ACCEPTED VERSION

1

Effect of Number of Elements of a
Reactively-Loaded Ring Antenna Array on the
Performance of Beamwidth Variation
Shinya Sugiura, Member, IEEE, Noriyoshi Suzuki, Member, IEEE, and Hideo Iizuka, Member, IEEE

Abstract— We herein investigate the effect of the number of
elements of a previously studied reactively-loaded ring antenna
array with respect to electronically variable beamwidth performance. The antenna has a unique ability to increase theeffective antenna length by adding parasitic ring elements, which
contributes to higher performance with respect to beamwidthvariation. Monte Carlo (MC) simulations clarify that variable
range of beamwidth can be improved effectively by increasing
the number of ring elements M to five. It is herein demonstrated
for the case of M = 5 that the beamwidth toward the broadsidedirection can be controlled from 40o to 145o in the E plane,
while maintaining the voltage standing-wave ratio (VSWR) to lessthan 3.0, where the antenna size is 0.32λ×1.32λ. In addition, it isalso confirmed that the number of estimated directions-of-arrival(DOAs) based on the reactance-domain multiple signal classification (MUSIC) algorithm can be also increased by increasing
the number of ring elements.
Index Terms— Active antennas, antenna array, direction-ofarrival estimation, reactively steered antennas, parasitic elements,
road vehicles, varactors, variable beamwidth.

I. I NTRODUCTION
EHICLE-to-vehicle (V2V) communications have received a great deal of attention due to their potential
for reducing the number of traffic accidents. The patternreconfigurable antenna is a promising choice for improving
system performance [1]. While most of the previous studies
have focused primarily on beam and/or null direction steering,
beamwidth control is also expected to be effective for a simple
algorithm based on terminal speed, i.e., broad beamwidth at
low speed and narrow beamwidth at high speed, which does
not require complicated cross-layer optimization.
A number of variable beamwidth antennas with a single
RF branch have been developed. Most of these studies werebased on the adjustment of geometrical parameters or on
utilization of a phased array technique [2]-[5]. Lim et al. [6]were the first to propose an approach to tune beamwidth in anelectronic manner, based on the composite right/left-handed(CRLH) leaky wave antenna technique, without changing thegeometrical parameters.

V

c 2008 IEEE. Personal use of this material is permitted.
Copyright ⃝However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org
The authors are with Toyota Central Research and Development Laboratories, Incorporated, Aichi 480-1192, Japan (email:sugiura@mosk.tytlabs.co.jp;
nori@mcl.tytlabs.co.jp;
hiizuka@mosk.tytlabs.co.jp). S. Sugiura is also with the School of Electronics
and Computer Science, University of Southampton, Southampton SO17 1BJ,
U.K.
DOI: 10.1109/LAWP.2008.919815

In the field of single-feed pattern-reconfigurable antennas,
reactively steered antennas have been developed extensively[7]-[9], focusing primarily on beam and/or null direction
steering. There is difficulty in applying these antennas to
beamwidth control, however, because the spacing between thefeed element and the parasitic elements must be limited toless than approximately λ/4 in order for the feed element tomaintain sufficient mutual couplings with parasitic elements.
Thus, an effective antenna length that is of sufficient length for
beamwidth control cannot be obtained in this configuration.
More recently, a conformal steerable antenna composed ofthree overlapping ring elements has been studied for automobile applications [10]. This antenna has the potential toincrease the effective antenna length while maintaining strong
mutual couplings. In the present paper, the beamwidth of theconformal steerable antenna is investigated with increasing thenumber of ring elements. Numerical investigations indicatethat the beamwidth of the antenna is sufficiently narrow to use
in beamwidth-variation application. The antenna configuration
is presented in Section II. In addition, the formulation of thedirectivity is derived. In Section III, radiation patterns arecalculated by Monte Carlo (MC) simulations, and the performance of the beamwidth variation is discussed. In addition,
we mention another capability of high-resolution directionsof-arrival (DOAs) estimation based on the MUSIC algorithm,
which can be expected to give additional information usefulfor improving beamwidth control as well as beam direction
control. This paper is concluded in Section IV.
II. A NTENNA C ONFIGURATION AND F ORMULATION
Fig. 1(a) and 1(b) show a top view and a side view of the
proposed antenna configuration. This configuration is basicallyan extension of the configuration proposed in [10], where thenumber of ring elements was three. The proposed antenna
is constructed of M one-wavelength ring elements, which
are situated so as not to have any nodal point. The antenna
has 2M ports, which are arranged along the y-axis. The kth
port (1 ≤ k ≤ 2M ) is chosen as a balanced feed point
among the 2M ports, and variable reactance circuit are set
at the remaining 2M − 1 ports. Both beamwidth and beam
direction are controlled by changing the values of the circuits.
The number of ring elements M and the antenna length W
are related as W = λ/π + (M − 1) G, where G represents
the array spacing in the y direction. Note that 2M − 1
overlapping areas contribute to strong mutual couplings among

ACCEPTED VERSION

2

G

z
x

L

θ

Port 2

Port
2M-1

Port
2M-2

Port 1
Port 3

0
Port
2M

H

y
W
(a) Top viewxzφPort 2yPort 1

Port 2M-1
Port 2M-2

Port 3

Port 2M

D(b) Side viewFig. 1. Configuration of the proposed antenna. Each figure shows (a) top
view and (b) side view.

the ports and enable the antenna to work even in the conformal
configuration with large antenna length.
One wavelength ring element is assumed as a two-dipole
array with a spacing of 0.27λ, and the antenna in Fig. 1 canbe represented by an array of 2M equivalent dipole. Thisequivalent model makes it possible to formulate the antenna
directivity in the ϕ plane as a function of reactances, as shownfor the case of M = 3 and k = 2 in [10]. Here, the directivity
function is generalized to the case of arbitrary values of M
and k, as defined by a function of values of reactance circuitsT
x = [x1 · · · xk−1 xk+1 · · · x2M ] as follows:

]B
[d -3
deu
itl -6
p
m
A -9
ev
it
lae
R -12

-15
-180

Equivalent model
MoM

-120

-60

0
60
Angle [deg.]

120

180

Fig. 2. Radiation patterns calculated by equivalent model and method of
moment for the case of M = 5 and k = 1.
TABLE IA NTENNA PARAMETER
Height H
Line width L
Array spacing G
Gap D
Number of ring elements M

λ/π
λ/80
λ/4
λ/200
1–8

(1)

direction.
This formulation greatly reduces the complexity required
to calculate directivity. More specifically, x is easier to obtainfor a desired beamwidth in the practical stochastic simulations
conducted in Section III-A. In addition, the derived steeringvector (3) enables the implementation of the reactance-domain
MUSIC algorithm described in Section III-B.

where α is a constant and the weight vector w (x) and steeringvector a (ϕ) are given by()−1
w (x)= Y −1 + Xr
uk
(2)
}
[
{
2π T
a (ϕ) = exp j r 1 L (ϕ)
λ
{
}]T
2π
· · · exp j r T2M L (ϕ),(3)λ

In this Section, computer simulations are conducted toclarify the effect of the number of ring elements on theperformance of beamwidth variation and DOA estimation
based on the MUSIC algorithm. Below, a feed point is chosen
as k = 1, so as to facilitate feed of the antenna. The otherstructural parameters of the calculated antenna are listed inTable I. The operating frequency is set to 2.4 GHz.

T

D (ϕ, x) = αw (x) a (ϕ)

III. P ERFORMANCE

respectively, where
Xr = diag [ jx1 · · · jxk−1 zs jxk+1 · · · jx2M ]uk = [ δk−1 · · · δk−2M ]T

L (ϕ)= [ cos ϕ sin ϕ 0 ] .

T

(4)
(5)
(6)

Here, r i (i = 1, · · · , 2M ) are the port positions of theequivalent dipoles, and Y is the mutual admittance matrix.
δj is the Kronecker delta. Note that Y must be calculated in
2M full-wave simulations before using the directivity function(1). Practically, the variable reactance circuits are made of chipparts such as varactors, resistors, capacitors, and inductors, as
described in [10].
To confirm the validity of the generalized directivity function, a pattern calculated by (1) was compared with a patterncalculated by the method of moment (MoM). Fig. 2 showsTthe result for the case of M = 5, k = 1, x = [ 0 · · · 0 ] . The
two patterns show good agreement, especially in the high-gain

A. Beamwidth Control
MC simulations were conducted to obtain a set of x̂ thatrealizes a desired beamwidth ϕh0 and a desired beam direction
ϕ0 . The adopted metric here is given as follows:x̂ = arg max {J} ,x(7)where J is a proposed cost function to be maximized, which
is defined as
J = (1 − β) D (ϕ0 , x) (1 − ρ(x))()|ϕh (x) − ϕh0 |+β 1 −.
ϕh0(8)

ϕh (x) and ρ(x) are the half-power beamwidth (HPBW) andreflection coefficient, respectively. In addition, 0 ≤ β ≤ 1 is asimulation parameter to weight the first term with respect tothe second term in (8). The first term represents the antenna

ACCEPTED VERSION

3TABLE IIS IMULATION PARAMETERS
Weight βBeam direction ϕ0
Beamwidth ϕh0
Number of ring elements
Variable range of x

180
.]g
ed
[ 150
thd
iw
120
m
ae
br 90
ew
op
-fl 60
a
H
30

]B
-3
[d
ed
uit -6
lp
m
A -9
ev
it
al
eR -120.5
0o (fixed)
30o – 150o (every 5o )1–8−500 Ω < xj < 500 Ω

-15
-180

Upper boundLower bound
1

2

3
4
5
6
Number of ring elements M

145 deg

040 deg

-120

-60

0
60
Angle [deg.]

120

180

Fig. 4. Calculated radiation patterns of the proposed antenna with M = 5
and k = 1 in the E plane. ( —-: ϕh =40o , – –: ϕh =69o , - - -: ϕh =93o , – –: ϕh =145o .)7

8Fig. 3. Dependency of number of ring elements M on performance of
beamwidth variation.

gain toward the desired beam direction, where the influence ofimpedance mismatch is taken into account. The second term
represents the contribution of an incident beamwidth to thedesired beamwidth.
Simulation parameters are listed in Table II. A total of
100,000 random sets of x were generated to obtain eachsolution for certain ϕh0 and ϕ0 . The variable range of eachcomponent of x was given by −500 Ω ≤ xj ≤ 500 Ω ( j =1, · · · , k −1, k +1, · · · , 2M ). In the present paper, we focus on
the performance of beamwidth variation, as mentioned above.
Thus, ϕ0 was fixed to 0o , and ϕh0 was varied from 30o to
150o every 5o . Note that x, which gave ρ(x) > 0.5, were
eliminated from the results of the MC simulations so as tomaintain the voltage standing-wave ratio (VSWR) below 3.0.
Fig. 3 shows the dependency of the number of ring elements
M on the beamwidth-variation performance. Both the upperand lower bound of HPBW are indicated in the figure. It can beseen that the upper bound provides a nearly flat characteristic
within the range of 1 ≤ M ≤ 8. The upper beamwidth ismainly limited by the beamwidth of a single element (M = 1).
On the other hand, the lower bound decreased with increase of
M in the range of 1 ≤ M ≤ 5. The effective antenna length
could be extended to M = 5, by increasing the number of ringelements. For the case of M = 5, the antenna size was with
H × W = 0.32λ × 1.32λ, and the upper and lower boundof HPBW were 145o and 40o , respectively. In the range ofM ≥ 5, the lower bound did not change significantly because
the effective antenna length cannot be extended effectively.
This is caused by the fact that it becomes difficult to retain
the sufficient mutual couplings between the feed port and all of
the other ports. In addition, the calculated dimension becomes
higher with increase of M , which makes it difficult to obtainsuboptimal solutions. In other words, higher computational

complexity, i.e., the number of generated x, is required inorder to achieve a reasonable solution for cases in which thenumber of ring elements M is large. Next, Fig. 4 shows thecalculated radiation patterns for case of M = 5. The reactancevalues obtained by MC simulation are listed in Table III. As
the results indicate, the beamwidth effectively varied from 40o
to 145o , while the main beam direction was approximately
fixed to 0o .
Note that it has been verified in [10] that the radiation
patterns calculated by MoM agree to the experimental resultsin case of M = 3.
B. MUSIC
Reactance-domain MUSIC [11] was calculated in order toconfirm that the number of estimated DOAs can be increased
by increasing the number of ring elements M . Here, thealgorithm is basically the same as that in [10].
The antenna with M = 5 was assumed, and the otherantenna parameters were the same as those in Section IIIA. Ten patterns are employed to implement MUSIC. The
corresponding sets of reactance values are listed in Table
IV. Each of the patterns is selected so that the beams havediverse directions. In the calculation, six uncorrelated waves
with equal powers were generated, the DOAs of which were
−170o , −130o , −60o , 0o , 55o , and 125o . The average received
signal-to-noise ratio (SNR) of each of the waves was given by
20 dB. The number of DOAs was assumed to be known inadvance.
Fig. 5 shows the results obtained by MUSIC with the total
number of 10 × 1000 samples, and 10 × 100 samples. All
six waves were estimated at high resolution in the case with
10 × 1000 samples. It can be also seen that, although thepeaks become less sharp with the decrease of samples from10 × 1000 to 10 × 100, the estimated DOAs remain precise.
The theoretical maximum number of estimated DOAs was fivefor case of M = 3 [10]. Therefore, it was confirmed that the
number of estimated DOAs can be increased with the increasein the number of ring elements.

ACCEPTED VERSION

4TABLE IIII NCIDENT VALUES OF R EACTANCE C IRCUITS U SED IN PATTERN S IMULATION .
ϕh = 40oϕh = 69oϕh = 93oϕh = 145ox2
487.1 Ω
495.5 Ω
466.2 Ω
-441.1 Ωx3
101.2 Ω
27.7 Ω
448.3 Ω
-75.1 Ω

x4
484.1 Ω
407.6 Ω
425.5 Ω
-355.7 Ωx5
187.3 Ω
399.6 Ω
-474.5 Ω-422.0 Ω

x6
172.8 Ω
451.0 Ω
217.1 Ω
57.0 Ω

x7
364.3 Ω
-378.6 Ω
111.0 Ω
391.5 Ω

x8
166.1 Ω
485.4 Ω
62.2 Ω-391.8 Ωx9447.8 Ω
-38.5 Ω
112.9 Ω
-97.0 Ω

x10-304.1 Ω-180.2 Ω-410.7 Ω
194.2 ΩTABLE IVI NCIDENT VALUES OF R EACTANCE C IRCUITS U SED IN MUSIC S IMULATION .

#1
#2
#3
#4
#5
#6
#7
#8
#9
#10

x2
412.2 Ω
-372.7 Ω-23.6 Ω
-297.5 Ω-1.7 Ω
472.5 Ω
-375.6 Ω-23.8 Ω
-208.0 Ω
138.8 Ω

x3
350.4 Ω
-142.3 Ω-141.4 Ω
89.1 Ω-281.1 Ω
221.5 Ω
-140.2 Ω-110.4 Ω
93.0 Ω-264.4 Ω

x4-182.9 Ω-80.3 Ω
494.0 Ω
-314.4 Ω-392.7 Ω-374.0 Ω
399.8 Ω
382.4 Ω
263.6 Ω
-67.4 Ω

x5
25.5 Ω
277.9 Ω
-101.6 Ω-57.3 Ω
459.2 Ω
-214.2 Ω
258.9 Ω
408.1 Ω
-208.6 Ω
129.4 Ω

x7
130.4 Ω
173.1 Ω
206.1 Ω
-300.5 Ω-14.2 Ω
100.5 Ω
218.8 Ω
-213.9 Ω
409.8 Ω
379.8 Ω

x8
142.5 Ω
-186.7 Ω-31.5 Ω
99.0 Ω
144.6 Ω
391.5 Ω
272.6 Ω
495.4 Ω
-351.4 Ω-192.7 Ωx9-444.2 Ω
204.4 Ω
-422.5 Ω
482.6 Ω
321.6 Ω
287.9 Ω
-114.1 Ω-82.1 Ω
-9.4 Ω-340.7 Ωx10257.4 Ω
20.8 Ω-112.2 Ω
371.7 Ω
418.5 Ω
348.4 Ω
-210.0 Ω
355.1 Ω
-184.3 Ω-74.0 Ω

performance of delay-restricted vehicle-to-vehicle communications without the requirement for a complicated cross-layer
algorithm.

]B 0d[mur -10tce
ps
CIS -20UMR EFERENCES-30-180 -120x6-434.9 Ω-469.9 Ω
247.7 Ω
53.7 Ω
246.5 Ω
-231.5 Ω-216.6 Ω-97.9 Ω
-2.4 Ω-459.2 Ω-60

060
Angle [deg.]

120

180

Fig. 5. Calculated MUSIC spectrum for 10×1000 samples (plain-line) and10×100 samples (dashed-line), DOAs = −170o , −130o , −60o , 0o , 55o , and125o . Average received SNR = 20 dB for each signal.

IV. C ONCLUSION
An electronic beamwidth-control approach has been presented as an extension of a previously-proposed reactivelyloaded ring antenna array. The antenna has a unique capability
to increase the effective antenna length by increasing thenumber of ring elements. Computer simulations have clarified
that the beamwidth-variation performance can be effectively
improved by increasing M to five. In addition, the numberof estimated DOAs based on the reactance-domain MUSIC
algorithm was found to increase as well.
In order to solve a problem that this beamwidth-variable
antenna radiates toward both sides, i.e., ϕ = 0o and 180o , thetransparent artificial magnetic conductor (AMC) application
described in [12] is a promising technique. The detailed
investigation of the beamwidth-variable antenna combinedwith the transparent AMC is a subject for future study.
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