,(((:LUHOHVV&RPPXQLFDWLRQVDQG1HWZRUNLQJ&RQIHUHQFH :&1&

A novel angle of arrival (AOA) positioning

algorithm aided by location reliability prior
information
1st Qing Zhu 2nd Kai Niu
2021 IEEE Wireless Communications and Networking Conference (WCNC) | 978-1-7281-9505-6/20/$31.00 ©2021 IEEE | DOI: 10.1109/WCNC49053.2021.9417489

Key Laboratory of Universal Wireless Communication. Key Laboratory of Universal Wireless Communication.
Ministry of Education Ministry of Education
Beijing University of Posts and Telecommunications Beijing University of Posts and Telecommunications
Beijing, China Beijing, China
zhuqing@bupt.edu.cn niukai@bupt.edu.cn

3rd Chao Dong 4th Yi Wang

Key Laboratory of Universal Wireless Communication. Huawei Technologies Co., Ltd.
Ministry of Education Shanghai, China
Beijing University of Posts and Telecommunications yi.wang@huawei.com
Beijing, China
dongchao@bupt.edu.cn

Abstract—Recently, the indoor positioning system based on locations, and the neighboring base stations can be seen as the
the angle of arrival (AOA) has been widely concerned. The positioning anchors (AN). Specifically, the wireless position-
positioning system often contains two steps. The first step is the ing technology utilizes one or more parameters measured in
AOA estimation algorithm and the second step is the positioning
algorithm using the estimated AOAs. However, due to the indoor several radio links between the equipment of a special user
signal multipath propagation, the AOA estimation errors can and different ANs for positioning. These parameters mainly
lower the positioning performance. To solve this problem, this include the strength of the received signal (RSS) [1], the
paper proposes a novel angle of arrival (AOA) positioning time of arrival (TOA) [2], [3], or the time difference of
algorithm which selects multiple candidate AOAs and selects arrival (TDOA) [4]. Also, with the development of multi-
the most reliable one from them. When multiple candidate
AOAs are selected and passed into the positioning algorithm, antenna technology, the positioning algorithm based on the
multiple estimated locations can be obtained. To select the most angle of arrival (AOA) can be well implemented, in which
reliable AOA, the location reliability prior information related synchronization requirement between adjacent base stations is
to these estimated locations is introduced. The AOA with the relaxed.
maximum location reliability prior information is the final AOA A least square (LS) solution for location estimation based on
estimation result and its corresponding estimated location is
the final positioning result. The simulation results show that AOA measurements is proposed in [5] where the location esti-
compared with the positioning algorithm which directly uses one mation is obtained as the intersection point of all angular lines
AOA for positioning, the proposed positioning algorithm provides from the ANs. When the LS algorithm is used for positioning,
better positioning performance. firstly, we need to estimate the AOA information. In [6] a
Index Terms—multiple candidate AOAs, location reliability joint angle and delay estimation multiple signal classification
prior information, positioning
(JADE MUSIC) algorithm is introduced to estimate the AOA
information. In [6] the spatial-temporal spectrum is computed
I. I NTRODUCTION
which is a function of the signal propagation delay and angle.
Positioning refers to the problem of determining the loca- The AOAs are the angles that correspond to the peaks on
tion of a target. It can be applied to many fields including the spectrum. In [5] the location estimation is assumed to be
navigation, sensing, radar and sonar. The most widely used po- independent of the AOA estimation. When the JADE MUSIC
sitioning technology is the Global Positioning System (GPS). algorithm is used for AOA estimation in [5], only the angle
GPS can provide reliable real-time positioning services for corresponding to the first largest peak is used for positioning.
user equipments in outdoor scenarios. However, due to the Because the first largest peak is assumed to correspond to the
occlusion of satellite signals in buildings, the performance line of sight (LOS) path which is the direct path between the
of GPS is often unsatisfactory in indoor scenarios. In this UE and the AN. Its propagation delay is the shortest.
case, the wireless positioning technology based on the base However, the signal multipath propagation can cause many
stations in the mobile network is used to estimate the users’ false peaks to appear on the JADE MUSIC spectrum. In this

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case, the first largest peak doesn’t correspond to the LOS

path. Especially, when the signal propagation between the  
UE and the AN is non-line-of-sight (NLOS) propagation, the x  y T T x  y
first largest peak can hardly correspond to the real AOA. y
Thus, if only the angle corresponding to the first largest peak
is selected as the AOA estimation result, the AOA estima-
tion errors will lower the positioning accuracy. To overcome 0
x

this problem, some improvement methods are proposed. In

[7], the measurements of RSS and AOA are combined to
T T
get a closed-form solution for the location estimation. A  

hybrid positioning system is introduced in [8] which uses x  y x  y

the combined measurements of RSS and AOA to derive an

AOA-RSS linear least squares (LLS) solution. A closed-form
Fig. 1. Antenna array layout
algebraic solution for location estimation with Bayesian priors
information is proposed in [9]. A positioning algorithm based
on soft information is proposed in [10] and the algorithm antenna arrays are deployed at the ANs to get the AOA
includes two steps. The first step is to obtain soft information. information. Fig .1 depicts the indoor antenna array layout
The second step is to pass the acquired set of soft information where the ANs are placed in the four corners of the rectangular
into a specific positioning algorithm for location estimation. room. The uniform linear antenna arrays are placed on the
In this paper, a novel AOA positioning algorithm is pro- y-axis, and the x-axis is the normal of the antenna arrays.
posed which selects multiple candidate AOAs and picks the The angle between the signal arrival direction and the normal
most reliable one based on the location reliability prior infor- is the AOA. The indoor communication channel is a typical
mation. The location reliability prior information is achieved multipath channel and its time-domain response can be written
from the pre-defined joint probability density function of loca- as follows
tion and angle. Specifically, this algorithm first selects multiple 
L−1
angles that correspond to the JADE MUSIC spectrum peaks as h(t) = αl (t)δ(t − τl (t) (1)
the candidate AOAs. Then the candidate AOAs at all ANs are l=0
combined and the corresponding location estimation results
where L represents the number of multipath, τl (t) is the delay
are calculated based on them. Bring the candidate AOAs
of the lth path, αl (t) is the complex gain of the channel,
and the corresponding location estimation results into the
and δ(t) is the impulse response. When a UE transmits a
joint probability density function, the AOA which maximums
positioning signal s(t) to the AN, the received signal at the
the function is the most reliable AOA and its corresponding
AN is as follows
estimated location is the final UE position estimation result.
Different from the algorithm proposed in [10], multiple sets 
L−1
(i) (i)
of AOAs and location estimations are obtained simultaneously, y (i) (t) = αl (t)s(t − τl (t)) + ω (i) (t) (2)
and the most reliable AOA and positioning result are selected. l=0

This paper is organized as follows. Section II introduces where i is the antenna index, ω (i) (t) is the Gaussian noise. In
the positioning system model which contains the JADE MU- this paper, the multipath channel model is the channel model
SIC algorithm and the LS positioning algorithm. Section in 5G NR [11]. The AOA information is contained in the
III describes the proposed positioning algorithm and gives complex channel gain and the relationship is as follows
the flowchart of the proposed positioning algorithm. The
(i)
simulation results are provided in section IV. In section IV αl (t) = αl (t)e(−jκd(i−1) sin(θl (t))) (3)
we evaluate and compare the positioning performance of
the proposed positioning algorithm and the LS positioning where κ = (2π/λ), d = λ/2, λ = c/fc . c is the speed of
algorithm in [5]. Finally, conclusions are drawn in Section light, fc is the frequency of the carrier, and θl (t) is the AOA
V. from the UE to the AN. It is worth noting that the relationship
between the AOA information and the complex channel gain
II. P OSITIONING S YSTEM M ODEL is based on the uniform linear antenna arrays [12]. Thus the
This section contains two parts. The first part is the AOA AOA information can be acquired from the complex channel
estimation process, where the JADE MUSIC algorithm is gains contained in the received signal.
described. The second part is the location estimation process, The JADE MUSIC algorithm estimates the AOA based on
where the LS positioning algorithm is depicted. the following three steps. Firstly, it computes the covariance
matrix of the received signal by the following equation
A. AOA Estimation Based on JADE MUSIC
Nt −1
Active positioning is assumed in this paper where the UE 1 
R= Y(n)YH (n) (4)
transmits a positioning signal to the ANs. The uniform linear Nt n=0

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angle values and delay values in the equation (5), we can get
a two-dimensional spatial-temporal JADE MUSIC spectrum.
The candidate AOAs are the angles corresponding to spectrum
peaks.
Fig.2 depicts the JADE MUSIC spectrum where the x-axis
is the angle, y-axis is the dealy, and Ts is the symbol time.
In the left image of Fig.2, many false peaks appear on the
JADE MUSIC spectrum, and the first largest peak deviates
from the true AOA. In the right image of Fig.2, the first largest
peak accurately corresponds to the true AOA. From Fig. 2,
we can see that the first largest peak is sometimes reliable
sometimes unreliable. Fig. 3 depicts the AOA measurement
error variances of the first largest peak in a 12×12 rectangular
Fig. 2. Normalized JADE MUSIC spectrum room. The x axis and the y axis are the user’s location
coordinates, the black triangle icons are the positions of the
AN1 error variance AN2 error variance ANs and the four figures in Fig. 3 respectively correspond to
1.5 1.4
10 10 1.2 the AOA measurement error variances of the UE at the four
y(meter)

y(meter)

1
1
0.8
ANs. From Fig. 3, we can see that the measurement error
5 5
0.5
0.6 variances at four ANs is related to the UE position. When
0.4

0 0 0.2 the UE is far away from the AN, the probability of NLOS
0 5 10 0 5 10
x(meter) x(meter)
propagation between the UE and the AN increases, and the
AN4 error variance
1.4
AN3 error variance corresponding error variance becomes large. We can also see
10 1.2 10 1.2
1
that when the signal arrival direction is far from the normal
y(meter)

y(meter)

1
0.8 0.8 of the antenna array, the AOA measurement error variance
5 5 0.6
0.6
0.4 0.4
also becomes large. So the AOA measurement error variances
0 0.2 0
0.2 are strongly dependent on the UE positions and are known a
0 5 10 0 5 10
x(meter) x(meter) priori. These prior measurement error variances can be used
to calculate the location reliability prior information in section
Fig. 3. AOA measurement error variance of the first largest peak III.
The LS algorithm only selects the first largest peak, but from
Fig. 2 and Fig. 3, we can see that the first largest peak can
where the H denotes the Hermitian operator and Nt represents deviate from the real AOA at some UE positions. In this case,
the frames of received signal. To get the Y, the received it’s hard to find the real AOA on the JADE MUSIC spectrum,
signal y (i) (t) at the ith array element is sampled and N so multiple candidate AOAs are selected in this paper and the
represents the time sampling points. Then the Discrete Fourier most reliable one will be used for positioning. Note that when
Transformation of the sampled signal is taken and the Discrete the number of the selected peaks is M then there are M NA
Fourier transformation at all array elements are arranged in a UE location estimation results, where NA is the number of the
row. Thus the Y ∈ R(N ×K)×1 where K is the number of array ANs. To reduce the algorithm complexity only the first largest
elements. Secondly, it takes the separation of eigenvectors of peak and the second largest peak are picked in this paper.
the above covariance matrix. The former L larger eigenvalues’
eigenvectors span the signal subspace and the last N K − L
eigenvectors span the noise subspace E. Thirdly, it computes B. LS Positioning Method
the spital-temporal spectrum by the following equation
1 After selecting multiple candidate AOAs from the JADE
P = (5) MUSIC spectrum, these AOAs are translated into the po-
U EEH U H
sitioning Cartesian Coordinate System at the ANs. That is
where U is the spatial-temporal direction eigenvector it can
the θˆi is translated to ϕ̂i . Then pass the ϕ̂i into the LS
be acquired by the following equations
positioning algorithm to get the corresponding UE locations.
U(τl , θl ) = d(θl ) ⊗ d(τl ) (6) The theoretical performance of the LS positioning algorithm
is analysed in [7]. The positioning diagram is depicted in Fig.
d(τl ) = [1, e−j2πΔf τl , ..., e−j2πΔf τl (N −1) ]T (7) 4. The angled lines at each AN intersect at one point that is
−1 −1 the location estimation. ϕ̂i is the angle between the ith anchor
d(θl ) = [1, e−j2πλ d sin θl
, ..., e−j2πλ d(K−1) sin θl T
] (8)
and the UE. [xi , yi ] is the location of the ith anchor which is
where d(τl ) is the temporal direction eigenvector and d(θl ) is known. [xo , yo ] is the location of the UE which is needed to
the spatial direction eigenvector. ⊗ means Kronecker product be estimated and di is the distance between the ith anchor and
and T means transpose operator. Thus by putting different the UE.

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where tan−1 is the 4-quadrant arctangent function and ei
x  y x  y is an independent zero-mean Gaussian noise ei ∼ N (0, σi2 )
M M Thus the joint probability density function of the angle and
xo  yo the location is a multivariate Gaussian probability density
function, given by

x  y M 1 −JG
f (Φ̂/p) = e 2 (19)
 (2π)NA /2 |Q|1/2

Fig. 4. Positioning diagram where Φ̂ is the estimated AOA vector and JG is as follows

JG = [Φ̂ − Φ]T Q−1 [Φ̂ − Φ] (20)

From Fig. 4 we can get the positioning equations at the ith
AN as follow where Φ = [ϕ1 (p)...ϕNA (p)] is the AOA given the p and Q
xi + di cos ϕi = xo (9) is as follows

yi + di sin ϕi = yo (10) Q = E{eeT } = diag[σ12 ...σN

2
A
] (21)

We can multiply the above equations by sin ϕi and cos ϕi where e = [e1 , ..., eNA ] is the AOA measurement error vector.
respectively. Then we get the following equations The measurement noise variance [σ12 ...σN 2
] are assumed to
xi sin ϕi + di cos ϕi sin ϕi = xo sin ϕi (11) be the same in [13] leading to the geometric dilution of
precision (GDOP). That is the geometric relation between
yi cos ϕi + di sin ϕi cos ϕi = yo cos ϕi (12) the UE position and the ANs position magnifies the error
of AOA measurements. Due to the GDOP, the UEs around
Thus we can get the following equation the ANs have worse positioning performance than the UEs
at other locations. When the noise variances differ from each
xi sin ϕi − yi cos ϕi = xo sin ϕi − yo cos ϕi (13)
other largely, the GDOP is strongly dependent on them. Thus,
Combine the equations of all ANs and rewrite them as follows: when the noise variances are assumed to be the same, the
⎡ ⎤ selected optimum UE position estimation also suffers from
x1 sin ϕ1 − y1 cos ϕ1 the GDOP. To overcome this problem the noise variance can
⎢ .. ⎥
b=⎣ . ⎦ (14) be measured in the AOA estimation process [9]. In this paper,
xNA sin ϕNA − yNA cos ϕNA the AOA measurement noise variance of the JADE MUSIC
⎡ ⎤ algorithm is measured. The measurement results of the first
sin ϕ1 − cos ϕ1
⎢ .. .. ⎥ largest peak are provided in Fig. 3. From Fig. 3 we can see
Φ=⎣ . . ⎦ (15) that the noise variances can vary from different ANs and are
sin ϕNA − cos ϕNA dependent on the UE position. When the angle corresponding
b = Φp (16) to the first largest peak is used to estimate the UE position,
its noise variance is brought into the joint probability density
where p = [xo , yo ]T is the location of the UE to be estimated. function. Thus when the angle corresponding to the second
Then the equation set can be solved by the LS method as largest peak is used for positioning, its AOA measurement
follows: noise variances are also measured and brought into the joint
p̂ = Φ† b (17) probability density function. Bringing the candidate AOAs,
their corresponding positioning results, and their measurement
where Φ† is the pseudoinverse of Φ. noise variances into equation (19), their location reliability
In the LS positioning algorithm [5], only one UE position prior information can be acquired. The candidate AOA with
is acquired. However, combining the two peaks at NA ANs, the maximum location reliability prior information is the most
2NA estimated UE locations are acquired in this paper. reliable AOA estimation, and its corresponding positioning
results is the optimum location estimation.
III. T HE P ROPOSED P OSITIONING A LGORITHM
The measurement noise is assumed to be zero-mean Gaus-
From the above positioning algorithm, we get 2NA UE sian in the above joint probability density function. When
location estimation results. Then the location reliability prior calculating the above function, the matrix operations are
information related to them can be calculated. The location used. To reduce the computational complexity, the noise is
reliability prior information is defined by the joint probability assumed to be a zero-mean Laplacian in this paper. Then the
density function of the angle and the location. From the Fig. joint probability density function is a multivariate Laplacian
4 we can see that the measured ϕ̂i at location p is probability density function and can be written as follows
x o − xi
ϕ̂i = ϕi + ei , ϕi = tan−1 ( ) (18) f (Φ̂/p) = e−JL NA 1
(22)
yo − y i i=1 2λi

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where 2λ2i = σi2 and σi2 is the measured AOA noise variances. 30
The JL is as follows AN
UE
25

NA
|ϕ̂i − ϕi |
JL = (23) 20

i=1
λi
15

y(m)
Thus the estimated candidate AOAs, the corresponding UE
10
positions and the measured noise variances can also be brought
into the above joint probability density function. The AOA 5

with the maximum function value is the optimum AOA estima-

0
tion and its positioning result is the final position estimation.
The computational complexity of (22) is lower than that of -5
-5 0 5 10 15 20 25 30
(19). x(m)

The flowchart of the proposed positioning algorithm is

Fig. 5. Indoor positioning scene
presented in Algorithm 1. The proposed positioning algorithm

Algorithm 1 Proposed Positioning Algorithm

1: Calculate the spatial-temporal spectrum by the JADE
of them are [0,20], [20,20], [20,0], and [0,0]. The angles
MUSIC algorithm according to expression (4) and (5). corresponding to the first largest and the second largest JADE
2: Select multiple AOAs from the spatial-temporal spectrum
MUSIC spectrum peaks are selected as the candidate AOAs.
and calculate the corresponding positioning results accord- Their AOA measurement noise variances at different UE
ing to expression (17). locations are pre-measured. For a single simulation, we scatter
3: Calculate the location reliability prior information related
points randomly in the room as the location of the UE. The
to the positioning results according to expression (19) and statistical results come from 3000 independent trials and the
(22). Select the AOA with the maximum reliability and its coordinate unit of all locations in the simulation scene is meter.
corresponding positioning result is the optimum location The CDF curves of simulation results are shown in Fig.
estimation result. 6. The LS curve corresponds to the LS positioning algorithm.
The Noval Positioning with Gaussian Distribution curve corre-
mainly contains the following three steps: sponds to the proposed positioning algorithm where the AOA
(a) When the ANs have received the signals from the UE, measurement noise is assumed to be Gaussian with the mea-
they calculate the spatial-temporal spectrum by the JADE sured noise variance. The Weighted Noval Positioning with
MUSIC algorithm . Gaussian Distribution curve corresponds to the simulations
(b) Then multiple candidate AOAs are selected from the where the AOAs corresponding to the 16 candidate positions
spatial-temporal spectrum and passed into the LS positioning are weighted, and then the weighted AOAs are used for
algorithm to get the corresponding candidate UE locations. positioning. The Noval Positioning with Laplacian Distribution
(c) Finally, bring the above AOAs and the corresponding curve corresponds to the proposed positioning algorithm where
candidate UE locations into the joint probability density func- the noise is assumed to be Laplacian with the measured noise
tion, and modify the noise variances according to candidate variance. From the four curves in Fig. 6, we can see that the
UE locations. Select the AOA with the maximum reliability Noval Positioning with Gaussian Distribution curve and the
and its corresponding candidate UE location is the optimum Weighted Noval Positioning with Gaussian Distribution curve
location estimation result. overlap each other. Before 40% the Noval Positioning with
Gaussian Distribution curve and the LS curve overlap each
IV. S IMULATION AND N UMERICAL R ESULTS other. This is because the AOA measurement noise variance
In this section, simulations are carried out to illustrate of the first largest peak is small when the UE is close to the
the achievable positioning performance of the proposed po- AN or the AOA between the UE and the AN is small. In this
sitioning algorithm. As a comparison, we also evaluate the case, the first largest peak is reliable and even the LS algorithm
positioning performance of the LS positioning algorithm in [5] only utilizes the first largest peak, it can perform as well
which only utilizes the first largest JADE MUSIC spectrum as the proposed algorithm. However, the Noval Positioning
peak. Because the final candidate AOA estimation and the with Gaussian Distribution curve has better performance than
final position estimation are selected at the same time, and the LS curve after 40%. This is because the AOA between
positioning is the final goal, in order to more intuitively reflect the UE and the AN becomes large and when the UE is far
the advantages of the algorithm, the positioning results are from the AN, there is no LOS path between them. In this
provided. The simulation channel is the multipath channel in case, the LS Positioning algorithm still only utilizes the first
5G NR [11] and the doppler frequency shift is 3Hz assuming largest peak, but the angles corresponding to the first largest
the velocity of users is 3m/s. The simulation scene is the peak have large noise variances at this time. The proposed
20m×20m rectangular room as depicted in Fig. 5. The four algorithm selects multiple peaks and picks the peak with
ANs are deployed at the four corners, and the coordinates the maximum reliability. Thus the proposed algorithm can

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prior information can be obtained. Then the AOA with the

1
maximum location reliability is selected and its positioning
0.9
result is the final location estimation. The complexity of the
0.8
proposed algorithm mainly comes from two parts. The first
0.7
is to measure the AOA measurement noise at each location
0.6
Probability

before positioning. The second is to calculate the position

0.5
estimations of multiple sets of candidate AOAs. The simu-
0.4
lation results show that the proposed positioning algorithm
0.3
LS
outperforms the LS positioning algorithm. Especially, the pro-
0.2
Noval Positioning with Gaussian Distribution
Weighted Noval Positioning with Gaussian Distribution
posed algorithm can greatly improve the positioning accuracy
0.1
Noval Positioning with Laplacian Distribution
in harsh communication scenarios. Our further work will study
0
0 5 10 15 20 25 30 35 the positioning performance of the proposed algorithm in other
Positioning Error(m)
two-dimensional geometric scene and in 3D space. Further,
Fig. 6. Comparison of CDF curve of different algorithms we will research the positioning in the fast-moving scene.
Combined with the UE’s movement direction, the proposed
algorithm can be extended to track the user.
1

0.9
ACKNOWLEDGMENT
0.8 This study was supported by the Key Program of National
0.7 Natural Science Foundation of China (No. 92067202), the
0.6 General Program of National Natural Science Foundation of
Probability

0.5 China (No. 62071058) and technology research of Huawei

0.4 Technologies Co., Ltd. (No. YBN2018085392)
0.3
LS
R EFERENCES
0.2
Noval Positioning with Gaussian Distribution
Weighted Noval Positioning with Gaussian Distribution
[1] H. Ketabalian, M. Biguesh, and A. Sheikhi, “A closed-form solution
0.1
Noval Positioning with Laplacian Distribution for localization based on rss,” IEEE Transactions on Aerospace and
0 Electronic Systems, vol. 56, no. 2, pp. 912–923, 2020.
0 20 40 60 80 100 120 140
Positioning Error(m)
[2] Y. Wang, S. Ma, and C. L. P. Chen, “Toa-based passive localization in
quasi-synchronous networks,” IEEE Communications Letters, vol. 18,
no. 4, pp. 592–595, 2014.
Fig. 7. Comparison of CDF curve of different algorithms [3] J. J. Caffery, “A new approach to the geometry of toa location,” in
Vehicular Technology Conference Fall 2000. IEEE VTS Fall VTC2000.
52nd Vehicular Technology Conference (Cat. No.00CH37152), vol. 4,
improve the positioning accuracy when the first largest peak 2000, pp. 1943–1949 vol.4.
[4] Yiu-Tong Chan, H. Yau Chin Hang, and Pak-chung Ching, “Exact
has a large AOA measurement noise variance. and approximate maximum likelihood localization algorithms,” IEEE
In the above simulations, the probability of NLOS propa- Transactions on Vehicular Technology, vol. 55, no. 1, pp. 10–16, 2006.
gation between the UE and the ANs is based on the distance [5] A. Pages-Zamora, J. Vidal, and D. H. Brooks, “Closed-form solution
for positioning based on angle of arrival measurements,” in The 13th
between the UE and the ANs. As a comparison, in the follow- IEEE International Symposium on Personal, Indoor and Mobile Radio
ing simulations, all links between the UE and the AN are set to Communications, vol. 4, 2002, pp. 1522–1526 vol.4.
NLOS. The CDF curves of simulation results are shown in Fig. [6] R. Feng, Y. Liu, J. Huang, J. Sun, C. Wang, and G. Goussetis, “Wireless
channel parameter estimation algorithms: Recent advances and future
7. In this case, the angles corresponding to the first largest peak challenges,” China Communications, vol. 15, no. 5, pp. 211–228, 2018.
have large noise variances. Thus the positioning performance [7] N. Salman, M. W. Khan, and A. H. Kemp, “Enhanced hybrid positioning
of the LS algorithm is degraded. However, the proposed in wireless networks ii: Aoa-rss,” in 2014 International Conference on
Telecommunications and Multimedia (TEMU), 2014, pp. 92–97.
algorithm greatly improves the positioning accuracy. These [8] S. Tomic, M. Beko, R. Dinis, and P. Montezuma, “A closed-form solu-
results show that in the harsh communication environment, tion for rss/aoa target localization by spherical coordinates conversion,”
the advantages of the proposed algorithm can be highlighted. IEEE Wireless Communications Letters, vol. 5, no. 6, pp. 680–683, 2016.
[9] N. H. Nguyen and K. Doğançay, “Closed-form algebraic solutions
In this case, the Weighted curve has the best positioning for angle-of-arrival source localization with bayesian priors,” IEEE
performance. What’s more, although the Laplacian distribution Transactions on Wireless Communications, vol. 18, no. 8, pp. 3827–
doesn’t perform as well as the Gaussian distribution, its 3842, 2019.
[10] A. Conti, S. Mazuelas, S. Bartoletti, W. C. Lindsey, and M. Z. Win,
algorithm complexity is lower than the Gaussian distribution. “Soft information for localization-of-things,” Proceedings of the IEEE,
vol. 107, no. 11, pp. 2240–2264, 2019.
[11] 3GPP, “Study on channel model for frequencies from 0.5 to 100 GHz,”
V. C ONCLUSION 3rd Generation Partnership Project (3GPP), Technical Reports (TR)
38.901, Jan 2018, release 14,version 14.3.0.
In this paper, a novel AOA positioning algorithm aided [12] D. Inserra and A. M. Tonello, “A frequency-domain los angle-of-
by location reliability prior information is proposed where arrival estimation approach in multipath channels,” IEEE Transactions
on Vehicular Technology, vol. 62, no. 6, pp. 2812–2818, 2013.
multiple candidate AOAs are selected and their correspond- [13] D. J. Torrieri, “Statistical theory of passive location systems,” IEEE
ing positioning results are calculated. Bringing them into Transactions on Aerospace and Electronic Systems, vol. AES-20, no. 2,
the joint probability density function, the location reliability pp. 183–198, 1984.

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