A simple power – based direction of arrival sensor

Kỹ thuật điều khiển & Điện tử 
 48 V. T. Nga, L. M. Thuy, “A simple power - based Direction of Arrival sensor.” 
A SIMPLE POWER – BASED DIRECTION OF ARRIVAL SENSOR 
Vu Thi Nga, Le Minh Thuy
* 
Abstract: In this paper, a simple power - based Direction of Arrival (DoA) sensor is 
investigated. This sensor is applied in direction finding systems working at 2.6 GHz. The 
proposed sensor can determine the DoA via a simple formula compared to the algorithms 
– based methods. The sensor structure consists of simple components: two receiving 
antennas and a power dividers which have a good isolation between output ports based on 
hybrid couplers (HCs). With the range of simulation DoA from 0
o
 to 35
o
, the proposed 
sensor yields the error of less than 5
o
. 
Keywords: Direction finding (DF); Direction of Arrival (DoA); Power – based; Hybrid coupler (HC). 
1. INTRODUCTION 
As can be seen, the world is at an explosive increasing rate with mobile communication. 
Array antennas and base - stations are playing an important role to meet the demands of global 
user equipments. With a large number of the user nowadays, adaptive signal processing array 
known as the smart antenna, which commonly used in new generations mobile systems, can 
locate mobile users by using DoA estimation techniques. The goal of direction of arrival (DoA) 
estimation is to use the data received on the downlink at the base-station to estimate the 
directions of the signals from the desired mobile users as well as the directions of interference 
signals. The result of DoA estimation is used to determine the location of users so that the 
maximum power towards the desired users while radiation nulls in the direction of interference 
signals. Therefore, direction finding (DF) for multiple wireless devices is paid more attention in 
communication applications. For examples, in the military, it is required to determine accurately 
the position of a potential enemy. It can be accomplished by finding the direction of the coming 
wave. Another application, in robotic technology, DF helps robots be aware of the around 
obstructions without the external remote control. Direction of arrival (DoA) estimation was 
found out and developed since the years of the last century. Watson Watt principle is a power – 
based method in which the DoA is obtained from the ratio of the amplitude of received signals 
applied on the x and y plane. The other method, which is phase – based, is accomplished by the 
output signals from interferometer that helps to know the phase – difference of input signals [1]. 
The DoA estimation algorithm – based then is applied to determine the direction of the incident 
wave. In [3], a low – complexity DoA estimation based on compressed MUSIC is investigated 
with its performance analysis. Performances of other algorithms which are commonly used 
currently such as MVDR, ESPRIT,... are known in [4], [5]. These methods are fully digital and 
complicated to find out the relationship between the direction of the incident wave and received 
signals. To deal with this problem, some recent publications proposed simpler approaches to 
obtain the direction of arrival. One of those, the interferometry – based DoA detection system in 
[2] whose structure composes of three receiving antennas, one hybrid coupler, two rat – race 
couplers. The estimation of the angle of arrival is deduced from the output DC voltages that are 
proportional to the magnitude of RF signals at their inputs. With the distance between the two 
consecutive antennas is half of the wavelength in free space, the unambiguity range of angle of 
arrival in the interval [-30
o
; 30
o
] and the range is [-14.4
o
; 14.4
o
] if decrease to a quater of 
wavelength in free space. 
In this work, we present a simple power – based sensor to obtain the DoA of any incident wave. 
Compared to the traditional methods which is used in most applications currently, this sensor has 
simple structure, low – cost, and good accuracy. The DoA of an incident wave is determined via a 
proposed simple equation of the powers at output ports of hybrid couplers (HCs) that are received 
Nghiên cứu khoa học công nghệ 
 Tạp chí Nghiên cứu KH&CN quân sự, Số 73, 06 - 2021 49 
from two receiving antennas. To the best of our knowledge, the simple, low cost and fully analog 
DOA sensor with the error of less than 5
o
 has not been published before. 
2. PROPOSED DOA SENSOR 
In this proposed DOA sensor as in figure 1, the angle of incoming wave on the receiving 
antennas ( ) is determined through the measured powers at the output ports of the HCs. The HC 
gives high isolation between the output ports as using a quarter of the wavelength transmission - 
line. The principle of the DOA sensor is described as follow: 
Figure 1. The schematic and actual image of the proposed system. 
The red and green paths in fig. 1 are the flow of incident signal from antenna 1 and antenna 2, 
respectively. Incident signals arrive at the two receiving antennas at different time that depends 
on the DoA α and the separation d between the two antennas. Thus, the phase – difference φ of 
received signals is expressed as equation (1): 
(1) 
where λ is a wavelength in free space. To validate our method, we picked randomly the distance 
of two antennas d as half of the wavelength in free space equivalent to 50 mm at 2.6 GHz. From 
equation (1) the corresponding range of the angle of the incident wave is from -35
o
 to 35
o
. The 
wider range is obtained by decreasing d. However, the closer distance of two antennas will result 
in less accuracy due to the mutual coupling of the antennas. To deal with this problem, we will 
address the solution in future works. 
The received power on the antennas 1 and 2 are denoted as P and P’, respectively. Then, the 
power at port 1 is and 
 is power at port 2 due to the power division of two 
HCs. The same amplitude of powers go to the third HC and are split equally at ports 3 and 4 
where there are the interferences of signals traveling from the antennas. 
Kỹ thuật điều khiển & Điện tử 
 50 V. T. Nga, L. M. Thuy, “A simple power - based Direction of Arrival sensor.” 
We then examined the interference at port 3. Similarity for port 4. Denote I and I’ are the 
amplitude of the currents signal interfering at port 3. In HC, the input- impedance seen from each 
port is 50 Ω. Then, the input power at the port is the equation of square of signal current 
amplitude multiplied by the real part of load impedance at the port. Thus, I and I’ are expressed 
by the following equations: 
(2) 
 (3) 
The current I3
at port 3 is the addition vector of I and I’ as in fig. 2. The phase – difference of 
the two currents is ( due to the property of the HC. Therefore, the amplitude of I3 is 
calculated using the Law of Cosine: 
 (4) 
Figure 2. The formula of current at port 3. 
Similarly, the output power at port 3 is expressed as: 
 (5) 
Thus, the phase – difference is deduced as: 
√ 
(6) 
Then, by using equations (1) and (6) DoA α is determined from the measured output powers 
at port 1, port 2, and port 3 or port 4. 
The power ratio at two output ports of the first two HCs must be designed 1:1 with all DoA 
sensor. The reason why HC is chosen instead of the T – junction is its good isolation. To design 
the DOA sensor, the HCs must be designed. 
In the next section, we will present the design of the proposed sensor. 
3. SIMULATION RESULTS 
Firstly, the HCs operating at the frequency of 2.6 GHz are designed using Advanced Design 
Simulation (ADS) software. As mentioned before, the HCs has four – ports: one input port, two 
output ports and two isolated ports that are terminated with a matched load of 50 Ω, it helps to 
split the input power into equal part and 90
o
 phase - difference at output ports. Here, we choose 
the hybrid branch – line coupler which consists of two main transmission – lines physically 
coupled together with two branches between them. The separation of lines is theoretically . 
The characteristic impedance of the main lines and branch lines are respectively 35 Ω and 50 Ω 
correspond with the width of 3 mm and 1.8 mm, respectively. Fig. 3 presents the dimension of 
HCs that uses the Roger 4003C substrate with a relative permittivity , dissipation 
factor tan = 0.0027 and a thickness h = 0.813 mm. The layout of HCs is shown in fig. 3: 
Nghiên cứu khoa học công nghệ 
 Tạp chí Nghiên cứu KH&CN quân sự, Số 73, 06 - 2021 51 
Substrate : 
h = 0.813 mm 
Dimension 
parameters of 
HCs: 
d = 50 mm 
l = 17 mm 
w1 = 3 mm 
w2 = 1.8 mm 
Figure 3. The layout of the proposed HCs. 
According to the principle of the proposed sensor in section 2, the received power of antenna 
1 and antenna 2 are respectively modeled as port 7 and port 8 as in fig. 3. The S – parameters 
expressing the reflection coefficient at the ports of HCs using CST and ADS are shown in fig. 4 
below. Because of the symmetry of the HCs, the reflections at pairs of ports 1 and 2; ports 3 and 
4; ports 7 and 8 are almost the same values. 
Figure 4. The simulated reflection coefficient parameters at output ports of HCs. 
The high isolation of HCs is expressed by the (S3,4) in fig. 5: 
Figure 5. The simulated isolation parameter between port 3 and port 4. 
Kỹ thuật điều khiển & Điện tử 
 52 V. T. Nga, L. M. Thuy, “A simple power - based Direction of Arrival sensor.” 
From fig. 4 and fig. 5, the reflection coefficient parameters in both softwares (ADS and CST) 
are Sii < -30 dB (i=1, 2, 3, 4, 7, 8) and the isolation parameter S34 is also approximately -30 dB at 
2.6 GHz. These S - parameters show that the HCs is well-matched impedance and have good 
isolation which is one of the most features we need about the power divisions for this sensor. 
The below diagrams expose the transmission parameters between input and output ports of HCs: 
Figure 6. The simulated transmission parameters between input and output ports of the first two 
HCs in ADS and CST software. 
From fig. 5, the simulated S – parameters in ADS and CST have nearly coincided. The small 
difference is due to the infinite ground in ADS (idea condition) while the dimension of ground is 
finite in CST. The S(7,1), S(8,2) are -3 dB and S(7,3), S(8,4) are -6 dB approximately at the 
operating frequency 2.6 GHz. 
Transmission parameter: 
 (dB) (7) 
where i = 1,3; j = 7 or i = 2,4; j = 8. 
From equation (7), these S – parameters above mean that when input power is applied at port 
7 and port 8 the two outputs are each half and one-quarter of input power respectively at port 1,2 
and port 3,4. The results are good as the desired property of HCs so, they can be fabricated for 
the measurement. 
Then, the sensor was numerically tested by Computer Simulation Technology (CST) 
software. The examined system was arranged as follows: the receiving antennas are two 
dipoleYagi antennas operating at 2.6 GHz and the modeling of HCs was imported from ADS 
software. The incident wave was modeled as a plane wave in CST. The plane wave was excited 
and the incident wave varies in the simulated range from -35o to 35o. Then, we applied the 
frequency domain solver method based on the tetrahedral meshing with the iteration accuracy of 
10
-4
. We believe that this meshing accuracy helps to the simulation is modulated like in the 
actual measurement. The simulation results were three F – parameters: F1, F2, and F3 which 
indicate the amplitude of the voltage at ports 1, 2, and 3 respectively in linear scale. The power at 
port 1, 2, and 3 can be easily deduced by the following equations: 
 (8) 
Nghiên cứu khoa học công nghệ 
 Tạp chí Nghiên cứu KH&CN quân sự, Số 73, 06 - 2021 53 
where i = 1,2,3. 
Thus, the phase – difference is expressed as (8) by the F – parameters: 
 (9) 
Where F1, F2, and F3 are the F – parameter at port 1, port 2, and port 3 respectively. 
By applying the simulated values of F1, F2, and F3 into equation (8), the phase - difference is 
calculated. Thus, the DoA α is easily estimated from equation (1). It is mentioned that because of 
the nature of the sine function of (8), the sine values strictly increase in range of -90
o
 to 90
o
, the 
 φ in our simulation is in this range. Due to the distance of antennas is chosen as 50mm, 
according to (1) it is deduced that the range of confidence interval examination DoA is from -35
o 
to 35
o
. The estimated angle is compared to the incident wave angle by the error. 
 The simulated result of incident wave angle estimation is shown in fig. 7: 
Figure 7. The simulation results. 
As be seen from fig. 7, the high accuracy is gained in the range of -35
o
 – 35o with an error of 
less than 5
o
. 
4. CONCLUSIONS 
In this work, the idea of a simple DoA sensor is presented and validated. The direction of an 
incident wave is easily determined via the power values on the HC ports by a simple equation. 
Through simulation results, we can see the key features of the system are its simplicity and low- 
cost but still achieved the accuracy within a range from -35
o
 to 35
o
 with the error of less than 5
o
. 
Because of its accuracy and simplicity, the proposed sensor is predicted to attain effective 
measured results and is a potential application in wireless systems. 
REFERENCES 
[1]. H. Chen and E. H. W. Chan, “Simple Approach to Measure Angle of Arrival of a Microwave 
Signal,” IEEE Photonics Technol. Lett., vol. 31, no. 22, pp. 1795–1798, Nov. 2019, doi: 
10.1109/LPT.2019.2947680. 
Kỹ thuật điều khiển & Điện tử 
 54 V. T. Nga, L. M. Thuy, “A simple power - based Direction of Arrival sensor.” 
[2]. B. Mnasri, P. Burasa, S. Tatu, and K. Wu, “Interferometer based Direction-Of-Arrival Detection 
System,” in 2018 18th International Symposium on Antenna Technology and Applied 
Electromagnetics (ANTEM), Aug. 2018, pp. 1–3. doi: 10.1109/ANTEM.2018.8573013. 
[3]. F. Yan, M. Jin, and X. Qiao, “Low-Complexity DOA Estimation Based on Compressed MUSIC and 
Its Performance Analysis,” IEEE Trans. Signal Process., vol. 61, no. 8, pp. 1915–1930, Apr. 2013, 
doi: 10.1109/TSP.2013.2243442. 
[4]. F. Akbari, S. Shirvani Moghaddam, and V. Tabataba Vakili, “MUSIC and MVDR DOA estimation 
algorithms with higher resolution and accuracy,” in 2010 5th International Symposium on 
Telecommunications, Tehran, Iran, Dec. 2010, pp. 76–81. doi: 10.1109/ISTEL.2010.5734002. 
[5]. T. B. Lavate, V. K. Kokate, and A. M. Sapkal, “Performance Analysis of MUSIC and ESPRIT DOA 
Estimation Algorithms for Adaptive Array Smart Antenna in Mobile Communication,” in 2010 
Second International Conference on Computer and Network Technology, Apr. 2010, pp. 308–311. 
doi: 10.1109/ICCNT.2010.45. 
TÓM TẮT 
CẢM BIẾN HƯỚNG SÓNG TỚI DỰA TRÊN CÔNG SUẤT THU 
Trong bài báo này, chúng tôi đề xuất một cảm biến đơn giản giúp xác định hướng sóng 
tới ở dải tần 2.6 GHz dựa trên các giá trị công suất thu. So với các thuật toán phức tạp 
được ứng dụng rộng rãi trong các hệ thống xác định hướng sóng tới hiện nay, cảm biến 
này có cấu trúc đơn giản và chỉ dựa trên công suất thu được từ bộ chia nguồn. Điều này 
dẫn đến sự đơn giản hơn trong việc xử lý để xác định hướng sóng tới. Hệ thống cảm biến 
hướng sóng tới đề xuất bao gồm 2 anten thu và 3 mạch hybrid coupler. Dải góc mô phỏng 
thực hiện trong khoảng từ 0o – 35o với sai số nhỏ hơn 5o. 
Từ khóa: Xác định hướng sóng tới; Mạch hybrid coupler. 
Received May 5
th
 2021 
Revised May 27
th
 2021 
Published June 10
th
2021 
Author affiliations: 
1 
School of Electrical Engineering, Hanoi University of Science and Technology. 
*
Corresponding author: thuy.leminh@hust.edu.vn.