Note: Descriptions are shown in the official language in which they were submitted.
CA 02946011 2016-10-21
METHOD AND APPARATUS FOR PHASED ANTENNA ARRAY
CALIBRATION
FIELD OF THE INVENTION
[0001] The present invention pertains to the field of radio antennas and in
particular to a
method and apparatus for calibrating a phased antenna array.
BACKGROUND
[0002] A phased antenna array system includes a group of antennas being used
for signal
communication through transmission and reception of electromagnetic waves. In
a typical
implementation, each antenna is connected to a phase shifter and an amplifier,
which
control the phase and amplitude of the radiated electromagnetic wave for that
antenna.
Changing the amplitudes and phases of the signals feeding the array's
different antennas
leads to changes in the far field radiation pattern of system. The beam of the
phased array
can therefore be controllably directed.
[0003] Precise controlling of the array's amplifiers and phase shifters is
important for
altering the radiation pattern in terms of power level and beam direction.
However,
practical considerations, such as physical limitations, environmental
conditions and
fabrication process variations, impose unwanted errors on the amplitude and
phase response
of these components, resulting in non-ideal behaviour. Imperfections can also
exist in the
antenna feed network which is responsible for dividing the input power and
distributing
signals to antennas. Furthermore, the geometrical parameters such as the
location of
fabricated antennas are subject to error. Calibration can be used to
counteract such
imperfections and is considered to be an important part of the operation of a
phased array
system. Having a priori knowledge about the antennas radiation
characteristics, calibration
can provide information on various system parameters such as the phase and
amplitude
response of electrical components and the location of antennas.
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CA 02946011 2016-10-21
[0004] Some existing calibration methods are based on changing the value of
phase
shifters for every single element sequentially, and maximizing the power
received (for
transmitting mode) or transmitted (for receiving mode) by one or an array of
external
reference antennas, which are typically located at a distance from the array.
The values of
phase shifters corresponding to the maximum received (transmitted) powers
determine the
offset to be applied to each phase shifter and amplifier. Other calibration
methods control
both the amplitude and phase of the radiated field for every phase shifter or
antenna.
- Through applying the control signal, the phase responses of the array's
component antennas
are obtained.
[0005] However, performing these measurements for an array with large number
of
antennas can be a time consuming process, particularly because calibration is
typically
required to be done at least once for each element. Furthermore, from a system
identification point of view, existing methods do not provide more detail on
other unknown
parameters of the system such as the geometrical parameters.
[0006] Therefore there is a need for a method and apparatus for phased antenna
array
calibration, that is not subject to one or more limitations of the prior art.
[0007] This background information is provided to reveal information believed
by the
applicant to be of possible relevance to the present invention. No admission
is necessarily
. intended, nor should be construed, that any of the preceding information
constitutes prior
art against the present invention.
SUMMARY
[0008] An object of embodiments of the present invention is to provide a
method and
apparatus for phased antenna array calibration. In accordance with embodiments
of the
= present invention, there is provided a method for calibrating an antenna
array comprising a
plurality of antennas in a two-dimensional arrangement, each of the antennas
operatively
coupled to a respective controllable phase shifter, the method comprising:
exciting the
antennas according to a sequence of excitation patterns, each of the
excitation patterns
defining a plurality of phases to be applied by the phase shifters during
concurrent
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CA 02946011 2016-10-21
excitation of the antennas, wherein the plurality of phases correspond to
phase values of a
basis function of a two-dimensional discrete Fourier transform, and wherein
each of the
excitation patterns is associated with a different basis function of the two-
dimensional
discrete Fourier transform; monitoring output of a calibration antenna to
provide a sequence
. of measurements, each measurement of the sequence of measurements indicative
of
response of the calibration antenna due to a superposition of radiated fields
of the antennas
excited according to a corresponding one of the excitation patterns; obtaining
indications of
radiated fields of the antennas based on the sequence of measurements, the
indications
corresponding to values of an inverse two-dimensional discrete Fourier
transform applied to
the measurements; and calibrating the antenna array based on the indications
of radiated
fields of the antennas.
[0009] In accordance with other embodiments of the present invention, there is
provided
a calibration apparatus for an antenna array having a plurality of antennas in
a two-
dimensional arrangement, each of the antennas operatively coupled to a
respective
controllable phase shifter, the calibration apparatus comprising: a
calibration antenna
configured to generate an electrical signal in response to radiated fields
generated by the
antennas; a calibration controller configured to: cause excitation of the
antennas according
to a sequence of excitation patterns, each of the excitation patterns defining
a plurality of
phases to be applied by the phase 'shifters during concurrent excitation of
the antennas,
wherein the plurality of phases correspond to phase values of a basis function
of a two-
dimensional discrete Fourier transform, and wherein each of the excitation
patterns is
associated with a different basis function of the two-dimensional discrete
Fourier transform;
monitor output of the calibration antenna to provide a sequence of
measurements, each
measurement of the sequence of measurements indicative of response of the
calibration
antenna due to a superposition of the radiated fields of the antennas excited
according to a
corresponding one of the excitation patterns; obtain indications of radiated
fields of the
antennas based on the sequence of measurements, the indications corresponding
to values
of an inverse two-dimensional discrete Fourier transform applied to the
measurements; and
calibrate the antenna array based on the indications of radiated fields of the
antennas.
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[0010] In accordance with other embodiments of the present invention, there is
provided
a phased antenna array comprising the calibration apparatus as described
above.
BRIEF DESCRIPTION OF THE FIGURES
[0011] Further features and advantages of the present invention will become
apparent
from the following detailed description, taken in combination with the
appended drawings,
in which:
[0012] FIG. 1 illustrates a phased antenna array system and calibration
apparatus,
according to embodiments of the present invention.
[0013] FIG. 2 illustrates a method for calibrating a phased antenna array
system,
according to embodiments of the present invention.
[0014] FIG. 3 illustrates another phased antenna array system and calibration
apparatus,
- according to embodiments of the present invention.
[0015] FIGs. 4A and 4B illustrate operations related to calibrating a phased
antenna array
system, according to embodiments of the present invention.
[0016] It will be noted that throughout the appended drawings, like features
are identified
by like reference numerals.
DETAILED DESCRIPTION
[0017] Embodiments of the present invention provide for the comparatively
reliable,
accurate and fast calibration and system identification for phased array
antenna systems,
involving significantly fewer measurements and less complexity than existing
approaches.
[0018] An object of present invention is to provide a method and apparatus for
calibrating
a phased antenna array system based on measurements at a single point, namely
the
=
location of a calibration antenna, also referred to as a sensor. The
calibration antenna may
be located close to the antenna array, for example within or adjacent to the
array. The
calibration procedure provides estimates of the phase and amplitude responses
of electrical
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CA 02946011 2016-10-21
components (e.g. electronic beam-forming components) of the phased array
system. The
calibration procedure can additionally indicate the errors associated with the
feeding
network and geometrical errors associated with the positioning of antennas.
[0019] FIG. 1 illustrates a phased antenna array system and calibration
apparatus
according to an embodiment of the present invention. The antenna array
includes a
plurality of antennas 110 in a two-dimensional arrangement. For clarity, the
antennas 110
are shown as being arranged in a regular grid on a flat surface. However,
other antenna
arrangements, such as antennas disposed on a curved surface and/or a staggered
or irregular
distribution of antennas can also be accommodated. The antennas may form a
conformal
array (i.e. an array conforming to a predetermined flat or curved surface).
Each of the
antennas 110 is operatively coupled to a respective controllable phase shifter
112, and
- typically also to a controllable variable gain amplifier 114.
[0020] In some embodiments, each antenna is coupled to a different phase
shifter. In
some embodiments, each antenna is coupled to a different variable gain
amplifier.
Therefore, for an array of MxN antennas, a branched antenna feed network can
terminate in
MxN branches, each associated with a different antenna and having its own
phase shifter
and variable gain amplifier. In other embodiments, a single phase shifter (and
variable gain
amplifier) can be shared by plural antennas. In this case, embodiments of the
present
invention can be understood by regarding the plural antennas sharing a phase
shifter as
being a single compound antenna having multiple elements.
[0021] The calibration apparatus includes a calibration antenna 120 configured
to
generate an electrical signal in response to radiated fields generated by the
antennas 110
due to excitation thereof. The calibration apparatus further includes a
calibration controller
130 which is operatively coupled to the antenna array and to the calibration
antenna. In
particular, the calibration controller 130 is configured to cause a
radiofrequency signal to be
fed to the antennas 110, and to cause the phase shifters 112 and variable gain
amplifiers 114
to adjust the radiofrequency signal by imparting gains and phase shifts which
are specified
by the calibration controller 130. In some embodiments, the calibration
controller is
directly coupled to a feed network of the antenna array and to control inputs
of the phase
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shifters 112 and variable gain amplifiers 114. In some embodiments, the
calibration
controller is operatively coupled to existing antenna control electronics 105
which perform
the antenna array excitation, phase shifter control and variable gain
amplifier control. In
the latter case, the calibration controller transmits control signals to the
antenna control
. electronics to cause the desired manner of operation.
[0022] In various embodiments, processing electronics 125, such as
radiofrequency and
baseband processing electronics, are either included in the calibration
controller 130 or
interposed between the calibration antenna 120 and the calibration controller
130. The
processing electronics receive and process the signal from the calibration
antenna, for
example by partially or fully demodulating the received signal of the
calibration antenna
- and performing other operations such as signal conditioning, quantization,
filtering, phase
discrimination, and the like, as would be readily understood by a worker
skilled in the art.
[0023] In more detail, the calibration controller 130 is configured to
(directly or
indirectly) cause excitation of the antennas 110 according to a sequence of
excitation
patterns. Each of the excitation patterns defines a plurality of phase shifts
(phases) to be
applied by the phase shifters 112 during concurrent excitation of multiple
ones of the
antennas 110. The phase shifts are applied for example to a common
radiofrequency signal,
such as a sinusoidal signal, which is fed (e.g. via a feed network of the
antenna array) to the
antennas 110 being excited by the current excitation pattern. Notably, the
pattern of
relative phase shifts correspond to phase values of a basis function of a two-
dimensional
discrete Fourier transform. Furthermore, each of the excitation patterns in
the sequence is
associated with a different basis function of the two-dimensional discrete
Fourier transform.
. The gains of variable gain amplifiers 114 can also be set by the calibration
controller 130
and/or antenna controller 105.
[0024] In various embodiments, each of the plurality of excitation patterns
corresponds to
a different two-dimensional discrete index value (k,l) between (1,1) and
(K,L). In various
embodiments K=M and L=N. In this case, for each of the index values (k,1), the
basis
function associated with the excitation pattern corresponding to the index
value (k,l) is a
= ---)27r1Ink
nl
two-dimensional function over discrete variables (m,n) given by: e N).
This is a
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CA 02946011 2016-10-21
typical basis function associated with the two-dimensional discrete Fourier
transform.
Each phase value, to be applied by a phase shifter, is given as the phase
angle of the
corresponding basis function for a given (m,n,k,1).
[0025] In various embodiments, the discrete variables (m,n) correspond to two-
dimensional indices associated with the antennas in the MxN array. The indices
may
. correspond to antenna spatial positions. For example, the variable (m,n) may
denote that
the corresponding antenna element is located in the /nth row and nth column of
a two-
dimensional antenna array having its antennas arranged in a grid of M rows and
N columns.
[0026] The calibration controller 130 is further configured to monitor output
of the
calibration antenna to provide a sequence of measurements. Each measurement of
the
sequence indicates an electrical response of the calibration antenna due to
placement in a
- superposition of the radiated fields of the antennas of the array. As
already noted, the
radiated fields in turn are due to antenna excitation according to a
corresponding one of the
excitation patterns. As each measurement is received, it may be stored in an
electronic
memory 132 of the calibration controller, for subsequent retrieval and
processing.
[0027] In some embodiments, the electrical response of the calibration antenna
is, is
assumed to be, and/or is filtered to provide, a sinusoidal signal. In some
embodiments, the
= electrical response may provide, or may be filtered to provide, a
narrowband signal having
a particular amplitude and phase. As such, some or all measurements of the
sequence of
measurements may indicate amplitude and phase of a sinusoidal electrical
signal provided
by the calibration antenna due to its response to the superposition of
radiated fields. The
phase of this signal is relative to the common sinusoidal signal used to
excite the array
antennas. In various embodiments, the same sinusoidal radiofrequency signal
used to
. excite the antennas (or a replica thereof) is also used for demodulating the
signal as
received by the calibration antenna, for example by multiplying the received
signal together
with this radiofrequency signal and low-pass filtering the result, as would be
readily
understood by a worker skilled in the art.
[0028] The calibration controller 130 is further configured to obtain
indications of
radiated fields of the antennas at a spatial location which corresponds to the
location of the
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CA 02946011 2016-10-21
calibration antenna. The indications are obtained based on the sequence of
measurements,
and may be obtained after all members of the sequence of excitation patterns
have been
applied and the corresponding measurements obtained. Obtaining the indications
may
- therefore include retrieving the stored measurements from memory for
processing.
Alternatively, a recursive function may be used to process the measurements as
they are
obtained. The recursive function may be stored in memory and updated as
measurements
are obtained. The indications are related to the sequence of measurements in
that the
indications correspond to values of an inverse two-dimensional discrete
Fourier transform
applied to the measurements.
[0029] In some embodiments, the indications of the radiated fields are
determined by
computing an inverse two-dimensional discrete Fourier transform on the
measurements, for
example using a processor included in the calibration controller. Various
algorithms can be
used to perform such computations, with the selected algorithm adequately
trading off
efficiency versus accuracy. In some embodiments, inverse two-dimensional
discrete
Fourier transform values corresponding to possible measurements may be pre-
computed
and stored in a lookup table, and the indications may be derived by a lookup
table operation
specifying the current measurements. In some embodiments, the indications may
be
obtained by performing computations by a microprocessor 134 executing program
instructions stored in memory. In some embodiments, the indications may be
obtained by
operation of a digital and/or analog electronic circuit configured to receive
electrical signals
indicative of the measurements and to output electrical signals indicative of
the indications.
- [0030] In various embodiments, computing the inverse two-dimensional
discrete Fourier
transform of the sequence of measurements is then performed as follows. For
each index
value (k,1), a corresponding spectral domain coefficient F(k,l) is set as
equal to (or
approximately equal to) a corresponding one of the sequence of measurements
obtained due
to the (k,/)th excitation pattern. The inverse two-dimensional discrete
Fourier transform of
a two-dimensional function having values F(k,l) is then computed or otherwise
obtained.
[0031] The calibration controller 130 is further configured to calibrate the
antenna array
based on the indications of radiated fields of the antennas (as obtained via
the inverse
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Fourier transform relationship). For a given antenna, the obtained indication
may be
indicative of the relationship between an input signal to the antenna and the
signal as
received by the calibration antenna due to the input signal. The relationship
may include
phase and amplitude differences between the input signal and the signal as
received. The
indication may be provided as or correspond to a complex transfer function,
for example.
In some embodiments, this relationship or transfer function can be compared to
a desired or
idealized relationship or transfer function, and a correction factor can be
derived from the
comparison. The correction factor may indicate the amount of phase shift, gain
variation,
or other pre-distortion that should be applied to the input signal so that the
input/output
relationship (or transfer function) more closely matches a desired
relationship (or transfer
function). The antenna array is then calibrated by adjusting the phase
shifters and variable
gain amplifiers (or other pre-processing elements) so as to apply the
determined correction
factor.
[0032] Computation of the correction factors may be performed by a
microprocessor of
the calibration controller executing stored program instructions, or via a
lookup table
operation which provides pre-computed correction factors for given indications
of radiated
fields, or by other digital and/or analog electronic circuits configured to
provide correction
factors, or the like.
[0033] The desired relationships or transfer functions to which the observed
indications
are compared may be pre-defined based on models, experimental measurements, or
a
combination thereof. For example, electromagnetic modeling software and/or
anechoic
chamber measurements may be used to determine the desired transfer function
indicative of
the relationship between the input to a feed network of the array and the
output of the
calibration antenna, when a single identified antenna of the array transmits.
The
relationship may be parameterized by gain and phase differences between the
input and
output signals.
[0034] In view of the above, FIG. 2 illustrates a method for calibrating an
antenna array,
according to an embodiment of the present invention. The antenna array
comprises a
plurality of antennas in a two-dimensional arrangement, and each of the
antennas is
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CA 02946011 2016-10-21
operatively coupled to a respective controllable phase shifter. The method
includes
exciting 210 the antennas according to a sequence of excitation patterns. Each
of the
excitation patterns defines a plurality of phases to be applied by the phase
shifters during
concurrent excitation of the antennas. The phases correspond to phase values
of a basis
function of a two-dimensional discrete Fourier transform (2D DFT). Each of the
excitation
patterns is associated with a different basis function of the two-dimensional
discrete Fourier
transform. The method further includes monitoring 220 output of a calibration
antenna to
provide a sequence of measurements. Each measurement of the sequence of
measurements
indicates of response of the calibration antenna due to a superposition of
radiated fields of
the antennas excited according to a corresponding one of the excitation
patterns. The
method further includes obtaining 230 indications of radiated fields of the
antennas based
on the sequence of measurements, the indications corresponding to values of an
inverse
two-dimensional discrete Fourier transform applied to the measurements. The
indications
may be obtained via computation, table lookup operation, or the like. The
method further
includes calibrating 240 the antenna array based on the indications of
radiated fields of the
antennas.
- [0035] Having generally described embodiments of the present invention,
further details
will now be described.
[0036] FIG. 3 illustrates a phased array antenna with built-in calibration
antenna 310,
according to another embodiment of the present invention, and which will be
referred to in
the discussion below. For clarity, only some antennas, and their corresponding
phase
shifters and amplifiers, are shown.
[0037] As set forth above, embodiments of the present invention comprise
exciting each
individual antenna 320 or a group of antennas 320 with predefined excitation
patterns
sequentially and measuring the amplitude and phase of radiated field for each
excitation
pattern using the built-in calibration antenna. Referring to FIG. 3, each
excitation pattern is
defined as a group of state signals being used to change the state of the
antennas, each by a
specific phase P 360 (and in various embodiments also by a specific amplitude
V 355). The
phases P 360 can be applied by corresponding phase shifters 362 and the
amplitudes V 355
CA 02946011 2016-10-21
can be applied by corresponding amplifiers 357. A calibration controller 330
may provide
- the amplitude and phase information 355, 360 for setting the amplitudes and
phases.
[0038] In some embodiments, excitation patterns are based at least in part on
a priori
knowledge of radiation patterns of antennas in presence of the other elements
and the
calibration antenna and also the radiation pattern of calibration antenna
obtained by
electromagnetic (numerical) solvers or anechoic chamber measurements. For
example,
either the electromagnetic solvers or anechoic chamber measurements can be
employed to
= obtain the radiation characteristics of both the phased array antennas
and/or the calibration
antenna, separately. This approach may also be used to calculate the effect of
calibration
antenna on the radiation of antenna elements and vice-versa. In this regard,
the calibration
antenna may be located at the predefined position near the phased array
structure and the
couplings between all different elements can be measured or simulated.
[0039] In various embodiments, following application of the excitation
patterns at the
antennas and the obtaining of measurements using the calibration antenna, each
antenna's
radiated electric field (denoted as f 365 in FIG. 3) at the location of
calibration antenna is
computed, and unknown system parameters are estimated. As such, the
calibration antenna
may be disposed in the near-field of the array. In various embodiments, the
far-field
radiation pattern can be determined based on near-field measurements. The
computation
and estimation are performed by the calibration controller 330 based at least
in part on the
= obtained measurements along with knowledge of the applied excitation
patterns.
[0040] It is noted that the calibration antenna may be in the near-field of
the phase array
system as a whole. However, at the same time, the calibration antenna may also
be located
at the far-field of each antenna (element) of phased array system.
[0041] The computed antenna electric fields and estimated system parameters
are referred
to as calibration information. The calibration information can be used in
order to adjust
phased antenna array operation, for example by applying appropriate correction
factors to
amplifiers and phase shifters of the array, for example located in the feed
network.
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CA 02946011 2016-10-21
[0042] In various embodiments, calibration occurs repeatedly over time, for
example on a
periodic basis. Notably, the number of excitation patterns applied can vary
between
different repetitions of the calibration procedure. For example, an initial
calibration may
apply a greater number of excitation patterns, for example equal to the number
of possible
data points in the discrete two-dimensional Fourier transform of the two-
dimensional
function f. Once the system is initially calibrated, subsequent recalibration
operations can
involve a selected number of excitation patterns which is less than the total
number of
excitation patterns applied during initial calibration.
Excitation Patterns
. [0043] As mentioned above, embodiments of the present invention comprise
exciting
selected antennas of the phased antenna array using a sequence of excitation
patterns. If an
=
antenna is to remain unexcited during a particular excitation pattern, the
gain of the variable
gain amplifier can be set to zero for that particular antenna, for example.
[0044] Some or all excitation patterns of the sequence are used to excite the
antennas of
the phased array. Each excitation pattern is defined by a selected set of
antennas and the
- control signals used to excite each member of the selected set of antennas
with a specified
phase and amplitude. The sequence of excitation patterns may be applied in an
arbitrary
order.
[0045] In some embodiment, the specified amplitude varies between antennas. In
some
embodiments, the specified amplitude is the same for all antennas. In some
embodiments,
the specified amplitude is zero for some antennas (i.e. antennas which are to
be refrained
from being excited) and nonzero for other antennas. The nonzero values can be
the same
for all antennas. In various embodiments, a group of antennas (e.g. 10 to 30
antennas of a
large array) are excited at a time.
[0046] According to embodiments of the present invention, the excitation
patterns being
used belong to a particular group of patterns, namely patterns which provide
the spectral
information of radiated fields of the array's antennas.
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CA 02946011 2016-10-21
[0047] For example, an antenna array may include antennas arranged according
to a
planar grid pattern, as illustrated in FIG. 3. The grid includes M rows of
antennas, indexed
from zero to M-1, and N columns of antennas, indexed from zero to N-1. The
antenna in
the ,nth row and the nth column is designated by the label [in, n]. The phasor
representation
of the received signal due to the radiated field of antenna [m, n], as
observed at the location
of the calibration antenna (sensor) is denoted by f[in, n]. That is, Amdi] is
a complex
number incorporating the amplitude and phase of the radiated field of [in,
11th element of
the antenna array at the location of calibration antenna.
[0048] Under these conditions, it is noted that the two-dimensional discrete
Fourier
transform of the two-dimensional functionftm,n] takes the form:
rnknl
F [k , 1] = ":10Nfj, f [m, -12" m N ). (1)
[0049] In various embodiments, f[m, n] = aninejq'mn and is a complex number
incorporating the amplitude and phase of received signal due to radiated field
of [777,411
element at the location of calibration antenna. This
can also be expressed as
a cos(cort + yonin) in the time domain representation.
[0050] The antenna array's phase shifters are set (via control signals) for
values
mk n1)
corresponding to phase shifts of ¨27r (¨M + ¨N with 1 and k being constant
(for a given
excitation pattern) and m and n varying with antenna location. The VGAs of the
different
antennas can be set to a common gain.
Obtaining Measurements via Calibration Antenna
[0051] The calibration antenna measures a signal due to a superposition of
radiated fields
of all of the excited antennas at the location of the calibration antenna. In
various
embodiments, the amplitude and phase of this signal provides the value of the
Fourier
. transform at the [k, l]th point corresponding to a particular [x, y]
coordinate in the spectral
domain. Namely, the coordinate in the spectral domain has x value Fr = k and y
value
F = 1
Y N
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CA 02946011 2016-10-21
=
[0052] In some embodiments, the measurements provided by the calibration
antenna can
be obtained by using the same sinusoidal reference signal used in the
transmitter to feed the
antennas as the local oscillator in the receiver antenna to down-convert the
received signal
for phase and amplitude extraction (see FIG. 3). To do so, a number Nt x Ns of
samples are
collected by the receiver, so as to obtain Ns samples from each of Nt periods
of received
signal, given by eikicos(cort+Cfikt). The
received signal eikicos(wrt-Fep ki) is denoted
F[k, 1] = aktexp(jCpkt) (Eq. (1)). The received signal (like f[m,n]) is a
complex number
incorporating the amplitude and phase of [k,/]th element of the two-
dimensional discrete
Fourier transform.
[0053] In more detail, the calibration antenna receives the summation of
signals due to all
antenna elements excited and radiating according to the current excitation
pattern. The
signal received by the calibration can be represented in phasor form by F[k,1]
which is as
specified in Equation (1). F is the discrete Fourier transform off. The
calibration receiver
measures the phase and amplitude of the received signal: eikicos(cort+(pkt)
which, in the
phasor form, gives F[k, 1] = ki exp(J(Pkt). One way to determine the phase and
amplitude
is by taking Ns. samples from Nt periods of received signal:
akicos(cort+Cpki).
[0054] It is noted that the received signal, being a summation of sinusoidal
signals having
- the same frequency (but different amplitudes and phases), is also a
sinusoidal signal. This
can be demonstrated by the following equation:
lilicos(wt + (pi) -- RefAiej(wt-kPi)1 ¨ RetisA
ei(wt) = RetAej(T)ej(wt)}
¨
t=i i=i i=1
= Acos(wt + (p) .
Here,
A el (`P) = i(Aiej(`P,)).
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Obtaining Indications of Radiated Fields
[0055] Performing the total number of MxN measurements for all [k,li points in
the
- spectral domain, the discrete two-dimensional Fourier transform F of the two
dimensional
discrete signal f is obtained. Taking the inverse Fourier transform, the f [m,
n] values are
obtained as:
/14-. N-1,
mk n1
f [m n] = > >F [k , l]e'ILTE M N (2)
k=0 l=0
= [0056] As mentioned above, f [m, n] indicates the radiated field (e.g.
amplitude and phase
thereof) of each antenna, as observed at the location of the calibration
antenna. This value,
in general, is different from the radiated field of an ideal (calibrated)
antenna. For instance,
the [m,n]th element's phase response to the control signal, for ¨21-r (¨mk
¨111) phase shift, is
M N
not necessarily equal to ¨2n (n4 + 11+11). The phase response depends on the
initial phase of
the components and is subject to unavoidable drifts. The differences between
ideal and
actual phase are absorbed in the coefficients of the f [m, n] values. One of
the purposes of
calibration is to extract these differences for all antenna elements. The
differences can be
then be applied as offset signals (correction factors) for adjusting the phase
shifters.
[0057] As such, instead of directly measuring the radiated field of each
antenna (f[m, n])
sequentially by turning on one antenna at a time, a spectral sampling scheme
is employed.
The applied excitation patterns involve multiple (e.g. all) antennas being
excited
simultaneously with a particular phase shift distribution. Each applied
excitation pattern
includes a different phase shift distribution, and corresponds to one point in
the spectral
domain representation of signal of interest.
[0058] A first potential advantage of this approach is that, because all
antennas are
radiating, the signal to noise ratio (SNR) at the calibration antenna (sensor)
may be
= significantly enhanced, as compared to the SNR in other methods in which
only one
antenna is excited at a time for each measurement.
15
CA 02946011 2016-10-21
Spectral Sampling
[0059] A second potential advantage of this approach is as follows. For
perfectly
calibrated systems, or systems slightly different from the calibrated systems,
a considerable
number of spectral coefficients become fairly small as compared to the rest of
the
coefficients. This leads to a potentially significant reduction in the number
of necessary
measurements, because the excitation patterns which correspond to negligible
values of
F[k,1] can be skipped. This approach may be used for a variety of phased array
systems, for
example which employ antennas with high directivity. This accelerates the
process of
recalibrating the systems which have been calibrated once before and small
correcting
changes are expected to be applied to the phase shifters and amplifiers.
[0060] Depending on the radiation pattern of each antenna, which may be the
same as
other antennas, and the distance of the calibration antenna from the plane of
phased array
antennas, the spectral information of the radiated field changes. When the
location of
antennas and the calibration antenna are fixed, the spectral domain features
such as the
location of non-zero coefficients of discrete Fourier transform in spectral
domain may also
be fixed. In other words, the [k,1] values corresponding to these coefficients
may be
substantially known (for calibrated systems). Therefore, there is little or no
need to excite
the patterns associated with coefficients having values close to zero or very
small compared
to other coefficients. This property is useful for example when the errors in
phase shifters
or amplifiers are bounded to certain limits. Otherwise, proper identification
of the system
may require excitation of the array antennas according to all of the (MxN)
defined
excitation patterns, in order to measure all spectral coefficients. This is
typically the case
for systems which have not been calibrated before.
[0061] In various embodiments, therefore, the antenna array is excited using a
sequence
of excitation patterns which belong to a strict subset of all applicable
excitation patterns.
The applicable excitation patterns correspond to those discrete values of k
and 1 for which
the coefficients of the Fourier transform function F[k,1] are defined. For the
two-
dimensional array with MxN antennas, there are also MxN applicable excitation
patterns
(since in and k can take on integer values from 1 to M and n and I can take on
integer values
16
CA 02946011 2016-10-21
from 1 to N). Exciting the antenna array using a strict subset of the
applicable excitation
patterns therefore means that fewer than MxN excitation patterns are applied.
[0062] In particular, excitation patterns can be selected for inclusion in the
subset based
= on the predicted value of their corresponding coefficients FR,11. For
example, when a
coefficient is expected to be greater than a predetermined threshold value,
then the
corresponding excitation pattern is included in the subset. As another
example, the size of
the subset can be set at a value Q which is less than the total number of
applicable
excitation patterns. The excitation patterns corresponding to the Q highest
coefficients can
then be included in the subset. The size of the subset can be set (e.g. by
setting the
threshold value or value Q) based on various considerations, for example in
order to trade
off calibration speed and accuracy. A smaller subset results in a shorter
calibration time,
because fewer excitation patterns are applied. However, accuracy of the
calibration
depends on the excluded excitation patterns corresponding to sufficiently
negligible Fourier
coefficients, which in turn depends on accurate prediction of the coefficient
values.
Therefore, the expected prediction accuracy should be taken into account when
configuring
the subset; when expected prediction accuracy is high, the subset size may be
increased,
whereas when expected prediction accuracy is low, the subset size may be
decreased.
Expected accuracy may depend on factors such as elapsed time since last
calibration,
changes in environmental conditions such as temperature, movement of the
antenna array,
or the like.
[0063] In various embodiments, the number of excitation patterns Q<MxN used is
selected so as to measure a selected number Q of samples of the discrete
Fourier transform
F(.) of the two dimensional function f(.). As already mentioned, ft-) is a
mapping from
two-dimensional values (m,n) to a complex value indicative of the amplitude
and phase of a
signal received at the calibration antenna due to the field radiated by the
antenna having
index [m,n]. The complex value given by f(m,n) is proportional to the radiated
field of
antenna element evaluated at the location of the calibration antenna. The
process of
measuring the Q samples can be considered to be a form of spectral sampling.
=
17
CA 02946011 2016-10-21
[0064] FIGs. 4A and 4B illustrate pre-calibration, calibration and
recalibration operations
according to an embodiment of the present invention. Referring now to FIG. 4A,
pre-
calibration 405 comprises obtaining information regarding the array antennas
and the
calibration antenna and their combination in the given phased array
configuration. This
may be performed using simulation, electromagnetic solvers, anechoic chamber
measurements, or the like. The information obtained from pre-calibration 405
may include
the observed and/or desired radiation patterns of antennas for both the phased
array system
and the calibration antenna. The pre-calibration information can then be used
in the
calibration and recalibration operations. Pre-calibration 405 may be performed
once, for
example during manufacture or prior to or during antenna array deployment. The
first time
the calibration operation 410 is performed after pre-calibration 405 is
referred to as the
initial calibration. Subsequent calibration operations 410 are referred to as
re-calibration
470.
[0065] The calibration operation 410 includes obtaining measurements 415 and
subsequently performing error estimation 460.
[0066] In various embodiments, obtaining measurements 415 comprises a number
of sub-
operations described as follows, with reference now to FIG. 4B. In an
initialization
operation 420, a number Q of excitation patterns are selected and an index
variable q is set
equal to 1. As described above, each excitation pattern can be defined by a
pre-specified
phase assigned to each antenna element. The phases can be set via control
signals applied
to the array's phase shifters, and also, in some embodiments, by a pre-
specified amplitude
assigned to each antenna element. The amplitudes can be set via control
signals applied to
the array's variable gain amplifiers.
[0067] Next, the antennas are excited according to the excitation patterns and
the output
of the calibration antenna is monitored to provide a sequence of measurements.
Starting
with the first excitation pattern, i.e. corresponding to q=1, and repeating
for q=2,3,4...Q,
the antennas are excited according to each excitation pattern sequentially, by
applying 425
suitable control signals to the array phase shifters (and VGAs) for each
antenna in order to
adjust the amplitudes and phase shifts in accordance with the current
excitation pattern (and
18
CA 02946011 2016-10-21
also applying a radiofrequency reference signal to which is adjusted by the
VGAs and
phase shifters and excites the antennas.
[0068] In addition, a number of samples received by the calibration antenna
are collected
430, the samples indicative of the calibration antenna response to the current
excitation
pattern. In one embodiment, taking Ns x Nt samples are obtained as described
above, for
example using an in-phase/quadrature receiver. Further, data such as the
amplitude and
phase of the received signal is extracted 435 (determined) based on the
samples, and the
results stored in memory in association with the current excitation pattern.
The next
excitation pattern is then applied and the above steps 425, 430, 435 are
repeated until all Q
excitation patterns have been applied.
[0069] Following application of all Q excitation patterns, indications of
radiated fields of
the antennas can be obtained 440 (e.g. calculated or estimated) based on the
extracted and
stored data obtained due to the excitation patterns. The indications
correspond to values of
an inverse two-dimensional discrete Fourier transform applied to the
measurements, and
can be calculated via Equation (2) or via equivalent methods, such as lookup
table
operations.
[0070] The error estimation 460 comprises extracting, based on the indications
of the
radiated fields and other stored data such as pre-calibration information,
unknown system
parameters such as the phase behaviour of the array phase shifters and the
gain behaviour of
the array VGAs. Based on these parameters, the array can be calibrated or
adjusted to
operate within desired tolerances. Using the obtained indications of radiated
fields of the
antennas and previously measured or simulated information obtained from pre-
calibration,
the unknown system parameters can be obtained.
[0071] The re-calibration operation 470 comprises repeating the calibration
operation
410, for example periodically, on an as-needed basis in response to monitored
performance
metrics falling below a threshold, or in response to an environmental (e.g.
temperature)
change or other operational change over time.
19
CA 02946011 2016-10-21
[0072] Once the system is initially calibrated using the procedure described
above, the
system may be re-calibrated during normal operation, for example periodically.
However,
it is desirable to limit recalibration in order to prevent or mitigate large
service interruption.
As such, various embodiments of the present invention employ a spectrally
compressed
sampling scheme in which, instead of exciting the antennas according to all
possible
excitation patterns, a subset of all excitation patterns is selected for use
during recalibration.
[0073] The selection of excitation patterns may be based on spectral
information of
. electric field. Due to the elimination of some of the excitation patterns,
the antenna
radiation information can be obtained from the measured signals more quickly
but with a
certain level of error. In some embodiments, comparing the new calibration
data with those
of the calibrated system determines if the differences are significant enough
to increase the
number of measurements by including more excitation patterns.
[0074] The use of a subset of excitation patterns in recalibration is based on
an
= assumption of limited drift in the array calibration. Essentially, the
rate and/or amount of
drift in calibrated components such as phase shifters and VGAs is assumed to
be limited,
which allows the recalibration to be performed using fewer measurements than
the initial
calibration.
[0075] For a variety of antenna arrays, it can be shown, for example based on
the
simulation and measurement results, that the signal matrix F [k , 1] is
sparse. In other words,
a significant number of the F[k, 1] values are substantially zero or
negligible. The [k,1]
values corresponding to the locations of zeros of F can be determined based on
the
simulation and measurement results, and can be assumed to be fixed, provided
that the
radiation characteristics and the location of calibration antenna with respect
to the system is
also fixed, which is a reasonable assumption in many practical cases.
[0076] The re-calibration operation proceeds similarly to the initial
calibration operation.
The location of the most significant elements of the signal matrix F[k, 11 can
be determined,
for example based on simulation and measurement results. Based on this
knowledge, Q'
excitation patterns, which includes some of the Q excitation patterns of the
initial
calibration but also excludes others, are selected. The Q excitation patterns
are selected as
CA 02946011 2016-10-21
those corresponding to non-negligible values of the signal matrix F[k, /].
Instead of
performing Q measurements, now, Q (<Q) measurements are made, and estimates of
f[rn,n]
are obtained based on the Q' measurements. In large phased array systems, this
approach
can save significant time by reducing the required number of measurements and
excitation
patterns.
[0077] In some embodiments, different calibration or re-calibration operations
may
involve applying different sets of excitation patterns. In
the above case, the set of
excitation patterns Q' is contained in Q, however in other cases different
sets may be
disjoint or overlapping. Different calibration operations may then obtain
indications of the
antenna radiated fields based on different spectral samples. In some
embodiments, the
indications may be aggregated together, averaged, or the like.
[0078] Obtaining the indications of the antenna radiated fields based on a
spectral sample
comprising less than all possible values of F[k,1] can be performed in a
variety of ways. In
one embodiment, the indications can be obtained based on Equation (2) (or an
associated
lookup or other operation), except that the values of F[k,1] corresponding to
excitation
patterns which were not applied in the calibration or re-calibration are
replaced with zeros.
In other embodiments, the indication of antenna radiated fields can be
directly measured for
the antennas relatively near the calibration antenna. This may be the case for
those array
antennas having signals which exhibit a higher signal-to-noise ratio at the
calibration
antenna (due to proximity). In other embodiments, different excitation
patterns can be
chosen to further improve accuracy. In particular, the extraction of the
radiated signals for
each array antenna can be achieved through different linear combinations of
measured
signals, relative to the linear combination expressed in Equation (2).
[0079] The need for performing a complete calibration procedure may arise
after the
system has been operating for a long time or if for any reason there may be
large drifts in
the phase shifters or amplifiers characteristics. In this case the initial
calibration process can
be performed again.
21
CA 02946011 2016-10-21
=
Error Estimation
[0080] Having measured the spectral domain coefficients F[k, 1], the f[m,n]
values are
estimated via an inverse Fourier transform relationship, for example via
computing an
inverse Fourier transform of the measured data, as described above. Based on
prior
information regarding the radiated field of antennas, for example as
previously obtained
analytically or by using EM solvers or measurements, the actual phase shift
values and gain
values applied by the array's phase shifters and amplifiers can be estimated.
The difference
between actual and desired values can be used to adjust control of the phase
shifters and
amplifiers, thereby calibrating them.
[0081] Moreover, in some embodiments, the errors associated with positioning
of
antennas with respect to calibration antenna can be determined, at least
approximately. In
. one embodiment, the Taylor series expansion about the parameters xi, yi, zi,
AVGA,i, (PVGA,i can be made use of in determining such errors. Here, xi, yi,
zi represent the
approximate relative locations of antennas, Aps,i,copsj represent the
approximate amplitude
and phase responses of the array phase shifters, respectively, and AvGA,i, W
VGA,i represent
the approximate amplitude and phase responses of the array VGAs, respectively.
If for a
particular antenna the measured signal is denoted as f [m, n1, then:
f [m,n] = Rnin(x,y, Z, A ps, CIO ps, AvGA, (PvGA)=
akm aR aR
R,õ(xr, yinn, AmPSn,i, P PMSn,ti, AMVGnA,i, VinGnA,i a xn
AX inn Ay + mn AZ +
ay az
aRm, mõ aRmõA mm , aR,õ A _,_ a Rmn A õ mm
_________________ AA + LAC p p s aAmõ (3)
a AI" PS'VGA PVGA
"WVGAI
PS PPS VGA
[0082] In the above, R() is a complex function depending on the radiation
pattern of
calibration antenna and phased array antenna, the geometrical orientation of
antennas and
the distance between the antennas. R can be written as:
Rmõ = Amõ exp(jcpmn) Arvin (12 v G A) exp ( VnGnA (vvGA)) AlpnsTi (v p s)
exp(j(pAn (-ups)) x
Pmn(emn, (Pmn)AI gmn(enin, Tmn) expjkrrnn) (4)
4n-rmn
22
CA 02946011 2016-10-21
= [0083] where r,n = V(xmn)2 (ymn)2 (zm7-02
) and Viimn(enin, (Pmn)
and
g (0,
(pm,i) incorporate the variation of signal's amplitude associated with the
polarization mismatch and directional gain of the both transmitter and
calibration antennas
for the [m, Oh transmitter's element. Having measured or calculated Rnin for
all pairs of
phased array elements and calibration antenna, initial values for parameters
are chosen.
Equation (3) can be solved for errors iteratively for all antennas. To do so,
initially one of
- the errors to is set to an initial value and all the other errors are set to
zero. Dividing the
difference of f [m, n] and Rnin(xTnn, yfl, zimn Ampsn coprrisn,i,
AinVGnjj) by the coefficient
ahead of the unknown error, the shifting value is obtained. Next, error values
are updated
by adding their previous values to the obtained shifting value. More accurate
estimation of
error can be obtained iteratively while minimizing the absolute difference
between
f[m,n] and Rinn(xinn , yjn , , Ampsn (.0
, PIS? AnIVGnA,i, VniGn) = The same or a similar
procedure can be performed for other types of errors, while for each of them
the values of
all other errors are set to their last iteration values.
[0084] It will be appreciated that, although specific embodiments of the
technology have
been described herein for purposes of illustration, various modifications may
be made
without departing from the scope of the technology. In particular, it is
within the scope of
the technology to provide a computer program product or program element, or a
program
= storage or memory device such as a magnetic or optical wire, tape or
disc, or the like, for
storing signals readable by a machine, for controlling the operation of a
computer according
to the method of the technology and/or to structure some or all of its
components in
accordance with the system of the technology.
Non-Planar/Non-Grid Arrays
. [0085] As noted above, embodiments of the present invention are applicable
to arrays of
antennas such as antennas disposed on a planar surface in a grid pattern, or
to another
phased array antenna architecture with a different spatial arrangement of
antenna elements.
This general applicability is due to the fact that the radiated fields of any
type of radiating
object(s) or system(s), regardless of their physical configuration, can be
described in terms
of the electromagnetic fields over an arbitrary mathematical surface which
encloses the
23
CA 02946011 2016-10-21
actual radiator. The radiator may be a general conformal phased array system
in the present
invention. This observation is based upon the Electromagnetic Equivalence
Theorem (or
Huygens Principle in optics). If the mathematical surface is chosen as having
a planar form
(which is compatible with the present Fourier transform formulation) then,
provided that
the size of this planar surface is sufficiently large to capture all the
radiation from the actual
radiator, the field radiated by this mathematical planar equivalent source
will be identical to
that of the actual radiator. Furthermore, the field sampling points on this
equivalent planar
source can be chosen over a rectangular grid of points. This provides
compatibility with the
Fourier transform formulation described above. Therefore, in this manner, the
approach
described herein for a planar array can be extended to an array structure with
arbitrary
= geometry by adding a linear transformation between the actual radiator
(the general non-
planar array with a non-uniform grid) and an equivalent mathematical planar
array with a
rectangular grid.
[0086] It is further noted that the spatial arrangement of antenna elements
(i.e. whether in
a planar grid pattern or other conformal pattern) does not change the
measurement
procedure of the present invention. Thus, the excitation basis functions, the
manner of
indexing and so on, may be as described above for a variety of non-planer
and/or non-grid
arrangements of antennas. As long as the calibration probe (antenna) is
properly positioned
over the mathematical planar surface described above, the same procedure as
described
with respect to the planar grid array may be used. However, due to the
conformal
configuration of antenna elements, the measured signals may not feature some
desired
properties, such as the sparsity property of the signal matrix. In this case
the linear
- transformation described above may be used to determine the amplitudes
and/or phases of
the actual array from the amplitudes and/or phases of the mathematical array
elements, and
vice-versa. The result of this transformation provides the required excitation
pattern (both
phases and amplitudes) needed to excite the antenna elements.
[0087] As such, embodiments of the present invention comprise, for an antenna
array
having its antennas in a non-planar and/or non-grid arrangement, performing a
linear
= transformation operation in order to translate between calibration data
of the antenna array
and corresponding calibration data of an equivalent virtual antenna array
having its
24
CA 02946011 2016-10-21
antennas arranged in a planar grid arrangement. The calibration data may
include
amplitudes and phases of calibration signals used to drive the antennas,
calibration
correction factors, properties of received calibration signal components, and
the like. The
linear transformation operation may be performed by a computer, or via a
lookup table
operation, equivalent electronic circuit operation, or the like.
[0088] Acts associated with the method described herein can be implemented as
coded
instructions in a computer program product. In other words, the computer
program product
is a computer-readable medium upon which software code is recorded to execute
the
method when the computer program product is loaded into memory and executed on
the
microprocessor of the wireless communication device.
[0089] Further, each step of the method may be executed on a computing device,
such as
a microprocessor, microcontroller, personal computer, server, or the like and
pursuant to
one or more, or a part of one or more, program elements, modules or objects
generated
from a programming language, such as C++, Java, or the like. In addition, each
step, or a
file or object or the like implementing each said step, may be executed by
special purpose
hardware or a circuit module designed for that purpose.
[0090] Although the present invention has been described with reference to
specific
features and embodiments thereof, it is evident that various modifications and
combinations
. can be made thereto without departing from the invention. The specification
and drawings
are, accordingly, to be regarded simply as an illustration of the invention as
defined by the
appended claims, and are contemplated to cover any and all modifications,
variations,
combinations or equivalents that fall within the scope of the present
invention.
