The document discusses modifications needed to beam steering algorithms when using a dielectric lens with an antenna array. It describes using ray tracing to model the refraction of signals through the lens, which is needed to compensate for the virtual angles measured by the antenna elements. Backward ray tracing is used to determine the true arrival angles from the virtual angles. The critical angle of the lens is analyzed, above which signals will be totally internally reflected rather than reaching the antennas. The MUSIC algorithm is investigated as an example, with modifications to the steering vector to estimate the correct directions of arrival when a lens is used.

1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 18-24 © IAEME
18
MODIFICATION TO BEAM STEERING ALGORITHMS IN THE PRESENCE
OF DIELECTRIC LENS
Prakash Biswagar, Dr. S. Ravishankar, Ph.D
RV College of Engineering, Bangalore (India)
ABSTRACT
Adaptive array smart antenna involves the array signal processing to manipulate the signals
induced on various antenna elements in such way that the main beam is directed towards the desired
user and nulls are formed towards the interferers. A smart antenna has to meet contrasting
requirements of compact form factor and high gain. A shaped dielectric lens can be used along with
the antenna elements to further collimate the rays in the specified direction, improving directivity,
reducing interference and significantly reducing the number of array elements. The dielectric lens
also acts as a radome protecting the array from environmental effects. However there are two
drawbacks with the use of dielectric lens: 1) Compensating the refractive effects of the lens in the
receiving mode to obtain the true angles of arrival to locate the desired signal, and 2) Computation of
the radiation pattern. This paper dwells on the first drawback viz. modification to the beam steering
algorithms to estimate the true Direction of Arrival (DOA). One popular algorithm, namely, Multiple
Signal Classification (MUSIC) is investigated in the presence of lens.
Keywords: Smart Antenna, Shaped Dielectric Lens Antenna, Refraction, DOA and ABF
1. INTRODUCTION
Smart antennas enable a higher capacity in wireless networks by effectively reducing
multipath and co-channel interference leading to better spectrum utilization. The link rate to a mobile
subscriber is dependent on the adaptive antenna system and its underlying signal processing
algorithms [1, 2 and 5].
Lens provides a collimation that helps to shrink the size of a larger array, which in effect
translates to a reduced RF cost [3]. But with a lens, direction of the signal received at the antenna
elements is different from that of the actual angle due to refraction; hence we need an angle
dependent correction factor in the steering vector to get the true angle. To obtain the correction
factor, the phase change inside the lens is considered before reaching the antenna elements.[5, 10].
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2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
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In this paper, ray tracing approach is used to generate the steering vector needed to implement
the direction of arrival estimate algorithms. The work contribution here includes
(i) Forward ray tracing through the lens to find the actual and virtual DOA.
(ii) Analysis of critical angle of refraction.
(iii)Backward ray retracing to determine the required angle.
(iv)Progressive blindness due to critical angle.
2. FORWARD RAY TRACING
The forward ray tracing is illustrated below in figure 1.
Figure 1: Ray tracing approach
Forward ray tracing helps in finding the angle of refraction (r2) through the lens, when the
angle of incidence (Ѳ) is known. It also helps in finding the rays that will hit the antenna elements.
Figure 2 below shows how the ray tracing was used to find angle of refraction through the lens for
different angles of incidence. Finally it helps in finding the critical angle which is of great
importance [4].
(a) Direction of angle of arrival is 200
(b) Direction of angle of arrival is 300
Figure 2: Forward ray tracing for different arrival angles of incidence
The parameters calculated in forward ray tracing are used for both DOA and backward ray
tracing.

3. International Journal of Electronics and Communication Engineering &
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp.
3. BACKWARD RAY TRACING
The backward ray tracing is
the antenna array to outside the lens.
Figure
Once the virtual angle at each elements are calculated using forward ray tracing technique,
our aim is to find true angle of incidence (in this case transmit di
direction. In the above figure,
i1= angle at which ray enters the
r2= angle of refraction
Once virtual DOA is calculated using forward ray
backward ray tracing.
4. CRITICAL ANGLE CONDITIONS
The critical angle corresponds to the angle, at which the ray will be reflected back from the
plane surface of the lens due to total internal reflection. At the
array elements. In this simulation, the number of elements and the diameter of the lens are fixed.
Figure 4 below depict one such case with red vertical lines represent
Figure 4
The refraction occurring in the lens for different arrival angles of 45
below in figures 5 (a) and (b) respectively.
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976
6472(Online), Volume 5, Issue 3, March (2014), pp. 18-24 © IAEME
20
The backward ray tracing is illustrated below in figure 3. Here the EM rays are traced from
the antenna array to outside the lens.
Figure 3: Backward ray tracing
Once the virtual angle at each elements are calculated using forward ray tracing technique,
our aim is to find true angle of incidence (in this case transmit direction) and forming beam in that
= angle at which ray enters the lens
= angle of refraction
Once virtual DOA is calculated using forward ray tracing, the aim is to find true DOA using
4. CRITICAL ANGLE CONDITIONS
The critical angle corresponds to the angle, at which the ray will be reflected back from the
plane surface of the lens due to total internal reflection. At the critical angle the rays will not hit the
array elements. In this simulation, the number of elements and the diameter of the lens are fixed.
below depict one such case with red vertical lines representing the antenna elements.
4: The rays showing partial blindness
The refraction occurring in the lens for different arrival angles of 450
and 50
(a) and (b) respectively.
Technology (IJECET), ISSN 0976 –
© IAEME
M rays are traced from
Once the virtual angle at each elements are calculated using forward ray tracing technique,
rection) and forming beam in that
tracing, the aim is to find true DOA using
The critical angle corresponds to the angle, at which the ray will be reflected back from the
critical angle the rays will not hit the
array elements. In this simulation, the number of elements and the diameter of the lens are fixed.
the antenna elements.
and 500
are as shown

4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 18-24 © IAEME
21
(a) Direction of angle of arrival is 450
(b) Direction of angle of arrival is 500
Figure 5: Finding the critical angle using ray tracing technique
When the rays lie above the critical angle range, all the rays are reflected back due to the
phenomenon of total internal reflection from the plane surface of the lens.
As in figure 5(a) above, at an angle of 450
, the EM rays will just graze the surface and as in
figure 5(b) at 500
, the total internal reflection will occur. Thus, the antenna array receives no rays to
calculate the virtual DOA. As we scan off bore sight, we progress from full visibility to all
elements, through a stage of partial blindness due to some elements becoming invisible to total
blindness where none of the elements are visible. Under these circumstances the usage of the lens
leads to loss of signal sources, especially at angles greater than 500
[5,6].
Referring to figure 3 above, the critical angle can be calculated as below.
At the point(x2, y2), bottom surface of the lens for critical angle r2=900
and i2=i2c
r
ci
r
ε=
2
2
sin
sin
(1)
r
ci
ε
1
sin 2 =
cci 1
0
2 90 θ−= and






−
= −
21
11
1 tan
xx
y
cθ (2)
At the point (x1, y1), let the critical angle be rc






=
−−=
−
1
11
1
0
tan
90
y
x
nawhere
nar cc θ
Therefore






−





−
−= −−
1
11
21
110
tantan90
y
x
xx
y
rc (3)
r
c
c
r
i
ε=
sin
sin
(4)

5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 18-24 © IAEME
22
Hence the critical angle is
naicc −−= 0
90θ




















−





−
−=
=
−−−
−
1
11
21
1101
1
tantan90sinsin
]sin[sin
y
x
xx
y
i
ri
rc
crc
ε
ε
(5)
5. DOA ALGORITHMS WITH LENS
The angle of arrival (AOA) using DOA algorithm is obtained in the absence and presence of
dielectric lens. In the presence of lens, the AOA will be altered because of the Snell’s law applied at
the boundaries of the dielectric lens. When DOA algorithm applied, it results in virtual DOA. To
overcome this problem the beam steering vector is modified as per the flow chart shown in figure 6
below.
Figure 6: Algorithm to obtain the correct DOA

6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 18-24 © IAEME
23
6. RESULTS AND OBSERVATIONS
While simulating the DOA algorithms with lens, following assumptions were made
(1) Frequency of operation be 10 GHz.
(2) Direction of signal detection has a range from [-90, 90] degrees
(3) Source to be in the far-field of the antenna array with lens
(4) Number of antenna elements to be 8
(5) Inter element spacing be λ/2
(6) Dielectric lens be made of Teflon with 08.2=rε
The results are shown in the figure 7 below.
Figure 7: MUSIC algorithm with and without lens
It can be observed from the above figure, that when lens is used for collimation, the direction
of signal received at the antenna elements is different from that of actual angle and hence correction
factor is needed in the steering vector to get the true angle.
7. CONCLUSION
It was shown that DOA algorithms provide better resolution and higher gain in the presence
of lens, as the power of the incoming signal will be enhanced due to the collimation provided by the
lens. Also, it was discussed, how corrections are added for the DOA algorithms to compensate for
the refractive effects of the lens.
8. REFERENCES
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approach”, IEEE Signal Processing Magazine. pp. 67-94, July 1996.
[2] H.V. Trees, Part IV, Optimal Array Signal Processing. John Wiley publication, 2002.
[3] Carlos A Fernandes, Jose G Fernandes, “Performance of Lens Antennas in Wireless Indoor
Millimeter Wave Applications,” IEEE Transactions on Microwave theory and Techniques,
vol 47, No 6, pp 732-736, June 1999.

7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 18-24 © IAEME
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[4] S. Ravishankar and H.V. Kumaraswamy, “Smart Antenna System using Dielectric Lens,”
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