Abstract:
A monopulse radar having a single set of adaptive weights shared by both sum and difference channels. The radar utilizes algorithm that effect simultaneous nulling in the sum and difference patterns of its phased array antenna. Algorithms are developed for both amplitude and phase nulling and for phase only nulling.

Description:
STATEMENT OF GOVERNMENT INTEREST 
     The invention described herein may be manufactured and used by or for the Government for governmental purposes without the payment of any royalty thereon. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to monopulse radars, and in particular to means for effecting simultaneous nulling in the sum and difference patterns of a monopulse phased array antenna using one set of adaptive weights shared by both channels. 
     In the past few years, considerable research and development has been expended on adaptive antennas. Communications and sonar systems have reaped some of the benefits of adaptive technology while radars generally lag behind. Some of the reasons for this dichotomy are many adaptive techniques are not suited for microwave frequencies; radars have large antennas, hence more adaptive loops; and a radar has tight time constraints for detecting and tracking targets. Consequently, only a handful of radars incorporating sidelobe cancelling techniques exist today. A fully adaptive phased array antenna is not practical to build at this time. 
     Monopulse radars add additional problems to the adaptive processing. The problems stem from the coextistence of a sum and difference pattern. A monopulse phased array antenna uses two antenna patterns: one to detect and range a target and a second to determine a target&#39;s angular location. Most adaptive antenna research has ignored the difference pattern, even though both patterns must have a null in the direction of interference to enhance the radar&#39;s performance. Adjusting the far field sum pattern to place a null in the direction of interference will not place a null in the difference pattern too. Hence, either the sum and difference channels are adapted separately or a technique of simultaneously nulling in both channels is used. Current research has assumed the first approach is the only feasible technique, and the possibility of simultaneous nulling has been ignored. 
     The current state of the art relating to radar system null pattern generation techniques is illustrated by U.S. Pat. No. 4,214,244 entitled Null Pattern Technique For Reduction of An Undesirable Interference Signal issued to Michael W. McKay July 22, 1980, U.S. Pat. No. 4,224,870 entitled Null Steering Antenna issued to Gene R. Marrs Sept. 30, 1980, and U.S. Pat. No. 4,298,873 entitled Adaptive Steerable Null Antenna Processor issued to Eugene L. Roberts Nov. 3, 1981. Adaptive nulling in these and other prior art systems is done with two separate sets of adaptive weights: one in the sum channel and one in the difference channel. The technique of the present invention allows nulling with one set of adaptive weights shared by the two channels thereby greatly reducing hardware complexity, computer software and the cost for adaptive processing. 
     SUMMARY OF THE INVENTION 
     The invention comprehends a monopulse radar having a null pattern generating capability that can be implemented with a single set of adaptive weights that are used by both sum and difference channels. 
     It comprises an apparatus and technique for simultaneously placing nulls in the sum and difference patterns of the monopulse phased array antenna and includes a phased array antenna having N equally spaced elements, a computer, and feedback circuitry. Connected to each element of the phased array antenna is a variable complex weight which steers the main beam as well as generates the nulls in the far field pattern. After the variable complex weights the signal is split into a sum and a difference channel. The sum channel receives a special constant amplitude weighting, a n , to lower the sidelobes of the far field pattern, while b n , is the amplitude weighting in the difference channel. The computer uses a special algorithm to determine the phase settings which yield a null in the antenna pattern in the direction of the interference and then sets the variable complex weights at the calculated values. 
     It is a principal object of the invention to provide a new and improved means for effecting simultaneous nulling in the sum and difference pattern of a monopulse radar antenna. 
     It is another object of the invention to provide simultaneous nulling in the sum and difference patterns of a monopulse radar antenna using a technique that allows nulling with one set of adaptive weights shared by the two monopulse channels. 
     It is another object of the invention to provide means for effecting simultaneous nulling in the sum and difference patterns of a monopulse radar antenna in which hardware complexity and computer software are greatly reduced. 
     It is another object of the invention to provide means for effecting simultaneous nulling in the sum and difference patterns of a monopulse radar antenna that is implemented by means of an amplitude and phase nulling algorithm. 
     It is another object of the invention to provide means for effecting simultaneous nulling in the sum and difference patterns of a monopulse radar antenna that is implemented by means of a phase only algorithm. 
     These together with other objects, features and advantages of the invention will become more readily apparent from the following detailed description when taken in conjunction with the illustrative embodiment of the accompanying drawing. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic illustration of a linear array of N antenna elements; 
     FIG. 2 is a schematic illustration of the components of a monopulse radar and linear antenna array utilized in practicing the invention; 
     FIG. 3 is a graph illustrating cancellation beam and quiescent patterns; 
     FIG. 4 is a graph illustrating a quiescent far field sum pattern; 
     FIG. 5 is a graph illustrating a quiescent far field difference pattern; 
     FIG. 6 is a graph illustrating a far field sum pattern with null at 33 degrees; 
     FIG. 7 is a graph illustrating a far field difference pattern null at 33 degrees; and 
     FIGS. 8 and 9 comprise a flow chart for the null forming algorithm of the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The invention is a monopulse radar with null pattern generating capability and includes a phased array antenna, a computer, and feed back circuitry. The phased array is linear with equal spacing between the N elements. Behind each element is a variable complex weight which steers the main beam as well as generates the nulls in the far field antenna pattern. After the variable complex weights the signal is split into two channels. One channel is the sum channel and the other the difference channel. The sum channel receives a special constant amplitude weighting, a n , to lower the sidelobes of the far field pattern. Likewise, b n  is the amplitude weighting in the difference channel. Also, half the array difference channels receive a 180° phase shift. All the difference channel signals are summed to get a single output. Similarly, all the sum channels are added together to get an output. Both outputs pass through a receiver, then are digitized and sent to the computer. The computer uses a special algorithm to determine the phase settings which yield a null in the antenna shifters at the calculated values. Algoriths for both amplitude and phase nulling and for phase only nulling are provided. In order to use this technique, the direction of all the inteference sources must be known. Their angle from the antenna&#39;s boresite is given by φ m  (1≦m≦M). These angles are read into the computer. The computer calculates the necessary phase settings to cancel the interference. 
     FIG. 2 is a schematic illustration of the components of the monopulse radar utilized in the practice of the invention. They comprise antenna elements 10, variable complex weights 11, constant amplitude weight 12, 180° phase shifters 14, summing means 15, differencing means 16, receivers 17, 18, analog/digital converters 19, 20 and computer 21. 
     An algorithm for implementing amplitude and phase nulling is hereinafter developed. 
     The algorithm described is a null synthesis technique rather than a closed loop adaptive algorithm. The location of the jammers must be known for the nulls to be placed. The phase and amplitude distribution that places nulls in the direction of the jammers while minimally perturbing the adaptive weights is then computed. The weights used to generate this distribution theoretically yield a far field pattern with the desired nulls. In a practical situation, however, antenna errors significantly limit this nulling technique unless the weights are adaptively adjusted using some form of feedback. It is possible to convert this open loop nul synthesis algorithm into a closed loop adaptive algorithm to compensate for the antenna errors. 
     FIG. 1 serves as the model for amplitude and phase nulling in both channels using separate weights for each channel. The quiescent weights for the sum channel are given by 
     
         w.sub.on =a.sub.n e.sup.-jd.sbsp.n.sup.u.sbsp.s            (1) 
    
     If the physical center of the array is also the phase center, then the phase of the signal at element n is ##EQU1## Assume a weight change of Δw n  will produce the required nulls in the far field pattern. The new cascaded weights are represented by 
     
         Δw.sub.n =w.sub.on (1+Δw.sub.n)                (5) 
    
     The weight change in complex form is 
     
         Δw.sub.n =α.sub.n +jβ.sub.n               (6) 
    
     When there are no weight changes, Δw n  =0 and w n  =w on . Substituting Eqs. (1) and (6) into Eq. (5) leads to ##EQU2## This new amplitude and phase distribution puts nulls in the direction of the jammers. 
     The far field sum pattern of the adapted antenna is given by ##EQU3## The sine terms sum to zero because d n  in Eq. (4) is odd symmetric and the sine is an odd function. In general, M nulls are required in the pattern to cancel M jammers at angular locations u m  (1≦m≦M). The resultant far field pattern equals zero when u=u m . ##EQU4## This system of equations may be looked at as the sum of the quiescent pattern and M cancellation beams. Each cancellation beam matches the quiescent pattern&#39;s amplitude in the jammer directions, but is opposite in phase. Therefore, the sum of the two quantities equals zero at u m . The process is pictorially represented in FIG. 3. 
     The above system of equations has M equations and N unknowns. To determine the values of Δw n , Eq. (13) is solved for α n  and ν n . Shore and Steyskai have shown that minimizing the quantity ##STR1## minimizes, in the least mean square sense, the adaptive weight perturbations. This is a very desirable characteristic, because the nulled pattern changes very little as possible from its quiescent form. 
     To solve the system of equations, we put it into matrix form. 
     
         AX=B                                                       (14) 
    
     where ##EQU5## where [ ] T  represents matrix transpose. The lease squares solution to AX=B is 
     
         A.sup.+ AX=A.sup.+ B                                       (18) 
    
     where () +  represents conjugate matrix transpose 
     
         (A.sup.+ A).sup.-1 (A.sup.+ A)X=(A.sup.+ A).sup.-1 A.sup.+ B (19) 
    
     
         X=A.sup.+ (AA.sup.+).sup.-1 B                              (20) 
    
     Since it can be shown that (A +  A) -1  A +  =A +  (AA + ) -1 . 
     The product of AA +  is a matrix whose elements are ##EQU6## The sine term sums to zero because d n  is odd symmetric and sine is an odd function, and it has been assumed a n  =a N+1-n . 
     Eq. (20) may be written as 
     
         X=A.sup.+ Y                                                (25) 
    
     where 
     
         Y=(AA.sup.+).sup.-1 B                                      (26) 
    
     The vector Y is found by inverting (AA + ) and post-multiplying the result by the vector B. Substituting Y into Eq. (20) gives ##EQU7## Next, the real and imaginary parts are equated ##EQU8## The derived weight changes, Δw n  =α n  +jβ n , are used to adjust the complex array weights to generate the nulls in the pattern. Using Eq. (5) the adapted weights may be expressed as 
     
         w.sub.n =w.sub.on δ.sub.n exp [jφ.sub.n ] 
    
     where 
     
         γ.sub.n =[(α.sub.n +1).sup.2 +β.sub.n.sup.2 ].sup.1/2(30) 
    
     
         φ.sub.n =tan.sup.-1 [β.sub.n /(α.sub.n +1)] (31) 
    
     The nulling technique can be extended to include difference patterns. Since the sum pattern is an even function and the difference pattern an odd function, the derivations require modification. Weight perturbations that create a desired null in the sum pattern do not create a null in the difference pattern, even if the amplitude distributions are uniform. 
     One way of producing a difference pattern is shown in FIG. 1 where half the element signals receive a 180° phase shift. The quiescent difference channel weights are 
     
         w.sub.on =b.sub.n e.sup.-jd.sbsp.n.sup.u.sbsp.s.           (32) 
    
     As before, the weight change w n  produce a null in a desired direction. ##EQU9## These weights have a far field pattern represented by ##EQU10## The quiescent far field pattern is ##EQU11## D(u) is zero in the direction of the jammers ##EQU12## Because b n  is an odd function ##EQU13## Eq. (38) in matrix form is AX=β where ##EQU14## The method of least square leads to a solution ##EQU15## The variable c m  is an element of the vector C. The matrix (AA + ) contains the elements ##EQU16## The sine terms sum to zero leaving ##EQU17## Rewriting Equation 45 results in ##EQU18## Finally, equating the real and imaginary parts of both sides of the equation produces the weight perturbations, ##EQU19## The phase-amplitude forms of the complex perturbations are used to adjust the variable complex weights. 
     Null synthesis for sum and difference patterns in the manner previously described requires two separate sets of adaptive weights. Implementing this technique on a monopulse radar antenna requires N complex weights in the sum channel and N complex weights in the difference channel as shown in FIG. 1. The following pages describe a technique that allows the sum and difference channels to share one set of complex weights (FIG. 2). The adaptive weight appears before the element signal is split into the sum and difference channels. Incorporating such a technique into an adaptive antenna would significantly reduce the cost and complexity of the system. 
     A linear array with N elements has N complex weights and N-1 degrees of freedom. For every jammer, the sum channel uses one degree of freedom and the difference channel another. The drawback to this technique is that the degrees of freedom available for nulling in the sum and difference channels are cut in half, so that (N-1)/2 degrees of freedom are available. 
     Eqs. (13) and (38) still hold true, but now they must be solved simultaneously. ##EQU20## This system of equations may be put in the form AX=B ##EQU21## The least mean square solution to the equation is 
     
         X=A.sup.+ (AA.sup.+)B                                      (58) 
    
     To make the computations easier to follow, the A matrix is partitioned. ##EQU22## The elements for (AA + ) are ##EQU23## 
     Inverting the complex matrix (AA + ) and multiplying it by Y results in a 2M×1 complex matrix R. The weight perturbations are ##EQU24## Equations (69) and (70) are rewritten in matrix notation as: 
     
         α.sub.n =Re{A.sup.+ (AA.sup.+).sup.-1 B}             (71) 
    
     
         β.sub.n =Im{A.sup.+ (AA.sup.+).sup.-1 B}              (72) 
    
     In another embodiment of the invention nulling is accomplished by means of phase only nulling techniques. 
     Nulling with phase shifters is much more desirable than nulling with complex weights. The hardware for phase only nulling is less complicated. Adjusting the signal amplitude requires an attenuator or two phase shifters in a bridge circuit for each element. The extra losses, mismatch, and cost of the amplitude control discourages its use. Also, phased arrays usually have only phase shifters and incorporation of amplitude weighting requires modifications to existing antennas. An adaptive technique that uses phase control rather than phase and amplitude control can more easily be implemented on existing phased arrays. 
     Phase only nulling in the sum channel of a low sidelobe antenna is discussed in the literature. The technique closely follows the process used in phase and amplitude nulling described above. The quiescent sum channel weights are given by Eq. (1). To put nulls in the antenna pattern, a phase shift of φ n  is given to each element. ##EQU25## The approximation e j φ n≃1+jφ n  is necessary to solve the problem, but it makes the answer approximate. Fortunately, this approximation works very well for low sidelobe antennas. 
     The far field pattern of these weights is calculated from ##EQU26## At the jammer angles, the pattern goes to zero ##EQU27## Next, equating the real and imaginary parts, assuming a n  real ##EQU28## The second equation equals zero because the sine is an odd function and d n  has odd symmetry, and a N+1-n  =a n  has been assumed. 
     Equation (79) can be put into the matrix form AK=B where ##EQU29## The unknown phase shifters are obtained from the method of least squares. 
     
         X=A.sup.T C                                                (84) ##EQU30## The variable c.sub.m is the mth element in the vector C. Nulls are made in the sum pattern in the directions of the jammers when φ.sub.n is applied to the phase shifters. 
    
     The derivation of the phase shifts for the difference channel follows that of the sum channel. ##EQU31## The far field difference pattern is ##EQU32## D(u) equals zero when u=u m . ##EQU33## Equating the real and imaginary parts of the equation, ##EQU34## Eq. (91) equals zero. The remaining system of equations can be solved using the method of least squares. ##EQU35## The X vector contains the values φ n  and C has elements c m . ##EQU36## These phase shifters produce nulls in the difference pattern in the directions of interference. 
     Normally, both the sum and difference channels share one set of phase shifters. The preceding nulling techniques place nulls in the sum pattern or the difference pattern, but not both. To place the nulls in both far field patterns, the conditions of the two equations must be met. Thus, Eqs. (78) and (90) remain unchanged, but in this case they are solved simultaneously. 
     The elements of the matrix equation AX=B are ##EQU37## The least squares solution is ##EQU38## The variables c m  are elements of the matrix C. These values of o n  simultaneously generate a null in the sum and difference patterns in the direction of interference. 
     By way of example, the low sidelobe synthesis techniques and nulling algorithm have been programmed in BASIC and implemented on a Tektronix 4052 computer. The computer included a Tektronix 4663 plotter which drew all plots shown in FIGS. 4-7. 
     FIG. 8 shows a block diagram of the computer algorithm. First, data such as the number of elements, element spacing, etc. are entered on the keyboard. Next, the program calculates the amplitude weights for either a uniform, Taylor, a Cheybchev sum distribution and for either a uniform or Bayliss difference distribution. This part of the program models a low sidelobe synthesis technique. Multiplying the zero factors together to obtain the polynomial p(s) is very inefficient. Only linear array distributions with up to 30 elements can be derived without taking excessive computer time. 
     After calculating the desired array distribution, the program enters into the nulling routines. The routine offers six different choices: 
     (1) Amplitude &amp; Phase Nulling in Sum Channel 
     (2) Amplitude &amp; Phase Nulling in Difference Channel 
     (3) Amplitude and Phase Nulling Simultaneously 
     (4) Phase only nulling in sum channel 
     (5) Phase only nulling in difference channel 
     (6) Phase only nulling simultaneously 
     The routine changes the quiescent sum and difference channels for one of the above choices. Both channels are assumed to share one set of adaptive weights. In cases 1 and 4 the adaptive weights are adjusted to place nulls in the sum channel. The difference channel receives the exact same weight change. For cases 2 and 5 the reverse holds true. In cases 3 and 6 the adaptive weights are adjusted to yield nulls simultaneously in the sum and difference channels. When the nulling routine is completed, the program stores the quiescent, adapted, and cancellation beam weights on tape. Next, the program calculates the far field pattern of any of the array weights stored on tape. The user interactively specifies the number of plots on the graph and the normalization value. In this way, the output can be modified to obtain the necessary details. Finally, the computer draws the graph on a CRT and/or plotter. The following program was used to implement the above described routine. ##SPC1## ##SPC2## 
     While the invention has been described in its presently preferred embodiments, it is understood that the words which have been used are words of description rather than words of limitation and that changes with the purview of the appended claims may be made without departing from the scope and spirit of the invention in its broad aspects.