U.S. patent application number 13/338002 was filed with the patent office on 2012-04-26 for wideband antenna pattern.
This patent application is currently assigned to SAAB AB. Invention is credited to Kent Falk.
Application Number | 20120098702 13/338002 |
Document ID | / |
Family ID | 39563501 |
Filed Date | 2012-04-26 |
United States Patent
Application |
20120098702 |
Kind Code |
A1 |
Falk; Kent |
April 26, 2012 |
WIDEBAND ANTENNA PATTERN
Abstract
Embodiments of the invention include a method to control an
antenna pattern of a wideband array antenna wherein a wideband
array antenna unit comprising the wideband array antenna and
transforming means is accomplished. Embodiments of the invention
further include the corresponding wideband array antenna unit and
transforming means arranged to control an antenna pattern of an
antenna system. The separation between antenna elements in the
wideband array antenna can be increased to above one half
wavelength of a maximum frequency within a system bandwidth when
the array antenna is arranged to operate with an instantaneously
wideband waveform.
Inventors: |
Falk; Kent; (Goteborg,
SE) |
Assignee: |
SAAB AB
Linkoping
SE
|
Family ID: |
39563501 |
Appl. No.: |
13/338002 |
Filed: |
December 27, 2011 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
12366351 |
Feb 5, 2009 |
8111191 |
|
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13338002 |
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Current U.S.
Class: |
342/372 |
Current CPC
Class: |
H01Q 3/2605 20130101;
H01Q 21/00 20130101; H01Q 3/2682 20130101 |
Class at
Publication: |
342/372 |
International
Class: |
H01Q 3/00 20060101
H01Q003/00 |
Foreign Application Data
Date |
Code |
Application Number |
Feb 7, 2008 |
EP |
08446502.0 |
Claims
1. A wideband array antenna arranged to be operational over a
system bandwidth and comprising: at least two antenna elements
(E.sub.1-E.sub.N), arranged to control an antenna pattern of the
wideband array antenna, is connected to an electronic system, the
antenna pattern control being arranged to be achieved by affecting
waveforms between the wideband array antenna and the electronic
system with parameters being individual for each antenna element,
including that the wideband array antenna is arranged to operate
with a waveform having an instantaneous bandwidth B by a separation
between the antenna elements in the wideband array antenna being
increased compared to conventional array antenna designs to above
one half wavelength of a maximum frequency within the system
bandwidth when the wideband array antenna is arranged to operate
with an instantaneously wideband waveform, thus resulting in a
substantially reduced number of antenna elements (E.sub.1-E.sub.N)
without the appearance of grating lobes in the antenna pattern.
2. The wideband array antenna according to claim 1, comprising that
the parameters are non frequency dependent.
3. The wideband array antenna according to claim 1, comprising that
the parameters are frequency dependent.
Description
RELATED
[0001] This application is a continuation application of U.S.
patent application Ser. No. 12/366,351, filed Feb. 5, 2009, which
application claims priority under 35 U.S.C. 119 to European Patent
Application No. EPO 08446502.0, filed 7 Feb. 2008, which
applications are incorporated herein by reference in their
entirety.
TECHNICAL FIELD
[0002] The invention relates to the field of Wideband array
antennas.
BACKGROUND ART
[0003] It is often desired to control the direction and shape of
one or several main lobe/lobes, the side lobe level in different
directions and cancellation directions of an array antenna. This
can be accomplished with phase shifters which allow narrow band
control of the main lobe, side lobe level and also to control the
positions of several narrow band cancellation directions in the
antenna pattern of the array antenna. A cancellation direction is a
direction in the antenna diagram where the radiated or received
power has a minimum. True time delay solutions are also used today.
In these solutions each antenna element has a fixed time delay for
all frequencies. The fixed time delay can be different for
different antenna elements. These solutions make it possible to
control a wideband main lobe but it is only possible to create
narrow band cancellation directions in the antenna pattern. In
order to create a cancellation direction over a wide frequency
range several narrow band cancellation directions have to be
designed around the desired wideband cancellation direction. This
leads to the unwanted side effect that the level of side lobes is
increased. In many applications such as radar antennas it is
desirable to achieve a wideband lobe forming while keeping the side
lobes at a low level.
[0004] In prior art solutions today methods thus exist to control
an antenna pattern of an array antenna connected to an electronic
system and comprising at least two antenna elements. The antenna
pattern control comprises control of the directions of one or
several main lobe/s and/or cancellation directions in the antenna
pattern. The control is achieved by affecting waveforms between the
antenna elements and the electronic system with phase shifts or
time delays being individual for each antenna element. The
electronic system can be a radar or communications system. The
connection between the array antenna and the electronic system can
be made directly or indirectly via e.g. phase shifters. The
drawbacks however being that the antenna pattern control only allow
narrow band control of the main lobe, side lobe level and also only
allow creation of narrow band cancellation directions in the
antenna pattern.
[0005] There is thus a need for an improved solution to control the
antenna pattern of a wideband array antenna or antenna system by
being able to control the antenna pattern over a wide bandwidth by
controlling characteristics such as the shape, direction and width
of one or several main lobe/lobes and the side lobe levels in
different directions as well as being able to create a number of
wideband cancellation directions in the antenna pattern.
SUMMARY OF THE INVENTION
[0006] The object of the invention is to remove the above mentioned
deficiencies with prior art solutions and to provide: [0007] a
method to control an antenna pattern of a wideband array antenna
[0008] a wideband array antenna unit arranged to control an antenna
pattern of a wideband array antenna [0009] a transforming means
arranged to control an antenna pattern of an antenna system [0010]
a wideband array antenna arranged to control an antenna pattern of
the wideband array antenna
[0011] to solve the problem to achieve an improved solution to
control the antenna pattern of a wideband array antenna or antenna
system over a wide bandwidth. The antenna pattern control
comprising controlling characteristics such as the shape, direction
and width of one or several main lobe/lobes and the side lobe
levels in different directions as well as being able to create a
number of wideband cancellation directions in the antenna
pattern.
[0012] This object is achieved by providing a method to control an
antenna pattern of a wideband array antenna connected to an
electronic system and comprising at least two antenna elements. The
antenna pattern control comprises control of the directions of one
or several main lobe/s and/or cancellation directions in the
antenna pattern. The control is achieved by affecting waveforms
between the antenna elements and the electronic system with phase
shifts or time delays being individual for each antenna element
wherein a wideband array antenna unit, comprising the wideband
array antenna and transforming means, the wideband array antenna
being operational over a system bandwidth and operating with an
instantaneous bandwidth B, is accomplished by: [0013] the
transforming means being inserted between each antenna element or
sub array in the wideband array antenna and the electronic system
(303), a sub array comprising at least two antenna elements, or the
transforming means being integrated in the antenna element/sub
array or the electronic system, [0014] a weighting function
W(.omega.) being calculated for Q spectral components q, resulting
from dividing the instantaneous bandwidth B in q components, q
being an integer index ranging from 0 to Q-1, for each antenna
element or sub array using standard methods taking into account
design requests valid for a centre frequency J of each spectral
component and [0015] the transforming means affecting the waveforms
between each antenna element or sub array (E.sub.1-E.sub.N) and the
electronic system (303), the waveforms being continuous or pulsed,
by use of one or several parameters calculated from the weighting
function W(.omega.) at discrete angular frequencies
.omega..sub.q
[0016] thus achieving extended control of the antenna pattern of
the wideband array antenna over the instantaneous bandwidth B.
[0017] The object is further achieved by providing a wideband array
antenna unit arranged to control an antenna pattern of a wideband
array antenna connected to an electronic system and comprising at
least two antenna elements. The antenna pattern control comprises
control of the directions of one or several main lobe/s and/or
cancellation directions in the antenna pattern. The antenna pattern
control being arranged to be achieved by affecting waveforms
between the antenna elements and the electronic system with phase
shifts or time delays being individual for each antenna element
wherein the wideband array antenna unit, comprising the wideband
array antenna and transforming means, the wideband array antenna
being arranged to be operational over a system bandwidth and being
arranged to operate with an instantaneous bandwidth B, is
accomplished by: [0018] the transforming means being arranged to be
inserted between each antenna element or sub array in the wideband
array antenna and the electronic system, a sub array comprising at
least two antenna elements, or the transforming means being
integrated in the antenna element/sub array or the electronic
system, [0019] a weighting function W(.omega.) being arranged to be
calculated for Q spectral components q, resulting from dividing the
instantaneous bandwidth B in Q components numbered q, q being an
integer index ranging from 0 to Q-1, for each antenna element or
sub array using standard methods taking into account design
requests valid for a centre frequency f.sub.q of each spectral
component and [0020] the transforming means being arranged to
affect the waveforms between each antenna element or sub array and
the electronic system (303), the waveforms being continuous or
pulsed, by use of one or several parameters calculated from the
weighting function W(.omega.) at discrete angular frequencies
.omega..sub.q
[0021] thus achieving extended control of the antenna pattern of
the wideband array antenna over the instantaneous bandwidth B.
[0022] The object is further achieved by providing a transforming
means arranged to control an antenna pattern of an antenna system
connected to an electronic system, the antenna system comprising at
least two antenna elements, the antenna pattern control comprising
control of the directions of one or several main lobe/s and/or
cancellation directions in the antenna pattern, the control being
arranged to be achieved by affecting waveforms between the antenna
elements and the electronic system with phase shifts or time delays
being individual for each antenna element wherein an extended
control of the antenna pattern arranged to occupy an instantaneous
bandwidth B is accomplished by: [0023] the transforming means being
arranged to be inserted between at least all but one of the antenna
elements or sub arrays (E.sub.1-E.sub.N) in the antenna system and
the electronic system, a sub array comprising at least two antenna
elements, or the transforming means being integrated in the antenna
element/sub array or the electronic system, [0024] a weighting
function W(.omega.) arranged to be calculated for Q spectral
components q, resulting from dividing the instantaneous bandwidth B
in Q components q, q being an integer index ranging from 0 to Q-1,
for each antenna element or sub array (E.sub.1-E.sub.N) using
standard methods taking into account design requests valid for a
centre frequency f.sub.q of each spectral component and [0025] the
transforming means arranged to affect the waveforms between at
least all but one of the antenna elements or sub arrays
(E.sub.1-E.sub.N) and the electronic system, the waveforms being
continuous or pulsed, by use of one or several parameters
calculated from the weighting function W(.omega.) at discrete
angular frequencies .omega..sub.q
[0026] thus achieving the extended control of the antenna pattern
of the antenna system over the instantaneous bandwidth B.
[0027] The object is further achieved by providing a wideband array
antenna arranged to be operational over a system bandwidth and
comprising at least two antenna elements. The wideband array
antenna is arranged to control an antenna pattern of the wideband
array antenna and is connected to an electronic system. The antenna
pattern control is arranged to be achieved by affecting waveforms
between the wideband array antenna and the electronic system with
parameters being individual for each antenna element wherein the
wideband array antenna is arranged to operate with a waveform
having an instantaneous bandwidth B by a separation between the
antenna elements in the wideband array antenna being increased
compared to conventional array antenna designs to above one half
wavelength of a maximum frequency within the system bandwidth when
the wideband array antenna is arranged to operate with an
instantaneously wideband waveform. This results in a substantially
reduced number of antenna elements without the appearance of
grating lobes in the antenna pattern.
[0028] Further advantages are achieved by implementing one or
several of the features of the dependent claims which will be
explained in the detailed description. Some of these advantages
are: [0029] The invention provides an extended control of the
antenna pattern comprising control of characteristics such as the
shape, direction and width of one or several main lobe/lobes and
the side lobe levels in different directions as well as creation of
a number of wideband cancellation directions in the antenna
pattern. [0030] The invention can be implemented with either an
analogue or a digital realization of the transforming means. [0031]
The invention is applicable to both continuous and pulsed waveforms
which is a further advantage.
[0032] Additional advantages are achieved if features of one or
several of the dependent claims not mentioned above are
implemented.
BRIEF DESCRIPTION OF THE DRAWINGS
[0033] FIG. 1a schematically shows a digital solution of a
realization of the transforming means in the frequency domain.
[0034] FIG. 1b schematically shows an analogue solution of a
realization of the transforming means in the frequency domain.
[0035] FIG. 2a schematically shows a realization of the
transforming means in the time domain.
[0036] FIG. 2b schematically shows a realization in the time domain
for an embodiment of the transforming means including also a
dominating non frequency dependent "true time delay".
[0037] FIG. 2c shows a diagram of attenuation/amplification and
time delays as a function of angular frequency .omega.
(2.pi.f).
[0038] FIG. 3 schematically shows a block diagram of one embodiment
of how the invention can be implemented.
[0039] FIG. 4 shows the definition of angles .phi. and .theta. used
in the definition of the wideband antenna pattern.
[0040] FIG. 5 schematically shows power as a function of antenna
element number and frequency.
[0041] FIG. 6a schematically shows delay as a function of antenna
element number and frequency.
[0042] FIG. 6b schematically shows an incident wave front in a main
lobe direction.
[0043] FIG. 7 schematically shows deviations from frequency
independent true time delay ("delta delays") as a function of
antenna element number and frequency.
[0044] FIG. 8 shows the Array factor with wideband cancellation
directions and main lobe resulting from the invention.
[0045] FIG. 9 shows antenna patterns of a wideband cancellation
direction at 20.degree. for different FFT length.
[0046] FIG. 10 shows antenna patterns of a main lobe at 30.degree.
for different FFT length.
[0047] FIG. 11 shows antenna patterns of a wideband cancellation
direction at 40.degree. for different FFT length.
[0048] FIG. 12 shows antenna patterns of a wideband cancellation
direction at 50.degree. for different FFT length.
[0049] FIG. 13 schematically shows power as a function of element
number and frequency with fixed width of one main lobe.
[0050] FIG. 14 schematically shows time delays as a function of
element number and frequency with fixed width of one main lobe.
[0051] FIG. 15 shows the Array factor with frequency independent
position and fixed width of one main lobe resulting from the
invention.
[0052] FIG. 16 shows antenna patterns of one main lobe at
30.degree. with adjacent wideband cancellation directions for
different FFT length.
[0053] FIG. 17 shows an example of a pulsed waveform.
[0054] FIG. 18 shows a resulting waveform for a pulsed waveform as
a function of time at a number of angles.
[0055] FIG. 19 schematically shows a flow chart for digital
realizations of the inventive method.
[0056] FIG. 20 shows antenna pattern for a linear array.
[0057] FIG. 21 shows antenna pattern for a circular array.
DETAILED DESCRIPTION
[0058] Embodiments of the invention will now be described in detail
with reference to the enclosed drawings. Embodiments of the
invention will be explained by describing a number of examples of
how the antenna pattern can be shaped over a wide bandwidth. This
is accomplished by affecting waveforms to the antenna elements in
the transmit mode or from the antenna elements in the receive mode
with certain parameters as will be explained further.
[0059] A wideband cancellation direction is henceforth in the
description used as a direction in the antenna pattern where the
radiated power/sensitivity has a minimum being substantially below
the radiated power/sensitivity in the direction having the maximum
radiation/sensitivity.
[0060] An antenna pattern is defined as radiated power as a
function of direction when the antenna is operated in transmit mode
and as sensitivity as a function of directions when the antenna is
operated in receive mode.
[0061] FIG. 1a schematically shows an example of a practical
realization of a frequency dependent "true time delay" solution for
a wideband array antenna. A wideband array antenna is defined as an
array antenna having a bandwidth greater than or equal to an
instantaneous operating bandwidth B. The instantaneous bandwidth B
is the instantaneous operating bandwidth which will be described
further in association with FIG. 3. In this example a time delay is
used as a parameter being frequency dependent. The wideband array
antenna comprises at least two antenna elements. The realization
also includes an optional frequency dependent
attenuation/amplification, i.e. the amplitudes of the waveforms are
attenuated or amplified. In this optional embodiment two frequency
dependent parameters are used; time delay and
attenuation/amplification. Due to the reciprocity principle of
antennas the inventive solution is applicable both for transmission
and reception if not otherwise stated. Henceforth in the
description the invention will be described for the receive mode if
not otherwise stated. An input waveform s.sub.in(t), 101, from an
antenna element n in the wideband array antenna is fed to a Fourier
Transformation (FT) unit 102 using for example a Fast Fourier
Transformation (FFT), but other methods for calculation of the
spectrum could be used. The FT unit transforms the instantaneous
bandwidth B of the input waveform s.sub.in(t), 101, into Q spectral
components 0 to Q-1, in this example into 8 spectral components
110-117, each spectral component having a centre frequency f.sub.q.
However the transformation can be made into more or less spectral
components. The time delay .tau..sub.q, (120-127) and the optional
frequency dependent attenuation/amplification a.sub.q (130-137) are
affecting each spectral component q through any suitable time delay
and/or attenuation/amplification means well known to the skilled
person. The spectral component 110 thus has a time delay
.tau..sub.0, 120, and an attenuation/amplification a.sub.0, 130,
the spectral component 111 a time delay .tau..sub.1, 121, and an
attenuation/amplification a.sub.1, 131, and so on until the
spectral component 117 having a time delay .tau..sub.7, 127, and an
attenuation/amplification a.sub.7, 137. All spectral components are
fed to an Inverse Fourier Transformation (IFT) unit, 103, using
Inverse Fast Fourier Transformation (IFFT) or any other method, as
for example IDFT (Inverse Discrete Fourier Transformation),
transforming from the frequency domain to the time domain thus
transforming all the spectral components back into the time domain
and producing an output waveform s.sub.out(t), 104.
[0062] The time delay .tau..sub.q and the attenuation/amplification
a.sub.q are examples of parameters for antenna element n affecting
each spectral component q where the parameters are frequency
dependent. The general designation for these frequency dependent
parameters are .tau..sup.n,q and a.sub.n,q where n ranges from 1 to
N and q from 0 to Q-1.
[0063] The FT unit, the time delay and attenuation/amplification
means and the IFT unit are parts of a first control element
100.
[0064] The invention can be implemented using only the frequency
depending time delay .tau.(.omega.). This solution is simpler to
realize as the frequency depending attenuation/amplification is not
required. However it heavily reduces the control of the main lobe
width.
[0065] The function of the implementation with both the frequency
dependent time delay and the attenuation/amplification according to
FIG. 1a will now be described.
[0066] Parameters calculated from a frequency dependent weighting
function W(.omega.)=A(.omega.)e.sup.-j.omega..tau.(.omega.) is
affecting the waveforms between each antenna element n and the
electronic system where A(.omega.), accounts for the frequency
dependency of the attenuation/amplification and .tau.(.omega.)
account for the frequency dependency of the time delay. As an
alternative the weighting function could be defined as
W(.omega.)=A(.omega.)e.sup.-j.phi.(.omega.) where A(.omega.), still
accounts for the frequency dependency of the
attenuation/amplification and .phi.(.omega.) account for the
frequency dependency of the phase shift. Each antenna element is
connected to one first control element 100. The output waveform
s.sub.out(t) 104 emitted from each first control element 100 as a
function of the input waveform s.sub.in(t) 101 entering the first
control element can be calculated with the aid of equation (1).
s.sub.in(t) is the video-, intermediate frequency-(IF) or radio
frequency (RF)-waveform from each antenna element when the antenna
is working as a receiving antenna, but can also be the waveform on
video, intermediate frequency (IF) or radio frequency (RF) level
from a waveform generator in an electronic system when the wideband
array antenna is working as a transmitting antenna.
s out ( t ) = 1 2 .pi. .intg. - .infin. .infin. W ( .omega. )
.intg. - .infin. .infin. s in ( .tau. ) - j .omega. .tau. .tau.
Fourier transform of s in ( .tau. ) j .omega. t .omega. Invers
Fourier transform back to the time domain = .intg. - .infin.
.infin. s in ( .tau. ) 1 2 .pi. .intg. - .infin. .infin. W (
.omega. ) j .omega. ( t - .tau. ) .omega. Invers Fourier transform
of W ( .omega. ) = w ( t - .tau. ) .tau. = .intg. - .infin. .infin.
s in ( .tau. ) w ( t - .tau. ) .tau. = s in ( t ) w ( t ) ( 1 )
##EQU00001##
[0067] In equation (1) the symbol {circle around (.times.)}
symbolize convolution. The principle of convolution is well known
to the skilled person and can be further studied e.g. in "The
Fourier Transform and its Applications", McGraw-Hill Higher
Education, 1965 written by Ronald N. Bracewell.
[0068] The symbols used above and henceforth in the description
have the following meaning: [0069] .omega.=angular frequency
(2.pi.f) [0070] w(t)=time domain weighting function [0071]
w(t-.tau.)=time delayed time domain weighting function [0072]
W(.omega.)=frequency domain weighting function being the Fourier
Transform of w(t) [0073] A(.omega.)=absolute value of W(.omega.)
[0074] a.sub.q=A(.omega..sub.q) absolute value of W(.omega.) at
.omega.=.omega..sub.q for antenna element n, generally designated
a.sub.n,q [0075] .tau.=time delay and integration variable [0076]
.tau..sub.q=time delay of .tau.(.omega.) at .omega.=.omega..sub.q
for antenna element n, generally designated .tau..sub.n,q=time
delay for spectral component q in antenna element n [0077]
.tau.(.omega.)=time delay as a function of .omega. [0078]
.phi.(.omega.)=phase shift as a function of .omega. [0079]
.phi..sub.q=phase shift of .phi.(.omega.) at .omega.=.omega..sub.q
for antenna element n, generally designated .phi..sub.n,q=phase
shift for spectral component q in antenna element n
[0080] As mentioned above .tau..sub.n,q and a.sub.n,q are examples
of frequency dependent parameters for antenna element n affecting
each spectral component q. The phase shift .phi..sub.n,q is another
example of a frequency dependent parameter for antenna element n
affecting each spectral component.
[0081] FIG. 1a describes a digital realization of the first control
element. FIG. 1b shows a corresponding analogue realization with
the input waveform s.sub.in(t) 101 entering a third control element
150. The input waveform 101 coming from each antenna element n is
fed to Q band pass filters F.sub.q having a centre frequency
f.sub.q where q assumes integer values from 0 to Q-1. The input
waveform 101 is thus split in Q spectral components and a time
delay .tau..sub.q or alternatively a phase shift .phi..sub.q and
the optional frequency dependent attenuation/amplification a.sub.q
are affecting each spectral component through any suitable time
delay or phase shift and attenuation/amplification means well known
to the skilled person. All spectral components are connected to a
summation network 151 producing the output waveform s.sub.out(t),
104. The centre frequency f.sub.q of each spectral component can be
calculated according to:
f q = f c - B 2 + ( q + 1 2 ) B Q ##EQU00002##
[0082] for a case with equividistant spectral component division,
where f.sub.c is the centre frequency in the frequency band with an
instantaneous bandwidth B. The instantaneous bandwidth B is the
instantaneous operating bandwidth. The third control element 150
comprises Q band pass filters F.sub.q, means for time delay and
amplification/attenuation as well as the summation network 151.
[0083] A further digital realization will now be described with
reference to FIGS. 2a and 2b. In many situations a time discrete
realization, with discrete steps T in time, might be preferable. An
output waveform s.sub.out(mT) emitted from a second control element
(200) can then be calculated with the aid of equation (2) as a
function of an input waveform s.sub.in(mT) entering the second
control element. The index is an integer value increasing linearly
as a function of time. W(.omega..sub.q) represents the time delay
and attenuation/amplification at the centre frequency of spectral
component q, see FIG. 1. The FFT and the IFFT described in
association with FIG. 1a, both requiring Qlog.sub.2(Q) operations,
are computational efficient methods for calculation of DFT
(Discrete Fourier Transform) and IDFT (Inverse Discrete Fourier
Transform), both requiring Q.sup.2 operations. Q is as mentioned
above the total number of spectral components. The output waveform
is calculated as:
s out ( m T ) = 1 Q q = 0 Q - 1 W ( .omega. q ) k = 0 Q - 1 s in (
k T ) - j 2 .pi. k q Q DFT of the input signal s in ( m T ) j 2
.pi. q m Q IDFT back to the time domain = k = 0 Q - 1 s in ( k T )
1 Q q = 0 Q - 1 W ( .omega. q ) j 2 .pi. q m - k Q IDFT { W (
.omega. q ) } = w mod [ ( m - k ) ( Q - 1 ) ] = k = 0 Q - 1 s in (
k T ) w mod [ ( m - k ) ( Q - 1 ) ] = s in ( m T ) w mod [ m ( Q -
1 ) ] ( 2 ) ##EQU00003## [0084] mod[x,y]=remainder after division
of x by y [0085] .omega..sub.q=2.pi.f.sub.q=discrete angular
frequency [0086] Q=Number of spectral components [0087] k=integer
raising variable used in the DFT and the IDFT [0088] m=integer
raising variable for discrete time steps [0089] q=integer raising
variable for spectral components and integer raising variable used
in the DFT.
[0090] As can be seen in equation (2) the desired functionality in
a time discrete realization can be achieved with Q operations.
[0091] FFT and DFT are different methods for Fourier Transformation
(FT). IFFT and IDFT are corresponding methods for Inverse Fourier
Transformation (IFT). As described above these methods have
different advantages and the method most suitable for the
application is selected. However any of the methods can be used
when FT and/or IFT are/is required in the different embodiments of
the invention.
[0092] FIG. 2a shows the input waveform s.sub.in(mT) 201, coming
from an antenna element in the wideband array antenna. The input
waveform 201 is successively time delayed in Q-1 time steps T, 203,
numbered from 1 to Q-1 and being time delayed copies of the input
waveform s.sub.in(mT). The input waveform is thus successively time
delayed with time steps T as illustrated in the upper part, 204, of
FIG. 2a. Q parameters comprising weighting coefficients w.sub.n,0
to w.sub.n,Q-1, for antenna element n is identified with two
indexes, the first representing antenna element number and the
second a consecutive number q representing a spectral component and
ranging from 0 to Q-1. The weighting coefficients are calculated as
the IDFT of W(w.sub.q) or alternatively as the IFFT of
W(.omega..sub.q) for the Q spectral components q, resulting from
dividing the instantaneous bandwidth B in q components, the
calculation being performed for each antenna element or sub array
(E.sub.1-E.sub.N) using standard methods and taking into account
design requests valid for a centre frequency f.sub.q of each
spectral component. The weighting coefficients w.sub.n,0 to
w.sub.n,Q-1 thus is the weighting coefficient for antenna element
n. The arrows 211 illustrate that the input waveform s.sub.in(mT)
is multiplied with the first weighting coefficient w.sub.n,0 and
each time delayed copy of the input waveform is successively
multiplied with the weighting coefficient having the same second
index as the number of time step delays T included in the in the
time delayed copy of the input waveform as illustrated in the
middle part, 205, of FIG. 2a. The result of each multiplication is
schematically illustrated to be moved, indicated with arrows 212,
to the bottom part, 206, of FIG. 2a, where each multiplication
result is summarized to the output waveform 207, s.sub.out(mT).
[0093] As will be described in association with FIGS. 6 and 7 the
dominating part of the time delay is not frequency dependent,
resulting in many very small consecutive weighting coefficients,
approximately equal to zero, at the beginning and end of the series
of weighting coefficient w.sub.n,0 to w.sub.n,Q-1 for each antenna
element. Assume that the first x weighting coefficients and the
last y weighting coefficients in the series of weighting
coefficients w.sub.n,0 to w.sub.n,Q-1 are approximately equal to
zero. It could then be suitable in a hardware realization, to set
the first x weighting coefficients and the last y weighting
coefficients to zero and to integrate the first x time delays T
into a time delay D, 202, equal to xT as illustrated in FIG. 2b,
and to exclude the last y multiplications to reduce the number of
required operations to less than Q operations. FIG. 2b otherwise
corresponds to FIG. 2a. The time delay D, 202, corresponds to the
non frequency dependent time delay, for each antenna element, which
is illustrated in FIG. 6a. The remaining frequency dependent time
delay will onwards be called "delta time delay" as illustrated in
FIG. 7. FIG. 2b is an example of a computational efficient
convolution, for calculation of the "delta time delay", preceded of
the frequency independent time delay D, 202, used mainly for
control of the main lobe direction.
[0094] The means for realizing the frequency independent time delay
D and the means for frequency dependent time delays and
attenuations/amplifications for each time delay T, are parts of the
second control element 200.
[0095] FIG. 2c shows the frequency dependency of the time delay
.tau. and attenuation A(.omega.) on the vertical axis 215 as a
function of .omega. (i.e. 2.pi.f) on the horizontal axis 216. The
weighting function is calculated for each antenna element n and for
a number of .omega.-values, .omega..sub.0, .omega..sub.1,
.omega..sub.2 . . . .omega..sub.Q-1 through classical realization
at each frequency using well known method as e.g the Schelkunoff's
method. This results in a number of values W.sub.n,Q, W.sub.n,1,
W.sub.n,2 . . . for each antenna element n. The time delay as a
function of .omega. then forms a curve 217 and the
attenuation/amplification a curve 218. The weighting coefficients
w.sub.n,0, w.sub.n,1, w.sub.n,2 . . . are calculated as the IDFT or
IFFT of W.sub.n,0, W.sub.n,1, W.sub.n,2 . . . for each antenna
element n.
[0096] FIGS. 2a and 2b thus shows a realization of a frequency
dependent time delay and attenuation/amplification in the time
domain and FIGS. 1a and 1b shows a corresponding realization in the
frequency domain. An advantage with the realization in the time
domain is that only Q operations are required while the realization
in the frequency domain requires Qlog.sub.2(Q) operations as
described above.
[0097] A fourth control element applicable in the transmit mode can
be realized by calculating the waveform in advance for each antenna
element/sub array and for each spectral component q, q ranging from
0 to Q-1 using the intended waveform and the weighting function
W(.omega.) for affecting the waveforms between each antenna element
or sub array (E.sub.1-E.sub.N) and the electronic system 303. The
result is converted in a DDS (Direct Digital Synthesis) unit to an
analogue waveform which is fed to each antenna element/sub array.
The means for calculating the waveform and the DDS unit are parts
of the fourth control element.
[0098] All four control elements could as mentioned earlier be
inserted either at video, intermediate frequency (IF) or directly
on radio frequency (RF) level. It is easier to realize the control
element at lower frequency but all hardware needed between the
control element and the antenna element/sub array need to be
multiplied with the number of antenna elements/sub arrays. In the
description the invention is henceforth described as being realized
at the RF level.
[0099] The four control elements are examples of transforming
means, transforming an input waveform to an output waveform. The
transforming means all have two ends, an input end receiving the
input waveform and an output end producing the output waveform.
[0100] FIG. 3 schematically shows a block diagram of one embodiment
of how the invention can be implemented. FIG. 3a shows the
situation when the wideband array antenna 301 is working in receive
mode. A wideband array antenna is defined as an array antenna
having a bandwidth greater than or equal to the instantaneous
operating bandwidth B. This bandwidth of the wideband array antenna
is called the system bandwidth of an electronic system ES, 303
using the wideband array antenna. The instantaneous bandwidth B is
the instantaneous operating bandwidth of the electronic system. The
wideband array antenna can optionally comprise of one or several
sub-arrays, each sub-array comprising two or more antenna elements.
There are a total of N antenna elements or combinations of antenna
elements and sub arrays, E.sub.1 to E.sub.N, and a corresponding
number of transforming means Tr.sub.1 to Tr.sub.N. One transforming
means is inserted between each antenna element or sub arrays and
the electronic system ES, 303, which e.g. can be a radar system or
a communication system. Tr.sub.1 is inserted between E.sub.1 and
the electronic system, Tr.sub.2 between E.sub.2 and the electronic
system and so on until Tr.sub.N being inserted between E.sub.N and
the electronic system ES, i.e. Tr.sub.n is inserted between
corresponding antenna element or sub array E.sub.n and the
electronic system ES. A wideband array antenna unit is defined as
the wideband array antenna and the transforming means. In FIGS. 3a
and 3b E.sub.2 is a sub array comprising three antenna elements e.
The input waveform in FIG. 3a s.sub.in(t) or s.sub.in(mT), 306, is
emitted from each antenna element or sub array and fed to the
corresponding transforming means. The output waveform s.sub.out(t)
or s.sub.out(mT), 307, is fed to the electronic system 303. The
waveforms 306 and 307 are individual for each antenna element or
sub array.
[0101] FIG. 3b shows a corresponding block diagram when the
wideband array antenna 301 is working in the transmit mode. The
difference from FIG. 3a being that the input waveform s.sub.in(t)
or s.sub.in(mT), 306, now is emitted from a waveform generator in
the electronic system and fed to the transforming means, Tr.sub.1
to Tr.sub.N, and the output waveform s.sub.out(t) or s.sub.out(mT),
307, is fed to the antenna elements or sub arrays E.sub.1 to
E.sub.N.
[0102] As mentioned above the transforming means are inserted
between each antenna element or sub array and an electronic system
ES. The transforming means are connected either directly or
indirectly to an antenna element or sub array at one end and either
directly or indirectly to the electronic system at the other end.
In one embodiment when the transforming means are inserted at video
level, one end of the transforming means can be directly connected
to the electronic system and the other end indirectly connected to
an antenna element or sub array via electronic hardware such as
mixers. In another embodiment when the transforming means are
inserted at RF-level one end of the transforming means can be
directly connected to an antenna element or sub array and the other
end directly to the electronic system. The required mixer hardware
in this embodiment is included in the electronic system. In yet
another embodiment when the transforming means are inserted at
IF-level one end of the transforming means can be indirectly
connected to an antenna element or sub array via electronic
hardware such as mixers and the other end indirectly connected via
electronic hardware such as mixers to the electronic system.
[0103] The transforming means can be separate units or integrated
in the antenna elements or sub arrays or in the electronic
system.
[0104] The transforming means can be arranged to achieve an
extended control of an antenna pattern of the wideband array
antenna or also of an antenna system. The antenna system is
connected to the electronic system 303 and comprises at least two
antenna elements. The extended antenna pattern control achieved
comprises controlling characteristics such as the shape, direction
and width of one or several main lobe/lobes and the side lobe
levels in different directions as well as being able to create a
number of wideband cancellation directions in the antenna pattern.
The antenna system can comprise an array antenna with at least two
antenna elements or a main antenna and an auxiliary antenna, each
comprising of at least one antenna element. The main antenna of the
antenna system can be any type of antenna comprising one or several
antenna elements, e.g. a radar antenna. The auxiliary antenna of
the antenna system can be a single antenna element or an array of
antenna elements. Each antenna element can also be a sub array
comprising at least two antenna elements. An extended wideband
control of the antenna pattern occupying the instantaneous
bandwidth B is accomplished by the transforming means 100, 200,
150, Tr.sub.1-Tr.sub.N being arranged to be inserted between at
least all but one of the antenna elements or sub arrays
(E.sub.1-E.sub.N) in the antenna system and the electronic system
(303), or the transforming means being integrated in the antenna
element/sub array or the electronic system. This means that all
waveforms, or all waveforms but one, from antenna elements or sub
arrays have to pass through the transforming means when the
transforming means are implemented in the antenna system. The
weighting function
W(.omega.)=A(.omega.)e.sup.-j.omega..tau.(.omega.) or
W(.omega.)=A(.omega.)e.sup.-j.phi.(.omega.) is arranged to be
calculated for Q spectral components q, resulting from dividing the
instantaneous bandwidth B in q components, q being an integer index
ranging from 0 to Q-1, for each antenna element or sub array
(E.sub.1-E.sub.N) using standard methods taking into account design
requests valid for a centre frequency f.sub.q of each spectral
component. The transforming means 100, 200, 150, Tr.sub.1-Tr.sub.N
are arranged to affect the waveforms between at least all but one
of the antenna elements or sub arrays (E.sub.1-E.sub.N) and the
electronic system 303, by use of one or several parameters
calculated from the weighting function W(.omega.) at discrete
angular frequencies .omega..sub.g thus achieving control of the
antenna pattern of the antenna system over the instantaneous
bandwidth B. The waveforms can be continuous or pulsed.
[0105] In the situation where the antenna system comprises a main
antenna with one antenna element, or sub array, and an auxiliary
antenna with at least one antenna element it is sufficient that a
transforming means is connected only to the antenna elements of the
auxiliary antenna and that the output waveforms from the
transforming means is added to the waveform of the main antenna,
having no transforming means connected. The important aspect is
that at least two waveforms are interacting, where all waveforms,
or all waveforms but one, have been transmitted through a
transforming means. In the case where one waveform is not affected
by a transforming means this waveform serves as a reference and the
parameters for the transforming means affecting the other waveforms
are adapted to this reference.
[0106] Henceforth in the description the invention will be
described as realized in the frequency domain as described in
association with FIGS. 1a and 1b. The invention can however, as
described in association with FIGS. 2a and 2b, also be realized in
the time domain.
[0107] Henceforth in the description a wideband antenna pattern
G(.theta.,.phi.) will be defined as the expected value of the
waveform power E[|A.sub..SIGMA.(.theta.,.phi.,t)|.sup.2] as a
function of the normal antenna pattern angle coordinates
(.theta.,.phi.). The antenna element/sub array pattern
g.sub.n(.theta.,.phi.), for antenna element/sub array n, is defined
in a corresponding manner. In equation (3) the normalization of the
antenna pattern is chosen to give max
{G(.theta.,.phi.)}.ident.1.
G ( .theta. , .PHI. | .A-inverted. s ) = E [ A .SIGMA. ( .theta. ,
.PHI. , t ) 2 ] max { E [ A .SIGMA. ( .theta. , .PHI. , t ) 2 ] } (
3 ) ##EQU00004##
[0108] The angles .theta. and .phi. are defined as illustrated in
FIG. 4. In a Cartesian coordinate system with X-axis 401, Y-axis
402 and Z-axis 403 the direction to a point 404 in space is defined
by an angle .theta., 405, and an angle .phi., 406. The angle .phi.
is the angle between a line 407 from the origin 408 to the point
404 and the Z-axis. The angle .theta. is the angle between the
vertical projection, 409, of the line 407 on the X-Y plane and the
X-axis.
[0109] A.sub..SIGMA.(.theta.,.phi.,t) is the sum of the waveform
amplitudes from all elements/sub arrays forming the antenna in the
direction (.theta.,.phi.), see equation (4).
A .SIGMA. ( .theta. , .PHI. , t ) = n = 1 N g n ( .theta. , .PHI. |
s n ) s n [ t - R c 0 + .tau. n ( .theta. , .PHI. ) - .tau. n (
.theta. s , .PHI. s ) ] ( 4 ) ##EQU00005##
[0110] Following symbols are used: [0111] g.sub.n(.theta.,.phi.|s)
Element pattern for antenna elements/sub array n in the direction
(.theta.,.phi.) given the waveform s being a function of t. [0112]
g.sub.m(.theta.,.phi.|s) Element pattern for antenna elements/sub
array m in the direction (.theta.,.phi.) given the waveform s being
a function of t. [0113] s.sub.n(t) Waveform from antenna
element/sub array n or from the electronic system as a function of
time. This corresponds to s.sub.in(t) for antenna element or sub
array [0114] s.sub.m(t) Waveform from antenna element/sub array m
or from the electronic system as a function of time. This
corresponds to s.sub.in(t) for antenna element or sub array m.
[0115] R Distance to the probing point. [0116] c.sub.0 Speed of
light. [0117] .tau..sub.n Waveform time delay from/to antenna
element/sub array [0118] .tau..sub.m Waveform time delay from/to
antenna element/sub array m. [0119] .theta..sub.s Antenna scan
angle in the .theta.-dimension. [0120] .phi..sub.s Antenna scan
angle in the .phi.-dimension. [0121] r.sub.n,m Cross correlation
function between the waveform from/to antenna element/sub array n
and the waveform from/to antenna element/sub array m. [0122] m
Antenna element/sub array index ranging from 1 to N. [0123] n
Antenna element/sub array index ranging from 1 to N. [0124]
g.sub.m* Complex conjugate of g.sub.m [0125] s.sub.m* Complex
conjugate of s.sub.m
[0126] Note that max {E[|A.sub..SIGMA.(.theta.,.phi.,t)|.sup.2]} is
a constant and introduce the constant K.sub.D=max
{E[|A.sub..SIGMA.(.theta.,.phi.,t)|.sup.2]} normalizing the antenna
pattern peak to unity. Equation (3) and equation (4) then gives
equation (5).
G ( .theta. , .PHI. | .A-inverted. s ) = 1 K D E [ n = 1 N g n (
.theta. , .PHI. | s n ) s n ( t - R c 0 + .tau. n ( .theta. , .PHI.
) - .tau. n ( .theta. s , .PHI. s ) ) 2 ] ( 5 ) ##EQU00006##
[0127] Expansion of the squared absolute value in equation (5)
gives equation (6).
G ( .theta. , .PHI. | .A-inverted. s ) = 1 K D E [ n = 1 N g n (
.theta. , .PHI. | s n ) s n ( t - R c 0 + .tau. n ( .theta. , .PHI.
) - .tau. n ( .theta. s , .PHI. s ) ) m = 1 N g m * ( .theta. ,
.PHI. | s m ) s m * ( t - R c 0 + .tau. m ( .theta. , .PHI. ) -
.tau. m ( .theta. s , .PHI. s ) ) ] ( 6 ) ##EQU00007##
[0128] Basic knowledge, regarding stationary stochastic processes,
gives:
E[cY]=cE[Y]
E[X+Y]=E[X]+E[Y]
[0129] c is a constant and X and Y are two stationary stochastic
processes. With the aid of these two basic roles equation (6) can
be transformed into equation (7):
G ( .theta. , .PHI. | .A-inverted. s ) = 1 K D n = 1 N m = 1 N g n
( .theta. , .PHI. | s n ) g m * ( .theta. , .PHI. | s m ) E [ s n (
t - R c 0 + .tau. n ( .theta. , .PHI. ) - .tau. n ( .theta. s ,
.PHI. s ) ) s m * ( t - R c 0 + .tau. m ( .theta. , .PHI. ) - .tau.
m ( .theta. s , .PHI. s ) ) ] ( 7 ) ##EQU00008##
[0130] Introduce the substitutions:
T n = t - R c 0 + .tau. n ( .theta. , .PHI. ) - .tau. n ( .theta. s
, .PHI. s ) and ##EQU00009## T m = t - R c 0 + .tau. m ( .theta. ,
.PHI. ) - .tau. m ( .theta. s , .PHI. s ) . ##EQU00009.2##
[0131] Note that
T.sub.m-T.sub.n=.tau..sub.m(.theta.,.phi.)-.tau..sub.m(.theta..sub.s,.phi-
..sub.s)-.tau..sub.n(.theta.,.phi.)+.tau..sub.n(.theta..sub.s,.phi..sub.s)-
. The expected value in equation (7) is recognized as the cross
correlation function r.sub.n,m between the waveform s.sub.n and
waveform s.sub.m. Equation (7) can consequently be reformulated as
equation (8).
G ( .theta. , .PHI. | .A-inverted. s ) = 1 K D n = 1 N m = 1 N g n
( .theta. , .PHI. | s n ) g m * ( .theta. , .PHI. | s m ) r n , m (
.tau. m ( .theta. , .PHI. ) - .tau. m ( .theta. s , .PHI. s ) -
.tau. n ( .theta. , .PHI. ) + .tau. n ( .theta. s , .PHI. s ) |
.A-inverted. s ) ( 8 ) ##EQU00010##
[0132] Equation (8) can be used to describe a wideband antenna
pattern.
[0133] This definition of the wideband antenna pattern is a
function of the cross correlation functions r.sub.n,m between the
waveform s.sub.n and waveform s.sub.m and their auto correlation
functions for the case with n=m. Grating lobes occur when identical
waveforms with a repetitive auto correlation function is used.
Sinus shaped waveform is an example of a waveform with repetitive
auto correlation function, that consequently should be avoided.
[0134] An instantaneous wideband waveform has at every moment a
wide bandwidth. This is in contrast to e.g. a stepped frequency
waveform that can be made to cover a wide bandwidth by switching to
different narrow frequency bands. An instantaneous narrow band
waveform having a narrow band instantaneous bandwidth B is defined
as BL.quadrature. c.sub.0, where L is the longest dimension of the
antenna, in this case the wideband array antenna and c.sub.0 is the
speed of light. Waveforms and bandwidths not being instantaneous
narrow band according to this definition are considered to be
instantaneous wideband waveforms or instantaneous wideband
bandwidths. This definition of an instantaneous wideband waveform
or an instantaneous wideband bandwidth is used in this description.
An advantage of the invention thus being the possibility to operate
with an instantaneously wideband waveform. An instantaneously
wideband waveform is a waveform occupying a wide bandwidth.
[0135] The wideband array antenna and the antenna system being
parts of the invention can be operated with any type of waveforms
being an instantaneous wideband or narrow band waveform within an
instantaneous narrowband or wideband bandwidth except for the
embodiment including the "array thin out" feature which has to be
operated with an instantaneously wideband waveform. This "array
thin out" embodiment will be described further in detail below. The
waveforms can be continuous or pulsed as will be explained under a
separate heading below.
[0136] When dividing an antenna aperture in sub arrays each sub
array must be small enough to fulfil the inequality BL.sub.sub
.quadrature. c.sub.0, where the longest dimension of the sub array
is L.sub.sub.
[0137] As mentioned earlier embodiments of the invention provide a
wideband array antenna unit and corresponding method by being able
to an extended control of the antenna pattern over the
instantaneous bandwidth B by controlling characteristics such as
the shape, width and direction of one or several main lobe/s and
the side lobe level in different directions as well as being able
to create a number of wideband cancellation directions in the
antenna pattern. The invention will now be described with two
examples showing how wideband cancellation directions and frequency
independent position and width of a main lobe in the antenna
pattern can be achieved. The means for providing the extended
control of the antenna pattern comprises the transforming means
using one or several parameters calculated from the weighting
function W(.omega.) at discrete angular frequencies .omega..sub.q.
The wideband antenna pattern can be defined according to equation
(8) above, but other definitions are possible within the scope of
the invention.
[0138] Wideband Cancellation Directions.
[0139] The method for creating the extended control of the antenna
pattern of the antenna system or the wideband array antenna
included in the wideband array antenna unit comprising wideband
cancellation directions shall now be described with an example.
[0140] The method will be explained with a wideband array antenna
comprising a 2.0 m long linear array antenna consisting of 64
antenna elements fed with white bandwidth limited noise in the
frequency range from 6.0 GHz to 18.0 GHz. The intension is to scan
one main lobe to 30.degree. and create three wideband cancellation
directions, at 20.degree., 40.degree. and 50.degree.. Following
designations are used:
TABLE-US-00001 Assumed values L (L = 2.0 m) Antenna length N (N =
64) Number of antenna elements f.sub.c (f.sub.c = 12 GHz) Centre
frequency in Hz f.sub.min (f.sub.min = 6.0 GHz) Minimum frequency
f.sub.max (f.sub.max = 18.0 GHz) Maximum frequency .theta..sub.max
(.theta..sub.max = 30.0.degree.) Main lobe direction
.theta..sub.min (.theta..sub.min = [20.0.degree., 40.0.degree.,
50.0.degree.]) Cancellation directions B (B = 12 GHz) Bandwidth in
Hz .tau..sub.p (.tau..sub.p = 1 ns) Pulse length in s Variabels f
Frequency in Hz n Antenna element number Physical constant c.sub.0
speed of light .apprxeq. 2.997925 10.sup.8 m/s
[0141] Commence by placing (N-1) evenly distributed zero points (z)
on the unit circle according to below references and according to
equation (9). The reason for this simple choice of tapering, i.e.
an even distribution of zero points, is to simplify the
calculations. The choice of tapering does not affect the
conclusions as tapering mainly affects the side lobe level and not
the positioning of the wideband cancellation directions.
z n = j ( n + 1 ) 2 .pi. N n .di-elect cons. 0 ( N - 2 ) ( 9 )
##EQU00011##
[0142] Schelkunoff's unit circle is well known to the skilled
person and can be further studied in following books:
[0143] S. A. Schelkunoff, "A Mathematical Theory of Linear Arrays",
Bell System Tech. J., 22 (1943), 80 107.
[0144] W. L. Weeks, "Antenna Engineering", McGraw-Hill Electronic
Science Series, 1968.
[0145] Robert S. Elliott, "Antenna Theory and design",
Prentice-Hall Inc., 1981
[0146] Samuel Silver, "Microwave Antenna Theory and Design"
McGraw-Hill Book Company Inc., 1949.
[0147] Calculate "the angles" (.PSI..sub.max, .PSI..sub.min)
corresponding to the main lobe and the zero points, on the unit
circle according to equation (10) and equation (11). The zero
points are positioned at each side of the main lobe.
.psi. max ( f ) = 2 .pi. f c 0 L N - 1 sin ( .theta. max ) ( 10 )
.psi. min ( f ) = 2 .pi. f c 0 L N - 1 sin ( .theta. min ) ( 11 )
##EQU00012##
[0148] Note that "the angles" (.PSI..sub.max, .PSI..sub.min) are
frequency dependent. Rotate all zero points (z) to new positions
(z.sub.rot(f)) according to equation (12) to steer the main lobe to
the correct direction.
z.sub.rot n(f)=z.sub.ne.sup.j.PSI..sup.max.sup.(f) (12)
[0149] The distance (d.sub.n(f)) between these new zero points and
the ones required to create desired cancellation directions in the
antenna pattern can be calculated with equation (13).
d.sub.n(f)=|z.sub.rot n(f)-e.sup.j.PSI..sup.max.sup.(f)| (13)
[0150] Observe that the distances (d.sub.n(f)) are frequency
dependent. Move the zero points in the set [z.sub.rot n] minimizing
the distance (d.sub.n(f)) to a position corresponding to
e.sup.j.PSI..sup.min.sup.(f) for each frequency and each
cancellation direction required in the antenna pattern. The
resulting set of zeros, which all are frequency dependent, is
represented by the set [z.sub.final n (f)] where n assumes values
from 0 to N-2 thus making a total of N-1 zero points. Now the array
factor (AF(.theta.,f)) can be formulated on it's product form
according to equation (14).
AF ( .theta. , f ) = n = 0 N - 2 ( j ( 2 .pi. f c 0 L N - 1 sin (
.theta. ) ) - z finaln ( f ) ) n = 0 N - 2 ( j ( 2 .pi. f c 0 L N -
1 sin ( .theta. max ) ) - z finaln ( f ) ) ( 14 ) ##EQU00013##
[0151] By formulating and solving a system of equations with the
excitation of each antenna element (E.sub.n(f)) as the unknown, the
array excitation will be calculated. Now the array factor
(AF(.theta.,f)) can be formulated on it's summa form according to
equation (15).
AF ( .theta. , f ) = n = 1 N E n ( f ) j ( n - 1 ) ( 2 .pi. f c 0 L
N - 1 sin ( .theta. ) ) ( 15 ) ##EQU00014##
[0152] The array factor describes the gain of the antenna array
structure assuming that each antenna element is an isotropic
radiator. The element excitations (E.sub.n(f)) describes both the
amplitude and phase dependency on frequency in each antenna element
n. The phases could thereafter be transformed to frequency
dependent time delays .tau..sub.n,q=.phi..sub.n,q/2.pi.f.sub.q.
Ambiguities arising in the transformation are resolved by selecting
the time delay closest to the time delay corresponding to the time
delay giving the main lobe direction in each element for each
frequency. FIG. 5 (power) and FIG. 6 (time delay) illustrates the
result.
[0153] FIG. 5 is a three dimensional representation of the power
|A.sub.n(.omega..sub.q|.sup.2 as a function of spectral component q
and antenna element n for the array antenna in transmit mode. Power
is shown on a vertical axis 501 in dB, 0 dB corresponding to no
attenuation. Axis 502 shows frequency between 6-18 GHz and axis 503
represents the antenna element number. In this example 64 antenna
elements are used. Area 504 represents high power, area 505
medium-high, area 506 medium-low, and area 507 low power. The power
variations in this example are relatively small, within about 2
dB.
[0154] FIG. 6a is a three dimensional representation of the
frequency dependent time delays as a function of frequency and
antenna element in the array antenna. The time delays are shown on
a vertical axis 601 in seconds. Axis 602 shows frequency between
6-18 GHz and axis 603 represents the antenna element number. In
this example the main lobe direction is designed to be 30.degree..
This is illustrated in FIG. 6b showing the array antenna 604 with
the end antenna elements 605 and 606. An incident plane wave front
609 then must have a time delay at antenna element 606
corresponding to the time it takes for the wave to travel the
distance 608 to reach antenna element 605. With a length of the
antenna array of 2 m and the main lobe direction 607 being
30.degree. the distance 608 becomes 1 m and the time for light to
travel this distance is about 3.3 ns. Thus the time delay at
element 606 should be 3.3 ns and the time delay at antenna element
605 shall be zero for the waveforms at each element to be in phase.
The time delay then varies linearly between 0 to 3.3 ns along the
array antenna as is shown in FIG. 6a. The time delay seems to be
constant with frequency, however as will be shown in FIG. 7 there
are some small time delay variations as a function of
frequency.
[0155] As can be seen in FIG. 5 and FIG. 6 the deviation in both
power and time delays relative to the time delays corresponding to
the time delays giving the main lobe direction are small. In FIGS.
6a and 6b a maximum time delay of approximately 3.3 ns gives the
direction 30.degree. of the main lobe. From FIG. 6a it seems as if
the time delay as a function of antenna element number and
frequency describes a flat plane. There is however small deviations
in the time delay from the flat plane which is illustrated in FIG.
7 where the time delay scale has been expanded with a factor of
1000. But these small deviations from the time delays giving the
main lobe direction shown in FIG. 7, called "delta time delays",
are essential for the creation of the desired cancellation
directions. These "delta time delays" are, as described, taken into
account in the weighting function W(.omega.). In this example both
power and time delay is controllable as a function of frequency in
each element. A hardware realization where the bandwidth is divided
in 8 spectral components is illustrated in FIG. 1. An alternative
realization in the time domain is described in FIG. 2a and FIG.
2b.
[0156] FIG. 7 is a three dimensional representation of the "delta
time delays" as a function of frequency and antenna element. The
"delta time delays" are shown on a vertical axis 701 in seconds.
Axis 702 shows frequency between 6-18 GHz and axis 703 represents
the antenna element number. As can be seen the time delay
variations decreases with increasing frequency. Area 704 represents
high "delta time delay", area 705 medium-high, area 706 medium-low
and area 707 low "delta time delay".
[0157] The array factor can now be calculated according to the
above definition in equation (8). The result is illustrated in FIG.
8 where the direction .theta. is represented on the horizontal axis
801 and the radiated power/sensitivity on the vertical axis 802. As
can be seen the main lobe is at 30.degree. and the cancellation
directions at 20.degree., 40.degree. and 50.degree. as expected.
The array factor shown in FIGS. 8-12 and 15-16 is identical to the
antenna pattern according to the definition of antenna pattern
above assuming omni directional element patterns. The vertical axis
thus shows radiated power in transmit mode and sensitivity in the
receive mode as a function of direction.
[0158] In most hardware realization neither the amplitudes of
E.sub.n(f) nor the phases of E.sub.n(f) can be varied continuously
as a function of frequency. The instantaneous bandwidth B normally
has to be divided in Q spectral components. In practice the
frequency division could be done with the aid of an FFT as
described in association with FIG. 1. The discrete
attenuations/amplifications a.sub.n,q (q=spectral component number
and n=antenna element number) and the discrete time delays
.tau..sub.n,q, alternatively discrete phase shifts .phi..sub.n,q,
are selected as the amplitude and time delay, alternatively phase
shifts, at the centre frequency of each spectral component. This
could be written as a.sub.n,q=|E.sub.n(f.sub.q)| and
.tau..sub.n,q=arctan
{Im[E.sub.n(f.sub.q)]/Re[E.sub.n(f.sub.q)])/(2.pi.f.sub.q),
alternatively phase shifts .phi..sub.n,q=arctan
{Im[E.sub.n(f.sub.q)]/Re[E.sub.n(f.sub.q)]}, where f.sub.q
represents the centre frequency of each spectral component q (q
.di-elect cons. 0 . . . (Q-1)). Im represents the imaginary part
and Re the real part of the expression. The array factor can now be
calculated as an average based on either the centre frequencies in
each spectral component, see equation (16), or based on the
frequencies joining adjacent spectral components, see equation
(17).
AF centre ( .theta. ) = q = 0 Q - 1 n = 1 N ( a n , q j 2 .pi. f q
.tau. n , q j ( n - 1 ) ( 2 .pi. f q c 0 L N - 1 sin ( .theta. ) )
) 2 q = 0 Q - 1 n = 1 N ( a n , q j 2 .pi. f q .tau. n , q j ( n -
1 ) ( 2 .pi. f q c 0 L N - 1 sin ( .theta. max ) ) ) 2 ( 16 ) AF
joint ( .theta. ) = q = 0 Q - 2 n = 1 N ( a n , q j 2 .pi. f q + f
q + 1 2 .tau. n , q j ( n - 1 ) ( 2 .pi. f q + f q + 1 2 c 0 L N -
1 sin ( .theta. ) ) ) 2 q = 0 Q - 1 n = 1 N ( a n , q j 2 .pi. f q
.tau. n , q j ( n - 1 ) ( 2 .pi. f q c 0 L N - 1 sin ( .theta. max
) ) ) 2 ( 17 ) ##EQU00015##
[0159] The correct array factor ought to be between AF.sub.centre
and AF.sub.joint. AF.sub.joint is assumed to give the lower
performance of the two array factors both for cancellation
directions and the main lobe.
[0160] In FIGS. 9-12 AF.sub.joint is plotted with expanded angle
scale around cancellation directions and the main lobe for
different numbers of spectral components in the FFT calculations.
The graphs thus illustrate the lower performance limit for each
case for the array antenna used as an example of a wideband array
antenna or antenna system when describing the method for creating
the wideband cancellation directions.
[0161] FIG. 9 shows angle .theta. on the horizontal axis 901 and
the radiated power on the vertical axis 902. The cancellation
direction at 20.degree. becomes sharper for increasing length of
the FFT. Curve 904 shows the radiation power/sensitivity with a
32-point FFT and curve 903 with 1024 points.
[0162] FIG. 10 shows angle .theta. on the horizontal axis 1001 and
the radiated power/sensitivity on the vertical axis 1002. The
maximum radiation/sensitivity direction at 30.degree. becomes
sharper for increasing FFT length. Curve 1004 shows the radiation
power/sensitivity with a 32-point FFT and curve 1003 with 1024
points.
[0163] FIG. 11 shows angle .theta. on the horizontal axis 1101 and
the radiated power/sensitivity on the vertical axis 1102. The
cancellation direction at 40.degree. becomes sharper for increasing
FFT length. Curve 1104 shows the radiation power/sensitivity with a
32-point FFT and curve 1103 with 1024 points.
[0164] FIG. 12 shows angle .theta. on the horizontal axis 1201 and
the radiated power/sensitivity on the vertical axis 1202. The
cancellation direction at 50.degree. becomes sharper for increasing
FFT length. Curve 1204 shows the radiation power/sensitivity with a
32-point FFT and curve 1203 with 1024 points.
[0165] Frequency Independent Position and Width of the Main
Lobe
[0166] The possibilities of the extended control of the antenna
pattern of the wideband array antenna included in the wideband
array antenna unit or the antenna system will now be described with
a further example showing how the invention can be used to achieve
a frequency independent position and fixed width of one main
lobe.
[0167] Assume the same conditions with the 2 m long array antenna
used as an example of a wideband array antenna or antenna system
when describing the method for creating the wideband cancellation
directions above. In this case no wideband cancellation directions
shall be created except for the wideband cancellation directions on
each side of the main lobe controlling the main lobe width.
Simplify the example and introduce frequency independence only to
the cancellation direction on each side of the main lobe. It is a
considerably harder problem to introduce frequency independence of,
for example, the 3 dB lobe width. This simplification does not
influence the conclusions as the main lobe primarily is depending
on the closest minimum. A frequency independent and fixed main lobe
width is desirable for minimizing the frequency filtering of the
used waveform within the main lobe width in order not to distort
the received/transmitted waveform within the main lobe width. Chose
the first zero point on each side of the main lobe coinciding with
the corresponding zero point at f.sub.min when all remaining zero
points are evenly distributed on the unit circle, see references
mentioned in association with equation (9).
[0168] Commence by calculating the angle from the main lobe centre
to the first zero point (.theta..sub.0). With above conditions this
angle could be calculated according to equation (18).
.theta. 0 = arc sin ( c 0 L f min N - 1 N ) ( 18 ) ##EQU00016##
[0169] Continue by calculating the "angles" (.PSI..sub.0l,
.PSI..sub.0r) corresponding to the first zero point on the left
side .PSI..sub.0l and the first zero point on the right side
.PSI..sub.0r of the main lobe on the unit circle with the aid of
equation (19) and equation (20) respectively.
.psi. 0 l ( f ) = 2 .pi. f c 0 l N - 1 sin ( .theta. 0 ) ( 19 )
.psi. 0 r ( f ) = 2 .pi. - .psi. 0 l ( f ) ( 20 ) ##EQU00017##
[0170] Spread all remaining zero points z.sub.n(f) evenly in angle
on the unit circle between .PSI..sub.0l and .PSI..sub.0r, according
to equation (21). This simple choice of evenly distributed zero
points simplifies the calculations to follow without affecting the
conclusions.
z n ( f ) = j [ .psi. 0 l ( f ) + n N - 2 ( .psi. 0 r ( f ) - .psi.
0 l ( f ) ) ] ( 21 ) ##EQU00018##
[0171] Calculate .PSI..sub.max(f) according to equation (10) and
rotate all zero points according to equation (22).
z.sub.rot n(f)=z.sub.n(f)e.sup.j.PSI..sup.max.sup.(f) (22)
[0172] The array factor (AF(.theta.,f)) can now be written in
product form in analogy with equation (14). By formulating and
solving a system of equations with the excitation E.sub.n(f) of
each antenna element as the unknown, the array excitation can be
calculated. The array factor (AF(.theta.,f)) can thereafter be
formulated on it's summa form according to equation (15).
[0173] The element excitations E.sub.n(f) describes both the
amplitude and phase dependency on frequency in each antenna element
as described above. Ambiguities arising in the transformation are
resolved by selecting the time delay closest to the time delay
corresponding to the time delay giving the main lobe direction in
each antenna element for each frequency. The result is illustrated
in FIG. 13 (power) and FIG. 14 (time delay). The graphs reveal
considerable variations in power, in contradiction to the situation
when calculating the cancellation directions, and time delays
according to FIG. 14 only marginally diverging from the time delays
corresponding to the time delays giving the main lobe direction as
shown in FIG. 6a. This fact lead to the conclusion that two
frequency dependent parameters, attenuation/amplification and time
delay or phase shift, ought to be adjustable as a function of
frequency in each antenna element when both wideband cancellation
directions and frequency independent width of the main lobe shall
be controlled. When only control of the width of the main lobe over
a wide frequency band is required it can be sufficient just to use
attenuation/amplification i.e. to use only one frequency dependent
parameter in conjunction with frequency independent time delay to
control the main lobe direction. However if only wideband
cancellation directions and/or frequency independent direction of
the main lobe is required it can be sufficient just to use time
delays i.e. to use only one frequency dependent parameter. An
example of realization with 8 spectral components is illustrated in
FIG. 1.
[0174] FIG. 13 is a three dimensional representation of radiated
power/sensitivity as a function of frequency and antenna element
for the array antenna used as an example of a wideband array
antenna or antenna system when explaining how to achieve frequency
independent position and fixed width of one main lobe. The radiated
power/sensitivity is shown on a vertical axis 1301 in dB. Axis 1302
shows frequency between 6-18 GHz and axis 1303 represents the
antenna element number. Area 1304 represents high power, area 1305
medium-high, area 1306 medium-low and area 1307 low power. As shown
in FIG. 13 the above choice of angles for the first zero point on
each side of the main lobe results in a "square" aperture
distribution at f.sub.min. For increasing frequencies a
successively smaller and smaller part of the aperture will be used,
leading to very low power/sensitivity levels at f.sub.max for the
edge elements. As shown the power/sensitivity variations are
substantial from 0 to 78 dB.
[0175] FIG. 14 is a three dimensional representation of the
frequency dependent time delays as a function of frequency and
antenna element for the array antenna used as an example of a
wideband array antenna or antenna system when explaining how to
achieve frequency independent position and fixed width of one main
lobe. The time delays are shown on a vertical axis 1401 in seconds.
Axis 1402 shows frequency between 6-18 GHz and axis 1403 represents
the antenna element number.
[0176] The array factor can now be calculated according to equation
(8) for the array antenna used as an example of a wideband array
antenna or antenna system when explaining how to achieve frequency
independent position and fixed width of one main lobe. The result
is illustrated in FIG. 15 where the direction .theta. is
represented on the horizontal axis 1501 and the radiated
power/sensitivity on the vertical axis 1502. As can be seen the
main lobe is at 30.degree..
[0177] As mentioned, when calculating the array factor in
association with creating the cancellation directions, neither the
amplitudes |E.sub.n(f.sub.q)| nor the time delays arctan
{Im[E.sub.n(f.sub.q)]/Re[E.sub.n(f.sub.q)]}/(2.pi.f.sub.q),
alternatively phase shifts arctan
{Im[E.sub.n(f.sub.q)]/Re[E.sub.n(f.sub.q)]}, can be varied
continuously as a function of frequency in a practical hardware
realization. Therefore the bandwidth in question must be divided in
spectral components in the same way as described when calculating
the array factor in association with creating the wideband
cancellation directions. AF.sub.centre and AF.sub.joint can
thereafter be calculated according to equation (16) and (17)
respectively. Also in analogy with the calculations of the wideband
cancellation directions described above a lower performance is
expected for AF.sub.joint. FIG. 16 is an illustration of
AF.sub.joint for the array antenna used as an example of a wideband
array antenna or antenna system when explaining how to achieve
frequency independent position and fixed width of one main lobe
with expanded angle scale around the main lobe for different
numbers of spectral components in the FFT calculation. FIG. 16
shows angle .theta. on the horizontal axis 1601 and the radiated
power/sensitivity on the vertical axis 1602. The maximum
radiation/sensitivity direction at 30.degree. becomes sharper for
increasing FFT length. Curve 1604 shows the radiation
power/sensitivity with a 32-point FFT and curve 1603 with 1024
points.
[0178] Conclusions from the above described examples "Wideband
cancellation directions" and "Frequency independent position and
width of the main lobe" are as follows: [0179] A frequency
independent main lobe width can be created. [0180] A frequency
dependent "true time delay" or phase shift is desired to be able to
combine frequency independent main lobe with wideband cancellation
directions. [0181] A frequency dependent attenuation is
advantageous to accomplish a fixed main lobe width over the
frequency bandwidth B. [0182] A relatively large FFT is required
for each antenna element. A minimum FFT length of 128 points is
required to maintain the shape of the main lobe reasonably fixed in
the examples above, operating in the very wide frequency range from
6 GHz to 18 GHz. However in many applications having a narrower
bandwidth than in this example it is sufficient with a shorter, or
much shorter, FFT length.
[0183] Pulsed Waveforms
[0184] The examples described above have been based on continuous
waveforms. The invention can however also be used for pulsed
waveforms which will be explained by the following example. Assume
the same conditions and use the weighting coefficients calculated
in the above example with the 2 m long array antenna as an example
of a wideband array antenna or antenna system describing the method
for creating the cancellation direction. The Fourier transform
U.sub.in(.omega.) of a bandwidth limited pulse can be written
according to equation (23).
U in ( .omega. ) = { 2 sin [ ( .omega. - .omega. c ) T 2 ] .omega.
- .omega. c .omega. c - .pi. B .ltoreq. .omega. .ltoreq. .omega. c
+ .pi. B 0 .omega. c + .pi. B < .omega. < .omega. c - .pi. B
( 23 ) ##EQU00019## [0185] .omega..sub.c=Angular frequency of the
carrier in the bandwidth limited pulse equal to the angular
frequency with peak amplitude in the spectral domain.
[0186] The Fourier transform of the waveform to each antenna
element (U.sub.elm(.omega.,n)) is given by equation (24).
U.sub.elm(.omega.,n)=U.sub.in(.omega.)A.sub.n(.omega.)e.sup.-j.omega..ta-
u..sup.n.sup.(.omega.) (24)
[0187] Finally the Fourier transform of the resulting waveform can
be written according to equation (25).
U out ( .omega. , .theta. ) = n = 0 N - 1 [ U elm ( .omega. , n ) j
.omega. c 0 d [ n - ( N - 1 2 ) ] sin ( .theta. ) ] N ( 25 )
##EQU00020##
[0188] The inverse transform according to equation (26) gives the
waveform as a function of time (t) and azimuth angle (.theta.).
u out ( t , .theta. ) = .intg. f c - B 2 f c + B 2 U out ( 2 .pi. f
, .theta. ) j 2 .pi. f t f ( 26 ) ##EQU00021##
[0189] A bandwidth limited pulse (6 GHz-18 GHz) with the duration
.tau..sub.p=1 ns is chosen as an example to illustrate that the
invention also is applicable to pulses. The envelope as a function
of time is illustrated in FIG. 17. FIG. 17 shows the pulse power on
the vertical axis 1701 and the pulse duration in ns on the
horizontal axis 1702.
[0190] The Fourier transform can be calculated with the aid of
equation (23). Use equation (25) with N=64 to calculate the Fourier
transform of the resulting waveform as a function of angle and
frequency. The inverse Fourier transform according to equation (26)
is used to calculate the waveform as a function of angle and time.
The result is illustrated in FIG. 18. According to the reciprocity
theorem the result can either be interpreted as if the test
waveform is connected to the antenna port and the radiated
resulting waveform is measured for all angles as a function of time
or as if the resulting waveform is transmitted from all angles and
the chosen test waveform is received and measured at the antenna
port as a function of time. Independently of interpretation it is
clear from FIG. 18 that three cancellation directions exists at
20.degree., 40.degree. and 50.degree. at all time.
[0191] FIG. 18 illustrates the resulting waveform in transmit mode
as a function of time on the horizontal axis 1801 and power on the
vertical axis 1802 for a number of angles. Curve 1803 shows
radiated power at 30.degree., curve 1804 at 40.degree., curve 1805
at 50.degree. and curve 1806 at 20.degree.. Curve 1807 shows
radiated power at 60.degree., where neither a main lobe nor a
cancellation direction is created.
[0192] The following conclusions can be made from the example when
a pulsed wave form is used: [0193] Wideband cancellation directions
can be created for pulsed waveforms. [0194] Frequency dependent
"true time delay" is advantageous. [0195] Frequency dependent
attenuation is advantageous.
[0196] Flow Chart
[0197] The method of the digital realization of embodiments of the
invention are described in a flow chart shown in FIG. 19 comprising
1901-1910. Waveform data such as centre frequency f.sub.c and
instantaneous bandwidth B is specified in 1901. In 1902, the
running integer q, representing the number of a spectral component,
is set at 0. In 1903, the weighting function
W(.omega.)=A(.omega.)e.sup.-j.omega..tau.(.omega.) or
W(.omega.)=A(.omega.)e.sup.-j.phi.(.omega.) is calculated for Q
spectral components q, resulting from dividing the instantaneous
bandwidth B in q components, q being an integer index ranging from
0 to Q-1, for each antenna element or sub array (E.sub.1-E.sub.N)
using standard methods taking into account design requests valid
for a centre frequency f.sub.q of each spectral component. The
centre frequency f.sub.q of each spectral component is calculated
as:
f q = f c - B 2 + ( q + 1 2 ) B Q ##EQU00022##
[0198] for a case with equividistant spectral component division.
The standard methods used for the calculation of the weighting
function can be any classical antenna synthesis method such as
Schelkunoff's method. The design requests can e.g. comprise: [0199]
shape of one or several main lobes [0200] direction of one or
several main lobes [0201] width of one or several main lobes [0202]
side lobe levels in different directions [0203] cancellation
directions
[0204] In the description above the invention is exemplified with
how to achieve wideband cancellation directions in combination with
wideband direction of one main lobe and how the width and direction
of this main lobe can be kept constant over the instantaneous
bandwidth B. Other combinations of design request can be used when
applying an antenna synthesis method as the Schelkunoff method such
as e.g. wideband cancellation directions in combination with fixed
width and direction of one or several main lobes over the entire or
parts of the instantaneous bandwidth B.
[0205] After 1903, has been performed the value of integer q is
checked in 1905, and if it is below Q-1 it is increased by 1 in
1906, and the calculations in 1903 is performed for the next
spectral component. When the check in 1905 results in q=Q-1 all
spectral components have been calculated and a choice of
realization method is made in 1907.
[0206] If a frequency domain realization 1908 is made, W(.omega.)
is used for antenna element/sub array n and frequency f.sub.q as
described in association with FIG. 1a.
[0207] If a time domain realization 1909 is made, weighting
coefficients w.sub.n,q are used for antenna element/sub array n for
each spectral component q as described in association with FIGS. 2a
and 2b. w.sub.n,q is calculated as the Inverse Fourier Transform of
W(.omega.), see equation (2).
[0208] If a DDS realization 1910 is made the resulting waveform is
digitally calculated for each antenna element/sub array in advance
and the result is fed to the DDS unit for each antenna element/sub
array. The calculation can be made either in the time domain or in
the frequency domain, see equation (2).
[0209] The calculations of the parameters from the weighting
function W(.omega.)=A(.omega.)e.sup.-j.omega..tau.(.omega.) or
W(.omega.)=A(.omega.)e.sup.-j.phi.(.omega.) can be performed at any
convenient location, e.g. in a calculation unit integrated in the
array antenna, the transforming means, the electronic system or a
separate calculation unit, and then transferred to the transforming
means.
[0210] Array Thin Out The invention also has the added advantage
that for a wideband array
[0211] antenna the number of antenna elements required for
instantaneous wideband operation can be reduced. This "array thin
out" feature of the invention will now be described. The element
separation in an antenna operating with an instantaneously wideband
waveform having an instantaneous bandwidth B can be increased to
above .lamda./2 without the appearance of grating lobes, .lamda.
being the wavelength corresponding to a maximum frequency within
the system bandwidth of e.g. a radar system. The system bandwidth
is greater or equal to the instantaneous bandwidth B. This results
in a reduced number of antenna elements needed compared to
conventional array antenna design using an element separation of
half a wavelength.
[0212] The antenna element reduction feature or "array thin out"
feature for the wideband array antenna will be described with two
examples, one for a linear array and one for a circular array.
[0213] In the examples to follow a simple antenna element diagram
according to equation (27) and identical waveform in all antenna
elements is assumed.
g ( .theta. , .PHI. ) = { cos 2 ( .theta. ) om cos ( .theta. ) >
0 0 om cos ( .theta. ) .ltoreq. 0 ( 27 ) ##EQU00023##
[0214] For a one dimensional linear array the time delays of the
waveform from/to element n can be calculated according to equation
(28).
.tau. n ( .theta. ) = n - 1 N - 1 L c 0 sin ( .theta. ) ( 28 )
##EQU00024##
[0215] L=Antenna length
[0216] N=Number of antenna elements
[0217] An example with white bandwidth limited Gaussian noise is
shown in FIG. 20, calculated according to equation (8), in the
transmit mode. FIG. 20 shows radiated power on the vertical axis
2001 as a function of the angle .theta. on the horizontal axis
2002. Curve 2003 visualizes the case with 64 elements, the angle
for the first grating lobe at maximum frequency is clearly visible
at the angles .+-.31.6.degree. marked with arrows 2010. Curve 2004
visualizes the case with 32 elements, the angles for the two first
grating lobes at maximum frequency is clearly visible at the angles
.+-.15.0.degree. marked with arrows 2011 and .+-.31.1.degree.
marked with arrows 2012 respectively. The angles for these narrow
band grating lobes are calculated by conventional methods well
known to the skilled person. Curve 2005 visualizes the case with 16
elements and several grating lobe angles are clearly visible. With
4 or less than 4 elements, curves 2006 and 2007, illustrates the
result. With 128 or more elements, see curve 2008, no grating lobe
angles appear in the case with a boar sight main lobe. A bore sight
main lobe has a direction perpendicular to the surface of the
antenna aperture.
[0218] For a circular array the time delays of the waveform from/to
element n can be calculated according to equation (29).
.tau. n ( .theta. ) = D 2 c 0 cos ( .theta. - n 2 .pi. N ) ( 29 )
##EQU00025##
[0219] D=Antenna diameter
[0220] N=Number of antenna elements
[0221] An example with white bandwidth limited Gaussian noise is
shown in FIG. 21, calculated according to equation (8), in the
transmit mode. FIG. 21 shows radiated power on the vertical axis
2101 as a function of the angle .theta. on the horizontal axis
2102. Curve 2103 includes 4 antenna elements, curve 2104 16 antenna
elements, curve 2105 64 antenna elements, curve 2106 128 antenna
elements, curve 2107 256 antenna elements and curve 2108 2048
antenna elements.
[0222] In FIGS. 20 and 21 no grating lobes are created as they are
located at different angles for different parts of the used
spectrum. The side lobe level for a fixed frequency, or narrow band
antenna, with equal distribution of power is, as is well known to
the skilled person, -13 dB. The same level for the wideband array
antenna as described above corresponds to about 32 elements for the
linear array as can be seen in FIG. 20. This means a separation
between antenna elements of approximately 65 mm. To achieve
electronic control of an array antenna the antenna elements are
normally separated one half wavelength of the maximum frequency
within the system bandwidth, in this example equal to the
instantaneous bandwidth B In this example with a maximum frequency
of 18 GHz this means a separation of 8.3 mm. The number of antenna
elements then becomes 240. This "array thin out" feature is only
valid when the wideband array antenna is operated with an
instantaneously wideband waveform.
[0223] A wideband array antenna 301 according to prior art,
operational over a system bandwidth, and comprising at least two
antenna elements (E.sub.1-E.sub.N), can thus be arranged to control
an antenna pattern of the wideband array antenna when connected to
an electronic system 303. The antenna pattern control is then
arranged to be achieved by affecting waveforms between the array
antenna and the electronic system with parameters being individual
for each antenna element. The parameters can in one embodiment be:
[0224] non frequency dependent attenuations and/or phase shifts
[0225] non frequency dependent attenuations and/or time delays.
[0226] In another embodiment the parameters can be: [0227]
frequency dependent attenuations and/or phase shifts [0228]
frequency dependent attenuations and/or time delays.
[0229] According to this "array thin out" embodiment of the
invention a wideband array antenna instantaneously occupying the
instantaneous bandwidth B is accomplished by a separation between
antenna elements in the array antenna being increased to above one
half wavelength of a maximum frequency within the system bandwidth
when the wideband array antenna is arranged to operate with an
instantaneously wideband waveform, thus resulting in a
substantially reduced number of antenna elements (E.sub.1-E.sub.N)
needed compared to conventional array antenna designs without the
appearance of grating lobes in the antenna pattern.
[0230] In all embodiments of the invention, except the "array thin
out" embodiment, the instantaneous bandwidth B can be both wide and
narrow. The "array thin out" embodiment requires a wide
instantaneous bandwidth.
[0231] For a wideband array antenna arranged to operate with an
instantaneously wideband waveform the separation between antenna
elements in the array antenna can as described be increased to
above one half wavelength of a maximum frequency within the system
bandwidth, in this example equal to the instantaneous bandwidth B.
In the described example only 13% of the antenna elements are
required compared to the fixed frequency or narrow band antenna
solution. In a two or three dimension wideband array antenna even
greater reduction of required number of antenna elements are
possible. A wideband array antenna instantaneously occupying an
instantaneous bandwidth B thus can be accomplished with a
drastically reduced number of antenna elements in any wideband
array antenna when operating with a waveform with high
instantaneous bandwidth. This has the obvious advantage of reducing
costs for the wideband array antenna. The connection of the
wideband array antenna to the electronic system can be made either
directly or indirectly via transforming means or other electronic
components.
[0232] The invention is not limited to the embodiments of the
description, but may vary freely within the scope of the appended
claims. An example of this is a variation of the embodiment
described in FIG. 1a.
[0233] In the embodiment described in FIG. 1a the transforming unit
is inserted between each antenna element and the electronic system.
A variation of this solution within the scope of the invention is
that a common IFT unit is used for all antenna elements/sub arrays,
i.e. the waveform from each antenna element/sub array is processed
in a separate FT unit for each antenna element/sub array but the
sum of the spectral component q from each antenna element/sub array
after suitable time delay or phase shift and/or
attenuation/amplification are processed in a common IFT unit.
* * * * *