Recent Patents on Engineering 2007, 1, 187-193
187
Decoupling Methods for the Mutual Coupling Effect in Antenna Arrays: A Review
Hon Tat Hui*
Department of Electrical and Computer Engineering, National University of Singapore, 10 Kent Ridge Crescent Singapore 119260,
Singapore
Received: February 9, 2007; Accepted: April 19, 2007; Revised: April 23, 2007
Abstract: Mutual coupling is a common problem in the applications of antenna arrays. It significantly affects the operation of almost all
types of antenna arrays. Over the past years, there have been many different kinds of methods suggested to decouple (or to compensate
for) the mutual coupling effect in antenna arrays. The effectiveness of these methods varied and depended upon the types of antenna
arrays being considered and the applications in which the antenna arrays were used. In this paper, a brief review of the decoupling
methods for the mutual coupling effect in antenna arrays is presented. These include patented and non-patented methods. The methods
are grouped under seven categories for antenna arrays in communications and four categories for antenna arrays in magnetic resonance
imaging (MRI). The various methods will be first briefly described and their operation principles will be explained. Then some comments
on their scopes of application and their comparisons or relations to other methods will be given. The problems associated with these
methods will also be analysed. This is the first review on this topic and we believe that it helps to give an overview of the decoupling
methods which have been so far proposed in the literature. We also believe that this review will help clarify some main differences and
relations between the various decoupling methods and provide some information for future research on the problem of mutual coupling.
Keywords: Mutual coupling, decoupling method, compensation method, communication, magnetic resonance imaging (MRI), antenna array,
MRI phased array, surface coil array, mutual impedance, receiving mutual impedance, element pattern, calibration, open-circuit voltage,
capacitive decoupling network.
1. INTRODUCTION
Mutual coupling is a common problem in the applications of
antenna arrays. It significantly affects the operation of almost all
types of antenna arrays. The study of mutual coupling problem
started several decades ago and attracted the interest of not just
antenna engineers and researchers but also many researchers from
other disciplines such as communications and biomedical imaging
where antenna arrays are frequently used. Compared with a single
antenna, an antenna array is able to provide spatial information of
the signal distributions. However, this function critically relies on
the independence or distinctiveness of the signals received or
transmitted from different antenna elements in the array. In reality,
this is simply impossible because antenna elements will interact
with each other, i.e., they will mutually couple with each other. In
order to restore the independent signals received or transmitted
from the antenna elements, the coupled effect has to be removed or
reduced. Hence, it is very important to find ways to decouple the
array signals received or transmitted from antenna arrays. Over the
past years, there have been many different kinds of methods
suggested to decouple the coupled array signals. The effectiveness
of these methods varied and depended upon the types of antenna
arrays being considered and the applications in which the antenna
arrays were used. In this paper, we present a brief review of these
decoupling methods (also known as compensation methods in some
cases) for antenna arrays which have been suggested in the
literature. Many of these decoupling methods have not been
patented but some of these, especially those found in magnetic
resonance imaging (MRI), are almost all patented. We shall review
those non-patented ones first while those patented ones will be
later. In the review, the various methods will be first briefly
described and their operation principles explained. Then some
comments on their scopes of application, their comparisons, or their
relations to other methods will be given. The problems associated
with these methods will also be analysed. It should be noted that for
a detailed understanding or for a direct reference to the specific
results regarding a particular method, readers have to be referred to
the particular paper or patent in which the method was first
*Address correspondence to this author at the Department of Electrical and
Computer Engineering, National University of Singapore 10 Kent Ridge
Crescent Singapore 119260, Singapore; E-mail: elehht@nus.edu.sg
1872-2121/07 $100.00+.00
reported. In our review, citations of previous literature or patents
will be grouped under the same method and will not be individually
addressed for the sake of brevity. Readers can choose to look into a
particular paper or patent listed under the same category which they
find more interested in. A section on “Current and Future
developments” serves to conclude this paper.
2. REVIEW OF DECOUPLING METHODS
There have been many decoupling methods suggested to tackle
the mutual coupling problem in antenna arrays. Each bases on
different principles and is designed for different applications. It is
necessary to categorize them so that they can be analysed and
reviewed together with other similar methods. We first review those
methods designed for conventional antenna arrays, i.e., those found
in communications. In the next section, we will review those
methods designed specially for magnetic resonance imaging (MRI)
antenna arrays.
2.1. Open-Circuit Voltage Method
The open-circuit voltage method (typically represented by [112]) is the earliest method used to analyse the mutual coupling
effect in antenna arrays. It was suggested by Gupta and Ksienski
[1]. In this method, mutual coupling between two antennas is
characterized by a mutual impedance whose definition is taken
from that used originally in circuit analysis, i.e., the Z parameters in
network analysis. Accordingly, it treats the antenna array as an Nport network and relates the antenna terminal voltages Vj (j = 1, 2,
,N) to the so-called open-circuit voltages Vocj through an
impedance matrix as
Z11
1+
ZL
Z 21
ZL
M
Z N1
Z L
Z12
ZL
Z
1+ 22
ZL
M
ZN 2
ZL
Z1N ZL Z2 N L
ZL O
M Z
L 1+ NN Z L L
© 2007 Bentham Science Publishers Ltd.
V1 Voc1 V2 = Voc2 M M VN VocN (1)
188 Recent Patents on Engineering 2007, Vol. 1, No. 2
Hon Tat Hui
where Zij (i, j = 1, 2, , N) are the mutual impedances between the
antenna elements and Zii are the self-impedances of the antennas.
The mutual impedances or the self-impedances in (1), for example
for wire antennas, are defined as below [13]
Zij =
Voci
1
=
I i (0)I j (0)
I j (0)
L
E (r ) I (r ) dl
j
i
(2)
0
where Ii(0) is the value of the current distribution Ii(r) of the ith
antenna at the feedpoint (and similarly for Ij(0)), Ej(r) is the
radiation electric field at the surface of the ith antenna (with its
terminals being shorted) which is generated by the current
distribution at the jth antenna, and L is the physical length of the ith
antenna. The definition in (2) is for a self-impedance if i = j and for
a mutual impedance if i j. Note that in (2), the current distribution
Ii(r) is obtained by driving the ith antenna in the transmitting mode
while the jth antenna’s terminals are shorted (and similarly for
Ij(r)). Eq. (2) can be calculated by using the EMF method [14] or
the moment method [15]. The following comments are made about
this method:
1. The open-circuit voltage method does not exactly match the
real situation in an antenna array, for example a receiving array, in
which all the antenna elements are excited by an external source
outside the array. In this case, the current distribution on a
particular antenna is not driven by an embedded current source
connected at its terminals but by the external source. Hence the use
of the definition in (2) will cause an error when applied to a
receiving antenna array. This error is likely to become large (i)
when the antennas’ electrical sizes are large, (ii) when the antenna
separations are small, or (iii) when the external excitation source
causes a different current distribution on an antenna element from
that caused by the embedded current source on that antenna.
2. The mutual impedance Zij in (2) is defined with one antenna
(the jth antenna) excited by an active current source and its
radiation in turn excites the other antenna (the ith antenna).
Furthermore, it assumes that the jth antenna is shorted while the ith
antenna is open circuited. The open-circuit voltage Voci in (2) is
calculated through a short circuit current by using the Thevenin’s
equivalent source method. The open-circuit voltage is obtained by
multiplying the short circuit current with an equivalent impedance
obtained by looking into the terminals of the ith antenna. The
concept of the open-circuit voltage is taken from circuit analysis in
which a circuit component or a network port can be equivalent to an
open circuit voltage source in series with an equivalent impedance
(the well-known Thevenin’s theorem). Once the open-circuit
voltage and the equivalent impedance are known, we can easily
calculate the current through any terminal load that will be
connected to that circuit component or network port under the
assumption that the open-circuit voltage source is not changed by
the terminal load. However, strictly speaking, the open-circuit
voltage concept cannot be directly applied to antennas. This is
because when a different terminal load is connected to a pair of
open-circuit terminals, a different current distribution is produced,
i.e., Ii(r) in (2) will be different and is not simply scaled uniformly
by a constant. That means that the open-circuit voltage is changed
and this change cannot be offset by a corresponding change in Ii(0)
in the denominator of (2). Hence the mutual impedance Zij is
changed. This argument shows that the previous assumption in the
definition of the mutual impedance in (2) being independent of the
terminal load connected to the antennas is wrong. This gives an
error when using (1). This argument also shows that an accurate
definition of mutual impedance should take the antenna terminal
loads into account.
3. Except the above two problems with the open-circuit voltage
method, the use of the open-circuit voltage concept in modelling an
antenna, especially a receiving antenna, into a circuit element has
still a number of problems and uncertainties being unsettled as seen
from some recent studies [16-21]. A common view from these
studies is that the Thevenin equivalent source model with an opencircuit voltage source in series with an equivalent impedance is not
sufficient to model a receiving antenna.
Notwithstanding these problems, the open-circuit voltage
method has actually become the most widely accepted method for
mutual coupling analysis in antenna arrays. This is probably due to
its ease of application with a formulation using circuit concepts. To
decouple the antenna voltages, we just need to calculate the system
in (1) with known (measured) antenna terminal voltages Vj (j = 1, 2,
, N) to obtain the open-circuit voltages Vocj (j = 1, 2, , N) on the
right-hand side, which are supposed to be caused by the external
source alone on the respective antenna elements. It is rather easy to
see why the open-circuit voltages are supposed to be free of mutual
coupling. This is because when all the antenna elements are opencircuited (with no current flowing), there would be no radiation
from the antennas and so the voltages developed on the antenna
terminals (open-circuited) are solely due to the external source. In a
strict sense, this argument is fallacious because an open-circuit
antenna will still re-radiate if it is excited by an external source.
Due to the problems with this method mentioned above, the
decoupled voltages (the open-circuit voltages) are actually not very
purely free from mutual coupling and errors from using the opencircuit voltages are expected. This can be seen from some recent
studies on this topic [22-29].
2.2. S-Parameter Method
In the s-parameter method (typically represented by [30-32]),
the receiving or transmitting antenna array is modelled as an N-port
network and the mutual coupling between antenna elements is
modelled using scattering parameters. Once the s-parameters are all
determined, the decoupled signals can be computed from the
coupled measurable terminals signals. However, by using this
method, only the transmitting array is modelled correctly with
respect to the handling of the mutual coupling effect. For a
receiving array, because the definition of s-parameters requires that
the antenna elements be driven by an active source connected at the
terminals of one of the antennas in the array, it fails to correctly
model the array whose antenna elements are all driven by an
external source outside the array. The consequence of this method
is that the mutual coupling in the receiving array is independent of
the external source (the impinging wave) which is incorrect as
explained in Section 2.1. Hence the performance of this method
(which can be measured by its decoupling power = 20log|coupled
signal/uncoupled signal|) is similar to that of the open-circuit
voltage method and it suffers from the same problems as that
method.
2.3. Full-Wave (Moment) Method
The full-wave method (typically represented by [32-35]) seeks
to solve the entire boundary value problem of the electromagnetic
field for the whole antenna array by the moment method [15]. It
uses the known array measurable quantities, such as terminal
voltages and currents (which come with mutual coupling), to
calculate the incident field on the array, which is coupling free.
However, since only terminal voltages or currents are known but
not the entire current or voltage distributions on the antenna
elements, this method results in an under-determined system of
equations. In order to solve the under-determined system, usually
some approximations have to be made, such as an assumed current
distribution [32], a known coming direction of the incident field
[34], or solving the under-determined system directly using a
compromised method [35]. The performance of this method
depends on the approximations made, which sometimes may not be
realistic, and its scope of application is therefore limited. On the
other hand, if we assume the incident field is completely known,
Decoupling Methods for Antenna Arrays
then this method can serve as an accurate analysis tool to
investigate mutual coupling effect on the performance of an antenna
array [33].
2.4. Element Pattern Method
A. Isolated Element Pattern Method (Typically Represented by
[36-41])
This method was first proposed by Steyskal and Herd in 1990
[36]. The terminal voltage (coupled voltage) developed on a
particular antenna element is expressed as a sum of two parts. The
first part is due to the response of the isolated radiation pattern of
that particular element to the incoming signal. The second part is a
linear combination of the responses of the isolated radiation
patterns of all the other antenna elements in the array to the
incoming signal. The mutual coupling between the particular
antenna element and the other elements in the array is modelled by
a set of combination coefficients, cmn, which, when taken together
for all the antenna elements, form a coupling matrix relating the
coupled and decoupled voltages. Once the combination coefficients
are all known, decoupled voltages can be obtained from the coupled
terminal voltages. The problem with this method is the determination of the combination coefficients (the coupling coefficients). One method to determine the coupling coefficients is
through the s-parameter measurement. However, this again
detaches mutual coupling from the incident signal and this method
will be similar to the open-circuit voltage method.
B. Coupled Element Pattern Method (Typically Represented by
[42-45])
A similar method to the isolated element method is the coupled
element method. In this method, the aim is to obtain the coupled
voltages from the antenna elements instead of the coupling free
voltages. More specifically, the aim is to be able to predict the
received coupled voltages through the responses of the so-called
coupled radiation patterns of the antenna elements. The coupled
radiation pattern of an antenna element is its radiation pattern
obtained in the presence of all other antenna elements in the array
(but which are not excited). That is, all the mutual coupling effect is
taken into account. By using this method, the total array response
will be expressed as a function of the coupled radiation patterns
instead of the isolated radiation patterns. Hence this method does
not decouple the coupled signals but rather takes the mutual
coupling effect into account. All signal processing algorithms
working with this method must be redesigned using coupled
radiation patterns instead of isolated radiation patterns. A
disadvantage of this method is the need to have a huge memory to
store all the coupled radiation patterns for the signal processing
algorithms because these coupled radiation patterns are in general
2D patterns. This method is suitable for analysis purposes in which
real time processing is not required.
2.5. Calibration Method
In the calibration method (typically represented by [46-51]), a
coupling matrix is usually formed first. This coupling matrix relates
the coupled signals to the uncoupled signals and is similar to the
impedance matrix in (1). The important step in this method is to
determine this coupling matrix by a carefully designed
experimental procedure or by an iterative calculation method based
on some known initial conditions. Once the coupling matrix is
known, decoupled signals can be obtained from the coupled signals
through a transformation using the coupling matrix. The
performance of this method critically depends on the accuracy in
measuring or calculating the coupling matrix which is usually not
an easy task because the number of unknowns to be determined can
be very large. A problem faced by this method is the tedious
measuring procedure or iterative steps to determine the coupling
matrix which are required to be carried out again once there is a
Recent Patents on Engineering 2007, Vol. 1, No. 2
189
change to the antenna array configuration or a change to the
external signal environment.
2.6. Decoupling by Antenna Design
Mutual coupling in arrays can be reduced or minimized by a
proper design of the antenna elements and/or the array
configuration [52,53]. For example, in [52] a two-element planar
Yagi antenna array shows a very low mutual coupling (S21 < -22
dB) when the Yagi antennas were aligned in a co-linear form rather
than in a parallel form. When the Yagi elements are in the co-linear
form, they are almost in the radiation null of the near field pattern
of the other element and this results in a low mutual coupling level.
In [53], an antenna array was designed to minimize the parasitic
current on the antenna elements by changing the load impedances
so that the parasitic radiation fields caused by adjacent elements are
reduced. This results in the active (coupled) element patterns of the
antenna elements similar to that of a single (uncoupled) element
pattern, i.e., mutual coupling is substantially reduced. Note that this
method, though rather effective and simple (requiring no additional
processing procedure), is only applicable to specific types of
antenna elements.
2.7. Receiving Mutual Impedance Method
The receiving mutual impedance method (typically represented
by [22-29]) is a method which aims to solve the problems faced by
the open-circuit voltage method as mentioned in Section 2.1. This
method was proposed by Hui in 2003 [22]. It defines a receiving
mutual impedance [25, 54] which takes into account of the antenna
terminal loads and the external signal source. Unlike the opencircuit voltage method, it seeks to obtain the decoupled voltages
across the terminal loads of the antennas rather than the opencircuit voltages. Hence it does not suffer from the problems with
the use of the open-circuit voltage concept. Similar to the opencircuit voltage method, it also models the antenna array as an Nport circuit network but bases on different circuit parameters, such
as receiving mutual impedances, terminal currents and voltages, but
not Thevenin equivalent sources or impedances. It relates the
measured terminal voltages (coupled voltages) Vj (j = 1, 2, , N) to
the decoupled terminal voltages across the same antenna terminal
loads through an impedance matrix which contains the receiving
mutual impedances [24, 27], i.e.,
1
Z 21
t
ZL
M
ZtN1
Z
L
Zt12
ZL
1
M
ZtN 2
ZL
Zt1N ZL Z 2N L t ZL O
M L
1 L V1 U1 V2 = U 2 M M VN U N (3)
where Uj (j = 1, 2, , N) are the decoupled terminal voltages and
Z tij is the receiving mutual impedance between the ith and the jth
antennas. Once the impedance matrix on the left hand side of (3) is
known, the decoupled terminal voltages can be obtained from the
measured coupled terminal voltages. The definition, the calculation
method, and the measurement method for the receiving mutual
impedance are all different from those of the conventional mutual
impedance in (2) and can be found in [25,29,54]. It has been shown
in a number of applications that the performance of the receiving
mutual impedance method is much better than that of the opencircuit voltage method. This can be seen in direction finding [22,
25, 26], in adaptive nulling [23, 24], and in magnetic resonance
imaging (MRI) [27, 28]. Note that this method is easy to apply,
190 Recent Patents on Engineering 2007, Vol. 1, No. 2
requiring the same amount of calculation and memory space as the
open-circuit voltage method. Hence it is applicable to situations
requiring real-time processing, such as adaptive direction finding,
adaptive nulling, or adaptive beamforming. It is also applicable to
situations for analysis or for array design purposes.
2.8. Other Methods
There are other decoupling methods [55-57] which cannot be
exactly grouped into the above categories and will not be reviewed
here.
3. DECOUPLING METHODS IN MAGNETIC RESONANCE
IMAGING (MRI) PHASED ARRAYS
Decoupling methods for MRI phased arrays deserves some
special attention because most of the patented decoupling methods
belong to this category. Some recent ones can be found in [60, 6267]. In MRI, antenna arrays are found increasingly important
because of the rapid development in parallel MRI [58, 59, 61]
which can substantially shorten the imaging time and increase the
image signal-to-noise ratio (SNR) for imaging over larger areas. In
MRI, antenna arrays are called phased arrays and they bear some
distinct differences from the antenna arrays in communications.
These include: (i) they receive in the near-field region rather than in
the far-field region as in communication arrays, (ii) their interelement spacings (around 0.1 wavelength) are much smaller than
those in communication arrays (around 0.5 wavelength) because of
the much lower operation frequencies in MRI arrays, and (iii) they
use magnetic field antennas rather than electric field antennas as in
communication arrays. These differences make MRI arrays even
more susceptible to the mutual coupling effect than communication
arrays and most of their decoupling methods are also different from
those for communication arrays. Basically, for MRI arrays, such as
phased coil arrays, there are three categories of decoupling
methods: (i) overlapping of adjacent coils combined with low input
impedance pre-amplifiers, (ii) capacitive or inductive decoupling
networks, and (iii) open-circuit voltage method. They are discussed
below.
3.1. Overlapping of Adjacent Coils Combined with Low Input
Impedance Pre-Amplifiers
This method was first proposed by Roemer and Edelstein [60,
61] for MRI surface coil arrays. Roemer and Edelstein noticed that
mutual coupling between surface coils is mainly in the form of
mutual induction, called inductive coupling, which is caused by
magnetic flux linkage between the coils. Hence they suggested
overlapping some parts of the adjacent coils in an array so that they
share a common area and the magnetic flux (coupled) through this
common area can cancel the magnetic flux through the non-
Fig. (1). The Overlapping method.
Hon Tat Hui
overlapping area and the inductive coupling can be substantially
reduced. This can be seen from the schematic drawing in Fig. (1).
This really works but overlapping is only possible between adjacent
coils. For non-adjacent coils (i.e., coils separated farther than
adjacent coils), mutual coupling still exists although not so
significant as that between adjacent coils. To reduce the mutual
coupling between non-adjacent coils, Roemer and Edelstein further
suggested using low-input-impedance pre-amplifiers. These lowinput-impedance pre-amplifiers are connected to the coils through
an impedance matching circuit which transforms the low input
impedance of a pre-amplifier to a very large impedance looking at
the terminals of a coil. This large impedance effectively limits the
current flowing through the coil and hence minimizes the mutual
coupling. This technique of course also applies to adjacent coils on
top of the overlapping technique. It turns out that Roemer and
Edelstein’s method is rather effective and was widely accepted in
the design of MRI surface coil arrays. This can be seen in [62] in
which a quadrature coil array adopted the same decoupling
techniques. In [63], an array of surface coils also used the same
decoupling techniques and it further demonstrated that the same
techniques could even be used for 2D arrays to provide a better
coverage of the human body. A modification to the original
overlapping method is seen in [64] in which overlapping of two
adjacent coils can be made in a vertical plane perpendicular to the
plane of the surface coils. This modification consists of a separate
intermediate coil placed between the two coplanar surface coils to
be decoupled. The intermediate coil was bent into two halves at a
right angle to each other so that one half overlapped with one
surface coil while the other half is placed at the vertical plane to be
joined to the other surface coil. A part of the other surface coil is
also bent through a right angle to the vertical plane joining the first
surface coil. In this way the two surface coils can be effectively
overlapped at the vertical plane through the intermediate coil. It was
claimed that such a design can allow the overlapping of two surface
coils or two surface coil sub-arrays in a very convenient way,
especially when the surface coils or surface coil sub-arrays are
already designed to be fixed inside some fittings and cannot be
made overlapped with each other.
Notwithstanding the widely accepted use of Roemer and
Edelstein’s overlapping method in MRI arrays, this method, like
other decoupling methods, has its limitations. Basically the
overlapping technique can be considered as the method of
decoupling by antenna design mentioned in the previous section
(Section 2.6) and has the same limitation as explained there. Except
that, in MRI, the use of phased arrays is mainly for expanding the
imaging area (a larger field-of-view). However, overlapping of
adjacent coils obviously works against this objective and results in
a smaller imaging area. Furthermore, overlapping of adjacent coils
Decoupling Methods for Antenna Arrays
only decouples the magnetic coupling effect but not the electric
coupling effect which couples through the electric field. Hence it
can be expected that the decoupling power of this method is
limited, around -10dB as reported previously. The use of low-inputimpedance pre-amplifiers is not a justifiable method by itself
because it seeks to reduce the coil currents in order to reduce
mutual coupling. Coil currents are the power sources which send
image signals to the processing circuits. An attempt to reduce the
coil currents will also reduce the signal powers in an equal amount
as the reduction in the mutual coupling. Thus this method reduces
mutual coupling and the signal power together. Because of these
problems, decoupling networks based on circuit construction were
proposed as described below.
3.2. Capacitive or Inductive Decoupling Networks
An inductive decoupling network was reported in [65] in which
two small inductor coils are connected to two large imaging coils.
The two small inductor coils are for decoupling the mutual coupling
between the two large imaging coils. The small inductor coils are
placed very close to each other so that their mutual coupling can
counteract the mutual coupling of the imaging coils. Capacitive
decoupling networks, on the other hand, employ capacitors rather
than inductor coils to decouple the mutual coupling effect. This can
be seen in the patents in [66-68]. Adjacent coils and non-adjacent
coils are connected together through a capacitor network whose
capacitor values, when carefully chosen, can decouple the mutual
coupling between adjacent coils as well as non-adjacent coils. The
capacitive decoupling networks are applicable to surface coils [66]
or volume coils [67, 68]. In [69], a capacity decoupling network
works at a high-field condition of 14.1 T and a decoupling power of
around -20 to -40 dB could be achieved. The method using
inductive or capacity decoupling networks requires an accurate
determination of the decoupling inductor or capacitor values which
is sometimes a formidable task, especially for large phased arrays.
Looking from a broader perspective, the inductive or capacitive
decoupling network is actually to realize (or approximately realize)
the impedance matrix obtained in the open-circuit voltage method
(in (1)) or the impedance matrix obtained in the receiving mutual
impedance method (in (3)). Hence depending on how the capacitor
or inductor values in the decoupling networks are determined, this
method is basically similar to either the open-circuit voltage method
or the receiving mutual impedance method.
3.3. Open-Circuit Voltage Method
The open-circuit voltage method was proposed by Lee et al.
[70]. It is basically the open-circuit voltage method (mentioned in
Section 2.1) applied to MRI phased arrays. In [70], the impedance
matrix was realized as a 2N-port circuit network: N input ports from
the phased coil array and N output ports to the signal processing
circuits. The inputs from the phased coil array to the decoupling
network are coupled signals while those output from the decoupling
network to the processing circuits are decoupled signals. The
problems of this method have been discussed in Section 2.1. In
MRI, as the coils are separated much closer together than the
antenna elements in communication arrays, these problems become
even more serious in MRI phased arrays.
3.4. Receiving Mutual Impedance Method
As mentioned in the last section (Section 2.7), the receiving
mutual impedance method is a more accurate method than the
open-circuit voltage method. Actually this method is even more
suitable for MRI phased arrays. As mentioned in Section 2.7, this
method takes into account the external source. This is done through
the definition of the receiving mutual impedance in which the
current distribution on the exciting antenna is excited by an external
source [27,28,54]. In MRI, the external source for the phased array
is the active slice excited by the RF pulse. The position of the active
slice is accurately controlled by the static magnetic field and the
Recent Patents on Engineering 2007, Vol. 1, No. 2
191
gradient magnetic fields. Hence the position information of the
active slice is available and can be used to define the receiving
mutual impedance for MRI phased arrays in a very accurate
manner. Studies using this method to decouple the array signals
have been found in MRI surface coil arrays [27] and MRI
quadrature coils [28]. It was shown that mutual coupling could be
almost totally removed and nearly coupling-free array signals can
be obtained. Comparisons with the open-circuit voltage method
have also been provided in these studies. However, care must be
taken that studies with this method are still limited to theoretical
investigations or experimental measurements in a simulated MRI
environment only. It should be noted that for the most effective
operation of the receiving mutual impedance method in MRI, the
receiving mutual impedances have to be measured in situ with the
MRI machine or be calculated with the practical MRI machine
environment taken into account.
CURRENT & FUTURE DEVELOPMENTS
Mutual coupling is a notorious problem in antenna arrays. With
the use of antenna arrays in an ever-increasing number of situations,
decoupling methods are found to be very important and necessary.
It is interesting to note that most of the patented decoupling
methods are found in MRI applications and almost none found in
the communication area. Currently, the open-circuit voltage method
is still the most popular decoupling method used in communication
arrays. This method was proposed over two decades ago and
notwithstanding some of its shortcomings such as lack of accuracy,
it has solid concepts based on circuit analysis and hence it is the
easiest method to understand and apply. Other more sophisticated
methods such as the element pattern method and the s-parameter
method are also frequently used in mutual coupling analysis and
array signal processing. The element pattern method offers a higher
decoupling power but is also more difficult to apply. The full-wave
(moment) method is more suitable for analysis purposes rather than
to decouple the coupled array signals in a real time processing
environment. The receiving mutual impedance method is a new
attempt to overcome the problems with the open-circuit voltage
method and retains most of the advantages of the open-circuit
voltage method. In some recent studies, this method has been
demonstrated to have a potential to become a powerful decoupling
method for antenna arrays. In MRI arrays, the overlapping method
combined with low input impedance pre-amplifiers is still the most
popular method currently in use. The use of inductive or capacitive
decoupling networks has been seen to attract more attention
recently. One of the reasons may be its greater flexibility in
application and its relatively higher decoupling power. However,
the open-circuit voltage method is not so frequently used in MRI
phased arrays. This may be probably due to its lower decoupling
power than other methods because of its inherent problems as
mentioned earlier. Again, for the receiving mutual impedance
method, some recent studies have shown that it can provide an
enormous decoupling power for MRI phased arrays. However, as
indicated in the past reports, studies with this method are still
limited to theoretical investigations or experimental measurements
in a simulated MRI environment. More stringent tests of this
method in real clinical MRI environments are still required and
necessary. Looking into the future, antenna arrays will find
increasing importance in a number of application areas. This
parallels the rapid development of array signal processing
techniques in such areas as communications, biomedical imaging,
radar detection, remote sensing, etc. The successful application of
antenna arrays in these areas critically relies on the availability of
powerful signal processing algorithms as well as equally powerful
and reliable decoupling methods to combat the problem of mutual
coupling. A future trend of antenna array design is seen towards
smaller or compact-size arrays for the purpose of portability such as
antenna arrays in mobile phones or in laptop computers. Obviously
this only exacerbates the problem of mutual coupling and makes it
192 Recent Patents on Engineering 2007, Vol. 1, No. 2
even more important and necessary to find solutions to this
problem. Because of these considerations, decoupling methods need
to be further developed to suit for new situations. New decoupling
methods are also required to provide better solutions in the new
situations. All existing decoupling methods, patented or unpatented,
as reviewed above have some kind of problems that need to be
solved or improved under different conditions. It can be expected
that there still have a lot to do with decoupling methods for antenna
arrays and the number of patents on these methods will be likely to
increase in the near future.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
Gupta IJ, Ksienski AA. Effect of mutual coupling on the performance of
adaptive arrays. IEEE Trans Antennas Prop 1983; 31(9): 785-791.
Lo KW, Vu TB. Simple s-parameter model for receiving antenna array.
Electron Lett 1988; 24(20): 1264-1266.
Yeh CC, Leou ML, Ucci DR. Bearing estimations with mutual coupling
present. IEEE Trans Antennas Prop 1989; 37(10): 1332-1335.
Lee KC, Chu TH. A circuit model for mutual coupling analysis of a finite
antenna array. IEEE Trans Electromag Compat 1996; 38(8): 483-489.
Friel EM, Pasala KM. Effects of mutual coupling on the performance of
STAP antenna arrays. IEEE Trans Aerospace Elect Sys 2000; 36(2): 518527.
Allen OE, Wasylkiwskyj W. Comparison of mutual coupling of blade
antennas with predictions based on minimum-scattering antenna theory.
IEEE Trans Electromag Compat 2000; 42(4): 326-329.
Leifer MC. Mutual coupling compensation accuracy. Proc IEEE Antennas
Prop Soc Inter Symp 2001. USA (2001); 3: 804-807.
Lee KC. A simplified model for the mutual coupling effects of adaptive
antenna arrays. J Electromagn Waves Appl 2004; 17(9): 1261-1268.
Ioannides P, Balanis CA. Mutual coupling in adaptive circular arrays. Proc
IEEE Antennas Prop Soc Inter Symp 2004. USA (2004); 1: 403-406.
Durrani S, Bialkowski ME. Effect of mutual coupling on the interference
rejection capabilities of linear and circular arrays in CDMA. IEEE Trans
Antennas Prop 2004; 52(4): 1130-1134.
Lee KC, Chu TH. Mutual coupling mechanisms within arrays of nonlinear
antennas. IEEE Trans Electrom Compat 2005; 47(4): 963-970.
Rogier H, Bonek E. Analytical spherical-mode-based compensation of
mutual coupling in uniform circular arrays for direction-of-arrival estimation.
Inter J Electron Commun 2006; 60(3): 179-189.
Jordan EC. Electromagnetic Waves and Radiating Systems. Prentice-Hall
Inc., Englewood Cliffs, N. J. 1968; Chapter 11.
Tai CT. A study of the EMF method. J Appl Phys 1949; 717-23.
Harrington RF. Field Computation by Moment Methods. New York: IEEE
Press 1993.
Bladel JV. On the equivalent circuit of a receiving antenna. IEEE Antennas
Prop Magazine 2002; 44(1): 164-165.
Love AW. Comment: on the equivalent circuit of a receiving antenna. IEEE
Antennas Prop Magazine 2002; 44(5): 124-125.
Collin RE. Limitations on the Thevenin and Norton equivalent circuits for a
receiving anenna. IEEE Antennas Prop Magazine 2003; 45(2): 119-124.
Love AW. Comment on “Limitations on the Thevenin and Norton equivalent
circuits for a receiving anenna”. IEEE Antennas Prop Magazine 2003 (4); 45:
98-99.
Andersen JB, Vaughan RG. Transmitting, receiving, and scattering properties of antennas. IEEE Antennas Prop Magazine 2003; 45(4): 93-98.
Su CC. On the equivalent generator voltage and generator internal
impedance for receiving antennas. IEEE Trans Antennas Prop 2003; 51(2):
279-285.
Hui HT. Compensating for the mutual coupling effect in direction finding
based on a new calculation method for mutual impedance. IEEE Antennas
Wireless Prop Lett 2003; 2: 26-29.
Hui HT, Chan KY, Yung EKN. Compensating for the mutual coupling effect
in a normal-mode helical antenna array for adaptive nulling. IEEE Trans
Vehicular Technol 2003; 52(4): 743-751.
Hui HT. A practical approach to compensate for the mutual coupling effect
of an adaptive dipole array. IEEE Transactions on Antennas and Propagation
2004; 52(5): 1262-1269.
Hui HT, Low HP, Zhang TT, Lu YL. Receiving mutual impedance between
two normal mode helical antennas (NMHAs). IEEE Antenna Prop Magazine
2006; 48(4): 92-96.
Zhang TT, Hui HT, Lu YL. Compensation for the mutual coupling effect in
the ESPRIT direction finding algorithm by using a more effective method.
IEEE Trans Antennas and Prop 2005; 53(4): 1552-1555.
Hui HT. An effective compensation method for the mutual coupling effect in
phased arrays for magnetic resonance imaging. IEEE Trans Antennas Prop
2005; 53(10): 3576-3583.
Hui HT, Li BK, Crozier S. A new decoupling method for quadrature coils in
magnetic resonance imaging. IEEE Trans Biomed Eng 2006; 53(10): 21142116.
Hon Tat Hui
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
[53]
[54]
[55]
[56]
[57]
[58]
Hui HT, Lu SY. Receiving mutual impedance between two parallel dipole
antennas. To be published in the Proceedings of the IEEE TENCON 2006.
Hong Kong (2006).
Segovia-Vargas D, Martin-Cuerdo R, Sierra-Perez M. Mutual coupling
effects correction in microstrip arrays for direction-of-arrival (DOA)
estimation. IEE Proceedings on Microwave, Antennas, and Propagation
2002; 149(2): 113-117.
Wallace JW, Jensen MA. Mutual coupling in MIMO wireless systems: a
rigorous network theory analysis. IEEE Trans Wireless Commun 2004; 3(4):
1317-1325.
Pasala KM, Friel EM. Mutual coupling effects and their reduction in
wideband direction of arrival estimation. IEEE Trans Aerospace Electron Sys
1994; 30(4): 1116-1122.
Yuan H, Hirasawa K. The mutual coupling and diffraction effects on the
performance of a CMA adaptive array. IEEE Trans Vehicular Technol 1998;
47(3): 728-736.
Adve RS, Sarkar TK. Compensation for the effects of mutual coupling on
direct data domain adaptive algorithms. IEEE Trans Antennas Prop 2000;
48(1): 86-94.
Lau CKE, Adve RS, Sarkar TK. Minimum norm mutual coupling
compensation with applications in direction of arrival estimation. IEEE Trans
Antennas Prop 2004; 52(8): 2034-2040.
Steyskal H, Herd JS. Mutual coupling compensation in small array antennas.
IEEE Trans Antennas and Prop 1990; 38(12): 1971-1975.
Darwood P, Fletcher PN, Hilton GS. Mutual coupling compensation in small
planar array antennas. IEEE Proceedings on Microwave, Antennas, and
Propagation 1998; 145(1): 1-6.
Chen S, Iwata R. Mutual coupling effects in microstrip patch phased array
antenna. Proceedings of the IEEE Antennas Prop Soc Inter Symp 1998. USA
(1998); 2: 1028-1031.
Su T, Ling H. On modeling mutual coupling in antenna arrays using the
coupling matrix. Microwave Optical Technol Lett 2001; 28(4): 231-237.
Fletcher PN, Dean M, Nix AR. Mutual coupling in multi-element array
antennas and its influence on MIMO capacity. Electron Lett 2003; 39(4):
342-344.
Zaharis ZD, Samaras T, Vafiadis E, Sahalos JN. Antenna array design by the
orthogonal method in conjunction with element patterns. Microwave Optical
Technol Lett 2006; 48(8): 1578-1583.
Kelly DF, Stutzman WL. Array antenna pattern modelling methods that
include mutual coupling effects. IEEE Transactions Antennas Prop 1993;
41(12): 1625-1632.
Fernandez del Rio JE, Conde-Portilla OM, Catedra MF. Estimating azimuth
and elevation angles when mutual coupling is significant. Proceedings of the
IEEE Antennas Prop Soc Inter Symp 1998. USA (1998); 1: 215-218.
Dandekar KR, Ling H, Xu G. Effect of mutual coupling on direction finding
in smart antenna applications. Electronics Letters 2000; 36(22): 1889-1891.
Li X, Nie ZP. Mutual coupling effects on the performance of MIMO wireless
channels. IEEE Antennas Wireless Prop Lett 2004; 3: 344-347.
Aumann HM, Fenn AJ, Willwerth FG. Phased array antenna calibration and
pattern prediction using mutual coupling measurements. IEEE Trans
Antennas Prop 1989; 37(7): 844-850.
Friedlander B, Weiss AJ. Direction finding in the presence of mutual
coupling. IEEE Trans Antennas Prop 1991; 39(3): 273-284.
Su T, Dandekar KR, Ling H. Simulation of mutual coupling effect in circular
arrays for direction-finding applications. Microwave Optical Technol Lett
2000; 26(5): 331-336.
Kim K, Sarkar TK, Palma MS. Adaptive processing using a single snapshot
for a nonuniformly spaced array in the presence of mutual coupling and nearfield scatterers. IEEE Trans Antennas Prop 2002; 50(5): 582-590.
Dandekar KR, Ling H, Xu G. Experimental study of mutual coupling
compensation in smart antenna applications. IEEE Trans Wireless Commun
2002; 1(3): 480-486.
Wang Y, Xu S. Mutual coupling calibration of DBF array with combined
optimisation method. IEEE Trans Antennas Prop 2003; 51(10): 2947-2952.
Qian Y, Dael W, Kaneda N, Itoh T. A uniplanar quasi-Yagi antenna with
wide bandwidth and low mutual coupling characteristics. Proceedings of the
IEEE Antennas Prop Soc Inter Symp 1999. USA (1999); 2: 924-927.
Fredrick JD, Wang Y, Itoh T. Smart antennas based on spatial multiplexing
of local elements (SMILE) for mutual coupling reduction. IEEE Trans
Antennas Prop 2004; 52(1): 106-114.
Hui HT. A new definition of mutual impedance for application in dipole
receiving antenna arrays. IEEE Antennas Wireless Prop Lett 2004; 3: 364367.
Kang YW, Pozar DM. Correction of error in reduced sidelobe synthesis due
to mutual coupling. IEEE Trans Antennas Prop 1985; 33(9): 1025-1028.
Himed B, Weiner DD. Compensation of mutual coupling for the ESPRIT
algorithm. Proceedings of the IEEE Antennas Prop Soc Inter Symp 1989.
USA (1989); 2: 966-969.
Himed B, Weiner DD. Compensation for mutual coupling effects in direction
finding. Proceedings of the IEEE Antennas Prop Soc Inter Sym 1990. USA
(1990); 5: 2631-2634.
Sodickson DK, Manning WJ. Simultaneous acquisition of spatial harmonics
(SMASH): fast imaging with radiofrequency coil arrays. Magn Reson Med
1997; 38: 591-603.
Decoupling Methods for Antenna Arrays
[59]
[60]
[61]
[62]
[63]
[64]
[65]
Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE:
sensitivity encoding for fast MRI. Magn Reson Med 1999; 42: 952-962.
Roemer, B. P., Edelstein, W. A.: US4825162 (1989).
Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The NMR
phased array. Magn Reson Med 1990; 16: 192-225.
Keren, H.: US5198768 (1993).
Belt, K. W., Reichel, M., Watral, J. M., Lewandowski, S. R., Adams, B. J.,
Augustine, L. A., Bell, Jr. R. S.: US20016323648 (2001).
Reykowski, A.: US20067136023B2 (2006).
Nabeshima, T., Takahashi, T., Matsunaga, Y., Yamamoto, E., Katakura, K.:
US5489847 (1996).
Recent Patents on Engineering 2007, Vol. 1, No. 2
[66]
[67]
[68]
[69]
[70]
193
Lian, J., Roemer, P. B.: US5804969 (1998).
Jevtic, J., Menon, A., Seeber, D.: US20046747452 (2004).
Jevtic, J.: US20067091721B2 (2006).
Zhang X and Webb A. Design of a capacitively decoupled transmit/receive
NMR phased array for high field microscopy at 14.1T. J Magn Reson 2004;
170: 149-155.
Lee RF, Giaquinto RO, and Hardy CJ. Coupling and decoupling theory and
its application to the MRI phased array. Magn Reson Med 2002; 48: 203213.