1

Abstract— In this paper, a system has been designed for an

operational frequency of 1.27 GHz consisting of an 8 element array of

parasitic dipoles illuminated by a 4 element center fed array of active

dipoles with Dolph-Chebyshev excitation coefficients. The array is

designed to achieve a fairly pencil beam pattern suitable for direction

of arrival estimation purposes. Array geometry and configuration is

optimized for both active and parasitic elements using the PSO tool in

FEKO. A directive radiation pattern is obtained with a gain of 14.5

dBi in the broadside direction along with a beamwidth of 30.29o.

VSWR of 1.58 is achieved. Further, an iterative least square valued

error estimation approach using phase control to achieve a desired

array factor pattern for an n-element linear array, has been shown to

be effective for larger number of iterations. The array excitation

coefficients achieved were consistent with the Dolph-Chebyshev

coefficients used in our antenna array design. With the ability to

introduce nulls and steering the main beam in desired directions

along with a pencil beam radiation pattern, beamsteering has been

illustrated and the MUSIC algorithm for direction of arrival

estimation has been implemented.

Index Terms—Linear Parasitic Array; Pattern Synthesis; Beam

Steering; DOA Estimation; MUSIC Algorithm

I. INTRODUCTION

Antenna arrays are increasingly being used for a variety of

applications due to their ability to control certain parameters of the

radiation pattern like pattern maximum steering, null angle

placement, increasing the Signal to Interference plus Noise ratio. A

pencil beam radiation pattern is generally obtained by increasing

the effective size of the active array by increasing the number of

elements and element spacing. However this leads to increased

cost, size and complexity. A workaround to this problem is to

make use of the mutual coupling between active and parasitic

elements in the array that allows us to use lesser active feed

elements. This technique also allows parasitic array elements to

introduce degrees of freedom that ensure that pattern can be

synthesized without modification of the active array feed.

Therefore, an 8 element array of parasitic dipoles is illuminated by

a 4 element active array above a finite ground plane to obtain a

pencil beam pattern and its characteristics are observed.

Furthermore, the pattern synthesis problem is crucial to any

array design problem. The desired pattern synthesis problem using

an iterative technique to get a desired radiation pattern is shown to

improve for larger iterations. With the ability to introduce nulls

and steer the beam, Beam steering by changing phases is observed

and the MUSIC algorithm is shown to effectively estimate the

angle of arrival.

II. DESIGN PROCEDURE

We look at the geometry of active/parasitic array combinations

which can be optimized to achieve the desired performance. We

consider the synthesis of low-sidelobe sum patterns generated by

antennas consisting of a parasitic linear array of half-wavelength

dipoles illuminated by similar uniformly fed active array. A real

non-infinite ground plane is included to increase the overall

directivity of the radiation pattern. The parameters which are

manipulated for the pattern synthesis are the distance of the

respective arrays from the ground, distance between adjacent

dipoles in each array and distance between the two arrays. The

effect of mutual coupling between the elements has been taken

care of and accounted by means of FEKO simulation with PSO

optimization. The proposed method is based on the optimization of

the array geometry in order to obtain a highly directive pattern. A

uniformly spaced planar array of parasitic dipoles of length λ/2 is

considered as a starting point in the optimization process. In this

procedure, the distance between the planar array and the ground

plane and the interspacing in the x-axis direction of the parasitic

array are modified. The aim is to find the optimal array geometry

that fulfill the requirements of a given design problem. The

variables mentioned above were optimized by means of PSO to

minimize a cost function C consisting of a term to increase the

directivity in the broadside (Θ=00, Φ=0

0):

C = 1/Directivity (D0) (1)

Taking into account the optimized values we consider an

antenna system consisting of 1.) A non-infinite ground in the x-y

plane with moist soil dielectric whose εr = 30 and tan δ = 0.007;

2.)A linear array of 4 center-fed half-wavelength wire dipoles

oriented parallel and above the x-y plane at a height hactive = λ/4

with their centers located at regular intervals of λ/2 along a line and

3.) A similar linear array of 8 parasitic elements arranged along the

line in the x-y plane at a height hparasitic= 5λ/4. The active dipoles

are excited according to the Dolph-Chebyshev array excitation

coefficients and these have been found out for a 4-element array

system with a side-lobe level to be 30 dB down from the main lobe.

If vector I represents the current distribution on this antenna then it

is given by

I = Z-1

V (2)

where V is the vector of voltages (Vn=22.22 or 9.53 if the element

n is active; Vn=0 if it is parasitic) and Z is the impedance matrix.

Figure 1: Antenna Array Design Schematic with real ground

III. PATTERN SYNTHESIS

Beam forming allows placement of single or multiple nulls in the

antenna pattern at specific interference directions. Prescribed nulls

in the radiation pattern are formed to suppress interferences from

specific directions. For broadband interference, null in the pattern

should be wide and deep enough to suppress peak side lobe levels

at the angular sector of arrival of interference. Nulling methods are

based on controlling complex weights. Having already achieved a

directive pattern for the Dolph-Chebyshev amplitude coefficient

arrangement, we have focused on optimizing array coefficients

further by using phase control.

Designing a pencil beam pattern with low

sidelobes using pattern synthesis technique and a

system of active linear array illuminating

parasitic dipoles

Gaurav Narula(1)

, Piyush Kashyap(2)

(1)(2)Graduate Student, ECEE Department,

University of Colorado at Boulder

Boulder, CO 80309

United States (1)gana2553@colorado.edu, (2)pika7816@colorado.edu

2

The problem considered is as follows. We want to find a weight

vector W for which the array factor has a beam maximum at some

angle ϴd and meets a given side lobe specification for other angles.

The prerequisites to this problem i.e. number of elements (n) of the

array, element spacing (d), and element patterns are obtained from

the array design performed in FEKO. Consider an n element linear

array as shown in Figure 2. Let fi(ϴ) be the pattern element of each

element.

Figure 2: N-element Linear Array

Let X be the received signal vector with xi(t) being the received

signal on ith element.

X=[x1(t), x2(t), x3(t)….. xn(t)]T

(3)

The array output signal s(t) can be obtained using the following

expression:

s(t) = WT

X (4)

where, W is the weight vector,

X = Aejωo

U is the received signal vector with xi(t) the received

signal on ith element.

Effective array output can be expressed as:

s(t)= Aejω0

WTU (5)

where A is the signal amplitude, U is a vector that includes inter

element phase shifts and pattern defined as follows

U=[f1 (ϴ) , f2 (ϴ) e-jϕ2(ϴ)

, f3 (ϴ) e –jϕ3(ϴ)

…… fn (ϴ) e–jϕn(ϴ)

]T

dk (6)

The algorithm we deploy to get desired nulls and maxima

essentially finds the vector W for which p(ϴ) = WTU has a beam

maximum at desired angle ϴd and nulls at other angles. As given in

[9] ,the expression obtained for the weight vector is given by

W = µϕu-1

Ud* (7)

where, Ud is vector of signal from desired direction, Ud*

is

conjugate of Ud, µ is an arbitrary non zero scalar, ϕu is covariance

matrix of undesired signal, Ui is matrix specified in (8) with ϴ=ϴi

and Ai is the interference amplitude.

Computations based on above formulae are performed on

MATLAB for introducing a null by introducing interference signal

at a specific or range of angles as shown in Fig. 3 and Fig. 4.

(a)

(b) Figure 3: Adapted patterns with one interference signal at ϴ = π/4 for n =

4element array with ideal isotropic elements (a) INR= -10 dB (b) INR = 10 dB.

These plots show Power variation (in dB) with angle ϴ (in degrees).

Using an iterative technique and the formulations given in [9] the

approach for desired pattern synthesis problem is as follows:

1. The main beam is steered in the desired direction by choosing a

steering vector Ud.

2. To reduce side lobes, a large number of interference signals are

assumed to be incident on the array from side lobe region. Matrix

Ui is generated.

3. Interference amplitude matrix Ai with 32 different combinations

of random numbers is formed to form a pattern P.

4. An adapted weight matrix is created that contains phase

coefficients to be multiplied with each element of the array to get

the desired pattern.

5. 32 adapted patterns are obtained and compared with the design

objective to get an Error matrix.

6. For next iteration, combination with 16 least valued errors are

used as elements of matrix Ai and 16 other random patterns are

obtained using the next16 random numbers in Ai.

After desired number of iterations, of the 32 patterns obtained, the

Weight matrix Wand Interference amplitude matrix Ai for the one

with least deviation is used for the pattern synthesis of the array.

An increase in the number of iterations leads to a better pattern as

shown in Figure 5 where 100 iterations brings down the sidelobe

levels by 10.43 dB approximately.

(a)

(b)

Figure 4: Adapted patterns with 21 interference signals from ϴ = -20oto -60

o

for an 8 element linear array with isotropic elements (a) INR = -10 dB (b) INR

= 10 dB. These plots show Power variation (in dB) with angle ϴ (in degrees).

3

(a)

(b)

(c)

Figure 5: Patterns obtained by the Iteration techniques taking least value

squared error values between desired pattern and obtained patterns (a) Desired

Pattern (b) 100th iteration (c) 50

th iteration. These plots show Power variation

(in dB) with angle ϴ (in degrees).

IV. RESULTS AND DISCUSSION

A. Gain

The structure parameters have been chosen in such a way that the

VSWR obtained is less than 2 and the antenna gain is maximized

at the frequency of operation. The value of gain obtained is 14.5

dBi as shown below in Figure 7.

Figure 7: Far field Gain pattern for antenna array with real ground plane

B. Radiation Pattern, Beamwidth and VSWR

The E-plane radiation pattern obtained for our antenna array at

operational frequency is below shown in Figure 8.

Figure 8: Electric Field radiation pattern for our antenna array system

At 1.27 GHz, the Half-Power Beamwidth, of our antenna array is

about 30.29o. This is shown below in Figure 9.

Figure 9: 3dB Beamwidth of antenna array system

VSWR obtained at 1.27 GHz is 1.58, as shown in Figure 10.

Figure 10: VSWR vs Frequency

C. 2:1 VSWR Bandwidth

The obtained 2:1 VSWR bandwidth for our antenna array system is

282 MHz as shown below in the Figure 11.

Figure 11: 2:1 VSWR Bandwidth

D. Performance of antenna array with no parasitic elements

Comparing the results obtained for our antenna array system to that

when there are no parasitic dipoles present in our antenna we found

that, at operational frequency, gain gets reduced to11.5 dBi so as

the directivity. As a result, the 3 dB beamwidth increases to 38.290.

Values of VSWR and Reflection Coefficient increase to 3.45 and

0.55, respectively. We conclude that using parasitic array of

dipoles does help us achieve substantially better antenna

performance in terms of increase gain (or directivity) and low

reflection coefficient.

E. Effect of height of active and parasitic array from the ground

and distance between the elements

Here we changed the value of hparasitic from 5λ/4 to 3λ/4 and

generated a curve for reflection coefficient which shows a drastic

change in the value of ρ. The new value of reflection coefficient

obtained is about 0.73. This is shown below in Figure 12.

Figure 12: 3dB Beamwidth when hparasitic = 3λ/4

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Also, the directivity of antenna array gets reduced to 12.7 dBi and

as a result beamwidth of antenna array increases to 40.780. VSWR

increases to 6.24.

V. VALIDATION

As is expected, increasing the number of active dipoles in the array

will improve the performance. This has been shown in [3]. The

same can be validated in Table 1 for a fixed parasitic/active ratio of

M/N. However , for a given number of active dipoles, increasing

the number of parasitic dipoles only improves performance upto a

M/N ratio of about 2 [3] . This is validated in Table 2. Table 1 and

Table 2 are obtained by simulation on FEKO for different number

of active and parasitic dipoles.

M N M/N Directivity(dBi) BW(o) VSWR

12 6 2 15.7 24.21 1.56

8 4 2 14.5 30.29 1.58

4 2 2 12.7 38.66 1.74 Table 1: Performance variation with change in number of active elements for a

fixed parasitic to active elements ratio (For constant M:N)

M N M/N Directivity(dBi) BW(o) VSWR

2 4 0.5 13.8 34.395 2.24

4 4 1 14.2 31.39 1.76

6 4 1.5 14.4 30.76 7.68

8 4 2 14.5 30.29 1.58

10 4 2.5 14.5 30.55 1.59

12 4 3 14.5 30.48 1.59 Table 2: Performance variation with change in parasitic to active elements

ratio (Change in M:N)

Fig. 9 shows the radiation pattern polar plot for the range ϴ = 0o to

180o, obtained by simulating our antenna design on FEKO. The

same can be validated in Figure 6 which is the array factor pattern

for a non-uniform 4 element array with Dolph-Chebyshev

coefficients obtained on MATLAB. Two anomalies in Figure 6,

which are the back lobe and two sidelobes, can be explained due to

lack of ground plane and the array of parasitic elements while

computing on MATLAB. This is understandable as the parasitic

array serves to bring side lobes down and increase the gain.

However, general shape of curve remains same.

VI. APPLICATION (DOA ESTIMATION)

Having obtained a pattern and the ability to synthesise one, our

antenna array system can be used for beam steering purpose to

estimate the direction of arrival. The resolution with which the

beam is steered further depends on the phase excitation

coefficients. An illustration of beamsteering is shown in Fig. 6

Figure 6: Beam Steering

We have seen that there is one-to-one relationship between the

direction of a signal and the associated received steering vector. It

should therefore be possible to invert the relationship and estimate

the direction of a signal from the received signals. An antenna

array therefore should be able to provide for direction of arrival

estimation. This serves as an application of the antenna array

system that we have designed above. The purpose of DOA

estimation is to use the data received by the array to estimate the

direction of arrival of the signal. The results of DOA estimation are

then used by the array to design the adaptive beam former in such a

way as to maximize the power radiated towards the users and to

suppress the interference.

MUltiple SIgnal Classfication (MUSIC) is one of the DOA

algorithms which can be used to estimate the direction of arrival

with a high spatial resolution. The basic idea of MUSIC is that the

eigenvalues and eigenvectors of a signal covariance matrix are

used to estimate the DOAs of multiple signals received by the

antenna array. In this paper, we have used MATLAB© to do some

simulations in order to determine which factors affect the DOA

estimation. A matlab program on basic MUSIC algorithm for DOA

estimation has been written for 4 elements with spacing of λ/2

between them and a plot of Spectrum Function P(Θ) vs Angle (Θ)

has been generated as shown below in Figure 13.

As can be seen from Figure 13, for a received signal at Θ = 450,

using MUSIC a needle spectrum peak algorithm can be

constructed. It may well estimate the number and direction of the

incidence signal, which can be used to estimate the independent

signal source DOA effectively.

Figure 13: DOA estimation based on Music Algorithm

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