Antenna system

Disclosed herein is an antenna system comprising a plurality of element antennas, a plurality of variable phase shifters and a plurality of variable amplitude type devices connected to the plurality of element antennas respectively, and an arithmetic unit used to perform the arithmetical operation of the excitation amplitude and phase for exciting each of the plurality of element antennas. The arithmetic unit includes the four means and performs the arithmetical operation of the excitation amplitude and phase used to define a desired radiation pattern composed by each of the element antennas with respect to a preset allowable variation width D of the excitation amplitude. Since the arithmetic unit serves to fix the excitation amplitude and perform the arithmetical operation of the excitation phase separately, the antenna system capable of performing the arithmetical operation of the excitation amplitude and phase for obtaining a desired radiation pattern with respect to the preset allowable variation width D of the excitation amplitude, and obtaining a desired radiation pattern even when the allowable variation width D of the excitation amplitude is given, can be realized.

BACKGROUND OF THE INVENTION 
Field of the Invention 
The present invention relates to an antenna system which performs the 
composition of directional properties of each antenna where an allowable 
variation width D of the excitation amplitude is given. 
Discussion of Background 
A method of composing directional properties of each antenna to define a 
desired radiation pattern in accordance with a flowchart shown in FIG. 5 
is disclosed, for example, in the article "Design of Shaped-Beam Antennas 
Through Minimax Gain Optimization" by Charles A. Klein, IEEE Transactions 
on Antennas and Propagation, Vol. AP-32, No. 9, Sep. 1984. 
A description will now be made of the procedure for composing the 
directional properties of the antennas employed in the conventional 
example in accordance with the flowchart shown in FIG. 5. 
The total number J of evaluation points and the total number I of element 
antennas are inputted in Steps S1 and S2, respectively. The desired 
antenna gain G.sub.oj, the patterns of array elements P.sub.ij, a 
weighting factor W.sub.j and the initial amplitude and phase A.sub.i 
(hereinafter called merely "excitation amplitude and phase") of the 
excitation currents or voltages are inputted in Steps S3, S4, S5, S6, 
respectively, with respect to i=l to I and j=l to J. Here, each of both 
the initial excitation amplitude and phase A.sub.i and the patterns of the 
array elements P.sub.ij is the complex number. The antenna gain G.sub.j is 
calculated in Step S7 with respect to all the directions of antennas to be 
observed, i.e., searched (evaluation points) j 32 1 to J. The antenna gain 
G.sub.j is given by the following equation: 
##EQU1## 
where the asterisk * represents the complex conjugate 
The, one antenna searching direction for bringing the difference between 
the antenna gain G.sub.j obtained in Step S7 and the desired antenna gain 
G.sub.oj into the maximum is selected in Step S8. The combination or set 
of values of A.sub.i (i=l to I) which provides a solution for minimizing 
an evaluation function F represented by the following equation is 
determined in Step S9 with respect to the antenna searching direction 
selected in Step S8. Incidentally, the non-linear programming or the like 
is used to minimize the evaluation function F, 
EQU F=W.sub.j .vertline.G.sub.j -G.sub.oj .vertline..sup.2 
The antenna gain G.sub.j (i=l to J) is calculated in Step S10 with respect 
to the set of the values of A.sub.i (i=l to I) which provides the solution 
determined in Step S9 in accordance with the following equation: 
##EQU2## 
where the asterisk * represents the complex conjugate 
After having finished the above procedure, it is determined in step S11 
whether or not all G.sub.j exceeds the desired antenna gain G.sub.oj. If 
it is determined that G.sub.j has exceeded the desired antenna gain 
G.sub.oj, then the excitation amplitude and phase A.sub.i determined in 
Step S9 are regarded as the desired excitation amplitude and phase, 
thereby terminating the arithmetical operation of the excitation amplitude 
and phase. If it is judged to be negative, the routine procedure returns 
to Step S6. Then, the arithmetical operation of the excitation amplitude 
and phase is repeatedly performed using the set of the values of A.sub.i 
(i=l to I) which provides the solution obtained in Step S9, and a judgment 
on the result of its arithmetical operation is made. 
The composition of the directional properties of the conventional antennas 
is carried out provided that the excitation amplitude and phase A.sub.i 
obtained by the arithmetical operation based on such procedure as 
described above are taken as the desired excitation amplitude and phase. 
Therefore, when the allowable variation width D of the excitation 
amplitude is established, there is a problem that the calculated 
excitation amplitude does not fall within the range of its allowable 
variation width D. In some instances, for example, there is a case where 
the allowable variation width D of the excitation amplitude is restricted 
to simplify a feeder circuit for an active phased array antenna. Thus, the 
method of composing the directional properties of the antennas in 
accordance with the arithmetical operation based on the above-described 
procedure cannot determine the excitation amplitude and phase for 
obtaining a desired radiation pattern. 
SUMMARY OF THE INVENTION 
With the foregoing problem in view, it is an object of the present 
invention to provide an antenna system which can obtain a desired 
radiation pattern even when the allowable variation width D of the 
excitation amplitude is given. 
According to one aspect of this invention, there is provided an antenna 
system which comprises: 
a plurality of element antennas; 
a plurality of variable phase shifters and a plurality of variable 
amplitude type devices connected to the plurality of element antennas 
respectively; and 
an arithmetic unit used to perform the arithmetical operation of the 
excitation amplitude and phase for exciting each of the plurality of 
element antennas, said arithmetic unit including respective means for 
determining the excitation amplitude and phase used to obtain a desired 
radiation pattern without limitations on both the excitation amplitude and 
phase; standardizing the excitation amplitude with the maximum value M and 
replacing all the values of the excitation amplitude, which are defined in 
such a manner that the result thus standardized is below the allowable 
variation width D of the excitation amplitude, by M.D; and then fixing all 
the excitation amplitude, thereby performing the arithmetical operation of 
the excitation phase used to define the desired radiation pattern. 
According to the present invention, the arithmetic unit comprises mean for 
representing the evaluation function F in the form of the sum of the 
following two equation: 
##EQU3## 
thereby to determine the set of the values of the excitation amplitude and 
phase A.sub.i (i=l to I) which provides a solution for minimizing the 
evaluation function F; means for standardizing the above excitation 
amplitude a.sub.i with the maximum value M provided that a.sub.i 
=.vertline.A.sub.i .vertline. and M=Max. a.sub.i (i=l to I) in the set of 
the values of A.sub.i obtained from the above and for replacing the values 
of the excitation amplitude a.sub.i, which are defined in such a manner 
that the value thus standardized is below the allowable variation width D 
of the excitation amplitude, by M.D; and means for fixing all of the 
excitation amplitude a.sub.i (i=l to I) obtained in the above so as to 
determine the set of the values of the excitation phase P.sub.i (i=l to I) 
which provides a solution for minimizing the evaluation function F. This 
arithmetic unit serves to fix all the excitation amplitude and perform the 
arithmetical operation of the excitation phase for obtaining a desired 
radiation pattern. Further, the arithmetic unit includes means for 
calculating the antenna gain G.sub.j (j=l to J) with respect to the set of 
the values of A.sub.i (i=l to I) obtained from a.sub.i and P.sub.i 
determined in the above, in accordance with the following equation: 
##EQU4## 
where the asterisk * represents the complex conjugate; means for regarding 
a.sub.i and p.sub.i (i=l to I) thus obtained as being the amplitude and 
phase respectively, if all the antenna gains G.sub.j obtained from the 
above equation exceed a desired antenna gain G.sub.oj (j=l to J), thereby 
terminating the arithmetical operation of the excitation amplitude and 
phase and for making a judgment on an advance to the following step if 
they do no exceed the desired antenna gain G.sub.oj ; and means for making 
a judgment as to the magnitude between G.sub.j and G.sub.oj in response to 
the determination that all the G.sub.j has not exceeded the desired 
antenna gain G.sub.oj, thus setting in such a manner that if G.sub.j 
.gtoreq.G.sub.oj, then W.sub.j is equal to 0 (i.e., W.sub.j =0) and if 
G.sub.j &lt;G.sub.oj, then W.sub.j is equal to 1 (i.e., W.sub.j =1 (j=l to 
J)), and for utilizing A.sub.i (i=l to I) obtained in the above as the 
initial excitation amplitude and phase and then returning again to the 
previous Step so as to execute the arithmetical operation of the 
excitation amplitude and phase. The arithmetic unit also performs the 
arithmetical operation of the excitation amplitude and phase used to 
obtain a desired radiation pattern with respect to the present allowable 
variation width D of the excitation amplitude.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
A preferred embodiment of the present invention will hereinafter be 
described with reference to the accompanying drawings. 
FIG. 1 is a diagram showing the structure of an antenna system according to 
one embodiment of the present invention. In the same drawing, there are 
shown element antennas 1, variable phase shifters 2 connected to the 
element antennas 1 respectively, variable amplitude type devices 3 
connected to the element antennas 1 respectively, an arithmetic unit 4 for 
performing the arithmetical operation of the excitation amplitude and 
phase used for the excitation of each of the element antennas 1. Here, the 
arithmetic unit 4 has means of (a) through (g) to be described below. 
(a) Means for calculating the antenna gain G.sub.j (j=l to J) in accordance 
with the following equation: 
##EQU5## 
where J=total number of inputted evaluation points 
I=total number of elements antennas 
P.sub.ij =patterns of array elements 
A.sub.i =initial excitation amplitude and phase 
i=l to I 
j=l to J 
*=complex conjugate 
(b) Means for determining the combination or set of values of A.sub.i (i=l 
to I) which provides a solution for minimizing an evaluation function F 
represented by the following equation: 
##EQU6## 
where G.sub.j (j=l to J)=antenna gain obtained in accordance with the 
equation in said means (a) 
G.sub.oj =inputted desired antenna gain 
Wj=weighting factor 
j=l to J 
(c) Means for standardizing the excitation amplitude a.sub.i with the 
maximum value M provided that a.sub.i =.vertline.A.sub.i .vertline., 
M=Max. a.sub.i (i=l to I) in the set of the values of A.sub.i obtained in 
the above so as to replace the value of the excitation amplitude a.sub.i, 
which is defined in such a manner that the value thus standardized is 
below the allowable variation width D of the excitation amplitude, by M.D. 
(d) Means for fixing all the excitation amplitude a.sub.i (i=l to I) so as 
to determine the set of the excitation phase P.sub.i (i=l to I), which 
provides a solution for minimizing the evaluation function F represented 
by the following equation: 
##EQU7## 
where p.sub.i =tan.sup.-1 I.sub.A i/R.sub.A i 
R.sub.A i=real part of A.sub.i 
I.sub.A i=imaginary part of A.sub.i 
(e) Means for calculating G.sub.j (j=l to J) with respect to the set of the 
values of A.sub.i (i=l to I) obtained from a.sub.i and p.sub.i determined 
in the above, in accordance with the following equation: 
##EQU8## 
where the asterisk * represents the complex conjugate (f) Means for 
regarding a.sub.i, p.sub.i (l=l to I) thus obtained as being desired 
excitation amplitude and phase, respectively, if all G.sub.j thus obtained 
exceeds a desired antenna gain G.sub.oj (j=l to J), thereby terminating 
the arithmetical operation of the excitation amplitude and phase, and for 
making a judgment on an advance to the following step if it does not 
exceed the antenna gain G.sub.oj. 
(g) Means for making a judgment as to whether or not G.sub.j is greater 
than G.sub.oj in response to the determination that all the G.sub.j has 
not exceeded the desired antenna gain G.sub.oj, thereby setting in such a 
manner that if G.sub.j .gtoreq.G.sub.oj, then W.sub.j =0, and if 
G.sub.j&lt;G.sub.oj, then W.sub.j =1 (j=l to J), and for utilizing A.sub.i 
(i=l to I) obtained by the above means (b) as the initial excitation 
amplitude and phase and then returning again to the above means (a) so as 
to execute the arithmetical operation of the excitation amplitude and 
phase. 
A description will now be made of the operation of the antenna system 
according to the present invention, laying stress on the operation of the 
arithmetic unit 4. 
FIG. 2 is a flowchart for describing the operation of the arithmetic unit 
4. Its description will be made below in accordance with the flowchart. 
The total number J of the evaluation points, the total number I of the 
element antennas, and the allowable variation width D of the excitation 
amplitude are inputted in Steps S1, S2, S21, respectively. The desired 
antenna gain G.sub.oj, the patterns of the array elements P.sub.ij, the 
weighting factor W.sub.j, the initial excitation amplitude and phase 
A.sub.i are inputted in Steps S3, S4, S5, S6, respectively, with respect 
to i=l to I and j=l to J. Here, each of both the initial excitation 
amplitude and phase A.sub.i and the patterns of the array elements 
P.sub.ij is the complex number. The antenna gain G.sub.j is calculated in 
Step S7 with respect to all the directions of the antennas to be observed 
or searched (evaluation points) i=l to J. The antenna gain G.sub.j is 
given by the following equation: 
##EQU9## 
where the asterisk * represents the complex conjugate 
Then, the set of the values of A.sub.i (i=l to I) which provides a solution 
for minimizing the evaluation function F is determined in Step S22 with 
respect to the above antenna gain G.sub.j. The evaluation function F is 
given by the following equation: 
##EQU10## 
In Steps S23 and S24, the routine procedure is executed such that the 
excitation amplitude a.sub.i is equal to .vertline.A.sub.i .vertline. (i=l 
to I) (i.e., a.sub.i =.vertline.A.sub.i .vertline.), and M is equal to 
Max. a.sub.i (i.e., M=Max. a.sub.i) (i=l to I) in the set of the values of 
A.sub.i (i=l to I) obtained in Step S22. It is determined in Step S25 
whether the above a.sub.i corresponds to the maximum value M or it is 
below the allowable variation width D. If it is determined that the result 
of the former is of no, then the above ai is standardized by the maximum 
value M in Step S27. If it is judged that the result of the latter is of 
yes, then all the values of the excitation amplitude a.sub.i, which are 
defined in such a manner that the value thus standardized is below the 
allowable variation width D of the excitation amplitude are replaced by 
the M.D in Step S26. All the values of the excitation amplitude a.sub.i 
are fixed and the set of the values of the excitation phase p.sub.i (i=l 
to I), which provides a solution for minimizing the evaluation function F, 
is determined in Step S28. The evaluation function F is given by the 
following equation: 
##EQU11## 
where p.sub.i =tan.sup.- I.sub.A I/R.sub.A i 
R.sub.A i=real part of A.sub.i 
I.sub.A i=imaginary part of A.sub.i 
The antenna gain G.sub.j (j=l to J) is calculated in Step S29 with respect 
to the set of the values of A.sub.i (i=l to I) obtained from a.sub.i and 
pi determined in the above in accordance with the following equation: 
##EQU12## 
where the asterisk * represents the complex conjugate 
It is determined in Step S11 that if all the antenna gains G.sub.j obtained 
from the above equation exceed a desired antenna gain G.sub.oj (j=l to J), 
then the arithmetical operation of the excitation amplitude and phase is 
terminated with a.sub.i and p.sub.i (i=l to I ) thus obtained being taken 
as the desired excitation amplitude and phase respectively, and if not so, 
the routine procedure advances to the following step. Further, it is 
determined in Step S30 whether or not G.sub.j exceeds the desired antenna 
gain G.sub.oj in response to the determination that all G.sub.j has not 
exceeded the desired antenna gain G.sub.oj. If G.sub.j .gtoreq.G.sub.oj, 
then W.sub.j is set to be equal to 0 in Step S31. If G.sub.j &lt;G.sub.oj, 
then W.sub.j is set to be equal to 1 (j=l to J) in Step S32. In addition, 
A.sub.i (i=l to I ) thus obtained is then used as the initial excitation 
amplitude and phase, and the routine procedure returns again to Step S5 
from which the arithmetical operation of the excitation amplitude and 
phase is repeatedly executed. 
As described above, the arithmetic unit 4 performs the arithmetical 
operation of the excitation amplitude and phase which are used to define a 
desired radiation pattern composed by each of the element antennas with 
respect to the preset allowable variation width D of the excitation 
amplitude. Then, the quantity of a shift in phase of each of the variable 
phase shifters 2 connected to the element antennas 1 respectively, and the 
amplitude of the output from each of the variable amplitude type devices 3 
are set based on the result of arithmetical operation of the excitation 
amplitude and phase in the arithmetic unit 4. As a consequence, each of 
the plural element antennas 1 is excited. 
Then, the above-described embodiment and the conventional example show the 
result obtained by representing, as the amount of attenuation of a desired 
antenna gain, the deterioration in a desired radiation pattern out of 
radiation patterns obtained with respect to the preset allowable variation 
width D of the excitation amplitude and making a comparison between the 
two. The present embodiment shows a desired radiation pattern which 
increases the antenna gain in a direction in which a plurality of antennas 
are to be searched, and a radiation pattern which decreases the antenna 
gain in a direction in which a plurality of other antennas are to be 
searched. This is a result realized by the combination of the 
above-described embodiment and the conventional example. 
FIG. 3 is a characteristic diagram showing the deterioration of a radiation 
pattern with respect to the allowable variation width D of the excitation 
amplitude, which is obtained by the above-described embodiment. In the 
same drawing, the solid line represents the minimum gain at a region in 
which the antenna gain is increased, and the broken line shows the maximum 
gain at a region in which the antenna gain is decreased. It is understood 
from FIG. 3 that the amount of attenuation of the antenna gain is 
approximately 0 dB and a desired radiation pattern can be obtained even 
when the allowable variation width D of the excitation amplitude is in a 
restrained state. 
In addition, FIG. 4 is a characteristic diagram showing the deterioration 
in a radiation pattern with respect to the allowable variation width D of 
the excitation amplitude, which pattern is obtained from the above 
conventional example. Similarly to FIG. 3, the solid line represents the 
minimum gain at a region in which the antenna gain is increased, whereas 
the broken line shows the maximum gain at a region in which the antenna 
gain is decreased. In this case, as for the excitation amplitude, the 
excitation amplitude obtained from the arithmetical operation effected in 
the conventional example is normalized by the maximum value M. As a 
result, the values of the excitation amplitude less than the allowable 
variation width D of the excitation amplitude are all replaced by M.D. As 
for the excitation phase, the excitation phase obtained from the 
arithmetical operation performed in the conventional example is used as 
is. It is understood from FIG. 4 that the amount of attenuation of the 
antenna gain at the region in which it is reduced becomes larger as the 
allowable variation width D of the excitation amplitude decreases, and the 
radiation pattern is deteriorated when the limitations on the excitation 
amplitude is made in the conventional example. Thus, in accordance with 
the present invention, it is feasible to realize the antenna system which 
can perform the arithmetical operation of the excitation amplitude and 
phase for obtaining a desired radiation pattern with respect to the preset 
allowable variation width D of the excitation amplitude, and obtain a 
desired radiation pattern even when the allowable variation width D of the 
excitation amplitude is given. 
Having now fully described the invention, it will be apparent to those 
skilled in the art that many changes and modifications can be made without 
departing from the spirit or scope of the invention as set forth herein.