# Outage Analysis for Active Reconfigurable Intelligent Surface-Enhanced
Wireless Powered Communication Networks
††thanks: This work was supported by Basic Science Research Program through
NRF funded by the MOE (NRF-2022R1I1A1A01071807, 2021R1I1A3041887), and
Institute of Information & communications Technology Planning & Evaluation
(IITP) grant funded by the Korea government (MSIT) (2022-0-00704, and
Development of 3D-NET Core Technology for High-Mobility Vehicular Service).

Waqas Khalid  Institute of Industrial Technology, Korea University, Sejong,
Korea<EMAIL_ADDRESS>gmail.com}  Heejung Yu  Dept. of Elec. & Inform.
Eng., Korea University, Sejong, Korea<EMAIL_ADDRESS>Alexandros-
Apostolos A. Boulogeorgos  Dept. of ECE, University of Western Macedonia,
Kozani, Greece<EMAIL_ADDRESS>
###### Abstract

Wireless powered communication (WPC) involves the integration of energy
harvesting and data transmission. This allows devices to communicate without
constant battery replacements or wired power sources. Reconfigurable
intelligent surfaces (RISs) can dynamically manipulate radio signals. In this
paper, we explore the use of active elements to mitigate double-fading
challenges inherent in RIS-aided links. We enhance the reliability performance
for an energy-constrained user by combining active RIS and WPC. The
theoretical closed-form analysis, which includes transmission rate, harvested
energy, and outage probability, provides valuable insights that inform
parameter selection.

###### Index Terms:

Wireless powered communication (WPC), Active RIS, Outage probability.

##  I Introduction

In the realm of sixth-generation (6G) wireless networks, the deployment of
reconfigurable intelligent surfaces (RIS) stands as a pivotal innovation,
shaping the foundation of intelligent wireless environments, alleviating radio
frequency (RF) complications, and bolstering connectivity under challenging
propagation conditions. By introducing controlled phase shifts to
electromagnetic signals, RIS systems substantially enhance network coverage
and reliability without complex signal processing or additional
infrastructure[1, 2]. Wireless powered communication (WPC) represents another
emerging field anticipated to play a pivotal role in 6G networks, seamlessly
merging energy harvesting with data transmission. This integration empowers
networked devices to communicate independently of conventional power sources,
eliminating dependence on batteries or a constant power supply [3].

###  I-A Motivation

In practical scenarios, the deployment of RIS-aided wireless communication
systems may confront challenges, including the significant issue of double-
fading [4, 5]. The strategic incorporation of active elements in RIS has been
proposed, demonstrating considerable potential in effectively overcoming the
double-fading challenge [6]. The synergistic amalgamation of active RIS with
WPC emerges as a highly promising strategy, substantially enhancing both
wireless reliability and energy efficiency, particularly for users facing
energy limitations. This innovative integration is poised to significantly
elevate network performance, energy efficiency, and connectivity, fostering a
new era of advanced, sustainable, and intelligent wireless communications. The
deployment of active RIS-WPC in 6G networks holds immense potential,
particularly in revolutionizing sectors such as the Internet of Things (IoT),
wearable technology, and autonomous vehicles [7].

###  I-B Contribution

In our paper, we focus on RIS-WPC networks, where we employ RIS with active
elements to enhance information transmission. Specifically, an energy-
constrained wireless user harvests RF energy and employs it for data
transmission. This approach capitalizes on RIS beamforming gain to optimize
information reception and provides superior adaptability compared to
conventional WPC systems without RIS. Our work presents significant
contributions including a detailed statistical channel characterization that
accounts for potential noise in active RIS modules, a comprehensive closed-
form outage probability analysis specific to Rayleigh fading channels, and
numerical results. These results not only validate our theoretical findings
but also offer essential guidance for parameter selection.

Figure 1: Active RIS-Enhanced WPC Network.

##  II System Model

We examine a WPC network, depicted in Fig. 1, consisting of a base station
(BS), a power station (PS), and a user (U). We introduce an RIS with $M$
elements strategically placed between the BS and U because a direct link is
obstructed. Each element within the RIS module is equipped with a power
amplifier to amplify the reflected signal. In this configuration, it becomes
possible to mitigate the substantial path loss associated with the RIS-aided
link, effectively overcoming the challenge posed by double-fading111Double-
fading can be mitigated by increasing passive RIS elements. However, this may
result in an increased physical size of the RIS module.. We adopt an
independent and identically distributed (i.i.d.) Rayleigh fading model for all
links [8]. The channel vectors are defined as follows:

  * •

$h_{1}$ for the PS-U link,

  * •

$\textbf{h}_{2}$ for the U-RIS link,

  * •

$\textbf{h}_{3}$ for the RIS-BS link.

We consider $h_{1}$ and each entry in $\textbf{h}_{2}$ and $\textbf{h}_{3}$ to
be an independent complex Gaussian distribution with a zero mean and a unit
variance. Within each channel coherence interval ($\tau_{c}$), communication
unfolds in two distinct phases: energy transfer and information transmission.
During the $\alpha\tau_{c}$ duration, the PS facilitates the transfer of RF
energy to $U$.

The energy harvested by U can be expressed as follows:

$\displaystyle E=\eta\alpha\tau_{c}P_{ps}|h_{1}|^{2}\zeta_{1}$ (1)

where

  * •

$0<\alpha<1$ is time switching factor between energy transfer and information
transmission.

  * •

$\eta$ denotes the energy conversion efficiency,

  * •

$P_{ps}$ denotes the transmission power of PS,

  * •

and $\zeta_{1}$ denotes the path loss from PS to U.

Following this, U transmits its information to BS via RIS during
$(1-\alpha)\tau_{c}$ using the energy harvested during $\alpha\tau_{c}$. The
transmission power of U can be calculated as,

$\displaystyle P_{u}=\frac{E}{(1-\alpha)\tau_{c}}=\frac{\eta\alpha
P_{ps}|h_{1}|^{2}\zeta_{1}}{(1-\alpha)}=P_{e}|h_{1}|^{2}\zeta_{1},$ (2)

where $P_{e}=\frac{\eta\alpha P_{ps}}{(1-\alpha)}$

At BS, the signal-to-noise ratio (SNR) can be written as,

$\displaystyle
z_{u}=\frac{P_{e}\zeta_{1}\zeta_{2}|h_{1}|^{2}|\textbf{h}_{3}^{T}\mathbf{\Theta}\textbf{h}_{2}|^{2}}{\sigma_{T}^{2}}=p_{e}\zeta_{1}\zeta_{2}|h_{1}|^{2}|\textbf{h}_{3}^{T}\mathbf{\Theta}\textbf{h}_{2}|^{2}$
(3)

where

  * •

$\mathbf{\Theta}\\!=\\!\rho\operatorname{diag}(e^{j\theta_{1}},...,e^{j\theta_{M}})$
is $M\times M$ diagonal response matrix of RIS

  * •

$\rho$ is the amplification gain of each RIS element222The amplification gain
for each reflection-type amplifier is set to $\rho$, reducing configuration
overhead and enabling variable beamforming design.

  * •

$p_{e}=\frac{P_{e}}{\sigma_{T}^{2}}$,
$\sigma_{T}^{2}=\sigma_{b}^{2}+\rho^{2}\sigma_{R}^{2}$ is sum of powers of
AWGN noises at the BS and RIS,

  * •

and $\zeta_{2}$ is the path loss from $U$ to BS via RIS.

All channels are assumed to be known [9]. This implies that the phase shifts
at the RIS can be intelligently controlled, i.e.,
$\theta_{m}\\!=-\\!\arg\left(\textbf{h}_{2,m}\textbf{h}_{3,m}\right)$, to
maximize the reception quality of BS [10]. In this case, the SNR in Eq. (3)
can be rewritten as,

$\displaystyle
z_{u}=p_{e}\zeta_{1}\zeta_{2}|h_{1}|^{2}\left(\rho\sum_{m=1}^{M}|\textbf{h}_{2,m}||\textbf{h}_{3,m}|\right)^{2}$
(4)

##  III Outage Probability Analysis

The outage probability is the probability of an event occurring when channel
capacity drops below the codeword rate of the transmission signal ($r$), and
is mathematically expressed as:

$\displaystyle
P_{Out}=\Pr\left[\left(1-\alpha\right)\log_{2}\left(1+z_{u}\right)<r\right]$
(5)

By substituting the SNR from Eq. (4), Eq. 5 can be accurately expressed as:

$\displaystyle P_{Out}$ $\displaystyle=$
$\displaystyle\Pr\left[\left(1-\alpha\right)\log_{2}\left(p_{e}\zeta_{1}\zeta_{2}|h_{1}|^{2}\left(\rho\sum_{m=1}^{M}|\textbf{h}_{2,m}||\textbf{h}_{3,m}|\right)^{2}\right)<r\right]$
$\displaystyle=$
$\displaystyle\Pr\left[\left(|h_{1}|\sum_{m=1}^{M}|\textbf{h}_{2,m}||\textbf{h}_{3,m}|\right)^{2}<\frac{\Delta}{p_{e}\zeta_{1}\zeta_{2}\rho^{2}}\right]$
(6)

Using the statistical characteristics of Rayleigh channels and employing
algebraic manipulations, Eq. (6) can be elegantly simplified as follows,

$\displaystyle P_{Out}=$ $\displaystyle
1-\frac{\pi^{2}}{4K}\sum_{k=1}^{K}\sqrt{1-\omega_{k}^{2}}\sec^{2}\mu_{k}\frac{\left(\tan\mu_{k}\right)^{v-1}}{\Gamma(v)\delta^{v}}$
$\displaystyle\times$
$\displaystyle\exp\left(-\frac{\Delta}{p_{e}\zeta_{1}\zeta_{2}\rho^{2}tan^{2}\mu_{k}}-\frac{tan\mu_{k}}{\delta}\right)$
(7)

where

  * •

$\mu_{k}=\frac{\pi\left(\omega_{k}+1\right)}{4}$,

  * •

$\omega_{k}=\cos\left(\frac{2k-1}{K}\pi\right)$,

  * •

$K$ is the accuracy versus complexity parameter,

  * •

$\Delta=2^{\frac{r}{1-\alpha}}-1$,

  * •

$v=M\frac{\frac{\pi}{4}}{\frac{4}{\pi}-\frac{\pi}{4}}$,

  * •

$\delta=\frac{4}{\pi}-\frac{\pi}{4}$,

  * •

and $\Gamma(.)$ denotes the Gamma function.

##  IV Numerical Results

Numerical results validate the theoretical expressions and provide valuable
insights. Monte Carlo simulations with $10^{4}$ independent trials are used.
Unless otherwise specified, the simulation parameters are as follows:
$\alpha=0.5$, $\tau_{c}=1$, $\eta=0.90$, $r=1.4$ bps/Hz, $P_{ps}=10$ dBm,
$M=\\{0,100\\}$, $\sigma_{b}^{2}=0$ dBm, and $\sigma_{R}^{2}=-80$ dBm, and
$\rho=\\{0,10\\}$ dB.

Fig. 2 shows the outage probability vs. number of active elements ($M$), and
amlification factor for active elements ($\rho$). The results validate the
analytical analysis and imply that an increase in $M$, and $\rho$ (which
demonstrates the amplification impact due to the active RIS) positively
impacts outage performance, subsequently increasing transmission reliability.
As an example, deploying an active RIS rather than a passive RIS allows for a
decrease in the transmit power as well as the number of elements required to
achieve a certain outage probability.

Figure 2: Outage probability vs. Number of active elements ($M$) for different
amplification gain ($\rho$)

##  V Conclusion

The integration of active RIS and WPC significantly enhances the reliability
and energy efficiency of users with limited energy resources. This paper
demonstrates how a user can harvest RF energy from a PS and utilize it for
data transmission to a BS via RIS, optimizing the use of available energy and
ensuring reliable communication. The theoretical analysis and numerical
results provide crucial insights and practical guidelines for parameter
selection, contributing to the advancement of energy-efficient and reliable
wireless communication, particularly as we transition into the 6G era.

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