U.S. patent application number 12/968446 was filed with the patent office on 2012-06-21 for calibration technique for phased array antennas.
This patent application is currently assigned to University of Massachusetts Amherst. Invention is credited to Rafael H. Medina Sanchez.
Application Number | 20120154206 12/968446 |
Document ID | / |
Family ID | 46177814 |
Filed Date | 2012-06-21 |
United States Patent
Application |
20120154206 |
Kind Code |
A1 |
Medina Sanchez; Rafael H. |
June 21, 2012 |
CALIBRATION TECHNIQUE FOR PHASED ARRAY ANTENNAS
Abstract
A method for calibrating a phased-array antenna that involves
transmitting a signal from a transmitting element, and sequentially
receiving the transmitted signal at two receiving elements each
spaced a first distance from the transmitting element. This step is
then repeated one or more times, but transmitting from a different
transmitting element in each repetition of the step, until each
element being calibrated has received at least one transmission.
Then, the first distance is changed to a second distance, and the
steps are repeated one or more times to gather additional
measurements. These measurements allow the determination from the
received signals of two separate element mutual coupling ratios,
one ratio for one subset of the elements being calibrated and the
other for a second subset comprising the remaining elements being
calibrated. Next, at least four additional transmissions and
receptions are made via two transmissions each from two
transmitting elements comprising one element of each subset, and
the reception of transmissions from each of these two transmitting
elements by each of two receiving elements, the two receiving
elements being different elements than the two transmitting
elements. From these last measurements a complex calibration ratio
for all of the elements being calibrated with respect to a single
element is determined. For calibration in the transmit mode, this
same procedure is followed, but the transmissions become receptions
and the receptions become transmissions.
Inventors: |
Medina Sanchez; Rafael H.;
(Amherst, MA) |
Assignee: |
University of Massachusetts
Amherst
Boston
MA
|
Family ID: |
46177814 |
Appl. No.: |
12/968446 |
Filed: |
December 15, 2010 |
Current U.S.
Class: |
342/174 |
Current CPC
Class: |
H01Q 21/08 20130101;
G01S 7/4004 20130101; H01Q 3/267 20130101 |
Class at
Publication: |
342/174 |
International
Class: |
G01S 7/40 20060101
G01S007/40 |
Goverment Interests
GOVERNMENT RIGHTS
[0001] This invention was made with government support under grant
number EEC-0313747 awarded by the National Science Foundation. The
government has certain rights in the invention.
Claims
1. A method for calibrating array elements of a phased array
antenna, comprising: (i) transmitting a signal from a transmitting
element, and sequentially receiving the transmitted signal at two
receiving elements each spaced a first distance from the
transmitting element; (ii) repeating step (i) one or more times,
transmitting from a different transmitting element in each
repetition of step (i), until each element being calibrated has
received at least one transmission; (iii) changing the first
distance to a second distance and repeating steps (i) and (ii) at
this second distance for at least some of the elements; (iv)
determining from the received signals of steps (i), (ii) and (iii)
two element mutual coupling ratios, one ratio for one subset of the
elements being calibrated and the other for a second subset
comprising the remaining elements being calibrated; (v) making at
least four additional transmissions and receptions via two
transmissions each from two transmitting elements comprising one
element of each subset, and the reception of transmissions from
each of these two transmitting elements by each of two receiving
elements, the two receiving elements being different elements than
the two transmitting elements; and (vi) determining from the
received signals of step (v) a complex calibration ratio for all of
the elements being calibrated with respect to a single element.
2. The method of claim 1 wherein the elements are regularly
spaced.
3. The method of claim 2 wherein the first distance is at least
twice the distance between elements.
4. The method of claim 3 wherein the second distance is at least
three times the distance between elements.
5. The method of claim 4 wherein the first distance is three times
the distance between elements and the second distance is four times
the distance between elements.
6. The method of claim 2 wherein the first distance is less than
the second distance.
7. The method of claim 6 wherein the second distance is greater
than the first distance by the amount of the distance between
elements.
8. The method of claim 1 wherein there are p spacing elements
between the transmitting element and the receiving elements, and
step (iii) comprises at least 2(p+1) transmissions and
receptions.
9. The method of claim 1 wherein the antenna comprises a
two-dimensional lattice of elements.
10. The method of claim 9 wherein the lattice orientation is either
square, rectangular, rhombic or parallelogram.
11. The method of claim 9 wherein the elements being calibrated
comprise a linear sub-array.
12. The method of claim 11 further comprising separately conducting
the method of claim 1 on a plurality of sub-arrays that together
include each active element of the two-dimensional lattice.
13. The method of claim 1 further comprising: (vii) sequentially
transmitting a signal from two transmitting elements each spaced a
first distance from a receiving element that receives the two
transmitted signals; (viii) repeating step (vii) one or more times,
receiving at a different receiving element in each repetition of
step (vii), until each element being calibrated has transmitted at
least once; (ix) changing the first distance to a second distance
and repeating steps (vii) and (viii) at this second distance for at
least some of the elements; (x) determining from the transmitted
signals of steps (vii), (viii) and (ix) two element mutual coupling
ratios, one ratio for one subset of the elements being calibrated
and the other for a second subset comprising the remaining elements
being calibrated; (xi) making at least four additional
transmissions and receptions via two receptions each by two
receiving elements comprising one element of each subset, and the
transmission of transmissions from each of two transmitting
elements, the two receiving elements being different elements than
the two transmitting elements; and (xii) determining from the
transmitted signals of step (xi) a complex calibration ratio for
all of the elements being calibrated with respect to a single
element.
14. A method for calibrating regularly-spaced array elements of a
phased array antenna that comprises a two-dimensional lattice of
elements, wherein the lattice orientation is either square,
rectangular, rhombic or parallelogram, the method comprising: (i)
transmitting a signal from a transmitting element, and sequentially
receiving the transmitted signal at two receiving elements each
spaced a first distance from the transmitting element, wherein the
first distance is at least twice the distance between elements;
(ii) repeating step (i) one or more times, transmitting from a
different transmitting element in each repetition of step (i),
until each element being calibrated has received at least one
transmission; (iii) changing the first distance to a second
distance and repeating steps (i) and (ii) at this second distance
for at least some of the elements, wherein the second distance is
greater than the first distance and is at least three times the
distance between elements, wherein there are p spacing elements
between the transmitting element and the receiving elements, and
step (iii) comprises at least 2(p+1) transmissions and receptions;
(iv) determining from the received signals of steps (i), (ii) and
(iii) two element mutual coupling ratios, one ratio for one subset
of the elements being calibrated and the other for a second subset
comprising the remaining elements being calibrated; (v) making at
least four additional transmissions and receptions via two
transmissions each from two transmitting elements comprising one
element of each subset, and the reception of transmissions from
each of these two transmitting elements by each of two receiving
elements, the two receiving elements being different elements than
the two transmitting elements; (vi) determining from the received
signals of step (v) a complex calibration ratio for all of the
elements being calibrated with respect to a single element; (vii)
sequentially transmitting a signal from two transmitting elements
each spaced a first distance from a receiving element that receives
the two transmitted signals; (viii) repeating step (vii) one or
more times, receiving at a different receiving element in each
repetition of step (vii), until each element being calibrated has
transmitted at least once; (ix) changing the first distance to a
second distance and repeating steps (vii) and (viii) at this second
distance for at least some of the elements; (x) determining from
the transmitted signals of steps (vii), (viii) and (ix) two element
mutual coupling ratios, one ratio for one subset of the elements
being calibrated and the other for a second subset comprising the
remaining elements being calibrated; (xi) making at least four
additional transmissions and receptions via two receptions each by
two receiving elements comprising one element of each subset, and
the transmission of transmissions from each of two transmitting
elements, the two receiving elements being different elements than
the two transmitting elements; and (xii) determining from the
transmitted signals of step (xi) a complex calibration ratio for
all of the elements being calibrated with respect to a single
element.
15. The method of claim 14 wherein the first distance is three
times the distance between elements and the second distance is four
times the distance between elements.
16. The method of claim 14 further comprising separately conducting
the method of claim 14 on a plurality of sub-arrays that together
include each active element of the two-dimensional lattice.
Description
FIELD
[0002] This invention relates to a method for calibrating phased
array antennas.
BACKGROUND
[0003] Active phased array antennas are composed of many radiating
elements, each with phase and amplitude control. Beams are formed
by weighing the amplitude and shifting the phase of the signal
emitted from each radiating element, to provide
constructive/destructive interference so as to steer the beams in
the desired direction. Planar phased array antennas can
electronically steer the beam in azimuth and the elevation plane
and provide faster beam steering rates than a mechanical steering
system.
[0004] A phased array antenna must be calibrated in the factory
before being deployed in the field in order to ensure that the
radiation pattern of the antenna meets the antenna performance
specification. The calibration is typically performed in a
near-field antenna range; during this process a sampling probe is
positioned in front each radiating element, with that element in
either transmit or receive mode and the remaining array elements
terminated in matched loads. The amplitude and phase of each
radiating element is accurately measured through each T/R module
amplitude and phase state. This data is used to develop correction
factors that minimize the element-to-element random errors. The
desired radiation pattern is then achieved by adjusting the T/R
module amplitudes and phases as indicated by the corrections
factors.
[0005] Solid-state radars for weather application require the
phased array antennas to be deployed for a long period of time. The
performance of the antennas may deteriorate over time as a result
of changes in the solid-state devices. In addition, failed T/R
modules must be replaced in the field. As a result, the T/R modules
must be re-calibrated to correct the component drift or the module
replacement. In order to avoid the radars being taken out of
service for a long time, a self-calibration is required.
[0006] Several techniques of self-calibration or auto-calibration
for active phased array antennas have been proposed and
implemented. These have an internal calibration source and use
mutual coupling measurements among array elements to determine the
element-to-element errors. Some such calibration techniques use the
inherent array mutual coupling to transmit and receive signals
between pairs of adjacent elements in the array, while all other
elements are turned off and terminated in matched loads.
[0007] Another calibration technique employs a small number of
dedicated passive calibration elements to calibrate the antenna.
The array is split into several blocks, each having a single
passive calibration element near its center. The calibration is
achieved by sequentially measuring the mutual coupling between each
passive element and a selected group of active array elements
belonging to adjacent blocks. However, this technique is not
suitable for small array antennas, because a small number of
dedicated passive elements for calibration would degrade the
sidelobe level and antenna gain.
SUMMARY
[0008] This disclosure relates to calibration techniques for array
antennas, without the use of a near-field antenna range. The
techniques use mutual coupling measurements between array elements
to characterize the relative amplitude and phase between them. The
measurements can be made between pairs of adjacent or non-adjacent
elements. By using the mutual coupling measurements between
non-adjacent elements, arrays with high power modules can be
calibrated. Simulated results of a linear array of columns of
elements in an electromagnetic simulator are used herein to
demonstrate a calibration technique and predict the array
patterns.
Theory
Array Aperture Distribution and Radiation Pattern
[0009] Consider a uniform N-element linear array of
uniformly-spaced identical elements, such as array 10, FIG. 1, with
elements 11, 12, 13 . . . 14, 15 and 16. For large arrays, the edge
diffraction effects can be neglected and the mutual coupling can be
assumed uniform, such that the element radiation patterns can be
considered approximately identical. Under this assumption, the
far-field vector radiation pattern is expressed as
E ( .theta. , .phi. ) = e a ( .theta. , .phi. ) n = 1 N V n j 2
.pi. .lamda. nd sin .theta. ( 1 ) ##EQU00001##
where, e.sub.a is the active element radiation pattern, V.sub.n is
the excitation of the nth element, .lamda. is the wavelength, and d
is the spacing between elements. The excitation function for each
array element is expressed as
V.sub.n=w.sub.n(i)u.sub.n.sup.TV.sub.in (2)
where, w.sub.n(i) is the module insertion attenuation and phase for
its ith complex state, u.sub.n.sup.T; represents the combined
effects in transmit mode of attenuation and phase delay in the
power dividers/combiners, RF cables, connectors, and the insertion
loss and phase due to attenuators and phase shifters when they are
set to their initial state. V.sub.in is the excitation at the
beamformer input.
[0010] Due to intentional or unintentional hardware differences in
the array, u.sub.1.sup.T.noteq.u.sub.2.sup.T.noteq. . . .
.noteq.u.sub.N.sup.T. These differences affect the relative gain
and phase between array elements. The random variations in u.sub.n
must be compensated with the attenuators and phase shifters such
that the desired excitation can be implemented. In a uniform linear
array the relative errors between elements can be determined by
comparing the excitation functions. For example, comparing the
first and nth element excitation,
w.sub.1(i.sub.1)u.sub.1.sup.TV.sub.in=w.sub.n(i.sub.n)u.sub.n.sup.TV.sub-
.in (3)
In particular, assuming the first module is set in the zero state,
i.sub.1=0, by definition, w.sub.1(0)=1, then solving (3) for
w.sub.n(i.sub.n) yields
w n ( i n ) = u 1 T u n T = C 1 , n T , n = 2 , 3 , , N . ( 4 )
##EQU00002##
[0011] The quantity C.sub.1,n.sup.T is the complex calibration
ratio used to align the nth element with respect to the first
element. This ratio contains information about the relative
amplitude and phase between the first and nth element. Hence, if
C.sub.1,n is known, the linear array can be calibrated for uniform
distribution by using (4). However, for any array aperture
distribution with complex excitation A.sub.n, the desired element
excitation can be achieved when the nth array module is set to some
state i.sub.n such that
w.sub.n(i.sub.n)=C.sub.1,n.sup.mA.sub.n,n=1,2,3, . . . ,N.;m=T,R
(5)
The array self-calibration procedure is used to determine the
complex calibration ratios using mutual coupling measurements
between array elements and permit the desired array excitation
V.sub.n to be implemented.
[0012] This invention features a method for calibrating array
elements of a phased array antenna, comprising transmitting a
signal from a transmitting element, and sequentially receiving the
transmitted signal at two receiving elements each spaced a first
distance from the transmitting element, repeating the first step
one or more times, transmitting from a different transmitting
element in each repetition of the step, until each element being
calibrated has received at least one transmission, changing the
first distance to a second distance and repeating the first two
steps at this second distance for at least some of the elements,
determining from the received signals of the first three steps two
element mutual coupling ratios, one ratio for one subset of the
elements being calibrated and the other for a second subset
comprising the remaining elements being calibrated, making at least
four additional transmissions and receptions via two transmissions
each from two transmitting elements comprising one element of each
subset, and the reception of transmissions from each of these two
transmitting elements by each of two receiving elements, the two
receiving elements being different elements than the two
transmitting elements, and determining from the received signals of
the previous step a complex calibration ratio for all of the
elements being calibrated with respect to a single element.
[0013] The elements may be regularly spaced. The first distance may
be at least twice the distance between elements. The second
distance may be at least three times the distance between elements.
The first distance may be three times the distance between elements
and the second distance may be four times the distance between
elements. The first distance may be less than the second distance.
The second distance may be greater than the first distance by the
amount of the distance between elements.
[0014] There may be p spacing elements between the transmitting
element and the receiving elements, and the third step may comprise
at least 2(p+1) transmissions and receptions. The antenna may
comprise a two-dimensional lattice of elements. The lattice
orientation may be either square, rectangular, rhombic or
parallelogram. The elements being calibrated may comprise a linear
sub-array. The method may further comprise separately conducting
the described method on a plurality of sub-arrays that together
include each active element of the two-dimensional lattice.
[0015] The method may further comprise sequentially transmitting a
signal from two transmitting elements each spaced a first distance
from a receiving element that receives the two transmitted signals,
repeating this step one or more times, receiving at a different
receiving element in each repetition of the step, until each
element being calibrated has transmitted at least once, changing
the first distance to a second distance and repeating the two
previous steps at this second distance for at least some of the
elements, determining from the transmitted signals of the three
previous steps two element mutual coupling ratios, one ratio for
one subset of the elements being calibrated and the other for a
second subset comprising the remaining elements being calibrated,
making at least four additional transmissions and receptions via
two receptions each by two receiving elements comprising one
element of each subset, and the transmission of transmissions from
each of two transmitting elements, the two receiving elements being
different elements than the two transmitting elements and
determining from transmitted signals a complex calibration ratio
for all of the elements being calibrated with respect to a single
element.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] FIG. 1 is a schematic diagram of an N element linear
array.
[0017] FIG. 2 is a schematic diagram comparing free space mutual
coupling and measured mutual coupling.
[0018] FIG. 3 is an illustration of mutual coupling measurements
and interleaved sub-arrays for a twenty-element linear array and
two spacing elements.
[0019] FIG. 4 shows the elements used to resolve the two-array
ambiguity.
[0020] FIG. 5 shows simulated and predicted patterns for an
un-calibrated array.
[0021] FIG. 6 shows simulated and predicted patterns for a -30 dB
Chebyshev distribution and one spacing element.
[0022] FIG. 7 shows radiation patterns for a 32-element calibrated
linear array with three different spacing elements and a -25 dB
Taylor distribution.
[0023] FIG. 8 is a schematic diagram of a system for accomplishing
the calibrations.
DESCRIPTION OF EMBODIMENTS
[0024] The calibration techniques or methods may be accomplished by
methods of calibrating array elements of a phased array antenna.
The methods (e.g., for calibration in the receive mode) involve
transmitting a signal from a transmitting element, and sequentially
receiving the transmitted signal at two receiving elements each
spaced a first distance from the transmitting element. This step is
then repeated one or more times, but transmitting from a different
transmitting element in each repetition of the step, until each
element being calibrated has received at least one transmission.
Then, the first distance is changed to a second distance, and the
steps are repeated to gather additional measurements. These
measurements allow the determination from the received signals of
two separate element mutual coupling ratios, one ratio for one
subset of the elements being calibrated and the other for a second
subset comprising the remaining elements being calibrated. Next, at
least four additional transmissions and receptions are made via two
transmissions each from two transmitting elements comprising one
element of each subset, and the reception of transmissions from
each of these two transmitting elements by each of two receiving
elements, the two receiving elements being different elements than
the two transmitting elements. From these last measurements a
complex calibration ratio for all of the elements being calibrated
with respect to a single element is determined.
[0025] For calibration in the transmit mode, this same procedure is
followed, but the transmissions become receptions, and the
receptions become transmissions.
[0026] Following is a description of one embodiment of the
calibration method. This is meant as an illustration of the
invention, not a limitation of the invention.
[0027] Mutual coupling effects are always present among radiating
elements of any array antenna. The coupling amount depends on
element separations and relative orientations. To measure the
coupling it is necessary that the system have the ability to
transmit with one element and simultaneously receive with another
element, which is achieved by using two separate beamforming
networks. The transfer function of the system (the ratio of the
received to transmitted signals) is called the mutual coupling. The
mutual coupling measurements between two elements include the
combined effects of the power combiner/divider, RF cables,
connectors, T/R modules and the free space mutual coupling. This
can be seen in linear array 20 shown in FIG. 2, where M denotes
free space mutual coupling and M' is the measured transfer function
(the prime mark is used herein to denote measured quantities, or
quantities calculated directly from measured quantities). In
particular, the transfer functions when transmitting from the nth
element and receiving first with the element (n-p-1) and then with
the element (n+p+1) are determined by the follow expressions
M'.sub.n-p-1,n.sup.R=w.sub.n-p-1.sup.Ru.sub.n-p-1.sup.RM.sub.n-p-1,nw.su-
b.n.sup.Tu.sub.n.sup.T (6.a)
M'.sub.n+p+1,n.sup.R=w.sub.n+p+1.sup.Ru.sub.n+p+1.sup.RM.sub.n+p+1,nw.su-
b.n.sup.Tu.sub.n.sup.T (6.b)
where, p is the number of spacing elements between the transmit and
receive elements. In a large uniform one-dimensional or
two-dimensional array antenna made with good tolerances, the free
space mutual coupling can be assumed the same for all pairs of
equidistant elements from a central element,
M.sub.n-p-1,n=M.sub.n+p+1,n. However, due to hardware differences,
the measured mutual coupling will not be equal,
M'.sub.n-p-1,n.sup.R.noteq.M'.sub.n+p+1,n.sup.R. Since the
transmitting element n is common to receiving elements (n-p-1) and
(n+p+1), any differences in M'.sub.n-p-1,n.sup.R and
M'.sub.n+p+1,n.sup.R are due differences in the signal paths at the
elements (n-p-1) and (n+p+1) alone. The gain and phase differences
in the quantities M.sub.n-p-1,n.sup.R' and M.sub.n+p+1,n.sup.R' can
be determined as
C n - p - 1 , n + p + 1 ' R = M n - p - 1 , n ' R M n + p + 1 , n '
R = w n - p - 1 R ( i n - p - 1 ) u n - p - 1 R w n + p + 1 R ( i n
+ p + 1 ) u n + p + 1 R ( 7 ) ##EQU00003##
In particular, if the measurements are made in zero state of each
TR module, i.sub.n-p-1=i.sub.n+p+1=0, then (7) reduces to
C n - p - 1 , n + p + 1 ' R ( 0 ) = u n - p - 1 R u n + p + 1 R ;
for any p = 0 , 1 , 2 , , floor ( N / 4 ) - 1 n = p + 2 , p + 3 , N
/ 2 + 4 ( 8 ) ##EQU00004##
This is the calibration ratio to align the element (n+p+1) with
respect to the element (n-p-1).
[0028] The maximum number of spacing elements (p) is limited to
floor(N/4)-1; any spacing beyond that number will not produce
enough data to calibrate the array (floor and ceil as used herein
are rounding functions in the MatLab.RTM. software that was used
for these calculations. The software is available from The
Mathworks, Inc., Natick, Mass., USA). When the above concept is
applied to the overall array, N-2(p+1) ratios for 2(p+1)
interleaved sub-arrays are obtained. The interleaved sub-arrays are
sets of elements that can be calibrated with respect to each
other.
[0029] FIG. 3 shows the mutual coupling measurements that are taken
in a linear array 30 of twenty elements, with two spacing elements.
In FIG. 3 the measurements are indicated by a series of arrows. For
example, the first series of measurements are aimed at determining
the calibration ratios for the first interleaved sub-array (labeled
on the left side with a "1"), C.sub.1,7, C.sub.7,13, C.sub.13,19.
These measurements involve transmitting from element 4 and
receiving this signal at elements 1 and 7, then transmitting from
element 10 and receiving this signal at elements 7 and 13, then
transmitting from element 16 and receiving this signal at elements
13 and 19. The second series of measurements (transmitting from
elements 5, 11 and 17) generate the calibration ratios for the
second interleaved sub-array (labeled with a "2"), C.sub.2,8,
C.sub.8,14, C.sub.14,20, and so on. The result is fourteen
calibration ratios and six interleaved sub-arrays (labeled 1-6 in
FIG. 3). Each sub-array is composed of only odd or even array
elements.
[0030] The elements of each interleaved sub-array can be calibrated
and referenced to its first element as
m = 1 , 2 , 3 , 2 ( p + 1 ) C m , n ' R ( 0 ) = i n C i , i + 2 ( p
+ 1 ) ' R ( 0 ) ; n = m + 2 ( p + 1 ) , m + 4 ( p + 1 ) , m + 6 ( p
+ 1 ) , , 2 ( p + 1 ) floor ( N - m 2 ( p + 1 ) ) + m i = m , m + 2
( p + 1 ) , m + 4 ( p + 1 ) , , n - 2 ( p + 1 ) ( 9 )
##EQU00005##
In this way, the 2(p+1) interleaved sub-arrays are self-calibrated,
but they are not referenced to each other.
[0031] The number of calibrated sub-arrays is then reduced to two
when the sub-arrays of even and odd elements are separately aligned
to each other. The sub-arrays can be tied together by using
additional calibration ratios, which must relate elements of
different interleaved sub-arrays. The new ratios can be obtained
from the mutual coupling measurements when a spacing element of p+1
is used. A minimum of 2(p+1) ratios are needed to tie the
sub-arrays, which can be obtained from the mutual coupling
measurements in the N-2(p+1) first array elements, that is,
C n , n + 2 ( p o + 1 ) ' R = M n , n + p o + 1 ' R ( 0 ) M n + 2 (
p + 2 ) , n + p o + 1 ' R ( 0 ) ; p o = p + 1 n = 1 , 2 , 3 , 2 ( p
+ 1 ) ( 10 ) ##EQU00006##
The ratios for the linear array depicted in FIG. 3 are C.sub.1,9,
C.sub.2,10, C.sub.3,11, C.sub.4,12, C.sub.5,13, and C.sub.6,14. The
coefficients C.sub.1,9, C.sub.3,11 and C.sub.5,13 can be used to
tie the first, third and fifth interleaved sub-arrays, while the
coefficients C.sub.2,10 C.sub.4,12 and C.sub.6,14 can tie the
second, fourth, and sixth interleaved sub-arrays. This procedure
can be realized by using the following expressions
C i , m ( 0 ) = C i , m + 2 ( p + 1 ) ( 0 ) C m , m + 2 ( p + 1 ) (
0 ) - 1 ; i = 1 , 2 ( 11. a ) C i , n ( 0 ) = C i , m ( 0 ) C m , n
( 0 ) ; m = i + 2 , i + 4 , i + 6 , 2 p + i n = m + 4 ( p + 1 ) , m
+ 6 ( p + 1 ) , , 2 ( p + 1 ) floor ( N - m 2 ( p + 1 ) ) + m ( 11.
b ) ##EQU00007##
The result is two interleaved calibrated sub-arrays that are not
referenced to each other, both consisting of only odd or even
elements and referenced to the first element of each sub-array.
[0032] To complete the overall calibration, the two interleaved
sub-arrays are tied together by taking additional mutual coupling
measurements. FIG. 4 shows how the measurements can be realized.
Since the array is precisely fabricated, geometrically identical
pairs of elements have the same free space mutual coupling, that
is, M.sub.p+2,1=M.sub.p+3,2(p+2) and M.sub.p+3,1=M.sub.p+2,2(p+2).
Hence, four separate pair-wise measurements are made by
transmitting from the elements 1 and 2(p+2) and receiving both
transmissions on the elements p+2 and p+3. The four measurements
can be combined as a ratio to obtain,
C p + 2 , p + 3 R ' ( 0 ) = .+-. M p + 2 , 1 ' R ( 0 ) M p + 2 , 2
( p + 2 ) ' R ( 0 ) M p + 3 , 1 R ' ( 0 ) M p + 3 , 2 ( p + 2 ) ' R
( 0 ) = .+-. u p + 2 u p + 3 ( 12 ) ##EQU00008##
[0033] This complex calibration ratio ties together the sub-array
of even and odd elements. This ratio has a sign ambiguity, which
can be solved by predicting the radiation pattern. The far-field
radiation pattern will have a null on broadside if the wrong sign
is selected. Once all transfer functions have been measured, the
even elements can be referenced to the first odd element by using
the following expression,
C 1 , n ' R ( 0 ) = C 1 , p_ ( 5 - k ) / 2 ' R ( 0 ) C p + 2 , p +
3 ' R ( 0 ) k C 2 , p + ( 5 + k ) / 2 ' R ( 0 ) C 2 , n ' R ( 0 ) ;
k = { - 1 , for even p 1 , for odd p n = 4 , 6 , 8 , ( 13 )
##EQU00009##
[0034] The results can be used in (5) to determine the complex
states to be set in the T/R modules in the receive mode. The
calibration in the transmit mode is the same as was described for
the receive mode, except that the words "transmit" and "receive"
are interchanged.
Test Array Description
[0035] The technique was tested in a planar electromagnetic (EM)
simulator (Ansoft Designer.RTM. available from ANSYS, Inc. of
Cannonsburg, Pa. 15317) using an 8.times.8 element linear array,
having 8 column sub-arrays of 8 elements. Each sub-array contained
intentional random amplitude and phase errors in the feed. The
maximum number of realizable spacing elements of this particular
array is 2 (p=0 to p=1). In addition, to validate the technique in
large numbers of realizable spacing elements, a 1.times.32 element
microstrip patch linear array antenna with intentional errors in
the feed was simulated. Calibrations with eight different spacing
elements are realizable in this array (p=0 to p=7). The
measurements of mutual coupling in both arrays were obtained from
the coupling coefficients of the simulated S-parameter matrix,
M'.sub.m,n(0)=S(m,n). Because the array antenna is passive, the
hardware differences for transmit and receive modes are the same,
but the implementable calibration ratios are completely different
if different excitation functions are used in each mode.
Results
[0036] The linear array of 8 columns of 8 elements was simulated in
a 2.5D EM simulator (Ansoft Designer.RTM.). The obtained coupling
coefficients were used in (5) to calculate the calibration ratios
and the excitation function; these results are later used to
predict the array far-field radiation pattern without calibration.
FIG. 5 shows a good agreement between the simulated and predicted
array far-field radiation pattern, the results also show how the
hardware differences degrade the sidelobe levels and affect the
beam position. Once the calibration ratios are determined, the
array can be calibrated in both transmit and receive modes. FIG. 6
shows an azimuth pattern for a -30 dB Chebyshev distribution: a
very good match is obtained for the main lobe and the sidelobes. To
test the efficiency of this technique in large numbers of spacing
elements, a 1.times.32 microstrip linear array with excitation
errors was simulated. The obtained mutual coupling matrix was used
to calculate the calibration rations for eight different numbers of
spacing elements (p=0 to p=7). FIG. 7 shows the simulated radiation
patterns after the alignment and calibration of the array with a 25
dB Taylor weighting and using three different spacing elements
(p=1, p=3 and p=7). The radiation patterns are almost the same as
are expected in a calibrated array, while the sidelobe level is -25
dB in the three cases indicating the errors due the calibration
technique are tolerable in this array.
[0037] FIG. 8 shows a system that can be used to accomplish the
method. System 40 for calibrating array 42 comprises network
analyzer 44 that sends, receives and analyzes test signals, and
computer 46 that controls network analyzer 44 and is used to make
the necessary calculations.
Non-Linear Arrays
[0038] The calibrations can also be performed on non-linear arrays,
including square, rectangular, rhombic and parallelogram arrays,
for example. Square and rectangular arrays can be calibrated by
separately calibrating each row and one column of the array.
Rhombic and parallelogram arrays can be calibrated in similar
manners, as would be apparent to those of skill in the field, via
separate calibration of diagonal rows of regularly-spaced
elements.
[0039] Other embodiments will occur to those skilled in the art and
are within the scope of the claims.
* * * * *