3GPP

    3rd Generation Partnership Project
5G

    fifth generation
AE-ELM

    auto-encoder extreme learning machine
AI

    artificial intelligence
AoA

    angle-of-arrival
AoD

    angle-of-departure
AP

    access point
AWGN

    additive white Gaussian noise
BLE

    Bluetooth Low Energy
BW

    bandwidth
BW-level

    bandwidth-level
BS

    base station
CM

    common model
CNN

    convolutional neural network
CR

    compression ratio
CSI

    channel state information
CU

    Centralized Unit
DL

    downlink
DL-AoD

    downlink angle-of-departure
DoA

    direction-of-arrival
DNN

    dense neural network
DU

    Decentralized Unit
ECDF

    empirical cumulative distribution function
EEG

    electroencephalogram
EKF

    extended Kalman filter
ELM

    extreme learning machine
EM

    Encoder Model
FFT

    Fast Fourier Transform
FR

    frequency response
FM

    full model
FP

    fingerprinting
FR-Complex

    complex frequency response
FR-Power

    power-domain frequency response
FR-Phase

    relative phase frequency response
FR-Power/Phase

    power and relative phase frequency response
FR1

    Frequency Range 1
FR2

    Frequency Range 2
HDim

    HIDDEN_DIM
GDA

    Generalized Discriminant Analysis
GELU

    Gaussian error linear unit
gNB

    gNodeB
GNSS

    Global Navigation Satellite System
ICA

    Independent Component Analysis
IoT

    Internet-of-Things
IPS

    indoor positioning system
KF

    Kalman filter
$k$-NN

     $k$-Nearest Neighbors
LBS

    location-based services
LDA

    Linear Discriminant Analysis
LMF

    Location Management Function
LoS

    line-of-sight
LR

    learning rate
LSTM

    long-short term memory
MAC

    Media Access Control
MDT

    Minimization of Drive Testing
MEE

    mean Euclidean error
MIMO

    multiple-input multiple-output
ML

    machine learning
mmWave

    millimeter-wave
MRTT

    multi-round trip time
NLoS

    non-line-of-sight
NN

    neural network
NR

    New Radio
OFDM

    orthogonal frequency-division multiplexing
path-AoA

    path-wise angle-of-arrival
path-RP

    path-wise received power
PRS

    positioning reference signal
path-ToF

    path-wise time-of-flight
PHY

    physical-layer
PCA

    principal component analysis
PF

    particle filter
PL

    path-loss
QoE

    quality of experience
QoS

    quality of service
RB

    resource block
RE

    resource element
ReLU

    rectified linear unit
RB-level

    resource block-level
RF

    radio frequency
RFID

    radio requency identification device
RMS

    root mean square
RMSEE

    root mean squared euclidean error
RNN

    recurrent neural network
RP

    reference point
RRC

    radio resource control
RS

    recommender system
RSRP

    reference signal received power
RSRQ

    reference signal received quality
RSS

    received signal strength
RSSI

    received signal strength indicator
RTT

    round trip time
RX

    receiver
SLAM

    simultaneous localization and mapping
SP

    scattering point
SS

    synchronization signal
SSB

    synchronization signal block
SRS

    sounding reference signal
SSS

    secondary synchronization signal
std

    standard deviation
SMV

    support vector machine
SVD

    single value decomposition
TDoA

    time-difference-of-arrival
TL

    transfer learning
TLCNN

    Transfer Learning Convolutional Neural Network
ToA

    time-of-arrival
ToF

    time-of-flight
t-SNE

    T-distributed Stochastic Neighbor Embedding
TX

    transmitter
UE

    user equipment
UL

    uplink
UL-AoA

    uplink angle-of-arrival
Wi-Fi

    IEEE 802.11 network
WLAN

    wireless LAN
WSN

    wireless sensors networks

# Robust NLoS Localization in 5G mmWave Networks: Data-based Methods and
Performance

Roman Klus , Jukka Talvitie , Julia Vinogradova , Gabor Fodor , Johan Torsner,
and
Mikko Valkama Limited subset of early-stage results presented at IEEE SPAWC
2022 [14].R. Klus, J. Talvitie, and M. Valkama are with Tampere University,
Finland. J. Vinogradova and J. Torsner are with Ericsson Research, Helsinki,
Finland. G. Fodor is with Ericsson Research and with KTH, Stockholm, Sweden.
Data and codes openly available at https://doi.org/10.5281/zenodo.12204893
0000-0002-0641-5931 0000-0001-7685-7666 0000-0001-8911-2065
0000-0002-2289-3159 0000-0003-0361-0800

###### Abstract

Ensuring smooth mobility management while employing directional beamformed
transmissions in 5G millimeter-wave networks calls for robust and accurate
user equipment (UE) localization and tracking. In this article, we develop
neural network-based positioning models with time- and frequency-domain
channel state information (CSI) data in harsh non-line-of-sight (NLoS)
conditions. We propose a novel frequency-domain feature extraction, which
combines relative phase differences and received powers across resource
blocks, and offers robust performance and reliability. Additionally, we
exploit the multipath components and propose an aggregate time-domain feature
combining time-of-flight, angle-of-arrival and received path-wise powers.
Importantly, the temporal correlations are also harnessed in the form of
sequence processing neural networks, which prove to be of particular benefit
for vehicular UEs. Realistic numerical evaluations in large-scale line-of-
sight (LoS)-obstructed urban environment with moving vehicles are provided,
building on full ray-tracing based propagation modeling. The results show the
robustness of the proposed CSI features in terms of positioning accuracy, and
that the proposed models reliably localize UEs even in the absence of a LoS
path, clearly outperforming the state-of-the-art with similar or even reduced
processing complexity. The proposed sequence-based neural network model is
capable of tracking the UE position, speed and heading simultaneously despite
the strong uncertainties in the CSI measurements. Finally, it is shown that
differences between the training and online inference environments can be
efficiently addressed and alleviated through transfer learning.

###### Index Terms:

5G New Radio, channel state information, deep learning, non-line-of-sight,
positioning, tracking, vehicular systems

##  I Introduction

Expanding to the millimeter-wave (mmWave) frequencies allows to harness large
channel bandwidths in the fifth generation (5G) New Radio (NR) mobile
communication networks, which improves the network capacity, peak data rates,
and latency characteristics compared to legacy systems [1, 2]. In such mmWave
networks, beamforming active antenna arrays are a critical technology,
allowing directional transmission and reception capabilities, thus improving
the link budget while mitigating co-channel interference and providing the
basis for angle-based _cellular positioning_.

In general, accurate real-time knowledge of the locations of the network UE is
critical to ensure smooth and seamless mobility management, efficient handover
management, and improved reliability of the radio link, while also allowing
for location-based services (LBS) [3, 4, 5, 6]. Baseline UE localization
builds commonly on Global Navigation Satellite System (GNSS) based approaches.
However, terrestrial positioning utilizing 5G and other signals of opportunity
is of increasing importance, and is also the main technical scope of this
article. This is well motivated, as the availability of GNSS is known to be
compromised not only indoors but also in outdoor urban areas [4, 7], while the
large channel bandwidths and directional antenna systems deployed in 5G allow
for accurate time- and angle-based measurements.

There is generally a wide selection of positioning methods available in the
literature [4], covering both model-based Bayesian filtering approaches [8, 9,
10, 11, 12, 13] as well as data-driven machine learning (ML) based methods
[14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31].
Majority of the works focus on the LoS scenarios, where the channel includes a
direct propagation path from the transmitter (TX) to the receiver (RX), and
thus the UE location can be estimated geometrically by utilizing pseudo-ranges
and/or angular information based on radio measurements. Good examples of such
LoS-oriented 5G positioning works include [11, 12], building commonly on
Bayesian filtering methods such as different variants of extended Kalman
filter (EKF) and particle filter (PF). In case the LoS path is unavailable,
geometry-based Bayesian filtering models still exist, e.g., [9, 10, 13]. Such
methods are, however, typically limited to single-bounce scenarios with a
single path per scattering point, and can thus easily become unreliable in
realistic scattering environments while being also computationally heavy and
complex [32, 33]. Therefore, UE positioning and tracking in _NLoS or LoS-
ambiguous scenarios_ call for novel solutions and models, capable of ensuring
fast and reliable operation in realistic scattering environments with feasible
real-time computational complexity. This is the main technical focus of this
article, with a specific emphasis on vehicular systems in challenging urban
environments, where NLoS scenarios commonly occur with realistic network
deployments [34].

In this article, building on our initial work in [14], we propose and describe
efficient ML based models for NLoS or LoS-obstructed positioning that offer
robust performance, low operational complexity, good generalization
properties, and wide architectural options. We harness the temporal
correlation of the channel features in vehicular systems and focus on sequence
processing neural network (NN) methods as the fundamental ML engine. We
propose two alternative feature sets capable of describing the radio channel
and further NN-based positioning, namely _frequency-domain and time-domain CSI
features_. Additionally, we include the vehicle speed and heading as
additional model outputs to enable efficient tracking using a single model.

ML-based positioning has been addressed in the recent literature, e.g. in [15,
14, 16, 17, 18, 20, 22, 23, 24, 25, 26, 27, 28, 21, 29, 30, 31]. To this end,
received signal strength (RSS) measurements were adopted in [19, 20, 21], in
indoor IEEE 802.11 network (Wi-Fi) fingerprinting context, while the
corresponding 5G deployment was considered in [35]. The work in [24] proposed
a CSI-based fingerprinting model that utilizes the amplitude response of the
channel. Due to the classifier-like NN, the proposed system is, however,
limited to small deployments. The authors of [15] developed an NN-based
feature extractor with Wi-Fi CSI measurements considering the amplitude
response only, followed by a $k$-Nearest Neighbors ($k$-NN) positioning
algorithm. Similar approaches building on channel amplitude response
measurements were considered also in [25] and [26]. In [27], a Wi-Fi
positioning approach utilizing the channel phase response as a feature was
proposed. The method is, however, not suitable for large-scale scenarios due
to the classifier-based NN, while the considered phase slope calculation is
also subject to ambiguities. The work in [22], in turn, presented a 5G
positioning system, however, being limited to the LoS scenario while utilizing
only the beam-specific reference signal received power (RSRP) values as the
features. In [23], a positioning system that generates probability maps using
an NN model was described with a feature representation that transforms the
frequency-domain uplink (UL) CSI data to a delay-domain. The probability maps
enable efficient sensor fusion, yet their scale directly affects the
complexity of the underlying NN model. Furthermore, [29] described a paradigm
to produce a high-accuracy 5G localization dataset, building on channel
frequency response measurements.

Different hybrid solutions also exist in the literature, either in terms of
aiding Bayesian filtering solutions through ML methods or fusing measurements
from various different sensors [16]. To this end, [17] proposed a series of
recurrent neural network (RNN) models to replace the EKF and thus enable
implicit and data-driven learning. Furthermore, a sensor fusion approach using
reinforcement learning-assisted particle filtering is described in [10].
Neural network based 5G fingerprinting and GNSS data fusion were, in turn,
considered in [18]. Recently, in [36], an NN model classifying different
propagation paths from time-domain CSI in the form of path parameters was
paired with geometry-based positioning algorithm considering LoS and single-
bounce NLoS paths.

ML-based localization with propagation time measurements has also gained
interest in recent works [30, 33, 14]. In [30], a bidirectional RNN is
employed to track the UE based on the time-of-arrival (ToA) measurements from
multiple nodes, while the authors of [33] utilize a convolutional neural
network (CNN) to estimate the accurate ToA from the raw channel impulse
responses in LoS/NLoS scenarios. However, only LoS measurements are used for
the actual localization. Finally, angular information at either the gNodeB
(gNB) or the UE can also be used for ML-based localization, as shown in [31].

TABLE I: Summary of related works

Reference | Technology | Features | ML model |  Tracking | Uncertainty | Vehicular |  NLoS
---|---|---|---|---|---|---|---
Feat. | Label | Envir. | Systems
[14] | 5G mmWave | AoA and ToF | DNN, LSTM | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\times$ | $\checkmark$ | $\checkmark$
[15] | Wi-Fi | channel amplitude response | CNN | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ |  $\checkmark$*
[18] | 5G mmWave | RSRP | DNN | $\times$ | $\checkmark$ | $\times$ | $\times$ | $\times$ | $\times$
[22] | 5G mmWave | RSRP | DNN | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ |  $\times$**
[23] | Wi-Fi | channel frequency response | DNN | $\times$ | $\checkmark$ | $\times$ | $\times$ | $\times$ | $\checkmark$
[24] | Wi-Fi | channel amplitude response | DNN | $\checkmark$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$
[25] | Wi-Fi | channel amplitude response | CNN | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ |  $\times$*
[26] | Wi-Fi | channel amplitude response | ML | $\checkmark$ | $\times$ | $\times$ | $\times$ | $\times$ |  $\times$*
[27] | Wi-Fi | channel phase response | DNN | $\checkmark$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$
[29] | 5G mmWave | channel frequency response | CNN | $\times$ | $\checkmark$ | $\times$ | $\times$ | $\times$ | $\times$
[30] | Unspecified | ToA | RNN | $\checkmark$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$
[31] | BLE | AoA | CNN | $\times$ | $\checkmark$ | $\times$ | $\times$ | $\times$ |  $\checkmark$***
[33] | LTE | channel impulse response | CNN | $\times$ | $\checkmark$ | $\times$ | $\times$ | $\times$ |  $\checkmark$*
[36] | mmWave | path-wise CSI | DNN | $\times$ | $\checkmark$ | $\times$ | $\times$ | $\checkmark$ |  $\checkmark$**
This Work |  5G mmWave |  time- and frequency-domain CSI |  DNN, LSTM | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$

* Some NLoS samples available in evaluation; ** Removing the detected NLoS samples before positioning; *** RX signal subject to Rayleigh fading.

The main related works and their relevant aspects are summarized in Table I.
Importantly, the NLoS positioning under rich and realistic scattering is not
explicitly addressed, in particular in the context of beamforming 5G mmWave
networks. Thus, complementary to the existing literature, this article focuses
on ML-based reliable network localization using time- and frequency-domain CSI
data with emphasis on challenging NLoS scenarios, while noting also various
relevant uncertainty aspects. The application focus is on vehicular systems in
urban environments with 5G mmWave deployments and CSI features that can be
obtained through 3GPP standardized UL and/or downlink (DL) measurements and
corresponding signaling. The contributions and novelty compared to the
existing ML-based positioning literature can be stated and summarized as
follows:

  * •

We introduce, derive, and evaluate efficient frequency-domain CSI features in
the form of sparse power and phase measurements, and their combinations, for
ML-based positioning models and compare their robustness with the ones
introduced previously in the literature;

  * •

We also introduce and evaluate alternative time-domain path-wise CSI features
and demonstrate their effectiveness in wireless positioning scenarios while
finding the relevant and best-performing feature combinations;

  * •

We develop a novel hybrid NN processing model in terms of instantaneous and
sequence data processing for simultaneous UE location, velocity, and heading
tracking using the above channel-based features;

  * •

We evaluate the performance of different features and processing models in a
large-scale, realistic, urban scenario with full ray-tracing-based channel
measurements under harsh NLoS conditions in the context of 28 GHz mmWave 5G
network, while also considering realistic training and measurement
uncertainties;

  * •

We show that the proposed time-domain and frequency-domain features outperform
the benchmark solutions, especially when combined with the sequence processing
ML model, in terms of the positioning accuracy and complexity – in particular,
in the challenging multi-bounce scattering environments, where the proposed
positioning approach achieves comparable accuracy in both LoS and NLoS
conditions, regardless of the number of bounces;

  * •

We also address the important practical issue of environment or gNB deployment
differences between the training phase and the actual online inference phase,
through transfer learning, and show that specializing to the current
deployment is feasible;

  * •

Finally, we address the complexity of the developed methods, in comparison to
the prior-art, while also openly share the data and codes for research
reproducibility and transparency.

For clarity it is stated that selected time-domain features were initially
considered in [14], however, the adopted NN models were lacking the advanced
sequence processing capabilities. Additionally, no frequency-domain features
were considered, while the transfer learning aspects were also fully
neglected.

The rest of this article is organized as follows. Section II introduces the
network measurements applicable for positioning and their acquisition with
3GPP compatible reference signals and measurement procedures. Section III
introduces the proposed frequency-domain and time-domain CSI data features and
the related pre-processing. Additionally, the NN processing models and
architectures are described incorporating both instantaneous and sequence
models. Section IV describes the considered urban vehicular positioning
scenario and evaluation environment, together with the practical measurement
or data uncertainties. Additionally, the obtained numerical results are
presented and analyzed, while also considering the important aspect of
specializing to the prevailing gNB deployment through transfer learning.
Finally, Section V concludes the work.

##  II Positioning Measurements and Data Acquisition

This section introduces the signals and standardized measurements, available
in 5G NR, to extract positioning data. Specific focus is on synchronization
signal block (SSB) based measurements in DL, in terms of frequency-domain
data, while in time-domain we harness multi-round trip time (MRTT) and UL
angle-of-arrival (AoA) based multipath measurements utilizing UL sounding
reference signal (SRS) and DL positioning reference signal (PRS). The relevant
measurements and data acquisition methods are illustrated conceptually in Fig.
1, while being described in detail below. For clarity, we state that the
frequency- and time-domain measurements are _alternative_ approaches to obtain
positioning features and data.

###  II-A Signals and Measurements for 5G NR Positioning

Measuring the received signal strength is one common approach utilized in
wireless positioning. In 5G NR, we distinguish RSRP, reference signal received
quality (RSRQ), and received signal strength indicator (RSSI), including their
beam-specific and resource-specific alternatives. Their acquisition is defined
in [37] building on different reference signals, such as UL SRS and DL
synchronization signal (SS) and PRS. The corresponding measurements are called
UL-SRS-RSRP, SS-RSRP and DL-PRS-RSRP, respectively. Signal strength
measurements are vital for numerous network functions, such as mobility
management, and thus regularly collected.

Compared to signal strength-based measurements, propagation delay or time-of-
flight (ToF)-based ranging benefits from large transmission bandwidths while
being less sensitive to channel effects, such as reflections, diffractions,
and scattering. To relax clock synchronization requirements between TX and RX,
the 5G NR standard supports MRTT measurements [38] where the gNB measures the
round trip time, denoted as ”gNB Rx–Tx time difference”, based on PRS
transmission in DL and SRS transmission in UL. In addition, the UE measures
the time between receiving the PRS and sending the SRS, denoted as the ”UE
Rx–Tx time difference”, which is reported to the gNB [37] in order to solve
the channel-dependent propagation delay. Alternatively, the ToF can be
estimated indirectly at the gNB via time-difference-of-arrival (TDoA) and the
related positioning calculations, as defined in [38]. Obtaining the ToF
directly at the UE is currently not explicitly standardized.

Beamformed radio access provides inherent support for angle estimation and
corresponding angle-based positioning schemes. In the current 5G NR standard,
angle estimation is directly specified only for the gNB-side angular
information either via the uplink angle-of-arrival (UL-AoA) or the downlink
angle-of-departure (DL-AoD) [38]. The UL-AoA is defined as the estimated
azimuth and vertical angles of a UE, observed at a gNB [37], based on UL SRS.
The exact angle estimation method used in the UL-AoA is not specified, which
allows for performance optimization. On the other hand, the estimation of the
gNB angle at the UE using the DL-AoD is practically restricted to the use of
spatial power measurements, i.e., DL-PRS-RSRP, which limits the achievable
angle estimation accuracy [38].

Figure 1: Illustration of the network data acquisition scheme with two gNBs, a
UE, and a network localization entity represented by the LMF. Different UL and
DL reference signals form the physical basis for obtaining positioning
measurements and data. Additionally, the baseline neural processing chains
from features to UE location, heading and velocity are highlighted, for both
time- and frequency-domain feature scenarios.

Importantly, estimating the ranges and angles also for paths beyond the LoS
component is feasible [13], offering added value to the positioning task [9].
Since the current 5G NR standard does not specify accurate estimation of path
ranges or angles at the UE side, for a DL-based positioning we consider
observing frequency-domain CSI measurements based on SSs transmissions by the
gNBs. This is beneficial since the SSs are periodically transmitted and thus
systematically available. Additionally, for an UL-based positioning method, we
consider observing time-domain multipath measurements, including path-wise
angles and propagation delays, directly at the gNBs. For obtaining the path-
wise angles and propagation delays in practice, it is possible to exploit the
above-discussed 5G NR specified UL-AoA and MRTT methods, respectively.

###  II-B Frequency-Domain Channel Measurements through Beamformed DL SSs

The frequency-domain CSI relates to the frequency response (FR) of the
effective channel between the gNB and the UE. Considering orthogonal
frequency-division multiplexing (OFDM) based transmission, the antenna-
element-wise FR at subcarrier $n$, denoted as
$\bm{\mathcal{H}}(n)\\!\in\\!\mathbb{C}^{N_{\text{RX}}\times N_{\text{TX}}}$,
can be written as [13, 9]

$\bm{\mathcal{H}}(n)=\sum_{k=0}^{K-1}h_{k}e^{-\frac{j2\pi
n\tau_{k}F_{s}}{N}}\bm{a}_{\text{RX}}(\theta_{\text{AOA},k})\bm{a}_{\text{TX}}^{H}(\theta_{\text{AOD},k}),$
(1)

where $K$ is the number of paths, while $h_{k}$, $\tau_{k}$,
$\theta_{\text{AOA},k}$ and $\theta_{\text{AOD},k}$ are the complex path
coefficient, ToF, AoA and angle-of-departure (AoD) for the $k^{\text{th}}$
path, respectively. Furthermore, $N_{\text{TX}}$ and $N_{\text{RX}}$ are the
numbers of transmit and receive antennas in respective order, $F_{s}$ is the
sampling frequency, and $N$ is the OFDM Fast Fourier Transform (FFT) size.
Finally, $\bm{a}_{\text{TX}}(\cdot)\in\mathbb{C}^{N_{\text{TX}}}$ and
$\bm{a}_{\text{RX}}(\cdot)\in\mathbb{C}^{N_{\text{RX}}}$ are the steering
vectors, which define the phases per antenna element with respect to the array
center, for given AoD and AoA. Considering further the analog phased-arrays in
mmWave systems, the TX and RX apply beamforming weights
$\bm{b}_{\text{TX}}\in\mathbb{C}^{N_{\text{TX}}}$ and
$\bm{b}_{\text{RX}}\in\mathbb{C}^{N_{\text{RX}}}$, respectively. The
corresponding effective beamformed channel at subcarrier $n$, considered as
the _frequency-domain CSI_, can then be expressed as

$\mathcal{H}(n)=\bm{b}_{\text{RX}}^{H}\bm{\mathcal{H}}(n)\bm{b}_{\text{TX}}.$
(2)

In practice, besides noise and interference, the CSI estimation can suffer
from inaccuracies [28] due to radio frequency (RF) impairments, clock and
frequency offsets between the gNB and the UE, and imperfect timing advance
information. Furthermore, due to signaling overhead, CSI is often reported per
blocks of subcarriers, which reduces the CSI resolution in frequency. In this
paper, we consider obtaining the frequency-domain CSI via 5G NR SSs,
transmitted periodically in DL by all gNBs.

###  II-C Time-Domain Multipath Measurements through MRTT and UL-AoA

In time-domain, the radio propagation channel can be modeled as a composition
of individual propagation paths with path-specific propagation delay, power
gain, phase shift, AoD, and AoA, together with additional distortion and
interference, among other channel effects. The antenna-element-wise channel
impulse response $\mathbf{H}(\tau)\in\mathbb{C}^{N_{\text{RX}}\times
N_{\text{TX}}}$ can be written as a function of propagation delay $\tau$ as
[36, 34]

$\mathbf{H}(\tau)=\sum_{k=0}^{K-1}h_{k}\bm{a}_{\text{RX}}(\theta_{\text{AOA},k})\bm{a}_{\text{TX}}^{H}(\theta_{\text{AOD},k})\delta(\tau-\tau_{k})$
(3)

where $\delta(\cdot)$ is a Dirac delta function (i.e., a unit impulse).
Similar to the frequency-domain representation, while again assuming analog
phased-arrays, the effective beamformed channel impulse response can be
written as

$H(\tau)=\bm{b}_{\text{RX}}^{H}\mathbf{H}(\tau)\bm{b}_{\text{TX}}.$ (4)

In this paper, the measured _time-domain CSI_ includes the path delays
$\tau_{k}$, the path powers $|h_{k}|^{2}$, and the gNB side path angles
$\theta_{\text{AOA},k}$. For the path delays $\tau_{k}$ and path powers
$|h_{k}|^{2}$, the estimation procedure is assumed to exploit 5G NR MRTT
measurements [38], as discussed in Section II-A. Furthermore, for estimating
the gNB side path angles $\theta_{\text{AOA},k}$, it is also possible to
utilize UL-AoA measurements [38] based on UL SRS transmissions, as noted in
Section II-A.

The overall data acquisition concept is illustrated in Fig. 1, highlighting
the different considered measurements. In general, within the current 5G NR
standard, the LMF is responsible for the localization and related signaling
management while the positioning calculations can be carried out either at the
UE or the network side. Moreover, reporting the MRTT and UL-AoA measurements
between the gNB and the LMF is supported by the so-called NR Positioning
Protocol A [39]. Different alternative ways to arrange for labeled training
data include crowdsourcing, crowdsensing, as well as utilization of synthetic
data. These are discussed further in Section IV.G.

##  III Proposed Methods

This section describes and introduces the novel approach of utilizing
frequency-domain CSI with relative phase, while also addressing the time-
domain CSI data pre-processing. In addition, the proposed architectures,
hyperparameters, and training algorithm of the proposed NN models are
presented. Finally, important system-level implementation alternatives and
aspects are discussed.

###  III-A Frequency-Domain CSI Data Preprocessing

####  III-A1 Proposed Relative Phase Approach

5G mmWave networks operate at high carrier frequencies, at and beyond 24 GHz,
with wavelengths approaching the millimeter-scale. In mobile scenarios,
utilizing absolute phase responses is highly impractical, as movement of a few
millimeters in distance results in a full rotation of the phase. Furthermore,
as is well-known, the frequencies and wavelengths relate through

$\lambda=\delta_{s}={c}/{f},$ (5)

where $\delta_{s}$ is the propagation distance between two points with equal
phases, $\lambda$ is the signal wavelength, $c$ is the speed of light, and $f$
is the signal frequency.

In this article, we consider obtaining the frequency-domain CSI in the
resolution of 12 subcarriers, which refers to a bandwidth of one resource
block (RB) in 5G NR, denoted as $\Delta f_{RB}$. The CSI is interpreted at the
$6^{\text{th}}$ subcarrier of each RB, and thus the corresponding subcarrier
index for the $m^{\text{th}}$ RB observation is given as
$n_{\text{RB,}m}=6+m\Delta f_{RB}$ with $m=0,...,M-1$, where $M$ is the number
of RBs. Moreover, we propose to take advantage of _differential phase
measurements between neighboring RBs_. Based on (1)-(2), and when considering
an individual propagation path, the phase difference between subcarriers is
equal across the spectrum and completely determined by the ToF through the
complex exponential term. Possible phase rotations due the other terms in (1)
are constant over all subcarriers, and thus do not induce phase difference
between the subcarriers. Thus, for an individual path with ToF of $\tau_{0}$,
the phase difference between two consecutive resource blocks can be given as

$\Delta\phi=2\pi\tau_{0}\Delta f_{RB}.$ (6)

While the above expression builds on a single propagation path, we utilize
this approach in this work also in case of realistic multipath propagation. As
elaborated further below, the differential phase approach allows to mitigate
the effect of phase periodicity, and thus extract relevant features for the
proposed NN-based positioning.

To this end, the linkage between the relative phase and a specific propagation
distance is unambiguous only when the relative phase is within one phase cycle
($\Delta\phi<2\pi$). A distance $d_{\phi}$, which inflicts the full $2\pi$
cycle of the relative phase between two neighboring RBs, can be solved based
on (6) as

$d_{\phi}=\frac{c}{\Delta f_{RB}}$ (7)

by denoting $\tau_{\phi}\Delta f_{RB}=1$, where $\tau_{\phi}=d_{\phi}/c$ is
the corresponding ToF resulting in a full phase cycle. By using the relative
phase difference $\Delta\phi$, instead of an absolute phase, as the frequency-
domain feature, the positioning performance can be significantly improved, as
shown in Section IV. Although the distance ambiguity issue still remains with
the phase difference recurrence at every $d_{\phi}$ meters, it is greatly
improved compared to the recurrence level with an absolute phase at every
$\delta_{s}$ meters, as $f\gg\Delta f_{RB}$.

####  III-A2 Frequency-Domain CSI Features and Visualization

To provide a short illustration, we consider a single representative user path
along an urban environment, as shown in Fig. 2a (for further details of the
environment, refer to Section IV). Then, Fig. 2b and Fig. 2c demonstrate the
utilized frequency-domain CSI feature representations along the path,
including the proposed features and the features from the related literature.
Specifically, the raw, complex channel response, further referred to as
complex frequency response (FR-Complex), is depicted in Fig. 2b, top, and Fig.
2b, center, which show the real and imaginary parts of FR-Complex for 10
consecutive resource blocks along the path. The feature is obtained from (2)
as $\text{real}(\mathcal{H}(n_{\text{RB,}m}))$ and
$\text{imag}(\mathcal{H}(n_{\text{RB,}m}))$ for $m=1,...,10$.

(a)

(b)

(c)

Figure 2: An example UE track in urban environment is shown in (a) where the
gNB location is depicted with the red rectangle while the track color
represents the mean normalized power across the resource blocks. The
frequency-domain features FR-Complex and FR-Power as well as the proposed FR-
Phase and FR-Power/Phase are visualized in (b) and (c), respectively, along
the UE track shown in (a). In (b) and (c), different colors represent the ten
different RB allocations within the full SSB transmission bandwidth.

Furthermore, Fig. 2b, bottom, depicts the channel power response, denoted as
the power-domain frequency response (FR-Power). Such channel feature is
utilized, e.g., in [24, 25], and can be expressed via (2) as
$10\text{log}_{10}(|\mathcal{H}(n_{\text{RB,}m})|^{2})$. In 5G NR, the FR-
Power corresponds to a RB-wise RSRP measurement, defined as the average power
of the resource elements carrying the reference symbols. As an input feature,
we also re-scale FR-Power to the normalized range of $[0,1]$.

Then, the top graph of Fig. 2c visualizes the proposed relative phase
difference as the frequency-domain feature, further denoted as the relative
phase frequency response (FR-Phase). Specifically, building on the discussion
in Section III-A1, the FR-Phase can be obtained and expressed following (2) as

$\Delta\phi(m)=\text{arg}(\mathcal{H}(n_{\text{RB,}m}))-\text{arg}(\mathcal{H}(n_{\text{RB,}m-1}))$
(8)

for RB indices $m=1,...,M-1$. The dependency between the signal path lengths
and the relative phases, especially in LoS regions, is clearly visible in the
figure. Moreover, it can be seen that the feature magnitude is recurring with
a path propagation distance at every $d_{\phi}$ meters, as derived in (7).

####  III-A3 Proposed Combined Feature

To utilize the maximum information enclosed in the measured channel responses,
we further propose the so-called power and relative phase frequency response
(FR-Power/Phase) approach as the ultimate frequency-domain feature. This
approach combines the FR-Phase and FR-Power by transforming the FR-Phase to
the complex unit circle, with subsequent element-wise multiplication with the
re-scaled FR-Power. This is expressed as

$\bar{P}_{\text{RB}}(m)\,\text{exp}({j\Delta\phi(m)})$ (9)

where $\bar{P}_{\text{RB}}(m)$ refers to the re-scaled normalized power for RB
indices $m=0,...,M-1$. Furthermore, since the FR-Phase has one element less
than FR-Power, we extend the FR-Phase array with an additional element for
$m=0$ by defining $\Delta\phi(0)=0$.

The real and imaginary components of the proposed FR-Power/Phase feature set
are visualized in Fig. 2c, center and bottom, respectively. The proposed
feature allows to accommodate the advantages of both received power and
relative phases in a single complex feature vector, while relaxing the
distance ambiguity of the relative phase feature.

###  III-B Time-Domain CSI Data Preprocessing

The time-domain CSI data utilized for localization includes propagation delays
$\tau_{k}$, powers $|h_{k}|^{2}$, and gNB side path angles
$\theta_{\text{AOA},k}$ for the observed LoS and NLoS paths. To this end, the
measured path-wise propagation delays $\tau_{k}$, referred to as path-wise
time-of-flight (path-ToF), are transformed to propagation distances by
multiplying them with the speed of light. The path-wise AoAs,
$\theta_{\text{AOA},k}$, are obtained at the gNB side, and transformed to
directions in Cartesian coordinates in the preprocessing, to omit the zero-
crossing problem with cyclic angular data. This results in a robust AoA
feature, called path-wise angle-of-arrival (path-AoA) in the following, which
is less susceptible to angular deviation and related uncertainties. The path-
wise received powers $|h_{k}|^{2}$ are expressed in decibels (dBm) to overcome
the extremely low feature magnitudes in linear scale. Such feature is the
time-domain equivalent of the frequency-domain FR-Power, which accumulates all
paths into the same observed frequency-domain measurement. Similar to the
propagation delay feature, the path power feature includes information on the
path propagation distance, but most importantly, it also provides information
on the number and type of channel interactions, such as reflections,
diffraction, or scattering, within the radio path. In general, different
combinations of the time-domain CSI data can be adopted. The aggregated path-
ToF+AoA and path-ToF+RP+AoA features, proposed in this work, are the most
powerful ones, as shown through the numerical results.

###  III-C NN Model Architectures and Hyperparameters

Among the various alternative data-aided approaches, we restrict ourselves to
NN models in this work, which currently dominate the ML area due to their
performance, scalability, generalization properties, and dynamic architecture
options [40].

####  III-C1 Activation Function

In this work, we utilize the Gaussian error linear unit (GELU) [41] as the
non-linear activation function. Its main advantages over traditional rectified
linear unit (ReLU) include resistance to a “dying ReLU” problem [42],
differentiability at all values while having also been shown to offer improved
performance already in a number of applications such as natural language
processing [41]. It can be defined as $\text{GELU}(x)=x\Phi(x)$ [43, 44] where
$\Phi(x)$ is the cumulative distribution function of the standard normal
distribution. The function can also be approximated for faster processing as

$\text{GELU}(x)=\frac{x}{2}\tanh\left(\sqrt{\frac{2}{\pi}(x+Cx^{3})}\right),$
(10)

where $C=0.044715$. Compared to ReLU, the higher complexity of GELU is
compensated by the faster convergence of the model, as well as the
corresponding improved positioning performance, based on our complementary
experiments.

####  III-C2 Utilized NN Architectures

As the functional NN layers, we utilize in this work both densely connected
layers and long-short term memory (LSTM) [45] layers, the later being used
only in the sequence-based implementation of models. Importantly, the LSTM
layer is a recurrent-based layer capable of preserving long-term and short-
term trends within the data.

The architecture of the densely-connected model is depicted in Fig. 3a. It
consists of 5 densely connected layers with GELU activation functions and a
single densely connected layer with linear activation and 2 neurons as the
output, estimating the UE position. The architecture of the sequence
processing capable model is, in turn, shown in Fig. 3b. It consists of 5
densely connected layers after the input, with a single LSTM layer connected
in parallel with the 5th dense layer. The concatenated output of these layers
is then fed to an LSTM layer with 5 neurons at the output with linear
activation. Specifically, the densely connected layers serve as instantaneous
feature extractors, while the intermediate LSTM layer learns the temporal
features. Due to the considered parallel architecture, the last functional
layer has access to both instantaneous and temporal features.  The resulting
output is then divided into a positioning output with $2$ variables, velocity
output with a single variable, and a heading output with an additional
$\text{tanh}(\cdot)$ activation and $2$ variables.

####  III-C3 Data Structures, Normalization and Training

In general, the input dimensions vary based on the selected features and
deployment scenario. For frequency domain features, and when considering the
evaluation scenario described in Section IV containing $3$ gNBs, $16$ beams,
and $10$ RBs, the input size is either $480$ for FR-Power and FR-Phase or
$960$ for FR-Power/Phase and FR-Complex. When considering the time-domain CSI
in the same scenario, the individual path-ToF, path-AoA, and path-RP features
have each an input size of $15$, the combined path-ToF+AoA and path-RP+AoA
features have $30$ inputs, and finally the aggregated path-ToF+RP+AoA feature
has an input size of $45$. Some of the features are also normalized prior to
the training, as demonstrated already along Fig. 2b and Fig. 2c. Specifically,
all power-related quantities as well as path-wise ToF measurements, when first
converted to pseudo-ranges, are all normalized between $[0,1]$ within the
overall sets of available measurements. Finally, all angle and phase
quantities are, by design, within $[-\pi,\pi]$. We emphasize that each
different feature scenario and combination corresponds to an individual NN,
trained and deployed on its own. The vast set of numerical results, provided
in Section IV, provides the corresponding mutual performance comparisons.

(a)

(b)

Figure 3: Architecture and hyperparameters of the densely connected NN, in
(a), and of the sequence processing NN, in (b). Each layer is specified by the
number of neurons and an activation function.

All considered NN models are trained using the Adam optimizer [46] with
learning rates of $0.001$ for the first $200$ epochs, and then an early-
stopping mechanism based on validation performance for additional $500$
epochs, while iteratively reducing the learning rate to $0.0005$ and $0.0001$
after each stop. The lowered learning rates ensure a fine-tuned performance
with a small number of epochs. The mean squared error (MSE) loss was selected
for each output, and for the sequence-based NN model, the loss weights were
selected as $0.8$, $0.1$, and $0.1$ for positioning loss, velocity loss, and
heading loss, respectively. Furthermore, stemming from the deployment area of
around $550\times 370~{}$m2 (see Fig. 5), the position labels are reduced by a
factor of $300$ to accelerate the training.

###  III-D System-Level Implementation Alternatives and Aspects

In general, there are alternative ways to organize and implement the use of
the CSI measurements and data for NN training and actual online inference
processing for localization. These are discussed below, in relation to the
proposed methods and the data acquisition visualized in Fig. 1, while noting
also the important role of UE radio resource control (RRC) state.

To this end, the time-domain CSI data, i.e., the MRTT-based ToF measurements
and the SRS-based UL-AoA measurements, are by definition obtained at the
network side. Thus, in this case, it is natural to also perform both the model
training as well as the localization inference processing at the network side.
Consequently, there is no need for additional signaling or feedback, and all
training data from different UEs is inherently gathered together for training
the model. Importantly, since MRTT and UL-AoA require scheduled SRS and PRS
transmissions, time-domain measurements are only available in the _connected
mode_ when it comes to the UE RRC state.

Frequency-domain RSRP and other CSI measurements are collected from periodic
and always available SSB transmissions at the UE side, thus enabling
utilization of efficient data crowdsourcing methods. Despite a possible
technical capability to perform training at the UE, assuming individually
trained models at different UEs can be considered unrealistic. Therefore, UEs
are expected to periodically share such measurement data with the network for
NN training, for example, through Minimization of Drive Testing (MDT)
messaging in the form of raw measurements and location tags, or alternatively
as locally pre-trained models following the principle of federated learning
(FL). Interestingly, unlike with MRTT and UL-AoA, the DL frequency-domain CSI
and RSRP measurements can be collected and obtained also in the RRC _idle
mode_ as part of standard mobility management procedures. This can be
considered a great asset enabling continuous data collection and localization
with very low power consumption. Furthermore, assuming a pre-shared model from
the network for the final inference phase, the UE can perform localization
independently without supplementary signaling with the gNB.

##  IV Evaluation Environment and Results

###  IV-A Evaluation Scenario and Assumptions

The evaluation environment builds on ray-tracing-based channel measurements
utilizing Wireless Insite®software [47]. We employ the map-based METIS Madrid
grid [48], recognized as the relevant urban scenario by 3GPP in 5G NR
specifications [34]. The Madrid grid layout introduces generally a rich radio
propagation environment with different street widths and open areas,
empowering generalization and scalability.

The simulated urban scenario illustrated in Fig. 4 contains three 5G mmWave
gNBs operating at $28$ GHz, such that clear NLoS regions also exist along the
streets. Each gNB is equipped with a uniform cylindrical antenna array with
$4$ elevated layers, each with $16$ antenna elements placed at $5$ m height.
The beam configuration includes 16 beams with uniformly separated azimuth
angles and a common down-tilted elevation angle fixed at $10$ deg. The AoD and
ToF measurements are obtained based on the corresponding characteristics of
the radio propagation path with the highest received power, building on the
signals and measurement procedures described in Section II. The obtained AoD
and ToF measurements are exposed to substantial measurement errors, as
discussed further in Section IV-B. The beam-wise frequency-domain CSI
measurements are obtained from SSB transmissions as an average of received
subcarrier powers per RB, with $120$ kHz subcarrier spacing. Measurements with
path-loss higher than 160 dB are not considered, while in general the
environment shown in Fig. 4 possesses large areas and street segments with
severe multi-bounce phenomena.

The combined time-domain and frequency-domain dataset consists of $40$
vehicle-like user tracks, where the UE collects measurements at $100$ ms
intervals. The UE locations are initialized with random locations along the
streets, and the UEs move within the area by considering an equal probability
to advance in any direction at intersections. The UE velocity varies between
$20$ km/h and $60$ km/h depending on the present street and possible proximity
of intersections while when approaching an intersection, the UE decelerates at
$3$ m/s2 until reaching a fixed velocity of $20$ km/h for smooth turning.
After the turn, the UE accelerates at $2$ m/s2 until reaching a street-
specific speed limit. The speed limit is generally defined as $40$ km/h, apart
from the top horizontal street which has the speed limit of $20$ km/h (see
Fig. 4) and the wider street below the pedestrian street having a limit of
$60$ km/h. The exact UE trajectories and associated measurement locations are
different for each simulated user track. As this work is heavily focused on
NLoS positioning, Fig. 4 visualizes the simulated tracks with the LoS/NLoS
indication at each sampled location. We note that in order to efficiently
track moving UEs with varying velocities through the sequence processing
models, a sufficiently rich training dataset is needed with representative
velocity statistics.

Figure 4: Illustration of the METIS Madrid map-based deployment and evaluation
scenario with 40 simulated UE tracks while distinguishing the LoS and NLoS
regions. Detailed example paths on one crossing are shown on the right.

The available $40$ user tracks are distributed into 32 UE traces for training,
4 for validation, and the remaining 4 for the actual testing. The validation
and testing paths are carefully selected, to avoid any area-specific bias in
the evaluation. Furthermore, as the work focuses on the NLoS positioning
performance, we validated the consistency of the LoS/NLoS split across the
datasets. The distribution of the samples in the individual datasets based on
the number of LoS gNBs is consistent with approx. $35\%$ NLoS samples, $60\%$
of samples having a single LoS gNB, and only $5\%$ samples having $2$ gNBs in
LoS. The distribution suggests that the traditional model-based solutions,
such as trilateration, are not applicable in the considered scenario. In
total, there are $25\,181$ samples in the dataset.

###  IV-B Network Data Uncertainties

In this work, we take into account the important practical aspect of
uncertainties in the measurements and thereon in the corresponding features.
To this end, the frequency-domain CSI is impaired in its FR-Complex
representation with complex additive white Gaussian noise (AWGN) samples with
magnitude equal to $30\%$ of the corresponding channel estimate’s root mean
square (RMS) magnitude. Such represents large practical measurement
uncertainties. The other related features such as the FR-Power/Phase are
impaired correspondingly, through the transformations from the impaired FR-
Complex to amplitude/power and phase domains.

To impair the time-domain features, we impose impairments separately to path-
ToF, path-RP and path-AoA quantities. The path-ToF feature uncertainty is an
AWGN with standard deviation (std) equal to $10$ m. We consider the constant
uncertainty scale regardless of the ToF magnitude, as the measurement errors
are mostly resulting from hardware inaccuracies and timing offsets in the UEs
and gNBs. Furthermore, we impair the path-RP feature with an AWGN with $2$ dB
std, which corresponds to the maximum impairment of $\pm 6$ dB range with
$99.7\%$ certainty, defined by 3GPP as the required absolute measurement
accuracy for SS-RSRP [49]. The path-AoA is, in turn, impaired with discretized
accuracy of $22.5^{\circ}$ ($360^{\circ}/16$ beams), rather than with a
randomized value, to incorporate the gNB limitations in accurately determining
the AoA.

Finally, as reviewed in the Introduction, a large majority of the state-of-
the-art works, such as [15, 29, 35, 25, 28, 24, 23, 18, 21], utilize channel
amplitude or power response, or even the integrated received power, as the
positioning feature. Hence, in the following, the results with FR-Power
feature represent essentially the state-of-the-art reference approach when it
comes to the frequency-domain features. In the time-domain feature case, the
use of the individual dominant path features has been considered in [8, 32, 5,
30, 31, 36], thus serving as the main reference schemes. Additionally, the
state-of-the-art schemes build commonly on snap-shot NNs without harnessing
the temporal correlation.

Data and codes are openly available at
https://doi.org/10.5281/zenodo.12204893.

###  IV-C Numerical Results with Dense Snap-Shot NNs

We next provide and analyze the results obtained with dense NN based ML models
while considering both the frequency-domain and time-domain features as well
as the impacts of the feature density or granularity in the two considered
domains. To establish an understanding on the baseline or reference
performance, we start with the results under perfect measurements (no
uncertainties), while then show also the performance under practical
measurement uncertainties.

####  IV-C1 Results with Frequency-Domain Features

First, we analyze and compare the different frequency-domain CSI features
introduced in Section III-A and their positioning capabilities with a densely
connected snap-shot NN with 5 hidden layers. We thus split all the user tracks
into individual samples and compare the performance without considering the
temporal dependencies within sequences or additional uncertainties, to focus
on the quality of the features themselves.

Fig. 5a visualizes the distributions of the positioning errors on the testing
dataset for each feature. Each boxplot marks the median (center) as well as
the first and third quartiles ($25^{th}$ and $75^{th}$ percentiles)
encapsulated in the box, while the whiskers mark the values of $5^{th}$ and
$95^{th}$ percentiles. The results show that the proposed FR-Power/Phase
feature representation enables the most efficient training in terms of
positioning error and that considering the FR-Complex features as the input
provides the poorest performance. The FR-Power and FR-Phase features achieve
comparable median performance, but in terms of outliers, FR-Power performs
better. The $95^{th}$ percentiles, referring essentially to the presence of
outliers, of FR-Complex and FR-Phase are significantly higher than those of
the remaining methods, as shown quantitatively in Table II. Furthermore, the
feature combination denoted as FR-Power+FR-Phase represents the simple
concatenation of the corresponding individual features. The numerical results
show that the positioning performance is improved when compared to the
individual features, but the novel FR-Power/Phase feature – utilizing the
same, yet pre-processed inputs – provides superior performance. The table
high-lights in bold the best performance numbers in different cases.

(a)

(b)

Figure 5: Distributions of positioning errors on the testing data when
evaluating (a) different frequency-domain features, and (b) different time-
domain features, with dense snap-shot NN and with no measurement
uncertainties.

We next further investigate the impact of the feature representation by
considering the LoS and NLoS data separately, with the results being shown in
Table II. We can observe that the proposed FR-Power/Phase feature
representation achieves the lowest positioning errors by a considerable
margin, when compared to the other methods ($3.35$ m and $4.70$ m mean
positioning error in LoS/NLoS, respectively) addressed earlier in the
literature. By comparing the performance in LoS and NLoS scenarios, we can
observe some increase in the error in NLoS, however, the exact impact is
clearly feature-dependent. Furthermore, when considering the $95^{th}$
percentiles of the error distributions, we can observe that the errors related
to the FR-Complex and FR-Phase features are drastically increased, in both LoS
and NLoS scenarios, while FR-Power+FR-Phase and FR-Power/Phase features
sustain a relatively stable performance across the majority of the testing
samples.

TABLE II: Baseline performance results: frequency-domain features, dense snapshot NN, no uncertainties Feature | FR-Complex | FR-Power | FR-Phase |  FR-Power+FR-Phase | FR-Power/Phase
---|---|---|---|---|---
Error [$\mathrm{m}$] | LoS | NLoS | LoS | NLoS | LoS | NLoS | LoS | NLoS | LoS | NLoS
Median | $7.88$ | $14.01$ | $5.57$ | $5.01$ | $5.26$ | $6.97$ | $3.35$ | $4.29$ | 2.42 | 2.84
Mean | $21.27$ | $25.63$ | $9.69$ | $8.89$ | $18.01$ | $27.99$ | $6.53$ | $8.67$ | 3.35 | 4.70
$80^{th}$ pc | $21.70$ | $33.73$ | $12.36$ | $11.11$ | $9.33$ | $17.67$ | $5.46$ | $8.57$ | 4.45 | 5.18
$95^{th}$ pc | $106.37$ | $92.05$ | $30.69$ | $27.53$ | $87.97$ | $166.66$ | $10.47$ | $21.43$ | 6.71 | 10.97

Overall, the obtained results clearly show and demonstrate that utilizing the
novel FR-Power/Phase feature offers the best performance by a large margin,
clearly outperforming the earlier state-of-the-art in the field of frequency-
domain features. Thus, in the further frequency-domain feature related
evaluations, we consider only the FR-Power/Phase feature representation.

####  IV-C2 Results with Time-Domain Features

Next, we evaluate the positioning capabilities and performance when utilizing
the different time-domain features (path-ToF, path-RP, and path-AoA) as the
input data. We also evaluate the combination of the features, while the model
can consider up to $5$ dominant multipath components above the 160 dB path-
loss threshold.

Fig. 5b visualizes the achieved positioning results, showing that the proposed
combinations of path-ToF and AoA or path-ToF, RP and AoA are the two best
performing aggregate features. The results also suggest that the path-RP
measurement provides less relevant information to the model than the path-ToF,
which the model can directly interpret as normalized pseudo-range measurement.
This can be seen by comparing the individual features (path-ToF vs. path-RP),
as well as the cases where they are combined with path-AoA.

TABLE III: Baseline performance results: time-domain features, dense snapshot NN, no uncertainties Feature | path-ToF | path-RP | path-AoA | path-ToF+AoA | path-RP+AoA | path-ToF+RP+AoA
---|---|---|---|---|---|---
Error [$\mathrm{m}$] | LoS | NLoS | LoS | NLoS | LoS | NLoS | LoS | NLoS | LoS | NLoS | LoS | NLoS
Median | $2.74$ | $2.19$ | $2.96$ | $4.49$ | $1.10$ | $1.67$ | 0.54 | 1.10 | $1.09$ | $1.73$ | $0.71$ | $1.21$
Mean | $11.08$ | $11.14$ | $10.17$ | $13.50$ | $2.79$ | $5.03$ | 1.23 | $3.61$ | $1.91$ | $4.29$ | $1.32$ | 2.63
$80^{th}$ pc | $8.59$ | $6.05$ | $6.35$ | $12.51$ | $2.57$ | $3.96$ | 1.35 | 2.33 | $2.45$ | $4.16$ | $1.67$ | $2.71$
$95^{th}$ pc | $45.26$ | $40.84$ | $29.91$ | $53.60$ | $8.48$ | $14.92$ | $3.77$ | $6.86$ | $5.31$ | $14.88$ | 3.44 | 6.73

The impacts of the features as well as the standalone performance in LoS/NLoS
are summarized in Table III, while also highlighting the best-performing
features in each scenario. The table shows that the combination of all
features (path-ToF+RP+AoA) together with path-ToF+AoA offer the best results
across all statistics. The corresponding performance of path-RP+AoA lags
already behind. When evaluating the individual features, the path-AoA provides
high-accuracy positioning capabilities with less than $2$ m median positioning
error in NLoS, as it can effectively capture the propagation patterns within
the given deployment. The path-RP and path-ToF provide, in turn, significantly
poorer performance as individual features, especially when considering the
higher percentile errors. These results thus clearly prove the value of the
directional measurements. Additionally, when compared to the results presented
in Table II, relative performance improvement can be observed, which we credit
to stronger interpretability of time-domain measurements as model inputs
compared to the frequency-domain CSI features. Notably, meter-scale
positioning accuracy can be reached through the time-domain features also in
NLoS.

####  IV-C3 Impact of Feature Granularity

Next, we assess and compare the performance of the snap-shot NN model while
varying the granularity or sparsity of the input measurements. We again
separate the testing dataset into LoS and NLoS parts, and first evaluate the
frequency-domain data as resource block-level (RB-level) features, and their
mean values across the RBs as the _ bandwidth-level (BW-level) features_. The
RB-level features are obtained per-RB, which contains $12$ subcarriers with a
subcarrier spacing of $120$ kHz, thus representing a bandwidth of $1.44$ MHz
per measurement. The BW-level feature considers the $14.4$ MHz bandwidth
across $10$ RBs. Technically, the full feature (RB-level) dataset consists of
$960$ features per sample (real and imaginary part, $10$ RBs, $16$ beams, $3$
gNBs), while the BW-level feature dataset contains only $96$ features per
sample ($2\times 16\times 3$). The purpose is to investigate and understand
whether the more sparse feature representations, which enable simpler and thus
faster models, are capable of achieving competitive performance to the non-
sparse data or full features.

Fig. 6a visualizes the empirical cumulative distribution functions of the
positioning errors, in the LoS and NLoS regions, when utilizing the RB-level
and BW-level data as the FR-Power/Phase features. We can observe that in the
LoS scenario, the BW-level features provide somewhat reduced performance
compared to the full RB-level features. In the NLoS scenario, the RB-level
features as the input again outperform the BW-level features. In general,
particularly in NLoS where the channel geometry is more complex, the wider
array of inputs can support the model in extracting more relevant positioning
information thus leading to an improved performance. On the other hand, one
can also conclude that the BW-level features provide a well-working solution
with large reductions in the model complexity.

(a)

(b)

Figure 6: ecdf of the positioning errors on the test data, (a) when evaluating
RB-level and BW-level FR-Power/Phase data, and (b) when evaluating path-
ToF+AoA and path-ToF+RP+AoA features with either dominant path only or with
all detected paths. The figures visualize the results of LoS and NLoS regions
separately using a dense snap-shot NN model with no measurement uncertainties.

Similarly, we next evaluate the impact of the time-domain feature granularity.
Earlier, we already concluded that the path-ToF+AoA and path-ToF+RP+AoA
features provide the best performance, thus these features are utilized also
here. In the following, we distinguish and compare between utilizing only the
dominant multipath component (in terms of power) and all available multipath
components as the input features.

The achieved performance results are depicted in Fig 6b, from which we can
draw the following observations. The model performance actually improves when
only the dominant multipath component is used as the input. This applies to
both LoS and NLoS regions, and the impact is particularly clear when the path-
ToF+RP+AoA feature case is considered. Additionally, Fig. 6b shows that
especially the outlier performance (the highest $10\%$ of errors) is clearly
improved, particularly in the LoS regions. Overall, the results in Fig 6b
demonstrate that very high positioning performance can be achieved also in
NLoS given that proper path features are utilized.

###  IV-D Numerical Results with Temporal Sequence Models

In this section, we evaluate the selected frequency-domain and time-domain CSI
features, namely RB-level FR-Power/Phase, path-ToF+RP+AoA with the dominant
component, and path-ToF+AoA with the dominant component, in the spirit of
vehicular user tracking. For this purpose, we utilize the novel temporal
sequence-processing NN model proposed and described in Section III-C, while
estimating the UE position, UE velocity and UE heading simultaneously.
Additionally, and importantly, we now also consider the realistic
uncertainties in all considered measurements and the corresponding features,
as introduced in Section IV-B.

Fig. 7 provides and visualizes the sequence-based model performance for the
different considered features while also explicitly comparing the cases
without and with measurement uncertainties, hence providing valuable insight
into the NN model generalization capabilities. In the uncertainty-free
scenario, time-domain features clearly outperform the frequency-domain ones,
similar to the earlier results with snap-shot models. In the practical case
where the uncertainties are present in the data, the performance with the
time-domain path-ToF+AoA and path-ToF+RP+AoA features deteriorates to a
certain extent, while the performance gap between the LoS and NLoS scenarios
also interestingly disappears. The frequency-domain FR-Power/Phase features
provide essentially the same distributions for the LoS and NLoS positioning
errors, while even outperforming the uncertainty-free model in NLoS. These
findings high-light the generalization properties of the NN model, as the NLoS
scenario itself is a source of additional uncertainties, as can be seen in
Fig. 2c already. To this end, Fig. 7 demonstrates that the increased amount of
uncertainty in the data does not necessarily lead to the degradation of
performance, given that the model is trained on sufficient amount of data
containing such uncertainties.

Figure 7: Distributions of the positioning errors with sequence-processing NN
model without (w/o) and with (w/) feature uncertainties along the LoS and NLoS
regions. The box center denotes the median value, box edges the $25^{th}$ and
$75^{th}$ percentiles, while the whiskers mark the $5^{th}$ and $95^{th}$
percentiles.

To further study the achievable performance of the proposed sequence-
processing model and the channel features, the positioning, speed, and heading
estimation performance is next assessed and shown. We also compare the
proposed sequence model’s performance against the selected benchmark
solutions, namely the NN model from our initial work in [14] (denoted in the
continuation as SPAWC benchmark), as well as an EKF-based robust Bayesian
tracking algorithm. To this end, the SPAWC model’s LSTM architecture,
parameters, and training setup are as described in [14], whereas the training
and testing data are naturally the same as for all other methods described in
this article such that comparative results and fair comparisons can be
obtained. The SPAWC benchmark utilizes path-ToF+AoA time-domain features as
the inputs.

The considered EKF benchmark, in turn, utilizes ToF and AoA measurements from
each gNB with LoS connection, while assuming ideal LoS detection such that the
EKF performance is the best possible in all LoS locations. In the absence of
any LoS link, only the prediction stage of the EKF is conducted. The
implementation of the used state-transition model and observation model,
together with the related Jacobians and process covariance matrix, follows the
descriptions given in [11]. Consequently, the used EKF state vector comprises
the UE position in x- and y-coordinates and the UE speed in x-y directions.
For each track, the UE state vector is initialized with a perfect state vector
estimate in order to provide the best available performance for the EKF
benchmark results. However, the performance is evaluated only after the first
LoS link is obtained, so that the unrealistic prediction during NLoS condition
with the perfect initialization is avoided. After a brief optimization of the
EKF parameters, the std of ToF and AoA, included in a diagonal measurement
covariance matrix, are defined as 50 ns and 15 deg, respectively. In addition,
the std of the velocity noise, used in the process covariance matrix, as
defined in [11], is set as 8 m/s.

The positioning performance of the different models is visualized and compared
in Fig. 8a, showing significantly improved positioning performance through the
proposed solution compared to the two benchmarks. While being evaluated with
the same data, the proposed time- and frequency-domain CSI features combined
with the proposed sequence processing engine achieve around $2$ m median
positioning error, compared to $5$ m of the SPAWC benchmark and $12$ m of the
EKF benchmark. The achieved performance improvement is stemming from the
combination of the novel feature engineering and the carefully crafted
sequence based NN processing system. Furthermore, besides estimating the UE
location, incorporating the estimation of UE heading and velocity leads to
reduced estimation variance through stabilization between individual
quantities. Compared to the EKF model, which is built on the assumption of LoS
geometry and unbiased measurements, the proposed approach can work in both LoS
and NLoS conditions and deal with biased measurements – such as the ones
encountered with the discretized path-AoA feature.

(a)

(b)

Figure 8: ECDFs of the positioning errors, in (a), and the split between the
LoS and NLoS samples, in (b), with realistic feature uncertainties. The
proposed sequence processing NN model with three different channel features is
compared against two benchmark solutions.

Fig. 8b provides the corresponding results when distinguishing between the LoS
and NLoS regions. The ECDFs show that with the uncertainties within the
received signals, the gap between the LoS and NLoS performance with the
proposed solution is strongly suppressed, as for the NN model, the NLoS
scenario itself represents an uncertainty on its own, which only complements
the ones in the input data. While time-domain CSI features offer LoS-agnostic
results, there is still a small performance gap when utilizing the frequency-
domain data. The SPAWC benchmark provides consistent results in the lower
parts of the distribution, but the distribution for the NLoS samples contains
significantly higher errors and outliers. The positioning performance of the
EKF in LoS suffers from the discretization of the path-AoA, leading to an
increasing positioning error with the increasing distance from the LoS gNB(s).
In NLoS, the EKF follows the direction of the last LoS sample, leading to
unreliable estimation. As noted already in the Introduction, there are
Bayesian filtering or other model-based methods deliberately crafted for NLoS
scenarios, such as [9, 13]. However, such possess very high computational
complexity and are typically limited to single-bounce scenarios, while in the
evaluation environment considered in this article severe multi-bounce
phenomena can occur.

Fig. 9a and Fig. 9b visualize the speed estimation and tracking performance in
the same scenario as the positioning evaluation above, yet excluding the SPAWC
benchmark which does not facilitate speed or heading estimation. The results
show that the speed estimation error of the proposed model and features is in
the majority of situations lower than $1$ m/s, regardless of the input feature
or LoS availability. The frequency-domain feature FR-Power/Phase has a
slightly higher estimation error in NLoS. Comparably, EKF is subject to
significantly higher estimation error even in LoS, while in NLoS loses the
tracking capabilities completely.

(a)

(b)

Figure 9: ECDFs of the speed estimation errors, in (a), and the split between
the LoS and NLoS samples, in (b), with realistic feature uncertainties. The
proposed sequence processing NN model with three different channel features is
compared against the EKF benchmark solution.

Furthermore, as shown in Fig. 10a and Fig. 10b, the UE heading is in the
majority of samples estimated correctly – with less than $1^{\circ}$ error in
more than $75$% of the samples. Interestingly, the NLoS heading estimates are
even more accurate than the ones with an unobstructed radio link to the gNB.
This phenomenon occurs when the UE starts turning and the heading rapidly
changes, while the data, such as discretized path-AoA, remain unaffected by
the change. The model is not capable of instantaneously reacting due to the
uncertainties included within the data.

(a)

(b)

Figure 10: ECDFs of the heading estimation errors, in (a), and the split
between the LoS and NLoS samples, in (b), with realistic feature
uncertainties. The proposed sequence processing NN model with three different
channel features is compared against the EKF benchmark solution.

For a comprehensive performance assessment, we next shortly address the
potential impact of the uncertainties in the training data positioning labels.
We model the uncertainty through AWGN and set the corresponding std in the x-y
coordinates to $5$ m. The obtained results are illustrated in Fig. 11. As can
be observed, additional uncertainties in the labels force the model to
generalize along the path. Consequently, the model is capable of tracking more
effectively in LoS, while in NLoS, the positioning results include an
increased number of outliers. These results show, that the proposed
combination of features and the sequential NN model can diminish the effects
of significant uncertainties in both features and labels.

Figure 11: Distributions of the positioning errors with sequence-processing NN
model with feature uncertainties along the LoS and NLoS regions, when
considering perfect position labels (feat.) and the labels with the
uncertainty modeled through AWGN with std of $5$ m along x-y coordinates
(feat. + labels).

###  IV-E Deployment Specialization through Transfer Learning

Being able to adapt the NN model to environmental changes is a critical task
in real-world applications, as any given model is essentially restricted to
the environment it was trained at. This is especially so if no direct
information about the environment, such as gNB locations, beam directions, or
buildings, is included in the feature vector. To address this practical
challenge, we explore next the capabilities of transfer learning (TL), which
relies on re-training the model from one scenario to another. For presentation
simplicity, we consider the snapshot model with FR-Power/Phase features and
assume no feature or label uncertainty. The models utilize the same training
parameters as described in Section III-C2, with the exception of applying the
early stopping mechanism also to the first training loop. In addition, for the
considered new gNB deployments, we limit the dataset size to _only $10\%$ of
the original_ to demonstrate the feasibility of the TL approach also with
small data sizes.

####  IV-E1 Scenario 1

We first consider _relocating a single gNB_ within the deployment, thus
altering the signal propagation geometry, as visualized in Fig. 12a. For the
evaluation, we consider three models, all sharing the same architecture: an
original model, a TL model, and a new model trained from scratch. The original
model was trained on a full dataset from the prior deployment, whereas the TL
model and the new model were trained on the data from the altered scenario.
Moreover, the newly trained model was initialized with random weights, while
the TL model was initialized with the weights of the original model before
(re-)training. In addition, only the first layer after the input was set to
“trainable”, while the rest of the model remain frozen.

The positioning error distributions of the considered models are visualized in
Fig. 12b. Although the original model is not trained with the data from the
altered deployment scenario, its positioning error is below $10$ m in
approximately $40\%$ of the samples. However, most of the accurately localized
samples of the original model are found in the southeast part of the
deployment, where the relocated gNB is not detected, and thus the environment
seems essentially unchanged. The TL model clearly outperforms the newly
trained model, especially when considering errors above the $40^{th}$
percentile. The model convergence during the training is visualized in Fig.
12c, where both training and validation losses across epochs are shown for the
TL and the newly trained models. While the TL model is able to converge within
less than $80$ epochs, the normally trained model requires more than $200$
epochs (not explicitly visible in the figure) to obtain the final weights.
This highlights the training efficiency of the TL model.

(a)

(b)

(c)

Figure 12: (a) Scenario 1 illustration where a single gNB is relocated. (b)
Positioning performance comparison between the model trained on the original
data, adapted model via TL, and a new model trained from scratch. (c) The
training histories of the TL model and the newly trained model.

####  IV-E2 Scenario 2

We next consider the more challenging case of _relocating all three gNBs_, as
shown in Fig. 13a. In this case, the changes in the gNB coordinates are up to
hundreds of meters, resulting in significantly altered radio propagation
characteristics. In Fig. 13b, the positioning errors are shown following
similar model cases as in Scenario 1. Due to the considerably changed gNB
locations, the performance of the original model clearly collapses.
Furthermore, the TL model provides clearly better performance compared to the
new model trained from scratch. In Fig. 13c, it can be seen that besides
providing the best positioning performance, the TL model significantly
accelerates the training rate, enabling fast model convergence in only some
$50$ epochs. These results show that TL is an efficient approach to adapt the
NN model to a new, previously unseen scenario with greatly reduced effort and
relaxed requirements on the availability of data.

(a)

(b)

(c)

Figure 13: (a) Scenario 2 illustration where all gNBs are relocated. (b)
Positioning performance comparison between the model trained on the original
data, adapted model via TL, and a new model trained from scratch. (c) The
training histories of the TL model and the newly trained model.

###  IV-F Notes on Complexity

Model complexity is an important aspect of any NN solution, and notable
efforts are commonly invested to reach beneficial performance-complexity
trade-offs. For comparability and presentation simplicity, we focus here
primarily on the parameter counts and input sizes as the main complexity-
related metrics. To this end, Table IV compares the proposed solutions with
the ones from the referred literature noting also the model structures.

TABLE IV: Complexity assessment of related works

Reference | ML model | Input size | Num. parameters
---|---|---|---
[15] | CNN | $18~{}432$ | $13M$
[18] | DNN | $224$ | $2~{}331~{}650$
[23] | DNN | N/A | $2.5M$
[25] | CNN | $2~{}700$ | $9M$
[28] | DNN | $18~{}432$ | $9~{}105~{}346$
[29] | CNN | $15~{}440$ | $2.6M$
Our models | Feature | Input size | Num. parameters
Snapshot |  path-ToF+AoA | $12$ | $1~{}058~{}306$
Snapshot |  path-ToF+RP+AoA | $15$ | $1~{}067~{}010$
Snapshot |  FR-Power/Phase | $960$ | $1~{}543~{}682$
Sequence |  path-ToF+AoA |  $50\times 12$* | $1~{}667~{}192$
Sequence |  path-ToF+RP+AoA |  $50\times 15$* | $1~{}670~{}264$
Sequence |  FR-Power/Phase |  $50\times 960$* | $2~{}637~{}944$

* Processing $50$ snapshot samples in a sequence

As can be observed, both the convolutional and fully connected models utilized
across the referred works consider a few million parameter models with up to
$18~{}432$ input sizes, corresponding to manageable computational complexity
when training on high-performance machines. In comparison, the path-ToF+AoA
model which achieved meter-level positioning accuracies requires only $12$
inputs and a model with around one million parameters, while increasing the
input size to $960$ with FR-Power/Phase feature results in $1~{}543~{}682$
trainable parameters. Our sequence-processing models, despite their extra
layers, retain relatively low parameter counts resulting in feasible
computational requirements. Overall, we can conclude that while outperforming
the prior-art methods in positioning accuracy, the proposed models are also
computationally feasible – and even lighter in complexity compared to many
reference models.

###  IV-G Discussion on Synthetic vs. Real-World Training Data

While we evaluate the performance of the methods and models on ray-tracing
data in this article, training the models with artificially created synthetic
data can be a feasible option also for true deployments and applications of
large-scale NN-operated systems. In general, the acquisition of synthetic data
is cheaper and faster than performing exhaustive site surveys and can
approximate reality with increasing accuracy and fidelity [50]. Considering
the availability of synthetic data, there are many possibilities to organize
the model training in practice. For example, initial training can be performed
already at the factory based on synthetic data from a specific intended
operation environment, and then the model can be fine-tuned on a limited set
of real-world measurements. Such real-world labelled data can be obtained
through different crowdsourcing or crowdsensing arrangements, as discussed
further below. On the other hand, training at the factory can be more generic
and cover numerous environments, while specialization to a specific
environment can be managed with a TL approach using synthetic data and/or
real-world measurements. Similarly, in case of any changes in the environment,
it is possible to update the model via TL by utilizing re-generated site-
specific synthetic data and/or newly obtained real-world measurements.

Employing _crowdsourcing_ campaigns, where the surveying software is offered
to the public to perform the measurements is one way of arranging real-world
labelled data in practice. One recognized challenge is that such an approach
is often biased by the human factor, such as inaccurate manual labeling. As
another alternative, while crowdsourcing requires the user to perform an
action to obtain the data, _crowdsensing_ is fully automated and unsupervised
by the user. Consequently, it can yield a massive volume of data, though at
the cost of potentially missing labels or other quality-related challenges.
Numerous solutions exist to cure and filter such data, although some
challenges still remain [51].

In general, the topic of synthetic data is currently explored by IEEE [52] and
can become a critical link enabling real-world systems driven by their digital
twins [53]. This is a key component in positioning-driven studies, where
obtaining realistic performance evaluations requires consideration of whole
network deployments with detailed physical-layer processing and measurement
capabilities. End-to-end simulated results play thus a crucial role in the
positioning system analysis before conclusive validation through experimental
field tests.

##  V Conclusions

This article addressed cellular network-based user localization and tracking
in challenging NLoS environments, with specific emphasis on 5G mmWave
deployments and urban vehicular systems. We first described the UL/DL
measurements, available for positioning purposes, together with their
acquisition in 5G mmWave networks. We then derived and proposed efficient
frequency-domain CSI features, most notably utilizing the relative phases and
powers of the received signal across the neighboring resource blocks. As time-
domain CSI data, we exploit the multipath components and proposed different
aggregate features combining time-of-flight, angle-of-arrival, and received
path-wise powers. Deep learning ML architectures were then described, covering
not only dense snapshot models but also sequence-processing NN models
harnessing the temporal correlations of the features in vehicular systems.

Realistic numerical evaluations in large-scale LoS-obstructed urban
environment with moving vehicles were provided, building on full ray-tracing-
based propagation modeling on METIS Madrid map at 28 GHz. The baseline results
without feature uncertainties show that the frequency-domain CSI in the form
of RB-level relative phases and powers allows for very good and robust
positioning performance, in both LoS and NLoS, while even further enhanced
performance can be obtained through the time-domain features when combining
multipath times-of-flight and angles-of-arrival. The results also show that
dominant multipath feature combinations are sufficient, or even favorable, for
robust positioning. Additionally, when considering practical levels of feature
measurement uncertainties, together with the sequence-processing NN models,
robust positioning in both LoS and NLoS was still shown to be feasible.
Finally, the important practical aspect of dealing with gNB deployment
differences between the training and inference phases was addressed. It was
shown that such environment related uncertainties can be addressed and
alleviated through transfer learning.

Overall, the provided numerical results clearly demonstrate that the proposed
methods harnessing the novel feature engineering and sequence processing
neural network models outperform the state-of-the-art, being able to
facilitate 1-2 m median positioning accuracy even in deep-NLoS regions with
feasible parameter counts. Our future work will focus on exploring the
opportunities with obtaining and processing positioning measurements from co-
existing C-band and mmWave cellular networks, as well as with further
improving the positioning accuracy and reliability through sensor fusion.

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  *[UE]: user equipment
  *[CSI]: channel state information
  *[NLoS]: non-line-of-sight
  *[LoS]: line-of-sight
  *[UEs]: user equipment
  *[mmWave]: millimeter-wave
  *[5G]: fifth generation
  *[NR]: New Radio
  *[LBS]: location-based services
  *[GNSS]: Global Navigation Satellite System
  *[ML]: machine learning
  *[TX]: transmitter
  *[RX]: receiver
  *[EKF]: extended Kalman filter
  *[PF]: particle filter
  *[NN]: neural network
  *[ CSI]: channel state information
  *[RSS]: received signal strength
  *[Wi-Fi]: IEEE 802.11 network
  *[$k$-NN]: k-Nearest Neighbors
  *[RSRP]: reference signal received power
  *[UL]: uplink
  *[RNN]: recurrent neural network
  *[ToA]: time-of-arrival
  *[CNN]: convolutional neural network
  *[gNB]: gNodeB
  *[DL]: downlink
  *[SSB]: synchronization signal block
  *[MRTT]: multi-round trip time
  *[AoA]: angle-of-arrival
  *[SRS]: sounding reference signal
  *[PRS]: positioning reference signal
  *[RSRQ]: reference signal received quality
  *[RSSI]: received signal strength indicator
  *[SS]: synchronization signal
  *[ToF]: time-of-flight
  *[TDoA]: time-difference-of-arrival
  *[UL-AoA]: uplink angle-of-arrival
  *[DL-AoD]: downlink angle-of-departure
  *[gNBs]: gNodeB
  *[LMF]: Location Management Function
  *[FR]: frequency response
  *[OFDM]: orthogonal frequency-division multiplexing
  *[AoD]: angle-of-departure
  *[FFT]: Fast Fourier Transform
  *[RF]: radio frequency
  *[RB]: resource block
  *[ RB]: resource block
  *[FR-Complex]: complex frequency response
  *[FR-Power]: power-domain frequency response
  *[FR-Phase]: relative phase frequency response
  *[FR-Power/Phase]: power and relative phase frequency response
  *[path-ToF]: path-wise time-of-flight
  *[path-AoA]: path-wise angle-of-arrival
  *[GELU]: Gaussian error linear unit
  *[ReLU]: rectified linear unit
  *[LSTM]: long-short term memory
  *[RBs]: resource block
  *[path-RP]: path-wise received power
  *[RRC]: radio resource control
  *[MDT]: Minimization of Drive Testing
  *[AWGN]: additive white Gaussian noise
  *[RMS]: root mean square
  *[std]: standard deviation
  *[RB-level]: resource block-level
  *[BW-level]: bandwidth-level
  *[ECDFs]: empirical cumulative distribution function
  *[TL]: transfer learning
  *[ gNB]: gNodeB
  *[ gNBs]: gNodeB