Abstract:
An improvement in monopulse radar achieves nulling of a single mainlobe jammer and multiple sidelobe jammers while maintaining the angle measurement accuracy of the monopulse ratio by cascading a multiple sidelobe canceller and a mainlobe canceller, and imposing a mainlobe maintenance technique during the sidelobe jammer cancellation process so that the results of the sidelobe jammer cancellation process do not distort the subsequent mainlobe cancellation process. In this manner, the sidelobe jammers and the mainlobe jammer are cancelled sequentially in separate processes.

Description:
RELATED APPLICATIONS 
   This application is related to Yu and Murrow application Ser. No. 07/807,546 now U.S. Pat. No. 5,600,326 filed concurrently herewith and assigned to the instant assignee. 

   BACKGROUND OF THE INVENTION 
   This invention generally relates to radar techniques for determining angular location of a target and, more particularly, to an improvement in the monopulse technique so as to maintain accuracy of the monopulse ratio in the presence of simultaneous jamming from multiple sidelobe jammers and a single mainlobe jammer. 
   The monopulse technique is a radar technique in which the angular location of a target can be determined within fractions of a beamwidth by comparing measurements received by two or more simultaneous beams. This technique for direction of arrival (DOA) estimation of a target is widely employed in modern surveillance and tracking radar. See, for example, D. K. Barton, “Modern Radar Systems Analysis,”  Artech House  (1988), M. Sherman, “Monopulse Principles and Techniques,”  Artech House  (1988), and I. Leanov and K. I. Fomichev, “Monopulse Radar,”  Artech House  (1986). In a typical phased array or digital beamforming (DBF) radar, one beam is formed in transmission and two beams are formed on reception for angle measurement. 
   The monopulse technique may be implemented for a linear array of N antenna elements which provide respective signals x( 0 ), . . . , x(N−1) to the beamforming network from the elemental receivers. The output signals of the beamforming network are the sum, Σ, and difference, Δ, signals which are processed in a processor to generate an output signal, θ, representing the direction of arrival estimation. 
   In the beamforming network, each of N input signals is split into two paths, linearly weighted, and then added together. The sum Σ and difference Δ signals may be expressed in the form 
             Σ   ⁢           =         W   Σ   H     ⁢   x     _             (   1   )               Δ   =         W   Δ   H     ⁢   x     _             (   2   )             
 
respectively, where W Σ  is real and even weighting, W Δ  is purely imaginary and odd weighting, H indicates the complex conjugate transpose and x is the vector of the measurements. When there is no jamming, Taylor and Bayliss weightings are typically used for sum beams and difference beams, respectively, so as to have a narrow mainlobe and low sidelobes. In the presence of jamming, the weights are adapted so as to form nulls responsive to the jammers. The quiescent Taylor and Bayliss weightings are designed for reducing the sidelobes in a practical system. See Y. T. Lo and S. W. Lee, “Antenna Handbook,”  Theory, Applications, and Design , Van Nostrand Reinhold Company, New York (1988), Chapter 13.
 
   In a typical antenna pattern, the mainlobe of the pattern is a central beam surrounded by minor lobes, commonly referred to as sidelobes. Typically, it is desired to have a narrow mainlobe, high gain and low sidelobes so that the desired target within the mainlobe is enhanced and the response to clutter and jamming outside the mainlobe is attenuated. The sidelobe levels of an antenna pattern can be described in any of several ways. The most common expression is the relative sidelobe level, defined as the peak level of the highest sidelobe relative to the peak level of the main beam. Sidelobe levels can also be quantified in terms of their absolute level relative to isotropic. 
   The term “monopulse” refers to the fact that the echo from a single transmitter pulse returning from a target is used to measure the angle of the target, and typically, one beam (instead of two beams) is formed in transmission, and two beams are formed on reception for angle measurement. The sum beam pattern has a symmetrical amplitude profile with its maximum at the boresight, and the difference beam pattern has an antisymmetrical amplitude profile with zero response at the boresight. The DOA of a target signal can be determined accurately through a look-up table by evaluating the monopulse ratio, i.e., the real part of Δ/Σ. In fact, for a noiseless case and for uniform weighting, the monopulse ratio is exactly given by 
               f   ⁡     (   θ   )       =         Δ   ⁡     (   θ   )         ∑           ⁢     (   θ   )         =     tan   ⁡     (     π   ⁢           ⁢   T   ⁢     Nd     2   ⁢   λ         )                 (   3   )             
 
where T=sin (θ) and θ is the desired DOA, d is the array element spacing, N is the number of sensor elements, and λ is the wavelength. This equation enables T and the corresponding θ to be determined exactly. In the presence of noise, the development of the DOA maximum likelihood estimator also leads naturally to monopulse processing using sum and difference beams. See R. C. Davis, L. E. Brennan, and I. S. Reed, “Angle Estimation with Adaptive Arrays in External Noise Field,”  IEEE Trans. on Aerospace and Electronic Systems , Vol. AES-12, No. 2, March 1976. For zero-mean noise, the estimator is unbiased with mean square error (MSE) given by 
             MSE   =     1     2   ⁢     k   2     ⁢   N   ⁢           ⁢   SNR               (   4   )             
 
where 
         k   =       (           f   .     2     ⁢            g   ⁡     (   T   )            2         1   +     f   2         )       1   2         ,       
 
which is known to be the monopulse sensitivity factor, f is the monopulse function, and {dot over (f)} is the derivative of f. SNR is the signal-to-noise ratio at the elemental level, and g(T) is the two-way sum beam antenna pattern.
 
   Various authors have defined the monopulse sensitivity factor in different ways (see R. R. Kinsey, “Monopulse Difference Slope and Gain Standards,”  IRE Trans ., Vol AP-10, pp. 343-344, May 1962). In this application, the monopulse sensitivity factor is defined as the constant of proportionality required in the denominator of the root-mean-square-error (RMSE) to convert the square root of twice the boresight signal-to-noise ratio in the beam to RMSE. Defined in this manner, the monopulse sensitivity factor has the desirable property of containing all target angle-of-arrival information. See D. J. Murrow, “Height Finding and 3D Radar,” Chapter 20, Radar Handbook (2nd Edition), McGraw-Hill. 
   This technique can also be considered for a planar array where the target azimuth and elevation angles are desired. In this setup, a set of sum (Σ e ) and difference (Δ e ) beams are formed along the elevation axis with input signals from each column of sensors. The Σ e  beams are then linearly combined in a row beamformer  63  to form the sum (Σ=Σ a Σ e ) and difference (Δ A =Δ a Δ e ) beams along the azimuth axis, where Σ a  and Δ a  are the effective row sum beam and row difference beam, respectively. Similarly, the Δ e  beams are linearly combined in a row beamformer  64  to form the sum (Δ E =Σ a Δ e ) and difference (Δ Δ =Δ a Δ e ) beams along the azimuth axis. Monopulse ratios along azimuth or elevation direction can then be formed giving the azimuth and elevation DOA estimates by using the following equations: 
                 f   a     ⁡     (     θ   a     )       =         Δ   A       ∑               =           Δ   a     ⁢     Σ   e           Σ   a     ⁢     Σ   e         =         Δ   a       Σ   a       ⁢           ⁢   and                 (   5   )                   f   e     ⁡     (     θ   e     )       =         Δ   E     Σ     =           Σ   a     ⁢     Δ   e           Σ   a     ⁢     Σ   e         =         Δ   e       Σ   e       .                 (   6   )             
 
These derivations make use of the separable property of the planar array patterns.
 
   The monopulse technique for DOA estimation fails when there is sidelobe jamming (SLJ) and/or mainlobe jamming (MLJ). If not effectively countered, electronic jamming prevents successful radar target detection and tracking. The situation is exacerbated by introduction of stealth technology to reduce the radar cross section (RCS) of unfriendly aircraft targets. The frequency dependence of the RCS encourages use of lower microwave frequency bands for detection. This leads to large apertures to achieve angular resolution. Large apertures to achieve small beamwidth results in interception of more jamming. On the other hand, constrained apertures lead to wider beamwidth, which implies interception of more mainlobe jamming. 
   Heretofore, no viable or practical technique for cancelling simultaneous mainlobe and sidelobe jammers has been developed or fielded in a radar. This makes the conception and development of such technique one of the more pressing and critical issues facing radar today. The challenge is to develop adaptive beamforming architectures and signal processing algorithms to cancel mainlobe and sidelobe jammers while maintaining target detection and angle estimation accuracy on mainlobe targets. 
   Clark (see C. R. Clark, “Main Beam Jammer Cancellation and Target Angle Estimation with a Polarization-Agile Monopulse Antenna,” 1989  IEEE Radar Conference , March 29-30, 1989, Dallas, Tex., pp. 95-100) addresses the problem of simultaneous mainlobe and sidelobe jamming cancellation but his work is distinguished from the present invention in three respects. First, Clark does not include the requirement of maintaining the monopulse ratio. Second, his approach uses the main array and sidelobe auxiliary array simultaneously. Third, as a consequence of using the arrays simultaneously, Clark&#39;s approach does not include mainlobe maintenance, thereby introducing distortion into the main beam. 
   SUMMARY OF THE INVENTION 
   It is therefore an object of the invention to cancel both mainlobe and sidelobe jammers while maintaining target detection and angle estimation accuracy on mainlobe targets. 
   More specifically, it is an object of the invention to combine cancellation techniques for multiple sidelobe jamming and mainlobe jamming in such a way that the monopulse accuracy for DOA estimation is maintained for mainlobe targets. 
   According to the invention, a multiple sidelobe jamming cancellation technique is cascaded with a mainlobe jamming cancellation technique. In the first stage of this process, the sidelobe jammer is cancelled by subtracting from the main beam a weighted sum of elements of the auxiliary array, and the main beam is maintained. In the second stage, the mainlobe cancellation is applied to cancel the mainlobe jammer while preserving the monopulse ratio. The beams from the first step are adapted using Applebaum&#39;s orthogonal nulling technique to cancel the mainlobe jammer along each axis while forming the monopulse ratio in the other axis. (See S. P. Applebaum and R. Wasiewicz,  Main Beam Jammer Cancellation for Monopulse Sensors , Final Tech. Report DTIC  25 . RADC-TR-86-267, December, 1984.) 
   It is essential to include an appropriate mainlobe maintenance (MLM) technique in the first stage to prevent an adverse interaction between the two techniques. The MLM prevents the multiple sidelobe cancelling technique from interfering with the mainlobe cancellation technique. 
   Thus the jammers are nulled before the receiver beamforming network employed in the known monopulse technique forms, at its output, the sum and difference beams for monopulse processing. The sidelobe jamming is suppressed using the auxiliary array inputs. The gain of the auxiliary elements is so low relative to the gain of the main antennas that the effect of the auxiliary elements may be ignored in determining the monopulse ratio, thus maintaining the sensitivity of the monopulse ratio as described, infra. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing and other objects, aspects and advantages will be better understood from the following detailed description of a preferred embodiment of the invention with reference to the drawings, in which: 
       FIG. 1  is a block diagram showing a monopulse beamforming network for estimating direction of arrival; 
       FIG. 2  is a detailed block diagram of a beamforming network; 
       FIG. 3  is a perspective view of a monopulse radar sum beam antenna pattern; 
       FIG. 4  is a graph of sum and difference beam patterns for monopulse antennas; 
       FIG. 5  is a graph of the monopulse ratio; 
       FIG. 6  is a block diagram of a monopulse radar; 
       FIG. 7  is a block diagram showing a sum-difference mainlobe canceller; 
       FIG. 8  is a block diagram showing a mainlobe canceller for monopulse processing; 
       FIG. 9  is a block diagram showing an adaptive array for forming sum and difference beam output signals; 
       FIG. 10  is a schematic diagram showing a multiple sidelobe canceller for sum and difference channels; 
       FIG. 11  is a pair of graphs showing sidelobe jammer nulling; 
       FIG. 12  is a diagram showing the Applebaum feedback loop; 
       FIG. 13  is a block diagram of the architecture of the invention, combining a multiple sidelobe canceller and mainlobe canceller for monopulse processing; 
       FIG. 13A  is a block diagram of a modification of the architecture of the invention shown in  FIG. 13 ; and 
       FIG. 14  is a diagram showing mainlobe maintenance in conjunction with a multiple sidelobe canceller. 
   

   DETAILED DESCRIPTION 
   A monopulse technique for DOA estimation is implemented for a linear array of antenna elements  10   0  to  10   N−1  which provide respective signals x( 0 ), . . . , x(N−1), shown in  FIG. 1 , to the beamforming (BF) network  12  for combining the input signals from the elemental receiver. The output signals of BF network  12  are the sum Σ and difference Δ signals which are processed in a processor  14  to generate an output signal θ representing the direction of arrival estimation. 
   Beamforming network  12  is more fully illustrated in FIG.  2  and comprises voltage splitters  21 , weighting networks  22  and adders  23 . Each of the N input signals is split into two paths which are linearly weighted, and in each of the two paths the N signals are added together. 
   The sum Σ and difference Δ signals are given by equations (1) and (2) as 
             Σ   ⁢           =         W   Σ   H     ⁢   x     _             (   1   )               Δ   =         W   Δ   H     ⁢   x     _             (   2   )             
 
respectively. When there is no jamming, Taylor and Bayliss weightings are typically used for sum beams and difference beams, respectively, so as to have a narrow mainlobe and low sidelobes. In the presence of jamming, the weights are adapted so as to form nulls responsive to the jammers. The quiescent Taylor and Bayliss weightings are designed for reducing the sidelobes in a practical system.
 
     FIG. 3  represents a typical sum beam antenna pattern. X The mainlobe of the pattern is a central beam  31  surrounded by minor lobes  32 , or sidelobes. Typically, it is desired to have a narrow mainlobe, high gain and low sidelobes so that the desired target within the mainlobe is enhanced and the response to clutter and jamming outside the mainlobe is attenuated. 
   In the monopulse technique, typically one beam (instead of two beams) is formed in transmission, and two beams are formed on reception for angle measurement. As shown in  FIG. 4 , the sum beam  41  has a symmetrical amplitude profile with its maximum at the boresight, and the difference beam  42  has an antisymmetrical amplitude profile with zero response at the boresight. The DOA of a target signal can be determined accurately through a look-up table by evaluating the monopulse ratio  51 , i.e., the real part of Δ/Σ, as shown in FIG.  5 . For a noiseless case and for uniform weighting, the monopulse ratio is exactly given by equation (3) as 
               f   ⁡     (   θ   )       =         Δ   ⁡     (   θ   )         ∑           ⁢     (   θ   )         =       tan   ⁡     (     π   ⁢           ⁢   T   ⁢     Nd     2   ⁢   λ         )       .               (   3   )             
 
Since T=sin (θ), T and the corresponding θ can be determined exactly. For zero-mean noise, the DOA maximum likelihood estimator is unbiased with mean square error (MSE) given by equation (4) as 
             MSE   =     1     2   ⁢     k   2     ⁢   N   ⁢           ⁢   SNR               (   4   )             
 
where 
           k   2     =           f   .     2     ⁢            g   ⁡     (   T   )            2         1   +     f   2           ,       
 
is the monopulse sensitivity factor, which contains all target angle-of-arrival information.
 
   This technique can also be used with a planar array where the target azimuth and elevation angles are desired, as shown in FIG.  6 . In this setup, a set of sum (Σ e ) and difference (Δ e ) beams are formed along the elevation axis with input signals from each column of sensors  66  by respective column beamformers  65 . The Σ e  beams may be appropriately Taylor and Bayliss weighted and then linearly combined in a row beamformer  63  to form the sum (Σ=Σ a Σ e ) and difference (Δ A =Δ a Σ e ) beams along the azimuth axis. Similarly, the Δ e  beams may be appropriately Taylor and Bayliss weighted and then linearly combined in a row beamformer  64  to form the sum (Δ E =Σ a Δ e ) and difference (Δ Δ =Δ a Δ e ) beams along the azimuth axis. Monopulse ratios along azimuth or elevation direction can then be formed giving the azimuth and elevation DOA estimates by using equations (5) and (6), which take advantage of the separable property of the planar array patterns. 
   The present invention concerns cancellation of one mainlobe jammer and multiple sidelobe jammers in a way that provides target detection and enables unbiased monopulse angle measurement. In order to show the motivation for the present invention, some existing approaches for jammer cancellation are reviewed: the multiple sidelobe canceller (MSLC) (see P. W. Howells, “Exploration in Fixed and Adaptive Resolution at GE and SURC”,  IEEE Trans. on Antennas and Propagation , AP-24, No. 5 (September 1976), p. 575); the sum-difference mainlobe canceller (MLC) (see S. P. Applebaum and R. Wasiewicz, “Main Beam Jammer Cancellation for Monopulse Sensors”,  Final Tech. Report DTIC RADC - TR -86-267, December 1984); and the adaptive array (see S. P. Applebaum, “Adaptive Arrays”,  Syracuse Univ. Research Corp., Report SPL -769, June 1964 and Widrow, et al., “Adaptive Antenna Systems”,  Proc. IEEE, Vol.  55, December 1967). 
   Multiple Sidelobe Canceller (MSLC) 
   The sidelobe canceller was actually the first type of adaptive antenna system to be deployed. It is used to reduce clutter and interference in radar systems and comprises a single high-gain antenna to which a number of small auxiliary elements are added. Both sum (Σ) and difference (Δ) channels are required for monopulse processing, as illustrated in FIG.  10 . The high gain antenna  101  is a typical radar antenna (e.g., a parabolic dish) with a narrow beamwidth. The auxiliary elements  102  are small, low-gain, and have much wider beamwidths than the high-gain antenna. The auxiliary element output signals are multiplied by adaptive weight signals  104  at a weighting network or multiplier  103 , combined by an adder  106 , and then added to the high-gain antenna output signal by a summer  105 . 
   By controlling the weights on the auxiliary elements adaptively, jamming in the sidelobes of the high-gain antenna can be nulled out, as illustrated in FIG.  11 . This can be achieved by analog or digital circuitry. For analog implementation at radio frequencies or intermediate frequencies, the weights are adjusted using the so-called Applebaum feedback loop, illustrated in FIG.  12 . This implementation requires a feedback loop for each weight and the weight is controlled by the input signal {tilde over (x)} j (t) and the error signal at multiplier input  122 . The weights will converge to the optimal weight and the jammer is thereby nulled. For the digital implementation, digital samples r Σ (k) for the main array and r a (k) for the auxiliary array are measured. Cross correlation samples between the main beam and the auxiliary array elements, as well as the auto correlation of the auxiliary elements, are estimated using the samples given by 
               r     Σ   a       =       1   N     ⁢       ∑     k   =   1     N     ⁢           ⁢         r   Σ     ⁡     (   k   )       ⁢         r   _     a     ⁡     (   k   )       ⁢           ⁢   and                 (   7   )                 r   aa     =       1   N     ⁢       ∑     k   =   1     N     ⁢           ⁢           r   _     a     ⁡     (   k   )       ⁢           r   _     a   H     ⁡     (   k   )       .                   (   8   )             
 
The adaptive weights for cancelling the jammers are given by
 
 W=r   aa   −1   r   Σa   (9) 
 
These weights are then downloaded to the weighting network  123  for combining the auxiliary elements.
 
   The target signal can be cancelled whenever 1) the signal enters the auxiliary elements, 2) the signal information is inaccurate, or 3) there is correlation between the desired signal and the interference signal. Constrained adaptation of the auxiliary array can be employed to prevent cancellation of the target signal. Robust methods have been employed to mitigate the effect of inaccurate signal knowledge in the adaptation process (see K. Jablon, “Steady State Analysis of the Generalized Sidelobe Canceler by Adaptive Noise Canceling Techniques,”  IEEE Trans. on Antennas and Propagation , Vol. AP-34, pp. 330-337, March 1986 and H. Cox, R. M. Zeskind and M. M. Owen, “Robust Adaptive Beamforming”,  IEEE Trans. on Acoustics, Speech and Signal Processing , Vol. ASSP-35, pp. 1365-1375, October 1987). Methods for reducing signal cancellation due to correlated jamming have also been suggested recently (see B. Widrow, K. M. Duvall, P. R. Gooch, and W. E. Newman, “Signal Cancellation Phenomena in Adaptive Arrays: Causes and Cures,”  IEEE Trans. on Antennas and Propagation , Vol. AP-30, pp. 469-478, May 1982) and T. Shan and T. Kailath, “Adaptive Beamforming for Coherent Signals and Interference,”  IEEE Trans. on Acoustics, Speech and Signal Processing , Vol. ASSP-33, pp. 527-536, June 1985). 
   However, the array elements do not have enough gain to cancel the mainlobe jammer (MLJ). Also, noise enters the system if the gain of the auxiliary array is increased. 
   Sum-Difference Mainlobe Canceller 
   The sum-difference mainlobe canceller (MLC) is shown in FIG.  7 . In the example illustrated, a single parabolic antenna  70  is used to generate the sum (Σ) and difference (Δ) signals. The high mainlobe gain output signal of the difference beam can be used to null the mainlobe jammer in the sum beam. 
   Except at the boresight, the difference beam has a high gain and thus can be used for cancelling the mainlobe jammer without introducing excessive noise in the main antenna. Suppose the jammer is at T j , where T j  is the direction cosine of the jammer. The optimal weight for cancelling the jammer is approximately given by 
             W   =         Σ   ⁡     (     T   j     )         Δ   ⁡     (     T   j     )         .             (   10   )             
 
   Equation 10 is a very good approximation for large jammer-to-noise ratio. The canceller weight W is actually given by the ratio of the cross-correlation between the sum and difference beam output signals to the auto-correlation of the difference beam output signals. Since Σ and Δ beams have comparable gain within the mainbeam, weight W would be a moderate number. If low gain auxiliary elements are used for mainlobe jamming cancellation, large weights are required for cancelling the jammer in the mainbeam, thus introducing high levels of noise into the system. 
   S. P. Applebaum et al. in the aforementioned Report DTIC RADC-TR-86-267 expanded on this idea and developed an architecture and algorithm for nulling the mainlobe jammer while preserving the monopulse ratio. The Applebaum et al. technique makes use of the idea that the patterns of the received beam are separable in azimuth and elevation, that is, the patterns can be expressed as products of sum and difference factors in both azimuth and elevation (i.e., Σ=Σ a Σ e , Δ A =Δ a Σ e , Δ E =Σ a Δ e , Δ Δ =Δ a Δ e ). 
   The MLC architecture is shown in FIG.  8 . In order to form the monopulse ratio along the elevation, the Σ and Δ E  beams can be adapted by the Δ A  and Δ Δ  beams to form Σ′ and Δ′ E  beams as follows:
 
Σ′=Σ− e   a1 Δ A   (11) 
 
Δ E ′=Δ E   −W   a2 Δ Δ ,  (12) 
 
where W a1  and W a2  are adaptation weights determined as set forth, infra. The adaptation of Equation (11) is implemented with a multiplier  81  and summer  80 . Multiplier  81  receives as input signals adaptation weight W a1  and the Δ A  beam, and the product is summed in summer  80  with the Σ beam. Similarly, the adaptation of Equation (12) is implemented with a multiplier  83  and summer  82 . Multiplier  83  receives as input signals adaptation weight W a2  and the Δ Δ  beam, and the product is summed in summer  82  with the Δ E  beam. The output signals of summers  80  and  82 , i.e., Σ′ and Δ′ E , are supplied to a processor  84  which generates the elevation monopulse ratio Δ′ E /Σ′.
 
   One mainlobe jammer can be cancelled along the azimuth by choosing the following adaptation weights W a1  and W a2  to minimize output signals for Equations (11) and (12): 
                 W   a1     =       R     ΣΔ   A         R       Δ   A     ⁢     Δ   Δ             ,           ⁢   and           (   13   )                   W   a2     =       R       Δ   E     ⁢     Δ   A           R       Δ   Δ     ⁢     Δ   Δ             ,           (   14   )             
 where
 
 R   ΣΔ     A     =E[ΣΔ   A *], 
 
 R   Δ     A     Δ     A     =E[Δ   AΔ   A *], 
 
 R   Δ     E     Δ     Δ     =E[Δ   E Δ Δ *], and 
 
 R   Δ     Δ     Δ     Δ     =E[Δ   Δ Δ Δ *],  (15) 
 
where Δ A * is the complex conjugate of Δ A  and Δ Δ * is the complex conjugate of Δ Δ . (The symbol * represents the complex conjugate.) W a1  should be equal to W a2  analytically. In practice, however, W a1  may not be equal to W a2 , as the weights are determined by data samples. In that case, we may force them to be equal (e.g., adapt W a  in the Σ channel and use it in the Δ channel or vice versa, or set 
             W   a     =         W   a1     +     W   a2       2       )     .       
 
The monopulse ratio along the elevation f e (θ e ), where f e  is the ratio of Δ E ′ to Σ′, is obtained in processor  84  by the following: 
                       f   e     ⁡     (     θ   e     )       =         Δ   E   ′       Σ   ′       =       ⁢         Δ   E     -       W   a     ⁢     Δ   Δ           Σ   -       W   a     ⁢     Δ   A                         =       ⁢           Σ   a     ⁢     Δ   e       -       W   a     ⁢     Δ   a     ⁢     Δ   e               Σ   a     ⁢     Σ   e       -       W   a     ⁢     Δ   a     ⁢     Σ   e                       =       ⁢         Δ   e     ⁡     (       Σ   a     -       W   a     ⁢     Δ   a         )           Σ   e     ⁡     (       Σ   a     -       W   a     ⁢     Δ   a         )                     =       ⁢         Δ   e       Σ   e       .                   (   16   )             
 
Thus, the monopulse ratio for the elevation angle θ e  estimation is maintained (except at the azimuth angle where there is a jammer), and the mainlobe jammer is cancelled.
 
   Cancellation of the mainlobe jammer and maintaining the monopulse ratio along the azimuth direction can be developed in a similar manner. The adapted sum and difference beams Σ″ and Δ A ′, respectively, are given by
 
Σ″=Σ− W   e1 Δ E , and  (17) 
 
Δ A ′=Δ A   −W   e2 Δ Δ ,  (18) 
 
where W e1  and W e2  are adaptation weights determined as set forth, infra. The adaptation of Equation (17) is implemented with a multiplier  86  and summer  85 . Multiplier  86  receives as input signals adaptation weight W e1  and the Δ E  beam, and the product is summed in summer  85  with the Σ beam. Similarly, the adaptation of Equation (18) is implemented with a multiplier  88  and summer  87 . Multiplier  88  receives as input signals adaptation weight W e2  and the Δ Δ  beam, and the product is summed in summer  87  with the Δ A  beam. The output signals of summers  85  and  87 , i.e., Σ″ and Δ A ′, are supplied to a processor  89  which generates the azimuth monopulse ratio Δ A ′/Σ″.
 
   The mainlobe jammer can be cancelled by choosing the following adaptive weights: 
                 W   e1     =       R     ΣΔ   E         R       Δ   E     ⁢     Δ   E             ,           ⁢   and           (   19   )                 W   e2     =         R       Δ   A     ⁢     Δ   Δ           R       Δ   Δ     ⁢     Δ   Δ           .             (   20   )             
 
Similarly, the weights can be set equal (e.g., W e =W e1 +W e2 /2), where
 
 R   ΣΔ     E     =E[ΣΔ   E *]
 
 R   Δ     E     Δ     E     =E [Δ E Δ E *] and 
 
 R   Δ     A     Δ     Δ     =E[Δ   A Δ A *]. 
 
The monopulse ratio for azimuth angle θ a  estimation can then be shown to be preserved: 
                       f   a     ⁡     (     θ   a     )       =         Δ   A   ′       Σ   ″       =       ⁢         Δ   A     -       W   e     ⁢     Δ   Δ           Σ   -       W   e     ⁢     Δ   E                         =       ⁢         Δ   a       Σ   a       .                   (   21   )             
 
Adaptive Array
 
   Adaptive receiving arrays for radar, which maximize the signal-to-noise ratio at the array output, were first developed by S. P. Applebaum, see Report SPL-769, supra. These arrays maximize the ratio of antenna gain in a specified scan direction to the total noise in the output signal. Similar techniques have been described for communications systems by Widrow et al., supra, which minimize the mean square error between the array output signal and a transmitted pilot signal which is known a priori at the receiver. The theory of adaptive arrays as applied to the angle measurement problem has been developed by R. C. Davis, L. E. Brennan and I. S. Reed, “Angle Estimation with Adaptive Arrays in External Noise Field,”  IEEE Trans. on Aerospace and Electronic Systems , Vol. AES-12, No. 2, March 1976. The Davis et al. analysis of using maximum likelihood theory of angle estimation leads naturally to the adaptive sum and difference beams. 
   The array architecture is shown in FIG.  9 . The sum and difference beams, represented by the symbols Σ and Δ, respectively, at array outputs  91  and  92 , respectively, are formed by adaptive receiving array techniques which serve to null the interference sources. Because of the adaptivity, which involves using multipliers  93  to apply an adaptive weight at multiplier inputs  94  to antenna array signals furnished at multiplier inputs  90 , the two patterns vary with the external noise field and are distorted relative to the conventional monopulse sum and difference beams which possess even and odd symmetry, respectively, about a prescribed boresight angle. The adaptive weights for the sum and difference beams are given by
 
 Ŵ   Σ   =R   −1   W   Σ , and  (22) 
 
 Ŵ   Δ   =R   −1   W   Δ ,  (23) 
 
where W Σ  and W Δ  are the nominal sum and difference weights used in a conventional monopulse system and R is the covariance matrix of the total interference, which may include jamming and noise. R can be estimated by ensemble averaging the outer-product of the data samples obtained within the observation interval. The antenna patterns are distorted according to the following expressions, where S represents the target signal array response vector: 
                       Σ   ^     ⁡     (   θ   )       =       ⁢         W   ^     Σ   H     ⁢   S                   =       ⁢       W   Σ   H     ⁢     R     -   1       ⁢   S       ,           ⁢   and                 (   24   )                         Δ   ^     ⁡     (   θ   )       =       ⁢         W   ^     Δ   H     ⁢   S                   =       ⁢       W   Δ   H     ⁢     R     -   1       ⁢     S   .         ⁢                         (   25   )             
 
The resulting monopulse ratio is distorted and equal to 
                       f   ′     ⁡     (   θ   )       =       ⁢     Re   ⁡     (         Δ   ^     ⁡     (   θ   )           Σ   ^     ⁡     (   θ   )         )                     =       ⁢     Re   ⁡     (         W   Δ   H     ⁢     R     -   1       ⁢   S         W   Σ   H     ⁢     R     -   1       ⁢   S       )         ,                 (   26   )             
 
where R e  signifies the real part of the expression, and the ideal monopulse ratio is 
               f   ⁡     (   θ   )       =       Re   ⁡     (         W   Δ   H     ⁢   S         W   Σ   H     ⁢   S       )       .             (   27   )             
 
This technique cancels both the mainlobe and sidelobe jammers but distorts the monopulse ratio. This approach for DOA estimation has been verified by computer simulation to work well for SLJs, but performance degrades when the jammers are within the mainbeam.
 
   Techniques for simultaneous nulling in the sum and difference channels of a monopulsed phased array using one set of adaptive weights shared by both beams can be found in L. Haupt, “Simultaneous Nulling in the Sum and Difference Patterns of a Monopulse Antenna,”  IEEE Trans. on Antennas and Propagation , Vol. Ap-32, No. 5, May 1984, pp. 486-493, L. Haupt, “Adaptive Nulling in Monopulse Antennas,”  IEEE Trans. on Antennas and Propagation , Vol. 36, No. 2, February 1988, pp. 202-208, and B. Vu, “Simultaneous Nulling in Sum and Difference Patterns by Amplitude Control,”  IEEE Trans. on Antennas and Propagation , Vol. 34, No. 2, February 1986. It should be noted that nulls may be inserted in the two patterns by using separate adaptive weights and controls for the sum and difference channels. However, this would require two sets of adaptive beamforming hardware. Moreover, inserting a null in the sum pattern does not automatically insert a null in the difference pattern and vice versa. Thus, attempts to adapt the beams separately to null the jammers will cancel the jammers but will also distort the monopulse ratio, thus impairing its usefulness for DOA estimation. Monopulse processing for DOA estimation requires simultaneous adaptation of the sum and difference beams. 
   Mulitple Sidelobe Canceller Followed by a Mainlobe Canceller 
     FIG. 13  shows a multiple sidelobe canceller  136  cascaded with a mainlobe canceller  137  for monopulse processing by a monopulse processor  138 . The main beam voltage measurements for the main antenna array  131  are given by 
                 r   Σ     =         ∑             ⁢           ⁢       (       T   x   s     ,     T   y   s       )     ⁢           ⁢   S       +       ∑     k   =   1     K     ⁢           ⁢       ∑             ⁢           ⁢       (       T   x   k     ,     T   y   k       )     ⁢           ⁢     J   k           +     n   Σ         ⁢     
     ⁢       r     Δ   A       =           Δ   ⁢             A     ⁢           ⁢     (       T   x   s     ,     T   y   s       )     ⁢           ⁢   S     +       ∑     k   =   1     K     ⁢           ⁢       Δ   A     ⁢           ⁢     (       T   x   k     ,     T   y   k       )     ⁢           ⁢     J   k         +     n     Δ   A           ⁢     
     ⁢       r     Δ   E       =           Δ   ⁢             E     ⁢           ⁢     (       T   x   s     ,     T   y   s       )     ⁢           ⁢   S     +       ∑     k   =   1     K     ⁢           ⁢       Δ   E     ⁢           ⁢     (       T   x   k     ,     T   y   k       )     ⁢           ⁢     J   k         +     n     Δ   E           ⁢     
     ⁢         r     Δ   Δ       =         Δ   Δ     ⁢           ⁢     (       T   x   s     ,     T   y   s       )     ⁢           ⁢   S     +       ∑     k   =   1     K     ⁢           ⁢       Δ   Δ     ⁢           ⁢     (       T   x   k     ,     T   y   k       )     ⁢           ⁢     J   k         +     n     Δ   Δ           ,             (   28   )               
where Σ, Δ A , Δ E , and Δ Δ  are the respective sum and difference values for the main antenna patterns, and appear on channels  132 ,  133 ,  134  and  135 , respectively, while k represents the k th  jammer signal. Pattern Σ has a symmetrical profile with respect to both the azimuth and elevation with maximum gain at the boresight. Output signals from multiple sidelobe canceller MSLC  136  are subtracted from patterns Σ, Δ A , Δ E  and Δ Δ  in summers  136   a ,  136   b ,  136   c  and  136   d , respectively, so as to modify those patterns such that sidelobe jamming is removed. Pattern Δ A  has a symmetrical profile with respect to the elevation but is antisymmetrical with respect to the azimuth. Pattern Δ E  is symmetrical with respect to the azimuth but is antisymmetrical with respect to the elevation. Pattern Δ Δ  is antisymmetrical with respect to both axes and has a zero response at the boresight. S and {J k } represent the signal and jamming vectors, respectively, while n Σ , n Δ     A   , n Δ     E   , and n Δ     Δ    are the measurement noise. The voltage measurements {r a     1   } for the auxiliary antenna array, which is comprised of elements  130 , are given by 
                 (     r     a   1       )     =           G     a   1       ⁢           ⁢     (       T   x   s     ,     T   y   s       )     ⁢           ⁢   S     +       ∑     k   =   1     K     ⁢           ⁢       G     a   1       ⁢           ⁢     (       T   x   k     ,     T   y   k       )     ⁢           ⁢     J   k         +       n     a   1       ⁢           ⁢   1       =   1       ,   2   ,   …   ⁢           ,   N   ,           (   29   )               
where {G a     1   } are the elemental gains; {n a     1   } are the elemental noise; r a     1    are used for SLJ cancellation; and r Σ , r Δ     A   , r Δ     E   , and r Δ     Δ    are used for target detection and angle estimation using monopulse processing.
 
   When there is no jamming and noise, the target angle estimation procedure can be derived by noting that the patterns are separable in azimuth and elevation. They can be expressed as the following product factors:
 
Σ( T   x,   T   y )=Σ a ( T   x )Σ e ( T   y ) 
 
Δ A ( T   x   ,T   y )=Δ a ( T   x )Σ e ( T   y ) 
 
Δ E ( T   x   ,T   y )=Σ a ( T   x )Δ e ( T   y ) 
 
Δ Δ ( T   x   ,T   y )=Δ a ( T   x )Δ e ( T   y ).  (30) 
 
The target DOA can be obtained exactly as 
                                   f   a     ⁢           ⁢     (     θ   a     )       =       ⁢         Δ   A     ⁢           ⁢     (       T   x     ,     T   y       )           ∑             ⁢           ⁢     (       T   x     ,     T   y       )                     =       ⁢           Δ   a     ⁢           ⁢     (     T   x     )           Σ   a     ⁢           ⁢     (     T   x     )         ⁢           ⁢   and                                                       (   31   )                         f   e     ⁢           ⁢     (     θ   e     )       =       ⁢         Δ   E     ⁢           ⁢     (       T   x     ,     T   y       )           ∑             ⁢           ⁢     (       T   x     ,     T   y       )                     =       ⁢           Δ   e     ⁢           ⁢     (     T   x     )           Σ   e     ⁢           ⁢     (     T   x     )         .                   (   32   )             
 
In the presence of jamming, cancellation techniques can be applied before measurements are used for monopulse processing. The SLJs can be cancelled using input signals from the array of auxiliary elements  130 . Consider the following adaptive main beam output signals:
 
 r   Σ   ′=r   Σ   −W   Σ   H   r   a    (33) 
 
 r   Δ     A     ′=r   Δ     A     −W   Δ     A     H   r   a  
 
 r   Δ     E     ′=r   Δ     E     −W   Δ     E     H   r   a  
 
 r   Δ     A     ′=r   Δ     a     −W   Δ     Δ     H   r   a . 
 
The optimal weights for minimizing the interference output signal for each of the main beams are given by
 
 W   Σ   ={circumflex over (R)}   aa   −1   {circumflex over (R)}   aΣ   (34) 
 
 W   Δ     A     ={circumflex over (R)}   aa   −1   {circumflex over (R)}   aΔ     A    
 
 W   Δ     g     =Ê   aa   −1   {circumflex over (R)}   aΔ     B    
 
 W   Δ     A     ={circumflex over (R)}   aa   −1   {circumflex over (R)}   aΔ     Δ   
 
where an appropriate mainlobe maintenance or a constrained adaptive procedure is imposed. For example, this can be achieved by measuring the mainlobe jammer contribution in the covariance matrix estimation. This procedure is illustrated in FIG.  14 . The voltage measurement model for the signal at the main antenna  141  and the signal at the auxiliary antenna elements  142  is given by: 
               r   Σ     =         ∑     k   =   1     K     ⁢           ⁢       g   Σ     ⁢           ⁢     (     T   J   k     )     ⁢           ⁢     J   k         +       n   Σ     ⁢           ⁢   and               (   35   )                   r   a     _     =         ∑     k   =   1     K     ⁢           ⁢         g   a     _     ⁢           ⁢     (     T   j   K     )     ⁢           ⁢     J   k         +       n   a     _               (   36   )             
 
while the covariance matrix and cross-correlation matrix are given by 
               R   aa     =         ∑     k   =   1     K     ⁢           ⁢         g   a     _     ⁢           ⁢     (     T   J   k     )     ⁢           ⁢       g   a   H     _     ⁢           ⁢     (     T   J   k     )     ⁢           ⁢     P   k         +       σ   2     ⁢           ⁢   I               (   37   )                   R     a   ⁢           ⁢   Σ       =       ∑     k   =   1     K     ⁢           ⁢         g   a     _     ⁢           ⁢     (     T   j   K     )     ⁢           ⁢       g   Σ   a     _     ⁢           ⁢     (     T   J   k     )     ⁢           ⁢     P   k           ,           (   38   )             
 
where P k  is the power representation of the k th  jammer, σ 2  is the noise power and I is the identity matrix. R aa  can be analyzed to obtain an estimate of the jammer angle and power. Specifically, the eigenvalue decomposition of R aa  is given as 
               R   aa     =       ∑     i   =   1     N     ⁢           ⁢       λ   i     ⁢           ⁢         q   i     ⁢           ⁢     q   i   H       _                 (   39   )             
 
where λ i , q i  are the eigenvalue-eigenvector pairs. If there are K jammers, K of the eigenvalues should be significant with respect to the rest, and the noise subspace E N =[q k+1  . . . q N ] should be orthogonal to the jammer manifold, i.e.
 
 E   N   H   g   a ( T   J )=0  (40) 
 
The above equation 40 can be solved for a set of jammer angles {T J }. One of them is within the mainbeam (if there is a mainlobe jammer). Let the directional cosine of the DOA of the mainlobe jammer be T l  The power of the mainlobe jammer can then be solved by equating the jammer part of the covariance matrix and the power representation, i.e., 
                 ∑     k   =   1     K     ⁢           ⁢         g   _     a     (   k   )       ⁢           ⁢       g   _     a       (   k   )     H       ⁢           ⁢     P   k         =       ∑     k   =   1     K     ⁢           ⁢       (       λ   k     -     σ   2       )     ⁢           ⁢       q   _     k   H     ⁢           ⁢         q   _     k   H     .                 (   41   )             
 
It should be noted that g a   (k) =g a (T J   K ) is used for convenience. P k  can be solved by using the following set of linear equations: 
                   λ   1     -     σ   2       =         ∑     k   =   1     K     ⁢           ⁢       (         g   _     1   H     ⁢           ⁢       g   _     a     (   k   )         )     ⁢           ⁢     (         g   _     a   H     ⁢           ⁢       g   _     1       )     ⁢           ⁢     P   k     ⁢           ⁢   1       =   1       ,   2   ,     …   ⁢           ⁢     K   .               (   42   )             
 
Then the jammer response vector g a   (k)  and the power P k  can be determined for each of the K jammers. If one of the jammers is within the mainbeam, it can be removed from the covariance matrix expression, that is, the modified covariance matrix and cross-correlation matrix are then given by:
 
 {circumflex over (R)}   aa   =R   aa   −P   1   g   a   (1)   g   a   (1)H   (43) 
 
  {circumflex over (R)}   aΣ   =R   aΣ   −P   1   g   a   (1)   g   Σ *.
 
The modified covariance matrices can then be used for adaptive weight computations as before.
 
   Another mainlobe maintenance procedure is to spatially filter out the mainlobe jammer in the auxiliary array. This procedure involves modifying the system of  FIG. 13  in the manner shown in  FIG. 13A ; i.e., by constructing a blocking matrix B such that the mainlobe jammer is filtered out of the signals supplied by the auxiliary array. If
 
 r   a   ′=Br   a ,  (44) 
 
B has the property of nulling out the mainlobe jammers, i.e.,
 
 Bg   a ( T   j )=0  (45) 
 
The spatial filtered samples can then be used for covariance matrix estimation and adaptive weight computation.
 
   The main channel output signals are thus freed of SLJ but may include MLJ. The MLJ cancellation technique can be applied as before, leading to the following:
 
 r   Σ     E     ″=r   Σ   ′−W   a     1     r   Δ     A   ′
 
 r   Δ     E     ″=r   Δ     E     ′−W   a     2     r   Δ     A   ′
 
 r   Σ     A     ″=r   Σ   ′−W   e     1     r   Δ     g   ′
 
 r   Δ     A     ″=r   Δ     A     ′−W   e     2     r   Δ     A   ′.  (46) 
 
The optimal weights for suppressing the MLJ can be derived to be 
                 W     a   1       =       E   ⁡     [       r     Σ   ′       ⁢     r     Δ     A   ′       *       ]         E   ⁡     [       r     Δ     A   ′         ⁢     r     Δ     A   ′       *       ]           ⁢     
     ⁢       W     a   2       =       E   ⁡     [       r     Δ     E   ′         ⁢     r     Δ   Δ       ′   *         ]         E   ⁡     [       r     Δ   Δ     ′     ⁢     r     Δ   Δ       ′   *         ]           ⁢     
     ⁢       W     e   1       =       E   ⁡     [       r   Σ   ′     ⁢     r     Δ   E       ′   *         ]         E   ⁡     [       r     Δ   E     ′     ⁢     r     Δ   E       ′   *         ]           ⁢     
     ⁢       W     e   2       =         E   ⁡     [       r     Δ   A     ′     ⁢     r     Δ   Δ       ′   *         ]         E   ⁡     [       r     Δ   Δ     ′     ⁢     r     Δ   Δ       ′   *         ]         .               (   47   )             
 
In order to evaluate performance of the technique, the antenna patterns and the monopulse ratio are derived. The antenna patterns are the response due to the testing signal and are given by
 
Σ E ″=(Σ S−W   a     1   Δ A   S )−( Ŵ   Σ   H   −W   a     1     Ŵ   Δ     A     H ) G   a   S  
 
=(Σ S−W   a     1   Δ A   S ) 
 
Δ E ″(Δ E   S−W   a     2     Δ   Δ   S ) 
 
Σ A ″=(Σ S−W   e     1   Δ E   S ) 
 
Δ A ″(Δ A   S−W   e     2   Δ Δ   S ).  (48) 
 
In each case, input signals from the auxiliary array are negligible as the auxiliary array gains are very much lower than the main antenna gains. The monopulse ratios for the elevation and azimuth angle estimation are given by 
                       f   e   ′     ⁢           ⁢     (     θ   e     )       =       ⁢     Re   ⁢     {           Δ   E     ⁢           ⁢   S     -       W     a   2       ⁢           ⁢     Δ   Δ     ⁢           ⁢   S             ∑                     ⁢           ⁢   S     -       W     a   1       ⁢     Δ   Δ     ⁢           ⁢   S         }                   =       ⁢     Re   ⁢     {           Σ   a     ⁢           ⁢     (     T   x   s     )     ⁢           ⁢     Δ   e     ⁢           ⁢     (     T   y   s     )       -       W     a   2       ⁢     Δ   a     ⁢           ⁢     (     T   x   s     )     ⁢           ⁢     Δ   e     ⁢           ⁢     (     T   y   s     )               Σ   a     ⁢           ⁢     (     T   x   s     )     ⁢           ⁢     Σ   e     ⁢           ⁢     (     T   y   s     )       -       W     a   1       ⁢     Δ   Δ     ⁢           ⁢     (     T   x   s     )     ⁢           ⁢     Δ   e     ⁢           ⁢     (     T   y   s     )           }                   =       ⁢     Re   ⁢     {         Δ   e     ⁢           ⁢     (     T   y   s     )     ⁢     (           ⁢         Σ   a     ⁢           ⁢     (     T   x   s     )       -       W     a   2       ⁢     Δ   a     ⁢           ⁢     (     T   x   s     )         )           Σ   e     ⁢           ⁢     (     T   y   s     )     ⁢     (           ⁢         Σ   a     ⁢           ⁢     (     T   x   s     )       -       W     a   1       ⁢     Δ   a     ⁢           ⁢     (     T   x   s     )         )         }                   =       ⁢           Δ   e     ⁢           ⁢     (     T   y   s     )           Σ   e     ⁢           ⁢     (     T   y   s     )         ⁢           ⁢     (       if   ⁢           ⁢     W     a   1         =     W     a   2         )     ⁢           ⁢   and                     f   a   ′     ⁢           ⁢     (     θ   a     )       =       ⁢     Re   ⁢     {           Δ   A     ⁢           ⁢   S     -       W     e   2       ⁢           ⁢     Δ   Δ     ⁢           ⁢   S             ∑                     ⁢           ⁢   S     -       W     e   1       ⁢     Δ   Δ     ⁢           ⁢   S         }                   =       ⁢         Δ   a     ⁢           ⁢     (     T   x   s     )     ⁢           ⁢     (         Σ   e     ⁢           ⁢     (     T   y   s     )       -       W     e   2       ⁢           ⁢     Δ   e     ⁢           ⁢     (     T   y   s     )         )           Σ   a     ⁢           ⁢     (     T   x   s     )     ⁢           ⁢     (         Σ   e     ⁢           ⁢     (     T   y   s     )       -       W     e   1       ⁢           ⁢     Δ   e     ⁢           ⁢     (     T   y   s     )         )                     =       ⁢           Δ   a     ⁢           ⁢     (     T   x   s     )           Σ   a     ⁢           ⁢     (     T   x   s     )         ⁢           ⁢       (       if   ⁢           ⁢     W     e   1         =     W     e   2         )     .                     (   50   )             
 
Thus monopulse ratios are preserved, and jamming is cancelled.
 
   While only certain preferred features of the invention have been illustrated and described herein, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.