=Paper=
{{Paper
|id=Vol-2880/paper3
|storemode=property
|title=5G Positioning Based on the Wideband Electromagnetic Vector Antenna
|pdfUrl=https://ceur-ws.org/Vol-2880/paper3.pdf
|volume=Vol-2880
|authors=Bo Sun,Bo Tan,Wenbo Wang,Mikko Valkama,Christophe Morlaas,Elena Simona Lohan
|dblpUrl=https://dblp.org/rec/conf/icl-gnss/Sun0WVML21
}}
==5G Positioning Based on the Wideband Electromagnetic Vector Antenna==
https://ceur-ws.org/Vol-2880/paper3.pdf
5G Positioning Based on the Wideband
Electromagnetic Vector Antenna
Bo Sun1 , Bo Tan1 , Wenbo Wang1 , Mikko Valkama1 , Christophe Morlaas2 and
Elena-Simona Lohan1
1
Tampere University, Korkeakoulunkatu 7, Kampusareena, 33720 Tampere, Finland
2
École Nationale de l’Aviation Civile, 7 Avenue Edouard Belin, 31400 Toulouse, France
Abstract
This work proposed a single base station positioning design in 5G networks, which can jointly estimate
user equipment (UE) distance (time of arrival, ToA) and direction (angle of arrival, AoA) by utilizing
the wideband 5G signal and vector antenna (VA). A statistics-based Expectation-maximization (EM)
algorithm and a subspace-spaced algorithm are adopted to estimate the UE position in this work. The
simulation results show that the proposed method can accurately estimate UE position by using the
uplink sounding reference signals (SRS) in a Line-of-Sight (LoS) scenario where the tapped delay line D
(TDL-D) channel model is used to construct delay and attenuation profiles for multiple paths. Also, the
impact of the strong reflections on angle estimation and polarization accuracy is studied in the subspace
algorithm. This work proves that the VA is able to provide high accuracy 3D UE positioning in 5G
networks without the requirement of multiple cells or multiple antennas. However, the performance of
the VA antenna is limited by the coarse angle resolution, which needs to be resolved by VA composed
antenna array in future works.
1. Introduction
5G networks are considered as the mainstream mobile network in the next decade and have
been deployed worldwide for mobile broadband access from 2019 onwards. 5G provides a
variety of communications scenarios like evolved mobile broadband (eMBB), massive machine-
type communications (mMTC), and ultra-reliable low latency communications (URLLC) [1].
Driven by the vast range of application scenarios, the mobile network is expected to provide
the functions transcending traditional radio connectivity access, for example, the accurate
positioning, which is an imperative function needed in the vertical applications, namely, vehicle
or drone networks and Industrial 4.0, etc.
ICL-GNSS 2021 WiP Proceedings, June 01–03, 2021, Tampere, Finland
Envelope-Open bo.sun@tuni.fi (B. Sun); bo.tan@tuni.fi (B. Tan); wenbo.wang@tuni.fi. (W. Wang); mikko.valkama@tuni.fi
(M. Valkama); christophe.morlaas@enac.fr (C. Morlaas); elena-simona.lohan@tuni.fi (E. Lohan)
GLOBE https://fi.linkedin.com/in/bo-sun-0a5130188 (B. Sun); https://www.tuni.fi/en/bo-tan (B. Tan);
https://www.tuni.fi/en/wenbo-wang (W. Wang); https://www.tuni.fi/en/mikko-valkama (M. Valkama);
http://ema.recherche.enac.fr/permanent-staff-2/christophe-morlaas/ (C. Morlaas);
https://www.tuni.fi/en/elena-simona-lohan (E. Lohan)
Orcid 0000-0002-5803-4778 (B. Sun); 0000-0002-9085-4266 (B. Tan); 0000-0002-4319-4103 (W. Wang);
0000-0003-0361-0800 (M. Valkama); 0000-0003-4533-1711 (C. Morlaas); 0000-0003-1718-6924 (E. Lohan)
© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
The Global Navigation Satellite System (GNSS) based positioning solutions are intensively
studied in literature and has been the default option for most the modern mobile devices when
location-based service (LBS) is needed. However, the GNSS solutions often suffer from the Urban
Caynon effect (multipath propagation, blockage, and interference) in the area with high building
density, where the vehicle/drone applications need the positioning support the most. In addition,
two meters positioning accuracy and around 10 Hz update rate of the GNSS solution may not
conform with the latency and security requirements in these 5G vertical applications. Thus,
to use 5G radio signals for positioning together with communications functions is becoming
explicit and trendy research genre, with potential to provide high accuracy and frequent update
rate for mission-critical applications. In 3GPP Release 16 [2], the multiple-cell and single-cell
positioning scenarios have been defined. The multiple-cell scenarios include the round-trip time
(RTT) based trilateration method, angle of arrival/departure (AoA/AoD) based trigonometric
method, and the time difference of arrival (TDoA). Researches in [3] and [4] provide the extended
Kalman filter (EKF) based positioning solutions of ToA estimation and shows the Cramér–Rao
lower bound (CRLB) of the positioning accuracy. Maximum likelihood estimator (MLE) based
5G positioning solution, and its ToA estimation CRLB is given in [5]. However, these multi-cell
approaches often require the systematic cooperation, which increases the system complexity
and deployment cost, for example, the synchronization between the BSs in TDoA solution.
Therefore, in this paper, we will focus on solutions of the single-cell (base station) positioning.
The single base station positioning solution proposed in[6] uses tensor-based methods to jointly
estimate the AoA and delay with 5G millimeter-wave channel.
The critical element to enable the single-cell positioning is to estimate the angle and delay of
the signal source simultaneously on the basestation. The requirement can be achieved by using
the phased antenna array receiver for wideband signal perception [7, 8]. Uniform linear array
(ULA), uniform circular array (UCA), or uniform rectangular array (URA) are often used for
this purpose [9, 10]. Receivers equipped with antenna array have the potential to achieve the
high angle resolution by increasing the number of array elements (i.e., increasing the physical
aperture); also exhibit limitations, for example limited dimensionality (in ULA and UCA), non-
identical angle estimation (in ULA and URA), and distortion occurring on the wideband signals.
In this paper, we will introduce the VA to overcome the limitations of the array-based approaches.
The VA has gained attention for electromagnetic waves angle-of-arrival (AoA) detection since
it was firstly introduced by Arye Nehorai and Eytan Paldi in 1994 [11]. According to Arye and
Eytan’s work [11], the VA has the capability to estimate the source AoA in a sphere space (i.e.,
360°of azimuth and 180°of elevation) without knowing the polarization [12]. The VA designed
in [12] can achieve the full space source AoA and polarization detection with various wideband
source frequencies from 2𝐺𝐻 𝑧 to 6𝐺𝐻 𝑧. This paper proposes a VA-based single-cell 3D UE
positioning method for the 5G system by using the uplink reference signal SRS. The following
remarks facilitate the proposed scheme: i). the SRS signal in the 5G uplink is used as carrier for
positioning information (delay and angle); ii). VA enabled time 3D space positioning; iii). high
accurate subspace- and statistical-based joint angle and time delay estimation methods for 5G
UE positioning with single BS.
The rest of this paper is organized as follows: Section 2 describes the 5G SRS signal and basics
of VA. Signal model and estimation algorithms are introduced in Section 3. In Section 4, we
show the simulation results and analysis. Section 5 concludes the paper and proposes future
work.
2. Reference Signal and Vector Antenna Structures
2.1. 5G Sounding Reference Signal (SRS)
The SRS signal is used in the 5G New Radio (NR) systems for detecting uplink (from UE to base
station) channel quality. In 3GPP standards TS 38.211 [13], the SRS is derived from the Zadoff-
Chu sequence whose entries are allocated to the specific time and frequency slot (physical
resource unit, PRU) by obeying a set of the configuration parameters, which are contained in
the signaling messages such as radio resource control (RRC) Connection Setup message and
RRC Connection Reconfiguration message. Once a Zadoff-Chu sequence is selected, each entry
in the sequence will be allocated to PRU in a resource block (RB) according to the parameters set
[l0 , k0 , K𝑡𝑐 , nrofSymbols, m𝑆𝑅𝑆 , C𝑆𝑅𝑆 , B𝑆𝑅𝑆 ]1 . l0 and k0 determine the initial frequency domain
subcarrier index and time domain symbol index. Comb parameter K𝑡𝑐 determines the interval
(number of subcarriers) between two contiguous SRS resource elements on frequency domain.
nrofSymbols defines the duration (number of symbols) of the SRS signal. m𝑆𝑅𝑆 is the total
number of PRBs that can be used for SRS transmission. The value of m𝑆𝑅𝑆 is selected from Table
6.4.1.4.3-1 in 3GPP TS 38.211 [13] according to the value of transmission bandwidth indicator
B𝑆𝑅𝑆 and bandwidth configuration parameter C𝑆𝑅𝑆 . The higher layer of network sends the B𝑆𝑅𝑆
and C𝑆𝑅𝑆 in the RRC message. An example of two UEs SRS signal generation are given in Fig.1.
2.2. Electromagnetic Vector Antenna Structure
Generally, the VA is a type of antenna composed of a total of 6 antenna elements. 3 electric
and 3 magnetic dipoles which can detect the 3 Electric(e) and 3 Magnetic(h) fields along x, y,
z axis in Cartesian coordinates. As shown in Fig. (2), the electric and magnetic elements of
VA are identically and orthogonally oriented between each other. Thus, the VA can detect the
electromagnetic wave coming from a sphere space where the center is the location of VA.
3. Research methodology
3.1. Wideband ToA Manifold Construction
5G NR (sub-6GHz) utilizes the wideband OFDM signal of up to 100 MHz in the frequency range
from 450 MHz to 6 GHz[14]. For an OFDM signal, the same propagation delay introduces
linearly increasing phase shifts on with the ascend subcarrier frequency. This phenomenon
makes the base station be able to estimate the UE signal propagation delay by measuring the
phase shifts on subcarriers. The delay manifold g(𝜏 ) ∈ ℂ1×𝑁 and received frequency domain
SRS signal 𝑠(𝜏 ) ∈ ℂ1×𝑁 can be described in mathematical models as eq. (1) and (2). Supposing
the propagation delay of a SRS signal is 𝜏 and the first subcarrier of SRS signal is the reference
subcarrier with phase shift 𝑒 −𝑗2𝜋𝑓0 𝜏 . The phase shift on the 𝑛𝑡ℎ subcarrier is 𝑒 −𝑗2𝜋𝑓𝑛 𝜏 , where
1
To avoid the misunderstanding, the symbols l0 , k0 , K𝑡𝑐 , nrofSymbols, m𝑆𝑅𝑆 , B𝑆𝑅𝑆 , C𝑆𝑅𝑆 are the same as 3GPP
TS 38.211 [13]
Figure 1: An example of two UEs’ SRS signals frequency domain resource allocation pattern. Two
resource blocks are exhibited in this example. SRS signals of both UEs start from the 8𝑡ℎ OFDM symbol
but the duration are 4 and 2 for UE1 and UE2.
𝑓𝑛 is constructed by SRS comb parameter 𝐾𝑡𝑐 and OFDM subcarrier space Δ𝑓; The value is
𝑓𝑛 = 𝑛𝐾𝑡𝑐 Δ𝑓. The [⋅]𝐻 denotes Hermitian transpose. Then, the received SRS signal 𝑠(𝜏 ) is the
dot multiplication product of the SRS sequence sSRS ∈ ℂ𝑁 ×1 and the delay manifold g(𝜏 ).
g(𝜏 ) = [1, 𝑒 −2𝑗𝜋𝑓1 𝜏 , 𝑒 −2𝑗𝜋𝑓2 𝜏 , ..., 𝑒 −2𝑗𝜋𝑓𝑁 −1 𝜏 ]𝐻 (1)
s(𝜏 ) = sSRS ⋅g(𝜏 ) (2)
Assumption 1: According the 3GPP TS 38.211 [13], the SRS signals of different users are
allocated into orthogonal time and frequency slots. Thus, there will be no SRS interference
from other users when using it for delay and angle estimation.
3.2. 3-D AoA manifold construction
Fig. 3 illustrates the Cartesian system contains one VA and UE. The impinging signal is on
direction u, to the base station equipped with the VA. The azimuth and elevation angles of
receiving signal are 𝜙 and 𝜃, respectively. The polarization state of the incoming electromagnetic
′ ′
wave are represented by horizontal and vertical polarization vectors v1 and v2 . By comparing
with the reference polarization state vector v1 and v2 , the auxiliary polarization angle 𝛾 can be
′ ′
measured. The polarization phase difference 𝜁 among v1 and v2 indicates the linear or elliptical
polarization state of the EM wave.
Figure 2: Electromagnetic Vector Antenna Structure, Electrical Dipoles (left), Magnetic Dipole (right)
Figure 3: 3D vector antenna Cartesian and orthogonal triad (n, v1 ,v2 )
Assumption 2: In the practical scenario, the range between UEs and the base station is more
prominent than the antenna near field region and antenna dimensions. The VA is consequently
can be treated as a point-like structure and the received electromagnetic wave is a planar wave.
Thus, the steering vector used for AoA estimation can be written in the form of eq. (3).
e cos 𝜙 cos 𝜃 − sin 𝜙
⎡ 𝑥⎤ ⎡ ⎤
e
⎢ 𝑦⎥ ⎢ sin 𝜙 cos 𝜃 cos 𝜙 ⎥
⎢ e ⎥ ⎢ − sin 𝜃 0 ⎥ sin 𝛾ej𝜁
d(𝜙, 𝜃, 𝛾 , 𝜁 ) = ⎢ 𝑧 ⎥ = ⎢ ⎥[ ] (3)
⎢h𝑥 ⎥ ⎢ − sin 𝜙 − cos 𝜙 cos 𝜃⎥ cos 𝛾
⎢h ⎥ ⎢ cos 𝜙 ⎥
− sin 𝜙 cos 𝜃 ⎥
⎢ 𝑦⎥ ⎢
⎣h𝑧 ⎦ ⎣ 0 sin 𝜃 ⎦
Assumption 3: The polarization phase difference 𝜁 is set as 90∘ in this work, as the electro-
magnetic wave received from UEs are mostly linear polarized [15].
3.3. Signal Model for 3-D Positioning
In the practical environment, the SRS symbols received by the base station from the 𝑚th UE are
usually affected by multipath propagation. Assume the 𝑁 length raw SRS signal sm SRS ∈ ℂ
𝑁 ×1
goes through 𝐾 multipaths and each path has different delay and angle that can be represented
by the delay manifold gm (𝜏𝑘𝑚 ) and angle steering vector dm (𝜃𝑘𝑚 , 𝜙𝑘𝑚 , 𝛾𝑘𝑚 ), respectively. Thus, the
received frequency-domain signal Ym (t) ∈ ℂ6𝑁 ×1 of 𝑚th UE can be expressed by the eq. (4a) and
the noise Nm ∈ ℂ6𝑁 ×1 is the Gaussian white additive noise (AWGN). Am 𝑚 𝑚 𝑚 𝑚 6𝑁 ×1
k (𝜃𝑘 , 𝜙𝑘 , 𝛾𝑘 , 𝜏𝑘 ) ∈ ℂ
in (4b) is the joint time-angle steering vector of 3D estimation. H and ⊗ are conjugate transpose
and Kronecker multiplication. To match the six elements of steering vector dm (𝜃𝑘𝑚 , 𝜙𝑘𝑚 , 𝛾𝑘𝑚 ), the
SRS signal are correspondingly expended into the form of eq. (4c). It should be noted that, AoA
steering vector dm (𝜃𝑘𝑚 , 𝜙𝑘𝑚 , 𝛾𝑘𝑚 ) is set with 𝜁 equals to 90∘ as the assumption 3 described.
𝐾
Y (t) = ∑ Am
m 𝑚 𝑚 𝑚 𝑚 m m
k (𝜃𝑘 , 𝜙𝑘 , 𝛾𝑘 , 𝜏𝑘 )⋅sk + N (t) (4a)
𝑘=0
Am (𝜃 𝑚 , 𝜙 𝑚 , 𝛾 𝑚 , 𝜏 𝑚 ) = dm (𝜃 𝑚 , 𝜙 𝑚 , 𝛾 𝑚 ) ⊗ gm (𝜏 𝑚 ) (4b)
k 𝑘 𝑘 𝑘 𝑘 𝑘 𝑘 𝑘 𝑘
sm
k = [1, 1, 1, 1, 1, 1] ⊗ sm
SRS (4c)
3.4. Estimation algorithms
The two estimation algorithms used in this work are: i) subspace-based signal classification and
ii) an Expectation and Maximization (EM) algorithm.
3.4.1. Subspace-Based Approach
The first approach is based on the subspace algorithm Multiple Signal Classification (MUSIC)
[8]. The searching space of this work Am 𝑚 𝑚 𝑚 𝑚
k (𝜙𝑘 , 𝜃𝑘 , 𝛾𝑘 , 𝜏𝑘 ) includes four parameters azimuth,
elevation, polarization angles and time delay. To performance the 4-D estimation, we first
calculate the auto-correlation matrix:
∗
𝑅YY = 𝔼[Ym (t)Ym (t) ] (5)
where 𝔼[⋅] denotes expectation, [⋅]∗ means the conjugate transpose. After applying eigenvalue
decomposition, we will have 𝜆 = [𝜆1 , 𝜆2 , ..., 𝜆6𝑁 ] (with ascending order) and eigen vector En =
[𝑒1 , 𝑒2 , ...𝑒6𝑁 ]. Then, we can define the noise subspace as:
En = [𝑒1 , 𝑒2 , ...𝑒6𝑁 −(𝐾 +1) ] (6)
K is the number of multipath propagation paths we want to estimate. As the we are focusing
on the LoS scenario and the processed SRS signal of different UEs are orthogonal in the time-
frequency domains, the estimation of multi UEs’ position propblem can be symplified into
single-target positioning as long as we extract the SRS signal according to the allocation pattern.
Thus, K is set to 1 in the simulation. Then, with the noise subspace, the 4-D spectrum of UE 𝑚
can be defined as:
A∗m (𝜙 𝑚 , 𝜃 𝑚 , 𝛾 𝑚 , 𝜏 𝑚 )Am (𝜙 𝑚 , 𝜃 𝑚 , 𝛾 𝑚 , 𝜏 𝑚 )
P(𝜙𝑘𝑚 , 𝜃𝑘𝑚 , 𝛾𝑘𝑚 , 𝜏𝑘𝑚 ) = m∗ k 𝑚 𝑘𝑚 𝑘𝑚 𝑘𝑚 𝑘 k∗ m𝑘 𝑘𝑚 𝑘𝑚 𝑘𝑚 𝑚 (7)
Ak (𝜙𝑘 , 𝜃𝑘 , 𝛾𝑘 , 𝜏𝑘 )En En Ak (𝜙𝑘 , 𝜃𝑘 , 𝛾𝑘 , 𝜏𝑘 )
After exhaust searching in 𝜙, 𝜃, 𝛾 and 𝜏 dimensions with defined searching steps (𝜙𝑠𝑡𝑒𝑝 , 𝜃𝑠𝑡𝑒𝑝 ,
𝛾𝑠𝑡𝑒𝑝 and 𝜏𝑠𝑡𝑒𝑝 ). The searching steps are chosen according to the trade-off between accuracy
requirement and computational complexity. The peak value of P(𝜙𝑘𝑚 , 𝜃𝑘𝑚 , 𝛾𝑘𝑚 , 𝜏𝑘𝑚 ) determines the
estimated signal source position and its polarization state.
3.4.2. Statistics-Based Approach
The EM method follows the space-alternating generalized expectation-maximization (SAGE)
design in [7]. This method iteratively uses Expectation step (E-step) and Maximization step
(M-step) to update expected signal until the variance between the received signal and expected
signal reach the convergence point. The received SRS signal of 𝑚th UE is Ym (t). It contains
𝐾 multipath components and 𝑘th component Ym ̂ (𝜏 𝑚 ) is described in eq. (8b). The multipath
k 𝑘
component includes the received signal m 𝑘 and noise 𝛽𝑘 Nm k . The value of 𝛽𝑘 is positive and
𝐾
∑𝑘=1 𝛽𝑘 = 1 holds to ensure the noise coming from 𝐾 paths are equal to the total received noise
Nm defined in eq. (4a). The steering vector and delay manifold of 𝑘𝑡ℎ path are dm 𝑚 𝑚 𝑚
k (𝜙𝑘 , 𝜃𝑘 , 𝛾𝑘 )
m 𝑚
and gk (𝜏𝑘 ).
𝐾
Ym (t) = ∑ Ŷm 𝑚
k (𝜏𝑘 ) (8a)
𝑘=0
̂ (𝜏 𝑚 ) = Lm (𝜏 𝑚 ) + 𝛽𝑘 Nm (𝜏 𝑚 )
Ym (8b)
k 𝑘 k 𝑘 k 𝑘
Lm (𝜏 𝑚 ) = dm (𝜃 𝑚 , 𝜙 𝑚 , 𝛾 𝑚 )×(sm ⋅gm (𝜏 𝑚 )) (8c)
k 𝑘 k 𝑘 𝑘 𝑘 SRS k 𝑘
m 𝑚
In the M-step the updated value of Lk (𝜏𝑘 ) can be obtained:
𝑇
̂ (𝜏 𝑚 )) = arg
𝜂̂′ (Ym max ∗ ̂𝑚 𝑚 ∗ 𝑚
k 𝑘 ∫ d (𝜙, 𝜃, 𝛾 )𝑌𝑘 (𝜏𝑘 )g (𝑡 − 𝜏𝑘 )𝑑𝑡
[𝜙𝑘𝑚 ,𝜃𝑘𝑚 ,𝛾𝑘𝑚 ,𝜏𝑘𝑚 ] 0
(9)
𝑇 is the OFDM signal observing duration to cover sequence length and maximum propagation
delay. The E-step and M-step will be iteratively implemented until the algorithm reach the
convergence point. The value of intermediate noise Nm k is used as the convergence condition.
m
The value of Nk keeps changing in each EM iteration and reaches its extreme limit point when
the estimated parameters are approximately fully recovered. The extreme limit point of Nmk is
m m
reached when the power difference of Nk,step(n−1) and Nk,step(n) in the continuous two steps
is approaching the threshold 𝜖. The flow chart of the algorithm is shown in Fig. 4
Figure 4: The signal flow of the EM algorithm
4. Simulation Results
4.1. Simulation Setting
Based on the assumptions listed in Section 3, the base station knows the SRS from different
UE to perform single target position estimation. In this work, the physical resource allocation
pattern of the target UE is the same as the UE1 in Fig.1. In the frequency domain, the total
PRB number m𝑆𝑅𝑆 and comb structure indicator K𝑡𝑐 are set to 40 and 2, respectively. The total
bandwidth used for SRS is 15MHz as the 15kHz subcarrier spacing is selected. In the time
domain, the SRS signal starts from the eighth OFDM symbol and lasts four symbols in every slot.
We treat one SRS OFDM symbol as one snapshot in the simulation, and the snapshot number in
the estimation is 20, which means the total collected samples last 5 slots.
A LoS communication environment is constructed by using a 3GPP standard TDL-D channel
model with 13 taps. The NLoS taps follow the Rayleigh distribution with average attenuation
values less than −18dB. The first tap (LoS tap) has a delay of 10ns, which equivalent to 3m radial
range. The LoS tap follows a Rice distribution with a K-factor of 𝐾1 = 13.3dB and 0dB mean
channel attenuation. 10ns is selected for the delay spread of TDL-D channel to simulate the
extreme case where multipath propagated signals are arriving with undetectable ToA difference.
In addition, we generate AoA profiles for 12 multipath taps, which are not defined in the 3GPP
report[16]. The angle step (𝜙𝑠𝑡𝑒𝑝 , 𝜃𝑠𝑡𝑒𝑝 ) and time step (𝜏𝑠𝑡𝑒𝑝 ) used in two position estimation
methods are 0.4∘ and 3.3ns (1m).
4.2. Positioning Performance
This subsection shows the VA-based 3D-positioning performance by using subspace and EM
approaches, respectively. We also use the URA as the reference for comparison. Both VA and
(3 × 3) URA-based approaches are capable to detect targets with high accuracy (less than 0.5m
RMSE Curves
1
EM VA
0.9 EM URA (3*3)
Subspace VA
0.8 Subspace URA (3*3)
0.7
RMSE (m)
0.6
0.5
0.4
0.3
0.2
-10 -5 0 5 10 15
SNR (dB)
Figure 5: RMSE VS SNR with VA and URA, Source AoA = [30, 30], Source ToA = 10ns, TDL-D Channel
with 13 Multipaths.
RMSE) even with 0dB SNR. However, EM methods of URA and VA are more sensitive than the
subspace-based counterparts with low SNR region. Through comparing VA and URA with the
EM method, VA shows lower accuracy than the URA configuration. The performance of both
VA and URA approaches gradually converge to 0.3 RMSE when the SNR increases. Thus, we can
conclude that the subspace method is more suitable for VA-based positioning systems with the
presence of high noise power. It is worth to mentioning that the EM-based method is sensitive
to noise power, but it costs less computation time than the subspace-based method. It means the
EM approach is a better choice for high SNR to computationally constrained scenarios. We set
the target time delay 𝜏𝑘𝑚 equals to 3.3ns in the simulation. But the sector shaped coverage area
expands with the increasing radial range (or increasing time delay 𝜏𝑘𝑚 ). Thus, the accuracy of far
target will degrade unless we use finer 𝜙𝑠𝑡𝑒𝑝 and 𝜃𝑠𝑡𝑒𝑝 values.We also observe the impact of time
searching step (𝜏𝑠𝑡𝑒𝑝 ) on RMSE in EM and subspace algorithms. As shown in Fig.6, the larger
(𝜏𝑠𝑡𝑒𝑝 ) causes the larger RMSE value for both EM- and subspace-based methods; though the
larger (𝜏𝑠𝑡𝑒𝑝 ) reduces the computation resources consumption in algorithms would, unavoidably,
introduces performance degradation. However, the RMSE with 5ns time step is 0.4m and it is
still acceptable for outdoor positioning systems.
4.3. Reflection influence
The signal strength of multipath components of the TDL-D channel is set with values at least
18dB less than the LoS path. To figure out the positioning capability of the proposed work in a
strong reflection appeared environment, this subsection explores the reflected signal impact
of AoA estimation, Fig.7. shows the results. We assume the VA-equipped station locates in
the middle between one wall and one drone; the base station received signal contains one LoS
component with 10𝑛𝑠 time delay (3m) and one reflection from the building has 15𝑛𝑠 time delay.
The AoA of LoS path and reflection are [30, 30] and [120, 120], respectively. To show VA used
RMSE Curves VS Time Searching Step, 15dB SNR
0.45
EM VA
0.4
MUSCI VA
0.35
RMSE (m)
0.3
0.25
0.2
0.15
0.1
1 1.5 2 2.5 3 3.5 4 4.5 5
Time Searching Step (ns)
Figure 6: RMSE VS Time Searching Step, Source AoA = [30, 30], Source ToA = 10ns, TDL-D Channel
with 13 Multipaths, SNR = 15dB.
AoA estimation capability, the Fig.7 plots the subspace spectrum in azimuth and elevation angle
dimensions with different reflected signal strengths. When signal power to reflection power
ratio (SPRP) equals to 0dB shown in Fig.7.d, the detected target located at a region in the middle
between [30, 30] and [120, 120], this means neither the LoS component nor NLoS component can
be properly estimated. The detected AoA region is close to [30, 30] when the SPRP is improved
to 3dB, but we still cannot correctly figure out the AoA of LoS path. By observing the single LoS
path estimation result in the Fig.7.a and weak reflection (10dB SPRP) influenced AoA estimation
result in the Fig.7.b; we can find the estimated AoA region are close to the ground truth. In
summary, Fig.7 shows AoA estimation with VA is vulnerable in face of multipath influence.
Strong multipath path introduces the AoA estimation errors unless the SPRP is higher than
10dB.
4.4. Auxiliary polarization angle impact on positioning performance
The auxiliary polarization angle 𝛾 of a UE is usually unknown by the base station in a realistic
situation. Thus, the measurement of 𝛾 and its relationship with reflections are explored in this
section. The setting of source and reflection positions is following subsection 4.3; varying the
relative polarization angles 𝛾 of the reflection and LoS paths is the new feature discussed in the
following content. 4.3.
In Fig.8, we plot the AoA estimation RMSE with the source polarization angle 𝛾 ranging from
0 to 2𝜋. The subspace method estimates AoA and polarization angle simultaneously with the
presence of only LoS path. The RMSE of AoA stays between 0.3∘ and 0.4∘ , which proves that the
VA-based design has a stable performance of AoA estimation no matter the signal polarization
state is.
According to [11], the polarization angle 𝛾 provides one degree of freedom to resolve two
impinging electromagnetic waves from the same location. Thus, we assume the signal comes
a. AoA Estimation, No Reflection b. AoA Estimation, SPRP 10dB
Azimuth angle/(degree)
Azimuth angle/(degree)
20
100 20 100 15
10
200 10 200
5
300 300 0
0
50 100 150 50 100 150
Elevation angle/(degree) Elevation angle/(degree)
c. AoA Estimation, SPRP 3dB d. AoA Estimation, SPRP 0dB
Azimuth angle/(degree)
Azimuth angle/(degree)
20
10
100 15 100
10 5
200 200
5
300 300 0
0
50 100 150 50 100 150
Elevation angle/(degree) Elevation angle/(degree)
Figure 7: VA-based AoA Estimation with/ without Reflections, Source AoA = [30, 30], Reflection Signal
AoA = [120 120], Subspace Method, Signal Power to Reflection Power Ratio = [10dB, 3dB, 0dB]
from a drone that has a fixed 10∘ polarization angle 𝛾𝐿𝑂𝑆 of LoS component and turning reflection
𝛾𝑁 𝐿𝑂𝑆 from 0 to 2𝜋 to check if polarization angle difference between two signals can mitigate
strong reflection impact occurs in subsection 4.3.
Fig.9.a shows that the RMSE of AoA estimation various with the different reflection polariza-
tion angles. Two RMSE minimum appear when 𝛾𝑁 𝐿𝑂𝑆 equals to 170∘ and 340∘ . To monitor the
relationship between the estimated source polarization angle and RMSE curves, the estimated
LoS path polarization angle corresponding to the RMSE figure is plot in Fig.9.b. From the
estimated polarization angle plot, we can see that the reflection also brings the error into the
𝛾𝐿𝑜𝑆 estimation. The curve of estimated 𝛾𝐿𝑜𝑆 reach its minimum when 𝛾𝑁 𝐿𝑂𝑆 has values close to
180∘ and 350∘ . Surprisingly, the minimum point of AoA RMSE curve and the correct 𝛾𝐿𝑜𝑆 value
(10∘ ), have strong connections; the AoA RMSE value reduces if the 𝛾𝑁 𝐿𝑂𝑆 and 𝛾𝐿𝑜𝑆 have about 𝜋
or 2𝜋 difference. However, Fig. 9 shows the AoA estimation error still is exists with the absence
of coherent signal from different paths even with orthogonal 𝛾 values (𝛾𝑁 𝐿𝑂𝑆 = 100∘ ).
5. Conclusion
This paper proposes a VA based 3D positioning method with EM- and subspace-based algorithms
under the 5G-NR network. The positioning function achieved using up-link dedicated reference
signal SRS, and the LoS scenario is constructed with TDL-D channel model. The simulation
results have shown that both subspace- and EM-based methods can estimate the target position
RMSE VS Source Polarization
1
0.9
0.8
0.7
RMSE (degree)
0.6
0.5
0.4
0.3
0.2
0.1
0
0 50 100 150 200 250 300 350
Source Polarization Angle (degree)
Figure 8: VA-based AoA Estimation with reflections, Source AoA = [30, 30], Without Reflection, Subspace
Method
a. Angle of Arrival RMSE VS Reflection Polarization Effects
AoA RMSE (degree)
12
11
10
9
50 100 150 200 250 300 350
Reflection Signal Polarization Angle(degree)
b. Estimated Polarization Angle VS Reflection Polarization Effects
Angle (degree)
20
10
0
50 100 150 200 250 300 350
Reflection Signal Polarization Angle(degree)
Figure 9: VA-based AoA Estimation with reflections, Source AoA = [30, 30], Reflection Signal AoA =
[120 120], SPRP Ratio = 8dB ,Subspace Method
accurately with either VA or URA; the subspace method provides better performance with low
SNR values, and EM costs less computation resource. Subspace method significantly improves
the VA’s performance with low SNR region. Although VA has slightly worse performance
than URA with the two estimation algorithms, it has an outstanding broader coverage than
URA, which is only capable of source detecting in a hemisphere area. We believe VA based 5G
positioning system can perform a reliable, accurate, and robust performance in a 3D space. In
practice, the proper time step selection is necessary to balance the limitations of computation
resources and desired accuracy. Moreover, the presence of a strong multipath reflection causes
the AoA estimation performance deterioration. The reflection influence can somehow be eased
if the multipath component auxiliary polarization angle has 𝜋 difference in comparison with
the LoS polarization angle. Since the communication environment is not controllable and the
adjustment of auxiliary polarization angle is almost impossible in real life. Our future work will
focus on the VA array constructed 5G positioning systems to improve the positioning accuracy
with the presence of strong reflections.
Acknowledgments
This research was partly funded by the SESAR Joint Undertaking (SJU) in project NewSense
(Evaluation of 5G Network and mmWave Radar Sensors to Enhance Surveillance of the Airport
Surface), Grant Number 893917, within the framework of the European Union’s Horizon 2020
research and innovation program. The opinions expressed herein re�ect the authors’ view
only. Under no circumstances shall the SJU be responsible for any use that may be made of the
information contained herein. This work was also partly supported by the Academy of Finland,
under the project ULTRA (328226, 328214).
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