Abstract:
Traditional airborne radar antennas are typically limited to placement above or below the aircraft, or in one or both of the wings, or in the nose. In the both-wing case, the fuselage prevents coherent array processing of both wing arrays without the introduction of grating lobes. Both wing arrays are coherently combined without grating lobes through appropriate geometric configurations of the arrays and the use of MIMO processing techniques. A virtual array is formed by convolving the transmit and receive apertures to fill in the gap created by the fuselage, thereby allowing fully coherent array processing and greater angular resolution than previously achievable through a conformal array. The signal-to-noise ratios are potentially improved.

Description:
BACKGROUND OF THE DISCLOSURE 
     The use of radar systems on aircraft for detecting other aircraft arose almost as soon as radar itself was devised, and that use has expanded to detection of ground targets. Range and clutter advantages arise from operating a radar system from a high and open location free from obstacles. The shape and aerodynamic requirements of aircraft make it difficult to attach the necessary antennas to the aircraft. Additionally, the antenna(s) must be suitable for both of the major radar functions which are required, namely volume search to identify targets anywhere in the relevant airspace, and tracking to maintain contact with particularly important targets. The types of antennas for these different functions are different. 
     Airborne Warning and Control System (AWACS) aircraft typically use either (a) one or more conformal antenna arrays affixed to the exterior of the fuselage or body of the aircraft, (b) one or more linear arrays located in a rotational disk-like structure mounted above the fuselage, where the rotation provides the 360° azimuth coverage required for surveillance applications, or (c) an array located in the nose of the aircraft. The conformal array approach orients the antenna parallel to the longitudinal axis of the aircraft, in which position, generally speaking, the antenna beams point laterally relative to the aircraft. This lateral radar coverage makes forward-looking performance difficult to obtain. The rotating-disk technique suffers from aerodynamic limitations, and an antenna contained in such a disk cannot be as large as might be desired to achieve the desired beamwidth(s). The nose location severely limits the possible aperture of the antenna and therefore limits the beamwidth. 
     Improved or alternative airborne radar arrangements are desired. 
     SUMMARY 
     A radar system comprises first and second point sources. The point sources may transmit mutually orthogonal waveforms. The radar system includes first and second line arrays of receive antennas for receiving radar return signals originating with the point sources, the first and second line arrays being separated by a gap. A digital multiple-input multiple-output (MIMO) processor coheres the arrays across the gap. In a particular embodiment, the first and second line arrays of receive antennas are mutually coaxial. In another embodiment, the gap between the first and second line arrays of receive antennas is no larger than the length of one of the first and second line arrays of receive antennas. The radar system may be associated with an aircraft including first and second wings and a fuselage separating the first and second wings, and in this embodiment the first and second line arrays of receive antennas lie generally along the first and second wings, respectively, with the fuselage occupying at least a portion of the gap. 
     A radar method according to an aspect of the disclosure comprises the steps of transmitting from first and second point sources, and receiving radar return signals originating with or from the point sources with first and second line arrays of receive antennas separated by a gap. The step of transmitting may include the step of transmitting mutually orthogonal waveforms from the first and second point sources. The method may further include the step of performing multiple-input multiple-output digital processing for cohering the arrays across the gap. In a particular mode of the method, the step of receiving radar return signals originating from the point sources with first and second line arrays of receive antennas separated by a gap includes the step of receiving radar return signals originating from the point sources. The step of receiving radar return signals may include the step of receiving radar return signals with first and second mutually coaxial arrays of receive antennas separated by a gap. In a particularly advantageous mode, the gap is no larger than the length of one of the first and second line arrays of receive antennas. The method may include the step of associating the first and second point sources, the first and second arrays, and the MIMO processor with an aircraft including a first wing bearing the first array, a second wing bearing the second array, and a fuselage separating the first and second arrays. 
     An aircraft-mounted radar system comprises an airplane defining first and second spaced-apart wings. A line receiving antenna array includes first and second separate receiving antenna array portions, which first and second portions lie mutually coaxially along respective ones of the wings. Each separate portion of the receiving antenna array defines an inside edge separated from the inside edge of the other array portion by a gap. The gap may be occupied by a fuselage of the aircraft. The radar system includes a line transmitting antenna array lying along an axis parallel with the axes of the receiving antenna array portions. A transmitter is coupled to the antennas of the transmitting antenna array, for exciting the antennas of the transmitting array with mutually orthogonal signals. A multiple-input multiple-output processor is coupled to the transmitter and to the receiving antenna array, for processing received signals for forming an effective array including real or physical elements, and also including virtual elements occupying positions along the gap. 
     A radar system comprises a first antenna array, which may be a line array, and includes antenna elements extending generally horizontally along a line, and having a first extent. A second antenna array, which may be a line array, includes antenna elements extending along the line, and has a second extent, which need not be the same as the first extent. The second antenna array is separated from the first antenna array by a distance no greater than the length of the larger extent, thereby defining an inside end of each of the first antenna array and the second antenna array. The radar system also comprises a first transmit antenna and second transmit antenna. The first transmit antenna lies in a vertical plane passing through the inside end of the first antenna array. The second transmit antenna lies in a vertical plane passing through the inside end of the second antenna array. The first and second transmit antennas lie in the same horizontal plane. The radar system also includes first and second transmitters for generating mutually orthogonally modulated RF signals. The first and second transmitters are coupled to the first and second transmit antennas, for transmitting first and second mutually orthogonal electromagnetic signals from the first and second transmit antennas. The radar system further includes first and second receiver arrays coupled to the first and second antenna arrays and to the first and second transmitters, for processing reflected signals for generating downconverted (baseband or intermediate frequency) first and second received signals from each of the elements of the first and second antenna arrays, respectively. Each of the downconverted received signals includes components attributable to the first and second mutually orthogonal electromagnetic signals. First and second processors are coupled to the first and second receiver arrays, respectively, and to the first and second transmitters, for processing the first and second downconverted signals to separate the first and second mutually orthogonal components of the received signals. A beamforming processor is coupled to the first and second processors for coherently combining the first components of the mutually orthogonal received signals with the second components of the mutually orthogonal received signals to thereby define at least a first beam. 
     A radar system according to another aspect of the disclosure comprises a first antenna array (which may include elements in a line array or in a planar array) extending along a line, and having a length, at least in a horizontal plane. The radar system also includes a second antenna array extending along the line, and having the length. The second array is separated from the first array by a distance no greater than the length, thereby defining an inside end of the first antenna array and an inside end of the second antenna array. The radar system also includes first and second transmit antennas, the first transmit antenna lying in a vertical plane passing through the inside end of the first antenna array, and the second transmit antenna lying in a vertical plane passing through the inside end of the second antenna array. The first and second transmit antennas lie at the same distance from the horizontal plane. The radar system also includes first and second transmitters for generating mutually orthogonal RF signals. The first and second transmitters are connected to the first and second transmit antennas, for transmitting first and second mutually orthogonal electromagnetic signals from each of the first and second transmit antennas. First and second receiver arrays are coupled to the first and second antenna arrays, for processing reflected signals for generating first and second received signals from each of the first and second antenna arrays, respectively, each of the received signals including components attributable to the first and second mutually orthogonal electromagnetic signals. First and second orthogonal separation processor arrays are coupled to the first and second receiver arrays, respectively, for processing the first and second received signals to separate the first and second components of the mutually orthogonal received signals. A beamforming processor is coupled to the first and second orthogonal separation processor arrays for coherently combining the first components of the mutually orthogonal received signals with the second components of the mutually orthogonal received signals to thereby define a first beam. A particularly advantageous embodiment of this radar system further comprises a radar control processor coupled to the second processor for adjusting the weighting of the coherent combining to thereby shape the first beam. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         FIG. 1  is a simplified plan view of an aircraft including a fuselage, left and right wings each bearing a receive antenna array and transmit horn, with a gap lying between the antenna arrays, and showing Cartesian coordinates associated with the aircraft; 
         FIG. 2  shows plots of beamwidth resulting from various types of integration using the wing array(s) of  FIG. 1 ; 
         FIGS. 3A ,  3 B, and  3 C are right elevation, front elevation, and plan views, respectively, of the aircraft of  FIG. 1 , showing some details of the location of certain antennas, and  FIG. 3D  is a simplified perspective or isometric view of one of the antennas of  FIG. 3A ,  3 B, or  3 C; 
         FIG. 4A  illustrates a notional transmit antenna configuration with mutually orthogonally coded signals from each transmit source,  FIG. 4B  illustrates a notional receive antenna array receiving reflected encoded signals originating from the transmit array of  FIG. 4A , and  FIG. 40  illustrates the effective receive antenna array arising from MIMO processing; 
         FIG. 5  is a simplified block diagram of an airborne radar system according to aspects of the disclosure; and 
         FIG. 6  is a notional illustration of a system geometry according to an aspect of the disclosure using left and right transmit antennas and left and right receive antenna arrays. 
     
    
    
     DESCRIPTION 
     The description herein includes relative placement or orientation words such as “top,” “bottom,” “up,” “down,” “lower,” “upper,” “horizontal,” “vertical,” “above,” “below,” as well as derivative terms such as “horizontally,” “downwardly,” and the like. These and other terms should be understood as to refer to the orientation or position then being described, or illustrated in the drawing(s), and not to the orientation or position of the actual element(s) being described or illustrated. These terms are used for convenience in description and understanding, and do not require that the apparatus be constructed or operated in the described position or orientation. 
     Terms concerning attachments, couplings, and the like, such as “connected,” “attached,” “mounted,” refer in a mechanical context to relationships in which structures are secured or attached to one another either directly or indirectly through intervening structures, as well as both movable and rigid attachments or relationships, unless expressly described otherwise. In an electrical context, such terms have a meaning which includes both direct electrical connection and connection through intermediate elements. 
       FIG. 1  is a simplified plan view of an aircraft  10  including a fuselage or body  12  and left and right wings  14   l  and  14   r , respectively. A tail assembly is illustrated as  16 . Coordinates in the X, Y, and Z direction are indicated. According to an aspect of the disclosure, left and right wing antenna arrays  24 E and  24   r , respectively, extend along the lengths of the right and left wings  14   l  and  14   r , respectively. The wing antenna arrays  24  are illustrated as elongated rectangles of length L to indicate their general locations and sizes. The antenna arrays may be mounted forward on the wings, or on the top or on the bottom, but must in any case have unobstructed views in the forward, upward, or downward directions respectively, depending on the region to be covered by the radar. 
       FIG. 2  is a conventional amplitude (dB) versus scan angle plot (in sines) illustrating the farfield radiation pattern of the antenna arrays  24  of  FIG. 1  under the condition that each array,  24   l  and  24   r , has a length of five wavelengths. More particularly, dotted-line plot  210  of  FIG. 2  shows the antenna beam response for one of the wing arrays of  FIG. 1 , taken alone. As illustrated, antenna beam  210  has a 3 dB beamwidth of about 0.178 sines, corresponding to a full beamwidth of about 10.2°. If the signals of both right and left arrays  24   l  and  24   r  were to be noncoherently combined as required to avoid grating lobes in the presence of the gap  26 , the resulting beamwidth for the two wing arrays  24   l  or  24   r  of  FIG. 1  would be the same as that of a single wing array, albeit with higher or greater magnitude. 
     Unfortunately, no array exists in the gap or interstice  26  between the “near” or “inside” ends  24   l  and  24   ri  of the left and right arrays  24   l  and  24   r , respectively, of  FIG. 1 . The presence of the fuselage  12  prevents the physical placement of a central array which might extend the effective length of the two wing arrays  24 . It is possible to coherently integrate (CI) the two arrays, yielding a tighter beam pattern (0.048 sines, 2.8°), as illustrated by dot-dash plot  212  in  FIG. 2 ; however, grating lobes exist near the main beam. If it were possible to extend the two wing arrays of set  24  of wing arrays of  FIG. 1  so as to close the gap  26 , the antenna beam pattern would be improved. Using the Winged Aircraft Cohered Arrays Multiple Input Multiple Output (WACA-MIMO) approach, which includes utilizing two transmit arrays, it is possible to achieve an improved beam pattern (0.044 sines, 2.5°) that is also grating lobe free, as illustrated by solid-line plot  214  in  FIG. 2 . The WACA-MIMO approach includes utilizing two transmit arrays,  30   l  and  30   r , as illustrated in  FIG. 1 . Plot  214  has a 3 dB beamwidth of 2.5°, which is superior to any of the other integrated beamwidths of  FIG. 2 . 
     The combination of the geometric configuration with MIMO processing enables a virtual array to be created across the physically-obstructed fuselage. The configuration or method is termed Winged Aircraft Cohered Arrays Multiple-Input-Multiple-Output, or WACA-MIMO for short. Freedom exists to make the arrays, both for transmit and receive, of shapes other than line arrays, as for example planes or warped planes (three-dimensional shapes) in order to create more complex WACA-MIMO configurations. 
     According to an aspect of the disclosure, the gap between the two wing arrays of set  24  of wing arrays is synthetically filled so as to obtain an effective array length which is greater than the physical extent of the physical arrays. This is accomplished, in part, by Multiple-Input, Multiple-Output (MIMO) signal processing to generate virtual arrays using receive wing arrays together with transmit antennas to form virtual arrays larger than the physical extent of the arrays. Thus, a transmitter array of M elements when MIMO combined with a receiver array of N elements forms or defines a virtual array of NM elements, not N+M elements. The spatial resolution for clutter is the same as that of a receiving array with NM physical elements. Put another way, NM degrees of freedom can be achieved or created using only N+M elements. 
     According to an aspect of the disclosure, the transmit array is made up of antenna elements, which are termed “horns” or ‘transmit horns” for ease of explanation;  FIG. 3D  is a simplified illustration of a horn antenna. These horns are shown as point sources (i.e., single antenna elements) but can be either line or 2-D arrays. Similarly, the receive arrays are shown as line arrays but can be either single elements or 2-D arrays. The locations of the transmit horns are selected as described in conjunction with  FIGS. 3A ,  3 B, and  3 C.  FIGS. 3A ,  3 B, and  3 C are simplified illustrations of the shape of an aircraft and the locations of some of the antennas according to aspects of the disclosure. Each of  FIGS. 3A ,  3 B, and  3 C is marked with X, Y, and Z coordinates. As illustrated in  FIGS. 3A ,  3 B, and  3 C, the receive antenna arrays  24   l  and  24   r  lie along a line  36  extending through the wings  24   l  and  14   r , respectively, and parallel with the X or −X axis. The transmit horns or antennas  30   l  and  30   r  are both located on a line  34  which is parallel with the X or −X axis. The transmit horns and the receive arrays are free to move parallel with Y-Z plane, so long as the transmit horns lie in the same line parallel with the X or −X axis (line  34 ) and the receive arrays lie in the same line parallel with the X or −X axis (line  36 ); the receive arrays need not lie in the same line as the transmit horns. The transmit and receive antennas must have an unobstructed view in the desired direction, which would ordinarily be in the forward or downward directions. In  FIG. 3B , the transmit horns  30   l  and  30   r  lie in the same Y-X plane and have the same Z offsets. In  FIG. 3C , the transmit horns  30   l  and  30   r  lie in the same plane parallel with the X-Y plane and have the same Y-offset; also, the receive arrays and elements lie in the same plane parallel with the X-Y plane, and have the same Z offset. These locations are those suited to forward direction, upward or downward search. Scan in other orthogonal directions may require other orientations of the antenna arrays, which should be apparent to those skilled in the art based on the teachings herein. 
     According to aspects of the disclosure, the radar antennas and arrays of  FIGS. 3A ,  3 B, and  3 C are cohered to provide a combined radiation pattern without grating lobes. The radar antennas and arrays of  FIGS. 3A ,  3 B, and  3 C are made a part of two digital array radars (DARs) with arrays  24   l  and  24   r  each of length L, with the arrays  24   l  and  24   r  separated by a gap  26 , also of length L. Transmit horn  30   l  lies in an axis illustrated as  32   l  in  FIG. 3C , which axis  32   l  lies parallel with the Y axis plane and which passes through the “inside” end  34   li  of the left receive array  24   l . The inside end of the array is that end nearest the fuselage  12 . Similarly, horn  30   r  lies in an axis illustrated as  32   r , which axis  32   r  lies parallel with the Y axis and which passes through the inside end  24   ri  of the right receive array  24   r . Clearly, planes  32   l  and  32   r  are mutually parallel. Mutually orthogonal waveforms are transmitted in a generally forward direction by each of the transmit antennas  30   l  and  30   r , so that the DAR arrangement can operate in Multiple-Input, Multiple-Output (MIMO) mode. Each receive antenna array  24   l ,  24   r  receives reflections from targets illuminated by each of the transmit horns. Since the waveforms transmitted by each transmit horn  30   l ,  30   r  are mutually orthogonal, the signals received by each receive array  24   l ,  24   r  can be separated to separately operate on the transmitted signals. Because the path from each transmitter to each receiver can be isolated, virtual elements can be created at the center of each transmit-receive pair.  FIGS. 4A ,  4 B, and  4 C show the combinations of these antenna arrays.  FIG. 4A  illustrates an arrangement  410  with two real or physical transmit antennas  30   l  and  30   r , spaced from each other by a distance d T =Nd R , transmitting mutually orthogonal signals φ 2 (t) and φ 1 (t) respectively. Signal φ 1 (t) transmitted from antenna  30   r  is represented by a dashed line, while φ 2 (t) transmitted from antenna  30   l  is represented by an unbroken line.  FIG. 4B  illustrates an arrangement  420  including a MIMO (Multiple-input, multiple-output) processor  430  and a set  424  of real or physical receive antenna elements designated  424   1 ,  424   2 ,  424   3 ,  424   4 , . . .  424   N . Antenna elements  424   1 ,  424   2 ,  424   3 ,  424   4 , . . .  424   N  represent actual or physical elements of arrays  24   l  and of array  24   r .  FIG. 4C  illustrates a virtual antenna line array designated generally as  450  and including virtual antenna elements designated  450   1 ,  450   2 ,  450   3 , . . .  450   MN . As indicated in  FIG. 4C , virtual antenna element  450   1  is synthesized from transmit antenna  30   l  and receive antenna  424   1 , virtual antenna element  450   2  is synthesized from transmit antenna  30   l  and receive antenna  424   2 , virtual antenna element  450   3  is synthesized from transmit antenna  30   l  and receive antenna  424   3 , virtual antenna element  450   N+1  is synthesized from transmit antenna  30   r  and receive antenna  424   1 , virtual antenna element  450   N+2  is synthesized from transmit antenna  30   r  and receive antenna  424   2 , and virtual antenna element  450   N+3  is synthesized from transmit antenna  30   r  and receive antenna  424   3 . Thus, each virtual element of  FIG. 4C  may be viewed as being made up from, or as being formed by, one transmit element and one receive element. The position of each virtual element is at the midpoint of the line segment joining the transmit and receive elements which make it up. Virtual antenna  450  of  FIG. 4C  has twice the angular resolution of a real or physical antenna array of similar size. This is a result of the fact that each virtual element has a unique transmit-element-to-receive-element path, thereby making the phase shift delta between virtual elements (which determines the angular resolution) depend on the round-trip path length as opposed to the usual one-way distance for a regular phased array. 
       FIGS. 4A ,  4 B, and  4 C together illustrate a principle that underlies an aspect of the disclosure. More particularly,  FIG. 4A  illustrates a transmit antenna array  410  with M elements driven by a plurality of sources, each with mutually orthogonal codings, which are represented by paths designated by dotted lines, dash lines, and chain (dot-dash) lines. The separation between the transmit antenna elements of  FIG. 4A  is d T =Nd R . The mutually orthogonal signals, as known, are capable of separation without interference.  FIG. 4B  illustrates a receive antenna array  420  including N elements, with inter-element spacing of d R . The two mutually orthogonal signals transmitted by elements in  410  reflect from a target and enter the receive antenna array  420 . The mutually orthogonal signals are separated, and flow to a MIMO processor  430  by way of multiple signal paths. As an alternative, the received signals may be coupled directly to MIMO processor  430  for separation and beamforming. The spatial resolution of the receive array for clutter under this condition is the same as that of a receive array of NM elements. That is, NM degrees of freedom can be achieved with only N+M elements. 
       FIG. 5  is a simplified block diagram of an aircraft  10  with a digital array radar system (DAR)  8  according to an aspect of the disclosure. In  FIG. 5 , elements corresponding to those of other FIGURES are designated by like reference alphanumerics. In  FIG. 5 , the receive antenna arrays  24   l  and  24   r  are of length L, and are separated by a gap  26 , also of length L. Each antenna element of left array  24   l  communicates by a separate path (which in the case of digital signals may include plural bit paths) with an individual receiver (not separately illustrated) of a set or array  512   l  of receivers. The set of paths is designated  511   l . Similarly, each antenna element of right array  24   r  communicates by a separate path of a set  511   r  with an individual receiver (not separately illustrated) of a set or array  512   r  of receivers. Also in  FIG. 5 , a first transmit antenna or horn  302  is driven from an output port  510   o   1   l  of a transmitter  510   l  with Radio Frequency (RF) electromagnetic signal or pulses modulated by a first code of a pair of mutually orthogonal codes. Second transmit antenna or horn  30   r  is driven from an output port  510   o   1   r  of transmitter  510   r  with electromagnetic signal at the same frequency and modulated by a second code of the mutually orthogonal pair. 
     The mutually-orthogonally-modulated signals transmitted by transmit horns  30   l  and  30   r  of  FIG. 5  reflect from targets which happen to be in the search volume, and the reflected signals or reflections are received by the individual antenna elements of the receive antenna arrays  24   l  and  24   r . The received signals flow from the individual elements of array  24   l  by way of paths illustrated as  511   l  to individual receivers of an array  512   l  of receivers, and the received signals flow from the elements of array  24   r  by way of paths illustrated as  511   r  to individual receivers of an array  512   r  of receivers. Receivers  512   l  and  512   r  also receive phase-controlled samples of the carrier RF signal, and downconvert to baseband or to intermediate frequency (IF) the received signals. Thus, the signals appearing at the output signal paths  514   l  and  514   r  represent the downconverted received signals, modulated by both of the mutually orthogonal signals. The downconverted signals are applied from receiver array  512   l  by way of paths  514   l  to a processor (Proc) array  516   l , and the downconverted signals are applied from receiver array  512   r  by way of paths  514   r  to a processor (Proc) array  516   r . Processor array  516   l  receives the first and second codes of the mutually orthogonal pair by way of path  510   o   3   l , and processor array  516   r  receives the first and second codes of the mutually orthogonal pair by way of path  510   o   3   r . Processors shown in the FIGURES are in separate blocks only for logical, conceptual, or explanatory grouping purposes. 
     Processor array  516   l  of  FIG. 5  separates the signals received by the left antenna array  24   l  for each code impressed on the signal, corresponding to the transmitter antenna from which the signal originated. It does this by deeming that component of the received signal which is encoded with the first code to have originated from transmit horn  30   l , and that component of the received signal which is encoded with the second code to have originated from transmit horn  30   r . Similarly, processor array  516   r  separates the signals received by the right antenna array  24   r  depending upon the transmitter antenna from which the signal originated. It does this by deeming that component of the received signal which is encoded with the first code to have originated from transmit horn  30   l , and that encoded with the second code to have originated from transmit horn  30   r . The processed received signals are coupled from processors  516   l  and  516   r  by way of paths  518   l  and  518   r  to a beamforming processor or beamformer  520 . Beamformer  520  forms beam signals through the use of analog or digital beamforming (DBF) in a known fashion and produces the beam signals on a set of paths  522 . The beam signals are applied by way of paths  522  to conventional radar processing illustrated as a block  530 , which produces conventional radar signals at output ports illustrated as  530   o . Radar Control Computer (RCC)  524  performs the usual functions of synchronizing the operation of the various parts of the radar system and establishing the operating parameters,  510 , including the operating frequency, repetition rate, pulse width or duration, the number and direction(s) of the antenna beams, pulse compression coding, receive sampling rate, amplifier gains, and the like. 
     The RCC  524  of  FIG. 5  also establishes the weighting of the signals transduced by the antenna elements of antenna array so as to shape the beam and establish the sidelobe level, as is well known in the antenna arts. 
     The beam(s) produced by MIMO beamformer  520  of  FIG. 5  will have improved angular resolutions, as described in conjunction with  FIG. 2 , regardless of the post-processing (e.g., Detection Processing, Doppler Filtering, Tracking) which is performed by the remaining portion of the radar system. 
       FIG. 6  illustrates in notional form the left (Rx 1 ) and right (Rx 2 ) receive arrays  24   l  and  24   r , respectively. The spacing between elements of the receive antenna arrays is designated d R . The left-most antenna element of array  24   l  is marked with its x-position x 0 , and the right-most antenna element of left array  24   l  is marked with x-position x 1 . The left-most antenna element of right receive array  24   r  is marked as being at x-position x 4 , separated from the position x 1  of the right-most element of left array  24   l  by the gap  26 . The right-most antenna element of right array  24   r  is marked with x-position x 5 . The lengths of the left array  24   l , gap  26 , and right array  24   r  are each given by length L. The X-position of the left transmit antenna (Tx 1 )  30   l  is designated x 2  and that of the right transmit antenna (Tx 2 )  30   r  is designated x 3 . There should be no overlap of the synthetic elements, which can limit the length of the synthetic array. Satisfying the following equations provides a satisfactory configuration: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     A radar system  10  according to an aspect of the disclosure comprises first  30   l  and second  30   r  point sources transmitting electromagnetic waveforms (from  510 ), and first  24   l  and second  24   r  line arrays of receive antennas for receiving radar return signals originating with the point sources, the first and second line arrays being separated by a gap  26 . A digital multiple-input multiple-output (MIMO) processor  512 ,  516 ,  520  processes the signals received by the elements of the line arrays to cohere the arrays across the gap  26 . In a preferred embodiment, mutually orthogonal waveforms are transmitted by the point sources. In a particular embodiment, the first  24   l  and second  24   r  line arrays of receive antennas are mutually coaxial. In another embodiment, the gap  26  between the first  24   l  and second  24   r  line arrays of receive antennas is no larger than the length of one of the first and second line arrays of receive antennas. The radar system may be associated with an aircraft  8  including first and second wings and a fuselage separating the first and second wings, and in this embodiment the first and second line arrays of receive antennas lie generally along the first and second wings, respectively, with the fuselage occupying at least a portion of the gap. 
     A radar method according to an aspect of the disclosure comprises the steps of transmitting mutually orthogonal waveforms from first  30   l  and second  30   r  point sources, and receiving radar return signals originating with or from the point sources  30   l ,  30   r  with first  24   l  and second  24   r  line arrays of receive antennas separated by a gap  26 . The method further includes the step of performing multiple-input multiple-output (MIMO) digital processing  520  for cohering the arrays  24   l ,  24   r  across the gap  26 . In a particular mode of the method, the step of receiving radar return signals originating with or from the point sources  30   l ,  30   r  with first  24   l  and second  24   r  line arrays of receive antennas separated by a gap  26  includes the step of receiving radar return signals originating with or from the point sources  30   l ,  30   r  with first  24   l  and second  24   r  mutually coaxial arrays of receive antennas separated by a gap  26 . In a particularly advantageous mode, the gap  26  is no larger than the length of one of the first  24   l  and second  24   r  line arrays of receive antennas. In a most advantageous mode, the step of associating the first and second point sources  30   l ,  30   r , the first and second arrays  24   l ,  24   r , and the MIMO processor  520  with an aircraft  10  including a first wing  14   l  bearing the first array  24   l , a second wing  14   r  bearing the second array  24   r , and a fuselage  12  separating the first  24   l  and second  24   r  arrays. 
     An airborne radar system  10  according to an aspect of the disclosure comprises an airplane  8  defining a first  14   l  and second  14   r  spaced-apart wings. A line receiving antenna array  24  includes first  24   l  and second  24   r  separate receiving antenna array portions. The receiving antenna array portions lie mutually coaxially  36  along the wings  14   l ,  14   r . Thus, the line receiving array  24  includes two separate, mutually coaxial ( 36 )  36  line receiving array portions  24   l  and  24   r . Each separate portion  24   l ,  24   r  of the receiving antenna array  24  defines an inside edge  24   l ,  24   r  separated from the inside edge  24   li ,  24   ri  of the other array portion by a gap  26 . The radar system  10  includes a line transmitting antenna array  30  lying along an axis  34  parallel with the axes  36  of the receiving antenna array portions  24   l ,  24   r . A transmitter  510   l ,  510   r  is coupled to the antennas  30   l ,  30   r  of the transmitting antenna array  30 , for exciting the antennas  30   l ,  30   r  of the transmitting array  30  with mutually orthogonal signals. A multiple-input multiple-output processor  520  is coupled to the transmitter  510   l ,  510   r  and to the receiving antenna array  24 , for processing received signals for forming an effective array including real or physical elements (antenna sets  410  and  424 ) and also including virtual elements (set  450 ) occupying positions along the gap  26 . 
     A radar system  10  according to an aspect of the disclosure comprises a first antenna array  24   l , which may be a line array, including antenna elements extending generally horizontally along a line  36 , and having a first extent (x 0  to x i ). The line array may be a portion of a two-dimensional array. A second antenna array  24   r , which may be a line array, includes antenna elements extending along the line  36 , and has a second extent (x 4  to x 5 ), which need not be the same as the first extent. The radar system  10  also comprises a first transmit antenna  30   l  and second transmit antenna  30   r . The first transmit antenna  30   l  lies in a vertical (parallel with the YZ plane) plane  32   l  passing through the inside end  24   li  of the first antenna array  24   l . The second transmit antenna  30   r  lies in a vertical (parallel with the YZ plane) plane  32   r  passing through the inside end  24   ri  of the second antenna array  24   r . The first  30   l  and second  30   r  transmit antennas lie in the same horizontal plane  34 . The radar system  10  also includes first  510   l  and second  510   r  transmitters for generating mutually orthogonal RF signals, the first  510   l  and second  510   r  transmitters being connected to the first  30   l  and second  30   r  transmit antennas, for transmitting first and second mutually orthogonal electromagnetic signals from the first  30   l  and second  30   r  transmit antennas, respectively. The radar system  10  further includes first  512   l  and second  512   r  receiver arrays coupled to the first  24   l  and second  24   r  antenna arrays and to the first  510   l  and second  510   r  transmitters, for processing reflected signals for generating downconverted received (baseband or intermediate frequency) first and second received signals from each of the elements of the first  24   l  and second  24   r  antenna arrays, respectively. Each of the downconverted received signals includes components attributable to the first and second mutually orthogonal electromagnetic signals. First  516   l  and second  516   r  processors are coupled to the first  512   l  and second  512   r  receiver arrays, respectively, and to the first  510   l  and second  510   r  transmitters, for processing the first and second downconverted signals to separate the first and second components of the mutually orthogonal received signals. A beamforming processor  520  is coupled to the first  516   l  and second  516   r  processors for coherently combining the first components of the mutually orthogonal received signals with the second components of the mutually orthogonal received signals to thereby define at least a first beam. In a particular embodiment, an airplane  10  including first  14   l  and second  14   r  wings separated by a fuselage  12  is associated with the radar, the first antenna array  24   l  lies along the first wing  14   l , and the second antenna array ( 24   r )  24   r  lies along the second wing  14   r , with the first  24   l  and second  24   r  arrays separated by a gap  26  at the location of the fuselage  12 . In this embodiment, the vertical (YZ) planes through which the third and fourth antennas lie pass through the inside ends  24   l ,  24   r  of the first  24   l  and second arrays  24   r , respectively. 
     A radar system  10  according to another aspect of the disclosure comprises a first antenna array  24   l  (which may include elements in a line array or in a planar array) extending along a line  36 , and having a length (L). The radar system  10  also includes a second antenna array  24   r  extending along the line  36 , and having the length (L). The second array is separated from the first array by a distance no greater than the length (L), thereby defining an inside end  24   li  of the first antenna array  24   l  and an inside end  24   ri  of the second antenna array  24   r . Outside end  24   lo  of the first antenna array  24   l  and outside end  24   ro  of the second antenna array  24   r  are also defined. The radar system  10  also includes first  30   l  and second  30   r  transmit antennas, the first transmit antenna  30   l  lying in a vertical plane (parallel with the YZ axis) passing through the inside end  24   li  of the first antenna array  24   l , and the second transmit antenna  30   r  lying in a vertical plane (parallel with the YZ plane) passing through the inside end  24   ri  of the second antenna array  24   i . The first  30   l  and second  30   r  transmit antennas lie at the same distance from the horizontal (XY) plane. The radar system— 10  also includes first  510   l  and second  510   r  transmitters for generating mutually orthogonal RF signals. The first  510   l  and second  510   r  transmitters are connected to the first  30   l  and second  30   r  transmit antennas, for transmitting first and second mutually orthogonal electromagnetic signals from the first  30   l  and second ( 30   f )  30   r  transmit antennas, respectively. First  512   l  and second  512   r  receiver arrays are coupled to the first  24   l  and second  24   r  antenna arrays, for processing reflected signals for generating first and second received signals (such as downconverted or baseband signals) from each of the first  24   l  and second  24   r  antenna arrays, respectively, each of the received signals including components attributable to the first and second mutually orthogonal electromagnetic signals. First  516   l  and second  516   r  orthogonal separation processor arrays are coupled to the first  512   l  and second  512   r  receiver arrays, respectively, for processing the first and second received signals to separate the first and second components of the mutually orthogonal received signals. A beamforming processor  520  is coupled to the first  516   l  and second  516   r  orthogonal separation processor arrays for coherently combining the first components of the mutually orthogonal received signals with the second components of the mutually orthogonal received signals to thereby define a first beam. A particularly advantageous embodiment of this radar system  10  further comprises a radar control processor  524  coupled to the second processor  520  for adjusting the weighting of the coherent combining to thereby shape the antenna beam.