Tracking Position and Orientation Through Millimeter Wave Lens MIMO
in 5G Systems
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Citation for the original published paper (version of record):
Shahmansoori, A., Uguen, B., Destino, G. et al (2019). Tracking Position and Orientation Through
Millimeter Wave Lens MIMO in 5G Systems. IEEE Signal Processing Letters, 26(8): 1222-1226.
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1
Tracking Position and Orientation through
Millimeter Wave Lens MIMO in 5G Systems
Arash Shahmansoori, Bernard Uguen, Member, IEEE ,GiuseppeDestino,Member, IEEE ,Gonzalo
Seco-Granados, Senior Member, IEEE,andHenkWymeersch,Member, IEEE
Abstract—Millimeter wave signals and large antenna arrays
are considered enabling technologies for future 5G networks.
Despite their benefits for achieving high data rate communica-
tions, their potential advantages for tracking of the location and
rotation angle of the user terminals are not well investigated. A
joint heuristic beam selection and user position and orientation
tracking approach is proposed. First, the user location is tracked
in the uplink by joint beam selection together with time-of-arrival
(TOA) and angle-of-arrival (AOA) tracking at the b ase station
(BS). Then, the user rotation angle is obtained using the location
information by joint beam selection and track in g at the mobile
station (MS). The beam selection, TOA and AOA tracking at
the BS and MS are performed during the data transmission
phase. Numerical results demonstrate that the prop osed method
performs close to the estimated position and rotation angle in the
training phase with reduced complexity and reduced number of
required pilots for the estimation.
Index Terms—5G networks, millimeter wave, lens arrays,
position and orientation tracking, heuristic beam selection.
I. INTRODUCTION
M
ILLIMETER WAVE and massive multiple-input-
multiple-output (MIMO) will likely be adopted tech-
nologies in fifth generation (5G) communication networks,
thanks to a number of favorable properties. Particularly, by
exploiting the carrier frequencies beyond 30 GHz and large
available bandwidth, millimeter wave (mm-wave) can provide
high data rate. This can be obtained through dense spatial mul-
tiplexing with large antennas [1], [2]. Despite the aforemen-
tioned properties that are desirable for 5G services, there are
anumberofchallengesregardingmm-wavecommunications.
One o f the most important challenges is the severe path loss
at high carrier frequencies. The loss in signal-to-noise ratio
(SNR) is compensated through beamforming at the transmitter
and/or receiver resulting in highly directional links [3]–[5].
Arash Shahmansoori and Bernard Uguen are with the Institute of
Electronics and Telecommunications of Rennes, Université de Rennes
1, 35042 Rennes, France, emails: arash.mansoori65@gmail.com and
Bernard.Uguen@univ-rennes1.fr. Gonzalo Seco-Granados is with the Depart-
ment of Telecommunications and Systems Engineering, Universitat Autònoma
de Barcelona, 08193 Barcelona, Spain, email: gonzalo.seco@uab.cat.
Henk Wymeersch is with the Department of Electrical Engineering,
Chalmers University of Technology, 412 96 Gothenburg, Sweden, email:
henkw@chalmers.se. Giuseppe Destino is with the center for wireless commu-
nications, Univ e rsity of Oulu, 90014 Oulu, Finland, and visiting research fel-
low at King’s College London, email: giuseppe.destino@ee.oulu.fi. This work
was financially supported by M5HESTIA (mmW Multi-user Massive MIMO
Hybrid Equipment for Sounding, Transmissions and HW Implementation)
project, the VINNOVA COPPLAR project,fundedunderStrategicVehicle
Research and Innovation grant nr. 2015-04849, FALCON (Fundamental of
simultaneous localization and communications) funded by the Academy of
Finland, and R&D Projects of Spanish Ministry of Economy and Competi-
ti veness TEC2017-89925-R. (Corresponding author: Arash Shahmansoori.)
Apossiblewayforlow-costimplementationofmm-wave
MIMO is achieved by using switching circuits together with
lens antenna arrays [6]–[12]. Position-based beamformer de-
sign requires the knowledge of propagation channel, e.g., user
position, scatterer locations, and so on. The relative location
of transmitter and receiver can be obtained using the estimated
AOA/angle-of-departure (AOD) for the line-of-sight (LOS)
condition [13]. To this end, position and orientation estimation
was previously explored in [14]–[19] and in [17], [20], [21]
for mm-wave and massive MIMO systems for static channels.
To speed up initial access between nodes, a location-aided
beamforming method was proposed in [22].
In the case of dynamic channels, a beam switching ap-
proach was suggested for tracking of AOA in [14]. A link
by link mm-wave AOA/AOD and channel gain tracking was
proposed in [23], while a tracking solution for all the links was
investigated in [24]. In [25] and [26] different solutions were
proposed mainly based on AOA tracking for mm-wave and
Terahertz lens antenna arrays by Markov model and a temporal
variation law of the physical direction, respectively . All of
the aforementioned papers propose the solutions for static
channels and AOA based tracking for time-varying channels.
However, for tracking the user location an d o rientation it is
essential to consider the combination of TOA and AOA.
In this letter, we propose a joint b eam selection position and
orientation tracking method using a lens antenna array with
one BS. The proposed method tracks the channel parameters
with a heuristic bea m selection me th od based on the angular
uncertainties provided by the an extended Kalman filter (EKF)
in the uplink followed by a downlink tran smission. This
enables tracking of the po sitio n and rotation an gle of the user
with reduced number of re quired beams within the o bservation
time. From the simulation results, it is observed that the pro-
posed algorithm provides position and rotation angle estimates
during the data transmission phase with similar accuracy to
those obtained during the training phase while involving a
reduced complexity and number of pilot transmissions.
II. P
ROPOSED METHOD
In this section, a joint heuristic beam selection and tracking
method is proposed for a mm-wave MIMO system with a lens
antenna array. The mm-wave lens MIMO channel model in the
uplink (UL) for the n-th subcarrier is obtained as [10], [27]
ˇ
H
UL
[n]=
K
!
k=0
γ
n
(
˜
h
k
,τ
k
)χ
BS,k
χ
T
MS,k
, (1)
2
where γ
n
(
˜
h
k
,τ
k
) is defined as γ
n
(
˜
h
k
,τ
k
)=
˜
h
k
e
−j2πnτ
k
/(NT
s
)
in which τ
k
is the delay of the k-
th path, K +1 denotes the total number of paths
with the LOS indexed by the subscript zero, N is
the number of subcarriers, T
s
=1/B is the sampling
period, and
˜
h
k
=
"
(N
BS
N
MS
)/ρ
k
h
k
in which ρ
k
denotes the path loss with complex channel gain of
h
k
.Thetermχ
MS,k
is an N
MS
× 1 vector denoting
lens array with N
MS
antenna elements and the entries
χ
MS
#
d
λ
c
sin(φ
k
) −
i
N
MS
$
with φ
k
being the AOA in the
downlink (DL) for −(N
MS
− 1)/2 ≤ i ≤ (N
MS
− 1)/2
where χ
MS
(φ) = sin(πN
MS
φ)/
#
√
N
MS
sin(πφ)
$
,andχ
BS,k
denotes an N
BS
× 1 lens arra y with N
BS
antenna elements
and defined similarly by replacing the subscript MS by BS
and the downlink AOA (DL-AOA) φ
k
by AOA in the UL θ
k
.
Using the information provided by the LOS path, the goal
is to track the user position
1
p = q + cτ
0
[cos(θ
0
), sin(θ
0
)]
T
where q denotes the location of the BS assumed to be known
and c is the speed of light, and rotation angle α = π +θ
0
−φ
0
with reduced number of pilot tr ansmissions. It is assume d
that the BS does not move and tracks the location of the
MS, and the MS tracks its rotation angle using the location
information provided by the BS.
A. Measurement and State Equations
Acontinuouswhitenoiseacceleration(CWNA)model
defines the state evolution used for tracking DL-AOA/uplink
AOA (UL-AOA), and TOA [28]. The state vector for the LOS
path can be written as
ψ
[m]
0
=
%
(η
[m]
0
)
T
(
˙
η
[m]
0
)
T
&
T
, (2)
where η
[m]
0
=[τ
[m]
0
,θ
[m]
0
,φ
[m]
0
]
T
and
˙
η
[m]
0
=
[˙τ
[m]
0
,
˙
θ
[m]
0
,
˙
φ
[m]
0
]
T
.Thetermsθ
[m]
0
and φ
[m]
0
denote the
UL-AOA and DL-AOA for the LOS path at the time instant
m,respectively.Similarly,τ
[m]
0
denotes the TOA for the LOS
path. Finally, the parameters ˙τ
[m]
0
,
˙
θ
[m]
0
,and
˙
φ
[m]
0
denote
the rate-of-change of the TOA, UL-AOA, and DL-AOA for
the block duration T
B
,thetimebetweentwoinstantsm
and m +1,respectively.AssumingCWNAmodel,thestate
evolution model can be written as
ψ
[m]
0
= Φψ
[m−1]
0
+ u
[m]
0
, (3)
where u
[m]
0
denotes the state noise with E
%
u
[m]
0
(u
[m]
0
)
T
&
=
Q
[m]
0
.Ingeneral,thebi-azimuthgeneralized Von-Mises-Fisher
(VMF) distribution fo r joint DL-AOA/UL-AOA or its approx-
imation by a 2-D truncated Gaussian pdf can be applied
for directional data [29], [30]. In this case, we apply the
approximation with a 2-D truncated Gaussian pdf with σ
φ
0
,
σ
θ
0
,andρ
θφ,0
denoting the direction spreads of the AOA,
AOD, and cross correlation for the LOS path, respectively.
Moreover, the amount of noise would depend on T
B
.The
state transition matrix Φ ∈ R
6×6
is defined as
Φ =
'
I
3
T
B
I
3
0
3
I
3
(
. (4)
1
The extension to the multi-user scenario is an exciting topic for future
research.
For m =1,theentriesofψ
[m−1]
0
in (3) are initialized
as: τ
[0]
0
=ˆτ
0
, φ
[0]
0
=
ˆ
φ
0
,andθ
[0]
0
=
ˆ
θ
0
where ˆτ
0
,
ˆ
φ
0
,
and
ˆ
θ
0
are obtained from the training phase. The rate-of-
change terms
2
are initialized by two c onsecutive estimates
of η
0
[m]=[τ
[m]
0
,θ
[m]
0
,φ
[m]
0
]
T
as: ˙τ
[1]
0
=(τ
[1]
0
− τ
[0]
0
)/T
B
,
˙
θ
[1]
0
=(θ
[1]
0
− θ
[0]
0
)/T
B
,and
˙
φ
[1]
0
=(φ
[1]
0
− φ
[0]
0
)/T
B
.
For tracking of the channel parameters, the EKF is applied
with the state comprising the LOS delay, DL-AOA, UL-AOA,
and their corresponding rates of changes, with the linear
process model and nonlinear measurement equations in the
downlink and the uplink. These parameters are initially avail-
able at the BS and th e MS from the training/initial access phase
[19]. The measurement equation in the uplink is obtained
for the orthogonal frequency division multiplexing (OFDM)
transmission as
ˇ
y
ul,[m]
r
= z
ul
0
(η
[m]
ul,0
; φ
[m]
0
)+
K
!
l=1
z
ul
0
(η
[m]
ul,l
; φ
[m]
l
)+
ˇ
n
[m]
, (5)
where η
[m]
ul,k
=[τ
[m]
k
,θ
[m]
k
]
T
,and
ˇ
y
ul,[m]
r
denotes the received
signal vector of size NM
BS
× 1 which M
BS
is the number
of received beams at the BS. In ( 5), the first term denotes the
received signal from the LOS, and the second term denotes
the superposition of all the other K non-line-of-sight (NLOS)
paths acting as an added
3
term to the Gaussian measurement
noise vector
ˇ
n
[m]
∈ C
NM
BS
with zero mean and variance
N
0
/2 per real dimension.
The
4
TO A-AOA are the parameters to be tracked for the
block index m in the BS, and z
ul
0
(η
[m]
ul,k
; φ
[m]
k
) denotes
z
ul
0
(η
[m]
ul,k
; φ
[m]
k
)=
˜
h
[m]
k
)
X
T
0
(F
[m−1]
MS,0
)
T
χ
[m]
MS,k
⊙ a
[m]
τ
k
*
⊗ F
H
BS,0
χ
[m]
BS,k
, (6)
where X
0
=[x
(0)
[0],...,x
(0)
[N − 1]]
T
denotes the pre-
coded signal where x
(0)
[n] is the M
MS
× 1 vector of si-
multaneously transmitted symbols for the n-th subcarrier
for the LOS link. The delay vector is defined as a
[m]
τ
k
=
[1,...,e
−j2π(N−1)τ
[m]
k
/(NT
s
)
]
T
.
The term
5
F
[m−1]
MS,0
denotes the uplink beam selection matrix,
i.e., a matrix of zeros and ones with all-zero elements in each
column except the index of the corresponding beam. The beam
selection matrix F
[m−1]
MS,0
selects the corresponding beams to
cover
ˆ
φ
[m−1]
0
with the uncertainty
+
[P
[m−1|m−1]
ψ
dl,0
]
1,1
.This
angular uncertainty is obtained from the first diagonal element
of the covariance estimation of ψ
[m]
dl,0
=[φ
[m]
0
,
˙
φ
[m]
0
]
T
by the
EKF. In the BS, the received beam selection matrix F
BS,0
is
fixed and selects the corresponding beams to cover
ˆ
θ
0
with
the max imum uncertainty during the observation time T
ob
.
2
If the underlying dynamic function is unknown, a Gaussian blurring kernel
centered on the previous time instant m − 1 can be applied with a covariance
corresponding to the process noise. This way, it is possible to consider time-
varying rate-of-change terms.
3
The NLOS paths are much weaker and susceptible to movement compared
to the LOS. Consequently, they do not significantly contribute to user location
and orientation tracking particularly for the outdoor scenarios [31].
4
Note that the term
˜
h
[m]
0
and DL-AOA φ
[m]
0
are considered as the nuisance
parameters in the uplink.
5
The operations ⊙ and ⊗ denote the Hadamard and Kronecker products.
3
Fig. 1. The normalized magnitude of the elements of χ
[m]
MS/BS,0
for the beam
selection (top) with and (bottom) without considering the effect of uncertainty.
Asimilarprocesscanbeformedfortracking
6
the AOA in
the MS. In Fig.1, the normalized magnitude response of lens
array in the BS or MS χ
[m]
MS/BS,0
with N
MS/BS
is shown.
Ideally, the true/estimated angle should be at the pre-defined
spatial direction {i/N
MS/BS
} for −(N
MS/BS
− 1)/2 ≤ i ≤
(N
MS/BS
−1)/2 to provide the maximum power. This is shown
by the dashed blue line with square marker as the best case
in the top plot. However, this usually does not happen as the
true/estimated spatial direction might be within 1/(2N
MS/BS
)
from the pre-defined value. Consequently, beam selection
without c onsidering the uncertainty leads to power reduction
shown in the bottom plot. This results non-robust tracking
performance as will be shown in the simulations. Using the
channel parameters after tracking in {ˆτ
[m]
0
,
ˆ
θ
[m]
0
,
ˆ
φ
[m]
0
},the
tracked values of position and rotation angle
,
ˆ
p
[m]
, ˆα
[m]
-
are obtained. The u ncertainty of position P
[m|m]
p
and rotation
angle P
[m|m]
α
are computed as
P
[m|m]
p
=
.
T
ˆτ
[m]
0
,
ˆ
θ
[m]
0
%
P
[m|m]
ψ
ul,0
&
−1
1:2,1:2
T
T
ˆτ
[m]
0
,
ˆ
θ
[m]
0
/
−1
, (7)
P
[m|m]
α
=
%
P
[m|m]
ψ
ul,0
&
2,2
+
%
P
[m|m]
ψ
dl,0
&
1,1
, (8)
where T
ˆτ
[m]
0
,
ˆ
θ
[m]
0
denotes the conversion matrix
T
τ
0
,θ
0
=[
∂τ
0
∂p
,
∂θ
0
∂p
] evaluated at (ˆτ
[m]
0
,
ˆ
θ
[m]
0
) with
∂τ
0
∂p
=
1
c
[cos(θ
0
), sin(θ
0
)]
T
and
∂θ
0
∂p
=
1
cτ
0
[−sin(θ
0
), cos(θ
0
)]
T
.
The term P
[m|m]
ψ
ul,0
denotes th e uncertainty obtained
by the covariance of the corresponding term
ψ
[m]
ul,0
=[τ
[m]
0
,θ
[m]
0
, ˙τ
[m]
0
,
˙
θ
[m]
]
T
from the EKF. The operation
[.]
−1
1:2,1:2
in (7) denotes the 2 × 2 upper left submatrix of the
inverse of the argument.
B. The Algorithm
The heur istic beam selection and position and orientation
tracking method is summarized in the Algorithm 1. The
estimated channel parameters
ˆ
η
[0]
0
=[ˆτ
[0]
0
,
ˆ
θ
[0]
0
,
ˆ
φ
[0]
0
]
T
and
6
For the case of asynchronous networks, rather than considering the joint
AOA-AOD tracking, the tracking is performed in the UL and DL. This way,
it is possible to cancel clock bias by two-way TOA estimation.
Algorithm 1: Heuristic Beam Selection and Position
and Orientation Tracking
Input : Set m =1,andT
ob
.
Output: Tracked position
ˆ
p
[m]
and rotation angle ˆα
[m]
within T
ob
with the corresponding
uncertainties in (7) and (8), respectively.
1 repeat
2 Compute ˆτ
[0]
0
and
ˆ
θ
[0]
0
in the BS,
ˆ
φ
[0]
0
in the MS,
and the corresponding values of
ˆ
p
[0]
and ˆα
[0]
in
the training;
3 Set the received beam selection matrix F
BS,0
in
the uplink, and F
MS,0
in the downlink to cover
ˆ
θ
[0]
0
and
ˆ
φ
[0]
0
,respectively,withthemaximum
uncertainty within T
ob
;
4 while mT
B
≤ T
ob
do
5 Set the transmit beam selection m atrix F
[m−1]
MS,0
in the uplink to direct the beams towards
ˆ
φ
[m−1]
0
covering the angular uncertainty
+
[P
[m−1|m−1]
ψ
dl,0
]
1,1
;
6 Compute ˆτ
[m]
0
,
ˆ
θ
[m]
0
,and
ˆ
p
[m]
in the BS;
7 Set the transmit beam selection m atrix F
[m−1]
BS,0
in the downlink to direct the beams towards
ˆ
θ
[m−1]
0
covering the angular uncertainty
+
[P
[m−1|m−1]
ψ
ul,0
]
2,2
;
8 Compute
ˆ
φ
[m]
0
in the MS;
9 Using
ˆ
p
[m]
communicated from the BS to the
MS and
ˆ
φ
[m]
0
,computeˆα
[m]
in the MS;
10 Set m = m +1;
11 end
12 until the next observatio n time T
ob
;
corresponding values of the position
ˆ
p
[0]
and rotatio n angle
ˆα
[0]
are obtained
7
in step 2. In step 3, the heuristic beam
selection is applied for the receiver in the uplink/downlink. In
step 5, th e up link beam selection matrix F
[m−1]
MS
selects the
beams directed towards the previous downlink AOA,
ˆ
φ
[m−1]
0
,
and covering the angular uncertainty
+
[P
[m−1|m−1]
ψ
dl,0
]
1,1
.In
step 6, the BS predicts the TOA-AOA and the location of the
MS in the uplink for the current state by the analytic solution
of maximum a posteriori probability (MAP) estimate:
ˆ
η
[m]
ul,0
= argmin
η
[m]
ul,0
∥
ˇ
y
ul,[m]
r
− z
ul
0
(η
[m]
ul,0
; φ
[m]
0
)∥
2
R,2
+ ∥η
[m]
ul,0
− f
m
)
ˆ
η
[m−1]
ul,0
*
∥
2
ˆ
S
[m]
ul,0
,2
, (9)
achieved by the EKF where R and
ˆ
S
[m]
ul,0
!
ˆ
P
[m−1]
f
m
+
˜
Q
[m]
ul,0
denote the corresponding covariance of the measurement
and current state, respectively. The term
ˆ
P
[m−1]
f
m
denotes the
covariance of the previous state estimate, and
˜
Q
[m]
ul,0
is the
7
These values can be obtained from the adopted support detection (SD)-
based method or simultaneous orthogonalmatchingpursuit(SOMP)for
mm-wave lens MIMO with refinement in the uplink and downlink [10], [19],
[32]. For m>0 they are obtained from the tracking phase.
4
corresponding process noise covariance. The operation ∥.∥
M,2
stands for weighted vector norms, f
m
(.) is the dynamic func-
tion that is in the form of f
m
)
ˆ
η
[m−1]
ul,0
*
=
ˆ
η
[m−1]
ul,0
+ const for
constant rate-of-change vector const.Instep7,thedownlink
beam selection matrix F
[m−1]
BS
selects the beams directed
towards the previous uplink AOA,
ˆ
θ
[m−1]
0
,coveringtheangular
uncertainty
+
[P
[m−1|m−1]
ψ
ul,0
]
2,2
.Instep8,theMStracksthe
AOA in the downlink in a similar way as explained in step
6. In step 9, the rotation angle is obtained using the location
information that is fed back to the MS and the AOA in the
downlink, and the block index is updated in step 10 until
mT
B
≤ T
ob
.Finally,thesteps2-11arerepeatedforthenext
observation time T
ob
.
III. S
IMULATION RESULTS
In this section, the performance of the proposed method for
different parameters is investigated.
A. Simulation Setup and Results
We consider a scenario representative of outdoor localiza-
tion based on METIS Madrid grid model [33]. We employ a
ray tracing simulation tool in order to model the propagation
of signals in the uplink and downlink for channel training
and tracking [34]. We set
8
f
c
[GHz] = 60, B [MHz] = 200,
c [m/ns] = 0.299792,andN =40.Thenumberofantennas
in the BS and MS are set to N
BS
=32and N
MS
=32,
respectively. The received SNR in the uplink/downlink is set
to 10 dB. During the tracking, the MS moves with the velocity
up to 50 km/h suggested for outdoor vehicular mobility
[33]. The angular rates for the UL-AOA and DL-AOA are
up to 0.5676 deg/T
B
and 0.3410 deg/T
B
,respectively.The
block duration and the observation time are on the order of
T
B
[ms] ≈ 18 and T
ob
[s] ≈ 1,respectively.Themaximum
angular spreads are set to σ
max
θ
0
[deg] = σ
max
φ
0
[deg] = 20
centered around
ˆ
θ
0
and
ˆ
φ
0
.Duringthetracking,thenumber
of beams M
MS
in the downlink and M
BS
in the uplink
are set to guarantee the aforementioned maximum angular
supports, e.g., M
MS
=7in the downlink and M
BS
=7
in the uplink for N
BS
= N
MS
=32.Thepowerofthe
process noise for the continuous-time state model is set to
Q
c
= diag{σ
2
τ
0
,σ
2
θ
0
,σ
2
φ
0
},andQ
[m]
0
is obtained by numerical
discretization [36]. The value of σ
τ
0
is set to σ
τ
0
[ns] = 0.5
as it only affects the tracking of the position and does not
influence the rotation angle tracking. The performance of the
root-mean-square error (RMSE) was assessed from 100 Monte
Carlo realizations.
Fig. 2 shows the performance of the training with refinement
(i.e., m =0)[19],andtrackingalgorithm(i.e.,m>0)
using heuristic beam selection with respect to the power of
the process noise for the aforementioned rate of changes. The
components of the standard deviation of the UL-AOA and
DL-AOA process noise for the continuous-time state model
Q
c
are set to σ
θ
0
[deg] = σ
φ
0
[deg] = {5, 12.5} during the
8
Although lower values of f
c
,e.g.,28 GHz, are commonly used in the
outdoor scenarios; however, using higher values of f
c
,e.g.,60 GHz, is of
great interest due to the increase in the demand of higher frequencies [35].
0 20 40 60 80 100
0
2
4
6
8
0 20 40 60 80 100
0
5
10
15
0 20 40 60 80 100
0
2
4
6
8
0 20 40 60 80 100
0
2
4
6
8
10
RMSE(
ˆ
p
[m]
)[m]
RMSE(
ˆ
p
[m]
)[m]
RMSE( ˆα
[m]
)[deg]
RMSE( ˆα
[m]
)[deg]
ProposedProposed
ProposedProposed
Method in [23]Method in [23]
Method in [23]Method in [23]
σ
θ
0
= σ
φ
0
=12.5 deg
σ
θ
0
= σ
φ
0
=12.5 deg
σ
θ
0
= σ
φ
0
=5deg
σ
θ
0
= σ
φ
0
=5deg
Block index mBlock index m
Block index mBlock index m
Fig. 2. The RMSE of the MS (top) rotation angle ˆα[m] and (bottom) position
ˆ
p
[m]
after training with refinement (block index 0)forthefirst100 block
indices with N
MS
= N
BS
=32and SNR [dB] = 10.
T
ob
,i.e.,ontheordersofσ
θ
0
[deg] = σ
φ
0
[deg] ≈{0.1, 0.2}
within T
B
.ItisobservedthattheRMSEofpositionand
rotation angle gradually increases versus the block index by
increasing the standard deviations of UL-AOA and DL-AOA
to σ
θ
0
[deg] = σ
φ
0
[deg] = 12.5 compared to the estimated
values, i.e., block index zero. This is mainly due to the limited
angular support o f the received beam selections based o n the
maximum angular spreads σ
max
θ
0
[deg] = σ
max
φ
0
[deg] = 20.
On the other hand , for the standard deviations of UL-AOA
and DL-AOA on the order of σ
θ
0
[deg] = σ
φ
0
[deg] = 5 the
RMSE of position and ro tation angle are close to the values
obtained from the training during T
ob
,i.e.,blockindexzero.
The main reason is th at the user is mostly moving within the
the angular support provided by the received beam selections.
After th e obser vation tim e T
ob
and σ
θ
0
[deg] = σ
φ
0
[deg] = 5,
the user starts to move out of the angular support that leads to
increasing the RMSE. For the sake of comparison, the method
in [23] is adopted to the state model including the rate of
change terms in (3) with lens antenna arrays. In [23], the
design is not based on maximum angular spreads and EKF
angular uncertainty that leads to beam misalignment and non-
robust p erformance. This is due to the fact that the EKF d oes
not converge to a steady state. Consequently, the measurement
cannot compensate for the increase in the angular uncertainty
due to process noise by updating a selected beam with half
beamwidth threshold criteria in [23]. Finally, due to tracking
in the UL and the DL the proposed method requires one more
transmission compared to [23].
IV. C
ONCLUSION
We have studied novel solutions based on joint heuristic
beam selection and position and orien tation tr acking in a
mm-wave lens MIMO system. Through simulation studies, we
have shown that the proposed method provides practical solu-
tions for updating the location and orientation information of
the user in dynamic conditions. In particular, the performance
of the proposed method is close to the estimated valu es with
the reduced complexity and pilot transmissions.
![Fig. 2. The RMSE of the MS (top) rotation angle α̂[m] and (bottom) position p̂[m] after training with refinement (block index 0) for the first 100 block indices with NMS = NBS = 32 and SNR [dB] = 10.](/figures/fig-2-the-rmse-of-the-ms-top-rotation-angle-a-m-and-bottom-1x5v08g7.webp)
![Fig. 1. The normalized magnitude of the elements of χ[m] MS/BS,0 for the beam selection (top) with and (bottom) without considering the effect of uncertainty.](/figures/fig-1-the-normalized-magnitude-of-the-elements-of-kh-m-ms-bs-id42exxa.webp)