# Micro-location for Smart Buildings in the Era of Internet of Things

Petros Spachos, Ioannis Papapanagiotou and Konstantinos Plataniotis Petros
Spachos is with the School of Engineering at the University of Guelph,
Ontario, Canada<EMAIL_ADDRESS>Papapanagiotou is with Platform
Engineering at Netflix, Los Gatos CA, USA<EMAIL_ADDRESS>Konstantinos N.
Plataniotis is with the Department of Electrical and Computer Engineering at
the University of Toronto, Ontario, Canada<EMAIL_ADDRESS>
###### Abstract

Micro-location plays a key role in the transformation of traditional buildings
into smart infrastructure. Micro-location is the process of locating any
entity with a very high accuracy, possibly in centimeters. Such technologies
require high detection accuracy, energy efficiency, wide reception range, low
cost, and availability. In this paper, we provide insights into various micro-
location enabling technologies, techniques, and services, and discuss how they
can accelerate the incorporation of the Internet of Things (IoT) in smart
buildings. We cover the challenges and examine some signal processing
filtering techniques such that micro-location enabling technologies and
services can be thoroughly integrated with an IoT equipped smart building. An
experiment with Bluetooth Low Energy (BLE) beacons used for micro-location is
also presented.

##  I Introduction.

The interconnectedness of all things is continuously expanding. The aim is to
have every individual interconnected with their surroundings, whether it be at
home, at work, or in public spaces. Some of these services might include but
are not limited to indoor mapping, personalized environment changes, such as
lighting and temperature settings, as well as directed advertisement. For
these systems to perform, it is essential to have reliable hardware and
accurate data. Outdoor localization technologies, such as the Global
Positioning System (GPS), do not work indoors due to the physical barriers
that block the signal while it does not provide location data accurate enough
for micro-location. Current solutions utilize Received Signal Strength
Indicators (RSSI) to determine position. A variety of solutions that utilize
RSSI have been proposed to provide location services for indoor environments,
though each solution presents its own drawbacks. Multiple technologies and
techniques have been adapted to provide indoor location information, all of
which attempt to overcome the noise and dynamics of a changing indoor
environment.

A promising approach includes the effective use of the plethora of Internet of
Things (IoT) devices that are available in the market. Bluetooth Low Energy
(BLE) beacons, usually referred to as beacons, are a promising candidate to
improve indoor localization accuracy. They are small Bluetooth transmitters
designed to attract attention to a specific location. As in many IoT based
networks, the performance of such networks relies on the network lifespan and
accuracy. BLE beacons are a cheap, simple, and very scalable means of
implementing indoor localization services. In recent years, BLE technology has
grown in popularity and much more research has been developed in using it for
indoor localization [1, 2, 3]. The fundamental operation of these beacons for
localization purposes is based on RSSI techniques, where the received RSSI
value is translated into a distance by using a best curve fit signal
propagation model. BLE beacon protocols, such as iBeacon [4], and Eddystone
[5], provide the necessary information and configuration capabilities for
micro-location. Along with the low power consumption of BLE, beacon devices
are easily deployed and require low maintenance, hence their scalability for
any complex indoor environment.

Intrinsic to any wireless technology, BLE beacons are highly susceptible to
noise and interference. To overcome the effects of noise and dynamic changes
to the physical environment, many methods devised around advanced positioning
algorithms and filtering techniques have been adapted to beacon-based systems
to improve the accuracy obtained in using RSSI localization techniques, as
shown in Fig. 1. Some of the most common filter implementations are the Kalman
filters as detailed in [6]. Kalman filtering has also been examined in the
context of indoor localization [7]. These filters provide a reasonably
accurate state estimation and can be adjusted for changes is environmental/
process noise. Other filters such as the particle filter are used. Particle
filters are highly accurate, but at the cost of greater computational
complexity, hence the need for a client-server based model, as outlined in [2,
8]. Positioning algorithms can also have an effect on beacon accuracy. The
work presented in [9] implements the K-Nearest Neighbor algorithm to calculate
the position of the user. The experiments showed an average error of 1 m.
Other algorithms, such as the Pedestrian Dead Reckoning (PDR) approach have
been implemented with BLE beacons [10]. In these experiments, the integration
of smartphone sensors for data regarding step detection, step direction, and
walking length, are combined with beacon calibration zones to provide a more
accurate position. All techniques may provide different accuracy results and
may behave differently depending on the environment, so it is important to
note the characteristics of each tested environment when deciding on what
technique to implement.

In this paper, we survey available wireless technologies for micro-location
systems in a smart building. Then we discuss signal processing techniques and
characteristics that can be used to improve micro-location performance, along
with filtering approaches. We focus on the use of BLE beacons and through an
experiment we discuss how they can enhance micro-location.

Figure 1: Micro-location system using Kalman Filter.

##  II Smart Buildings with Internet of Things Technologies.

The IoT revolution has brought a swarm of continuously interconnected and
sensor-packed devices opening a vast number of opportunities in equipping
existing infrastructures. IoT has enabled applications that transform
facilities to intelligent spaces able to critically affect and improve
productivity and life quality of the occupants. Reducing energy costs,
detecting and building knowledge based on human patterns as well as improving
the human-building interaction is only some cases in point.

The Institute for Building Efficiency [11] defines smart buildings as the
buildings that can provide low-cost services such as air conditioning,
heating, ventilation, illumination, security, sanitation and various other
services to the tenants without adversely affecting the environment. This
requires the collaboration of multiple sensors that form a building’s IoT
ecosystem. The basic motive behind the construction of smart buildings is to
provide the highest level of comfort and efficiency. At the same time, the
interconnection of the automation systems can assist with the disaster
management and provide emergency services. For example, the collaboration of
the fire system with the air conditioning system can create an environment
where a fire will not expand in the rest of the building.

To the end, indoor-focused Location-Based Services (LBS) is the fundamental
component for providing a tenant to building interaction. LBS provide the
ability to efficiently track occupants in real-time. They either attempt to
estimate the users’ 2D coordinates, which is referred to as micro-location or
assign the user in the locality of certain points of interest (PoI), which is
known as proximity sensing.

The integration of smart buildings with IoT creates a number of challenges. A
smart building with an IoT ecosystem requires mainly three components: the
sensors, the integration, and the actuators. The sensors must be connected to
a reliable highly available network that optimally can self-diagnose and heal.
The integration is probably the part where innovation is nowadays taking
place. The integration consists of some software that would receive the input
from the sensors, process and analyze, and provide some actuator as a service
to the tenants. For example, unlocking a door, switching on the TV, calling
the elevator or configuring the room temperature based on the needs.

##  III Overview of micro-location Systems.

This section describes the wireless technologies and the radio signal features
that can be used for micro-location in a complex indoor environment, followed
by a brief description of the techniques that can be used to extract
information location from the wireless signals.

###  III-A Wireless Technologies.

Micro-location systems can leverage existing wireless infrastructure for
micro-location to minimize the cost or may require a specific wireless
deployment [1]. By wireless technologies, we refer both to high-frequency
technologies as well as low frequency. For example, the most common high-
frequency wireless technologies that have been used in a micro-location
deployment are WiFi [12], Zigbee [13], RFID [14] and Bluetooth [15]. However,
low-frequency technologies like the ones based on physical light have also
seen some research and commercial use [16]. For example, Light Fidelity, or
else Li-Fi is one of the wireless technologies in the form of Visible Light
Communication (VLC) technology. These technologies have been used successfully
in the past for indoor location and navigation and their popularity among the
IoT devices make them an ideal solution for micro-location as well. There are
also technologies such as WiFi HaLow [17], BLE version 5.0 [15] and LoRaWAN
[18] which are specifically designed for IoT devices.

  * •

IEEE 802. 11 - WiFi. The IEEE 802.11 standard [12], commonly known as WiFi, is
among the most popular technologies used for localization when the GPS is
inadequate. The great distribution of access points and signal availability at
indoor environment make it easy to collect the received signals from various
access points and calculate the location of the receiver. The indoor
transmission range can vary from 3.3 m with a bandwidth of 6.7 Gbit/s (IEEE
802.11 ad), up to 70 m with a bandwidth of 600 Mbit/s (IEEE 802.11 n), while
it can operate in 2.4 GHz, 5 GHz, and 60 GHz.

WiFi networks are deployed for communication, hence data rate and connectivity
are important while localization is not their priority. Also, WiFi networks
are designed for a plethora of devices from smartphone and laptops to phablets
and smartwatches. This is a trade-off for micro-location techniques. The
availability of the WiFi signals and WiFi-enabled devices is an advantage for
micro-location as the number of the portable devices and potential reference
points for localization increases. Advanced signal processing techniques can
be used to improve the quality of the WiFi signals for localization. At the
same time, there is no need for extra hardware deployment with WiFi
technology.

On the other hand, IoT devices have unique characteristics, such as the size
and the limited energy resources, that are not taken into consideration from
the general WiFi technology. As the number of these devices increases, the 2.4
GHz and 5 GHz channels become overcrowded while the interference increases
with a drop in the network capacity. Unfortunately, traditional Wi-Fi was not
originally designed to tackle these interference issues and the increasing
capacity in dense environments. To fill this gap, WiFi Alliance announced the
WiFi HaLow (IEEE 802.11 ah).

  * •

IEEE 802.11ah - WiFi HaLow. WiFi HaLow [17] was designed to enable
connectivity to a variety of new, power-efficient use cases in smart homes and
smart cities, connected vehicles and supporting the concept of the IoT in
general. It extends the WiFi into the 900 MHz band to enable low power
connectivity which is necessary for the IoT devices. The transmission range is
twice the range of WiFi while it increases the signal robustness in
challenging environments, such as complex indoor environments with lots of
furniture and walls. It can operate in multiple transmission modes from low-
rate starting from 150 Kbp/s and up to 347 Kbp/s.

The ability to operate in low power, the high transmission range and the low
propagation loss makes WiFi HaLow a good candidate for micro-location with IoT
devices. On the other hand, it is relatively new in comparison with other
technologies, published in 2017, hence it is not widely available and it will
be a while before we see HaLow clients and infrastructure device. This delays
the experimentation that is necessary before deciding if it is suitable for
micro-location.

  * •

Zigbee. Zigbee is a high-level communication protocol known for its
simplicity, low-power usage, and secure networking [13]. It is based on the
IEEE 802.15.4 standard, which defines the operating point of Wireless Personal
Area Networks (WPANs) with low data rate antennas. They are able to control
the flow of information and prevent any loss of data by using Carrier-Sense
Multiple Access with Collision Avoidance (CSMA/CA). Devices using Zigbee are
designed with additional features such as link quality and energy detection,
which allow for measurements such as the RSSI to be easily determined.

Zigbee is commonly used for localization in WSN due to its low power
requirements. Among the IoT devices through it is not popular due to the extra
hardware that is needed.

  * •

Bluetooth.  Bluetooth is another wireless technology for exchanging data over
short distances [15]. The IEEE standardized Bluetooth as IEEE 802.15.1, but no
longer maintains the standard, which is managed by the Bluetooth Special
Interest Group (SIG). According to the Group, Bluetooth is all about
proximity, not about exact location. Bluetooth was not intended to offer a
pinned location like GPS. However is known as a geo-fence or micro-fence
solution which makes it an indoor proximity solution, not an indoor
positioning solution.

Introduced by Bluetooth Special Interest Group in 2010, Bluetooth Low Energy
(BLE) was designed for applications that do not require large amounts of data
transfer, while reducing the power consumption and cost of devices. Micro-
location and indoor mapping have been linked to Bluetooth and to the BLE-based
iBeacon promoted by Apple Inc. [4]. Large-scale indoor positioning systems
based on iBeacons have been implemented and applied in practice.

Similar to Zigbee, BLE is a technology used in WPANs. The low power
consumption of BLE has led to a number of new devices in the IoT. BLE 4.0 can
reach 25 Mbit/s at a distance of 60 m. Applications utilizing BLE have greatly
increased over the past couple of years. A number of new devices have been
developed, ranging in fields such as healthcare [19], sports, fitness,
security, and home entertainment. One device that has been created is known as
a beacon. Beacons are small, inexpensive devices, which contain only a CPU, a
radio, and batteries.

Bluetooth 5.0 [15] is the competitor of WiFi HaLow in the IoT domain. It is
claimed to have twice the speed of the previous version, four times longer
transmission range, and exchange data eight times faster.

The simplicity and the popularity among IoT devices are advantages of
Bluetooth for micro-location. The small size of beacons and their low cost
with the energy efficiency of the BLE and the extended lifespan that it can
provide, can be used to enhance micro-location in a complex environment
without interfering with other wireless infrastructures. On the disadvantages,
even though the security of BLE is good, it is even better on Wi-Fi.

  * •

RFID. Radio Frequency Identification Device (RFID) was primarily designed for
data transferring and storing [14]. There is a need for an RFID reader that
can communicate with the RFID tags. There are two types of RFIDS. The Active
RFIDs operate in the Ultra High Frequency (UHF) and microwave frequency range.
They need to be connected to a local power source while the transmit their ID
periodically up 100 m. On the other hand, Passive RFIDs, they operate without
battery but within 1-2 m transmission range.

In the IoT era, RFID is not a promising solution for micro-location. Their
accuracy is not high enough while they are not available on many portable
devices.

  * •

LoRaWAN. LoRaWAN is a long-range, low power consumption technology used in the
development of Personal Wide Area Networks (PWAN) [18]. Originally developed
by the LoRa Alliance, the LoRaWAN protocol transmits at a lower frequency of
915MHz. The benefit of using a lower frequency is that the smaller wavelength
allows for a greater distance that the signal can reach. Due to that, it can
pass through walls and obstacles without issue. It is also no longer as easily
susceptible to noise since it does not interfere with any devices transmitting
on the 2.4GHz band.

The disadvantage of using such a low frequency is a reduction in the data rate
that can be sent between transmitting devices. For micro-location, this is not
an issue as the nodes are not transmitting large amounts of information. Due
to the 915MHz band being unlicensed it is free for anyone to use for their
personal networking needs.

For devices that are moving at high speed in a large area, LoRa might be a
candidate for localization with IoT. Unfortunately, in short range, LoRa
performance does not overcome the high cost and the extra equipment that is
needed to set up a LoRa node.

  * •

LiFi: LiFi is a VLC technology [20]. VLC is a subset of Optical Wireless
Communication (OWC), which utilizes the light emitting diodes as a medium to
enable high speed communication. Data is transmitted by modulating the
intensity of LED light at nanosecond intervals, too quick to be detected by
the human eye.

Table I summarizes the specifications of each wireless technology along with
the advantages and disadvantages of usage for micro-location.

Technology | Throughput | Transmission Range | Power Consumption |  Advantages |  Disadvantages
---|---|---|---|---|---
IEEE 802.11ac | 3.5 Gbit/s | 35 m | Moderate |  Availability in many environments |  Prone to noise and interference
IEEE 802.11ad | 6.7 Gbit/s | 3.3 m
IEEE 802.11ah | 347 Mbit/s | 1 km | Low |  Wide reception range |  Not widely available
ZigBee | 250 kbit/s | 75 m | Low |  Easy to setup |  Extra hardware
BLE v4.0 | 25 Mbit/s | 60 m | Low |  High throughput |  Prone to interference
BLE v5.0 | 50 Mbit/s | 240 m
RFID Active | 1067 | 100 m | Low |  Low power |  Low accuracy
RFID Passive | 1067 | 2 m
LoRaWAN | 50kbps | 15 km | Extremely Low |  Wide range |  Extra hardware
LiFi | 1Gbps | 10m | Low |  Dense Environments |  Low Range
TABLE I: Wireless Technologies for micro-location.

###  III-B Radio Signal Features for Micro-location.

As the wireless signal propagates from the sender to the receiver, there are
signal characteristics that can be used for the localization of one of the
communicating devices. There are four main signal features that can be used
for localization:

  * •

Received Signal Strength Indication (RSSI). Received Signal Strength
Indication (RSSI) is one of the most commonly used characteristics for indoor
localization [1]. It is based on measuring the power present in a received
signal from a client device to an access point. As radio waves propagate
according to the inverse-square law, the distance can be approximated based on
the relationship between transmitted and received signal strength, as long as
no other errors contribute to faulty results. The combination of this
information with a propagation model can help to determine the distance
between the client device and the access points. Lateration-based methods are
commonly used along with RSSI to estimate the location of the client.

It can be assumed that the more access points, the more information can be
collected hence, the accuracy can be increased. This, however, works also as a
trade-off. An increase of the access points will also increase the
interference between different signal. A key challenge in wireless
localization systems is that the range measurements are often associated with
errors. Although RSSI techniques are among the cheapest and easiest methods to
implement, its disadvantage is that it does not provide very good accuracy,
with a median of 2 to 4 m. This is mainly because the RSSI measurements tend
to fluctuate according to environmental changes or multipath fading, events
that are common in indoor environments.

  * •

Angle of Arrival (AoA). Angle of arrival (AoA) is another characteristic that
can be used for localization. It tries to estimate the direction of the signal
propagation, i.e. the angle from which the signal arrives at a receiver. AoA
is typically achieved by using an array of antennas. The line connecting two
reference points may be used as an internal reference. The spatial separation
of antennas leads to differences in arrival times, amplitudes, and phases.

  * •

Time of Arrival (ToA). In Time of Arrival (also know as time of flight), the
distance between sender and receiver of a signal can be determined using the
measured signal propagation time and the known signal velocity. ToA is the
amount of time a signal takes to propagate from transmitter to receiver. The
signal propagation rate is constant and known hence, the travel time of a
signal can be used to directly calculate distance. This is the technique used
by GPS.

The accuracy of the TOA-based methods often suffers from massive multipath
conditions in indoor localization, which is caused by the reflection and
diffraction of the RF signal from objects (e.g., interior wall, doors or
furniture) in the environment. However, it is possible to reduce the effect of
multipath by applying temporal or spatial sparsity-based techniques

  * •

Time Difference of Arrival (TDoA). The Time Difference of Arrival (TDoA) is
the time of arrival of a specific signal, at physically separate receiving
stations with precisely synchronized time references. TDoA measures the
difference in ToA at two different receivers. Three or more TDoA measurements
can be used to locate a device using hyperbolic lateration.

Although TDoA sounds similar with ToA, there is a difference. In ToA the
absolute time at a base station is used. In TDoA the measured time difference
between departing from one and arriving at the other station is used.

###  III-C Indoor Positioning Techniques.

In this section some commonly used techniques for localization are discussed.

  * •

Proximity Detection. Proximity detection techniques, shown in Fig. 7a, are
based on the proximity of the mobile device to previously known locations.
These techniques determine the position of an object based on closeness to a
reference in the physical space. When the mobile device receives the signal
from a reference point, then the device should be in within the coverage range
of the reference point, i.e. in close proximity to the reference point.
Proximity detection does not provide the location in form of coordinates but
rather in form of sets of possible locations.

This method also based on the premise that the reference point has a limited
range. For simplicity, it is common to assume that the range of a wireless
infrastructure would be well represented by a circle of given radius $r$.
Then, the result of the proximity detection in being located inside this
circle. For several circles, one can limit the possible location to the
intersection of the different circles.

  * •

Lateration. Lateration is the process of estimating the location of a mobile
device given distance measurements to a set of points with a known location,
shown in Fig. 7b. Lateration-based methods use the distance measurements from
multiple reference points to compute the position of a receiver. Trilateration
is a commonly used technique to calculate the estimated client device position
relative to the known position of three access points. It uses the distance
from the three reference points to estimate the location and track the
position of the receiver when the receiver is moving within the three points.
Given the distance to an anchor, it is known that the node must be along the
circumference of a circle centred at anchor and a radius equal to the node-
anchor distance. In two-dimensional space, at least three non-collinear
anchors are needed and in three-dimensional space, at least four non-coplanar
anchors are needed.

  * •

Angulation. Angulation-based positioning techniques can be used to employ the
angle of arrival of a wireless signal and determine the position of a
receiver, shown in Fig. 2c. A commonly used approach is triangulation were the
location of a point is determined by forming triangles to it from known
points. In triangulation, a known baseline can be used to find the location
relative to two anchor transmitters. It uses the geometric properties of
triangles to estimate the location and relies on angle (bearing) measurements.
It requires a minimum of two bearing lines and the locations of anchor nodes
or the distance between them, for two-dimensional space.

  * •

Fingerprinting. Fingerprinting techniques are based on the reproducibility of
patterns of measurable variables, shown in Fig. 2d. Traditional fingerprinting
records the signal strength from several access points and store them in a
database, along with the known coordinates of the client device in an offline
phase. Then, during the localization phase, the current vectors at an unknown
location are compared to those in the database and the closest match is
returned as the estimated user location.

Fingerprinting has the advantage that it does not require any assumption
regarding the nature of the propagation environment. It just creates a
modelled environment based on the training data. At the same time, this can be
a disadvantage. Any change of the environment, such as adding or removing
furniture or access points, require an update to the model.

(a) Proximity.

(b) Lateration.

(c) Angulation.

(d) Fingerprinting.

Figure 2: Localization Techniques.

###  III-D Localization Metrics.

To evaluate the performance of a localization system, accuracy and precision
are used. Accuracy measures the deviation of the estimated location from the
truth, while precision measures the deviation of location estimates from each
other for the same location. A system with high accuracy can be used for an
application that focuses on the long-term localization determination and the
errors cancel out over time. On the other hand, a system with high precision
can be used to find the proximity between devices but it is hard to be used
for localization.

##  IV Improve Accuracy through Signal Processing Filtering Techniques.

There are a number of signal processing filtering techniques that are used for
indoor localization. In the following, we summarize two: Kalman Filtering (KF-
ST) and Dynamic Kalman Filtering (KF-DN).

###  IV-A Indoor Localization Model.

We model the indoor localization problem as posed by Arulampalam et al. [21].
Extended versions as applied in BLE can also be found in [7]. Since we seek to
estimate the user position/state under a set of measurements obtained in a
typical noisy indoor environment, Bayesian filtering is an attractive approach
for such problems. However, Bayesian filtering requires the following two
models.

  1. 1.

System Model: A system model describes the variation of the state (user
position in our case) with time. The system model relates the position vector
$y_{i}$ with the process noise $m_{i}$ and previous state.

  2. 2.

Measurement Model: A measurement model relates the noisy measurements (RSSI
for PF and the user position for EKF) with the state/position.

We construct the Posterior Probability Density Function (PDF) describing the
state from all available information, including the measurements from the
reference nodes (beacons in our case). The PDF is considered as the complete
solution to the state estimation problem, since it contains all the required
information. The problem involves recursively estimating the user
state/position as we receive measurements from the beacon. Therefore, we
require a recursive filter. Recursive filters consist of the prediction and
update stage in which the state is predicted and then updated once the
measurements are available. The presence of noise in indoor settings affects
the position calculation so the pdf is usually distorted. The obtained
measurements in the update state are used to modify the prediction pdf using
Bayes theorem.

Mathematically, state $y_{i}$ at time $i$ is a function of the state at time
step ($i-1$) as well as the process noise $m_{i-1}$ [22] as described in
Equation (1):

$y_{i}=f_{i}(y_{i-1},m_{i-1})$ (1)

$f_{i}:\Re^{n_{y}}$ x $\Re^{n_{m}}\rightarrow\Re^{n_{y}}$ is the non-linear
function (as indoor localization is a non-linear problem) that relates the
previous state $y_{i-1}$ and process noise $m_{i-1}$ with the current state
$y_{i}$ as described by Arulampalam [21]. The sequence
$\\{m_{i},i\in\aleph\\}$ represents an independent, identically distributed
(i.i.d) process noise sequence. The integer ${n_{y}}$ represents the state
noise vector, and ${n_{m}}$ represents the process noise vector. $\aleph$
represents the set of Natural numbers. The measurement model relates the
obtained measurement $x_{i}$ to the state $y$ and measurement noise $n$ at
time $i$ [22] as given in Equation (2):

$x_{i}=h_{i}(y_{i},n_{i})$ (2)

The mapping function $h_{i}:\Re^{n_{y}}$ x $\Re^{n_{n}}\rightarrow\Re^{n_{x}}$
can be either linear or non-linear. Functions $f_{i}$ and $h_{i}$ rely on the
laws of motion/physics. The sequence $\\{n_{i},i\in\aleph\\}$ is a measurement
noise sequence that is independent and identically distributed. The integers
${n_{x}}$ and ${n_{n}}$ represent the measurement and measurement noise
vectors dimension respectively.

Recursively calculating the pdf $p(y_{i}|x_{1:i})$ allows us to continuously
calculate the belief in the state $y_{i}$ at any particular time instance $i$
in the presence of noisy measurements. The initial pdf $p(y_{o}|x_{0})$ is
assumed to be equivalent to state vector’s prior $p(y_{0})$ [21]. We assume
that the prior is available. The available information is enough to calculate
the pdf $p(y_{i}|x_{1:i})$ recursively in the prediction and update stages. In
the prediction stage if the pdf $p(y_{i-1}|x_{1:i-1})$ is available, we can
use Chapman-Kolmogorov equation given in Equation (3) to obtain the prior pdf
of the state at any time instance $i$.

$p(y_{i}|x_{1:i-1})=\int p(y_{i}|y_{i-1})p(y_{k-1}|x_{1:i-1})dy_{i-1}$ (3)

At any time instance $i$, we collect the observations $x_{i}$ from the sensors
to update the prior using Bayes rule given in Equation (4) [21]. The
denominator in Equation (4) is explained in Equation (5).

$p(y_{i}|x_{1:i})=\frac{p(x_{i}|y_{i})p(y_{i}|x_{1:i-1})}{p(x_{i}|x_{i-1})}$
(4)

$p(x_{i}|x_{i-1})=\int{p(x_{i}|y_{i})p(y_{i}|x_{i-1})dy_{i}}$ (5)

The collected measurements $x_{i}$ in the update stage are then used to update
the prior density, resulting in the required current state’s posterior
density. Recursively updating the system using Equations (3) and (4) result in
an optimal Bayesian solution. However analytically, it is not possible to
obtain the recursive propagation of posterior probability density as done in
Equations (3) and (4). Therefore, a number of different algorithms including
PF, KF and EKF are used to obtain a solution.

###  IV-B Kalman filter.

The Kalman filter based RSSI smoother is based on the work of Guvenc [23]. The
state $x_{i}$ that in our case consists of RSSI and rate of change of RSSI, at
time $i$ is a function of the state at time $i-1$ and the process noise
$w_{i-1}$ which is given mathematically by Equation 6. The obtained RSSI
measurements $z_{i}$ at instant $i$ from the iBeacons is a function of the
state at $i-1$ and the measurement noise $v_{i}$ as given by Equation 7 as
described in Arulampalam [21].

$x_{i}=f(x_{i-1},w_{i-1})$ (6) $z_{i}=h(x_{i-1},v_{i})$ (7)

The traditional Bayesian based approach consists of the prediction and update
stage as described by Guvenc [23] and is given below:

  1. 1.

Prediction Stage

$p(x_{i}|z_{1:i-1})=\int p(x_{i}|x_{i-1})p(x_{i-1}|z_{1:i-1})dx_{i-1}$ (8)

  2. 2.

Update Stage:

$\displaystyle p(x_{i}|z_{1:i})=$
$\displaystyle\frac{p(z_{i}|x_{i})p(x_{i}|z_{1:i-1})}{p(z_{i}|z_{1:i-1})}$ (9)

where

$\displaystyle p(z_{i}|z_{1:i-1})=$ $\displaystyle\int
p(z_{i}|x_{i})p(x_{i}|z_{1:i-1})dx_{i}$ (10)

We assume that both the process noise and measurement noise are Gaussian and
the functions $f$ and $h$ in Equations 6 and 7 are linear. Because of the
linearity assumption, we can apply a Kalman filter since it is the optimal
linear filter.

Due to the aforementioned assumptions, Equations 6 and 7 can be rewritten as
described by Guvenc [23]

$x_{i}=Fx_{i-1}+w_{i}$ (11) $z_{i}=Hx_{i}+v_{i}$ (12)

where $w_{i}\sim N(0,Q)$ and $v_{i}\sim N(0,R)$. Table II lists the parameters
of a Kalman filter.

TABLE II: Kalman filter parameter notation Symbol |  Meaning
---|---
x |  State vector
z |  Measurement/observation vector
F |  State transition matrix
P |  State vector estimate covariance or Error covariance
Q |  Process noise covariance
R |  Measurement noise covariance
H |  Observation matrix
K |  Kalman Gain
w |  Process noise
v |  Measurement noise

The prediction and update stages for the Kalman filter as described by Guvenc
[23] are

  1. 1.

Prediction Stage:

$\hat{x}_{\bar{i}}=F\hat{x}_{i}$ (13) $P_{\bar{i}}=FP_{i-1}F^{T}+Q$ (14)

  2. 2.

Update State:

$\displaystyle K_{i}=$ $\displaystyle
P_{\bar{i}}H^{T}(HP_{\bar{i}}H^{T}+R)^{-1}$ (15) $\displaystyle\hat{x}_{i}=$
$\displaystyle\hat{x}_{\bar{i}}+K_{i}(z_{i}-H\hat{x}_{\bar{i}})$ (16)
$\displaystyle P_{i}=$ $\displaystyle(I-K_{i}H)P_{\bar{i}}$ (17)

The higher the Kalman gain, the higher will be the influence of the
measurements on the state. The prediction and update steps are recursive in
nature. For the purpose of filtering the RSSI values, we utilize a state
vector $x_{i}$ that consists of the RSSI value $y_{i}$ and the rate of change
of RSSI $\Delta y_{i-1}$ as given below.

$x_{i}=\begin{bmatrix}y_{i}\\\ \Delta y_{i}\end{bmatrix}$

$\Delta y_{i}$ is dependent on the environment and signifies how drastically
RSSI value fluctuates. The higher the noise in the environment, the higher
will be the fluctuation. The current value of RSSI $y_{i}$ is assumed to be
the previous RSSI $y_{i-1}$ plus the change $\Delta y_{i}$ and process noise
$w_{i}^{y}$. Hence Equation 11 can be written as

$\begin{bmatrix}y_{i}\\\ \Delta y_{i}\end{bmatrix}=\begin{bmatrix}1&\delta
t\\\ 0&1\end{bmatrix}\begin{bmatrix}y_{i-1}\\\ \Delta
y_{i-1}\end{bmatrix}+\begin{bmatrix}w_{i}^{y}\\\ w_{i}^{\Delta
y}\end{bmatrix}$ (18)

which means that the state transition matrix F is given by

$F=\begin{bmatrix}1&\delta t\\\ 0&1\end{bmatrix}$

The parameter $\delta t$ is to be adjusted as per the variation in RSSI which
depends on the environment. For our set of experiments, $\delta t$ was taken
as 0.2 (using trial and error). Similarly, Equation 12 can be rewritten as

$\begin{bmatrix}z_{i}\end{bmatrix}=\begin{bmatrix}1&0\par\end{bmatrix}\begin{bmatrix}y_{i}\\\
\Delta y_{i}\end{bmatrix}+\begin{bmatrix}v_{i}^{y}\end{bmatrix}$ (19)

The observation matrix H is given by

$H=\begin{bmatrix}1&0\end{bmatrix}$

Parameters P, Q and R used in the experiments were obtained using trial and
error, and are given below.

$P=100\textbf{I}_{22},\;\;Q=0.001\textbf{I}_{22},\;\;R=\begin{bmatrix}0.10\end{bmatrix}$

The Kalman filter, once calibrated, effectively smooths the RSSI values. The
smoothed RSSI values were then input into the path-loss model to obtain
distances between the iBeacons and the user, and the user’s proximity to the
beacon was classified in any of the aforementioned zones.

###  IV-C Dynamic Kalman.

A dynamic variation of the Kalman filter computes $Q$ as the variance of a set
number of previously collected RSSI values to make up for real-world process
noise changes. It is continuously recalculated at each iteration of reading in
the next RSSI value.

Different set sizes of recorded RSSI values can be used to find the ideal
number of values to utilize in this calculation. It can be inferred that as
the array size increases the accuracy increases as well, up to an array size
of $n$. After a size of $n$, any increase of the size leads to the decrease of
the accuracy. The optimal $n$ can be found through experimentation while the
increase of the size can lead to waste of resources without any increase in
the accuracy. At the same time, a decrease of the size below $n$ does not give
sufficient information to the system to increase its prediction accuracy.

The set of RSSI values is stored in an array list of data type double.
Algorithm 1 illustrates the procedure. It adds entries to each index in
increasing order starting from index 0. When an entry is deleted, all entries
ahead get pushed down one index value. At the start of each iteration the
algorithm checks the size of the array, and once it reaches the desired size
$n$, it removes the oldest entry (index 0) and adds in the newest measurement.

Algorithm 1 Maintain RSSI Set.

1:if $RSSIArray.size()==n$ then

2: $removeRSSIArray[0]$.

3:$lastIndex\leftarrow RSSIArray.size()$

4:$RSSIArray[lastIndex]\leftarrow\textit{newRSSI}$

When developing the dynamic noise component of the Kalman filter, it is
essential to find the ideal number of previously obtained RSSI values to
maintain, for calculation purposes. This is because the size of this set will
have a direct impact on the performance of the filter.

##  V BLE Beacon Technology.

In this section, an introduction to BLE beacons is presented along with their
characteristics and their most commonly used wireless protocols.

###  V-A BLE beacons.

BLE beacons are small wireless transmitters that broadcast their identifier to
nearby electronic devices, such as smartphones, wearables, and other IoT
devices. An analogy of the way beacons work is with the operation of a
lighthouse. The lighthouse represents a known location which can be uniquely
identified by its light. All the ships that can see the light, they know about
the existence of the lighthouse. On the other hand, the lighthouse neither
communicates with the ships nor does it knows how many ships see its light or
how many other lighthouses are in the area. Similarly, every beacon is sending
out a radio signal to inform all the radio enable devices in its range that
the beacon is there. It does not know how many beacons or receiving devices
are in the area and it does not connect with them. An example of beacon
operation is shown in Fig. 3.

Beacons broadcast signals at a certain interval and within a certain
transmission range. A beacon broadcasts a signal to all nearby devices that
can receive the Bluetooth signal, i.e. the devices that have a Bluetooth
receiver and the receiver is on. In order to collect the signal from the
beacon, it is necessary to have a device with a BLE receiver. This can be a
smartphone or a single-board computer like Raspberry Pi. Applications or
functions can be implemented based on the signal from the beacons. However,
these applications are running on the hosting device, i.e. a smartphone or a
Raspberry Pi, and not on the beacon.

Beacons are using BLE. The way how the peripheral device announces its
existence to the other devices is the opposite of how it is in the original
Bluetooth Classic. BLE enables a peripheral device to transmit an
advertisement packet without being paged by the master/ central device [24].
Due to this communication model, it is possible to construct energy-efficient
transmitters. Moreover, when two BLE 4.0 devices are paired, they waste less
battery power because the connection is dormant unless critical data is being
shared. With the previous generation of Bluetooth, it was best to shut down
your hardware when it was not in use. the Bluetooth Special Interest Group
estimates between 1 and 2 years of battery power in some devices with
Bluetooth 4.0.

Figure 3: A BLE beacon broadcasting a signal to the nearby devices. Each
device can receive the signal and take an action in response.

###  V-B Configuration parameters.

BLE beacons have configuration parameters and a set of values that can
determine their performance and their utility for different applications. Some
of these parameters are important when beacons are used in micro-location
applications.

  * •

Transmission power. Transmission power is the required power to broadcast the
beacon signal. As in every wireless device, transmission power directly
affects the transmission range. The higher the transmission power, the longer
the signal range of the beacon. This is an important trade-off for most of the
beacon applications. Technically, a beacon’s range can reach up to 70 m
however, the battery might only last for six months. If the transmission range
is constrained to 2 m, then the beacon might go up to two years without the
need of battery replacement. A small transmission power can also increase the
required number of beacons to cover an area while a large transmission power
can increase the collisions and the interference. As it can be inferred, an
optimal transmission range can help to extend the lifetime of the beacons and
minimize the battery replacement cost. At the same time, it can minimize
unnecessary collisions with other beacons in the area.

  * •

Advertising interval. Advertising interval is another characteristic that
affects the overall performance of beacons. It describes the time between
consecutive transmissions. Applications that need to notify or detect the
users that are moving in the area, they need a short advertising interval
while applications where the users are moving less frequently, they might
improve their performance with a longer advertising interval. Similar to the
transmission power, the advertising interval affects beacons performance. The
shorter the interval the more stable the signal from the beacon. At the same
time, the shorter the interval the higher the power consumption. Once again,
there is a trade-off between beacon performance and power consumption.

  * •

BLE beacon protocols. Beacon protocols are standards of BLE communication.
Each protocol describes the structure of the advertisement packet beacons
broadcast. It is necessary for the advertisement packet to have the MAC
address of the beacon. There are different protocols, the most popular of
which are the following:

    * –

iBeacon. Apple’s iBeacon was the first BLE Beacon technology to come out [4].
iBeacon is a proprietary, closed standard. It broadcasts four pieces of
information:

      1. 1.

A Universally Unique IDentifier (UUID) that identifies the beacon.

      2. 2.

A Major number identifying a subset of beacons within a large group.

      3. 3.

A Minor number identifying a specific beacon within the subset.

      4. 4.

A transmission power level in 2’s complement, indicating the signal strength
one meter from the device. This number must be calibrated for each device by
the user or manufacturer.

iBeacon has a simple implementation and large documentation but it has fewer
features in comparison with the following protocols. iBeacon works with iOS
and Android, but are native to iOS.

    * –

Eddystone. Eddystone was announced from Google and it is another protocol that
defines a BLE message format for proximity beacon messages [5]. Eddystone
protocol is able to transmit four different frame-types:

      1. 1.

UID which is used to identify the individual beacon.

      2. 2.

URL which can be a website link that redirects to a website that is secured
using SSL, eliminating the need for a mobile app.

      3. 3.

TLM which includes sensor and administrative data from the beacon through
telemetry. Examples include the beacon’s battery level and its temperature.

      4. 4.

EID which is an encrypted ephemeral identifier that changes periodically at a
rate determined during the initial registration with a web service. This frame
type is intended for use in security and privacy-enhanced devices.

Eddystone also works with both iOS and Android.

    * –

AltBeacon. It is an open source beacon protocol [25] that was designed by
Radius Networks. It has the same functionality as an iBeacon but it is not
company-specific. This makes AltBeacon compatible with any mobile operating
platform and more flexible since they have customizable source code.

    * –

GeoBeacon. It is another open source beacon protocol, designed for usage in
GeoCaching applications [26]. It has a very compact type of data storage.
GeoBeacon can provide high-resolution coordinates and it is also compatible
with different mobile operating platforms.

###  V-C Hardware Solutions

There is a great variety of BLE beacon devices on the market, most of them
operate on batteries such as Estimote, Kontakt, Gimbal, Glimworm, BlueCats and
more [27], while there are also solar power beacons like the CYALKIT- E02.
Each has its own unique features, such as additional sensors, battery life,
reconfigurability, and dimensions, though all fundamentally work the same.

At the physical layer, BLE transmits in the 2.4 GHz Industrial, Scientific,
and Medical (ISM) band with 40 channels, each 2.0 MHz wide. From those
channels, 37 are used to exchange the data among paired devices and 3 channels
are designated for broadcasting advertisements. These 3 channels are primarily
used by beacons and are chosen deliberately to minimize any collision with the
WiFi channels. Beacon broadcasts its advertisement packet repetitively based
on the selected advertising interval while hopping over the 3 designated
channels [28].

###  V-D Beacon Advantages for micro-location

Beacons have several advantages to be used for micro-location.

  * •

Size. Beacons are small in size hence, they can be placed almost in any indoor
environment with no problem. They can be placed behind the ceiling, under
objects or even on the walls.

  * •

Energy efficiency. The great advantage of beacons comes from the energy
efficient BLE protocol. At the same time, as the market of the beacons
increases so does the different design approaches. There are small beacons
that work with one single coin cell battery, there are beacons with two AA
batteries and there are solar powered beacons [29]. The lifetime of these
beacons can be up to two years without the need of battery replacement [27].

  * •

Cost. Most of the beacons in the market are cheap. Many beacons can be placed
in a complex indoor environment to improve micro-location with minimum cost.

  * •

Inferences. Beacons use BLE and they will not interfere with other wireless
infrastructures in the area.

  * •

Passive mode. Beacons are broadcasters that do not do anything else besides
sending a piece of information. The logic behind each signal is done by the
supporting device, such as smartphones. Beacon signals are used by
applications to trigger events and call actions, allowing the users to
interact with physical things. All the implementation is done on the device
while the beacons just broadcast the signal.

  * •

Platform independent. Beacons can be used with iOS and Android devices. Each
platform required different protocols which have different packet layouts but
most platforms are able the listen to the different protocols.

##  VI Using BLE Beacons for micro-location.

In this section, a scenario where beacons can be used for micro-location is
described, followed by some experimental results.

###  VI-A Test case.

Museums and art galleries usually provide visitors either with paper booklets
or with audio guides. Unfortunately, interest may vary from person to person,
while each visitors experience is also related to the available time to visit
most of the exhibits. Interactive and personalized museum tour needs to be
developed. BLE beacons as a newly emerged technology can enhance visitors
experience through micro-location, as shown in Fig. 4.

Figure 4: BLE beacons used in an interactive museum scenario.

Beacons can offer museums an opportunity to provide context to visitors
through a smartphone application. Micro-location technology can make locating
an exhibit much easier while at the same time it can provide personalized
suggestions to the user, regarding the available exhibits. A mobile
application can be developed which interacts with the available beacons.

When visitors are close to an exhibit, they can get all the necessary
information about the exhibit on their smartphone or BLE enabled mobile device
in general. The application can also provide a recommendation to the visitor
on the next exhibit they can visit, based on their current location and
interest. At the same time, the application can provide an optimal tour of the
museum based on each individual preferences. Beacon will also provide useful
analytics to the museum. The number of visitors per exhibit can be collected,
without violating visitors privacy. This analytics can be used to improve
exhibits visibility.

The use of beacons provides several advantages for the museum and the
visitors:

  * •

Promote exploration. The application can encourage users to visit exhibits in
different places of the museum. Usually, visitors tend to spend most of their
time in exhibits near to the entrance, missing the opportunity to explore
exhibits across all the museum. Micro-location can help them identify the room
they are interested in faster.

  * •

Personalized tour. When a user is interested in an exhibit, the application
can provide a guided tour based on that interest. An interactive and
personalized tour with exhibits from the same chronological period or within
the same interest category can be provided to the user, who would miss them
without the application.

  * •

Tour optimization. For many visitors, the available time to spend in the
museum is limited. The real-time analytics from the beacons can be used to
provide an optimal route for the visitor, based on the available time for the
visit.

  * •

Data analytics. Beacons analytics can be used to improve general visitor
experience. There are exhibits that are missed due to their location while
there are exhibits that are overcrowded during a specific time of the day.
Analytics can be used to optimize both cases and enhance visitors experience.

###  VI-B Experimental results.

In this subsection, we showcase the performance of the BLE beacons through a
simple experimentation. We used BLE beacons from Gimbal Series 21 to examine
the proximity estimation performance along with a smartphone which was used to
collect the signals [30]. The Kalman filter (KF-ST) was applied on the
collected data offline.

The Kalman filter estimation is shown in Fig. 5. These are the collected RSSI
values when the smartphone is 2 m away from the beacon. It is clear that
Kalman filter can minimize the effect of interference between the beacon and
the smartphone, such as when people are moving between the two communicating
devices.

Figure 5: Received RSSI values in two meters from the BLE beacon.

To examine the performance of the Kalman filter, we placed the smartphone in
ten different distances, starting from 50 cm and up to 5 m, increasing the
distance 50 cm every time. In every location, we collected data in the
smartphone for approximately two minutes. The average RSSI values are shown in
Fig. 6. When the smartphone is close to the beacon, the accuracy is high
enough without filtering. As the distance increases, the accuracy without
filtering decreases while the standard deviation of the data increases as
well. Interference and noise affect the data transmission hence, as the
distance between the communicating devices increase, these factors increase as
well. Kalman filtering helps to keep the data close to the real value while
the standard deviation is smaller. The use of Kalman filter helps minimize the
effect of random noise and interference during the experiment.

Figure 6: Distance estimation in ten different spots from the BLE beacon.

We further examine the error between the estimated distance and the real
distance, and the number of occurrences of each group of errors as shown in
Fig. 7. Without filtering, the error is within 3 m from the real location when
distances up to 5 m are tested. In many applications that use micro-location
such as the test case, the location error should be smaller. A smaller error
comes when Kalman filter is used. The error is within 1 m from the real
location, which can be acceptable from many micro-location applications.

(a) Raw data.

(b) Kalman filter.

Figure 7: Histogram of experimental error.

##  VII Concluding Remarks.

This paper provides an overview of wireless technologies that can be used for
micro-location in smart buildings, with the use of IoT devices. BLE is among
the most energy-efficient technologies. BLE beacons are small, low-cost
devices that can be used for localization. Unfortunately, they are prone to
interference due to their wireless nature. Signal processing techniques, such
as Kalman filters can be used to enhance their performance.

A case study of BLE beacons in an interactive museum is also discussed.
According to the experimental results, signal processing techniques can
enhance beacons performance and provide accurate micro-location in the era of
IoT.

## Author Biographies

Petros Spachos (IEEE Senior Member, Ph.D., University of Toronto, 2014) is an
Assistant Professor at School of Engineering, University of Guelph, Canada. He
received the Diploma degree in Electronic and Computer Engineering from the
Technical University of Crete, Greece, and the M.A.Sc. and the Ph.D. degree
both in Electrical and Computer Engineering from the University of Toronto,
Canada. His research interests include experimental wireless networking and
mobile computing with a focus on wireless sensor networks, smart cities and
the Internet of Things. He is a senior member of the IEEE.

Ioannis Papapanagiotou (IEEE Senior Member, Ph.D., NC State University, 2012)
is an engineering manager at Netflix, a research assistant professor at the
University of New Mexico, a graduate faculty at Purdue University, and a
mentor at the International Accelerator. He holds a dual Ph.D. degree in
Computer Engineering and Operations Research. His main focus is on distributed
systems, cloud computing, and the Internet of Things. He has been awarded the
NetApp faculty fellowship and established an Nvidia CUDA Research Center at
Purdue University. Ioannis has also received the IBM Ph.D. Fellowship and
Academy of Athens Ph.D. Fellowship for his Ph.D. research, and best paper
awards in several IEEE conferences for his academic contributions. Ioannis has
authored a number of research articles and patents. Ioannis is a senior member
of ACM and IEEE.

Konstantinos N. Plataniotis (IEEE Fellow, Ph.D., Florida Institute of
Technology, 1997) is a Professor and Bell Canada Chair in Multimedia with the
ECE Department at the University of Toronto. He is a registered professional
engineer in Ontario, Fellow of the IEEE and Fellow of the Engineering
Institute of Canada. He has served as Signal Processing Society Vice President
for Membership (2014 -2016) and the Editor-in-Chief for IEEE Signal Processing
Letters (2009-2011). He was Technical Co-Chair for ICASSP 2013 and the General
Co-Chair for 2017 IEEE GlobalSIP. He co-Chairs the 2018 IEEE International
Conference on Image Processing, and the 2021 IEEE International Conference on
Acoustics, Speech and Signal Processing.

## References

  * [1] S. Sadowski and P. Spachos, “Rssi-based indoor localization with the internet of things,” _IEEE Access_ , pp. 1–1, 2018.
  * [2] F. Zafari, I. Papapanagiotou, and K. Christidis, “Microlocation for internet-of-things-equipped smart buildings,” _IEEE Internet of Things Journal_ , vol. 3, no. 1, pp. 96–112, Feb. 2016.
  * [3] D. Sikeridis, B. P. Rimal, I. Papapanagiotou, and M. Devetsikiotis, “Unsupervised crowd-assisted learning enabling location-aware facilities,” _IEEE Internet of Things Journal_ , pp. 1–1, 2018.
  * [4] Apple. (2014, June 2) Getting started with ibeacon. [Online]. Available: https://developer.apple.com/ibeacon/Getting-Started-with-iBeacon.pdf
  * [5] Google. (2017, July 5) Google eddystone format. [Online]. Available: https://developers.google.com/beacons/eddystone
  * [6] J. Bordoy, A. Traub-Ens, A. Sadr, J. Wendeberg, F. H flinger, C. Schindelhauer, and L. Reindl, “Bank of kalman filters in closed-loop for robust localization using unsynchronized beacons,” _IEEE Sensors Journal_ , vol. 16, no. 19, pp. 7142–7149, Oct. 2016.
  * [7] F. Zafari, I. Papapanagiotou, M. Devetsikiotis, and T. Hacker, “An ibeacon based proximity and indoor localization system,” _arXiv preprint arXiv:1703.07876v2_ , 2017.
  * [8] F. Zafari and I. Papapanagiotou, “Enhancing ibeacon based micro-location with particle filtering,” in _2015 IEEE Global Communications Conference (GLOBECOM)_ , Dec. 2015, pp. 1–7.
  * [9] C. Takahashi and K. Kondo, “Accuracy evaluation of an indoor positioning method using ibeacons,” in _2016 IEEE 5th Global Conference on Consumer Electronics_ , Oct. 2016, pp. 1–2.
  * [10] Z. Chen, Q. Zhu, H. Jiang, and Y. C. Soh, “Indoor localization using smartphone sensors and ibeacons,” in _2015 IEEE 10th Conference on Industrial Electronics and Applications (ICIEA)_ , June 2015, pp. 1723–1728.
  * [11] Institute for Building Efficiency. [Online]. Available: http://www.buildingefficiencyinitiative.org/
  * [12] The Working Group for WLAN Standards. IEEE 802.11 Wireless Local Area Networks. [Online]. Available: http://www.ieee802.org/11/
  * [13] P. Baronti, P. Pillai, V. W. Chook, S. Chessa, A. Gotta, and Y. F. Hu, “Wireless sensor networks: A survey on the state of the art and the 802.15.4 and zigbee standards,” _Computer Communications_ , vol. 30, no. 7, pp. 1655 – 1695, 2007, wired/Wireless Internet Communications. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0140366406004749
  * [14] R. Want, “An introduction to rfid technology,” _IEEE Pervasive Computing_ , vol. 5, no. 1, pp. 25–33, Jan. 2006.
  * [15] Bluetooth Special Interest Group. Bluetooth 5.0 core specification. [Online]. Available: https://www.bluetooth.com/specifications/bluetooth-core-specification/bluetooth5
  * [16] M. Kusens, “Electronic location identification and tracking system with beacon clustering,” Sep. 26 2017, uS Patent 9,774,991.
  * [17] E. Khorov, A. Lyakhov, A. Krotov, and A. Guschin, “A survey on ieee 802.11ah: An enabling networking technology for smart cities,” _Computer Communications_ , vol. 58, pp. 53 – 69, 2015, special Issue on Networking and Communications for Smart Cities. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0140366414002989
  * [18] Lora Alliance Technology. Lorawan. [Online]. Available: https://lora-alliance.org/about-lorawan
  * [19] B. Kennedy, G. Taylor, and P. Spachos, “Ble beacon based patient tracking in smart care facilities,” in _2018 IEEE International Conference on Pervasive Computing and Communications Workshops (PerCom Workshops)_ , March 2018\.
  * [20] M. Ayyash, H. Elgala, A. Khreishah, V. Jungnickel, T. Little, S. Shao, M. Rahaim, D. Schulz, J. Hilt, and R. Freund, “Coexistence of wifi and lifi toward 5g: concepts, opportunities, and challenges,” _IEEE Communications Magazine_ , vol. 54, no. 2, pp. 64–71, February 2016.
  * [21] M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking,” _Signal Processing, IEEE Transactions on_ , vol. 50, no. 2, pp. 174–188, 2002\.
  * [22] P. M. Djuric, J. H. Kotecha, J. Zhang, Y. Huang, T. Ghirmai, M. F. Bugallo, and J. Miguez, “Particle filtering,” _Signal Processing Magazine, IEEE_ , vol. 20, no. 5, pp. 19–38, 2003.
  * [23] I. Guvenc, C. Abdallah, R. Jordan, and O. Dedoglu, “Enhancements to RSS based indoor tracking systems using kalman filters,” in _In GSPx & International Signal Processing Conference_, 2003.
  * [24] F. M. P. Kriz and T. Kozel, “Improving indoor localization using bluetooth low energy beacons,” in _Mobile Information Systems_ , March 2016, pp. 1–7.
  * [25] AltBeacon. (2016, June 7) Specifications on altbeacon. [Online]. Available: https://github.com/AltBeacon/spec
  * [26] Geobeacon. [Online]. Available: https://github.com/Tecno-World/GeoBeacon
  * [27] Aislelabs. (2015) The hitchhikers guide to ibeacon hardware: A comprehensive report. [Online]. Available: http://www.aislelabs.com/ reports/beacon-guide/
  * [28] E. Vlugt. (2013) Bluetooth low energy, beacons and retail. [Online]. Available: , http:// global.verifone.com/media/3603729/bluetooth-low-energy-beacons-retail-wp.pdf
  * [29] P. Spachos and A. Mackey, “Energy efficiency and accuracy of solar powered ble beacons,” _Computer Communications_ , vol. 119, pp. 94 – 100, 2018. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0140366417309891
  * [30] A. Mackey and P. Spachos, “Performance evaluation of beacons for indoor localization in smart buildings,” in _2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP)_ , Nov. 2017, pp. 823–827.


# Capacitive crosstalk in gate-based dispersive sensing of spin qubits

Eoin G. Kelly  Alexei Orekhov  Nico Hendrickx  Matthias Mergenthaler  Felix
Schupp  Stephan Paredes  IBM Research – Zurich, Säumerstrasse 4, CH-8803
Rüschlikon, Switzerland  Rafael S. Eggli  Andreas V. Kuhlmann  Department of
Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel,
Switzerland  Patrick Harvey-Collard  Andreas Fuhrer  Gian Salis
<EMAIL_ADDRESS>IBM Research – Zurich, Säumerstrasse 4, CH-8803 Rüschlikon,
Switzerland

(August 28, 2024)

###### Abstract

In gate-based dispersive sensing, the response of a resonator attached to a
quantum dot gate is detected by a reflected radio-frequency signal. This
enables fast readout of spin qubits and tune up of arrays of quantum dots, but
comes at the expense of increased susceptibility to crosstalk, as the
resonator can amplify spurious signals and induce fluctuations in the quantum
dot potential. We attach tank circuits with superconducting NbN inductors and
internal quality factors $Q_{\mathrm{i}}>1000$ to the interdot barrier gate of
silicon double quantum dot devices. Measuring the interdot transition in
transport, we quantify radio-frequency crosstalk that results in a ring-up of
the resonator when neighbouring plunger gates are driven with frequency
components matching the resonator frequency. This effect complicates qubit
operation and scales with the loaded quality factor of the resonator, the
mutual capacitance between device gate electrodes, and with the inverse of the
parasitic capacitance to ground. Setting qubit frequencies below the resonator
frequency is expected to substantially suppress this type of crosstalk.

High-bandwidth readout of spin qubits can be achieved by radio-frequency (RF)
reflectometry [1], where an RF signal is reflected off a resonator that is
either connected directly to a gate of the quantum dot (QD) that defines the
spin qubit, or to additional QDs that serve as charge sensors [2, 3]. The
former approach is known as gate-based sensing and avoids the additional
footprint of the charge sensors and the necessary leads connected to them [4,
5, 6, 7, 8]. Rather than detecting the absolute charge state of the spin qubit
system, this method detects charge susceptibility in the form of a quantum
capacitance [9]. Pauli spin blockade leads to a spin-dependent tunneling
between two neighbouring QDs, which is seen as a variation in the resonator
load capacitance [10] and thereby enables the readout of spin states.

The sensitivity of gate-based dispersive readout can be improved by increasing
the internal quality factor $Q_{\textrm{i}}$ and reducing the parasitic
capacitance $C_{\textrm{p}}$ of the resonator [11]. Both can be achieved by
using a superconducting inductor fabricated from a thin film of a high-kinetic
inductance material such as NbN, which also enables a small resonator
footprint and is compatible with the magnetic fields necessary for spin qubit
operation [12, 13, 8, 14, 15].

In this work, we show that attaching a high-quality factor resonator to the
gate of a spin qubit device drastically increases the sensitivity of that gate
to crosstalk with control pulses applied to neighbouring gates, e.g., to
manipulate the spin state via electric-dipole spin resonance (EDSR) [16, 17,
18, 19, 20, 21, 22]. We introduce a method of quantifying such AC crosstalk in
a dispersive readout setup and apply it to a double QD in a Si fin field-
effect transistor (finFET) device with a tank circuit connected to the barrier
gate. The tank circuit is composed of a high-kinetic-inductance NbN nanowire,
providing a high $Q_{\mathrm{i}}\approx 1500$ and a low $C_{\mathrm{p}}$. The
resonator is excited whenever control pulses on neighbouring gate lines
spectrally overlap with its resonance frequency, giving rise to a strongly
amplified modulation of the barrier gate and thereby of the double-QD
confinement potential. The amplitude of the crosstalk voltage induced on the
barrier gate is measured in transport by analysing the corresponding
broadening of an interdot charge transition line. This provides an efficient
way of characterising AC crosstalk on the device level that does not rely on
the tune-up and calibration of qubits [23, 24, 25, 26]. In addition to
unintentional driving of neighbouring qubits [27], this ring-up is expected to
lead to increased qubit decoherence in systems with strong spin-orbit
interaction (SOI), intrinsic to holes in Si [19, 16] and Ge [28, 22], which
possess highly anisotropic electric-field dependent $g$-tensors [29, 30, 31].

We find that in our device, the main contribution to this type of crosstalk
comes from capacitance between the bondpads of neighbouring gate electrodes.
Our electrical circuit model predicts that the crosstalk scales proportionally
with the loaded quality factor $Q_{\mathrm{l}}$ and with the ratio between the
crosstalk capacitance $C_{\mathrm{ct}}$ and $C_{\mathrm{p}}$. Above the
resonator frequency $f_{\textrm{r}}$, the crosstalk induced on the barrier
gate saturates at a value of $C_{\mathrm{ct}}/C_{\mathrm{p}}$, whereas for
frequencies below $f_{\mathrm{r}}$ it is suppressed. These findings can aid in
the the design of spin qubit architectures with gate-based readout.

The QD devices consist of a fin patterned from bulk silicon, along with two
gate layers each consisting of a silicon-oxide dielectric and a TiN gate metal
patterned in a self-aligned process [32]. For the first device (device A), a
double QD is formed by accumulating holes underneath gates P1 and P2 in the
second gate layer (GL2), while the tunnel coupling between the dots is tuned
by the barrier gate B in the first gate layer (GL1), see Fig. 1(a). Lead gates
LL and LR (GL1) are used to accumulate charge reservoirs which are tunnel
coupled to the respective dots and contacted to source and drain contacts made
of PtSi. All gates and the contacts are connected to tungsten bondpads through
vias in a silicon oxide encapsulation layer. Devices similar to the ones used
here have been shown to host hole spin qubits with operation of both single-
and two-qubit gates [16, 33].

High-kinetic-inductance superconducting nanowire inductors with a wire width
of 400 nm are fabricated by dry etching a $\sim$$12\text{\,}\mathrm{nm}$ thick
film of NbN exhibiting a nominal sheet inductance of 66 pH per square,
deposited on an intrinsic silicon substrate by DC magnetron sputtering. A
scanning electron microscopy image of a typical inductor is shown in Fig.
1(d). One end of such an inductor with a nominal inductance of
$1.5\text{\,}\mathrm{\SIUnitSymbolMicro H}$ was connected to the barrier gate
of device A by wirebonding from the inductor chiplet to the QD chiplet. The
other end of the inductor was connected to a (multiplexed) readout line on the
PCB [Fig. 1(a)]. Such multi-module assemblies consisting of a resonator
chiplet separate to the spin qubit device chiplet offer advantages in terms of
separation of fabrication steps and choice of materials [34, 15, 35].

The resonator formed by this inductor together with $C_{\mathrm{p}}$ has a
resonance frequency $f_{\textrm{r}}$ of $\sim$$299\text{\,}\mathrm{MHz}$. The
magnitude and phase response is plotted in Fig. 1(b). The superconducting
nature of the inductor leads to a large $Q_{\textrm{i}}$ of $1480\pm 480$, as
determined from a fit of the resonance circle in the complex plane with the
method outlined in [36]. The large error bar in $Q_{\mathrm{i}}$ arises from
the resonator being overcoupled, with a loaded quality factor of
$Q_{\textrm{l}}=370\pm 50$ that is dominated by the coupling quality factor of
$Q_{\textrm{c}}=500\pm 56$. Modeling the parasitic capacitance as a lumped
element attached to the devices side of the inductor provides an estimate of
$C_{\mathrm{p}}=$ $0.19\text{\,}\mathrm{pF}$. The resonance frequency does not
exactly match the point at which the magnitude of the reflection coefficient
$|S_{11}|$ is minimal as displayed in Fig. 1(b). This is due to a rotation of
the resonance circle in the complex plane, typically attributed to non-ideal
interference effects [37].

Figure 1:  (a) Reflectometry setup with a NbN nanowire inductor on a separate
Si chiplet, wire bonded on one side to the barrier gate of a Si finFET double
QD device, and on the other side to a multiplexed readout line on a printed
circuit board (PCB). Total parasitic capacitance $C_{\mathrm{p}}$ is given by
capacitance to ground $C_{\mathrm{p},0}$ and sum of crosstalk capacitances
$C_{\mathrm{ct}i}$. (b) Normalised reflection amplitude and phase of the
resonator and corresponding fit, giving $Q_{\textrm{i}}=1478\pm 480$ and
$Q_{\textrm{c}}=500\pm 56$. (c) Charge stability diagram of the finFET double-
QD at fixed $V_{\mathrm{B}}=-0.845\,\textrm{V}$ obtained by reflectometry at
$299.3\text{\,}\mathrm{MHz}$ revealing the few-hole regime with
$(N_{1},N_{2})$ holes in the two QDs. (d) False-coloured scanning electron
microscope image of a similar NbN nanowire inductor with a wire width of 400
nm.  Figure 2: (a) Charge stability diagram at the $(0,1)-(1,0)$ transition,
detected in the phase of $V_{\mathrm{out}}$ by indirect excitation on gate P1.
(b) Finite bias triangles measured in $I_{\mathrm{SD}}$ at the $(0,1)-(1,0)$
transition, and axis of the detuning voltage $V_{\varepsilon}$. (c)
$I_{\mathrm{SD}}$ as a function of $V_{\mathrm{P2}}$ while varying the AC
drive amplitude $\Delta V_{\mathrm{B}}$ applied to gate B at frequency
$f_{\textrm{r}}$. The peak broadening (white dots, arrow shows twice the
broadening amplitude) is a measure of the resonator ring-up amplitude on gate
B. (d) Linecuts of $I_{\mathrm{SD}}$ for two different sinusoidal drive
amplitudes $\Delta V_{\mathrm{B}}$ and their corresponding fits. (e) Extracted
ring-up amplitude $\delta V_{\mathrm{B}}$ on gate B as a function of $\Delta
V_{\mathrm{B}}$, yielding an average amplification of $\Delta V_{\mathrm{B}}$
by a factor of $100\pm 3$ (solid line). (f) $\delta V_{\mathrm{B}}$ as a
function of AC drive amplitudes $\Delta V_{\mathrm{P1}}$ ($\Delta
V_{\mathrm{P2}}$) applied to neighbouring gates P1 (P2), demonstrating
amplification of the drive signal by factors 26.2 (20.3). In (e) and (f),
diamonds (circles) represent data obtained for DC scans of the interdot lines
along P1 (P2).

The resonator can be operated as a gate-based dispersive sensor by probing the
reflected signal at resonance while sweeping the plunger gates. The obtained
charge stability diagram of the double QD system is shown in Fig. 1(c) with
clear dot-to-lead transitions visible down to the last hole. Interdot
transitions are also visible because gate B has different lever arms to the
two dots. The signal amplitude is smaller than that of the dot-to-lead
transitions.

Surprisingly, the charge stability diagram can also be observed in $\Delta
V_{\mathrm{out}}$ when driving a neighbouring plunger gate. Such an indirect
excitation of the resonator indicates the presence of a finite crosstalk
capacitance $C_{\textrm{ct}}$ between that plunger gate and gate B. The
measured phase of $\Delta V_{\mathrm{out}}$ when exciting an AC amplitude
$\Delta V_{\mathrm{P1}}$ on gate P1 at resonance is shown in Fig. 2(a) around
the $(0,1)-(1,0)$ charge region. We note that such crosstalk is distinct from
the harmonic voltage conversion observed in Ref. [38], where it is induced by
transitions of single charges at interdot and dot-to-lead transitions.

The crosstalk in this device is quantified by measuring the broadening of the
interdot charge transition line in the source-drain current $I_{\mathrm{SD}}$
and relating this to a ring-up peak voltage amplitude $\delta V_{\mathrm{B}}$
on gate B. We first determine the line broadening when directly exciting the
tank circuit with an oscillation amplitude $\Delta V_{\mathrm{B}}$ [see
Fig.1(a)] at a frequency that is on resonance with the tank circuit. The
typical bias triangles with a bright interdot line are shown in a map of
$I_{\mathrm{SD}}$ in Fig. 2(b) for an applied source-drain bias
$V_{\textrm{SD}}$ of $5\text{\,}\mathrm{mV}$ and with $\Delta
V_{\mathrm{B}}=0$. Fig. 2(c) shows scans of the interdot line along the DC
voltage $V_{\mathrm{P2}}$ and for different amplitudes $\Delta
V_{\mathrm{B}}$. The broadening is fit by a time-averaged sinusoidally-shifted
Lorentzian function, see Fig. 2(d) and supplementary material Sec. I for
details. The amplitude of the broadening (i.e., half the distance between the
extreme positions of the fitted Lorentzian peaks) is more than 400 times
larger than $\Delta V_{\mathrm{B}}$ and is a consequence of a resonant ring-up
of the voltage on gate B. The amplitude $\delta V_{\mathrm{B}}$ of this ring-
up is obtained by multiplying the broadening amplitude scanned along
$V_{\mathrm{P}i}$ by $\beta_{\mathrm{B,P}i}$, where $\beta_{\mathrm{B,P}i}$
denotes the ratio between voltage changes on gate B and on gate $\mathrm{P}i$
required to stay on the interdot line. We find $\beta_{\mathrm{B,P2}}=-0.23$
and $\beta_{\mathrm{B,P1}}=0.40$, see Sec. II of the supplementary material.

Figure 2(e) shows the obtained amplitude $\delta V_{\mathrm{B}}$ as a function
of $\Delta V_{\mathrm{B}}$ by individually fitting the scans of the interdot
line along P1 and P2 and adjusting for the relative voltage ratios
$\beta_{\mathrm{B,P1}}$ and $\beta_{\mathrm{B,P2}}$ respectively. We find a
linear relationship with an average amplification factor of $100\pm 3$. This
value is consistent with the amplification factor as calculated from numerical
simulation of the readout circuit (see Sec. IV of the supplementary material).

Using the same method but for indirect excitation of the tank circuit by a
resonant AC drive with amplitude $\Delta V_{\mathrm{P1}}$ ($\Delta
V_{\mathrm{P2}}$) on gate P1 (P2), we find a significant ring-up of gate B
with an amplitude $\delta V_{\mathrm{B}}$ that is 26.2 (20.3) times larger
than the exciting amplitude on the P1 (P2) gate [Fig. 2(f)]. As we show next,
this crosstalk-induced excitation of the resonator and thereby of the
potential on gate B occurs for any signal that contains spectral components
within the bandwidth of the resonator frequency.

Figure 3:  (a) Measurement of $I_{\mathrm{SD}}$ while applying a square
(upper) and sawtooth (lower) wave with frequency $f_{\mathrm{bb}}$ and peak
amplitude at gate P1 of $3.15\text{\,}\mathrm{m}\mathrm{V}$. (b) Fitted peak
broadening $\delta V_{\varepsilon}$, revealing the amplitudes of the harmonics
$n=f_{\mathrm{r}}/f_{\mathrm{bb}}$ of the sawtooth wave applied. (c) Typical
Rabi pulse sequence with a square wave component (period $T$) alternating
between the manipulation point $V_{\textrm{m}}$ and the readout point
$V_{\textrm{r}}$, superposed with a sinusoidal qubit drive pulse of length
$t$. (d) Peak broadening $\delta V_{\varepsilon}$ when Rabi pulses with
frequency $f_{\mathrm{drive}}$ and length $t$ are applied repeatedly with
period $T=$$1\text{\,}\mathrm{\SIUnitSymbolMicro s}$ and peak amplitude of
$0.7\text{\,}\mathrm{mV}$ at gate P1. (e) Same as (d) but varying the baseband
pulse period $T$.

In spin qubit experiments, baseband signals are typically applied to plunger
gates when transitioning from a qubit manipulation point to a readout point in
charge configuration space. The repetition of such baseband signals may lead
to harmonics that excite the resonator gate. To illustrate this effect, we
apply a square wave [Fig. 3(a), upper] or sawtooth wave [Fig. 3(a), lower] of
varying frequency $f_{\mathrm{bb}}$ to gate P1. We fit the broadening of the
interdot line $\delta V_{\varepsilon}$ by sweeping the interdot detuning
voltage $V_{\varepsilon}$ (see Sec. III of the supplementary material for
definition) across the $(0,1)-(1,0)$ transition, as indicated in Fig. 2(b).
When varying the baseband frequency $f_{\mathrm{bb}}$, a crosstalk-induced
broadening of the interdot line is observed every time a harmonic $n$ of the
signal matches the resonator frequency $f_{\mathrm{r}}$, see Fig. 3(a). Figure
3(b) shows the fitted interdot peak broadening $\delta V_{\varepsilon}$ as a
function of $f_{\mathrm{r}}/f_{\mathrm{bb}}$ for a sawtooth wave. Excitations
occur whenever $f_{\mathrm{bb}}\crossproduct n=f_{\textrm{r}}$, indicated by
the white dots in Fig. 3(a), with the expected Fourier amplitudes scaling with
$\frac{1}{n}$. Similarly, only odd harmonics are observed for a square wave
excitation. The adverse effect of this ring-up on the operation of QDs as
qubits can be reduced for larger $n$ by filtering the baseband pulses.
However, fast ramp times between different charge states may be necessary to
fulfill diabaticity requirements when initialising spin states via rapid
adiabatic passage [39, 40].

When manipulating a spin qubit, a series of sinusoidal drive pulses are
applied to the gates, see Fig. 3(c). We focus on a typical Rabi experiment
where the duration $t$ of the drive pulses is varied in order to observe Rabi
oscillations induced by EDSR. The fitted interdot peak broadening for such a
pulse train with a repetition rate 1/$T$ of $1\text{\,}\mathrm{MHz}$ is shown
in Fig. 3(d), where both the drive pulse frequency $f_{\mathrm{drive}}$ and
the pulse duration $t$ are swept. The baseband amplitude is set to zero. The
observed peak broadening as a function of $f_{\mathrm{drive}}$ and $t$ matches
the sinc function $\sin(x)/x$ expected for the Fourier transformation of a
sinusoidal pulse of a finite length, with $x=\pi
t(f_{\mathrm{drive}}-f_{\mathrm{r}})$. Note that the observed pattern
resembles but is not related to the typical Rabi chevron pattern observed when
varying $f_{\mathrm{drive}}$ and $t$ for pulses applied to a qubit. While the
fringes of the sinc function can be reduced by using a Gaussian envelope of
the drive pulses, the broadening of the Fourier spectrum remains and therefore
extends the crosstalk into a bandwidth $1/t$ around $f_{\mathrm{r}}$. We
additionally resolve the effect of the repetition of the pulses with period
$T$ as lines spaced by the repetition rate, as displayed in Fig. 3(f) for a
fixed $t=$250\text{\,}\mathrm{ns}$$.

Figure 4: (a) Measured signal $|\Delta V_{\mathrm{out}}|$ (dots) transmitted
through resonator attached to gate B of device B (inset) when applying an AC
drive to one of the neighbouring gates $i$. The simulated transmitted signal
$|\Delta V_{\mathrm{out}}|$ is indicated as solid lines. (b) Simulated
amplification factor $\delta V_{\mathrm{B}}$/$\Delta V_{\mathrm{P2}}$ of the
crosstalk as a function of the drive frequency on the neighbouring gate P2.

The indirect excitation of the resonator can be reproduced in a discrete-
element circuit model, see Sec. V of the supplementary material for details of
the circuit diagram. The resonator is indirectly excited by a drive signal on
the neighbouring gate through a mutual capacitance $C_{\mathrm{ct}}$. The
total parasitic capacitance to ground, $C_{\mathrm{p}}$, is given by the sum
of $C_{\mathrm{p},0}$ and $C_{\mathrm{ct}}$, which is kept constant at
$0.19\text{\,}\mathrm{pF}$. The amplification factors between $\delta
V_{\mathrm{B}}$ and $\Delta V_{\mathrm{P1}}$ ($\Delta V_{\mathrm{P2}}$) are
found to match those in Fig. 2(f) by choosing $C_{\mathrm{ct}}$ equal to
$16.0\text{\,}\mathrm{fF}$ ($11.9\text{\,}\mathrm{fF}$) when exciting on P1
(P2). This can mostly be accounted for by the mutual capacitance between the
corresponding bondpads, for which we find values of $12.1\text{\,}\mathrm{fF}$
($7.3\text{\,}\mathrm{fF}$) using Ansys Maxwell (Table 1). We assign the
remaining coupling capacitance of around $4\text{\,}\mathrm{fF}$ to mutual
capacitance between bond wires and to the PCB side of our setup. Capacitances
between neighbouring gates at the device level were found to be on the order
of $\sim$ $0.5\text{\,}\mathrm{fF}$ and therefore negligible.

To further confirm that the observed crosstalk is dominated by the capacitance
between bondpads, another Si finFET device (device B) was measured. This
device has two nanogates in GL1 and three nanogates in GL2, as depicted in the
inset of Fig. 4(b), with a $750\text{\,}\mathrm{nH}$ inductor attached to one
of the first-gate-layer gates, named gate B. This leads to the formation of a
resonator with a resonance frequency of $454\text{\,}\mathrm{MHz}$. Three of
the other gates, labelled gate 1 (nearest neighbour), gate 2 (next-nearest
neighbour), and gate 3 (next-next nearest neighbour), were individually
excited with an AC drive tone of varying frequency, and the voltage amplitude
$|\Delta V_{\mathrm{out}}|$ transmitted through the resonator was measured.
The transmitted signal peaks at the resonator frequency. The peak amplitude is
a measure for the voltage amplitude at gate B induced by AC crosstalk. A
discrete-element circuit model (see Sec. V of the supplementary material) was
used to model the results. In this model, the various crosstalk capacitances
between the different gates were obtained from electrostatic simulations,
taking into account that the bondpad layout where the order of the bondpads is
the same as that of the nanogates. The measured $|\Delta V_{\mathrm{out}}|$ is
presented in Fig. 4(a) along with the simulated results from the circuit model
(solid lines). The transmission magnitude decreases with the distance of the
excited gate to gate B, in good agreement with the simulation. We thus
attribute the dominant source of crosstalk to the capacitance between gate
electrodes in the bondpad layer.

The frequency dependence of the AC crosstalk $\delta V_{\mathrm{B}}/\Delta
V_{\mathrm{P2}}$ is simulated for device A, see Fig. 4(b) for the case of
$C_{\mathrm{ct}}=$11.9\text{\,}\mathrm{fF}$$. The maximum value of 20.3 is
reached at $f_{\mathrm{r}}$. For our typical case, $C_{\mathrm{p}}\gg
C_{\mathrm{ct}}$, this maximum value is well approximated by
$Q_{\mathrm{l}}C_{\mathrm{ct}}/C_{\mathrm{p}}$. Below $f_{\mathrm{r}}$, the
crosstalk reaches a minimum and is suppressed. Above $f_{\mathrm{r}}$, it
saturates at a value of approximately $C_{\mathrm{ct}}/C_{\mathrm{p}}=6\%$ .
This suggests that placing qubit frequencies well below the resonator
frequency is optimal to suppress crosstalk in architectures with gate-based
dispersive qubit readout. Note that our model does not account for higher-
order resonator modes, where additional resonances at higher frequencies would
lead to crosstalk amplitudes well above this saturation value.

| P1 | B | P2
---|---|---|---
P1 | $51.8\text{\,}\mathrm{f}\mathrm{F}$ | $12.1\text{\,}\mathrm{f}\mathrm{F}$ | $1.7\text{\,}\mathrm{f}\mathrm{F}$
B | $12.1\text{\,}\mathrm{f}\mathrm{F}$ | $42.0\text{\,}\mathrm{f}\mathrm{F}$ | $7.3\text{\,}\mathrm{f}\mathrm{F}$
P2 | $1.7\text{\,}\mathrm{f}\mathrm{F}$ | $7.3\text{\,}\mathrm{f}\mathrm{F}$ | $41.9\text{\,}\mathrm{f}\mathrm{F}$
Table 1:  Simulated capacitance matrix between the bondpads of the gate
electrodes for device A.

In conclusion, gate-based dispersive sensing has been used to measure the
charge stability diagram of a Si finFET double QD device down to the last hole
with a superconducting NbN tank circuit attached to the barrier gate. The high
quality factor of the resonator comes at the expense of increased AC crosstalk
where a ring-up of the gate electrode attached to the tank circuit is observed
when other gate electrodes are driven with frequency components matching the
resonator frequency. We have demonstrated a method of quantifying such
crosstalk by measuring the source-drain current through the double QD device
and fitting the broadening of the interdot current peak due to the ring-up of
the resonator gate.

These findings identify some limitations of gate-based dispersive sensing as a
qubit readout technique. The crosstalk amplitude on resonance scales as
$Q_{\mathrm{l}}C_{\mathrm{ct}}/C_{\mathrm{p}}$ and reaches the limit
$C_{\mathrm{ct}}/C_{\mathrm{p}}$ above the resonator frequency
$f_{\mathrm{r}}$. Pulses applied to QD gates that contain spectral components
above $f_{\mathrm{r}}$ should therefore be avoided, even more so if higher
modes of the resonator exist. Below the resonator frequency, crosstalk is
found to be largely suppressed. This suggests to place qubit frequencies well
below $f_{\mathrm{r}}$ to increase the bandwidth for qubit driving. In
general, crosstalk can be reduced by optimising the bondpad layout, improving
signal routing or using differential signalling schemes [41, 42, 27].
Unfortunately, an increase of $C_{\mathrm{p}}$ or decrease of
$Q_{\mathrm{l}}$, while reducing the crosstalk, decreases the sensitivity of
the readout circuit to the device capacitance, i.e., the spin readout signal.
One way to overcome this would be to reduce the interaction of the spin qubits
with the resonator in the qubit manipulation phase, e.g. using a transistor
between tank circuit and QD gate [43] or by switching $C_{\mathrm{p}}$ by
varactor diodes.

See supplementary material for details on the fit function for the broadening
of the interdot peak, measured ratios of voltage changes on each gate to stay
on the interdot line, definition of detuning voltage, circuit models of both
devices and the device bondpad layout.

This project has received funding from the European Union’s Horizon 2020
research and innovation programme under the Marie Skłodowska-Curie grant
agreement number 847471, and by the NCCR SPIN under grant number 51NF40-180604
of the Swiss National Science Foundation. We thank the Cleanroom Operations
Team of the Binnig and Rohrer Nanotechnology Center (BRNC) for their help and
support.

## References

  * Vigneau  _et al._ [2023] F. Vigneau, F. Fedele, A. Chatterjee, D. Reilly, F. Kuemmeth, F. Gonzalez-Zalba, E. Laird, and N. Ares, Appl. Phys. Rev. 10, 021305 (2023).
  * Barthel  _et al._ [2010] C. Barthel, M. Kjærgaard, J. Medford, M. Stopa, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Phys. Rev. B 81, 161308 (2010).
  * House  _et al._ [2016] M. G. House, I. Bartlett, P. Pakkiam, M. Koch, E. Peretz, J. van der Heijden, T. Kobayashi, S. Rogge, and M. Y. Simmons, Phys. Rev. Appl. 6, 044016 (2016).
  * Colless  _et al._ [2013] J. I. Colless, A. C. Mahoney, J. M. Hornibrook, A. C. Doherty, H. Lu, A. C. Gossard, and D. J. Reilly, Phys. Rev. Lett. 110, 046805 (2013).
  * Pakkiam  _et al._ [2018] P. Pakkiam, A. V. Timofeev, M. G. House, M. R. Hogg, T. Kobayashi, M. Koch, S. Rogge, and M. Y. Simmons, Phys. Rev. X 8, 041032 (2018).
  * Crippa  _et al._ [2019] A. Crippa, R. Ezzouch, A. Aprá, A. Amisse, R. Laviéville, L. Hutin, B. Bertrand, M. Vinet, M. Urdampilleta, T. Meunier, M. Sanquer, X. Jehl, R. Maurand, and S. De Franceschi, Nat. Comm. 10, 2776 (2019).
  * Urdampilleta  _et al._ [2019] M. Urdampilleta, D. J. Niegemann, E. Chanrion, B. Jadot, C. Spence, P.-A. Mortemousque, C. Bäuerle, L. Hutin, B. Bertrand, S. Barraud, R. Maurand, M. Sanquer, X. Jehl, S. De Franceschi, M. Vinet, and T. Meunier, Nat. Nanotechnol. 14, 737 (2019).
  * Zheng  _et al._ [2019] G. Zheng, N. Samkharadze, M. L. Noordam, N. Kalhor, D. Brousse, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Nat. Nanotechnol. 14, 742 (2019).
  * Mizuta  _et al._ [2017] R. Mizuta, R. M. Otxoa, A. C. Betz, and M. F. Gonzalez-Zalba, Phys. Rev. B 95, 045414 (2017).
  * Petersson  _et al._ [2010] K. D. Petersson, C. G. Smith, D. Anderson, P. Atkinson, G. A. C. Jones, and D. A. Ritchie, Nano Lett. 10, 2789–2793 (2010).
  * Ahmed  _et al._ [2018] I. Ahmed, J. A. Haigh, S. Schaal, S. Barraud, Y. Zhu, C. Lee, M. Amado, J. W. A. Robinson, A. Rossi, J. J. L. Morton, and M. F. Gonzalez-Zalba, Physical Review Applied 10, 014018 (2018).
  * Samkharadze  _et al._ [2016] N. Samkharadze, A. Bruno, P. Scarlino, G. Zheng, D. P. DiVincenzo, L. DiCarlo, and L. M. K. Vandersypen, Phys. Rev. Appl. 5, 044004 (2016).
  * Niepce  _et al._ [2019] D. Niepce, J. Burnett, and J. Bylander, Phys. Rev. Appl. 11, 044014 (2019).
  * Yu  _et al._ [2021] C. X. Yu, S. Zihlmann, G. Troncoso Fernández-Bada, J.-L. Thomassin, F. Gustavo, E. Dumur, and R. Maurand, Appl. Phys. Lett. 118, 054001 (2021).
  * Ibberson  _et al._ [2021] D. J. Ibberson, T. Lundberg, J. A. Haigh, L. Hutin, B. Bertrand, S. Barraud, C.-M. Lee, N. A. Stelmashenko, G. A. Oakes, L. Cochrane, J. W. Robinson, M. Vinet, M. F. Gonzalez-Zalba, and L. A. Ibberson, PRX Quantum 2, 020315 (2021).
  * Camenzind  _et al._ [2022] L. C. Camenzind, S. Geyer, A. Fuhrer, R. J. Warburton, D. M. Zumbühl, and A. V. Kuhlmann, Nat. Electron. 5, 178 (2022).
  * Koppens  _et al._ [2006] F. H. L. Koppens, C. Buizert, K. J. Tielrooij, I. T. Vink, K. C. Nowack, T. Meunier, L. P. Kouwenhoven, and L. M. K. Vandersypen, Nature 442, 766 (2006).
  * Nadj-Perge  _et al._ [2010] S. Nadj-Perge, S. M. Frolov, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Nature 468, 1084 (2010).
  * Maurand  _et al._ [2016] R. Maurand, X. Jehl, D. Kotekar-Patil, A. Corna, H. Bohuslavskyi, R. Laviéville, L. Hutin, S. Barraud, M. Vinet, M. Sanquer, and S. De Franceschi, Nat. Comm. 7, 13575 (2016).
  * Watzinger  _et al._ [2018] H. Watzinger, J. Kukučka, L. Vukušić, F. Gao, T. Wang, F. Schäffler, J.-J. Zhang, and G. Katsaros, Nat. Comm. 9, 3902 (2018).
  * Hendrickx  _et al._ [2020a] N. W. Hendrickx, D. P. Franke, A. Sammak, G. Scappucci, and M. Veldhorst, Nature 577, 487 (2020a).
  * Froning  _et al._ [2021] F. N. M. Froning, L. C. Camenzind, O. A. H. van der Molen, A. Li, E. P. A. M. Bakkers, D. M. Zumbühl, and F. R. Braakman, Nat. Nanotechnol. 16, 308 (2021).
  * Xue  _et al._ [2019] X. Xue, T. Watson, J. Helsen, D. Ward, D. Savage, M. Lagally, S. Coppersmith, M. Eriksson, S. Wehner, and L. Vandersypen, Phys. Rev. X 9, 021011 (2019).
  * Undseth  _et al._ [2023] B. Undseth, X. Xue, M. Mehmandoost, M. Rimbach-Russ, P. T. Eendebak, N. Samkharadze, A. Sammak, V. V. Dobrovitski, G. Scappucci, and L. M. Vandersypen, Phys. Rev. Appl. 19 (2023).
  * Weinstein  _et al._ [2023] A. J. Weinstein, M. D. Reed, A. M. Jones, R. W. Andrews, D. Barnes, J. Z. Blumoff, L. E. Euliss, K. Eng, B. H. Fong, S. D. Ha, D. R. Hulbert, C. A. Jackson, M. Jura, T. E. Keating, J. Kerckhoff, A. A. Kiselev, J. Matten, G. Sabbir, A. Smith, J. Wright, M. T. Rakher, T. D. Ladd, and M. G. Borselli, Nature 615, 817 (2023).
  * Lawrie  _et al._ [2023] W. I. Lawrie, M. Rimbach-Russ, F. van Riggelen, N. W. Hendrickx, S. L. Snoo, A. Sammak, G. Scappucci, J. Helsen, and M. Veldhorst, Nat. Comm. 14 (2023).
  * Heinz and Burkard [2021] I. Heinz and G. Burkard, Phys. Rev. B 104 (2021).
  * Hendrickx  _et al._ [2020b] N. W. Hendrickx, W. I. L. Lawrie, L. Petit, A. Sammak, G. Scappucci, and M. Veldhorst, Nat. Comm. 11, 3478 (2020b).
  * Malkoc  _et al._ [2022] O. Malkoc, P. Stano, and D. Loss, Physical Review Letters 129, 247701 (2022).
  * Piot  _et al._ [2022] N. Piot, B. Brun, V. Schmitt, S. Zihlmann, V. P. Michal, A. Apra, J. C. Abadillo-Uriel, X. Jehl, B. Bertrand, H. Niebojewski, L. Hutin, M. Vinet, M. Urdampilleta, T. Meunier, Y.-M. Niquet, R. Maurand, and S. D. Franceschi, Nat. Nanotechnol. 17, 1072 (2022).
  * Hendrickx  _et al._ [2023] N. Hendrickx, L. Massai, M. Mergenthaler, F. Schupp, S. Paredes, S. Bedell, G. Salis, and A. Fuhrer,  arXiv:2305.13150 (2023).
  * Geyer  _et al._ [2021] S. Geyer, L. C. Camenzind, L. Czornomaz, V. Deshpande, A. Fuhrer, R. J. Warburton, D. M. Zumbühl, and A. V. Kuhlmann, Appl. Phys. Lett. 118, 104004 (2021).
  * Geyer  _et al._ [2022] S. Geyer, B. Hetényi, S. Bosco, L. C. Camenzind, R. S. Eggli, A. Fuhrer, D. Loss, R. J. Warburton, D. M. Zumbühl, and A. V. Kuhlmann, arXiv:2212.02308 (2022).
  * Holman  _et al._ [2021] N. Holman, D. Rosenberg, D. Yost, J. L. Yoder, R. Das, W. D. Oliver, R. McDermott, and M. A. Eriksson, Npj Quantum Inf. 7, 1 (2021).
  * von Horstig  _et al._ [2023] F.-E. von Horstig, D. J. Ibberson, G. A. Oakes, L. Cochrane, N. Stelmashenko, S. Barraud, J. A. W. Robinson, F. Martins, and M. F. Gonzalez-Zalba, arXiv:2304.13442 (2023) .
  * Probst  _et al._ [2015] S. Probst, F. Song, P. Bushev, A. Ustinov, and M. Weides, Rev. of Sci. Instrum. 86, 024706 (2015).
  * Khalil  _et al._ [2012] M. S. Khalil, M. J. A. Stoutimore, F. C. Wellstood, and K. D. Osborn, J. Appl. Phys. 111, 054510 (2012).
  * Oakes  _et al._ [2022] G. A. Oakes, L. Peri, L. Cochrane, F. Martins, L. Hutin, B. Bertrand, M. Vinet, A. G. Saiz, C. J. B. Ford, C. G. Smith, and M. F. Gonzalez-Zalba, arXiv:2211.14127 (2022) .
  * Taylor  _et al._ [2007] J. M. Taylor, J. R. Petta, A. C. Johnson, A. Yacoby, C. M. Marcus, and M. D. Lukin, Phys. Rev. B 76, 035315 (2007).
  * Harvey-Collard  _et al._ [2019] P. Harvey-Collard, N. T. Jacobson, C. Bureau-Oxton, R. M. Jock, V. Srinivasa, A. M. Mounce, D. R. Ward, J. M. Anderson, R. P. Manginell, J. R. Wendt, T. Pluym, M. P. Lilly, D. R. Luhman, M. Pioro-Ladrière, and M. S. Carroll, Phys. Rev. Lett. 122, 217702 (2019).
  * Blanvillain  _et al._ [2012] S. Blanvillain, J. I. Colless, D. J. Reilly, H. Lu, and A. C. Gossard, J. Appl. Phys. 112 (2012).
  * Machida  _et al._ [2023] M. Machida, R. Mizokuchi, J. Yoneda, T. Tomura, and T. Kodera, Jpn. J. Appl. Phys. 62 (2023).
  * Schaal  _et al._ [2018] S. Schaal, S. Barraud, J. J. L. Morton, and M. F. Gonzalez-Zalba, Phys. Rev. Appl. 9, 054016 (2018).