Off-axis indicator algorithm for electrically large antennas

A technique is described which makes novel use of monopulse data to augment the normal CFAR detection processing by incorporating monopulse data in a computationally simple way into the detection decision process such that off-axis signals which are of sufficient strength to pass a CFAR detection threshold are effectively rejected by a second detection threshold. The signal compared to the second detection threshold is formed from all of the monopulse channels. Detection processing is thus a two step process, incorporating not only the information contained in the magnitude of the Sum channel, but information contained in all of the monopulse channels.

STATEMENTS REGARDING FEDERALLY SPONSORED RESEARCH
 Not applicable.
 FIELD OF THE INVENTION
 This invention relates generally to radar systems and more particularly to
 systems and techniques for monopulse processing in such radar systems.
 BACKGROUND OF THE INVENTION
 One of the most common uses for military radar systems is discerning the
 angle of arrival of a signal relative to the radar. The fundamental way in
 which a radar determines angle of arrival is to use a directional antenna
 on both transmit and receive. The antenna sidelobes significantly
 attenuate off axis signals, thereby making the radar most sensitive to
 signals entering through the mainbeam. The mainbeam signal is then
 processed to determine its angle of arrival relative to the direction in
 which the antenna is pointing. Meaningful angle of arrival information is
 available only for targets located in the mainbeam of the radar antenna.
 Sidelobe targets, when they are of sufficient strength to overcome the
 sidelobe attenuation of the antenna, yield erroneous angle of arrival
 data. A radar used to search for and track targets must therefore have
 some means for discerning off-axis signals in the sidelobes from those
 entering the mainbeam.
 Typically, three primary techniques for identifying off-axis signals are
 currently in widespread use. The first is the use of a guard channel or
 channels having a separate broad beam antenna with more gain than the side
 lobes of the primary receive channel (in the case of a monopulse radar,
 the Sum channel is the primary receive channel). When the guard channel
 signal level exceeds that of the Sum channel, off-axis indication is
 given. The second is the Track method, where off-axis signals are placed
 under track, and then ignored when their range and/or Doppler do not match
 that expected for the target of primary interest. The Track method is used
 primarily to reject discrete clutter when the target of interest is moving
 relative to the clutter (i.e., is separated in Doppler relative to that of
 the discrete clutter), and finds application in Medium Pulse Repetition
 Rate Frequency (MPRF) radars where the processed Doppler space is
 ambiguous with the Doppler of both the target signal and sidelobe clutter
 signal. The final technique, applicable to a monopulse radar, is to
 compare the detected boresight error to a threshold. When the detected
 boresight error exceeds the threshold in one or both of the principle
 angle tracking planes of the radar (e.g., pitch or yaw), an off-axis
 indication is given. This two channel OR technique is based on the
 principle that in the sidelobe region, the difference pattern sidelobes
 typically exceed the sum pattern sidelobes over a significant portion of
 angle space. The two channel OR techniques works best for off-axis signals
 located on or near one of the principal angle tracking planes of the
 radar.
 While both the guard channel and Track methods can be highly effective,
 neither is very appealing in an airborne missile application. In airborne
 missile applications, both packaging volume and time are in very short
 supply. Available space to package the radar hardware is generally very
 limited, and with the high velocities involved with missile applications,
 there is very little time to search for and acquire targets (modern
 missiles generally have a terminal sensor which is cued to the general
 location of the target by either off-board or on-board tracks). Guard
 channels require additional hardware, while placing off-axis targets under
 track complicates the on-board computer hardware (in terms of having
 sufficient throughput to process a potentially large number of extraneous
 tracks) and slows the radar search process by the time needed to initiate
 tracks and resolve any range and Doppler ambiguities that may be present
 with the waveforms in use. With the trend toward the use of millimeter
 wave seekers in missile applications, the seeker antenna is electrically
 large, thus having high gain. The near in sidelobes, which cover an
 important portion of angle space, can be well above isotropic, meaning
 that the guard channel antenna required to cover the near in sidelobe
 region must be directional. To cover both the near in and far out
 sidelobes, multiple guard channels can be required, depending on the
 characteristics of the seeker antenna.
 The two channel OR method of off-axis indication is simple, requiring no
 additional hardware or calculation beyond that used for normal angle of
 arrival processing. For planes well off of the principle angle tracking
 planes, however, off-axis identification degrades compared to that in the
 principal planes.
 It would, therefore, be desirable to provide a technique which addresses at
 least the above problems with prior art systems.
 SUMMARY OF THE INVENTION
 In accordance with the present invention, a method of operating a monopulse
 radar system includes the steps of: forming a sum signal, .SIGMA., an
 azimuth difference signal, .DELTA..sub.az, an elevation difference signal,
 .DELTA..sub.el, and a quadrupole, or diagonal difference signal, Q, and
 obtaining magnitudes of each of the respective signals; comparing the
 magnitude of the azimuth difference signal, .DELTA..sub.az with the
 magnitude of the sum signal, .SIGMA.; comparing the magnitude of the
 elevation difference signal, .DELTA..sub.el with the magnitude of the sum
 signal, .SIGMA.; comparing the magnitude of the Q difference signal, Q
 with the magnitude of the sum signal, .SIGMA.; summing each result of the
 comparing steps; and comparing the summed result with a threshold value to
 determine an off-axis indication. With such a technique, use of monopulse
 data is provided to augment the normal CFAR detection processing. Normal
 CFAR processing typically uses only the magnitude of the Sum channel
 signal to make detection decisions. The invention described herein
 incorporates monopulse data in a computationally simple way into the
 detection decision process such that off-axis signals which are of
 sufficient strength to pass the CFAR detection threshold are effectively
 rejected by a second detection threshold. The signal compared to the
 second detection threshold is formed from all of the monopulse channels.
 Detection processing is thus a two step process, incorporating not only
 the information contained in the magnitude of the Sum channel, but
 information contained in all of the monopulse channels. The invention can
 eliminate off-axis detections with 95% or greater certainty, with minor
 loss in mainlobe detection probability. Detailed quantitative performance
 data as a function of signal to noise ratio is also provided.
 Essential features of the invention are demonstrated for the W-Band 150 mm
 diameter aperture described in "Principles and Applications of
 Millimeter-Wave Radar" by Currie and Brown (1987, Artech House). The
 Currie and Brown aperture has been modified with a 0.375 in. radius
 blockage to simulate an amplitude monopulse aperture with low sum and
 difference sidelobes.
 In accordance with another feature of the invention, a method of operating
 a monopulse radar system includes the steps of: forming a respective
 digital signal indicative of a signal from each quadrant of a monopulse
 antenna; forming a sum signal indicative of a combined signal from all
 quadrants of the monopulse antenna and deriving a magnitude of said sum
 signal; forming difference signals of each possible combination of signals
 from each quadrant of the monopulse antenna and deriving a magnitude of
 each of the respective difference signals; comparing the magnitude of each
 of the difference signals to a magnitude of the sum signal; and summing
 any result. The result is compared with a threshold value to determine if
 an off-axis indication is warranted. With such an arrangement, improved
 off-axis signal rejection is obtained by being able to detect such
 off-axis signals and then filtering such signals from the desired signals.

DETAILED DESCRIPTION OF THE INVENTION
 Referring now to the drawings, in which like reference characters designate
 like or corresponding parts or signals throughout the several views, there
 is shown in FIG. 1 a block diagram of a radar system 100 comprising a
 computer 150, a master oscillator 112, transmitter 110, a receiver 120, a
 duplexer 130 and an antenna 140. The transmitter 110 includes an exciter
 114, exciter control circuitry 116 and a transmitter power amplifier 118.
 The receiver 120 includes a receiver 124, analog-to-digital (A/D)
 converter 126, and a digital signal processor 128. The radar system 100
 further includes monopulse arithmetic circuitry 132 to form a sum channel
 and an azimuth, an elevation and a Q channel according to the present
 invention. The system of FIG. 1 represents a pulse radar system, although
 it is to be understood that the present invention may be adapted for use
 in other systems.
 The computer 150 provides reference signals 13a-13d to provide the various
 components of the radar system 100 the requisite control signals as
 described hereinafter. In a conventional manner, the master oscillator 112
 in response to the computer 150 provides a signal to the exciter 114 which
 in turn provides an RF signal at the output thereof. The RF signal 11 is
 then fed to the transmitter power amplifier 118 where the transmitted
 signal is amplified, and via duplexer 130, is fed to antenna 140. The
 antenna 140 is a monopulse antenna. As antenna 140 scans the search area,
 a received signal 19 is reflected by objects within the operating range of
 the radar system 100. Received signal 19 is then received by antenna 140.
 In conventional fashion, received signal 19 is fed from the antenna 140 to
 the monopulse arithmetic circuitry 132 to form a sum signal and an azimuth
 difference signal, an elevation difference signal and a Q difference
 signal which are fed to the receiver 124 which in turn heterodynes the
 just mentioned signals with a signal from the master oscillator 112 to
 produce baseband signals. The baseband signals are fed to the A/D
 converter 126 which in turn produces discrete time samples of the baseband
 signals, the sampled baseband signals then being fed to the digital signal
 processor 128. In accordance with the present invention, the digital
 signal processor 128 then performs additional analysis such as a discrete
 Fourier transform to determine Doppler frequencies and other information
 of interest in a manner as described hereinafter. The latter is then fed
 to the computer 150 to provide control signals to control a vehicle as
 well as the various components of the radar system 110. It is to be
 understood that while digital signal processor 128 and computer 150 are
 shown separately, a single computer may be alternatively used or a
 combination of multiple computers and digital signal processors may be
 used. The receiver 120 also includes a CFAR detection circuit to filter
 out undesired signals including signals from antenna sidelobes and a
 nulling circuit to reject off-axis signals which are of sufficient
 strength to pass the CFAR detection circuit when there is a positive off
 axis indication signal.
 The radar system 100, here a four-channel monopulse receiver, according to
 this invention, is conventional in construction to produce. In the
 monopulse antenna 140 and monopulse arithmetic circuitry 132, a sum beam
 (not shown) of radio frequency energy, such beam here having a boresight
 line orthogonal to the aperture of the monopulse antenna as shown is
 produced. That aperture, as shown, here is divided into four equal sectors
 (or quadrants), each with a phase center A, B, C or D. As is known, the
 radio frequency (RF) signal in the receive mode at each phase center A, B,
 C and D is the vectorial sum of the RF signals received by the antenna
 elements (not shown) in the corresponding quadrant. It will be
 appreciated, therefore, that (in the receive mode) a monopulse sum signal,
 .SIGMA.(RF), an elevation difference signal, .DELTA..sub.el (RF), an
 azimuth difference signal .DELTA..sub.az (RF) and Q signal .DELTA..sub.Q
 (RF) derived from a single target and appearing at the various output
 ports of the illustrated monopulse arithmetic circuitry may be described
 as follows:
EQU .SIGMA.(RF)=V.sub.A +V.sub.B +V.sub.C +V.sub.D
EQU .DELTA..sub.el (RF)=(V.sub.A +V.sub.B)-(V.sub.C +V.sub.D)
EQU .DELTA..sub.az (RF)=(V.sub.A +V.sub.D)-(V.sub.B +V.sub.C)
EQU .DELTA..sub.Q (RF)=(V.sub.A +V.sub.C)-( V.sub.B +V.sub.D)
 where V.sub.A, V.sub.B, V.sub.C and V.sub.D each is a vectorial quantity.
 It should be noted that for a target (not shown) on boresight of a
 monopulse antenna 140 having four quadrants, in an ideal monopulse system,
 signals from each of the four quadrants of the monopulse antenna 140 would
 be equal. The signals can be combined in monopulse arithmetic circuitry
 132 to yield a sum channel and an azimuth difference channel, an elevation
 difference channel and a Q difference channel. The sum channel would be a
 maximum and the remaining channels would be zero. In a non-ideal monopulse
 system, signals detected by sidelobes of the monopulse antenna 140, can
 cause errors in the resulting control signals produced by the radar system
 100.
 The invention is a set of techniques and algorithms which indicate to a
 monopulse radar whether a signal is arriving from a direction
 corresponding to the pointing direction of the antenna main beam, or from
 a direction corresponding to directions covered by the antenna sidelobes.
 With these algorithms, reliable indication is achieved with information
 already available to the typical tracking radar. The algorithms can be
 applied in phase or amplitude monopulse configurations and for fixed beam
 or phase array antenna architectures. The algorithms are applicable to
 existing four-channel monopulse systems and implementation would not
 require changes to the hardware configurations of four-channel monopulse
 antennas or radars. The common thread unifying the set of algorithms is
 comparison of signals in all data channels of a four-channel monopulse
 radar.
 Before departing on a detailed description of the invention, it may be
 helpful to review the state of the art. Reliable sidelobe indication is
 achieved by comparing the response to a common signal in four channels of
 a monopulse radar. The common generic monopulse radars use amplitude
 monopulse or phase monopulse antennas. In an amplitude monopulse system,
 the antenna forms orthogonal RF channels by adding and subtracting common
 source responses of four beams sharing a common phase center and pointed
 in known, but specifically not overlapped, directions in space as
 illustrated for a two beam amplitude monopulse antenna in FIG. 2A. The
 radar derives angle information by comparing the amplitudes and signs of
 the sum and difference channel outputs. In a phase monopulse system, the
 antenna forms orthogonal channels by adding and subtracting common source
 complex responses of parallel beams associated with the half apertures of
 the antenna as shown in FIG. 2B. Note the beams do not share a common
 phase center. Angle information is derived as for amplitude monopulse.
 In most typical monopulse radars, the antenna provides monopulse RF
 outputs. That is, prior to active operation on the received signal, a
 microwave monopulse network (i.e. monopulse arithmetic circuitry) is used
 to combine the RF energy in each beam or from each aperture segment to
 form the standard monopulse output set of sum, two differences and
 (sometimes) the difference of difference (sometimes referred to as the Q
 Channel) outputs. This is not a necessary condition of operation,
 particularly with the advances in digital processing over the last decade.
 RF processing works well in numerous fielded systems. The four beams of an
 amplitude monopulse antenna can be added and subtracted in an RF network
 comprised of line lengths and magic tee power dividers as shown in FIG.
 2C. The network in the FIG. 2C is generally associated with combining, the
 four beams in pairs of pairs across the aperture phase center although
 other configurations are possible. In particular, the beams can be
 combined in simple pairs across the phase center, as shown in FIG. 2D,
 though this arrangement leads to lower difference channel antenna gain
 relative to the sum. The same networks can be used to combine the outputs
 of each phase center of the phase monopulse network.
 A major distinction between amplitude and phase monopulse is the fall off
 rate of the far field tracking pattern sidelobe response relative to that
 of the sum pattern. Typical phase monopulse pattern cuts are shown in FIG.
 2E for a uniformly illuminated 150 mm diameter circular aperture operating
 at 94 GHz. (This aperture and its applications are discussed in
 "Principles and Applications of Millimeter-Wave Radar" by Currie and
 Brown.) As subtracting the responses of aperture halves creates a phase
 monopulse antenna difference pattern, a large (effective) illumination
 discontinuity is produced at the full aperture phase center. This
 discontinuity results in high difference pattern sidelobes in the plane
 orthogonal to the excitation (the sidelobe level difference decreases as
 the cut plane moves off the plane of the difference). Furthermore, as the
 sum pattern sidelobe response improves (that is, as the sum sidelobes go
 down relative to full antenna gain), the influence of the discontinuity
 increases, further increasing the difference pattern sidelobe levels. In
 the plane of the difference, an amplitude monopulse system has
 intrinsically lower difference channel sidelobes than a phase monopulse
 system: with an amplitude monopulse antenna the strong central
 discontinuity is eliminated and the individual beam pattern symmetry with
 respect to the full aperture phase center is maintained. Amplitude
 monopulse pattern cuts with the characteristics typical of large aperture
 antenna patterns are shown in FIG. 2F.
 Note that the difference pattern sidelobes of the phase monopulse antenna
 patterns in FIG. 2E are high relative to the sum pattern sidelobes and
 that the nulls of the difference pattern are filled. Two mechanisms
 contribute to null fill for this particular phase monopulse antenna.
 First, the aperture is circular, resulting in asymmetric half aperture
 illumination distributions: patterns produced by asymmetric distributions
 have filled nulls. FIG. 2G compares pattern cuts produced by halves of an
 electrically large uniformly illuminated circular planar aperture with
 random errors: the sum pattern is shown for reference. Patterns are taken
 in the plane orthogonal to the plane of the discontinuity. The half
 aperture patterns are substantially identical and symmetric. Note that the
 half aperture pattern sidelobe region forms the sum pattern sidelobe
 envelope when properly normalized. Secondly, half aperture patterns have
 conjugate symmetry with respect to the full aperture phase center. This is
 illustrated in FIG. 2H. FIG. 2H shows half aperture pattern phase for the
 specific measurement condition of rotation about the full aperture phase
 center. Pattern phase is substantially &gt;90 degrees in the sidelobe
 region. Difference pattern formation (a subtraction process) adds nearly
 identical responses having no nulls thereby producing a total pattern
 without nulls. Sum pattern formation (an addition process) subtracts
 nearly identical responses, thereby producing a total pattern with deep
 nulls.
 The previous discussion presented the characteristics of monopulse antenna
 patterns in the principal planes (planes of the differences). However,
 indication of an off-axis source is an issue over the entire field of view
 of a radar antenna, including backlobe regions. FIGS. 3A and 3B present
 spectral distribution charts showing the ratio of difference channel
 response to sum channel response over a quadrant of the forward hemisphere
 for the Currie and Brown aperture at 94 GHz with 0.75" blockage introduced
 to approximate prime focus blockage effects. The spatial region sample
 rate is approximately 6 points per beamwidth. In first regions of the
 Figures, the sum pattern is at least 5 dB above the difference. In second
 regions, the sum is slightly greater than the difference. In third
 regions, the difference pattern is 0 to 5 dB greater than the sum (the
 third regions in the lower left corners of the Figures are outside the
 forward hemisphere of the antenna). All other levels indicate the
 difference is significantly greater than the sum. As seen in FIGS. 3A and
 3B, the difference pattern is substantially below the sum over
 approximately half of the forward hemisphere and the diagonal plane (225
 degrees off the sin .alpha.-axis, here) is relatively ambiguous in level.
 It is obvious that by comparing pitch difference to sum and,
 independently, yaw difference to sum, a moderately successful indication
 of an off-axis source can be achieved (we refer to this as OR processing).
 That is, a pitch to sum comparison pretty well identifies an off-axis
 source in the pitch plan and maintains a sufficiently large ratio out to
 about 30 degrees off the pitch plan for a high probability of
 identification and similarly for the yaw channel. As the differences
 derive from the sum, a high incidence of null alignment can be expected
 near the 45 degree plane, and no significant reinforcement is expected
 using the OR process. A spectral density plot illustrating the use of OR
 processing for sidelobe indication is shown in FIG. 3C for an amplitude
 monopulse antenna. The plot represents the OR as the greater of pitch to
 sum and yaw to sum ratios plotted in dB. Again, first and second regions
 identify regions in which the sum always exceeds the differences and third
 regions identifies regions in which the difference pattern exceeds the sum
 by 5 dB or less. As expected, the 45-degree plane is not well covered.
 An alternate representation of OR data is shown in FIG. 3D. A trace of the
 FIG. 3D shows the density of ratio level occurrence throughout the forward
 hemisphere, excluding the region within the sum beam 3-dB contour. A
 second trace shows the distribution of level occurrence outside the
 mainbeam. The third trace shows the percentage of the mainbeam 3-dB region
 area that is covered by ratio levels at and below the value on the
 abscissa. The next largest integer to the ratio level for 100% mainbeam
 coverage is taken as the base threshold for the system. At the base
 threshold level of -2 dB for the OR algorithm, the distribution function
 trace shows that the algorithm declares a signal arriving from a sidelobe
 direction to be a mainbeam target 19.46% of the time. For these traces,
 the quadrant is sampled at about 7 points per mainbeam beamwidth outside
 the sum beam 3-dB contour, and at about 7800 points within the sum beam
 3-dB contour.
 If the square roots of the difference to sum power ratios are added (linear
 addition of electric field quantities is an AND process) rather than Ored,
 a small improvement in coverage is obtained in and around the 45-degree
 plan without significantly changing the distribution within the mainbeam
 3-dB region. The base thresholds for the AND or OR algorithms are at the
 95% level for mainbeam coverage and the AND algorithm declares a signal
 arriving from a sidelobe direction to be a mainbeam target 21.17% of the
 time. AND algorithm data is shown with the spectral density plot in FIG.
 3E and in the distribution traces in FIG. 3F. Neither the OR nor AND
 algorithm offers a very robust approach to sidelobe indication for radars
 with large amplitude monopulse antennas.
 The spectral density plots for the 2-channel algorithms indicate that
 neither fills the intercardinal plane well. In both cases, the individual
 difference patterns fall off rapidly as the null plane is approached, and
 the reinforcement provided by either comparison method is insufficient to
 achieve robust sidelobe indication.
 Each tracking difference pattern of a monopulse antenna is antisymmetric
 with respect to a single plane. The two planes of antisymmetry contain the
 antenna phase center and are, in absence of noise and antenna
 manufacturing error, spatially orthogonal. Tracking difference patterns
 are functionally orthogonal to the sum pattern. As discussed in the
 previous section, the Q-channel is an additional port of a classical
 monopulse network that supports a fourth orthogonal response with a
 pattern that has a pair of null planes that are spatially orthogonal and
 coincident with the null planes of the tracking difference patterns.
 Q-channel patterns have high sidelobe ridges in the intercardinal planes
 as shown in FIG. 3G over a quadrant of the forward hemisphere. Q-channel
 response is functionally orthogonal to the other three channels of the
 monopulse network.
 If the Q-channel response magnitude is added to the AND algorithm, the weak
 response in the intercardinal planes is reinforced, resulting in
 significantly improved sidelobe indication without adversely effecting
 system sensitivity in the mainbeam region. The new algorithm is given as:
EQU A.sub.1
 ={.vertline..DELTA..sub.az.vertline.+.vertline..DELTA..sub.
 el.vertline.+.vertline.Q.vertline.}/.vertline..SIGMA..vertline. Eq. 1
 Where .SIGMA. denotes a sum channel response, .DELTA. denotes a difference
 channel response and .vertline. .vertline. denotes magnitude only. The
 latter is implemented in digital signal processor 128.
 The significant improvement in sidelobe indication that can be achieved
 with the new algorithm is illustrated in FIGS. 3H and 3I for the same
 large amplitude monopulse antenna considered previously. For historical
 reasons, this algorithm is referred to as the First Order Algorithm.
 Comparison of FIG. 3D, FIG. 3F and FIG. 3I shows that relative to the AND
 or OR algorithms, the First Order Algorithm produces a significant
 reduction in the spectral density plot area associated with sum response
 dominance or near equality. The traces in FIG. 3I further emphasize the
 improvement wherein the addition of the Q-channel response increases
 sidelobe indication probability to 93.01% for 2 dB base threshold.
 It should now be appreciated a significant improvement over state of the
 art performance in sidelobe indication probability is offered by the First
 Order Algorithm.
 As described herein above, the typical monopulse implementation adds and
 subtracts the responses in four ports, each port corresponding to an
 independent beam emanating from a single center, as in amplitude
 monopulse, or to an independent phase center, as in phase monopulse. If
 the response amplitude for each beam or the response amplitude for each
 monopulse channel is available to the signal processor, an alternate
 sidelobe indication algorithm with even better performance can be
 constructed.
 An objective of the present invention is to seek methods of reducing or
 eliminating nulls in the combined difference channel sidelobe response.
 The First Order Algorithm only partially succeeds in this regard because
 aperture symmetry is maintained in some sense for each of the difference
 responses, that is, sidelobe region nulls retain a concentric relation to
 the aperture phase center for all four channels. It is therefore clear
 that a method of decorrelating difference response sidelobe nulls while
 maintaining difference response nulls over the aperture phase center is to
 pair the beams asymmetrically, then add magnitudes of these new responses
 and compare the summation to the sum pattern.
 Results for the simplest and, it turns out, most effective application of
 multibeam sidelobe indication algorithm are shown in FIGS. 3J and 3K. The
 algorithm, which is known as a Four Term Algorithm, produces a 96.7%
 probability of sidelobe indication for 96.3% mainbeam coverage at a base
 threshold of 1 dB. The algorithm is constructed by forming differences of
 the four possible combinations of contiguous beam pairs, comparing the
 magnitudes of these differences to the sum pattern magnitude and summing
 the result. That is, let the constituent beams (or antenna quadrant phase
 centers for phase monopulse antennas) be numbered sequentially about the
 antenna phase center beam. The responses are then B.sub.1, B.sub.2,
 B.sub.3 and B.sub.4, and the sum pattern is given by
EQU .SIGMA.=B.sub.1 +B.sub.2, +B.sub.3 +B.sub.4 Eq. 2
 The four term algorithm is given by
EQU A.sub.4 ={.vertline.B.sub.1 -B2.vertline.+.vertline.B.sub.2
 -B.sub.3.vertline.+.vertline.B.sub.3 -B.sub.4.vertline.+.vertline.B.sub.4
 -B.sub.1.vertline.}/.vertline..SIGMA..vertline. Eq. 3
 It should be appreciated the improvement over state of the art performance
 in sidelobe indication probability offered by the Four Term Algorithm is
 very significant.
 The success of the Four Term Algorithm prompted an investigation of a Six
 Term Algorithm which adds .vertline.B.sub.1
 -B.sub.3.vertline.+.vertline.B.sub.2 -B.sub.4.vertline. to A.sub.4.
 Application of the Six Term Algorithm is shown in FIGS. 3L and 3M. The Six
 Term Algorithm does an excellent job of pushing up the ratio in all
 regions, but also results in a significant increase in base threshold. The
 net result is slightly poorer performance than is obtained with the Four
 Term Algorithm.
 Provided the four complex outputs of the monopulse network are maintained
 at RF or at IF, the individual beam responses can be reconstructed with
 simple arithmetic operations. Let the monopulse outputs be .SIGMA.,
 .DELTA..sub.az, .DELTA..sub.el and Q. For both amplitude and phase
 monopulse systems, the pattern functions are formed as
EQU .SIGMA.=B.sub.1 +B.sub.2 +B.sub.3 +B.sub.4 Eq. 4
EQU .DELTA..sub.az =B1-B2-B.sub.3 +B.sub.4 Eq. 5
EQU .DELTA..sub.el =B.sub.1 +B.sub.2 -B.sub.3 -B.sub.4 Eq. 6
EQU Q=B.sub.1 -B.sub.2 +B.sub.3 -B.sub.4 Eq. 7
 By inspection, we can write equations for B.sub.1, B.sub.2, B.sub.3, and
 B.sub.4.
EQU B.sub.1 =0.25*(.SIGMA.+.DELTA..sub.az +.DELTA..sub.el +Q) Eq. 8
EQU B.sub.2 =0.25*(.SIGMA.-.DELTA..sub.az +.DELTA..sub.el -Q) Eq. 9
EQU B.sub.3 =0.25*(.SIGMA.-.DELTA..sub.az -.DELTA..sub.el +Q) Eq. 10
EQU B.sub.4 =0.25*(.SIGMA.+.DELTA..sub.az +.DELTA..sub.el -Q) Eq. 11
 At this point, either the First Order Algorithm or the Four Term Algorithm
 becomes available to the system. The selection then depends on system
 thermal noise and signal processor calculations noise issues.
 Selection of the off-axis indicator threshold is a process that considers
 not only the desired probability of correct off-axis indication, but also
 the overall system probability of detection for legitimate mainlobe
 targets. The off-axis indicator algorithm is applied to detections
 produced by the CFAR process, such as would be implemented in a coherent
 pulse Doppler radar to process the range, Doppler output of the radar's
 processor. The off-axis indicator thus represents a second detection
 threshold; those signals which are less than the off-axis threshold are
 declared detections, while those that are above the threshold are declared
 off-axis and discarded. To be detected, a signal must not only be above
 the normal CFAR threshold, but also below the off-axis indicator
 threshold. It is the joint probability that a mainlobe signal is above the
 CFAR threshold and below the off-axis indicator threshold that defines the
 overall system probability of detection when the off-axis algorithm is
 implemented. When selecting the off-axis threshold, one would like the
 threshold to be low so as to give a positive off-axis indication over as
 much angle space outside the mainbeam as possible, but not so low as to
 reject a significant portion of the mainlobe returns (for purposes of this
 discussion, mainlobe return means any signal having angle of arrival
 within the 3 dB one way contour of the Sum mainlobe pattern).
 The CFAR detection threshold is normally selected to achieve a desired
 single look false alarm probability on noise alone. The combination of
 desired detection and false alarm probability then sets the signal to
 noise ratio required to meet those two system performance parameters. The
 radar transmit power required to meet the signal to noise ratio factors in
 a beamshape loss which assumes that a target is equally likely anywhere
 within the mainbeam of the radar; the beamshape loss is calculated by
 averaging the two way sum pattern gain over the mainlobe region, with the
 mainlobe region taken to be that within the 3 dB one way gain contour of
 the mainbeam. Curves of detection probability versus signal to noise ratio
 with false alarm probability as parameter are available in a host of radar
 textbooks.
 When calculating the overall probability of detection with off-axis
 indication, not only must the signal to noise ratio as a function of beam
 position be factored into the equation, but also the value of the off-axis
 indicator within the mainbeam. The overall probability of detection is the
 joint probability of three events:
EQU P.sub.det =P(mainlobe detection, CFAR detection, mainbeam position) Eq. 12
 where
 mainlobe detection=probability that the off-axis indicator for a mainlobe
 signal is below the off-axis indicator threshold in the presence of
 receiver noise
 CFAR detection=probability that the mainlobe signal exceeds the CFAR
 detection threshold in the presence of receiver noise
 mainbeam position=probability that the mainlobe signal is at a given
 angular position within the mainbeam (taken to be uniformly distributed
 within the mainbeam)
 The normal detection probability without off-axis processing as discussed
 above is the joint probability of CFAR detection and mainbeam position,
 with the dependence on mainbeam position included by factoring in a
 beamshape loss factor.
 The probability of detection with off-axis processing is relatively easy to
 calculate if the above joint probability is broken down into its
 constituent components. Using Bayes rule, the detection probability can be
 expressed as the product of the beam position and two conditional
 probabilities:
 ##EQU1##
 The first conditional probability in the above expression, P(CFAR
 detection.vertline.mainbeam position), is the signal to noise dependent
 detection probability (for a given false alarm probability) characterized
 by the detection curves commonly found in radar texts. When integrated
 over the mainbeam, the product of the above conditional probability and
 the first term in the above expression, P(mainbeam position), provides the
 detection probability when off-axis indication is not implemented (i.e.,
 the normal system CFAR detection performance including the effects of beam
 shape loss). The second conditional probability in the above expression,
 P(mainlobe detection.vertline.CFAR detection, mainbeam position), thus
 represents the contribution of off-axis processing to the overall system
 detection probability. The effect of off-axis processing on detection
 probability is thus readily evident; since probabilities are always less
 than or equal to one, the penalty for implementing off-axis processing is
 a reduction in overall system detection probability by a factor equal to
 the value of P(mainlobe detection.vertline.CFAR detection, mainbeam
 position).
 Further reflection on the dependence of the above two conditional
 probabilities on beam position reveals that the two "work" together to
 minimize the detrimental effects of off-axis processing. Consider first
 P(CFAR detection.vertline.mainbeam position). The probability of CFAR
 threshold crossing as a function of signal to noise ratio is typically a
 steep curve; a change of several dB in signal to noise ratio can produce a
 dramatic change in detection probability, especially for relatively small
 signal to noise ratio (10 dB or less). The two way gain at the edge of the
 beam is 6 dB less than it is at the center of the beam. Therefore, when
 the product of P(mainbeam position) and P(CFAR detection.vertline.mainbeam
 position) are integrated near the edge of the mainbeam, little is added to
 the overall system detection probability; most of the detection
 probability accumulates from a region closer to the center of the
 mainbeam. Now consider the dependence of P(mainlobe
 detection.vertline.CFAR detection, mainbeam position) on beam position.
 The off-axis indicator algorithms described in this invention disclosure
 work by considering the relation between the difference channel signals
 and the sum channel signal. Fundamentally, when one or more of the
 difference channel signal levels are significant in relation to the sum
 channel signal level, an off-axis indication is given. Within the
 mainbeam, the region where one or more of the difference channel signals
 is likely to be significant in relation to the sum channel signal is near
 the edge of the mainbeam; that is, difference channel signal plus noise is
 most likely to be comparable in magnitude to sum channel signal plus noise
 near the edge of the main beam. P(mainlobe detection.vertline.CFAR
 detection, mainbeam position) is small when signal plus noise in one or
 more of the difference channels is comparable to signal plus noise in the
 sum channel (i.e., the signal has a high probability of being identified
 as off-axis and rejected). Therefore P(mainlobe detection.vertline.CFAR
 detection, mainbeam position) is small near the edges of the mainbeam and
 greatest near the center, the region where off-axis processing tends to
 generate the greatest penalty is near the edges of the mainbeam, which is
 also the region where there is not much CFAR detection performance.
 Significant off-axis rejection can be achieved with fairly minor impact on
 overall system probability of detection.
 A MATLAB computer simulation was written to evaluate the probability of
 off-axis indication and mainlobe detection for a 94 GHz seeker design
 example taken from the text "Principles and Applications of
 Millimeter-Wave Radar" by Currie and Brown, 1987 Artech House. The design
 example (see pages 663 to 680 in Currie and Brown) is for 10 dB signal to
 noise ratio, and false alarm probability of 10.sup.-4. The simulation has
 been used to evaluate detection performance for three algorithms; the
 first is the two channel OR technique currently in use in some missile
 systems, while the second and third are the first order and four term
 algorithms described herein. The three algorithms are summarized below:
 Two channel OR Algorithm--
 ##EQU2##
 First Order Algorithm--
 ##EQU3##
 Four Term Algorithm--
EQU .SIGMA.=B.sub.1 +B.sub.2 +B.sub.3 +B.sub.4 Eq. 16
 ##EQU4##
 In the above expressions, .DELTA..sub.p, .DELTA..sub.y, .SIGMA., and Q are
 the pitch, yaw, sum, and quadrupole channels, respectively. Note the above
 expressions are sometimes also referred to as .DELTA..sub.el,
 .DELTA..sub.az, .SIGMA. and Q. B.sub.1, B.sub.2, B.sub.3, and B.sub.4 are
 the four monopulse beams used to construct the .SIGMA., .DELTA..sub.p,
 .DELTA..sub.y and Q signals. The results are summarized in FIGS. 4A, 4B
 and 4C for the above three algorithms, respectively. The left plot in each
 figure shows the probability of off-axis indication as a function of
 off-axis detection threshold, while the right plot shows the probability
 of detection as a function of off-axis threshold for mainlobe signals. The
 left plot is therefore a measure of the algorithm's effectiveness in
 identifying off-axis signals, while the right plot is a measure of the
 algorithm's impact on mainlobe detection performance. Two curves are shown
 on the mainlobe detection plot: probability of detection with and without
 off-axis processing. Note in every case that as the threshold increases,
 the probability of detection with off-axis processing eventually equals
 that without off-axis processing. The above result is expected, because as
 threshold increases, it becomes less likely that an off-axis indication
 will be given, thus increasing P(mainlobe detection.vertline.CFAR
 detection, mainbeam position). When P(mainlobe detection.vertline.CFAR
 detection, mainbeam position) approaches 1, the detection probability with
 off-axis processing approaches that obtained with CFAR processing alone.
 FIG. 4A summarizes the performance of the two channel OR algorithm applied
 to the design example taken from Currie and Brown. Referring to the right
 hand plot of FIG. 4A, when the off-axis threshold is 2 dB, the mainlobe
 detection probability is essentially that obtained with CFAR processing
 alone, while the probability of correctly identifying off-axis signals
 (left plot) is about 70%.
 Referring to FIG. 4B, it can be seen that the probability of off-axis
 detection for the first order algorithm exceeds 88% for thresholds less
 than or equal to 5 dB. A 5 dB threshold, referring to the probability of
 mainlobe detection curve, is also about where the CFAR and off-axis
 detection performance become equal. With a 5 dB threshold, off-axis
 signals can be identified with 88% probability while incurring only a
 small loss in mainlobe detection probability. If one is willing to incur a
 slightly larger loss in mainlobe detection probability, a threshold of3 dB
 produces off-axis identification performance of about 94%.
 FIG. 4C summarizes the performance of the four term algorithm. An off-axis
 detection threshold of 7 dB results in a minor loss in mainlobe detection
 performance, while producing off-axis identification performance of about
 88%. If slightly greater loss in mainlobe detection performance can be
 tolerated, a threshold of 5 dB produces off-axis identification
 performance of about 94%.
 Referring now to FIG. 5, there is shown a block diagram of a radar system
 200 comprising a computer 250, a master oscillator 212, transmitter 210, a
 receiver 220, a duplexer 230 and a monopulse antenna 240. The transmitter
 210 includes an exciter 214, exciter control circuitry 216 and a
 transmitter power amplifier 218. The receiver 220 includes a receiver 224,
 analog-to-digital (A/D) converter 226, a digital signal processor 228
 including an off-axis indicator according to the present invention. The
 system of FIG. 5 represents a pulse radar system, although it is to be
 understood that the present invention may be adapted for use in other
 systems.
 The computer 250 provides reference signals 213a-213d to provide the
 various components of the radar system 200 the requisite control signals
 as described hereinafter. In a conventional manner, the master oscillator
 in response to the computer 250 provides a signal to the exciter 214 which
 in turns provides an RF signal at the output thereof. The RF signal is
 then fed to the transmitter power amplifier 218 where RF signal is
 amplified, and via duplexer 230, is fed to antenna 240 and transmitted as
 a transmit signal 211. The antenna 240 is a monopulse antenna. As antenna
 240 scans the search area, a received signal 219 is reflected by objects
 within the operating range of the radar system 200. Received signal 219 is
 then received by antenna 240. Received signal 219 is fed from the antenna
 240, via duplexer 230, to the receiver 224 which in turn heterodynes the
 received signal with a signal from the master oscillator 212 to produce
 baseband signals. The baseband signals is fed to the A/D converter 226 in
 turn produces discrete time samples of the baseband signals, as sampled
 baseband signals which is fed to the digital signal processor 228. In
 accordance with the present invention, the digital signal processor 228
 then performs computational processing as described herein and additional
 analysis such as a discrete Fourier transform to determine Doppler
 frequencies and other information of interest in a manner as described.
 The latter is then fed to the computer 250 to provide control signals to
 control a vehicle as well as the various components of the radar system
 210. It is to be understood that while digital signal processor 228 and
 computer 250 are shown separately, a single computer may be alternatively
 used or a combination of multiple computers and digital signal processors
 may be used.
 The radar system 200 is arranged to capture the received signal 219 using
 the four quadrants of the monopulse antennna 240 to produce quadrant
 signal B.sub.1, quadrant signal B.sub.2, quadrant signal B.sub.3, and
 quadrant signal B.sub.4. The respective signals, B.sub.1, B.sub.2,
 B.sub.3, and B.sub.4 from each of the four quadrants are coupled to the
 receiver 224 where each of the four signals are respectively heterodyned
 with a signal from the master oscillator 212 to produce four baseband
 signals. Each of the four base band signals are fed to the A/D converter
 226 which in turn produce discrete time samples of each of the four
 baseband signals which are then fed to the digital signal processor 228.
 Having fed four digital signals indicative of the four quadrant signals
 B.sub.1, B.sub.2, B.sub.3, and B.sub.4 to the digital signal processor
 228, the digital signal processor 228 can now perform monopulse
 arithemetic to produce the necessary monopulse signals .SIGMA.,
 .DELTA..sub.az, .DELTA..sub.el and Q. Using the First Order Algorithm as
 described hereinabove, the digital signal processor 228 is able to produce
 an Off-Axis Indication when I.gtoreq.a defined threshold. The digital
 signal processor 228 is also able to produce the Off-Axis Indication using
 the Four Term Algorithm as described when I.gtoreq.defined threshold.
 Furthermore by adding.vertline.B.sub.1
 -B.sub.3.vertline.+.vertline.B.sub.2 -B.sub.4.vertline.to A.sub.4, the
 digital signal processor can also provide a Six Term Algorithm, if needed.
 It should now be appreciated that using the above described technique, an
 off-axis indication can be obtained by forming a respective digital signal
 indicative of a signal from each quadrant of a monopulse antenna; forming
 a sum signal indicative of a combined signal from all quadrants of the
 monopulse antenna and deriving a magnitude of said sum signal; forming
 difference signals of each possible combination of signals from each
 quadrant of the monopulse antenna and deriving a magnitude of each of the
 respective difference signals; comparing the magnitude of each of the
 difference signals to a magnitude of the sum signal; summing any result;
 and comparing the result with a threshold value such that when the
 threshold value is exceeded an of-axis indication is provided.
 Referring now to FIG. 6, a flow diagram to implement the technique
 described above using digital signal processor 128 and computer 150 is
 shown. After the radar system 200 provides digital signals indicative of
 each of the quadrant signals to the digital signal processor 128, a
 subroutine is initiated at step 300. In processing step 302, a form a sum
 signal indicative of a combined signal from all quadrants of the monopulse
 antenna and derive a magnitude of the sum signal step is performed to
 obtain the magnitude of the sum signal. Next a form difference signals of
 each possible combination of signals from each quadrant of the monopulse
 antenna and deriving a magnitude of each of the respective difference
 signals processing step 304 is performed to obtain the magnitude of each
 of the difference signals. Next a compare the magnitude of each of the
 difference signals to a magnitude of the sum signal processing step is
 performed to obtain the ratio of the magnitudes of each of the difference
 signals to the magnitude of the sum signal. Next a sum any result from the
 comparing step 306 processing step is performed to obtain an off-axis
 indication signal. In processing step 310, the summing result is compared
 with a threshold value and in processing step 132 and Off-Axis Indication
 is provided when the summing result exceeds the threshold value. The
 subroutine then comes to an end at step 314 until it is called again.
 It should now be appreciated that the inventive concept is the realization
 that by including the information in the difference channels of the
 monopulse radar in the detection decision process, off-axis indication
 with high probability can be achieved with little or no impact on the
 detection probability of mainlobe signals. Normally, only the magnitude of
 the Sum channel signal is used in making detection decisions. Use of only
 Sum magnitude data ignores useful information contained in the difference
 channels that is relevant to the detection decision process. The
 algorithms described are implemented in two ways. The first is with the
 Sum and three difference signals (pitch, yaw, and quadrupole, or diagonal
 difference) commonly available from a monopulse network. The second is
 with the quadrant patterns directly. In most fielded systems, the
 monopulse signals are formed at microwave. Alternatively, it is preferable
 to bring back the quadrant patterns directly to form the monopulse
 patterns digitally. With both of the above methods, the algorithms are
 implemented in a computationally simple way which allows off-axis
 detection probability to be traded versus mainlobe detection probability
 with signal to noise ratio as parameter. This novel implementation of the
 algorithms allows simple programmable control of the above two performance
 parameters. One can thus achieve the required level of system performance
 as a function of signal to noise ratio, analogous to the currently
 accepted practice of controlling detection and false alarm probability as
 a function of signal to noise ratio with the CFAR threshold.
 All references made herein are hereby incorporated by reference in their
 entirety.
 Having described preferred embodiments of the invention, one of ordinary
 skill in the art will now realize further features and advantages of the
 invention from the above-described embodiments. It should be understood,
 therefore, that the foregoing is only illustrative of the principles of
 the invention and that various modifications can be made by those skilled
 in the art without departing from the scope and spirit of the invention.
 Accordingly, the invention is not to be limited by what has been
 particularly shown and described, except as indicated by the appended
 claims.