# Google COVID-19 Search Trends Symptoms Dataset: Anonymization Process
Description (version 1.0)

Shailesh Bavadekar<EMAIL_ADDRESS>Andrew Dai
<EMAIL_ADDRESS>John Davis  covid-19-search-
<EMAIL_ADDRESS>Damien Desfontaines  covid-19-search-trends-
<EMAIL_ADDRESS>Ilya Eckstein<EMAIL_ADDRESS>Katie Everett<EMAIL_ADDRESS>Alex Fabrikant
<EMAIL_ADDRESS>Gerardo Flores  covid-19-search-
<EMAIL_ADDRESS>Evgeniy Gabrilovich  covid-19-search-trends-
<EMAIL_ADDRESS>Krishna Gadepalli  covid-19-search-trends-
<EMAIL_ADDRESS>Shane Glass<EMAIL_ADDRESS>Rayman Huang<EMAIL_ADDRESS>Chaitanya Kamath
<EMAIL_ADDRESS>Dennis Kraft  covid-19-search-
<EMAIL_ADDRESS>Akim Kumok  covid-19-search-trends-
<EMAIL_ADDRESS>Hinali Marfatia  covid-19-search-trends-
<EMAIL_ADDRESS>Yael Mayer<EMAIL_ADDRESS>Benjamin Miller<EMAIL_ADDRESS>Adam Pearce
<EMAIL_ADDRESS>Irippuge Milinda Perera
<EMAIL_ADDRESS>Venky Ramachandran
<EMAIL_ADDRESS>Karthik Raman  covid-19-search-
<EMAIL_ADDRESS>Thomas Roessler  covid-19-search-trends-
<EMAIL_ADDRESS>Izhak Shafran<EMAIL_ADDRESS>Tomer Shekel<EMAIL_ADDRESS>Charlotte Stanton
<EMAIL_ADDRESS>Jacob Stimes  covid-19-search-
<EMAIL_ADDRESS>Mimi Sun  covid-19-search-trends-
<EMAIL_ADDRESS>Gregory Wellenius  covid-19-search-trends-
<EMAIL_ADDRESS>Masrour Zoghi<EMAIL_ADDRESS>
###### Abstract

This report describes the aggregation and anonymization process applied to the
initial version of COVID-19 Search Trends symptoms dataset [1], a publicly
available dataset that shows aggregated, anonymized trends in Google searches
for symptoms (and some related topics). The anonymization process is designed
to protect the daily symptom search activity of every user with
$\varepsilon$-differential privacy for $\varepsilon$ = 1.68.

##  1 Introduction

The COVID-19 Search Trends symptoms dataset is a publicly available dataset
that shows aggregated, anonymized trends in Google searches for symptoms (and
some related topics). The dataset provides a daily or weekly time series for
each region showing the relative volume of searches for each symptom. Its goal
is to help researchers, public health experts and data analysts better
understand the impact of COVID-19, while protecting our users’ privacy. For
this purpose, the dataset covers approximately 400 symptoms, such as cough,
fever and difficulty breathing. To ensure strict privacy standards, all
published data is aggregated and anonymized, protecting each user’s symptom
search activity on a given day using a differentially private mechanism. No
personal data or individual searches are included in the dataset.

The data of the symptoms dataset reflect the volume of Google searches that
may be associated with a particular medical symptom. For this purpose, we
count the daily number of searches relating to that symptom within a given
geographic region and normalize this number based on the total search activity
in that region. The resulting dataset is either a daily or a weekly series
showing the relative frequency of searches for a particular symptom in a
particular region. The dataset covers the recent period and we’ll gradually
expand its range as part of regular updates.

Similar to the Google COVID-19 Community Mobility Reports [2, 3] and as
explained in greater technical detail below, the anonymization process of the
symptoms dataset is based on differential privacy [4], which is a well
established concept for producing data that satisfy formal privacy guarantees.
For this purpose, we intentionally perturb our data by adding random noise and
drop data that is deemed to be unreliable. The symptoms dataset is designed to
maintain the privacy of our users while releasing aggregated and anonymized
data that is as accurate and useful as possible.

The remainder of this report is structured as follows: First, we introduce
some basic concepts and terminology of the symptoms dataset. We then explain
how differential privacy is used to produce anonymized aggregates. Finally, we
elaborate on how the published data is built from anonymized aggregates.

##  2 Definitions

The following definitions explain some common terms and concepts that we use
throughout this report.

#### User

A user who did a web search on Google.

#### Symptom Search

A symptom search is a Google search query issued by a search user that relates
to a particular medical symptom or health condition. The symptoms we are
considering are compiled in a predefined list including medical issues such as
cough, fever and difficulty breathing.

#### Geographic Granularity

The COVID-19 Search Trends symptoms dataset is aggregated per geographic
region. Similarly to the Google COVID-19 Community Mobility Reports [2, 3], we
distinguish between three levels of geographic regions, which we call
granularity levels:

  * •

Granularity level 0 corresponds to data aggregated by country.

  * •

Granularity level 1 corresponds to data aggregated by top-level geopolitical
subdivisions (e.g., US states or equivalent geographical regions in other
countries).

  * •

Granularity level 2 corresponds to data aggregated by higher-resolution
granularity (e.g., US counties or equivalent geographical regions in other
countries).

Granularity levels 1 and 2 are defined differently in different countries to
account for the differences between countries’ public health systems. Note
that in general, the area of a geographic region gets smaller as the
granularity number increases. All regions of the symptoms dataset have an area
of at least 3km2.

#### Temporal Granularity

For each geographic region and symptom, the data is released either as daily
or weekly aggregates. The particular temporal granularity depends on the
quality of the data. In general, we try to provide daily aggregates whenever
possible. However, if the accuracy of our data is affected too much by our
privacy protections, we may choose to release weekly aggregates instead.
Weekly aggregates help to improve accuracy while maintaining the same level of
privacy. Since weekly aggregates are based on more data points, the noise
added for differential privacy introduces less relative error.

The decision between daily and weekly aggregates is made per symptom and
region based on the data available at the time of the initial release of the
symptoms dataset, and is made in a differentially private manner (more details
can be found in the final paragraph of this report). We keep the temporal
granularity fixed for a given region and symptom throughout the full time
range of the dataset release.

#### Differential Privacy

Let $A$ be a randomized algorithm for computing some metric over a given
dataset. In the context of this report, we consider a pair of datasets $D_{1}$
and $D_{2}$ neighboring if $D_{2}$ can be obtained from $D_{1}$ by adding or
removing a single user’s search activity on a given day. We then call $A$
$\varepsilon$-differentially private if for any pair of neighboring datasets
$D_{1}$ and $D_{2}$ and for all sets $S$ of the possible outputs of $A$111We
generate a fixed set of metrics (all $<$day, symptom, region$>$ combinations)
and add Laplace noise to all of them independent of whether they contain user
data or not. Thus, the released metrics satisfy ($\varepsilon$,
$\delta$)-differentially privacy, with $\delta=0$.:

$\textrm{Pr}[A(D_{1})\in S]\leq\exp(\varepsilon)\cdot\textrm{Pr}[A(D_{2})\in
S].$

##  3 Anonymizing User Data

The COVID-19 Search Trends symptoms dataset is based on anonymized counts
designed to protect personal data. More precisely, we protect every user’s
symptom search activity on a particular day with $\varepsilon$-differential
privacy for $\varepsilon=1.68$. The majority of this $\varepsilon$, $97.5\%$,
is used to anonymize symptom search counts, while $2.5\%$ is used to anonymize
general search activity for normalization purposes. See Figure 1 for a system
diagram of the anonymization process. All counts are anonymized by adding
appropriately scaled Laplace noise [5]. We generate this noise using our open-
source differential privacy library [6].

privacy boundaryoriginalqueriesper-user contributionnormalization count$<$day,
region$>$per-user contributionsymptom count$<$day, sym., region$>$daily
normalizationcount$<$day, region$>$weekly normalizationcount$<$week,
region$>$daily symptom count$<$day, sym., reg.$>$weekly symptom count$<$week,
sym., reg.$>$noisy dailynormalization count$<$day, region$>$noisy
weeklynormalization count$<$week, region$>$noisy daily/weeklysymptom
count$<$d./w., sym. reg.$>$publisheddaily/weekly metric$<$d./w., sym.
reg.$>$extractandboundextractandboundadd noiseadd noiseaggregateacross
usersaggregateacross usersdecide d./w.and add noisecompute metric andfilter
unreliableresult Figure 1: System diagram of the data generation and
anonymization process

###  3.1 Symptom Search Counts

To generate the symptoms dataset, we count the number of searches that relate
to a particular medical symptom and group them by date and geographical
region. As a result, each count corresponds to a triplet of $<$day, symptom,
region$>$. For each day and geographic granularity level, a user can
contribute at most once to any given count (per-symptom bound) and to no more
than three counts in total (cross-symptom bound). Similar to the process
described by Wilson et al. [7], we arbitrarily discard symptom searches of a
user that exceed their contribution bound. Approximately $75\%$ of users
search at most three symptoms per day, so the amount of data dropped is
relatively small.

As an example, assume that on June 3, 2020 a user made two searches related to
fever in Santa Clara county (CA), one search related to fever in San
Bernardino county (CA), one search related to fever in Clark county (NV), and
one search related to cough in Clark county (NV). The following table lists a
possible configuration of the user’s contribution to the respective counts
after contribution bounding.

level | count | contribution | bound type
---|---|---|---
0 |  $<$2020-06-03, fever, United States$>$ | 1 (originally 4) | per-symptom
0 |  $<$2020-06-03, cough, United States$>$ | 1 |
1 |  $<$2020-06-03, fever, California$>$ | 1 (originally 3) | per-symptom
1 |  $<$2020-06-03, fever, Nevada$>$ | 1 |
1 |  $<$2020-06-03, cough, Nevada$>$ | 1 |
2 |  $<$2020-06-03, fever, Santa Clara$>$ | 1 (originally 2) | per-symptom
2 |  $<$2020-06-03, fever, San Bernardino$>$ | 1 |
2 |  $<$2020-06-03, fever, San Bernardino$>$ | 1 |
2 |  $<$2020-06-03, fever, Clark$>$ | 1 |
2 |  $<$2020-06-03, cough, Clark$>$ | 0 (originally 1) | cross-symptom
Table 1: Example of per-symptom and cross-symptom contribution bounding

To protect a user’s daily symptom searches with $1.638$-differential privacy
($97.5\%$ of the total $\varepsilon$), we then add appropriately scaled
Laplace noise. In the case of daily granularity, the noise is added directly
to the respective count. In the case of weekly granularity, we first sum the
daily counts to obtain a weekly count and then add the noise to the weekly
count. The following table lists the noise parameterization for each
granularity level in terms of its scale b and standard deviation
$\sigma=\sqrt{2}b$. The total $\varepsilon$ sums up to $1.638$, i.e., the
privacy budget we spend on computing symptom searches.

level | noise added to daily or weekly count |  $\varepsilon$ per level
---|---|---
0 | $b=3/\varepsilon_{0}\approx 17.857\quad(\sigma\approx 25.254)$ | $\varepsilon_{0}=0.168$
1 | $b=3/\varepsilon_{1}\approx 8.108\quad(\sigma\approx 11.467)$ | $\varepsilon_{1}=0.37$
2 | $b=3/\varepsilon_{2}\approx 2.727\quad(\sigma\approx 3.857)$ | $\varepsilon_{2}=1.1$
Table 2: Noise parameters for daily and weekly symptom search counts

###  3.2 Normalization Counts

To normalize our data, we scale each daily or weekly symptom search count
proportional to the total search activity in the given geographical region
during the respective time period. We estimate the search activity based on
the number of unique users who have issued a search query in a particular
geographical region during a day. Consequently, each daily normalization count
corresponds to a tuple of $<$day, region$>$.

For each day and each geographic granularity level, a user can contribute to
at most one normalization count. Similarly to the symptom search counts, we
arbitrarily discard contributions that exceed this contribution limit.

The daily and weekly normalization counts are protected with
0.021-differential privacy each, or $0.042$-differential privacy in
combination ($2.5\%$ of the total $\varepsilon$). In the case of daily counts,
we add appropriately scaled Laplace noise to the respective count. In the case
of weekly counts, we first sum the respective daily counts and then add
Laplace noise to the sum. The following table lists the noise parameterization
for each granularity level in terms of its scale b and standard deviation
$\sigma=\sqrt{2}b$. Note that the total privacy budget sums up to $0.042$.

level | noise added to daily and weekly count |  $\varepsilon$ per level
---|---|---
0 | $b=1/\varepsilon^{\prime}_{0}\approx 434.783\quad(\sigma\approx 614.875)$ | $\varepsilon^{\prime}_{0}=0.0023$
1 | $b=1/\varepsilon^{\prime}_{1}\approx 212.766\quad(\sigma\approx 300.897)$ | $\varepsilon^{\prime}_{1}=0.0047$
2 | $b=1/\varepsilon^{\prime}_{2}\approx 71.429\quad(\sigma\approx 101.015)$ | $\varepsilon^{\prime}_{2}=0.014$
Table 3: Noise parameters for daily and weekly normalization counts

##  4 Reporting the Metrics

The daily or weekly data published in the COVID-19 Search Trends symptoms
dataset are based exclusively on the anonymized counts described in the
previous section. Due to the post-processing property of differential privacy,
the following process does not consume any privacy budget.

#### Computing the Reported Data

Given a particular geographic region, symptom and time interval (either day or
week), the normalized search count published in the COVID-19 Search Trends is
computed as

$c\cdot\max\\{(A/B),0\\}$

, where $A$ is the noisy symptom search count, $B$ is the normalization count
and $c$ is a scaling factor specific to the geographic region. For each
geographic region, $c$ is chosen in a way that maps the data in the initial
release of the symptoms dataset to values between 0 and 100. Because we keep
$c$ fixed, future releases may contain metrics that exceed the value of 100.
We also want to note that $c$ is determined purely based on noisy symptom
search counts and normalization counts, so no privacy budget is spent on its
computation.

#### Removing Unreliable Data

In some geographic regions, the noise added for differential privacy reasons
can introduce a disproportionate amount of uncertainty to a metric. Typically,
this happens when the respective symptom search count is empty or small. To
address this uncertainty, we only keep a metric if it has a chance of $50\%$
or more to be within $25\%$ points of its raw value, i.e., the metric before
adding noise.

More precisely, let $A$ be some noisy symptom search count obtained after
adding Laplace noise to the raw symptom search count $a^{*}$ (note that
$a^{*}$ is not noisy but still subject to contribution bounding). Similarly,
let $B$ be the corresponding noisy normalization count computed from the raw
count $b^{*}$. To decide whether the data associated with $A$ will be kept or
dropped we:

  * •

Compute a confidence interval $[l,r]$ based on $A$ and $B$ that contains
$a^{*}/b^{*}$ with a probability of at least $50\%$.

  * •

Keep the data if $|A/B-l|\leq 0.25\cdot A/B$ and $|A/B-r|\leq 0.25\cdot A/B$.
Otherwise drop it.

The confidence interval $[l,r]$ is entirely based on the anonymized counts $A$
and $B$. As a result, no privacy budget is spent on removing unreliable data.

#### Deciding Between Daily and Weekly Granularity

The decision whether a certain symptom is published at the daily or weekly
granularity within a given geographic region is based on the amount of data
for this symptom in that region. Intuitively, if metrics are available for
more than half of the days within the sample period from February 2020 to July
2020 (i.e., not dropped as unreliable, as explained in the previous section),
we want to produce data for this symptom at the daily resolution. Otherwise,
if too many daily metrics are dropped, we opt for the weekly resolution, which
is more reliable.

For the sake of usability, we make the decision between daily and weekly
granularity once and stick to it over the course of the entire data release.

To avoid consuming additional privacy budget, we switch between daily and
weekly granularity based on the anonymized volume of search activity. More
precisely, for each symptom we make our decision according to the following
process:

  * •

All level 0 regions are published with daily granularity.

  * •

We order all other regions that are of the same level and contained in the
same level 0 region by the total search activity, which we approximate based
on the anonymized normalization counts.

  * •

Starting with the geographic region that has the highest search activity, we
start publishing daily metrics according to the process described above.

  * •

We continue down the list of regions, by decreasing volume of search activity.
For each new region, we look at the last 20 regions we published222If less
than 20 regions were published, we only consider the regions published so
far.. If 11 or more had more than $50\%$ of metrics dropped in the time period
from February 2020 to July 2020, we switch from daily to weekly granularity
and publish weekly metrics for all regions from this point forward. Otherwise,
we publish the current region with daily granularity, and repeat the process.

Taking a majority vote over the last 20 regions mitigates potential outliers
in the ordering.

The key insight is that this process uses anonymised data only to order the
regions, i.e., the daily normalization counts. Thus the privacy budget we
spend on the ordering is already accounted for. Moreover, we never compute
anonymized daily and weekly symptom search counts for the same symptom and
region pair at the same time. This means we only spend privacy budget on one
of the two counts, resulting in the promised $\varepsilon=1.68$.

## References

  * [1] Google covid-19 search trends symptoms dataset.  https://goo.gle/covid19symptomdataset.
  * [2] Google covid-19 community mobility reports.  https://www.google.com/covid19/mobility/.
  * [3] Ahmet Aktay, Shailesh Bavadekar, Gwen Cossoul, et al.  Google covid-19 community mobility reports: Anonymization process description (version 1.0).  Technical report, Google, 2020.
  * [4] Differential privacy.  https://en.wikipedia.org/wiki/Differential_privacy.
  * [5] Laplace distribution.  https://en.wikipedia.org/wiki/Laplace_distribution.
  * [6] Google differential privacy library.  https://github.com/google/differential-privacy.
  * [7] Royce J. Wilson, Celia Yuxin Zhang, William Lam, Damien Desfontaines, Daniel Simmons-Marengo, and Bryant Gipson.  Differentially private sql with bounded user contribution.  Proceedings on Privacy Enhancing Technologies, 2020(2):230 – 250, 2020.


# A Hybrid Energy Harvesting Protocol for Cooperative NOMA: Error Performance
Approach

Faical Khennoufa, Khelil Abdellatif, Ferdi Kara, Hakan Kaya, Xingwang Li,
Khaled Rabie, and Halim Yanikomeroglu  F. Khennoufa and A. Khelil are with
Laboratory of Exploitation and Valorization of the Saharan Energetics
Resources (LEVRES), Department of Electrical Engineering, Echahid Hamma
Lakhdar University, El-Oued, Algeria, email:{khennoufa-faical, abdellatif-
<EMAIL_ADDRESS>Kara is with the Department of Computer Engineering,
Zonguldak Bulent Ecevit University, Zonguldak, Turkey, 67100, e-mail:
<EMAIL_ADDRESS>Kaya is with the Electical and Electronics Engineering,
Zonguldak Bulent Ecevit University, Zonguldak, Turkey, 67100, e-mail:
<EMAIL_ADDRESS>Li is with School of Physics and Electronic
Information Engineering, Henan Polytechnic University, Jiaozuo, China, e-mail:
<EMAIL_ADDRESS>Rabie is with the Department of Engineering,
Manchester Metropolitan University, Manchester M1 5GD, U.K. e-mail:
<EMAIL_ADDRESS>Yanikomeroglu is with the Department of Systems and
Computer Engineering, Carleton University, Ottawa, K1S 5B6, ON, Canada,
e-mail<EMAIL_ADDRESS>
###### Abstract

Cooperative non-orthogonal multiple access (CNOMA) has recently been adapted
with energy harvesting (EH) to increase energy efficiency and extend the
lifetime of energy-constrained wireless networks. This paper proposes a hybrid
EH protocol-assisted CNOMA, which is a combination of the two main existing EH
protocols (power splitting (PS) and time switching (TS)). The end-to-end bit
error rate (BER) expressions of users in the proposed scheme are obtained over
Nakagami-$m$ fading channels. The proposed hybrid EH (HEH) protocol is
compared with the benchmark schemes (i.e., existing EH protocols and no EH).
Based on the extensive simulations, we reveal that the analytical results
match perfectly with simulations which proves the correctness of the
derivations. Numerical results also show that the HEH-CNOMA outperforms the
benchmarks significantly. In addition, we discuss the optimum value of EH
factors to minimize the error probability in HEH-CNOMA and show that an
optimum value can be obtained according to channel parameters.

###### Index Terms:

BER, cooperative, EH, hybrid, NOMA.

##  I Introduction

Non-orthogonal multiple access (NOMA) is widely renowned for increasing the
number of users and improving spectral efficiency in next-generation wireless
networks [1]. Besides, NOMA can be easily integrated with other physical layer
schemes. Hence, the cooperative-NOMA (CNOMA) has been one of the most
investigated topics, recently due to its ability to increase spectral
efficiency, user fairness and expand network coverage [2]. On the other hand,
to increase the energy efficiency and recharge the battery-limited devices,
the energy harvesting (EH) in CNOMA has also received significant attention
[3]. In literature, there are two major protocols in EH: power splitting (PS)
and time switching (TS). In the PS protocol, the EH and information detection
will be performed simultaneously with a PS factor, whereas in TS protocol, the
EH and information detection will be implemented at different times slots [4].

In order to show the performance gain of EH-NOMA over NOMA without EH, the
ergodic capacity and outage probability of simultaneous wireless information
and power transfer (SWIPT) aided CNOMA (SWIPT-CNOMA) have been evaluated [5,
6, 7, 8, 9]. Through examining the previous works, although most of the
existing EH-CNOMA papers discuss investigating outage probability and ergodic
capacity, the error performance (one of the most important key performance
indicators (KPIs)) investigation is very limited. In [10, 11, 12], the error
performance of CNOMA with EH (with PS protocol) amplify-and-forward (AF) relay
has been performed. The authors of [13] evaluated the error performance of the
$m$th best relay selection in EH (with PS protocol) AF multiple relay-assisted
CNOMA. Then in [14], the authors investigate the error performance of CNOMA
with a EH relay (with TS protocol). As seen above discussion, the related EH-
CNOMA papers deal with only one EH harvesting protocol. However, a comparison
of the existing EH protocols is important to select the proper protocol to
guarantee the best performance in CNOMA. Regardless superiority of EH to
schemes without EH, it is possible to improve EH to reach the best
performance. In order to improve the energy efficiency of EH, an optimized
protocol called hybrid EH that combines PS and TS jointly has been proposed
and evaluated in terms of throughput [15]. According to the findings in [15],
the hybrid protocol outperforms both TS and PS protocols. The hybrid protocol
can become one of the important manners to improve EH performance in CNOMA.
The hybrid protocol has been evaluated in terms of ergodic capacity and outage
probability for CNOMA in [16, 17, 18].

To the best of the authors’ knowledge, most of the existing papers investigate
the EH-CNOMA schemes by using either TS or PS protocol and no work provides
hybrid EH for CNOMA in terms of bit error rate (BER). Nevertheless, the hybrid
protocol can improve the performance of EH [15], and it is considered as a
practical scheme, which is a combination of the existing EH protocols. In
addition, the BER performance of the EH-CNOMA schemes has not been studied
well by considering different EH protocol. Motivated by aforementioned
discussions, in this paper, we investigate a hybrid EH protocol in CNOMA (HEH-
CNOMA) in terms of BER. The main contributions of the paper are given as
follow.

  * •

We propose HEH-CNOMA scheme where the relay applies a hybrid EH protocol to
improve the performance of the existing EH schemes in CNOMA networks.

  * •

We also present three benchmark schemes (i.e., PS, TS and no EH) to evaluate
the performance of the proposed HEH-CNOMA. We derive the exact end-to-end BER
expressions for HEH-CNOMA and three benchmarks over Nakagami-$m$ fading
channels. The simulations validate the perfect match of the analysis. Based on
the extensive simulations, we reveal that the proposed HEH-CNOMA outperforms
all three benchmarks remarkably.

  * •

We also discuss the optimum values for EH parameters and power allocation
coefficient in HEH-CNOMA and we present that optimum values can be obtained to
improve performance of both users.

The rest of the paper is presented as follows. The considered HEH-CNOMA system
model is introduced along with three benchmark schemes. In Section III we
analyze the closed-forms BER of all schemes. The numerical results are
presented in Section IV to validate analysis and compare with the benchmarks.
Finally, Section V concludes the paper.

##  II System Model

We consider a CNOMA network consisting of a source (S), a decode-and-forward
(DF) relay (R), and two users named user 1 (U1) and user 2 (U2). We assume
that the R assists the users to receive the signal since the direct link
between source and users does not exist due to large path-loss or obstacles.
Each node is equipped with a single antenna. We suppose that the R node works
in half-duplex (HD) mode. All communication links are exposed to a
Nakagami-$m$ fading. The R node harvests energy from the radio frequency (RF)
signal transmitted by the source (i.e., using three EH protocols defined
below). In the second phase, the R node forwards the signal to two users using
the harvested energy. The transmission block period is $T$. The EH protocols,
namely i) PS; ii) TS; and iii) hybrid (i.e., proposed) and their operations
are described below.

  * •

PS: In the first $T/2$ time slot, the received signal’s power is split into
two parts at the R: The first part ($\rho$) is used to harvest energy, while
the second part (1-$\rho$) is utilized to decode data in the decoder (where
$\rho$ is the PS factor). The remaining time (i.e., $T/2$) is devoted to
delivering the data to the users.

  * •

TS: In the first $\beta T$ time slot, the R harvests energy, where
$0\leq\beta\leq 1$ and $\beta$ is the TS factor. Then, in the first
$(1-\beta)T\textfractionsolidus 2$ of the remaining time, the S sends a
superimposed coding (SC) information to the R. Then, in the last
$(1-\beta)T\textfractionsolidus 2$ time slot, the R uses the harvested energy
to deliver this information signal to the users.

  * •

Hybrid (proposed): In the first $\beta T$ time slot, the R harvests energy as
being in TS mode, where $0\leq\beta\leq 1$. Then, the S transmits an SC
information to the R in the first $(1-\beta)T\textfractionsolidus 2$ of the
remaining time. Also, during this first $(1-\beta)T\textfractionsolidus 2$
time period, the R harvest energy from the received information, where 0
$\leq\rho\leq 1$ ($\rho$ is the PS factor for energy harvesting during the
first $(1-\beta)T\textfractionsolidus 2$ at the R). Subsequently, the R uses
the harvested energy from $\beta T$ plus $(1-\beta)T\textfractionsolidus 2$
time slots to forward the information signal to the users in the last
$(1-\beta)T\textfractionsolidus 2$.

  * •

No EH: The R is not capable of harvesting energy, and it uses its own energy
source (e.g., battery). The S and the R cover half of the communication (T/2
time), and both consume equal power during these data transfers.

At the S, the messages of users are combined in an SC information signal with
different power levels according to the users’ channel gain111In the NOMA
system, the S or R combines the users’ messages in an SC signal with different
power levels according to the channel gains for each user, where the user with
higher channel gain will mostly have less power. Thus, we take into account
that the U2 has a higher channel gain than U1, i.e., $|h_{1}|^{2}<|h_{2}|^{2}$
and the R receives this information signal in the first phase. Thus, the
received information signal by the R node is given as

$y_{r}=\sqrt{P_{s}\varpi}(\sqrt{\alpha_{1}}s_{1}+\sqrt{\alpha_{2}}s_{2})h_{r}+n,$
(1)

where $\varpi$ is the coefficient that indicates how much of the source power
is dedicated to information transfer, it will be $(1-\rho)$ for PS and hybrid
mode whereas equals to 1 for TS and no-EH modes. $s_{1}$ and $s_{2}$ are the
U1 and U2 signals, respectively. $\alpha_{1}$ and $\alpha_{2}$ are the power
allocation coefficients of U1 and U2, respectively in which
$\alpha_{1}>\alpha_{2}$, such that $\alpha_{1}+\alpha_{2}=1$. $P_{s}$ is the
transmit power. $h_{r}$ is the Nakagami-$m$ fading channel coefficient222The
envelope of $h_{r}$ and $h_{k}$ follows Nakagami-$m$ fading with $\Omega_{r}$
and $\Omega_{k}$ spread and $m_{r}$ and $m_{k}$ shape parameters. between S-R.
$n\sim\mathcal{CN}(0,\sigma^{2})$ is the additive white Gaussian noise (AWGN)
at R. When the information signal is received, the $R$ node decodes the
$s_{1}$ firstly. Then, through the SIC, $s_{2}$ is recovered.

For fairness, we consider the total consumed energy in all protocols is equal
to $\epsilon_{T}$. Thus, $\epsilon_{T}$ is consumed equally by the S and R in
the no-EH mode, while it is consumed only by the S in EH protocols, the source
power is expressed as

$P_{s}=\phi P_{T},\ \text{where}\ P_{T}=\epsilon_{T}/T,$ (2)

where $\phi$ is equal to 1 for no-EH, 2 for PS and $\frac{2}{\beta+1}$ for TS
and hybrid. In EH protocols, the harvested energy during the power transfer in
each protocol is given as

$E_{h}=\left\\{\begin{array}[]{lll}\eta
P_{s}\rho\frac{T}{2}|h_{r}|^{2},&\mbox{PS},\\\ \eta P_{s}\beta
T|h_{r}|^{2},&\mbox{TS},\\\ \eta
P_{s}(\frac{2\beta+\rho(1-\beta)T)}{2})|h_{r}|^{2},&\mbox{Hybrid},\\\
\end{array}\right.$ (3)

where $\eta$ ($0<\eta<1$) is the energy conversion efficiency factor. Thus,
the transmit power of the relay through the harvested energy is given by

$P_{r}=\left\\{\begin{array}[]{ll}P_{s}|h_{r}|^{2}\Psi,&\mbox{PS, TS and
Hybrid},\\\ P_{s},&\mbox{no EH},\end{array}\right.$ (4)

where

$\Psi=\left\\{\begin{array}[]{lll}\eta\rho,&\mbox{PS},\\\
\nicefrac{{2\eta\beta}}{{(1-\beta)}},&\mbox{TS},\\\
\eta(\rho+\nicefrac{{2\beta}}{{(1-\beta)}}),&\mbox{Hybrid}.\end{array}\right.$
(5)

Based on the received information signal, the R implements maximum likelihood
detection (MLD)/successive interference cancellation (SIC), to detect $s_{1}$
and $s_{2}$ symbols respectively.Based on the signals decoded in the previous
phase, the R implements a new SC signal and by using the harvested energy, it
forwards this new SC signal to the users. The received information at the
users is given by

$y_{k}=\sqrt{P_{r}\varpi}(\sqrt{\alpha_{1}}s_{1}+\sqrt{\alpha_{2}}s_{2})h_{k}+n,\
k={1,2},$ (6)

where $h_{k}$, $k={1,2}$ is the Nakagami-$m$ fading channel coefficient
between $R-$Uk. Through the information signal received by users, the U1
detects its symbols $s_{1}$ directly, while the U2 use the SIC to detect its
symbols $s_{2}$.

##  III Performance analysis

In this section, over Nakagami-$m$ fading channels, we derive the closed-form
BER of the two phases. Then, we obtain the end-to-end (e2e) BER expressions
for each user. At both S and R, a binary phase-shift keying (BPSK) modulation
is utilized to obtain the $s_{1}$ and $s_{2}$ signals. Hence, two different
energy levels with similar probabilities could be presented. By using a MLD,
for all EH protocols and no EH, the R detects $s_{1}$ firstly by treating
$s_{2}$ as noise. Thereafter, $s_{2}$ is detected using the SIC. Then, the R
implements an SC signal again for detected $s_{1}$ and $s_{2}$ symbols and
forwards it to users by using the harvested energy (i.e., for the case of the
EH protocols) or its own power (i.e., case of no EH). Through MLD, U1 detects
its own symbols $s_{1}$, whereas U2 uses a SIC to identify its symbols
$s_{2}$. By using the common probability of independent error event in two
phases, the e2e BER at each user is given as in [19] by

$P_{e2e,k}(e)=1-\left.(1-P_{r,k}(e)\right.)\left.(1-P_{k}(e)\right.),\
k={1,2},$ (7)

where $P_{r,k}(e)$ is the BER of Uk at the relay. $P_{k}(e)$ is the BER at Uk
in the second phase.

###  III-A BER in the first phase

Based on the discussion above (i.e., for EH and no EH), R detects $s_{1}$ in
the first step. The BER of $s_{1}$ at R, by following the steps in [20], can
be given as

$P_{r,1}(e)=\frac{1}{2}\sum_{{i}=1}^{2}\mathrm{Q}(\sqrt{\varpi\gamma\zeta_{i}|h_{r}|^{2}}),$
(8)

where $\gamma=\frac{P_{s}}{\sigma^{2}}$,
$\zeta_{i}=[(\sqrt{\alpha_{1}}+\sqrt{\alpha_{2}})^{2},(\sqrt{\alpha_{1}}-\sqrt{\alpha_{2}})^{2}]$.
The average BER (ABER) of (8) over a Nakagami-$m$ fading channel by using [21]
is given as

$\begin{split}&P_{r,1}(e)=\frac{1}{2}\sum_{{i}=1}^{2}\frac{1}{\sqrt{2\pi}}\frac{\Gamma({m_{r}+0.5})}{\Gamma(m_{r}+1)}\\\
&\times(\frac{\sqrt{\varpi\gamma\zeta_{i}\delta/2m_{r}}}{(1+\sqrt{\varpi\gamma\zeta_{i}\delta/2m_{r}})^{(m_{r}+0.5)}})\nabla_{1}(m_{r},\varpi\gamma\zeta_{i}\delta),\\\
\end{split}$ (9)

where
$\nabla_{1}(m_{r},\varpi\gamma\zeta_{i}\delta)=_{2}F_{1}(1,m_{r}+0.5,m_{r}+1,\frac{2m_{r}}{2m_{r}+\varpi\gamma\zeta_{i}\delta})$
and $\delta=\Omega_{r}$. ${}_{2}F_{1}(.,.;.,.)$ is the Gauss hypergeometric
function.

We also need to analyze the BER performance of the correct and erroneous SIC
as [20] to find the BER of $s_{2}$ at R. Thus, the BER performance of $s_{2}$
at R is given by

$P_{r,2}(e)=\frac{1}{2}\sum_{{j}=1}^{5}\nu^{j}\mathrm{Q}(\sqrt{\varpi\gamma\zeta_{j}|h_{r}|^{2}}),$
(10)

where $\nu^{j}=[2,-1,1,1,-1]$,
$\zeta_{j}=[\alpha_{2},(\sqrt{\alpha_{1}}+\sqrt{\alpha_{2}})^{2},(\sqrt{2\alpha_{1}}+\sqrt{\alpha_{2}})^{2},(\sqrt{\alpha_{1}}-\sqrt{\alpha_{2}})^{2},(2\sqrt{\alpha_{1}}-\sqrt{\alpha_{2}})^{2}]$.
By using [21], the ABER of (10) over the Nakagami-$m$ fading channel can be
given as

$\begin{split}&P_{r,2}(e)=\frac{1}{2}\sum_{{j}=1}^{5}\nu^{j}\frac{1}{\sqrt{2\pi}}\frac{\Gamma({m_{r}+0.5})}{\Gamma(m_{r}+1)}\times\\\
&(\frac{\sqrt{\varpi\gamma\zeta_{j}\delta/2m_{r}}}{(1+\sqrt{\varpi\gamma\zeta_{j}\delta/2m_{r}})^{(m_{r}+0.5)}})\nabla_{2}(m_{r},\varpi\gamma\zeta_{j}\delta),\\\
\end{split}$ (11)

where
$\nabla_{2}(m_{r},\varpi\gamma\zeta_{j}\delta)=_{2}F_{1}(1,m_{r}+0.5,m_{r}+1,\frac{2m_{r}}{2m_{r}+\varpi\gamma\zeta_{j}\delta})$.

###  III-B BER in the second phase

Using the harvested energy (i.e., using the power harvested of the three EH
protocols as presented in section II), the R node forwards the SC signal to
the users. The U1 detect its symbols directly using MLD, so the BER at U1 can
be given by

$P_{1}(e)=\frac{1}{2}\sum_{{i}=1}^{2}\mathrm{Q}(\sqrt{\gamma\zeta_{i}\psi|h_{1}|^{2}|h_{r}|^{2}}).$
(12)

As seen in (12), the conditional BER includes multiplying of two random
variables which belong to first and second phase link qualities. Although, the
conditional BER in (12) defines the BER of second phase, it includes
$|h_{r}|^{2}$ since the transmit power of the relay (i.e., $P_{r}$) is a
function of it (4). Thus, the ABER of (12) can not be simply obtained by
averaging Gamma distribution (i.e., the absolute square of Nakagami-$m$).
Firstly, the joint probability density function (PDF) of
$|h_{1}|^{2}|h_{r}|^{2}$ should be derived. By following steps in [22] through
the PDF of the product of two Chi-Square distributions, the PDF can be
obtained. After simplification and using [23, eq. (3.478.4)], we derive the
ABER of (12) by using the Meijer-G function [23, eq.(9.311)] by following the
steps of [22, 24], and the closed-form ABER at U1 is given as

$P_{1}(e)=\frac{1}{2}\sum_{{i}=1}^{2}\frac{\Delta_{1}}{2\sqrt{\pi}}G\begin{smallmatrix}3&3\\\
4&5\end{smallmatrix}\left(\begin{smallmatrix}0,1-u_{2},0.5-u_{2},1-u_{2}\\\
0.5u_{1},-0.5u_{1},1-u_{2},u_{2},0\end{smallmatrix}\middle|\frac{\Delta_{3}}{4}\right),$
(13)

where
$u_{1}=m_{r}-m_{1},u_{2}=0.5(m_{r}+m_{1}),\Delta_{1}=\Delta_{2}(\frac{m_{1}\Omega_{r}}{m_{r}\Omega_{1}})^{\frac{u_{1}}{2}}(\frac{1}{\gamma\zeta_{i}\psi})^{u_{2}},\Delta_{2}=\frac{(\frac{m{r}}{\Omega_{r}})^{m{r}}(\frac{m{1}}{\Omega_{1}})^{m{1}}}{\Gamma(m_{r})\Gamma(m_{1})},\Delta_{3}=2\sqrt{\frac{m_{1}m_{r}}{\Omega_{1}\Omega_{r}\gamma\zeta_{i}\psi}}$,
$m_{r}$ and $m_{k}$ are the Nakagami fading parameters.

Also, we obtain the BER at U2 through the correct and erroneous SIC. Thus, the
BER at U2 is given by

$P_{2}(e)=\frac{1}{2}\sum_{{j}=1}^{5}\nu^{j}\mathrm{Q}(\sqrt{\gamma\zeta_{j}\psi|h_{2}|^{2}|h_{r}|^{2}}).$
(14)

As discussed above, the ABER of (14) needs further modification. Thus, we find
the ABER of (14) by using the same method of (13) and it is given as

$P_{2}(e)=\frac{1}{2}\sum_{{j}=1}^{5}\nu^{j}\frac{\Delta_{4}}{2\sqrt{\pi}}G\begin{smallmatrix}3&3\\\
4&5\end{smallmatrix}\left(\begin{smallmatrix}0,1-u_{4},0.5-u_{4},1-u_{4}\\\
0.5u_{3},-0.5u_{3},1-u_{4},u_{4},0\end{smallmatrix}\middle|\frac{\Delta_{6}}{4}\right),$
(15)

where
$u_{3}=m_{r}-m_{2},u_{4}=0.5(m_{r}+m_{2}),\Delta_{4}=\Delta_{5}(\frac{m_{2}\Omega_{r}}{m_{r}\Omega_{2}})^{\frac{u_{1}}{2}}(\frac{1}{\gamma\zeta_{j}\psi})^{u_{4}},\Delta_{5}=\frac{(\frac{m{r}}{\Omega_{r}})^{m{r}}(\frac{m{2}}{\Omega_{2}})^{m_{2}}}{\Gamma(m_{r})\Gamma(m_{2})}$
and
$\Delta_{6}=2\sqrt{\frac{m_{2}m_{r}}{\Omega_{2}\Omega_{r}\gamma\zeta_{j}\psi}}$.

Finally, we obtain the e2e ABER expression of U1 as (16) by substituting (9)
and (13) into (7). Also, by substituting (11) and (15) into (7), we get the
e2e ABER expression of U2 as (17) (please see the top of the next page).

$\begin{split}&P_{e2e,1}(e)=\\\
&1-\left(1-\frac{1}{2}\sum_{{i}=1}^{2}\frac{1}{\sqrt{2\pi}}\frac{\Gamma({m_{r}+0.5})}{\Gamma(m_{r}+1)}\times\frac{\sqrt{\varpi\gamma\zeta_{i}\delta/2m_{r}}}{(1+\sqrt{\varpi\gamma\zeta_{i}\delta/2m_{r}})^{(m_{r}+0.5)}}\nabla_{1}(m_{r},\varpi\gamma\zeta_{i}\delta)\right)\left(1-\frac{1}{2}\sum_{{i}=1}^{2}\frac{\Delta_{1}}{2\sqrt{\pi}}G\begin{smallmatrix}3&3\\\
4&5\end{smallmatrix}\left(\begin{smallmatrix}0,1-u_{2},0.5-u_{2},1-u_{2}\\\
0.5u_{1},-0.5u_{1},1-u_{2},u_{2},0\end{smallmatrix}\middle|\frac{\Delta_{3}}{4}\right)\right)\\\
\end{split}$ (16) $\begin{split}&P_{e2e,2}(e)=\\\
&1-\left(1-\frac{1}{2}\sum_{{j}=1}^{5}\nu^{j}\frac{1}{\sqrt{2\pi}}\frac{\Gamma({m_{r}+0.5})}{\Gamma(m_{r}+1)}\times\frac{\sqrt{\varpi\gamma\zeta_{j}\delta/2m_{r}}}{(1+\sqrt{\varpi\gamma\zeta_{j}\delta/2m_{r}})^{(m_{r}+0.5)}}\nabla_{2}(m_{r},\varpi\gamma\zeta_{j}\delta)\right)\left(1-\frac{1}{2}\sum_{{j}=1}^{5}\nu^{j}\frac{\Delta_{4}}{2\sqrt{\pi}}G\begin{smallmatrix}3&3\\\
4&5\end{smallmatrix}\left(\begin{smallmatrix}0,1-u_{4},0.5-u_{4},1-u_{4}\\\
0.5u_{3},-0.5u_{3},1-u_{4},u_{4},0\end{smallmatrix}\middle|\frac{\Delta_{6}}{4}\right)\right)\\\
\end{split}$ (17)

##  IV Numerical Results

In this section, we validate the theoretical analysis by Monte Carlo
simulation. In all figures, the lines represent the simulation results, while
the markers represent the analytical results. The channel parameters for all
simulations are given in Table I and in all simulations, $\eta=0.95$ and for a
fair comparison, total transmit SNR is defined as
$\nicefrac{{P_{T}}}{{N_{0}}}$. In simulations, we use normalized i.e., T=1
transmission time.

In Fig. 1, we present ABER performances of both users for all protocols, where
$\alpha_{1}=0.9$, and $\beta=\rho=0.1$. Firstly, it is worthy noting that our
analysis matches perfectly with simulations in all protocols and scenarios
which proves the correctness of our closed-from expressions. Besides, the
analysis refers to both integer and non-integer values of $m$ and it can be
seen that this shape parameter $m$ drives the diversity order. In Fig. 1, we
can observe that the proposed HEH-CNOMA outperforms all three benchmarks. By
examining the comparisons in Fig. 1, we observe that the performance in
Scenario I is better than Scenario III and in the same manner, the performance
in Scenario IV is superior to Scenario II. These observations are a natural
expectation of channel quality differences in various scenarios. The shape
parameter in Scenario I is greater than Scenario III so that Scenario I has
better ABER performance and improved diversity order since in both phases less
erroneous detection is performed. Likewise, Scenario IV outperforms Scenario
II since the spread parameters are higher which improves the performance. On
the other hand, please note that in Scenario I and Scenario IV, the linear sum
of spread parameters (i.e., $\Omega_{r}+\Omega_{k}$) of links are fixed which
can reflect the relay position. In other words, the higher $\Omega_{r}$ means
that the relay is closer to the source than the users. By comparing the
performances of Scenario I and Scenario IV, we can observe that Scenario IV is
superior. Thus, we can easily say that the CNOMA schemes have better
performance when the relay is close to the middle of the source and users.

TABLE I: Channel parameters in simulations | Scenario I | Scenario II | Scenario III | Scenario IV
---|---|---|---|---
$\left[\Omega_{r},\ \Omega_{1},\ \Omega_{2}\right]$ | $[10,\ 2,\ 10]$ | $[2,\ 2,\ 10]$ | $[10,\ 2,\ 10]$ | $[8,\ 4,\ 12]$
$m_{r}=m_{1}=m_{2}$ | $1.5$ | $1.5$ | $1$ | $1.5$

(a)

(b)

Figure 1: ABER performance comparisons between HEH-CNOMA and benchmarks w.r.t.
SNR. Figure 2: ABER performance comparisons between HEH-CNOMA and benchmarks
w.r.t. power allocation.

(a)

(b)

Figure 3: ABER performance comparisons between HEH-CNOMA and benchmarks w.r.t.
EH parameters.

The power allocation has prevailing effects on the ABER performance. To this
end, to discuss the optimal power allocation (PA), in Fig. 2, we present ABER
performances of users in Scenario I for $\nicefrac{{P_{T}}}{{N_{0}}}=20$ dB.
Regardless of the PA changes, the HEH-CNOMA still outperforms all three
benchmarks. Nevertheless, as expected, with the increase of $\alpha_{2}$, the
performance of U1 is always decayed (i.e., ABER is increasing) since
$\alpha_{1}$ so the allocated power to U1 symbols is reduced. On the other
hand, by increasing $\alpha_{2}$, we firstly have better performance for ‘U2;
however, it becomes worse with so much increase in $\alpha_{2}$. This can be
explained as follows. By increasing $\alpha_{2}$, we allocate more power to U2
symbols so that the performance is improved. However, U2 should implement SIC
(i.e., detect U1 symbols firstly and subtract it) to detect its symbols.
Therefore, if we increase $\alpha_{2}$, U1 symbols will be detected
erroneously during SIC at the U2 and it will cause an error floor in detection
of U2 symbols. Based on the above discussion and Fig. 2, by considering both
users’ performances, we can say that the optimum value of power allocation
should be $0.1\leq\alpha_{2}\leq 0.25$.

In order to better illustrate the effects of the EH parameters ($\beta$,
$\rho$) on the performance, in Fig. 3, we present the ABER versus $\beta$ and
$\rho$ in Scenario I and Scenario IV. In both comparisons, we can say that an
optimal $\beta$-$\rho$ pair can be obtained to minimize the ABER in HEH-CNOMA.
According to channel conditions, $\beta$ and $\rho$ can be chosen jointly. For
instance, in Scenario I, since the relay is close to the source, the link
between $S$-$R$ has already a good quality and less erroneous detection is
performed at the relay. Hence, we can increase $\beta$ and $\rho$ to increase
the harvested energy to guarantee a reliable communication in the second phase
by increasing the transmit power of the relay. On the other hand, when the
relay is located nearby the middle (i.e., Scenario IV), we should select lower
$\beta$ and $\rho$ values. If we choose $\beta$ and $\rho$ too much, the
information processing in the first phase becomes unreliable since less power
is devoted to information transfer. In addition to this, the channel quality
of the first phase is relatively worse, so the relay makes more error in
detection and this causes an error propagation from relay to users.

##  V Conclusion

This paper proposes a hybrid protocol-assisted CNOMA, which is a combination
of existing EH protocols (i.e., PS and TS). The aim of the study is to improve
the performance of the existing EH protocols with a more realistic protocol
for practical assumptions. The e2e BER expressions of users are analyzed over
the Nakagami-$m$ fading channel. We discuss the optimal hybrid protocol values
with the power allocation factor. The results illustrate that proposed HEH-
CNOMA outperforms all benchmarks. The optimum value of EH factors to achieve
more satisfactory performance for both users jointly in HEH-CNOMA can be
obtained according to spread and shape parameters of the channel.

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