing circuit  560 ). The object detection apparatus  570  detects a target on the road or near the road, by using not only the information is obtained by the radar system  510  but also the information which is obtained by the image processing circuit  720 . For example, while the driver&#39;s vehicle is traveling in one of two or more lanes of the same direction, the image processing circuit  720  can distinguish which lane the driver&#39;s vehicle is traveling in, and supply that result of distinction to the signal processing circuit  560 . When the number and azimuth(s) of preceding vehicles are to be recognized by using a predetermined algorithm for direction-of-arrival estimation (e.g., the MUSIC method), the signal processing circuit  560  is able to provide more reliable information concerning a spatial distribution of preceding vehicles by referring to the information from the image processing circuit  720 . 
     Note that the onboard camera system  700  is an example of a means for identifying which lane the driver&#39;s vehicle is traveling in. The lane position of the driver&#39;s vehicle may be identified by any other means. For example, by utilizing an ultra-wide band (UWB) technique, it is possible to identify which one of a plurality of lanes the driver&#39;s vehicle is traveling in. It is widely known that the ultra-wide band technique is applicable to position measurement and/or radar. Using the ultra-wide band technique enhances the range resolution of the radar, so that, even when a large number of vehicles exist ahead, each individual target can be detected with distinction, based on differences in distance. This makes it possible to identify distance from a guardrail on the road shoulder, or from the median strip, with good precision. The width of each lane is predefined based on each country&#39;s law or the like. By using such information, it becomes possible to identify where the lane in which the driver&#39;s vehicle is currently traveling is. Note that the ultra-wide band technique is an example. A radio wave based on any other wireless technique may be used. Moreover, a LIDAR (Light Detection and Ranging) may be used together with a radar. LIDAR is sometimes called “laser radar”. 
     The array antenna AA may be a generic millimeter wave array antenna for onboard use. The transmission antenna Tx in this Application Example emits a millimeter wave as a transmission wave ahead of the vehicle. A portion of the transmission wave is reflected off a target which is typically a preceding vehicle, whereby a reflected wave occurs from the target being a wave source. A portion of the reflected wave reaches the array antenna (reception antenna) AA as an arriving wave. Each of the plurality of antenna elements of the array antenna AA outputs a reception signal in response to one or plural arriving waves. In the case where the number of targets functioning as wave sources of reflected waves is K (where K is an integer of one or more), the number of arriving waves is K, but this number K of arriving waves is not known beforehand. 
     The example of  FIG. 28  assumes that the radar system  510  is provided as an integral piece, including the array antenna AA, on the rearview mirror. However, the number and positions of array antennas AA are not limited to any specific number or specific positions. An array antenna AA may be disposed on the rear surface of the vehicle so as to be able to detect targets that are behind the vehicle. Moreover, a plurality of array antennas AA may be disposed on the front surface and the rear surface of the vehicle. The array antenna(s) AA may be disposed inside the vehicle. Even in the case where a horn antenna whose respective antenna elements include horns as mentioned above is to be adopted as the array antenna(s) AA, the array antenna(s) with such antenna elements may be situated inside the vehicle. 
     The signal processing circuit  560  receives and processes the reception signals which have been received by the reception antenna Rx and subjected to preprocessing by the transmission/reception circuit  580 . This process encompasses inputting the reception signals to the arriving wave estimation unit AU, or alternatively, generating a secondary signal(s) from the reception signals and inputting the secondary signal(s) to the arriving wave estimation unit AU. 
     In the example of  FIG. 30 , a selection circuit  596  which receives the signal being output from the signal processing circuit  560  and the signal being output from the image processing circuit  720  is provided in the object detection apparatus  570 . The selection circuit  596  allows one or both of the signal being output from the signal processing circuit  560  and the signal being output from the image processing circuit  720  to be fed to the travel assistance electronic control apparatus  520 . 
       FIG. 31  is a block diagram showing a more detailed exemplary construction of the radar system  510  according to this Application Example. 
     As shown in  FIG. 31 , the array antenna AA includes a transmission antenna Tx which transmits a millimeter wave and reception antennas Rx which receive arriving waves reflected from targets. Although only one transmission antenna Tx is illustrated in the figure, two or more kinds of transmission antennas with different characteristics may be provided. The array antenna AA includes M antenna elements  11   1 ,  11   2 , . . . ,  11   M  (where M is an integer of 3 or more). In response to the arriving waves, the plurality of antenna elements  11   1 ,  11   2 , . . . ,  11   M  respectively output reception signals s 1 , s 2 , . . . , s M  ( FIG. 27B ). 
     In the array antenna AA, the antenna elements  11   1  to  11   M  are arranged in a linear array or a two-dimensional array at fixed intervals, for example. Each arriving wave will impinge on the array antenna AA from a direction at an angle θ with respect to the normal of the plane in which the antenna elements  11   1  to  11   M  are arrayed. Thus, the direction of arrival of an arriving wave is defined by this angle θ. 
     When an arriving wave from one target impinges on the array antenna AA, this approximates to a plane wave impinging on the antenna elements  11   1  to  11   M  from azimuths of the same angle θ. When K arriving waves impinge on the array antenna AA from K targets with different azimuths, the individual arriving waves can be identified in terms of respectively different angles θ 1  to θ K . 
     As shown in  FIG. 31 , the object detection apparatus  570  includes the transmission/reception circuit  580  and the signal processing circuit  560 . 
     The transmission/reception circuit  580  includes a triangular wave generation circuit  581 , a VCO (voltage controlled oscillator)  582 , a distributor  583 , mixers  584 , filters  585 , a switch  586 , an A/D converter  587 , and a controller  588 . Although the radar system in this Application Example is configured to perform transmission and reception of millimeter waves by the FMCW method, the radar system of the present disclosure is not limited to this method. The transmission/reception circuit  580  is configured to generate a beat signal based on a reception signal from the array antenna AA and a transmission signal from the transmission antenna Tx. 
     The signal processing circuit  560  includes a distance detection section  533 , a velocity detection section  534 , and an azimuth detection section  536 . The signal processing circuit  560  is configured to process a signal from the A/D converter  587  in the transmission/reception circuit  580 , and output signals respectively indicating the detected distance to the target, the relative velocity of the target, and the azimuth of the target. 
     First, the construction and operation of the transmission/reception circuit  580  will be described in detail. 
     The triangular wave generation circuit  581  generates a triangular wave signal, and supplies it to the VCO  582 . The VCO  582  outputs a transmission signal having a frequency as modulated based on the triangular wave signal.  FIG. 32  is a diagram showing change in frequency of a transmission signal which is modulated based on the signal that is generated by the triangular wave generation circuit  581 . This waveform has a modulation width Δf and a center frequency of f0. The transmission signal having a thus modulated frequency is supplied to the distributor  583 . The distributor  583  allows the transmission signal obtained from the VCO  582  to be distributed among the mixers  584  and the transmission antenna Tx. Thus, the transmission antenna emits a millimeter wave having a frequency which is modulated in triangular waves, as shown in  FIG. 32 . 
     In addition to the transmission signal,  FIG. 32  also shows an example of a reception signal from an arriving wave which is reflected from a single preceding vehicle. The reception signal is delayed from the transmission signal. This delay is in proportion to the distance between the driver&#39;s vehicle and the preceding vehicle. Moreover, the frequency of the reception signal increases or decreases in accordance with the relative velocity of the preceding vehicle, due to the Doppler effect. 
     When the reception signal and the transmission signal are mixed, a beat signal is generated based on their frequency difference. The frequency of this beat signal (beat frequency) differs between a period in which the transmission signal increases in frequency (ascent) and a period in which the transmission signal decreases in frequency (descent). Once a beat frequency for each period is determined, based on such beat frequencies, the distance to the target and the relative velocity of the target are calculated. 
       FIG. 33  shows a beat frequency fu in an “ascent” period and a beat frequency fd in a “descent” period. In the graph of  FIG. 33 , the horizontal axis represents frequency, and the vertical axis represents signal intensity. This graph is obtained by subjecting the beat signal to time-frequency conversion. Once the beat frequencies fu and fd are obtained, based on a known equation, the distance to the target and the relative velocity of the target are calculated. In this Application Example, with the construction and operation described below, beat frequencies corresponding to each antenna element of the array antenna AA are obtained, thus enabling estimation of the position information of a target. 
     In the example shown in  FIG. 31 , reception signals from channels Ch 1  to Ch M  corresponding to the respective antenna elements  11   1  to  11   M  are each amplified by an amplifier, and input to the corresponding mixers  584 . Each mixer  584  mixes the transmission signal into the amplified reception signal. Through this mixing, a beat signal is generated corresponding to the frequency difference between the reception signal and the transmission signal. The generated beat signal is fed to the corresponding filter  585 . The filters  585  apply bandwidth control to the beat signals on the channels Ch 1  to Ch M , and supply bandwidth-controlled beat signals to the switch  586 . 
     The switch  586  performs switching in response to a sampling signal which is input from the controller  588 . The controller  588  may be composed of a microcomputer, for example. Based on a computer program which is stored in a memory such as a ROM, the controller  588  controls the entire transmission/reception circuit  580 . The controller  588  does not need to be provided inside the transmission/reception circuit  580 , but may be provided inside the signal processing circuit  560 . In other words, the transmission/reception circuit  580  may operate in accordance with a control signal from the signal processing circuit  560 . Alternatively, some or all of the functions of the controller  588  may be realized by a central processing unit which controls the entire transmission/reception circuit  580  and signal processing circuit  560 . 
     The beat signals on the channels Ch 1  to Ch M  having passed through the respective filters  585  are consecutively supplied to the A/D converter  587  via the switch  586 . In synchronization with the sampling signal, the A/D converter  587  converts the beat signals on the channels Ch 1  to Ch M , which are input from the switch  586 , into digital signals. 
     Hereinafter, the construction and operation of the signal processing circuit  560  will be described in detail. In this Application Example, the distance to the target and the relative velocity of the target are estimated by the FMCW method. Without being limited to the FMCW method as described below, the radar system can also be implemented by using other methods, e.g., 2 frequency CW and spread spectrum methods. 
     In the example shown in  FIG. 31 , the signal processing circuit  560  includes a memory  531 , a reception intensity calculation section  532 , a distance detection section  533 , a velocity detection section  534 , a DBF (digital beam forming) processing section  535 , an azimuth detection section  536 , a target link processing section  537 , a matrix generation section  538 , a target output processing section  539 , and an arriving wave estimation unit AU. As mentioned earlier, a part or a whole of the signal processing circuit  560  may be implemented by FPGA, or by a set of a general-purpose processor(s) and a main memory device(s). The memory  531 , the reception intensity calculation section  532 , the DBF processing section  535 , the distance detection section  533 , the velocity detection section  534 , the azimuth detection section  536 , the target link processing section  537 , and the arriving wave estimation unit AU may be individual parts that are implemented in distinct pieces of hardware, or functional blocks of a single signal processing circuit. 
       FIG. 34  shows an exemplary implementation in which the signal processing circuit  560  is implemented in hardware including a processor PR and a memory device MD. In the signal processing circuit  560  with this construction, too, a computer program that is stored in the memory device MD may fulfill the functions of the reception intensity calculation section  532 , the DBF processing section  535 , the distance detection section  533 , the velocity detection section  534 , the azimuth detection section  536 , the target link processing section  537 , the matrix generation section  538 , and the arriving wave estimation unit AU shown in  FIG. 31 . 
     The signal processing circuit  560  in this Application Example is configured to estimate the position information of a preceding vehicle by using each beat signal converted into a digital signal as a secondary signal of the reception signal, and output a signal indicating the estimation result. Hereinafter, the construction and operation of the signal processing circuit  560  in this Application Example will be described in detail. 
     For each of the channels Ch 1  to Ch M , the memory  531  in the signal processing circuit  560  stores a digital signal which is output from the A/D converter  587 . The memory  531  may be composed of a generic storage medium such as a semiconductor memory or a hard disk and/or an optical disk. 
     The reception intensity calculation section  532  applies Fourier transform to the respective beat signals for the channels Ch 1  to Ch M  (shown in the lower graph of  FIG. 32 ) that are stored in the memory  531 . In the present specification, the amplitude of a piece of complex number data after the Fourier transform is referred to as “signal intensity”. The reception intensity calculation section  532  converts the complex number data of a reception signal from one of the plurality of antenna elements, or a sum of the complex number data of all reception signals from the plurality of antenna elements, into a frequency spectrum. In the resultant spectrum, beat frequencies corresponding to respective peak values, which are indicative of presence and distance of targets (preceding vehicles), can be detected. Taking a sum of the complex number data of the reception signals from all antenna elements will allow the noise components to average out, whereby the S/N ratio is improved. 
     In the case where there is one target, i.e., one preceding vehicle, as shown in  FIG. 33 , the Fourier transform will produce a spectrum having one peak value in a period of increasing frequency (the “ascent” period) and one peak value in a period of decreasing frequency (“the descent” period). The beat frequency of the peak value in the “ascent” period is denoted by “fu”, whereas the beat frequency of the peak value in the “descent” period is denoted by “fd”. 
     From the signal intensities of beat frequencies, the reception intensity calculation section  532  detects any signal intensity that exceeds a predefined value (threshold value), thus determining the presence of a target. Upon detecting a signal intensity peak, the reception intensity calculation section  532  outputs the beat frequencies (fu, fd) of the peak values to the distance detection section  533  and the velocity detection section  534  as the frequencies of the object of interest. The reception intensity calculation section  532  outputs information indicating the frequency modulation width Δf to the distance detection section  533 , and outputs information indicating the center frequency f0 to the velocity detection section  534 . 
     In the case where signal intensity peaks corresponding to plural targets are detected, the reception intensity calculation section  532  find associations between the ascents peak values and the descent peak values based on predefined conditions. Peaks which are determined as belonging to signals from the same target are given the same number, and thus are fed to the distance detection section  533  and the velocity detection section  534 . 
     When there are plural targets, after the Fourier transform, as many peaks as there are targets will appear in the ascent portions and the descent portions of the beat signal. In proportion to the distance between the radar and a target, the reception signal will become more delayed and the reception signal in  FIG. 32  will shift more toward the right. Therefore, a beat signal will have a greater frequency as the distant between the target and the radar increases. 
     Based on the beat frequencies fu and fd which are input from the reception intensity calculation section  532 , the distance detection section  533  calculates a distance R through the equation below, and supplies it to the target link processing section  537 .
 
 R={C·T /(2·Δ f )}·{( fu+fd )/2}
 
     Moreover, based on the beat frequencies fu and fd being input from the reception intensity calculation section  532 , the velocity detection section  534  calculates a relative velocity V through the equation below, and supplies it to the target link processing section  537 .
 
 V={C /(2· f 0)}·{( fu−fd )/2}
 
     In the equation which calculates the distance R and the relative velocity V, C is velocity of light, and T is the modulation period. 
     Note that the lower limit resolution of distance R is expressed as C/(2Δf). Therefore, as Δf increases, the resolution of distance R increases. In the case where the frequency f0 is in the 76 GHz band, when Δf is set on the order of 660 megahertz (MHz), the resolution of distance R will be on the order of 0.23 meters (m), for example. Therefore, if two preceding vehicles are traveling abreast of each other, it may be difficult with the FMCW method to identify whether there is one vehicle or two vehicles. In such a case, it might be possible to run an algorithm for direction-of-arrival estimation that has an extremely high angular resolution to separate between the azimuths of the two preceding vehicles and enable detection. 
     By utilizing phase differences between signals from the antenna elements  11   1 ,  11   2 , . . . ,  11   M , the DBF processing section  535  allows the incoming complex data corresponding to the respective antenna elements, which has been Fourier transformed with respect to the time axis, to be Fourier transformed with respect to the direction in which the antenna elements are arrayed. Then, the DBF processing section  535  calculates spatial complex number data indicating the spectrum intensity for each angular channel as determined by the angular resolution, and outputs it to the azimuth detection section  536  for the respective beat frequencies. 
     The azimuth detection section  536  is provided for the purpose of estimating the azimuth of a preceding vehicle. Among the values of spatial complex number data that has been calculated for the respective beat frequencies, the azimuth detection section  536  chooses an angle θ that takes the largest value, and outputs it to the target link processing section  537  as the azimuth at which an object of interest exists. 
     Note that the method of estimating the angle θ indicating the direction of arrival of an arriving wave is not limited to this example. Various algorithms for direction-of-arrival estimation that have been mentioned earlier can be employed. 
     The target link processing section  537  calculates absolute values of the differences between the respective values of distance, relative velocity, and azimuth of the object of interest as calculated in the current cycle and the respective values of distance, relative velocity, and azimuth of the object of interest as calculated 1 cycle before, which are read from the memory  531 . Then, if the absolute value of each difference is smaller than a value which is defined for the respective value, the target link processing section  537  determines that the target that was detected 1 cycle before and the target detected in the current cycle are an identical target. In that case, the target link processing section  537  increments the count of target link processes, which is read from the memory  531 , by one. 
     If the absolute value of a difference is greater than predetermined, the target link processing section  537  determines that a new object of interest has been detected. The target link processing section  537  stores the respective values of distance, relative velocity, and azimuth of the object of interest as calculated in the current cycle and also the count of target link processes for that object of interest to the memory  531 . 
     In the signal processing circuit  560 , the distance to the object of interest and its relative velocity can be detected by using a spectrum which is obtained through a frequency analysis of beat signals, which are signals generated based on received reflected waves. 
     The matrix generation section  538  generates a spatial covariance matrix by using the respective beat signals for the channels Ch 1  to Ch M  (lower graph in  FIG. 32 ) stored in the memory  531 . In the spatial covariance matrix of eq. 4, each component is the value of a beat signal which is expressed in terms of real and imaginary parts. The matrix generation section  538  further determines eigenvalues of the spatial covariance matrix Rxx, and inputs the resultant eigenvalue information to the arriving wave estimation unit AU. 
     When a plurality of signal intensity peaks corresponding to plural objects of interest have been detected, the reception intensity calculation section  532  numbers the peak values respectively in the ascent portion and in the descent portion, beginning from those with smaller frequencies first, and output them to the target output processing section  539 . In the ascent and descent portions, peaks of any identical number correspond to the same object of interest. The identification numbers are to be regarded as the numbers assigned to the objects of interest. For simplicity of illustration, a leader line from the reception intensity calculation section  532  to the target output processing section  539  is conveniently omitted from  FIG. 31 . 
     When the object of interest is a structure ahead, the target output processing section  539  outputs the identification number of that object of interest as indicating a target. When receiving results of determination concerning plural objects of interest, such that all of them are structures ahead, the target output processing section  539  outputs the identification number of an object of interest that is in the lane of the driver&#39;s vehicle as the object position information indicating where a target is. Moreover, When receiving results of determination concerning plural objects of interest, such that all of them are structures ahead and that two or more objects of interest are in the lane of the driver&#39;s vehicle, the target output processing section  539  outputs the identification number of an object of interest that is associated with the largest count of target being read from the link processes memory  531  as the object position information indicating where a target is. 
     Referring back to  FIG. 30 , an example where the onboard radar system  510  is incorporated in the exemplary construction shown in  FIG. 30  will be described. The image processing circuit  720  ( FIG. 30 ) acquires information of an object from the video, and detects target position information from the object information. For example, the image processing circuit  720  is configured to estimate distance information of an object by detecting the depth value of an object within an acquired video, or detect size information and the like of an object from characteristic amounts in the video, thus detecting position information of the object. 
     The selection circuit  596  selectively feeds position information which is received from the signal processing circuit  560  or the image processing circuit  720  to the travel assistance electronic control apparatus  520 . For example, the selection circuit  596  compares a first distance, i.e., the distance from the driver&#39;s vehicle to a detected object as contained in the object position information from the signal processing circuit  560 , against a second distance, i.e., the distance from the driver&#39;s vehicle to the detected object as contained in the object position information from the image processing circuit  720 , and determines which is closer to the driver&#39;s vehicle. For example, based on the result of determination, the selection circuit  596  may select the object position information which indicates a closer distance to the driver&#39;s vehicle, and output it to the travel assistance electronic control apparatus  520 . If the result of determination indicates the first distance and the second distance to be of the same value, the selection circuit  596  may output either one, or both of them, to the travel assistance electronic control apparatus  520 . 
     If information indicating that there is no prospective target is input from the reception intensity calculation section  532 , the target output processing section  539  ( FIG. 31 ) outputs zero, indicating that there is no target, as the object position information. Then, on the basis of the object position information from the target output processing section  539 , through comparison against a predefined threshold value, the selection circuit  596  chooses either the object position information from the signal processing circuit  560  or the object position information from the image processing circuit  720  to be used. 
     Based on predefined conditions, the travel assistance electronic control apparatus  520  having received the position information of a preceding object from the object detection apparatus  570  performs control to make the operation safer or easier for the driver who is driving the driver&#39;s vehicle, in accordance with the distance and size indicated by the object position information, the velocity of the driver&#39;s vehicle, road surface conditions such as rainfall, snowfall or clear weather, or other conditions. For example, if the object position information indicates that no object has been detected, the travel assistance electronic control apparatus  520  may send a control signal to an accelerator control circuit  526  to increase speed up to a predefined velocity, thereby controlling the accelerator control circuit  526  to make an operation that is equivalent to stepping on the accelerator pedal. 
     In the case where the object position information indicates that an object has been detected, if it is found to be at a predetermined distance from the driver&#39;s vehicle, the travel assistance electronic control apparatus  520  controls the brakes via a brake control circuit  524  through a brake-by-wire construction or the like. In other words, it makes an operation of decreasing the velocity to maintain a constant vehicular gap. Upon receiving the object position information, the travel assistance electronic control apparatus  520  sends a control signal to an alarm control circuit  522  so as to control lamp illumination or control audio through a loudspeaker which is provided within the vehicle, so that the driver is informed of the nearing of a preceding object. Upon receiving object position information including a spatial distribution of preceding vehicles, the travel assistance electronic control apparatus  520  may, if the traveling velocity is within a predefined range, automatically make the steering wheel easier to operate to the right or left, or control the hydraulic pressure on the steering wheel side so as to force a change in the direction of the wheels, thereby providing assistance in collision avoidance with respect to the preceding object. 
     The object detection apparatus  570  may be arranged so that, if a piece of object position information which was being continuously detected by the selection circuit  596  for a while in the previous detection cycle but which is not detected in the current detection cycle becomes associated with a piece of object position information from a camera-detected video indicating a preceding object, then continued tracking is chosen, and object position information from the signal processing circuit  560  is output with priority. 
     An exemplary specific construction and an exemplary operation for the selection circuit  596  to make a selection between the outputs from the signal processing circuit  560  and the image processing circuit  720  are disclosed in the specification of U.S. Pat. No. 8,446,312, the specification of U.S. Pat. No. 8,730,096, and the specification of U.S. Pat. No. 8,730,099. The entire disclosure thereof is incorporated herein by reference. 
     &lt;First Variant of Application Example&gt; 
     In the radar system for onboard use of the above Application Example, the (sweep) condition for a single instance of FMCW (Frequency Modulated Continuous Wave) frequency modulation, i.e., a time span required for such a modulation (sweep time), is e.g. 1 millisecond, although the sweep time could be shortened to about 100 microseconds. 
     However, in order to realize such a rapid sweep condition, not only the constituent elements involved in the emission of a transmission wave, but also the constituent elements involved in the reception under that sweep condition must also be able to rapidly operate. For example, an A/D converter  587  ( FIG. 31 ) which rapidly operates under that sweep condition will be needed. The sampling frequency of the A/D converter  587  may be 10 MHz, for example. The sampling frequency may be faster than 10 MHz. 
     In the present variant, a relative velocity with respect to a target is calculated without utilizing any Doppler shift-based frequency component. In the present embodiment, the sweep time is Tm=100 microseconds, which is very short. The lowest frequency of a detectable beat signal, which is 1/Tm, equals 10 kHz in this case. This would correspond to a Doppler shift of a reflected wave from a target which has a relative velocity of approximately 20 m/second. In other words, so long as one relies on a Doppler shift, it would be impossible to detect relative velocities that are equal to or smaller than this. Thus, the inventors have found that a method of calculation which is different from a Doppler shift-based method of calculation is preferably adopted. 
     As an example, this variant illustrates a process that utilizes a signal (upbeat signal) representing a difference between a transmission wave and a reception wave which is obtained in an upbeat (ascent) portion where the transmission wave increases in frequency. A single sweep time of FMCW is 100 microseconds, and its waveform is a sawtooth shape which is composed only of an upbeat portion. In other words, in the present embodiment, the signal wave which is generated by the triangular wave/CW wave generation circuit  581  has a sawtooth shape. The sweep width in frequency is 500 MHz. Since no peaks are to be utilized that are associated with Doppler shifts, the process is not one that generates an upbeat signal and a downbeat signal to utilize the peaks of both, but will rely on only one of such signals. Although a case of utilizing an upbeat signal will be illustrated herein, a similar process can also be performed by using a downbeat signal. 
     The A/D converter  587  ( FIG. 31 ) samples each upbeat signal at a sampling frequency of 10 MHz, and outputs several hundred pieces of digital data (hereinafter referred to as “sampling data”). The sampling data is generated based on upbeat signals after a point in time where a reception wave is obtained and until a point in time at which a transmission wave completes transmission, for example. Note that the process may be ended as soon as a certain number of pieces of sampling data are obtained. 
     In this variant, 128 upbeat signals are transmitted/received in series, for each of which some several hundred pieces of sampling data are obtained. The number of upbeat signals is not limited to 128. It may be 256, or 8. An arbitrary number may be selected depending on the purpose. 
     The resultant sampling data is stored to the memory  531 . The reception intensity calculation section  532  applies a two-dimensional fast Fourier transform (FFT) to the sampling data. Specifically, first, for each of the sampling data pieces that have been obtained through a single sweep, a first FFT process (frequency analysis process) is performed to generate a power spectrum. Next, the velocity detection section  534  performs a second FFT process for the processing results that have been collected from all sweeps. 
     When the reflected waves are from the same target, peak components in the power spectrum to be detected in each sweep period will be of the same frequency. On the other hand, for different targets, the peak components will differ in frequency. Through the first FFT process, plural targets that are located at different distances can be separated. 
     In the case where a relative velocity with respect to a target is non-zero, the phase of the upbeat signal changes slightly from sweep to sweep. In other words, through the second FFT process, a power spectrum whose elements are the data of frequency components that are associated with such phase changes will be obtained for the respective results of the first FFT process. 
     The reception intensity calculation section  532  extracts peak values in the second power spectrum above, and sends them to the velocity detection section  534 . 
     The velocity detection section  534  determines a relative velocity from the phase changes. For example, suppose that a series of obtained upbeat signals undergo phase changes by every phase θ [RXd]. Assuming that the transmission wave has an average wavelength λ, this means there is a λ/(4π/θ) change in distance every time an upbeat signal is obtained. Since this change has occurred over an interval of upbeat signal transmission Tm (=100 microseconds), the relative velocity is determined to be {λ/(4π/θ)}/Tm. 
     Through the above processes, a relative velocity with respect to a target as well as a distance from the target can be obtained. 
     &lt;Second Variant of Application Example&gt; 
     The radar system  510  is able to detect a target by using a continuous wave(s) CW of one or plural frequencies. This method is especially useful in an environment where a multitude of reflected waves impinge on the radar system  510  from still objects in the surroundings, e.g., when the vehicle is in a tunnel. 
     The radar system  510  has an antenna array for reception purposes, including five channels of independent reception elements. In such a radar system, the azimuth-of-arrival estimation for incident reflected waves is only possible if there are four or fewer reflected waves that are simultaneously incident. In an FMCW-type radar, the number of reflected waves to be simultaneously subjected to an azimuth-of-arrival estimation can be reduced by exclusively selecting reflected waves from a specific distance. However, in an environment where a large number of still objects exist in the surroundings, e.g., in a tunnel, it is as if there were a continuum of objects to reflect radio waves; therefore, even if one narrows down on the reflected waves based on distance, the number of reflected waves may still not be equal to or smaller than four. However, any such still object in the surroundings will have an identical relative velocity with respect to the driver&#39;s vehicle, and the relative velocity will be greater than that associated with any other vehicle that is traveling ahead. On this basis, such still objects can be distinguished from any other vehicle based on the magnitudes of Doppler shifts. 
     Therefore, the radar system  510  performs a process of: emitting continuous waves CW of plural frequencies; and, while ignoring Doppler shift peaks that correspond to still objects in the reception signals, detecting a distance by using a Doppler shift peak(s) of any smaller shift amount(s). Unlike in the FMCW method, in the CW method, a frequency difference between a transmission wave and a reception wave is ascribable only to a Doppler shift. In other words, any peak frequency that appears in a beat signal is ascribable only to a Doppler shift. 
     In the description of this variant, too, a continuous wave to be used in the CW method will be referred to as a “continuous wave CW”. As described above, a continuous wave CW has a constant frequency; that is, it is unmodulated. 
     Suppose that the radar system  510  has emitted a continuous wave CW of a frequency fp, and detected a reflected wave of a frequency fq that has been reflected off a target. The difference between the transmission frequency fp and the reception frequency fq is called a Doppler frequency, which approximates to fp−fq=2·Vr·fp/c. Herein, Vr is a relative velocity between the radar system and the target, and c is the velocity of light. The transmission frequency fp, the Doppler frequency (fp−fq), and the velocity of light c are known. Therefore, from this equation, the relative velocity Vr=(fp−fq)·c/2fp can be determined. The distance to the target is calculated by utilizing phase information as will be described later. 
     In order to detect a distance to a target by using continuous waves CW, a 2 frequency CW method is adopted. In the 2 frequency CW method, continuous waves CW of two frequencies which are slightly apart are emitted each for a certain period, and their respective reflected waves are acquired. For example, in the case of using frequencies in the 76 GHz band, the difference between the two frequencies would be several hundred kHz. As will be described later, it is more preferable to determine the difference between the two frequencies while taking into account the minimum distance at which the radar used is able to detect a target. 
     Suppose that the radar system  510  has sequentially emitted continuous waves CW of frequencies fp1 and fp2 (fp1&lt;fp2), and that the two continuous waves CW have been reflected off a single target, resulting in reflected waves of frequencies fq1 and fq2 being received by the radar system  510 . 
     Based on the continuous wave CW of the frequency fp1 and the reflected wave (frequency fq1) thereof, a first Doppler frequency is obtained. Based on the continuous wave CW of the frequency fp2 and the reflected wave (frequency fq2) thereof, a second Doppler frequency is obtained. The two Doppler frequencies have substantially the same value. However, due to the difference between the frequencies fp1 and fp2, the complex signals of the respective reception waves differ in phase. By utilizing this phase information, a distance (range) to the target can be calculated. 
     Specifically, the radar system  10  is able to determine the distance R as R=c·Δφ/4π(fp2−fp1). Herein, Δφ denotes the phase difference between two beat signals, i.e., a beat signal fb1 which is obtained as a difference between the continuous wave CW of the frequency fp1 and the reflected wave (frequency fq1) thereof and a beat signal fb2 which is obtained as a difference between the continuous wave CW of the frequency fp2 and the reflected wave (frequency fq2) thereof. The method of identifying the frequencies fb1 and fb2 of the respective beat signals is identical to that in the aforementioned instance of a beat signal from a continuous wave CW of a single frequency. 
     Note that a relative velocity Vr under the 2 frequency CW method is determined as follows.
 
 Vr=fb 1· c/ 2· fp 1 or  Vr=fb 2· c/ 2· fp 2
 
     Moreover, the range in which a distance to a target can be uniquely identified is limited to the range defined by Rmax&lt;c/2(fp2−fp1). The reason is that beat signals resulting from a reflected wave from any farther target would produce a Δφ which is greater than 2π, such that they are indistinguishable from beat signals associated with targets at closer positions. Therefore, it is more preferable to adjust the difference between the frequencies of the two continuous waves CW so that Rmax becomes greater than the minimum detectable distance of the radar. In the case of a radar whose minimum detectable distance is 100 m, fp2−fp1 may be made e.g. 1.0 MHz. In this case, Rmax=150 m, so that a signal from any target from a position beyond Rmax is not detected. In the case of mounting a radar which is capable of detection up to 250 m, fp2−fp1 may be made e.g. 500 kHz. In this case, Rmax=300 m, so that a signal from any target from a position beyond Rmax is not detected, either. In the case where the radar has both of an operation mode in which the minimum detectable distance is 100 m and the horizontal viewing angle is 120 degrees and an operation mode in which the minimum detectable distance is 250 m and the horizontal viewing angle is 5 degrees, it is preferable to switch the fp2−fp1 value be 1.0 MHz and 500 kHz for operation in the respective operation modes. 
     A detection approach is known which, by transmitting continuous waves CW at N different frequencies (where N is an integer of 3 or more), and utilizing phase information of the respective reflected waves, detects a distance to each target. Under this detection approach, distance can be properly recognized up to N−1 targets. As the processing to enable this, a fast Fourier transform (FFT) is used, for example. Given N=64 or 128, an FFT is performed for sampling data of a beat signal as a difference between a transmission signal and a reception signal for each frequency, thus obtaining a frequency spectrum (relative velocity). Thereafter, at the frequency of the CW wave, a further FFT is performed for peaks of the same frequency, thus to derive distance information. 
     Hereinafter, this will be described more specifically. 
     For ease of explanation, first, an instance will be described where signals of three frequencies f1, f2 and f3 are transmitted while being switched over time. It is assumed that f1&gt;f2&gt;f3, and f1−f2=f2−f3=Δf. A transmission time Δt is assumed for the signal wave for each frequency.  FIG. 35  shows a relationship between three frequencies f1, f2 and f3. 
     Via the transmission antenna Tx, the triangular wave/CW wave generation circuit  581  ( FIG. 31 ) transmits continuous waves CW of frequencies f1, f2 and f3, each lasting for the time Δt. The reception antennas Rx receive reflected waves resulting by the respective continuous waves CW being reflected off one or plural targets. 
     Each mixer  584  mixes a transmission wave and a reception wave to generate a beat signal. The A/D converter  587  converts the beat signal, which is an analog signal, into several hundred pieces of digital data (sampling data), for example. 
     Using the sampling data, the reception intensity calculation section  532  performs FFT computation. Through the FFT computation, frequency spectrum information of reception signals is obtained for the respective transmission frequencies f1, f2 and f3. 
     Thereafter, the reception intensity calculation section  532  separates peak values from the frequency spectrum information of the reception signals. The frequency of any peak value which is predetermined or greater is in proportion to a relative velocity with respect to a target. Separating a peak value(s) from the frequency spectrum information of reception signals is synonymous with separating one or plural targets with different relative velocities. 
     Next, with respect to each of the transmission frequencies f1 to f3, the reception intensity calculation section  532  measures spectrum information of peak values of the same relative velocity or relative velocities within a predefined range. 
     Now, consider a scenario where two targets A and B exist which have about the same relative velocity but are at respectively different distances. A transmission signal of the frequency f1 will be reflected from both of targets A and B to result in reception signals being obtained. The reflected waves from targets A and B will result in substantially the same beat signal frequency. Therefore, the power spectra at the Doppler frequencies of the reception signals, corresponding to their relative velocities, are obtained as a synthetic spectrum F1 into which the power spectra of two targets A and B have been merged. 
     Similarly, for each of the frequencies f2 and f3, the power spectra at the Doppler frequencies of the reception signals, corresponding to their relative velocities, are obtained as a synthetic spectrum F1 into which the power spectra of two targets A and B have been merged. 
       FIG. 36  shows a relationship between synthetic spectra F1 to F3 on a complex plane. In the directions of the two vectors composing each of the synthetic spectra F1 to F3, the right vector corresponds to the power spectrum of a reflected wave from target A; i.e., vectors f1A, f2A and f3A, in  FIG. 36 . On the other hand, in the directions of the two vectors composing each of the synthetic spectra F1 to F3, the left vector corresponds to the power spectrum of a reflected wave from target B; i.e., vectors f1B, f2B and f3B in  FIG. 36 . 
     Under a constant difference Δf between the transmission frequencies, the phase difference between the reception signals corresponding to the respective transmission signals of the frequencies f1 and f2 is in proportion to the distance to a target. Therefore, the phase difference between the vectors f1A and f2A and the phase difference between the vectors f2A and f3A are of the same value θA, this phase difference θA being in proportion to the distance to target A. Similarly, the phase difference between the vectors f1B and f2B and the phase difference between the vectors f2B and f3B are of the same value θB, this phase difference GB being in proportion to the distance to target B. 
     By using a well-known method, the respective distances to targets A and B can be determined from the synthetic spectra F1 to F3 and the difference Δf between the transmission frequencies. This technique is disclosed in U.S. Pat. No. 6,703,967, for example. The entire disclosure of this publication is incorporated herein by reference. 
     Similar processing is also applicable when the transmitted signals have four or more frequencies. 
     Note that, before transmitting continuous wave CWs at N different frequencies, a process of determining the distance to and relative velocity of each target may be performed by the 2 frequency CW method. Then, under predetermined conditions, this process may be switched to a process of transmitting continuous waves CW at N different frequencies. For example, FFT computation may be performed by using the respective beat signals at the two frequencies, and if the power spectrum of each transmission frequency undergoes a change over time of 30% or more, the process may be switched. The amplitude of a reflected wave from each target undergoes a large change over time due to multipath influences and the like. When there exists a change of a predetermined magnitude or greater, it may be considered that plural targets may exist. 
     Moreover, the CW method is known to be unable to detect a target when the relative velocity between the radar system and the target is zero, i.e., when the Doppler frequency is zero. However, when a pseudo Doppler signal is determined by the following methods, for example, it is possible to detect a target by using that frequency. 
     (Method 1) A mixer that causes a certain frequency shift in the output of a receiving antenna is added. By using a transmission signal and a reception signal with a shifted frequency, a pseudo Doppler signal can be obtained. 
     (Method 2) A variable phase shifter to introduce phase changes continuously over time is inserted between the output of a receiving antenna and a mixer, thus adding a pseudo phase difference to the reception signal. By using a transmission signal and a reception signal with an added phase difference, a pseudo Doppler signal can be obtained. 
     An example of specific construction and operation of inserting a variable phase shifter to generate a pseudo Doppler signal under Method 2 is disclosed in Japanese Laid-Open Patent Publication No. 2004-257848. The entire disclosure of this publication is incorporated herein by reference. 
     When targets with zero or very little relative velocity need to be detected, the aforementioned processes of generating a pseudo Doppler signal may be adopted, or the process may be switched to a target detection process under the FMCW method. 
     Next, with reference to  FIG. 37 , a procedure of processing to be performed by the object detection apparatus  570  of the onboard radar system  510  will be described. 
     The example below will illustrate a case where continuous waves CW are transmitted at two different frequencies fp1 and fp2 (fp1&lt;fp2), and the phase information of each reflected wave is utilized to respectively detect a distance with respect to a target. 
       FIG. 37  is a flowchart showing the procedure of a process of determining relative velocity and distance according to this variant. 
     At step S 41 , the triangular wave/CW wave generation circuit  581  generates two continuous waves CW of frequencies which are slightly apart, i.e., frequencies fp1 and fp2. 
     At step S 42 , the transmission antenna Tx and the reception antennas Rx perform transmission/reception of the generated series of continuous waves CW. Note that the process of step S 41  and the process of step S 42  are to be performed in parallel fashion by the triangular wave/CW wave generation circuit  581  and the antenna elements Tx/Rx, rather than step S 42  following only after completion of step S 41 . 
     At step S 43 , each mixer  584  generates a difference signal by utilizing each transmission wave and each reception wave, whereby two difference signals are obtained. Each reception wave is inclusive of a reception wave emanating from a still object and a reception wave emanating from a target. Therefore, next, a process of identifying frequencies to be utilized as the beat signals is performed. Note that the process of step S 41 , the process of step S 42 , and the process of step  43  are to be performed in parallel fashion by the triangular wave/CW wave generation circuit  581 , the antenna elements Tx/Rx, and the mixers  584 , rather than step S 42  following only after completion of step S 41 , or step  43  following only after completion of step  42 . 
     At step S 44 , for each of the two difference signals, the object detection apparatus  570  identifies certain peak frequencies to be frequencies fb1 and fb2 of beat signals, such that these frequencies are equal to or smaller than a frequency which is predefined as a threshold value and yet they have amplitude values which are equal to or greater than a predetermined amplitude value, and that the difference between the two frequencies is equal to or smaller than a predetermined value. 
     At step S 45 , based on one of the two beat signal frequencies identified, the reception intensity calculation section  532  detects a relative velocity. The reception intensity calculation section  532  calculates the relative velocity according to Vr=fb1·c/2·fp1, for example. Note that a relative velocity may be calculated by utilizing each of the two beat signal frequencies, which will allow the reception intensity calculation section  532  to verify whether they match or not, thus enhancing the precision of relative velocity calculation. 
     At step S 46 , the reception intensity calculation section  532  determines a phase difference Δφ between the two beat signals fb1 and fb2, and determines a distance R=c·Δφ/4π(fp2−fp1) to the target. 
     Through the above processes, the relative velocity and distance to a target can be detected. 
     Note that continuous waves CW may be transmitted at N different frequencies (where N is 3 or more), and phase information of the respective reflected wave, distances to plural targets which are of the same relative velocity but at different positions may be detected. 
     In addition to the radar system  510 , the vehicle  500  described above may further include another radar system. For example, the vehicle  500  may further include a radar system having a detection range toward the rear or the sides of the vehicle body. In the case of incorporating a radar system having a detection range toward the rear of the vehicle body, the radar system may monitor the rear, and if there is any danger of having another vehicle bump into the rear, make a response by issuing an alarm, for example. In the case of incorporating a radar system having a detection range toward the sides of the vehicle body, the radar system may monitor an adjacent lane when the driver&#39;s vehicle changes its lane, etc., and make a response by issuing an alarm or the like as necessary. 
     The applications of the above-described radar system  510  are not limited to onboard use only. Rather, the radar system  510  may be used as sensors for various purposes. For example, it may be used as a radar for monitoring the surroundings of a house or a building. Alternatively, it may be used as a sensor for detecting the presence or absence of a person at a specific indoor place, or whether or not such a person is undergoing any motion, etc., without utilizing any optical images. 
     The aforementioned onboard radar system is only an example. The aforementioned array antenna is usable in any technological field that makes use of an antenna. 
     A waveguide device according to the present disclosure can be used for the transmission of a radio frequency signal, in the place of a microstrip line or a hollow waveguide. Moreover, an antenna device according to the present disclosure is available for various applications where transmission/reception of electromagnetic waves in the gigahertz band or the terahertz band is to be made, and especially suitably used in onboard radars and wireless communication systems that need downsizing. 
     While the present invention has been described with respect to exemplary embodiments thereof, it will be apparent to those skilled in the art that the disclosed invention may be modified in numerous ways and may assume many embodiments other than those specifically described above. Accordingly, it is intended by the appended claims to cover all modifications of the invention that fall within the true spirit and scope of the invention. 
     This application is based on Japanese Patent Applications No. 2015-203453 filed Oct. 15, 2015 and No. 2016-142181 filed Jul. 20, 2016, the entire contents of which are hereby incorporated by reference.