Received September 2, 2020, accepted September 10, 2020, date of publication September 14, 2020,

date of current version September 25, 2020.

Digital Object Identifier 10.1109/ACCESS.2020.3024031

Improving Accuracy of an Amplitude

Comparison-Based Direction-Finding System
by Neural Network Optimization
ENQI YAN , XIYE GUO, JUN YANG, ZHIJUN MENG, KAI LIU, XIAOYU LI, AND GUOKAI CHEN
College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China
Corresponding author: Jun Yang (nudtpaper@163.com)

ABSTRACT In the positioning and navigation field, it is essential to use the direction-finding system
to obtain the signal direction of arrival (DOA) and target position. The amplitude comparison-based
monopulse (ACM) DOA algorithm performs a few calculations, has a simple system structure, and is widely
used. The traditional ACM DOA algorithm uses the first-order Taylor expansion to introduce the nonlinear
errors, and the angle measurement range is limited. In response to this problem, this study establishes a
neural network model for error compensation, and it optimizes the traditional algorithm to obtain a better
angle estimation performance. In order to perform an experiment with the proposed algorithm, a novel
experimental device was designed. Two measurements at different angles were obtained by rotating the
antenna. The ACM angle estimation used only one directional antenna. The results verified the optimization
algorithm. The experimental results demonstrated that in comparison with the traditional first-order and
the improved third-order Taylor expansion ACM DOA algorithm, the mean absolute error of this method
reduced by 81.62% and 72.62%, respectively.

INDEX TERMS Positioning, direction-finding, amplitude comparison, neural network, signal direction of
arrival estimation.

I. INTRODUCTION prospects. In terms of achieving precise positioning, in addi-

Presently, satellite navigation and positioning systems are tion to traditional mobile cellular positioning technology and
widely used. But in locations such as mines, tunnels, and GNSS-based satellite navigation and positioning technology,
high-rise ‘‘urban canyons’’ in valleys, satellite signals are direction-finding positioning methods can also be introduced.
blocked; hence, they cannot receive and provide accurate On the one hand, the positioning function can be com-
positioning services. The pseudo-satellite regional position- pleted independently through direction-finding, and it can
ing system’s appearance offers the possibility to solve the also be combined with ranging and positioning to improve
positioning problem in the above scenarios. A pseudolite is a the positioning performance.
device that is placed on the ground and can emit signals that In terms of the research of direction-finding technology,
are similar to the global navigation satellite system (GNSS). a multi-channel direction-finding algorithm based on the
The pseudo-satellite station that is established on the ground array antenna and the corresponding system is currently
can enhance the regional satellite navigation and positioning being studied. It has successively proposed the minimum
system and also improve the satellite positioning system’s variance distortionless response (MVDR) beamformer algo-
reliability and anti-interference ability [1]. rithm [2], the multiple signal classification (MUSIC) algo-
With the advent of the 5G era, the large-scale deployment rithm [3], and the estimation signal parameter via rotational
of mobile communication base stations has led to the inte- invariance techniques (ESPRIT) method [4]. In particular,
gration of pseudo-satellite positioning systems and mobile the MUSIC algorithm, which is based on the spatial spec-
communication systems. The development of integrated nav- trum direction-finding estimation, can provide a high res-
igation and communication systems has broad development olution. The MUSIC algorithm needs to search the power
spectrum function’s peak value to determine the estimated
The associate editor coordinating the review of this manuscript and DOA; thus, it requires a considerable amount of calcula-
approving it for publication was Mohammad Tariqul Islam . tions. Some scholars have studied and optimized the MUSIC

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
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algorithm and achieved individual results [5]–[8]. However, signals with a direction of arrival that deviates more from
for an array antenna-based direction-finding system, each the bisector, they adaptively used adjacent or spare antennas
array unit corresponds to the corresponding receiver. There- to make the signal as close as possible to the bisector of the
fore, the implementation of this algorithm requires multi- two boresights for the DOA measurement. Chengzen C. per-
ple receiving channels that can be sampled simultaneously, formed a third-order Taylor series expansion on the adaptive
which may introduce additional phases in the actual imple- monopulse ratio at the beam center [18]. They applied the
mentation process, which is difficult to guarantee. The con- polynomial root-finding formula to estimate the target angle,
sistency of these multiple receiving channels is ideal [9]–[11]. and verified that the method can be improved in comparison
It is necessary to maintain and calibrate the antenna array, with the traditional first-order Taylor series expansion. But
which contains multiple antenna units, and it often brings in its essence, it applies the Taylor series expansion; thus,
disadvantages such as complex systems, a large power con- the algorithm optimization effect is limited. Therefore, it is of
sumption, and a high cost. considerable significance to study the ACM DOA algorithm’s
The amplitude comparison-based monopulse (ACM) angle performance and to improve it.
estimation system has a simple structure and it is conve- For complex regression and fitting problems, there are
nient for installing and deploying a mobile carrier. Many some methods and models that have been proven effec-
scholars have studied the ACM DOA algorithm and its sys- tive. Multiple regression model and artificial neural network
tems. Reference [12] uses a second-order Taylor expansion model were established to predict influenza activity, which
approximation to solve the quadratic function extremum and can accurately reflect influenza epidemic characteristics [19].
they derived the monopulse angle measurement formula. The Ruan et al. [20] compared BP neural network model with
authors also presented a theoretical accuracy analysis of the linear regression model and Support Vector Machine (SVM)
monopulse angle measurement and pointed out the relation- in predicting the citation counts of individual papers. In [21],
ship between the monopulse angle measurement error, the classification and regression trees model was used to predict
beamwidth, and the array signal-to-noise ratio (SNR). The blood pressure for people.
narrower the beamwidth, the higher the SNR and the smaller In terms of the realization of the direction finding system,
the angle measurement error. In another study [13], the hard- some novel ideas have emerged. A two-antenna, single radio-
ware comparator is not used in the monopulse antenna sys- frequency (RF) front-end DOA estimation system is proposed
tem, and the sum and difference signal are obtained by and it extends the measurements to different locations by
performing signal processing to achieve the ACM angle shifting the antenna tuple together as a single entity [22].
estimation. Priyanka et al. [14] proposed a classifier-based Reference [23] uses two commercial wifi panel antennas to
amplitude comparison direction-finding (ACDF) algorithm, build a convenient system, and uses the amplitude monopulse
which uses a fuzzy c-means algorithm and interpolation tech- function to achieve DOA estimation.
niques to enhance the DOA’s performance accuracy. In [15], In this investigation, we studied the ACM DOA algorithm.
a passive angle estimation using the monopulse correlation For the problem of nonlinear errors in the estimation process,
method is proposed. Guo and Li [16] further improved the we established a neural network model to compensate for
algorithm and solved the direction-finding problem in two the initial estimation results. This improves the accuracy
steps. The improved algorithm first roughly measures the of the angle estimation results, it enhances the limitation
direction of arrival (DOA), then it only measures the DOA of the original algorithm on the measurement range, and
within a limited angular interval, and then it searches for it improves the robustness of the algorithm. We designed
the maximum correlation coefficient; thus, speeding up the a novel test method that uses a single directional antenna
algorithm. to form two antenna beams with a specific angle by rota-
However, the traditional ACM DOA algorithm has a prac- tion. The ACM algorithm is implemented and the effec-
tical angle measurement interval. This shortcoming is caused tiveness of the algorithm that is proposed in this study is
by the algorithm theory itself. In the process of the algo- verified.
rithm, the first-order Taylor expansion formula is used to The contributions of this investigation are as follows:
approximate the received signal. According to the nature 1) This study is focused on the shortcomings of the
of Taylor expansion, a polynomial can be used to approxi- traditional ACM DOA algorithm’s active angle mea-
mate the function value at a specific point., The higher the surement interval. In addition, this investigation
polynomial order, the more accurate the approximation, and addresses the limitation of the angle measurement
the closer to a specific point, the smaller the approxima- range; thus, a method based on a neural network model
tion error. For the traditional ACM algorithm, it provides is proposed for compensation. Because the first-order
an angle estimation result with an accuracy higher than the Tayler series is used in the bisector of the two bore-
Rayleigh criterion in a smaller angle range near the bisector sights, the algorithm has a large error at the position
of the two boresights, but when the signal direction deviates deviating from the bisector. In this study, the neural
from the bisector, the angle estimation deviation is larger. network model is used to compensate for the error, and
Iqbal et al. [17] proposed a method to reduce the error of the then the final DOA estimation result is obtained, which
amplitude comparison-based direction-finding system. For increases the angle measurement performance.

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2) This study constructed a novel system that uses only

one antenna and one radio frequency (RF) front end.
Smart test methods were applied to achieve the tra-
ditional ACM DOA algorithm. These methods were
tested and they verified the proposed optimization
method.
The remainder of this paper is structured as follows.
In Section II, the signal model is established, the ACM DOA
algorithm is introduced, and the nonlinear error that is intro-
duced by the algorithm is analyzed. In Section III, by focusing
on the mistakes in the second part of the analysis, a neural
network model is established, and the model is used to com-
pensate for the initial estimation results to obtain the final
estimation results. In Section IV, by performing simulation
experiments, the proposed method’s effectiveness is verified,
and the simulation shows the optimization performance of the
proposed algorithm under the conditions of the different real
signal arrival directions. In Section V, by using a standard
gain horn antenna and other related devices, a measurement
system was built. In addition, the angle measurement experi-
ments were carried out by using the method that is proposed
in this study, which proves the effectiveness of the proposed
algorithm. Finally, the conclusion is presented in Section VI.

II. SIGNAL MODEL

The ACM direction-finding system uses multiple directional
antennas that are located at the same phase center but with a
FIGURE 1. Schematic diagram of the ACM angle estimation algorithm. The
squint angle difference and it simultaneously receives signals. angle between the two directional antenna is 2θk . The authentic signal
By comparing the amplitude information of the received DOA is θ , and the signals received by the two antennas are u1,rx (θ) and
u2,rx (θ ) since the gain difference of the antenna is in different directions.
signals for the different antennas, the signal arrival direction
is estimated. This section takes two antennas as an example
to build a signal model and it analyzes the messages that are
antennas receive signals at different angles and they use the
received by the different antennas.
antennas’ directional characteristics to obtain the different
In order to understand this approach, let us first consider
received signal strengths.
Friis’s transmission equation at the receiving antenna for the
As shown in the Fig.1, the two beams in the plane partially
omni-directional transmission antennas.
overlap each other, and the direction of the bisector of the
Pm,rx = Ptx + Gtx + Gm,rx + Lc + Ls (1) two boresights is known. The antenna squint angle θk is also
known. Suppose the angle between the direction of the target
where m = 1, 2, Ptx is the transmitted power, Gtx is the transmitted signal and the bisector of the two boresights is θ,
transmitter antenna gain, Gm,rx is the mth receiver antenna then the antenna gain pattern function is g(θ). In this study,
gain, Lc is the cable loss, and Ls is the free space propagation the beam pattern is assumed to be a Gaussian pattern [24].
loss. Ls can be calculated as follows. h
2 i
g(θ) = exp −2 ln 2 θ θ1/2

c (4)
Ls = 20 lg( ) (2)
4πfdtx,m where θ1/2 is the half-power beamwidth (HPBW) of the beam.
where c is the speed of light, f is the carrier frequency, and According to the received signal strength of the two antennas,
dtx,m is the distance between the transmitter and the mth it is only determined by the directional antenna gain, which
receiver. can be expressed as follows.
According to the equation, the difference between the two (
u1,rx (θ) = Kg(θk + θ)
received signal strengths is determined from Eq. (3). (5)
u2,rx (θ) = Kg(θk − θ)
P1,rx − P2,rx = G1,rx − G2,rx (3)
Among them, K is the proportionality factor, which is
According to the above formula, the difference in the related to the parameters of the transmitting antenna, the tar-
received signal strength depends only on the difference in the get distance, the target characteristics, and other factors.
gain that is between the two receiving antennas. It has nothing According to the ACM DOA algorithm, by using the
to do with the other factors. This is because the different received signal strength, the sum signal uP,rx (θ ) and the

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difference signal u1,rx (θ ) can be calculated from u1,rx (θ ) and coefficient ρ that corresponds to θ1/2 and θk from the lookup
u2,rx (θ) as follows. tables, and use the two receiving antennas to obtain the sig-
( nals u1,rx (θ) and u2,rx (θ). Finally, use the above conditions to
uP,rx (θ ) = u1,rx (θ ) + u2,rx (θ ) = K [g(θk + θ) + g(θk − θ)] obtain the DOA estimation result θ̂.
u1,rx (θ) = u1,rx (θ ) − u2,rx (θ ) = K [g(θk + θ) − g(θk − θ)] According to the previous introduction and analysis,
(6) the traditional ACM DOA algorithm uses a first-order Taylor
expansion to approximate the calculation when calculating
Among them, gP (θ) = g(θk + θ) + g(θk − θ) is the sum the normalized slope coefficient, ρ, which introduces errors.
beam pattern, and g1 (θ) = g(θk + θ) + g(θk − θ) is the Especially for the direction that deviates from the bisector
difference beam pattern. of the two boresights, this method can estimate the angle,
According to the Taylor expansion, when θ tends to be 0 the error is substantial, and it is determined by the nature of
(infinitely close to the bisector of the two boresights), the the Taylor expansion itself. Therefore, the traditional ACM
approximate results can be expressed as follows. angle estimation algorithm has an effective angle measure-
ment interval in a practical application. In the interval around
(
g(θk + θ) = g(θk ) + g0 (θk )θ + o(θ 2 ) ≈ g(θk ) + g0 (θk )θ
the bisector of the two boresights, an accurate angle estima-
g(θk − θ) = g(θk ) − g0 (θk )θ + o(θ 2 ) ≈ g(θk ) − g0 (θk )θ tion can be obtained. But as the target angle deviates from
(7) the bisector of the two boresights, the algorithm is no longer
active. Figure 3 uses a Gaussian antenna with an HPBW
The first-order Taylor expansion formula is used to approx-
of 20◦ as an example to show the theoretical angle estimation
imate the second order polynomials and above to zero. This
performance of the ACM DOA algorithm under the different
processing brings errors to the final angle estimation results,
antenna squint angles without considering the influence of the
which is also the research content of this paper. In this approx-
noise. Fig. 3(a) is a three-dimensional surface diagram which
imation, the ratio of the sum amplitude of the signal and
shows the angle estimation error under conditions of differ-
the signal’s difference amplitude the can be expressed as the
ent antenna squint angles (θk ) and different authentic signal
following Eq. (8).
DOA. Fig. 3(b) shows four specific conditions of different θk .
u1,rx (θ) g0 (θk )
= θ = ρθ (8)
uP,rx (θ) gθk )
0
Among them, ρ = ggθ(θkk)) is the normalized slope coefficient
of the antenna pattern at the beam squint angle θk .
Through the above derivation, the target signal DOA esti-
mation result can be calculated by applying Eq. (9).
u1,rx (θ) 1
θ̂ = (9)
uP,rx (θ) ρ
According to the above ACM DOA algorithm and the
system model, the block diagram of the algorithm for the
angle estimation can be expressed as Fig. 2.

FIGURE 2. Block diagram of the traditional ACM angle estimation

algorithm. Before measuring, determine the antenna HPBW θ1/2 and the
antenna squint angle θk , measure the strength of the received signals of
the two antennas, and then calculate the angle estimate θ̂ .

Before estimating the target angle, according to the receiv-

ing antenna gain pattern function g(θ), the normalized slope FIGURE 3. The theoretical error of the traditional ACM angle estimation
coefficient ρ corresponds to the different θk that is calculated algorithm. The antenna pattern type is Gaussian and the HPBW is 20◦ .
(a) The angle estimation error corresponding to the different antenna
and stored in the lookup tables. When it is time to estimate squint angles and the different real signal arrival directions. (b) The
the position of the target signal, look up the normalized slope situations of the squint angles at 5◦ , 10◦ , 15◦ , and 20◦ .

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It can be observed from Fig. 3 that for the traditional ACM the calculation process.
DOA algorithm, the angle measurement error, in theory,
is smaller in the interval around the bisector of the two bore- H = f1 (W [1] I + b[1] ) (10)
sights. When the real signal arrival direction deviates from where W [1] = [wqm ]Q×M , which is the weight matrix from
the bisector, the algorithm angle measurement error gradu- the input layer to the hidden layer, b[1] ∈ RQ×1 is the hidden
ally increases. When the true signal arrival direction is 20◦ , layer’s bias matrix, and f1 (∗ ) is the activation function of the
the angle estimation error reaches 13◦ , which cannot provide hidden layer. Similarly, the calculation expression from the
a valid angle estimation result. In summary, the traditional hidden layer to the output layer can be obtained.
ACM algorithm’s active angle measurement interval is only
near the bisector of the two boresights, which is inconvenient O = f2 (W [2] H + b[2] ) (11)
in practical applications. Therefore, to obtain a better target
angle estimation performance and to effectively extend the where W [2] = [wnq ]N ×Q is the weight matrix from the hidden
target angle’s accurate measurement range, the traditional layer to the output layer, b[2] ∈ RN ×1 is the bias matrix of the
ACM algorithm needs to be optimized. output layer, and f2 (∗ ) is the activation function of the output
layer.
III. PROPOSED OPTIMIZATION MODELS
The traditional ACM DOA algorithm performs a first-order B. THE NEURAL NETWORK-OPTIMIZED AMPLITUDE
Taylor series expansion at the bisector of the two boresights. COMPARISON-BASED MONOPULSE (NN-ACM)
The angle estimation error at the direction deviating from ALGORITHM
the bisector has nonlinearity and it is difficult to eliminate 1) INPUT AND OUTPUT OF THE MODEL
through a theoretical calculation. The neural network can Using the neural network model, the traditional ACM DOA
fit any nonlinear object with a high accuracy, it has robust algorithm is optimized, mainly for the case of the deviation
nonlinear mapping, and it is easy to implement. It is an from the bisector of the two boresights. This is based on
effective method to optimize the traditional ACM algorithm known parameters and accurate DOA estimation results are
by using the neural network method. obtained. According to the analysis of the traditional ACM
DOA algorithm in Section II, the parameters that determine
A. BASIC MODEL OF THE NEURAL NETWORK the performance of the DOA estimation are mainly the half-
In general, the typical three-layer neural network structure is power beamwidth and the antenna squint angle. The setting
illustrated in Fig. 4. required for the DOA estimation that uses the traditional
ACM DOA algorithm is the signal strength that is obtained
from two directional antennas. Besides, the noise will also
affect the angle estimation result. Therefore, the model is
designed as a four-input and one-output model, that is, M = 4
and N = 1. The input variables are the half-power beamwidth
(HPBW) θ1/2 , the angle 2θk between the antenna boresight,
the angle calculation result θ̃ of the traditional ACM DOA
algorithm, and the SNR. The output variable is the angle
estimation result of the target signal.

2) GENERATION OF THE DATA SET

The influence of the number of training samples on the neural
network is reflected in the network’s generalization ability.
In the ideal case, its training parameters are expected to map
the arbitrary functions within the ideal accuracy. Accord-
ing to the structure of the designed neural network model,
the selected training samples should cover the situations as
much as possible. The value range of each parameter deter-
mines the value of each input parameter of the model in
FIGURE 4. Schematic diagram of the three-layer neural network. This the data set. The HPBW θ1/2 values ranging of [10◦ , 60◦ ]
includes an input layer, a hidden layer, and an output layer. with a step of 10◦ . Under this condition, the angle of the
two antenna boresights 2θk takes on the value [10◦ , 2θ1/2 ]
In the Fig. 4, I = [I1 , I2 , I3 , . . . IM ]T represents the input with a step of 10◦ , which ensures that the main lobes of
vector, O = [O1 , O2 , O3 , . . . ON ]T represents the output the two antenna beams overlap. The other input parameter
vector of the output layer, and H = [H1 , H2 , H3 , . . . HQ ]T in the model is the traditional ACM DOA algorithm’s angle
represents the output vector of the hidden layer. From the calculation result θ̃. This parameter cannot be given directly,
input layer to the hidden layer, a matrix is used to describe but it is obtained by performing a calculation based on the

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received signal. Therefore, when generating the training data rate is too large, the model may not converge. The function of
set, θ̃ is calculated by providing the authentic signal DOA θ, the activation function is to add nonlinear factors to the neural
and then θ̃ is used as the input variable of the training set. network so that it can solve more complex problems more
That is, the range of θ̃ is determined by θ. Regardless of the effectively. The most commonly used activation functions are
changes in the other parameters, any given will always have the Sigmoid function and the rectified linear unit (ReLU)
a corresponding θ̃. Considering that the algorithm requires function.
the target signal’s authentic angle of arrival between the two After the above analysis and optimization, the neural
beams. The value range of θ is [−θ1/2 , θ1/2 ] and it has a network-optimized ACM DOA algorithm can be obtained.
step of 0.2◦ . The model also considers the impact of the The Fig. 5 presents the flow chart of the neural network
different noise conditions and it uses the SNR to quantify the optimized ACM angle estimation algorithm.
noise, its value range is [−20dB, 20dB], and the step is 10dB.
In summary, the variables of the data set are show in Table 1.
TABLE 1. Variables of the data set.

3) MODEL NORMALIZATION
In order to solve the influence of the dimension between
the different data and to improve the accuracy of the neural
network model, the input variables and output variables of the
model are normalized; hence, the input variables and output FIGURE 5. The block diagram of the neural network optimized ACM angle
estimation algorithm.
variables of the model have the same order of magnitude.
When using the model, the output of the model needs to be Based on the traditional ACM DOA algorithm, the training
denormalized. The normalization formula is as follows. data set is used to train the neural network, and the training
y = (ymax − ymin )∗ (x − xmin )/(xmax − xmin ) + ymin (12) result is saved. According to the diagram, when making an
angle estimate, the measurement result is first used to cal-
Among them, [ymin , ymax ] is the range of values for the culate θ̃ according to the traditional ACM DOA algorithm.
variables after normalization, which is [−1,1] in this study, Then, the result is inputted into the neural network together
[xmin , xmax ] is the real range of the values for the variables ∧
with the other conditions (θ1/2 , θk , SNR) to obtain the esti-
before normalization, and x is the variable being normalized. ∧
mated value θ̂ of the target angle. Among them, SNR can
4) MODEL TRAINING PARAMETERS be obtained by the SNR estimation method, which is not the
The neural network model’s training parameter settings focus of this article and this will not be explained in detail. For
mainly include the number of hidden layer neurons, the max- the entire process, the neural network training process con-
imum number of iterations, the training target, the learning sumes a lot of computing resources and time; however, it can
rate, and the activation function. The simplest model uses be performed offline. In actual use, the training results are
a three-layer neural network structure, which includes an directly used; thus, it will not significantly impact real-time
input layer, a hidden layer, and an output layer. The input processing.
and output variables determine the number of neurons in the
input layer and the output layer. According to Kolmogorov’s IV. ALGORITHM EVALUATION
theorem [25], M = 4, N = 1, and the neuron of the hidden This section assesses the performance of the proposed neural
layer has a value of nine. The maximum number of itera- network-optimized amplitude comparison-based monopulse
tions, Niteration , and the training target are used for stopping (NN-ACM) DOA algorithm.
the training. After reaching either of these two parameters,
the training will end and it needs to be set according to the A. ALGORITHM PERFORMANCE OF THE TEST DATA SET
performance of the model. If the learning rate is too small, the Using the data set in Section III, we randomly selected 60%
model’s convergence rate may be too slow, and if the learning as the training set, 20% as the verification set, and 20% as

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the test set. Through experimentation, the network training

parameters with the best performance are determined based
on the Table 2.

TABLE 2. Neural network training parameters.

FIGURE 6. Simulation error results of the different algorithms. The blue

◦
‘‘ ’’ represents the traditional ACM algorithm, the green ‘‘’’ represents
the third-order Taylor expanded ACM algorithm, and the red ‘‘∗ ’’
By using the above model parameters, the training data set represents the NN-ACM algorithm.
is used to train the neural network model, and the obtained
network model is used to verify the test set. As a comparison,
we also used the traditional ACM DOA algorithm and the
In order to accurately show the angle estimation results of
ACM DOA algorithm that is based on a third-order Taylor
the different algorithms, 100 samples were randomly selected
expansion to obtain the angle estimation results of the differ-
from the test data set. This compares the traditional ACM
ent algorithms.
DOA algorithm, the third-order ACM, and the proposed
To quantify and evaluate the performance of the different
NN-ACM DOA algorithm.
algorithms, we used the mean absolute error (MAE), mean
It should be noted that the data of the test set is randomly
square error (MSE) and root mean square error (RMSE) to
selected so that each sample may correspond to a different
obtain statistics on the three algorithms’ results to verify the
HPBW, different antenna squint angles θk , different authentic
angle measurement accuracy of the NN-ACM algorithm.
signal directions of arrival θ, and different SNR conditions,
The formulas for MAE, MSE, and RMSE are as follows.
which can represent the performance of the algorithm under
N
1 X ∧ a variety of measurement conditions. It can be clearly seen
MAE = θn −θn (13) that the proposed NN-ACM DOA algorithm can significantly
N
n=1 reduce the angle estimation error.
N
1 ∧X
MSE = (θn −θn )2 (14)
N B. ALGORITHM OVERALL PERFORMANCE VALIDATION
n=1
v In order to show the performance of the algorithm completely
u N
u1 X ∧ and comprehensively, we used the Monte Carlo method to
RMSE = t (θn −θn )2 (15) simulate the angle estimation results of the three algorithms
N
n=1
under different conditions. The SNR was set to 20 dB,
∧ the HPBW was set to 10◦ , 20◦ , 30◦ , 40◦ , 50◦ , 60◦ , the antenna
In the formula, θn is the true angle of the nth sample, θn is
squint angle θk was set so that it equals the HPBW, and the
the estimated angle of the nth sample, and N is the number of
authentic signal arrival direction was set to [−θk , θk ]. The
samples.
number of Monte Carlo experiments for each set of parameter
It can be observed from Table 3 that for the test data set,
conditions was set to 1,000. The specific simulation condi-
the DOA estimation obtained by the NN-ACM algorithm
tions are presented in Table 4.
proposed in this paper, in comparison with the traditional
According to the simulation results, which are obtained
ACM algorithm and the third-order Taylor expansion ACM,
from antennas with different HPBW, the accuracy the DOA
the MAE reduced by 82.8% and 77.69%, and the RMSE
estimation results varies with the authentic DOA of the signal,
reduced by 86.5% and 84.5%, respectively.
as shown by Fig. 7.
It can be observed from Fig. 7 that for the traditional
TABLE 3. Performance metrics of different algorithms. ACM DOA algorithm, when the real signal arrival direction
is near the bisector of the two boresights, the algorithm
can accurately estimate the DOA. However, since the actual
signal arrival direction deviates from the bisector of the two
boresights, the algorithm estimation result gradually becomes
more substantial, and the third-order ACM algorithm has a
similar rule, which is consistent with the theoretical anal-
ysis. For our proposed NN-ACM algorithm, when the real

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FIGURE 7. Comparison of the Monte Carlo experimental results of the performance of the different algorithms. The HPBW = 10◦ , 20◦ , 30◦ , 40◦ , 50◦ , and
60◦ , the antenna squint angle is equal to the HPBW, the angle estimation mean square root error results correspond to the different real signal arrival
◦
directions, and the Monte Carlo times are set to 1000. The blue ‘‘ ’’ represents the traditional ACM algorithm, the green ‘‘’’ represents the third-order
Taylor expanded ACM algorithm, and the red ‘‘∗ ’’ represents the NN-ACM algorithm that is proposed in this study.

signal arrival direction is near the bisector of the two bore- ACM algorithm and the third-order Taylor expansion ACM
sights, the angle estimation result is close to the traditional algorithm, respectively.
ACM algorithm. When the real signal arrival direction devi- The above results show that the proposed NN-ACM algo-
ates from the bisector of the two boresights, the proposed rithm has a better performance for the signal DOA estimation,
NN-ACM algorithm can avoid large angle estimation errors. especially for target signals that deviate significantly from
For the antenna with the HPBW of 10◦ , the antenna squint the bisector of the two boresights. This improves the angle
angle of 10◦ , and the signal arrival direction of 10◦ , the RMSE measurement accuracy and extends the effective angle mea-
of the proposed NN-ACM algorithm is reduced by 70.86% surement range.
and 69.89% in comparison with the traditional ACM and
the third-order Taylor expansion ACM, respectively. For the V. EXPERIMENT
antenna with the HPBW of 60◦ , the antenna squint angle This section describes a system that uses the traditional ACM
of 60◦ , and the signal arrival direction of 60◦ , the RMSE algorithm, the third-order Taylor expansion ACM algorithm,
indicators of the proposed NN-ACM algorithm are reduced and the proposed NN-ACM algorithm to estimate the DOA of
by 88.16% and 87.76% in comparison with the traditional the signal and to compare the performance of the algorithms.

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FIGURE 8. The experimental system includes a directional antenna, a rotary table, a receiver, and a DOA estimation component.

TABLE 4. Simulation conditions settings. The dataset can be get capability, and the DOA estimation component, as depicted
according to the simulation settings.
in Fig. 8. The system components prior to the DOA estima-
tion block provide data acquisition. The steps of this pro-
cess are as follows. First, the antenna is roughly pointed in
the target direction, which is recorded as position 1, and it
uses the receiver to receive the target signal while measur-
ing the amplitude of the received signal at this time. Sec-
ond, the rotary table is turned to rotate the antenna by a
specific angle 2θk , and this is recorded as position 2. Third,
the receiver obtains the target signal again, and it measures
the amplitude of the received signal at this time. This process
completes a set of measurements.
In two measurements, the angle of the antenna rotation is
accurately controlled by the controller, and its value is passed
to the DOA estimation block. In the signal receiving stage,
a super-heterodyne receiver is used to process and collect
the signals that are received by the antenna. The primary
mechanism is to down-convert the high-frequency signal that
is received by the antenna into a lower-frequency signal
through mixing to facilitate subsequent processing. The sig-
nal received from the receiving antenna is doped with noise,
and there may be other signal interference outside the signal
band. As a result, the first step of processing the received
signal is to perform a RF signal adjustment. The preliminary
processed signal passes through the mixer, and the signals
from the local oscillator are multiplied. After filtering out
the high-frequency components in the product, the signal
frequency drops from the radio frequency to the intermediate
frequency. The analog-to-digital converter (ADC) is used to
A. MEASUREMENT SETUP SYSTEM perform analog-to-digital (A/D) conversion on the interme-
The proposed system consists of a directional antenna diate frequency signal to obtain discrete digital sampling
that is mounted on a rotary table, a controller board, results; thus, completing a data acquisition operation. The
a super-heterodyne receiver with a complex signal recording collected signals are then transmitted to the DOA estimation

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block through the central processing unit (CPU). In the DOA TABLE 5. Parameter settings of the experimental system.
estimation module, the acquired digital signal is first calcu-
lated by using the correlation method to calculate the ampli-
tude of the measured signal, and then the angle estimation
result is obtained. The set-up of the experimental system is
presented in Fig. 9.

FIGURE 10. The directional antenna HD-58SGAH20N that is used in the

experiment. The blue line is the actual test pattern and the red line is the
result of fitting the range over [−30◦ , 30◦ ].

curve of the gain pattern of the horn antenna. According to

the calibration results, the antenna has an HPBW of approxi-
mately 7◦ .
To verify the DOA estimation algorithm, the transmitting
antenna should transmit signals from different angles of the
FIGURE 9. Experimental test system. (a) The overall test environment and
system. (b) The horn antenna and a signal receiver. receiving antenna. It is necessary to measure the direction of
the transmitting antenna accurately each time. However, it is
Currently, the DOA estimation component is not embed- not easy to move the transmitting antenna and to accurately
ded in the super-heterodyne receiver but it is completed in measure the direction of the transmitting antenna.
a portable computer. Therefore, the data collected by the On the other hand, since the receiving antenna is fixed
antenna is first processed by the receiver and then it is dumped on the turntable, it is accurate and convenient to calibrate
into the portable computer through the universal serial bus the receiving antenna’s direction. Using this feature, we have
interface. Based on the algorithm flow that is introduced in developed a measurement verification scheme that is easy to
Sections II and III, it is executed in the portable computer implement.
DOA estimation process. The entire measurement process is ¬ Control the turntable, use the calibration device to
carried out in a microwave darkroom to reduce the interfer- align the boresight of the antenna with the transmitting
ence that is caused by the electromagnetic wave reflection. antenna, and record the pointing position of the receiv-
The specific parameter settings of the experimental system ing antenna as α = 0◦ .
are listed in Table 5. ­ The fixed transmitting antenna does not move; thus,
control the turntable and rotate the receiving antenna.
B. DATA COLLECTION Afterwards, make the antenna point from −15◦ to
Before data acquisition and measurement, the antenna is 15◦ so it is spaced by 1◦ for a total of 31 positions.
calibrated to obtain the antenna gain pattern, and the gain For each position of the transmitting antenna, use the
pattern results are fitted to obtain the pattern function. In order super-heterodyne receiver for the data collection.
to improve the fitting accuracy, we selected [−30,30] as the ® As described in Section II, using the ACM algorithm
range for fitting. Fig. 10 shows the test result and the fitting to achieve angle estimation requires two signals to be

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FIGURE 11. Experimental error results of the different algorithms. One hundred sets of the measurement samples were randomly selected. The green
histogram represents the traditional ACM algorithm. The blue histogram represents the third-order Taylor expanded ACM algorithm. The red histogram
represents the proposed NN-ACM algorithm.

collected. Therefore, the 31 pieces of collected data are TABLE 6. Performance metrics of different algorithms.
divided into two groups: α1 ∈ [−15◦ , 0◦ ] and α2 ∈
[0◦ , 15◦ ]. By doing this, θk = α2 −α
2
1
and θ = − α1 +α
2
2

can be expressed. A total of 256 (16 × 16) data samples

were obtained.
¯ To increase the number of samples, repeat step ® five
times, which results in a total of 1280 (256 × 5) data
samples. Take 60% of the data set as the training data
set, 20% as the validation data set, and the remaining
20% as the test data set.
selecting 100 experimental samples from the test data set,
the angle estimation error results are shown in the Fig. 11.
Fig. 11 shows that the third-order ACM algorithm is
C. EXPERIMENTAL RESULTS slightly better than the traditional ACM algorithm, and the
Using the measurement results that were obtained in part B, proposed NN-ACM algorithm can effectively improve the
the traditional ACM algorithm, the third-order Taylor expan- angle estimation accuracy in comparison with the other two.
sion ACM algorithm, and the NN-ACM algorithm are used to The angle estimation error is less than 1◦ .
estimate the angle. Moreover, calculate the MAE indicators
of the three algorithms, as listed in Table 6. D. DISCUSSION
It can be observed from Table 6 that in comparison with In the previous part, we have verified the performance of the
the traditional ACM algorithm and the third-order Taylor proposed NN-ACM algorithm through simulation and exper-
expansion ACM algorithm, the proposed NN-ACM algorithm iment, and have compared it with the traditional ACM algo-
reduces the MAE indicators by 81.62% and 72.62%, respec- rithm and the improved third-order ACM algorithm, which
tively, and the optimization effect is noticeable. By randomly proved that the traditional ACM algorithm can be optimized

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by the neural network. Similarly, some other regression mod- obtained by training is used to verify the algorithm of the test
els can complete this work. In this part, we use the data set data set. The MAE index of the NN-ACM algorithm proposed
obtained in part B to compare the performance of different in this study reduced by 82.8% and 77.69%, respectively, in
regression models, including Line-ar Regression (LR) model, comparison with the traditional ACM algorithm and the third-
Regression Tree (TR) model, and Support Vector Regression order ACM algorithm.
Machine (SVRM). The parameters of different models are In this study, we set up a single antenna and a single
shown by Table 7. RF front-end wireless signal DOA estimation system to
verify the proposed algorithm. The system uses a standard
TABLE 7. Parameters settings for different models. gain horn antenna. By rotating the antenna to achieve two
measurements at different angles, based on the ACM angle
estimation algorithm, the signal DOA is estimated. Through
experiments, the NN-ACM algorithm that is proposed in this
study is verified. In comparison with the traditional ACM
angle estimation algorithm and the third-order amplitude
comparison-based angle estimation algorithm,the MAE indi-
cators reduce by 81.62% and 72.62%, respectively, the value
reaches 0.1091◦ , and the optimization effect is obvious. Com-
pared with other regression models, the proposed neural net-
We trained the above three models and compared the work model also performs well.
performance of them with that of the proposed NN-ACM
algorithm. Table 8 shows that some other regression models REFERENCES
can also be used to optimize the traditional ACM algorithm to [1] N. Kaur and S. K. Sood, ‘‘An energy-efficient architecture for the Internet
of Things (IoT),’’ IEEE Syst. J., vol. 11, no. 2, pp. 796–805, Jun. 2017.
improve the accuracy of angle estimation. The neural network [2] J. Capon, ‘‘High-resolution frequency-wavenumber spectrum analysis,’’
model proposed in this paper has better performance than LR Proc. IEEE, vol. 57, no. 8, pp. 1408–1418, Aug. 1969.
model, RT model, and SVRM. However, it should be noted [3] R. Schmidt, ‘‘Multiple emitter location and signal parameter estimation,’’
that the focus of our research is to provide a method that uses IEEE Trans. Antennas Propag., vol. 34, no. 3, pp. 276–280, Mar. 1986.
[4] R. Roy, A. Paulraj, and T. Kailath, ‘‘ESPRIT—A subspace rotation
neural network to optimize the traditional ACM algorithm to approach to estimation of parameters of cisoids in noise,’’ IEEE Trans.
obtain better angle estimation results. In the future, with the Acoust., Speech, Signal Process., vol. 34, no. 5, pp. 1340–1342, Oct. 1986.
development of artificial intelligence and machine learning, [5] A. Barabell, ‘‘Improving the resolution performance of eigenstructure-
based direction-finding algorithms,’’ in Proc. IEEE Int. Conf. Acoust.,
there may be models that can achieve better results. This is Speech, Signal Process. (ICASSP), Boston, MA, USA, Apr. 1983,
worth looking forward to. pp. 336–339.
[6] D. Wang, R. Chai, and F. Gao, ‘‘An improved root-MUSIC algorithm and
MSE analysis,’’ in Proc. Int. Conf. Comput., Inf. Telecommun. Syst. (CITS),
TABLE 8. Performances of different models. Kunming, China, Jul. 2016, pp. 1–4.
[7] M. A. Yaqoob, A. Mannesson, B. Bernhardsson, N. R. Butt, and
F. Tufvesson, ‘‘On the performance of random antenna arrays for direction
of arrival estimation,’’ in Proc. IEEE Int. Conf. Commun. Workshops (ICC),
Sydney, NSW, Australia, Jun. 2014, pp. 193–199.
[8] A. M. Elbir and T. E. Tuncer, ‘‘Compressed sensing for single snapshot
direction finding in the presence of mutual coupling,’’ in Proc. 24th Signal
Process. Commun. Appl. Conf. (SIU), Zonguldak, Turkey, May 2016,
pp. 1109–1112.
[9] K.-L. Du and M. N. S. Swamy, ‘‘A deterministic direction finding approach
using a single snapshot of array measurement,’’ in Proc. Can. Conf. Electr.
Comput. Eng., 2005, pp. 1188–1193.
VI. CONCLUSION [10] B. Baygun and Y. Tanik, ‘‘Performance analysis of the MUSIC algorithm
For the amplitude comparison-based direction-finding sys- in direction finding systems,’’ in Proc. Int. Conf. Acoust., Speech, Signal
Process., Glasgow, U.K., vol. 4, 1989, pp. 2298–2301.
tems in the positioning and navigation field, an NN-ACM [11] U. Sarac, F. Harmanci, and T. Akgul, ‘‘Experimental analysis of detection
angle estimation algorithm is proposed in this investigation. and localization of multiple emitters in multipath environments,’’ IEEE
This algorithm solves the shortcomings of the traditional Antennas Propag. Mag., vol. 50, no. 5, pp. 61–70, Oct. 2008.
[12] Z. Xu, Y. Huang, Z. Xiong, and S. Xiao, ‘‘On the consistency of mono-
algorithm with a smaller angle measurement range. Based pulse and maximal likelihood estimation with array radar,’’ Modem Radar.,
on the traditional ACM algorithm, the proposed algorithm vol. 35, no. 10, pp. 32–35, Oct. 2013.
uses a neural network model to compensate for the nonlinear [13] T. L. Sheret, C. G. Parini, and B. Allen, ‘‘Monopulse sum and difference
signals with compensation for a failed feed element,’’ IET Microw., Anten-
error that is caused by the first-order Taylor expansion and it nas Propag., vol. 10, no. 6, pp. 645–650, Apr. 2016.
obtains the final angle of the arrival estimation result. The [14] B. Priyanka, V. S. Rani, M. K. Das, and S. Sounak, ‘‘An improved
simulation results show that in comparison with the tradi- amplitude comparison based direction of arrival estimation,’’ Int. J. Emerg.
tional algorithm and the third-order Taylor expansion algo- Technol. Adv. Eng., vol. 4, no. 9, pp. 305–311, 2014.
[15] A. A. Loginov and M. Y. Semenova, ‘‘Applying correlation method to the
rithm, the NN-ACM angle estimation algorithm can improve problem of passive amplitude monopulse direction finding,’’ in Proc. IEEE
the angle estimation accuracy. The neural network that is 3rd Int. Conf. Commun. Softw. Netw., Xi’an, China, May 2011, pp. 66–68.

VOLUME 8, 2020 169699

 E. Yan et al.: Improving Accuracy of an Amplitude Comparison-Based Direction-Finding System

[16] D. L. Guo and Z. H. Li, ‘‘A fast direction finding algorithm based on JUN YANG received the B.S., M.S., and Ph.D.
correlation processing,’’ Appl. Mech. Mater., vols. 373–375, pp. 880–883, degrees from the College of Mechatronics Engi-
Aug. 2013. neering and Automation, National University of
[17] M. F. Iqbal, Z. Khalid, M. Zahid, and A. Abdullah, ‘‘Accuracy improve- Defense Technology, China, in 1994, 1999, and
ment in amplitude comparison-based passive direction finding systems 2007, respectively. He is currently a Professor with
by adaptive squint selection,’’ IET Radar, Sonar Navigat., vol. 14, no. 5, the College of Intelligence Science and Technol-
pp. 662–668, May 2020. ogy, National University of Defense Technology.
[18] C. Chengzen, ‘‘Monopulse angle estimation with adaptive array based on
His teaching and research interests include sig-
the third-order Taylor series,’’ Modern Radar, vol. 35, no. 8, pp. 32–36,
nal processing, space instruments, global naviga-
Aug. 2013.
[19] H. Xue, Y. Bai, H. Hu, and H. Liang, ‘‘Influenza activity surveillance based tion satellite system applications, and intelligent
on multiple regression model and artificial neural network,’’ IEEE Access, satellite.
vol. 6, pp. 563–575, 2018.
[20] X. Ruan, Y. Zhu, J. Li, and Y. Cheng, ‘‘Predicting the citation counts of
individual papers via a BP neural network,’’ J. Informetrics, vol. 14, no. 3,
Aug. 2020, Art. no. 101039.
[21] B. Zhang, Z. Wei, J. Ren, Y. Cheng, and Z. Zheng, ‘‘An empirical study on
predicting blood pressure using classification and regression trees,’’ IEEE ZHIJUN MENG received the Ph.D. degree in
Access, vol. 6, pp. 21758–21768, 2018. instrument science and technology from the
[22] A. Gorcin and H. Arslan, ‘‘A two-antenna single RF front-end DOA estima- National University of Defense Technology
tion system for wireless communications signals,’’ IEEE Trans. Antennas (NUDT), China, in 2017. He is currently an
Propag., vol. 62, no. 10, pp. 5321–5333, Oct. 2014. Assistant Research Fellow with the College of
[23] M. Poveda-Garcia, J. A. Lopez-Pastor, A. Gomez-Alcaraz, Intelligence Science and Technology, NUDT. His
L. M. Martinez-Tamargo, M. Perez-Buitrago, A. Martinez-Sala, research interests include digital signal process-
D. Canete-Rebenaque, and J. L. Gomez-Tornero, ‘‘Amplitude-monopulse
ing, on-board intelligent processing platform,
radar lab using WiFi cards,’’ in Proc. 48th Eur. Microw. Conf. (EuMC),
inter-satellite link of navigation constellation, and
Madrid, Spain, Sep. 2018, pp. 464–467.
[24] Y. J. Han, J. W. Kim, S. R. Park, and S. Noh, ‘‘An investigation into high-precision ranging and time synchronization.
the monopulse radar using tx-rx simulator in electronic warfare settings,’’
in Proc. Symp. Korean Inst. Commun. Inf. Sci., Jeongseon, South Korea,
Jan. 2017, pp. 705–706.
[25] V. Ku̇rková, ‘‘Kolmogorov’s theorem and multilayer neural networks,’’
Neural Netw., vol. 5, no. 3, pp. 501–506, Jan. 1992.
KAI LIU received the M.S. degree in instrument
science and technology from the National Uni-
versity of Defense Technology, in 2016, where
he is currently pursuing the Ph.D. degree with
the College of Intelligence Science and Technol-
ogy. His research interests include global naviga-
tion satellite system positioning, global navigation
satellite system signal processing, and pseudolite
application.
ENQI YAN received the B.S. degree from the
College of Intelligence Science and Technol-
ogy, National University of Defense Technology,
in 2018, where he is currently pursuing the M.S.
degree. His research interests include signal pro-
cessing, ground-based positioning, and navigation
technology. XIAOYU LI received the B.S. degree from the
College of Intelligence Science and Technology,
National University of Defense Technology,
in 2018, where he is currently pursuing the
M.S. degree. His research interests include
ground-based positioning and navigation
technology.

XIYE GUO received the B.S., M.S., and Ph.D.

degrees from the College of Mechatronics Engi-
neering and Automation, National University of GUOKAI CHEN received the B.S. degree in
Defense Technology, China, in 2003, 2005, and measurement and control technology from the
2010, respectively. From December 2016 to Febru- National University of Defense Technology,
ary 2017, he was a Visiting Scholar with the in 2019, where he is currently pursuing the Ph.D.
University of New South Wales (UNSW). He is degree with the College of Intelligence Science.
currently an Associate Research Fellow with the His research interests include complex environ-
College of Intelligence Science and Technology, ment positioning and spatial machine intelligence.
National University of Defense Technology. His
current research interests include global navigation satellite systems, navi-
gation augmentation, and precise positioning and timing.

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