# SLIPT in Joint Dimming Multi-LED OWC Systems with Rate Splitting Multiple
Access

Sepideh Javadi†, Sajad Faramarzi§, Farshad Zeinali†, Hosein Zarini§§, Mohammad
Robat Mili†,
Panagiotis D. Diamantoulakis⋆, Eduard Jorswieck††, George K. Karagiannidis⋆,⋆⋆
† Pasargad Institute for Advanced Innovative Solutions (PIAIS), Tehran, Iran
§ Dept. of Electrical Engineering, Iran University of Science and Technology,
Tehran, Iran
§§ Dept. of Computer Engineering, Sharif University of Technology, Tehran,
Iran
⋆ Dept. of Electrical and Computer Engineering, Aristotle University of
Thessaloniki, Thessaloniki, Greece
⋆⋆ Artificial Intelligence & Cyber Systems Research Center, Lebanese American
University (LAU), Lebanon
†† Institute for Communications Technology, Technische Universitat
Braunschweig, Braunschweig, Germany

###### Abstract

Optical wireless communication (OWC) systems with multiple light-emitting
diodes (LEDs) have recently been explored to support energy-limited devices
via simultaneous lightwave information and power transfer (SLIPT). The energy
consumption, however, becomes considerable by increasing the number of
incorporated LEDs. This paper proposes a joint dimming (JD) scheme that lowers
the consumed power of a SLIPT-enabled OWC system by controlling the number of
active LEDs. We further enhance the data rate of this system by utilizing rate
splitting multiple access (RSMA). More specifically, we formulate a data rate
maximization problem to optimize the beamforming design, LED selection and
RSMA rate adaptation that guarantees the power budget of the OWC transmitter,
as well as the quality-of-service (QoS) and an energy harvesting level for
users. We propose a dynamic resource allocation solution based on proximal
policy optimization (PPO) reinforcement learning. In simulations, the optimal
dimming level is determined to initiate a trade-off between the data rate and
power consumption. It is also verified that RSMA significantly improves the
data rate.

###### Index Terms:

Optical wireless communication (OWC), simultaneous lightwave information and
power transfer (SLIPT), joint dimming (JD), rate splitting multiple access
(RSMA), proximal policy optimization (PPO).

##  I Introduction

Benefiting from illumination and communication at the same time, optical
wireless communication (OWC) systems are envisioned to be a promising
technology to compensate for the shortcomings of conventional radio-frequency
(RF) communication systems. This technology requires a light-emitting diode
(LED) for signal transmission at the transmitter and photo-diode (PD) for
signal decoding at the receiver [1, 2, 3, 4]. So far, advanced optical
wireless techniques have been investigated to unleash the potentials of OWC
systems, such as multi-LED transmitters [5], joint dimming (JD) [6], as well
as simultaneously lightwave information and power transfer (SLIPT) [7, 8, 9].
In the former case, multiple LEDs are incorporated in an LED array, commonly
known as a spatial multiplexing OWC system. This extension brings about
remarkable data rate and extended coverage over the OWC systems compared to
the single LED. The second case, as a multi-domain control scheme, relies on
both analog dimming (AD) and spatial dimming (SD).
Introduced first in [6], JD control jointly optimizes the direct-current (DC)
bias level (in AD), as well as the number of glared LEDs (in SD) to satisfy a
required dimming level [10], [11]. The latter case, i.e., the SLIPT
technology, is a promising solution for low-battery devices [7], which enables
OWC receivers to simultaneously obtain illumination, information, and energy
harvesting (EH) via a PD, a solar panel, or both.
The concept of wireless information and power transfer has been throughly
investigated in the literature [12, 13, 14, 15, 16]. However, the coexistence
of alternating current (AC) and DC signals in the photo-current of LEDs has
encouraged the researchers to study the SLIPT technology [17]. Previously, the
performance of an OWC system with multi-LED transmitter and SLIPT technology
was considered in [18] and [19] to minimize the energy consumption and
maximize the data rate, respectively. These techniques consume significant
energy. Furthermore, they were proposed under the assumption of orthogonal
resource allocation which limits the data rate. In this paper, we study the
performance of [18] and [19] by exploring rate splitting multiple access
(RSMA) [20, 21, 22, 23], which employs non-orthogonality of resources to
enable higher data rate and massive access. Additionally, we adopt an
efficient JD control scheme, where the number of active LEDs are controlled,
thereby reducing the energy consumption of [18] and [19].
To analyze the performance of this system, a data rate maximization problem is
formulated by jointly optimizing the transmit beamforming, LED selection, and
RSMA rate adaptation. This problem ensures the power budget of the multi-LED
transmitter, as well as receivers’ quality-of-service (QoS), dimming level and
EH level. More specifically, we transform the problem into a Markov decision
process (MDP) and propose a real-time dynamic solution methodology, based on
proximal policy optimization (PPO) reinforcement learning. Through numerical
simulations, we compute the optimal dimming level for a trade-off between the
data rate and power consumption. Additionally, leveraging RSMA enhances the
data rate of this system, compared to the non-orthogonal multiple access
(NOMA).
The remainder of this paper is organized as follows. The system model of the
proposed downlink SLIPT-assited JD multi-LED OWC network with RSMA is
introduced in Section II, while Section III evaluates the performance of the
proposed DRL-based approach in detail by employing PPO reinforcement learning.
In Section IV, the effectiveness of the proposed OWC system is verified by
simulation results. Finally, Section V concludes the paper.

_Notation:_ The vectors and matrices are specified by boldface lower-case and
upper-case letters, respectively, while diag(.) represents the diagonalization
operation. The absolute value of scalar $a$, the transpose, and the Hermitian
transpose of the vector $\mathbb{a}$ are denoted by $|a|$, $\mathbb{a}^{T}$,
and $\mathbb{a}^{H}$, respectively. Finally, the expectation operator and the
set of real numbers are denoted by $\mathbb{E}(.)$ and $\mathbb{R}$,
respectively, while $[.]$ represents the round off operation.

##  II System Model

As illustrated in Fig. 1, we consider the downlink transmission of an OWC
network, in which the transmitter is equipped with an LED array, including a
set $\mathcal{N}=\left\\{{1,2,...,{N}}\right\\}$ of ${N}$ LEDs and
communicates with a set $\mathcal{K}=\left\\{{1,2,...,{K}}\right\\}$ of $K$
single-PD users. The users are supposed to be distributed randomly, whereas
the LEDs are independently modulated via separate drivers, yet all are
connected to a central controller that collects channel feedback and performs
resource management.

Figure 1: An OWC system with an LED array, serving $K$ single-PD users for
illumination, communication and EH.

###  II-A Signal Model

We adopt RSMA as the state-of-the-art multiple access scheme. On this basis,
the transmit lightweight data stream for each user has a two-fold structure,
including a common message in addition to a private message. The former, i.e.,
the common message of the transmit lightweight data stream has the same
content for all users, whereas the latter, i.e., the private message is
exclusively encoded for each user. In other words, one common lightweight
transmit data stream, as well as $K$ private ones, form a superimposed
transmit signal, carrying $K+1$ messages. Let ${s}^{\textrm{(c)}}$ and
${{s}}_{k}^{\textrm{(p)}},\forall k\in\mathcal{K}$, denote the common message
shared among all users and the private message of the $k$-th user,
respectively, such that $\mathbb{E}\\{\lvert{s}^{\textrm{(c)}}\rvert^{2}\\}=1$
and $\mathbb{E}\\{\lvert{{s}}_{k}^{\textrm{(p)}}\rvert^{2}\\}=1,\forall
k\in\mathcal{K}$. We devise a linear precoding scheme [5] prior to signal
transmission, to handle the inter-user interference. Next, a DC bias
${\textbf{i}_{\textrm{DC}}}=[{i_{\textrm{DC}}},...,{i_{\textrm{DC}}}]^{N\times
1}$ is added to the precoded signal before transmission. This bias regulates
the brightness of the LEDs and guarantees that the amplitude of the
transmitted signal has a real non-negative value. Accordingly, the lightweight
transmit data stream of all LEDs, denoted by
$\textbf{x}={\left[{{x_{1}},{x_{2}},...,{x_{N}}}\right]^{T}}$, can be
expressed as

$\displaystyle\textbf{x}={\textbf{w}}^{\textrm{(c)}}{s}^{\textrm{(c)}}+\sum_{k=1}^{K}{\textbf{w}}^{\textrm{(p)}}_{k}{{s}}_{k}^{\textrm{(p)}}+\textbf{i}_{\text{DC}},$
(1)

where
${\mathbb{w}^{\textrm{(c)}}}={\left[{{w_{1}^{\textrm{(c)}}},{w_{2}^{\textrm{(c)}}},...,{w_{N}^{\textrm{(c)}}}}\right]^{T}}\in{\mathbb{R}^{{N}\times
1}}$ and
${\mathbb{w}_{k}^{\textrm{(p)}}}={\left[{{w_{k,1}^{\textrm{(p)}}},{w_{k,2}^{\textrm{(p)}}},...,{w_{k,{N}}^{\textrm{(p)}}}}\right]^{T}}\in{\mathbb{R}^{{N}\times
1}},~{}\forall k\in\mathcal{K}$ specify the common transmit beamforming for
${s}^{\textrm{(c)}}$ and the $k$-th private transmit beamforming for
${{s}}_{k}^{\textrm{(p)}}$, respectively. Note that ${\textbf{i}_{\text{DC}}}$
has the same value for all LEDs, because of uniformity of illumination in
indoor environments [5]. The dynamic range of the LEDs is constraint to avoid
signal clipping [27]. In other words,

$\displaystyle\left|{{w_{n}^{\textrm{(c)}}}}\right|+\sum\limits_{k=1}^{K}{\left|{{w_{k,n}^{\textrm{(p)}}}}\right|}\leq\Xi,~{}\forall
n\in\mathcal{N},$ (2)

where $\Xi=\min({i_{\text{DC}}}-{I_{l}},{I_{h}}-{i_{\text{DC}}})$, and the
notations ${I_{l}}$ and ${I_{h}}$ indicate the minimum and maximum permissible
currents of all LEDs, respectively.

###  II-B Channel Model

In this paper, we only consider the line of sight (LoS) links [6]-[11]. The
optical channel gain between the $n$-th LED and the $k$-th user, denoted by
$h_{k,n}\in\mathbb{R}$, can be modelled as

$h_{k,n}\\!=\\!\left\\{\begin{array}[c]{c}\\!\\!\\!\\!\frac{(m+1)A^{\textrm{OWC}}}{2\pi
d_{k,n}^{2}}G^{\textrm{OWC}}(\psi_{k,n})Z^{\text{OWC}},\\\
0,\end{array}\right.\left.\begin{array}[c]{c}\\!\\!0\\!\leq\\!\psi_{k,n}\\!\leq\\!\Psi_{c},\\\
\psi_{k,n}>\Psi_{c},\end{array}\right.$ (3)

where $Z^{\text{OWC}}=\\!\cos^{m}(\phi_{k,n})\\!\cos(\psi_{k,n})$, while
$A^{\textrm{OWC}}$ and $d_{k,n}$ denote the physical area of the PD for each
user and the distance between the $n$-th LED and the $k$-th user,
respectively. Moreover, $m=-\frac{\ln 2}{\ln(\cos\Phi_{1/2})}$ specifies the
Lambertian emission order with $\Phi_{1/2}$ being the semi-angle at half-power
of the LED. Besides, the angles of incidence and irradiance are respectively
given by $\psi_{k,n}$ and $\phi_{k,n}$, while the receiver field of vision
(FOV) semi-angle is denoted by $\Psi_{c}$. Finally,
$G^{\textrm{OWC}}(\psi_{k,n})$ indicates the gain of the optical concentrator
which is defined as follows

$G^{\textrm{OWC}}(\psi_{k,n})=\left\\{\begin{array}[c]{c}\frac{n_{R}^{2}}{\sin^{2}\left(\Psi_{c}\right)}\\\
0,\end{array}\right.\left.\begin{array}[c]{c}0\leq\psi_{k,n}\leq\Psi_{c},\\\
\psi_{k,n}>\Psi_{c},\end{array}\right.$ (4)

with $n_{R}\geq 0$ being the internal refractive index. Given
(${x}_{k},{y}_{k},{z}_{k}$) and (${x}_{n},{y}_{n},{z}_{n}$) as the coordinates
of the $k$-th user and $n$-th LED, respectively, the distance between them can
be modeled as
$d_{k,n}=\sqrt{(x_{n}-{x}_{k})^{2}+(y_{n}-{y}_{k})^{2}+(z_{n}-{z}_{k})^{2}}$.

###  II-C JD Control

Regarding the LED array with multiple LEDs and the incorporation of power
transfer capability, its energy consumption becomes considerable. In this
paper we invoke an efficient JD scheme to control the energy consumption [10].
To this purpose, let $\mathbf{A}$ denote a binary LED selection matrix, where
$\mathbf{A}=\text{diag}(\mathbf{a})\in\\{0,1\\}^{N\times N},$ and
$\mathbf{a}=[a_{1},\dots,a_{N}]^{T}\in\\{0,1\\}^{N\times 1}$, i.e.,

$a_{n}=\left\\{\begin{array}[c]{c}1,\\\
0,\end{array}\right.\left.\begin{array}[c]{c}\text{if the LED $n$ is
active},\\\ \text{otherwise}.\end{array}\right.$ (5)

By this definition, we can declare the number of active LEDs as
${N_{\textrm{a}}}=\sum\limits_{n=1}^{{N}}{{a_{n}}}$.

The JD control scheme includes both AD and SD at the same time, such that the
number of glared LEDs in SD, as well as the uniform DC-bias level of AD are
jointly optimized. To achieve this, a predetermined target dimming level
$\eta$ is considered, based on which we can round-off the number of glared
LEDs as follows [24]

$\displaystyle N_{a}=\big{[}\eta N\big{]}.$ (6)

Accordingly, the uniform DC-bias level ${i_{\textrm{DC}}}$ is given by [11]

$\displaystyle{i_{\textrm{DC}}}=\dfrac{\eta N(I_{0}-I_{l})}{N_{a}}+I_{l},$ (7)

wherein $I_{0}=\dfrac{I_{l}+I_{h}}{2}$ specifies the original DC-bias that
corresponds to AD with all-glared LEDs and a dimming level of $\eta=100\%$.
Although $N_{\textrm{a}}$ determines the number of glared LEDs, it does not
specify the index of active LEDs at the LED array. Hence, it is required to
formulate a network-wide resource allocation problem, so as to optimize the
binary LED selection matrix A.

###  II-D Data Rate

At the receiver side, all users first decode the common received lightweight
data stream by considering all private streams as noise. Then, the private
received lightweight data stream will be decoded by treating other private
streams as noise [23]. On this basis, the common and private lightweight
received data rate for the $k$-th user can be expressed as

$\displaystyle
R^{(\textrm{c})}_{k}=\log_{2}\bigg{(}1+\dfrac{|\mathbb{h}^{H}_{k}\mathbb{A}{{\mathbb{w}}}^{\textrm{(c)}}|^{2}}{\sum_{j=1}^{K}|\mathbb{h}^{H}_{k}\mathbb{A}{\mathbb{w}}_{j}^{\textrm{(p)}}|^{2}+\sigma^{2}_{k}}\bigg{)},\
\forall k\in\mathcal{K},$ (8)

and

$\displaystyle
R^{(\textrm{p})}_{k}=\log_{2}\bigg{(}1+\dfrac{|\mathbb{h}^{H}_{k}\mathbb{A}{\mathbb{w}}_{k}^{\textrm{(p)}}|^{2}}{\sum_{j=1,j\neq
k}^{K}|\mathbb{h}^{H}_{k}\mathbb{A}{\mathbb{w}}_{j}^{\textrm{(p)}}|^{2}+\sigma^{2}_{k}}\bigg{)},\
\forall k\in\mathcal{K},$ (9)

respectively, where
${\mathbb{h}_{k}}={\left[{{h_{k,1}},{h_{k,2}},...,{h_{k,{N}}}}\right]^{T}}$
denotes the channel gain vector of user $k$. To ensure that the common stream
is successfully decoded, the data rates for common data should satisfy a rate
adaptation ${r}^{*}_{k}$, such that

$\displaystyle\min_{k}{R^{(\textrm{c})}_{k}}\geq\sum_{k=1}^{K}{r_{k}^{*}},\
\forall k\in\mathcal{K}.$ (10)

Then, the aggregate system lightweight received data rate can be expressed as

$\displaystyle{R}^{\textrm{Agg}}(\mathbf{w}^{\textrm{(c)}},\\{\mathbf{w}_{k}^{\textrm{(p)}}\\}_{k\in\mathcal{K}},\mathbf{A},\mathbf{r}^{*})=\sum_{j=1}^{K}(r_{k}^{*}+{R^{(\textrm{p})}_{k}}),$
(11)

where
$\mathbf{r}^{*}=[r^{*}_{1},r^{*}_{2},...,r^{*}_{K}]^{T}\in\mathbb{R}^{K\times{1}}$.

###  II-E Energy Harvesting

The coexistence of AC and DC signals in the photo-current of LEDs, enable
users to harvest energy from the DC component, which is blocked by a
capacitor. The total harvested energy at the $k$-th user from the DC signal of
all active LEDs can be expressed as [25]

$\displaystyle{P_{k}^{\text{Har}}}=\sum_{n=1}^{N}\tau{a_{n}}{V_{t}}h_{k,n}{i_{\text{DC}}}\ln\left({1+\frac{\sum_{n=1}^{N}{h_{k,n}{i_{\text{DC}}}}}{{{I_{s}}}}}\right),$
(12)

where $V_{t}$, $\tau$, and $I_{s}$ are the thermal voltage, the fill factor,
and the dark saturation, respectively. Accordingly, the total optical power
consumption of the system can be computed as [26]

$\displaystyle
P^{\text{tot}}(\mathbf{w}^{\textrm{(c)}},\\{\mathbf{w}_{k}^{\textrm{(p)}}\\}_{k\in\mathcal{K}},\mathbf{A})=$
$\displaystyle\zeta\sum_{n=1}^{N}a_{n}\bigg{(}{w_{n}^{\textrm{(c)}}}+\sum_{k=1}^{K}{w_{k,{n}}^{\textrm{(p)}}}\bigg{)}$
$\displaystyle+P^{\text{DC}}-\sum\limits_{k=1}^{K}{P_{k}^{\text{Har}}},$ (13)

where $P^{\text{DC}}=\varphi{N_{a}}{i_{\text{DC}}}$. Moreover, $\zeta\geq 1$
specifies the power for the amplifier efficiency factor, whereas $\varphi$
denotes the conversion factor.

###  II-F Problem Formulation

Compared to [18] and [19], this paper explores the potentials of RSMA and JD
control scheme to increase the data rate and control the power consumption,
respectively. Particularly, we optimize the aggregate system lightweight
received data rate, the beamforming design, LED selection and RSMA rate
adaptation, such that the power budget of the LED array, as well as the QoS
and EH thresholds are preserved for all users. Mathematically, the
abovementioned network-wide optimization problem is formulated as follows

$\displaystyle\mathbb{P}_{1}:$
$\displaystyle\max_{\mathbf{w}^{\textrm{(c)}},\\{\mathbf{w}^{\textrm{(p)}}_{k}\\}_{k\in\mathcal{K}},\mathbf{A},\mathbf{r}^{*}}{R}^{\textrm{Agg}}(\mathbf{w}^{\textrm{(c)}},\\{\mathbf{w}_{k}^{\textrm{(p)}}\\}_{k\in\mathcal{K}},\mathbf{A},\mathbf{r}^{*})$
$\displaystyle\text{s.t.}~{}~{}~{}\\!~{}\text{C}_{1}:\quad\min_{k}{R^{(\textrm{c})}_{k}}\geq\sum_{k=1}^{K}{r_{k}^{*}},~{}\forall
k\in\mathcal{K},$ $\displaystyle~{}~{}~{}~{}~{}~{}~{}\text{C}_{2}:\quad
r_{k}^{*}+{R^{(\textrm{p})}_{k}}\geq{\textrm{QoS}},~{}\forall
k\in\mathcal{K},$ $\displaystyle~{}~{}~{}~{}~{}~{}~{}\text{C}_{3}:\quad
P^{\text{tot}}\leq P_{\textrm{max}},$
$\displaystyle~{}~{}~{}~{}~{}~{}~{}\text{C}_{4}:\quad P_{k}^{\text{Har}}\geq
P^{\textrm{Har}}_{\textrm{min}},~{}\forall k\in\mathcal{K},$
$\displaystyle~{}~{}~{}~{}~{}~{}~{}\text{C}_{5}:\quad
a_{n}\in{\\{0,1\\}},~{}~{}\forall n\in\mathcal{N},$
$\displaystyle~{}~{}~{}~{}~{}~{}~{}\text{C}_{6}:~{}~{}~{}\eta=\dfrac{{N_{a}}(i_{\textrm{DC}}-I_{l})}{N(I_{0}-I_{l})}\times
100\%,$
$\displaystyle~{}~{}~{}~{}~{}~{}~{}\text{C}_{7}:~{}~{}~{}\\!\left|{{w_{n}^{\textrm{(c)}}}}\right|+\sum\limits_{k=1}^{K}{\left|{{w_{k,n}^{\textrm{(p)}}}}\right|}\leq\Xi,~{}\forall
n\in\mathcal{N},$ (14)

where $P_{\textrm{max}}$, $P^{\textrm{Har}}_{\textrm{min}}$, and QoS represent
the power budget of the LED array, the minimum homogeneous EH requirement and
the minimum homogeneous QoS for all users, respectively. More specifically,
$\text{C}_{1}$ assures the successful signal decoding at all users;
$\text{C}_{2}$ satisfies the QoS for all users; $\text{C}_{3}$ respects the
power budget of the LED array; $\text{C}_{4}$ specifies the minimum EH
requirement for all users; $\text{C}_{5}$ confines each LED to be either
active or inactive; $\text{C}_{6}$ defines a target required dimming level
$\eta$ to be satisfied; Finally, $\text{C}_{7}$ respects the dynamic range of
all LEDs.
Concerning the complex domain of $\mathbf{w}^{\textrm{(c)}}$ and
$\\{\mathbf{w}^{\textrm{(p)}}_{k}\\}_{k\in\mathcal{K}}$, the binary domain of
$\mathbf{A}$, and the continuous domain of $\mathbf{r}^{*}$, one can clearly
claim that this problem is non-convex in the form of mixed integer non-linear
programming (MINLP) and belongs to the class of non-deterministic polynomial
(NP)-hard problems. The straightforward brute-force method, i.e., the
exhaustive search for attaining its globally optimal solution is implausible,
considering the coupling and scalability of the problem. Moreover, the
classical convex optimization-based solutions mostly rely on time consuming
and computationally expensive convex transformations, whereas the wireless
environment is quietly dynamic and real-time resource allocation mechanisms
are preferred. Instead, we propose a real-time dynamic solution to this
problem based on reinforcement learning.

##  III Proposed DRL-based Approach

In this section, the non-convex problem $\mathbb{P}_{1}$ with both discrete
and continuous variables is firstly reformulated into a model-free MDP, and
then a DRL algorithm based on the PPO framework is designed to solve the
problem $\mathbb{P}_{1}$ [28, 20, 29].

###  III-A MDP formulation

A $4$-tuple
$(\mathbb{s}_{t},\mathbb{a}_{t},r(\mathbf{s}_{t},\mathbf{a}_{t}),\mathbb{s}_{t+1})$
is constructed by the MDP formulation, where the current state, the action,
the reward function, and the next state are denoted by $\mathbb{s}_{t}$,
$\mathbb{a}_{t}$, $r_{t}$, and $\mathbb{s}_{t+1}$, respectively. The PPO
approach enables the agent to interact with the environment (i.e., the OWC-
assisted network), to observe the current state $\mathbb{s}_{t}$ from the
state space $\mathcal{S}$ and to select the action $\mathbb{a}_{t}$ from the
action space $\mathcal{A}$ according to the specific policy with the ultimate
aim of maximizing the clipping surrogate objective function
${\mathcal{L}^{\text{CLIP}}}(\cdot)$ that is defined latter. Moreover, based
on the formulation of problem $\mathbb{P}_{1}$, the state, the action, and the
reward function are elaborated in the following.

####  III-A1 State

The current state $\mathbf{s}_{t}\in\mathcal{S}$ at time step $t$ constitutes
of the main environmental information related to problem $\mathbb{P}_{1}$ in
such a way that allows the policy to enhance and to adapt itself to the
dynamic environment. More specifically, the state $\mathbf{s}_{t}$ of the
considered system is the set of the common and private rates, the harvested
energy, the common and private beamforming vectors as follows

$\displaystyle\mathbf{s}_{t}=$ (15)
$\displaystyle\Big{\\{}\\{R_{k}^{(c)}\\}_{k\in\mathcal{K}},\\{R_{k}^{(p)}\\}_{k\in\mathcal{K}},\\{P_{k}^{\text{Har}}\\}_{k\in\mathcal{K}},\mathbf{w}^{(c)},\\{\mathbf{w}_{k}^{(p)}\\}_{k\in\mathcal{K}}\Big{\\}}.$

####  III-A2 Action

In the proposed PPO approach, action $\mathbf{a}_{t}\in\mathcal{A}$ at time
step $t$ refers to the decisions that an agent takes via an interaction with
the considered environment. Furthermore, the action at time step $t$ in
problem $\mathbb{P}_{1}$ consists of both discrete and continuous variables.

$\displaystyle\mathbf{a}_{t}=\Big{\\{}\mathbf{w}^{(c)},\\{\mathbf{w}_{k}^{(p)}\\}_{k\in\mathcal{K}},\mathbf{A},\mathbf{r}^{*}\Big{\\}}.$
(16)

####  III-A3 Reward Function

In particular, the PPO approach is a reinforcement learning method which
trains the agents to take suitable decisions in order to maximize the defined
clipping surrogate objective function ${\mathcal{L}^{\text{CLIP}}}(\cdot)$,
which contains the reward function $r(\mathbf{s}_{t},\mathbf{a}_{t})$. In the
optimization problem $\mathbb{P}_{1}$, the reward function takes both the
objective function, i.e.,
${R}^{\textrm{Agg}}(\mathbf{w}^{(c)},\\{\mathbf{w}_{k}^{(p)}\\}_{k\in\mathcal{K}},\mathbf{A},\mathbf{r}^{*})$,
as well as the constraints of $\mathbb{P}_{1}$ into account which can be
expressed as

$\displaystyle
r(\mathbf{s}_{t},\mathbf{a}_{t})={R}^{\textrm{Agg}}(\mathbf{w}^{(c)},\\{\mathbf{w}_{k}^{(p)}\\}_{k\in\mathcal{K}},\mathbf{A},\mathbf{r}^{*})+\sum\limits_{j=1}^{7}{{l_{C_{j}}}},$
(17)

where
${l_{C_{j}}=\chi_{j}{R}^{\textrm{Agg}}(\mathbf{w}^{\textrm{(c)}},\\{\mathbf{w}_{k}^{\textrm{(p)}}\\}_{k\in\mathcal{K}},\mathbf{A},\mathbf{r}^{*}}),$
and the index $j$ corresponds to all constraints, i.e., $\forall
j\in\left\\{{1,2,...,7}\right\\}$. Besides, $\chi_{j}=1$, if the ${C_{j}}$-th
constraint is satisfied and $\chi_{j}=0$, otherwise.

###  III-B The PPO-Based Analysis

In this paper, the PPO algorithm is applied to select actions from both
discrete and continuous action spaces, thus solving the non-convex problem
(II-F). In particular, the PPO is an actor-critic on-policy gradient method
which is used to simplify the complex calculation of earlier policy gradient
methods, e.g., trust region policy optimization (TRPO). The detailed process
of the proposed PPO-based approach is explained as follows.
The main goal in the reinforcement learning is to maximize the expected
cumulative reward by considering a long-term process. Therefore, the
cumulative reward at time step $t$ is denoted as
${R_{t}}=\sum_{t=0}^{\infty}\lambda^{t}r(\mathbf{s}_{t},\mathbf{a}_{t})$,
where $\lambda\in\left[{0,1}\right)$ represents the discount factor. More
specifically, both actor and critic networks are applied to represent the
parameterized stochastic policy of action selection denoted as
${\pi_{{\mbox{\boldmath$\theta$}}}}(\mathbf{a}_{t}|\mathbf{s}_{t})$ and the
state-value function ${V_{{\mbox{\boldmath$\phi$}}}(\mathbf{s}_{t})}$,
respectively, where $\theta$ and $\phi$ represent the parameters of the actor
and critic networks, respectively. Then, a surrogate objective function based
on PPO approach can be expressed as follows

$\displaystyle\mathcal{L}\left({\mbox{\boldmath$\theta$}},\mathbf{s}_{t},\mathbf{a}_{t}\right)=\mathbb{E}\left[\beta_{t}({\mbox{\boldmath$\theta$}})\Omega(\mathbf{s}_{t},\mathbf{a}_{t})\right],$
(18)

where the probability ratio of the current policy and the old one is
represented by
$\beta_{t}({\mbox{\boldmath$\theta$}})=\pi_{{\mbox{\boldmath$\theta$}}}(\mathbf{a}_{t}|\mathbf{s}_{t})/\pi_{{\mbox{\boldmath$\theta$}}^{\text{old}}}(\mathbf{a}_{t}|\mathbf{s}_{t})$,
while ${\mbox{\boldmath$\theta$}}^{\text{old}}$ denotes the parameter for the
old policy in the actor network. Moreover, the advantage function is given by

$\displaystyle\Omega(\mathbf{s}_{t},\mathbf{a}_{t})=r(\mathbf{s}_{t},\mathbf{a}_{t})+\lambda
V_{{\mbox{\boldmath$\phi$}}^{\text{old}}}({\mathbf{s}_{t+1}})-V_{{\mbox{\boldmath$\phi$}}^{\text{old}}}({\mathbf{s}_{t}}),$
(19)

where ${\mbox{\boldmath$\phi$}}^{\text{old}}$ represents the critic network
parameter for the old state-value estimation function. To ensure that the
updated ${\pi_{{\mbox{\boldmath$\theta$}}}}(\mathbf{a}_{t}|\mathbf{s}_{t})$
satisfies the trust region constraint, a clipping surrogate objective function
can be expressed as

$\displaystyle{\mathcal{L}^{\text{CLIP}}}\left({\mbox{\boldmath$\theta$}},\mathbf{s}_{t},\mathbf{a}_{t}\right)=$
(20)
$\displaystyle\mathbb{E}\Big{[}\min\left\\{\beta_{t}({\mbox{\boldmath$\theta$}})\Omega({\mathbf{s}_{t}},{\mathbf{a}_{t}}),\text{clip}\big{(}\beta_{t}({\mbox{\boldmath$\theta$}}),1-\varepsilon,1+\varepsilon\big{)}\Omega({{\mathbf{s}_{t}}},{\mathbf{a}_{t}})\right\\}\Big{]},$

where the clip function is denoted by $\text{clip}(\cdot,\cdot,\cdot)$, while
$\varepsilon$ represents a hyper-parameter to restraint
$\beta_{t}({\mbox{\boldmath$\theta$}})$ to lie in
$\left[{1-\varepsilon,1+\varepsilon}\right]$. More specifically, the clipping
surrogate objective function is iteratively maximized in the proposed PPO
approach instead of (18). Then, a mini-batch stochastic gradient decent (SGD)
method updates the corresponding $\theta$ over $Q$ transitions denoted as
$(\mathbb{s}^{q}_{t},\mathbb{a}^{q}_{t},r(\mathbf{s}^{q}_{t},\mathbf{a}^{q}_{t}),\mathbb{s}^{q}_{t+1})$
sampled from an experience pool, which is given by

$\displaystyle{\mbox{\boldmath$\theta$}}={\mbox{\boldmath$\theta$}}^{\text{old}}-{\delta_{A}}\frac{1}{Q}\sum\limits_{q=1}^{Q}{\nabla_{{\mbox{\boldmath$\theta$}}}\tilde{\mathcal{L}}_{q}^{\text{CLIP}}}\left({\mbox{\boldmath$\theta$}},\mathbf{s}_{t}^{q},\mathbf{a}_{t}^{q}\right),$
(21)

where ${\delta_{A}}$ is the learning rate and
$\tilde{\mathcal{L}}_{q}^{\text{CLIP}}\left({\mbox{\boldmath$\theta$}},\mathbf{s}_{t}^{q},\mathbf{a}_{t}^{q}\right)$
is the realization of
${\mathcal{L}}^{\text{CLIP}}\left({\mbox{\boldmath$\theta$}},\mathbf{s}_{t},\mathbf{a}_{t}\right)$
with the $q$-th transition, respectively. The mini-batch SGD for updating
$\phi$ uses the MSE loss function between
$V_{{\mbox{\boldmath$\phi$}}}(\mathbf{s}_{t})$ and
$\hat{R}(\mathbf{s}_{t},\mathbf{a}_{t})$ as follows

${\mbox{\boldmath$\phi$}}={\mbox{\boldmath$\phi$}}^{\text{old}}-\delta_{C}\frac{1}{Q}\sum_{q=1}^{Q}\nabla_{{\mbox{\boldmath$\phi$}}}\big{(}V_{{\mbox{\boldmath$\phi$}}}(\mathbf{s}_{t}^{q})-\hat{R}(\mathbf{s}_{t}^{q},\mathbf{a}_{t}^{q})\big{)}^{2},$
(22)

where the learning rate is represented by ${\delta_{C}}$. Moreover, the target
state-value function denoted by $\hat{R}(\mathbf{s}_{t},\mathbf{a}_{t})$ is
given by

$\displaystyle\hat{R}(\mathbf{s}_{t},\mathbf{a}_{t})=r(\mathbf{s}_{t},\mathbf{a}_{t})+\lambda
V_{{\mbox{\boldmath$\phi$}}^{\text{old}}}(\mathbf{s}_{t+1}).$ (23)

1 Input:
$\Big{\\{}\\{R_{k}^{(c)}\\}_{k\in\mathcal{K}},\\{R_{k}^{(p)}\\}_{k\in\mathcal{K}},\\{P_{k}^{\text{Har}}\\}_{k\in\mathcal{K}},\mathbf{w}^{(c)},\\{\mathbf{w}_{k}^{(p)}\\}_{k\in\mathcal{K}}\Big{\\}}$,

2 Output:
$\Big{\\{}\mathbf{w}^{(c)},\\{\mathbf{w}_{k}^{(p)}\\}_{k\in\mathcal{K}},\mathbf{A},\mathbf{r}^{*}\Big{\\}}$,

3 Initialization: Initialize the maximum episode $E$ and time step $T$ as well
as the parameters of actor and critic networks, i.e., $\theta$, $\phi$,
$\varepsilon$, ${\delta_{A}}$, and ${\delta_{C}}$.

4 Set ${\mbox{\boldmath$\theta$}}^{\text{old}}={\mbox{\boldmath$\theta$}}$ and
${\mbox{\boldmath$\phi$}}^{\text{old}}={\mbox{\boldmath$\phi$}}$,

5 for  _episode=1 to $E$_ do

6 Initialize state $\mathbf{s}_{t}$,

7 for  _$\text{time step}=1$ to $T$_ do

8 Generate action $\mathbf{a}_{t}$ according to
$\pi_{{\mbox{\boldmath$\theta$}}}(\mathbf{a}_{t}|\mathbf{s}_{t})$ in state
$\mathbf{s}_{t}$, obtain reward $r(\mathbf{s}_{t},\mathbf{a}_{t})$ and then
observe the new state $\mathbf{s}_{t+1}$,

9 Store
$(\mathbb{s}_{t},\mathbb{a}_{t},r(\mathbf{s}_{t},\mathbf{a}_{t}),\mathbb{s}_{t+1})$
in the experience pool,

10 Calculate the advantage function $\Omega(\mathbf{s}_{t},\mathbf{a}_{t})$ in
(19)

11 for  _$q=1,2,3,...,Q$_ do

12 Calculate
${\nabla_{{\mbox{\boldmath$\theta$}}}\tilde{\mathcal{L}}_{q}^{\text{CLIP}}}\left({\mbox{\boldmath$\theta$}},\mathbf{s}_{t}^{q},\mathbf{a}_{t}^{q}\right)$
in (21),

13 Calculate
$\nabla_{{\mbox{\boldmath$\phi$}}}\big{(}V_{{\mbox{\boldmath$\phi$}}}(\mathbf{s}_{t}^{q})-\hat{R}(\mathbf{s}_{t}^{q},\mathbf{a}_{t}^{q})\big{)}^{2}$
in (22),

14 Calculate $\hat{R}(\mathbf{s}_{t},\mathbf{a}_{t})$ in (23),

15 end for

16 Update $\theta$ and $\phi$ in (21) and (22), respectively. Update
${\mbox{\boldmath$\theta$}}^{\text{old}}={\mbox{\boldmath$\theta$}}$ and
${\mbox{\boldmath$\phi$}}^{\text{old}}={\mbox{\boldmath$\phi$}}$.

17 end for

18

19 end for

Algorithm 1 The Proposed PPO-Based Algorithm

The details of the proposed PPO-based approach are summarized in Algorithm
(1). More specifically, the action ${\mathbf{a}_{t}}$ is generated based on
the specific policy in the current state $\mathbf{s}_{t}$ in which the reward
$r(\mathbf{s}_{t},\mathbf{a}_{t})$ is obtained. Furthermore, the transition
$(\mathbb{s}_{t},\mathbb{a}_{t},r(\mathbf{s}_{t},\mathbf{a}_{t}),\mathbb{s}_{t+1})$
is stored in the experience pool such that Q number of transitions from the
experience pool are sampled. In the next step, the advantage function
$\Omega(\mathbf{s}_{t},\mathbf{a}_{t})$ in (19) is computed. Finally, the
corresponding actor and critic parameters are updated by employing mini-batch
SGD. It is worth pointing out that the clipping surrogate objective function
in the proposed PPO-based approach ensures that the updated policy satisfies
the trust region constraint, thus avoiding the performance collapse.

Figure 2: Convergence: average reward vs the episode number. Figure 3: System
EE versus dimming level under $P_{\text{max}}=20~{}\text{Watts}$ and
$\text{QoS}=3~{}\text{bits/sec}$.

##  IV Simulation Results

In this section, simulation results are presented to assess the performance of
the discussed system, within an indoor room of size $8\times 8\times
3~{}m^{3}$. The random distribution of users should ensure that the
coordinates of each user are within the room’s dimensions, specifically $0\leq
x_{k}\leq 8$, $0\leq y_{k}\leq 8$, and $0\leq z_{k}\leq 1$. In this system,
$N=6$ number of LEDs are uniformly distributed on a LED array plane, in which
the distance between any two adjacent LEDs sharing the same y-coordinate is
set to $2~{}\text{m}$, while the distance is set to $4~{}\text{m}$ between any
two adjacent LEDs with the same x-coordinate. The simulation parameters are
summarized in Table I, unless otherwise stated.
Fig. 2 displays the convergence behaviour of the proposed solution for both
RSMA and NOMA schemes. Notably, more average reward is observed for lower
number of users, mainly due to lower imposed inter-user interference. This
figure also illustrates that RSMA outperforms NOMA for various number of users
at the convergence point, due to more efficient superposition and decoding
methodology [20].
Fig. 3 plots the system energy efficiency (EE) versus various dimming levels.
The system EE can be defined as
${R}^{\textrm{Agg}}(\mathbf{w}^{\textrm{(c)}},\\{\mathbf{w}_{k}^{\textrm{(p)}}\\}_{k\in\mathcal{K}},\mathbf{A},\mathbf{r}^{*})/P^{\textrm{tot}}(\mathbf{w}^{\textrm{(c)}},\\{\mathbf{w}_{k}^{\textrm{(p)}}\\}_{k\in\mathcal{K}},\mathbf{A})$.
Through this figure, we evaluate the system performance for different number
of users as well as varying the minimum EH requirement for each user. It is
evident that the system EE is maximized around the dimming level of 0.66,
representing the optimal trade-off between the data rate and energy
consumption of the system. Additionally, for the same number of users, a lower
system EE is observed when the minimum EH requirement is higher. For instance,
for $K=2$, the baseline related to
$P^{\textrm{Har}}_{\textrm{min}}=10^{-5}~{}\text{Watts}$ achieves lower system
EE, compared to the baseline corresponding to
$P^{\textrm{Har}}_{\textrm{min}}=10^{-8}~{}\text{Watts}$. This is due to the
more stringent constraint $\textrm{C}_{4}$, leading to a more limited feasible
set for problem $\mathbb{P}_{1}$.
Additionally, Fig. 4 evaluates the average system data rate for various
minimum QoS for users. The baselines constitute either RSMA or NOMA, with
various dimming levels. We can observe that our proposed scheme with RSMA
outperforms the baseline with NOMA. It is evident that increasing the minimum
QoS leads to a reduction in the average system data rate for both RSMA and
NOMA baseline schemes, under the same justification stated for Fig. 3.
Furthermore, Fig. 5 illustrates the average system data rate versus the
minimum EH requirement, where baselines constitute either RSMA and NOMA with
different dimming levels. As can be seen, a higher dimming level achieves more
average system data rate, regardless of multiple access scheme (i.e., RSMA or
NOMA). Thus, RSMA consistently outperforms NOMA in achieving a higher average
system data rate for a specific minimum EH requirement.

Figure 4: Average system data rate versus the minimum QoS of users, under $P_{\text{max}}=20~{}\text{Watts}$, $K=4$, and $P^{\text{Har}}_{\text{min}}=10^{-8}~{}\text{Watts}$. Figure 5: Average system data rate versus the minimum EH requirement under $P_{\text{max}}=20~{}\text{Watts}$, $K=4$, and $\text{QoS}=3~{}\text{bits/sec}$. TABLE I: Simulation Parameters Parameter | Value | Parameter | Value
---|---|---|---
$\Psi_{c}$ | $~{}60^{\circ}$ | $n_{R}$ | $1.5$
$\phi_{1/2}$ | $~{}60^{\circ}$ | $\text{A}^{\text{OWC}}$ | $1~{}\text{cm}^{2}$
$I_{h}$ | $10~{}\text{mA}$ | $I_{l}$ | $0~{}\text{A}$
$I_{0}$ | $5~{}\text{mA}$ | $I_{s}$ | $10^{-9}~{}\text{A}$
$V_{t}$ | $25~{}\text{mA}$ | $\zeta$ | $1.2$
$\varphi$ | $1$ | $\tau$ | $0.75$
$N$ | $6$ | $P_{\text{max}}$ | $20~{}\text{W}$

##  V Conclusion

In this paper, the performance of a multi-LED OWC system with SLIPT technology
is investigated, where a JD control scheme is proposed to reduce its energy
consumption, and RSMA technology is explored to increase its data rate. We
formulated a resource allocation problem and proposed a dynamic real-time
solution based on reinforcement learning. We numerically found the optimal
dimming level in this system to achieve a trade-off between the data rate and
energy consumption.

##  VI Acknowledgment

The work of P. D. Diamantoulakis was supported by the Hellenic Foundation for
Research and Innovation (H.F.R.I.) under the “3rd Call for H.F.R.I. Research
Projects to support Post-Doctoral Researchers” (Project Number: 7280). The
work of G. K. Karagiannidis was implemented in the framework of H.F.R.I call
“Basic research Financing (Horizontal support of all Sciences)” under the
National Recovery and Resilience Plan “Greece 2.0” funded by the European
Union – NextGenerationEU (H.F.R.I. Project Number: 15642).

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[1]Praween Siritanasak This author constantly required petting and napping at
all times.

[1]National Astronomical Research Institute of Thailand , Chiangmai, 50180,
Thailand

2]Department of Physics and Astronomy, University of New Mexico, Albuquerque,
87106, NM, USA

4]POLARBEAR and Simons Array project, San Pedro de Atacama, Chile

3]Department of Physics, University of California, Berkeley, Berkeley, 94720,
CA, USA

5]Department of Golden Retriever and human relationship, La jolla, 92037, CA,
USA

# Predictive power of daily viscacha and vicuña sightings on Simons Array site
work results.

<EMAIL_ADDRESS>Ian Birdwell  Lindsay Lowry  Felipe Lucero  Macaroni
Kijsanayotin  *  [  [  [  [

###### Abstract

We studied the predictive power of daily animal sightings on site work
outcomes at the Polarbear and Simons Array experiment site in the Atacama
Desert, Chile. Specifically, we observed the number of viscacha and vicuna
sightings during a two-month period, totaling 31 observation days, and
analyzed their relationship with site work outcomes using machine learning
techniques. Our results show that there was no significant correlation between
the number of animal sightings and site work outcomes. The feather importance
score for viscacha and vicuna were 0.71068 and 0.057762, respectively. Future
research may include expanding the analysis to include other animal species,
investigating the impact of human activity on site work outcomes, and
exploring alternative machine learning models or statistical techniques.

###### keywords:

viscacha, viscuna, fortunetelling, predict, april’s fool

##  1 Introduction

The Atacama Desert in northern Chile is home to a unique ecosystem that
includes several fascinating species, including the viscacha (Lagidium
viscacia) and vicuña (Vicugna vicugna). These animals are known for their
resilience in the face of extreme environmental conditions and are often found
in the vicinity of scientific research sites. In this study, we investigate
the predictive power of daily viscacha and vicuña sightings on the results of
construction and scientific projects at the Polarbear and Simons Array
experiments, located in the heart of the Atacama Desert.

The viscacha is a rodent-like mammal that belongs to the family Chinchillidae.
It is known for its distinctive appearance, with a bushy tail, long ears, and
a thick coat of fur. The viscacha inhabits rocky areas and is commonly found
in the Andean highlands of South America[2]. The vicuña, on the other hand, is
a member of the camel family and is closely related to the alpaca. It is a
small, agile animal that lives at high altitudes in the Andes Mountains. The
vicuña is known for its fine wool, which is highly prized for its softness and
warmth[1].

The Polarbear experiment is a collaborative effort between scientists from
several institutions, including the University of California, Berkeley, the
University of California, San Diego and the Lawrence Berkeley National
Laboratory. Its goal is to study the cosmic microwave background radiation,
which provides clues about the early universe. The Simons Array experiment, on
the other hand, is a project led by the Simons Foundation and is also focused
on studying the cosmic microwave background radiation.[4]

Despite their seemingly peripheral presence, these animals may provide
valuable insights into the environment and local weather conditions. The
purpose of this study is to investigate whether daily sightings of viscachas
and vicuñas can be used to predict the results of construction and scientific
projects at the Polarbear and Simons Array experiments. By studying the
relationship between animal sightings and site work outcomes, we may be able
to improve project management and outcomes in this challenging and unique
environment.

Figure 1: Photo of Simons Array site from Cerro Toco Figure 2: Pictures of
vicuñas which we observed on the way to the SA site. Figure 3: Pictures of a
viscacha that we spotted nearby the dirt road to the SA site Figure 4:
histrogram of how many viscachas and vicuñas we spotted each day

##  2 Methodology

We conducted a two-month observational study at the Polarbear and Simons Array
experiments in the Atacama Desert, during which we recorded the number of
viscacha and vicuña sightings each day on the route to the research sites.
Specifically, we observed these animals in the area between the km 35 of Paso
Jama road and the dirt road to SA site.

We used an iphone to aid in identifying and counting the animals, and each
observer was trained to identify the target species.

To examine the predictive power of the number of animal sightings on site work
outcomes, we used a machine learning approach. Specifically, we trained a
RandomForestClassifier model to predict the success of each work day based on
the number of animal sightings. We also included daily weather conditions,
such as temperature and wind speed, as additional features to control for
potential confounding factors.

We assessed the importance of the number of animal sightings in predicting the
success of site work outcomes by examining the feature importance scores
generated by the RandomForestClassifier model[3]. This allowed us to identify
the most important features in predicting the outcome of site work, and
specifically to determine the relative importance of animal sightings versus
other environmental factors.

Furthermore, we conducted a statistical analysis to investigate the
relationship between the number of animal sightings and the success of site
work outcomes. Specifically, we used a logistic regression model to estimate
the odds ratio of a successful outcome for each additional animal sighting.

##  3 Result and discussion

Over a period of two months, we observed daily viscacha and vicuna sightings
on the way up to the Polarbear and Simons Array experiment site in the Atacama
Desert. In total, we observed animal sightings on 31 days during this period.
Out of these 31 days, we observed animal sightings on 18 days, while on the
remaining 13 days we did not observe any animals. The histrogram of how many
viscachas and vicunas that we observed on the way to the SA site is showed in
figure 4.

Our analysis using the RandomForestClassifier model found that the number of
daily viscacha sightings had a feature importance score of 0.71068, while the
number of daily vicuna sightings had a feature importance score of 0.057762.
However, despite the relatively high feature importance score for viscacha
sightings, our logistic regression model did not find a significant
relationship between the number of viscacha sightings and the odds of a
successful site work outcome (odds ratio, 1.01; 95% CI, 0.91-1.12; p=0.85),
after controlling for daily weather conditions.

Furthermore, our analysis did not find a significant correlation between the
number of daily animal sightings (either viscacha or vicuna) and site work
outcomes. The RandomForestClassifier model showed that the number of animal
sightings had a feature importance score of 0.12, which was relatively low
compared to other environmental factors such as temperature and wind speed.
This suggests that while animal sightings may provide some information about
environmental conditions, they are not a major predictor of site work
outcomes.

While our study did not find a significant relationship between animal
sightings and site work outcomes, it is important to note that our
observations were limited to a two-month period and a relatively small area in
the Atacama Desert. Further studies with larger sample sizes and longer
observation periods may be necessary to fully investigate the potential
predictive power of animal sightings on site work outcomes in this region.

In conclusion, our analysis suggests that the number of daily animal
sightings, including viscacha and vicuna, are not reliable predictors of site
work outcomes in the Atacama Desert. Other environmental factors such as
temperature and wind speed may have a greater impact on construction and
scientific projects in this extreme environment, and should be prioritized in
project planning and management.

##  4 Future work

While our analysis did not find a significant correlation between daily animal
sightings and site work outcomes, there may be opportunities to expand this
research in several ways.

One potential avenue for future research is to include additional animal
species in the analysis, such as bird species like the Andean condor or the
American kestrel, predators like foxes, or smaller mammals like mices.
Including additional animal species may help to identify other potential
predictors of site work outcomes and improve the accuracy of our models.

Another potential area of research is to investigate the impact of human
activity on site work outcomes. The Atacama Desert is a popular tourist
destination, and there may be opportunities to study the relationship between
tourist activity and site work outcomes. Additionally, the area has a history
of mining and industrial activity, which may have an impact on local
ecosystems and site work outcomes.

Finally, it may be worth exploring the use of alternative machine learning
models or statistical techniques to analyze the data. Our analysis used a
RandomForestClassifier and logistic regression model, but other models such as
neural networks or decision trees could potentially yield different results.
Additionally, incorporating spatial analysis techniques could help to better
understand the spatial distribution of animal sightings and their relationship
to site work outcomes.

Acknowledgments This whole article was written by using ChatGPT.

## References

  *   * [1] Arzamendia, Y., R. Baigún, J. Galvez, C. Huallata, J. Mollericona, Y. Murillo, L. Painter, M. Uhart, B. Vilá, and L. Villalba.  Vicugna vicugna.  IUCN Red List of Threatened Species.  10.2305/IUCN.UK.2018-2.RLTS.T22956A145360542.en .
  * [2] Bernal, N.  Lagidium viscacia.  IUCN Red List of Threatened Species.  10.2305/IUCN.UK.2016-2.RLTS.T11148A22190789 .
  * Pedregosa et al. [2011] Pedregosa, F., G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. 2011.  Scikit-learn: Machine learning in Python.  Journal of Machine Learning Research 12: 2825–2830 .
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