26
IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 2, 2003
Compensating for the Mutual Coupling Effect in
Direction Finding Based on a New Calculation
Method for Mutual Impedance
H. T. Hui, Member, IEEE
Abstract—A new method for calculation of the mutual
impedance is introduced for the compensation of mutual coupling
effect in a dipole antenna array employed for direction finding.
This method uses an estimated current distribution and a different
method for the calculation of the open-circuit voltage. It is shown
that the new method can significantly improve the performance
of the array in terms of the sharpness and accuracy of the spatial
spectrum response of the MUSIC algorithm.
Index Terms—Direction finding, MUSIC algorithm, mutual coupling, mutual impedance.
I. INTRODUCTION
P
REVIOUS studies [1]–[4] have shown that mutual coupling has a significant effect on an antenna array employed
for direction finding, especially when using those eigenstructure-based direction-finding algorithms, such as MUSIC, which
rely on the accurate knowledge of the received signal voltages.
There have been many methods suggested to solve this problem,
for example, [1]–[4]. In [1] (by using the method developed in
[5]), the open-circuit voltages were derived from the antenna
terminal voltages by using the mutual impedances between the
antenna elements. The mutual coupling effect in these open-circuit voltages have been substantially reduced and significant improvement in the sharpness of the spatial spectrum response was
observed. As shown in [1], mutual impedance plays a key role in
effectuating the compensation for (or the reduction of) the mutual coupling effect. In this letter, a further improvement to this
method is introduced. The compensation for the mutual coupling effect in a dipole array employed for direction finding is
further enhanced by using a new and more accurate method to
calculate the mutual impedance. The new calculation method
is based on an estimated current distribution, which carries a
direction reference of the incoming signals. Furthermore, we
calculate the open-circuit voltages in a different way from the
conventional method. It is shown that these two steps can significantly improve the reduction of the mutual coupling effect
and lead to an improved performance of the MUSIC direction
finding algorithm.
Manuscript received December 6, 2002; revised January 10, 2003.
The author is with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail:
ehthui@ntu.edu.sg).
Digital Object Identifier 10.1109/LAWP.2003.810763
II. NEW CALCULATION METHOD FOR THE MUTUAL
IMPEDANCE
We first introduce the new method for the calculation of the
mutual impedance, which is the central parameter in the compensation method. Consider a linear dipole antenna array with
dipole antennas shown in Fig. 1 deployed for direction finding.
The dipole antenna elements are assumed to be thin wires of
and radius
, where is the
equal length
wavelength. The array is placed along the -axis with an equal
spacing between antenna elements. All the antenna elements
are connected at their centres to a terminal load . The voltages
across the terminal loads contain the incoming signals and noise.
For a particular antenna element in the array, for example, the
th antenna, the relation between the measured terminal voltage
and the open-circuit voltage,
can be expressed as [5]
(1)
where
is the mutual impedance between
the th antenna and the th antenna (or the self impedance of
).
is the value of the th anthe th antenna when
tenna current distribution at the terminal position. Ideally, for
any direction-finding algorithm, we should use the open-circuit
, which is free from the mutual coupling effect. Howvoltage
ever, practically we can only obtain the measured voltage
on the th antenna terminals (which also contains the mutual
coupling voltages from other antenna elements in the array).
from
by using (1), we have to know the muTo find
tual impedances which, unfortunately, can only be calculated
in an approximation manner unless we know the exact current
distributions on the antenna elements (whose values at the ter). In all previous studies,
minal loads are
the conventional method [6] has been used to calculate the mutual impedances. The definition of the mutual impedance
is the ratio of the induced open-circuit voltage
on the terminal (open-circuited) of the th antenna to the driving-point
current flowing through the terminal (short-circuited) of the
th antenna. It should be noted that in this definition,
not just
depends on the terminal current
but also critically depends
on the current distribution on the th antenna. In the conven,
is calculated by using
tional method of calculation of
the reciprocity theorem by assuming an equal-phase sinusoidal
current distribution flowing on the th antenna with its terminal
shorted [6], [7]. The excitation field produced by the driving current distribution on the th antenna is usually calculated by assuming that the th antenna element is in the transmitting mode
1536-1225/03$17.00 © 2003 IEEE
HUI: COMPENSATING FOR MUTUAL COUPLING EFFECT IN DIRECTION FINDING
27
Fig. 1. The linear dipole antenna array and the coordinate system.
Fig. 2. The spatial spectrum of the MUSIC algorithm for the detection of the two coherent signals in Table II by using a seven-antenna dipole array with the
mutual impedances calculated by the new method and the conventional method. The dimensions of the array are n = 7, d = 0:5, ` = 0:5, a = =200, and
Z = 96:70 j 41:20.
0
[6], [8] (some further assumed a sinusoidal current distribution
also flowing on the th antenna such as [7]). Errors are expected
from this method, mainly due to the assumption of one of the antennas (the exciting antenna) in the transmission mode whereas
in the real situation (described by (1)), both antennas should be
in the receiving mode. To correct these errors, we implement the
following two changes. First, the current distribution on the th
antenna is obtained by exciting it with an incident plane wave
instead of ascoming from the horizontal direction
suming the antenna to be in the transmitting mode. This estimated current distribution is to simulate the real current distribution on the th antenna which is in the receiving mode and
excited by the incoming signals. Second, instead of calculating
by using the reciprocity theorem, we simply calculate
as the total voltage dropped across the self impedance
and
of the th antenna. The effect of these
the load impedance
two changes is that the mutual impedance so calculated is much
more accurate to indicate the amount of coupling between two
antenna elements. The result of using the new mutual impedance
to compensate for the mutual coupling effect will be demonstrated below by using the MUSIC direction finding algorithm.
III. NUMERICAL EXAMPLES
We first calculate the mutual impedances of a seven-element
linear dipole array, as shown in Fig. 1, by using the new calcu-
28
IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 2, 2003
Fig. 3. The spatial spectrum of the MUSIC algorithm for the detection of the two coherent signals as in Fig. 2 but with Signal 2 coming from an elevation angle
of = 70 (perfect sampling of voltage is assumed in both methods).
TABLE I
MUTUAL IMPEDANCES CALCULATED BY THE NEW METHOD AND THE CONVENTIONAL METHOD FOR THE DIPOLE ARRAY SHOWN
WITH n = 7, d = 0:5, ` = 0:5, a = =200, AND Z = 96:70 j 41:20
0
lation method as described above. The open-circuit voltage
and the estimated current distribution on the th antenna are calculated by the moment method. The mutual impedances calculated by the new method are shown in Table I in comparison with
those calculated by the conventional method [6]. The array pa,
,
,
, and
rameters are
(conjugate of the self impedance). Comparison
in Table I shows that the mutual impedances calculated by the
new method are very different from the results obtained by the
conventional method. The new mutual impedances are then used
from the measured terto calculate the open-circuit voltage
IN
FIG. 1
by using (1) for each antenna element. The
minal voltage
open-circuit voltages are then passed to the MUSIC algorithm
to search for the directions of arrival (DOAs) of the signals.
Two numerical examples will be shown. In the first example,
the signal environment is shown in Table II. Two coherent signals are to be detected. The spatial smoothing technique [11]
is implemented to detect coherent signals. A noise power level
of 3.3116 W is assumed. This corresponds to a maximum
signal-to-noise ratio of 5.6 dB in the measured terminal voltages. Note that the process of calculation of the open-circuit
voltages from the measured terminal voltages also affects the
HUI: COMPENSATING FOR MUTUAL COUPLING EFFECT IN DIRECTION FINDING
29
TABLE II
SIGNAL PARAMETERS FOR THE DETECTION RESULTS IN FIG. 2
noise subspace and the modified MUSIC algorithm as described
in [1] is used to account for the distorted noise subspace. This
detection problem has actually been studied before [1]. The result by using our new method is shown in Fig. 2, in comparison
with that obtained by using the conventional method in [1]. Note
that the result in [1] is based on a 300 samples of voltage, while
our result is based on a perfect sampling of voltage. To show
the effect due to the sampling error, we have also recalculated
the result using the conventional method but based on a perfect
smapling of voltage. As shown in Fig. 2, a significantly better
performance can be obtained by using the new method. The
sharpness and the accuracy of the peaks are greatly increased
compared with the result obtained by using the conventional
method. A limitation of the new method is that the calculation
of the mutual impedances uses an estimated current distribution
excited by a plane wave coming from the horizontal direction
. In the second example, we show the performance of
the new method when a signal comes from an elevation angle
different from 90 . The signal environment is same as that in
(Signal 2) is changed
Table II except that the signal at
to come from an elevation angle of
. The result is shown
in Fig. 3. It can be seen that even under this condition, the result
obtained by using the new method is still better than that obtained by the using the conventional method (perfect sampling
of voltage is assumed in both methods). Hence, the limitation
of estimated current distribution will not significantly affect the
result provided that the signals are coming from elevation angles that are not too far from 90 .
IV. CONCLUSION
A new method for the calculation of the mutual impedance
is introduced for the compensation of mutual coupling effect
in a dipole antenna array employed for direction finding. This
method uses an estimated current distribution and a different
method for the calculation of the open-circuit voltage. It has
been shown that the new method can significantly improve the
performance of the MUSIC algorithm.
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