Null steering antenna

Where there is a difference in the angle of arrival between desired incom signals and interfering signals, the reception of the desired signals is maximized by the creation of nulls in the direction of the interfering signals. A high quality receiving (or transmitting) beam is formed by a one-time calculation of the proper phase or amplitude adjustment required to create a null in the direction of each interfering signal. The antennae are then appropriately adjusted to establish the nulls.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The invention relates, in general, to the area of art known as null 
steering and, more particularly, to a method and apparatus for receiving 
radio signals from a desired source while at the same time reducing the 
response to interfering signals, if there is a difference in the angle of 
arrival of the two signals. 
2. Description of Prior Art 
Highly directive transmission and receiving beams have been developed and 
are used extensively in the antenna art. One type of directive beam 
antenna is the well-known "phased array", wherein array elements phase 
commands are used to scan the beam of a planar phased array. This 
technique is typified by U.S. Pat. Nos. 3,877,012 to Nelson, 3,806,930 to 
Gobert, and 3,319,249 to Blachier. Although "phased arrays" use phase 
adjustments, they do not relate to null steering art contemplated by the 
present invention. 
In addition there have been developments in the area of both simultaneous 
formation of a null in the pattern of reception and for changing the 
direction of a null. This technique is usually termed "null steering 
phased arrays" or "adaptive arrays." Prior patents in this area include 
U.S. Pat. Nos. 3,670,335 to Hirsch; 3,964,065 to Roberts; and 3,725,929 to 
Spanos. The creation of pattern nulls in phased antenna arrays require 
devices for varying phase and amplitude of the signals received from or 
fed to each antenna of the array. The correct values of signal amplitude 
and phase relationship to be fed to each antenna are then calculated. By 
means of attenuators to adjust amplitude and phase shifters to adjust 
phase, the correct values are obtained. Thus, to create a null in a 
desired direction, a calculation and an adjustment to the attenuator and 
phase shifter for each antenna is required. 
It is also known to use phase shifters alone and still obtain a pattern 
null in the desired direction. The adjustments, however, were very 
complicated. Since no exact solution was available from theory, the phase 
shifters for each antenna were set at the value obtained from the previous 
theory of amplitude and phase adjustment. The attenuator device was not 
needed since the amplitude was not varied. The phase shifter of one 
antenna was then changed a small amount. If the amplitude of the 
interfering signal decreased, then the change was deemed proper. If the 
interference signal increased, the phase shifter was changed in the 
opposite direction. This trial and error method was then repeated for each 
antenna of the array. The whole procedure was repeated over and over again 
until a stable result was obtained. This process, an iterative procedure, 
requires many rapid calculations which are time consuming unless a 
relatively high speed computer is available. A high speed accurate phase 
shifter for each antenna is required along with a highly sophisticated 
control system. In addition, since decisions have to be made very rapidly 
for each phase change, the criteria used to evaluate the null depth are 
very limited. 
SUMMARY OF THE INVENTION 
It is, therefore, an object of the invention to reduce the response-time of 
a radio receiver to interfering signals, if there is a difference between 
the arrival angle of the interfering singals and the desired signal. 
Another object of this invention is to provide an improved means for 
determining the phase or amplitude adjustments required for null steering. 
Another object of the invention is to improve on known null steering 
techniques with regard to speed of calculation, computation simplicity, 
and the overall rejection of an interfering signal relative to the desired 
signal. 
Briefly, the present invention enhances the conventional directivity 
characteristics of antennae by creating a null in the arrival direction of 
the interfering signal while at the same time forming a beam for 
preferential reception in the direction of the desired signal source. The 
antenna system is an array of antennae in which phase or amplitude 
adjustments are made in the signal lines. The lines are added to obtain a 
composite signal which is then applied to the receiver.

DETAILED DESCRIPTION 
A linear array of antenna elements for the phased array is shown in FIG. 1. 
It is assumed that the amplitude and phase of the signal from each antenna 
can be separately adjusted before they are added together in a summing 
circuit. The antenna array is also assumed to be large, with the element 
voltages tapered if necessary to reduce side lobes. For large arrays of 
this type, minor lobes are usually quite small, 20 to 30 db down from the 
maximum. The following discussion is not limited by the requirement for 
small minor lobes but their implications are taken into account. 
In FIG. 1, a linear phased array of (m+1) antennae 0, 1, . . . m is shown 
spaced a distance of d electrical radians apart at the frequency of 
operation. The signal is shown coming in from a direction .theta. 
measured from a reference direction perpendicular to the array as shown at 
antenna number 2. 
Assuming that all antennae are similar, the phase of the signal received by 
each antenna is assumed dependent only upon the time of arrival relative 
to the other antennae. Although amplitude variations in received signals 
may or may not be introduced for minimum side lobes, each voltage is 
considered separately (E.sub.n). The relative signal received by summing 
the antennas through a phase shifting and summing network is given by 
##EQU1## 
where d=spacing between antennas in radians of wavelength 
.theta.=direction of reception 
E.sub..theta. =total summed signal received from direction .theta. 
E.sub.n =signal amplitude transmitted to combining network from n.sup.th 
antenna 
.phi.=phase shift introduced into the antenna labeled one spaced d from the 
reference antenna labeled zero received signal before summing 
n.phi.=phase shift introduced into the n.sup.th antenna received signal 
before summing 
f=signal frequency 
.omega.=2.pi.f 
E.sub..theta. is a maximum, E.sub..phi., when 
EQU .phi.=d sin.theta. (2) 
so that 
##EQU2## 
Thus the angle at which maximum reception occurs is given by .theta.' 
where 
EQU .theta.'=sin.sup.-1 (.phi./d) (4) 
Null Formation 
The antenna pattern, for any specific value of .phi., as given by equation 
(1), has minor lobes and nulls that naturally exist. Sometimes when heavy 
interference or noise is coming from a specific direction .theta.* and no 
null normally exists there, it is desirable to create a deep null in that 
direction. 
For instance, in a direction .theta.* where a side lobe exists 
E.sub..theta. would have the value E.sub..alpha. at .theta. equal to 
.theta.* namely 
##EQU3## 
To create the null, another receiving pattern E.sub..theta. ' is created 
where 
##EQU4## 
where 
EQU .alpha.=d sin.theta.* (7) 
Now at .theta.* 
##EQU5## 
Taking K outside the summation sign and substituting from (3) 
EQU E.sub..alpha. =KE.sub..theta. (9) 
so that 
EQU K=(E.sub..alpha. /E.sub..phi.)=K .gamma. (10) 
Since, as shown in equation (5), K has both amplitude and phase, it is 
noted that K consists of an amplitude factor k and a phase factor .gamma.. 
Phase relationships have to be maintained. 
It is possible to make K real instead of complex by using the center of 
radiation (or phase center) of the antenna as a reference instead of the 
edge of the array. 
The null at .theta.* is obtained by subtracting E.sub..theta. ' from 
E.sub..theta. 
##EQU6## 
The phase relationships are better illustrated by adding and subtracting 
n.phi. in the second term and simplifying. 
##EQU7## 
Each term of the summation (12) is the voltage from a single antenna. In 
this case, in the n.sup.th antenna the received voltage would be divided, 
one would be delayed by the phase of n.phi., the other would be delayed by 
a phase of .gamma.+n.alpha. (the n.phi. terms cancel out) and attenuated 
by a factor k. The two voltages would be combined using the difference as 
shown. 
FIG. 2 shows a phasor diagram of the two components of equation (12). As 
can be seen, the phase angle between the two components is always constant 
with time- and angle-of-arrival of the signal, namely .gamma.-n(.phi.-a). 
The amplitude kE.sub.n is usually quite small but is magnified in the 
illustration for clarity. In FIG. 2, it can be seen that as n varies, 
while keeping t constant, the small phasor (-kE.sub.n) will rotate around 
the end of the main signal (E.sub.n) very much like a single sideband 
modulating signal. However, its phase is dependent upon n and not upon t 
or .theta.. The relationship is shown in FIG. 3 for the first few antennae 
where the second part of equation (12) (amplitude kE.sub.n) varies around 
E.sub.n with n like a modulating signal. E.sub.n is used as the reference 
normalized to a fixed amplutude and phase. 
Phase-Only Null Steering 
Analogous to modulation techniques, null steering is then obtained by 
adding phase shift only between the signals in the n antennae. Using phase 
modulation theory, the components of equation (12) shown in FIG. 3 are 
analogous to the carrier and one of the sidebands of a phase modulated 
wave. Another component, E.sub..theta. ", is analogous to the second of 
the first pair of sidebands, where 
##EQU8## 
so that 
##EQU9## 
This sideband has been chosen so that it completes the first pair of 
sidebands of an equivalent phase modulated wave. Noting the first 
component as A and the second (new) component as B, the effect is shown in 
FIG. 4. Introducing B results in a phase shift from antenna to antenna 
with only a small change in amplitude. (Actually the change in amplitude 
is much smaller than shown because the amplitude of A and B have been 
exaggerated for clarity of illustration. The side lobes are normally over 
20 db down so that the magnitudes of A and B would be less than one-tenth 
E.sub.n.) 
Using 
EQU -cos a+cos b=2 sin1/2(a-b) sin1/2(a+b) (15) 
(14) becomes 
##EQU10## 
where E.sub.Rn is the resultant shown in FIG. 4. Thus the phase shift is 
determined by (2k sin [.gamma.-n(.phi.-.alpha.)]) which is a constant for 
each antenna depending upon .phi.,.alpha.,.gamma. and k and does not vary 
with time- or angle-of -arrival. Thus the additional phase shift for the 
n.sup.th antenna for a null in the direction .theta.* (where the maximum 
is in the direction .theta.') is B.sub.n given by 
EQU .beta..sub.n =tan.sup.-1 (2k sin [.gamma.-n(.phi.-.alpha.)]) (17) 
This equation for B.sub.n is correct for the added phase shift when k is 
very small, which is usually the case. A more exact equation is required 
where k is larger and the derivation thereof follows after the discussion 
of Amplitude-Only Null Steering. 
Equation (16) can be used for the case of small side lobes, however there 
may still remain a small amount of amplitude modulation as can be seen by 
the variation in size of E.sub.Rn, the resultant in FIG. 4. This amplitude 
modulation can be negated by introducing the equivalent of additional 
pairs of sidebands, as in phase or frequency modulation. A basic 
requirement for pure phase modulation is that the amplitudes of the main 
beam and components be related to one another as Bessel Functions of the 
first kind to the same argument. Letting Z represent the argument and 
J.sub.n the Bessel Function, then the resultant E.sub.R is given by 
##EQU11## 
FIG. 3 can be used to determine the argument (Z). From (16) it can be seen 
that 
##EQU12## 
The ratio of J.sub.1 over J.sub.0 is plotted in FIG. 5. There is a specific 
value of Z for every ratio of J.sub.1 over J.sub.0. For instance, for 20 
db down, J.sub.1 over J.sub.0 is 0.1 and referring to the curve, the 
approximate value of Z is 0.2. For this argument the value of J.sub.0 
(0.2) is 0.990, J.sub.1 (0.2) is 0.0995, J.sub.2 (0.2) is 0.005 and all 
other terms are negligible. Thus, the amplitude of the main beam will 
decrease by about one percent, a negligible amount, when the small 
variation in amplitude is removed by inserting only phase variation. 
It will be noted that the only function of the J.sub.2 (Z) sidebands, the 
added harmonics, is to remove the amplitude variation introduced by the 
first pair of sidebands. For this portion of the discussion the only 
component that needs to be adjusted to create the desired null is the 
phase shift introduced by the first pair of sidebands (as in equation 16). 
Keeping the amplitude constant is equivalent to introducing the added set 
of sidebands. 
The previous calculations result in a very simple method for producing 
specific new deep nulls in a phased array where the minor lobes are 
relatively small (about 20 db down from the major lobe maximum). One 
procedure which can be used is as follows: 
Calculate the progressive phase shift (.phi.) for the creation of a maximum 
in the main lobe in the desired direction. This is the progressive phase 
shift for the main beam voltage E. 
Calculate the amplitude of the minor lobe of the main beam in the direction 
of the desired null. Determine its phase relative to the main beam voltage 
E.sub..phi.. 
Calculate k, the amplitude ratio of the amplitude of the minor lobe in the 
direction of the null, to the peak amplitude of the main beam and 
determine .gamma., the phase relationship. 
Determine the progressive phase shift necessary to obtain a maximum lobe 
peak in the direction of the desired null. This will determine .alpha.. 
For each antenna, determine the value of (2k sin 
[.gamma.-n(.phi.-.alpha.)]). 
Taking the arc tangent of the above value will determine the added phase 
shift for each antenna to obtain a null in the desired direction. 
The resultant variation in pattern can be obtained by referring to FIG. 5. 
The ratio of J.sub.1 over J.sub.0 is given by k. Thus the value of k on 
the curve J.sub.1 over J.sub.0 gives the value of the argument Z. The 
value of Z determines J.sub.0 (Z), J.sub.1 (Z) and J.sub.2 
(Z).multidot.J.sub.0 (Z) is the factor by which the main beam decreases. 
Ony J.sub.1 (Z) sideband creates a major beam pattern at the desired null 
point which is just equal and opposite to the minor lobe amplitude at that 
point. The other sideband creates a maximum to the other side of the main 
lobe, its actual displacement being dependent upon d sin.theta.. The 
difference in d sin.theta. between the main lobe position and the null 
position will be the same as the difference between the new maximum and 
the main lobe. The second set of components, the J.sub.2 sidebands, will 
create two indentations in the pattern at twice the d sin.theta. 
displacement but their effect will be negligible. 
Usually the main beam calculation is well behaved and the characteristics 
are predictable. However the actual side lobe patterns do not conform 
perfectly to its mathematical model. They may be distorted by 
irregularities in spacing, variations in feeder line link length, etc. 
They are not well behaved. The patterns however can be obtained 
empirically thereby obtaining the value of k as a function of .theta.. 
This value can be used in equation (17) because the new pattern which we 
wish to superimpose will have a well behaved main beam in the direction in 
which a null is desired. The foregoing discussion is therefore applicable. 
Amplitude-Only Null Steering 
It is also possible to create specific new deep nulls in a phased array 
antenna pattern using only added amplitude variation. Equation (13) is 
again used, only it is combined with (12) without changing the sign. Thus 
##EQU13## 
Using the relationship of the sum of the two cosines, (20) becomes 
##EQU14## 
which is equivalent to the results illustrated in FIG. 6 where only the 
amplitude of E.sub.n is varied to obtain the null. 
Thus, the method required for amplitude-only null steering is as follows: 
Calculate the progressive phase shift (.phi.) for the creation of a maximum 
in the main lobe in the desired direction. This is the progressive phase 
shift for the main beam voltage E. 
Calculate the amplitude of the minor lobe of the main beam in the direction 
of the desired null. Determine its phase relative to the main beam voltage 
E. 
Calculate k, the ratio of the voltage of the minor lobe in the direction of 
the desired null to the peak voltage of the main beam and determine 
.gamma., the phase relationship. 
Determine the progressive phase shift necessary to obtain a maximum lobe 
peak in the direction of the desired null. This will determine .alpha.. 
For each antenna determine (2k cos [.gamma.-n(.phi.-.alpha.)]). This 
determines the amplitude variation to be incorporated into each antenna 
voltage for creation of the desired null. The phase of E.sub.n is not 
changed. The resultant phasors will have no added phase variation 
introduced into them since the added phasor, as shown in FIG. 6, removes 
any orthogonal component. The added phasor introduces an added null an 
equal delay angle distance of d sin.theta. equivalent to the d sin.theta. 
angle distance between the main lobe and the desired null. The added null 
is at a mirror image point in the pattern taking into account the 
sin.theta. distortion. 
Supplemental Derivation 
As mentioned above, equation (17) is only correct for the added phase shift 
when the amplitude to be nulled is very small (where k is very small). 
This is normally a valid assumption inasmuch as the steerable nulls are 
usually created in the side lobes where they are nominally 20 db down from 
the main lobe. To aid demonstrating when k is small enough to make the 
above assumption, it is helpful to consider the following derivation. 
Simplifying (14) by using the center of radiation so that .gamma. is zero 
and letting 
EQU C=.omega.t+n(.phi.-d sin.theta.) 
EQU D=-n(.phi.-.alpha.) 
EQU E=E.sub.74 -E.sub.74 '+E.sub.74 " (22) 
Then 
##EQU15## 
Expanding the cosines of C+D and C-D 
##EQU16## 
and simplifying it becomes 
##EQU17## 
Consider now the following equation of pure phase variations 
EQU cos (C-2K sin D)=cos C cos (2k sin D)+sin C sin (2k sin D) (26) 
now 2k is very small so that the following assumptions can be made 
EQU cos (2k sin D)=1 
and 
EQU sin (2k sin D)=2k sin D 
(This is true only when 2k sin D is small enough so that its cosine can be 
considered equal to 1 and its sine could be considered equal to the angle 
itself.) (26) becomes 
EQU cos (A-2k sin D)=cos C+2k sin C sin D (27) 
when (27) is substituted into (25) 
##EQU18## 
Thus the above assumptions give the required result; each voltage in each 
of the antennas is constant in voltage and only incorporates an added 
phase shift. 
When k is too large to make the assumption necessary for equation (17), 
amplitude variation would result unless added sets of signals are 
introduced. Equation (18) is derived as follows for the case of larger 
values of k. Since the simplification cannot be introduced in (26), the 
function is expanded into a Bessel Function series. Thus using the 
relationships for Bessel functions 
##EQU19## 
gives for the phase modulated wave of (26) 
##EQU20## 
but 
EQU cos (2lD) cos D=1/2[cos (C+2lD)+cos (C-l2 D)] 
and 
EQU sin (2l-1)B sin A=1/2[cos (C+[2l-1]D)-cos (C-[2l-1]D)] (31) 
so that (30) becomes 
EQU cos (C-u sin D)=J.sub.0 (u) cos C+J.sub.1 (u)[cos (C+D)-cos (C-D)]+J.sub.2 
(u)[cos (C+2D)+cos (C-2D)]+J.sub.3 (u)[cos (C+3D)-cos (C-3D)]+. . . (32) 
Comparing (32) with the equation for E.sub.1, equation (23), it can be seen 
that the first two terms (the J.sub.0 and J.sub.1 terms) are the same type 
as the terms inside the brackets of (23), and k would now be equal to 
J.sub.1 (u)/J.sub.0 (u) similar to equation (19). However, there are added 
terms which have to be introduced in order to avoid any amplitude 
variation. These are the J.sub.2 (u) and J.sub.3 (u) terms in equation 
(32). For the values referred to above, the higher order terms could be 
neglected. 
Using the relationships 
EQU cos(C+D)-cos(C-D)=2 sinC sinD 
EQU cos(C+D)+cos(C-D)=2 cosC cosD (33) 
equation (32) becomes 
EQU cos(C-u sinD)=J.sub.0 (u) cosC+2J.sub.1 (u) sinC sinD+2J.sub.2 (u) cosC 
cos2D+2J.sub.3 (u) sinC sin3D+. . . (34) 
which is the equation (18) for E.sub.R using the center of radiation so 
that k is real making .gamma. zero. 
Specific Application 
A linear array of m+1 antennae 0, 1, . . . m is shown in FIG. 7, each 
antenna output on lines 50, 51, 52, etc being connected to a device 
A.sub.n (n=0, 1, . . . m), which is capable of phase and/or amplitude 
adjustment of its respective antenna output signal. For clarity in 
description the array will be considered as planar with one-dimensional 
adjustments (forming fan beams rather than pencil beams), the signals will 
be considered as fixed, single frequencies, and a single interfering 
source will be considered. Computer 58 feeds command signals via lines 60, 
61, 62 etc. to phase or amplitude adjusters A.sub.0, A.sub.1, . . . 
A.sub.m thereby adjusting the phase or amplitude signal from the antennae. 
Computer 58 is a general purpose digital computer such as the Varian V-73, 
the DEC PDP-11/45 or the interdata Mod 85 if there are many antenna 
elements and rapid adaptation is desired. 
The characteristics of computer 58 can be determined from requirements 
discussed and the performance characteristics desired. The signal lines 
60, 61, 62, etc from computer 58 to the adjuster A.sub.o -A.sub.m may 
carry either digital or analog signals depending upon the type of circuit 
desired. In addition to the data stored in the computer memory, inputs to 
computer 58 are required specifying the directions of the desired signal, 
.theta.', and the undesired signal, .theta.*. In FIG. 7, arbitrarily 
selected values .theta.' and .theta.* are referenced into computer but it 
should be apparent that a feedback or tracking circuit could be used to 
provide command signals to computer 58. The antenna signals, as modified 
by adjusters A.sub.o -A.sub.m, are fed via lines 70, 71, 72 etc to a 
summing junction and, from there via line 64 to radio receiver 65. The 
summing junction and/or antenna lines can also add fixed amounts of phase 
and amplitude, if desired, in order to establish the symmetry center of 
the array and to achieve desired sidelobe characteristics. The electrical 
length of the lines are assumed to be equal. 
i. Phase-Only 
A null can be formed in the direction .theta.* while a mainbeam is formed 
in the direction .theta.' by pure phase adjustments. In this case, the 
adjusters A.sub.o -A.sub.m are phase shifters which add pure phase shifts, 
B.sub.n, B.sub.n being computed according to equation (17) for the nth 
device and nth antenna: 
EQU B.sub.n =tan-.sup.1 (2k sin.gamma.-n(.phi.-.alpha.)) (17) 
Here n.phi. is the phase shift which would be required in the nth antenna 
lead in order to form a beam in the direction .theta.' from the normal to 
the array. .phi. is determined by inverse of equation (4), 
EQU .phi.=d sin.theta.' (4) INVERSE 
d being the spacing between antennas, measured in wavelengths 
(d=D/.lambda.). The quantities n.alpha. are the phase shifts which would 
be needed to form a beam in the direction .theta.* where .alpha.=d 
sin.theta.*. .gamma. is the phase and k is the amplitude of the antenna 
signal which would be experienced in the direction .theta.* if a main beam 
were formed in the direction .theta. and no null were formed. Both .gamma. 
and k are measured relative to the center of the main beam. These can be 
calculated from the general expression, (1), for the amplitude of the 
summer output 64 as a function of angle of arrival: 
##EQU21## 
Thus, determining the mean beam position to be .theta.=.theta.' by setting 
.phi.=d sin.theta.'. 
##EQU22## 
The corresponding phase angle is .gamma.. This not only forms a perfect 
null by pure phase adjustment only, but also the desired main beam 
amplitude is essentially unaffected by the formation of this null. 
However, when the desired null is quite close to the main beam there will 
be some deterioration in the main beam. This can also be avoided by using 
the more complicated expression given in the supplemental derivation. 
Thus it is possible, in the ideal case, to form a good null and a good beam 
directly by a single sequence of computations without going through an 
iterative process of phase adjustment, measurement of results and further 
adjustment. The advantages over the present Phase-Only Null Steering 
Systems are significant. For example, when using an iterative type 
procedure in typical high performance systems, it is found necessary to 
perform 100-200 iterative adjustments in order to establish good null-beam 
combinations. Regardless of computation speed, a minimum amount of time is 
needed for each iteration so that the receiver output can be analyzed to 
determine if the iterative adjustment has made an improvement or a 
degradation. If this analysis is performed by minimizing the output power 
in cases in which the output power is dominated by undersired signal, the 
process may be carried out rather rapidly, but the composite signal 
(receiver output) will be dominated by the undersired signal. If an 
attempt is made to improve the output quality by identifying some feature 
in the desired signal and performing successive iterations to maximize the 
desired signal, subject to minimizing the total signal or the undersired 
signal, the measurement time per iteration will normally be relatively 
long. With any of these iterative approaches based on quasi-emperical or 
random phase adjustments the following undesirable conditions may be 
experienced: 
A large number of iterations is required. 
A considerable amount of computation is required. 
A significant amount of time must be spent during the adjustment process. 
Signal quality during the adjustment process is poorer than that attainable 
when the null and beam have reached their optimum adjustment. 
There is a significant limitation on the angle of arrival rates which can 
be accommodated. 
If either angle of arrival is changing, poor signal quality during the 
adjustment process causes a deterioration in the desired/undesired signal 
ratio. 
As can be seen from comparing the two methods, the novel method proposed 
here of direct calculation of the values of phase shift necessary for 
creation of the nulls and their direct implementation not only minimizes 
computer time and increases speed, but will directly lead to increase in 
signal-to-noise ratio for the received desired signal. 
ii. Amplitude-Only 
It is also possible to create nulls by pure amplitude adjustment within the 
adjusters A.sub.o -A.sub.m of FIG. 7. In this case, the adjusters A.sub.o 
-A.sub.m would be amplitude adjusters, such as power dividers or 
attenuators. In some circumstances an adaptive array utilizing only 
amplitude adjustments is preferable. For instance, the attenuating 
circuitry may be simpler and more economical to implement. Also, the 
superposition of additional patterns to create a null also creates a 
spurious null which is desirable. Further, the requisite computations are 
simpler. Equation (21) shows that a multiplicative adjustment of the 
antenna outputs by the factor 
EQU 1-2k cos [.gamma.-n(.phi.-.alpha.)] (36) 
will create the desired null. This process is additive, so an additional 
null can be formed by adding a third term to expression (36) of the same 
form as the second, with the parameters k and .phi. chosen to create the 
desired null. This can be extended to additional nulls. Steering of the 
main beam is accomplished by phase adjustments in the amount 
EQU n(.phi.-d sin .theta.') (37) 
as in the phase array case. 
iii. Other embodiments 
The null steering antenna concept can be extended in several ways. First, 
the antenna array can be two dimensional, forming a pencil beam and a 
pencil null rather than a fan beam and a fan null. This can be 
accomplished by adding additional antenna elements with accompanying phase 
shifters/attenuators in the orthognal direction, applying the one 
dimensional discussion independently in each dimension and thereby 
deriving composite phase shifts and/or amplitude adjustments by combining 
the values required for each. 
Secondly, use of the antenna array can be extended to include separate sets 
of feeder lines, phase shifters and/or attenuators and summers, as well as 
computer output lines, to serve separate receivers, thereby establishing 
multiple sets of beams and nulls, independently serving separate 
receivers. A matched power divider is required at the output of each 
antenna element so that the output of that element can serve additional 
receivers. 
Third, in each single set of beam/null forming circuitry serving each 
receiver, it is possible to form and steer more than one null. To a first 
approximation, this can be accomplished by applying equation (17) or 
equation (21), as appropriate, for each null desired. In the case of pure 
phase adjustment, creation of the first null causes a small spurious beam 
for reception on the other side of the main beam. Normally, this will not 
be troublesome. If the angle of arrival of a second interferring signal 
should occur in this special direction, it is not possible to create a 
second null in that direction without interfering with the first null. 
However, this problem can be solved by moving the main beam slightly, 
thereby changing the location of the spurious beam. But, with this one 
possible exception, multiple nulls can be added by successive 
superposition of additional pairs of patterns by using equation (17) where 
the value of k must take into account the pattern already established in 
the creation of the earlier nulls. Unless the nulls are closely spaced, 
the value of k at the location of each additional null will be unaffected 
by the superposition of the prior nulls. 
The formation of the first null by amplitude adjustment according to 
equation (36) causes a spurious zero value to be added on the other side 
of the main beam. Since this does not affect the original pattern, it does 
not cause additional response to an interfering signal. Further, an 
additional null can be developed by superimposing an additional pair of 
patterns, using equation (36) for each null. 
Fourth, the discussion up to the present point has assumed that the desired 
signal and the interfering signal were at the same, fixed, single 
frequency. The analysis, of course, is applicable to any frequency. It 
should be noted that the spacing between antennas in wavelengths, the 
sidelobe to main beam ratio k, and the phase shifts .gamma., .phi. and 
.alpha. are all functions of frequency. Use of normal engineering 
practices will result in the specification of the signal bandwith and/or 
the frequency difference which can be tolerated between the signal and the 
unwanted interfering signal. Of course, if the frequency difference is 
large, the receiver selectivity and other bandwidth limiting components of 
the system will provide some rejection of the signal as the quality of the 
null deteriorates due to the frequency difference. 
In the case of a strong broadband interfering signal which overlaps the 
acceptance bandwidth of the receiver, it is possible to generate a 
wideband null by forming multiple nulls at slightly different positions 
which provides the proper dispersive characteristics. This is done by 
repetitive application of equation (17), calculating a subsequent value of 
k for the composite pattern which would be formed with the first null at 
the desired position of the second null, etc. The incremental angle 
between adjacent nulls would be selected by several engineering 
considerations, but for maximum performance it should be somewhat smaller 
than the angular spacing between adjacent sidelobe minima in the original 
array pattern. 
Finally, although the foregoing discussion was directed to a radio 
receiving system, the same principles apply to a transmitting system, 
particularly when it is desired to transmit in a specific direction or to 
avoid transmitting in certain other directions. The apparatus would be 
similar except that the receiver 65 is replaced by a transmitter, the 
summer is replaced by a power divider, and all components are designed to 
handle the high power involved. The pure phase shift control method is 
especially advantageous relative to current practice since power 
dissipating attenuators, which are conventionally used to control 
amplitude, would not be necessary. Very high power efficiency is thereby 
achieved. 
Thus, an antenna array has been described which creates nulls in a desired 
direction by the use of phase variation, or amplitude variation. No longer 
is it necessary to vary the phase or amplitude of an antenna by a small 
amount and then iteratively continue making small adjustments until the 
correct value is obtained. A method and apparatus has been set forth which 
permits more rapid adjustment and less complex equipment than has 
heretofore been known. The variations and modifications will be apparent 
to those skilled in the art, with the true spirit and scope of the 
invention being limited only by the following claims.