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1. Introduction
Following the advancement of the fifth and upcoming sixth-generation communication, simultaneous wireless information and power transfer (SWIPT) holds its place to be a promising technology for self-sustaining communication systems as it can offer notable system performance gains, indicated by the improvements of spectral efficiency (SE), power consumption, interference management and delay of transmission, thanks to its nature of facilitating simultaneous information and energy transmission Perera et al. (2018) , Sidhuet al. (2019), Nguyen et al. (2019) . For SWIPT cooperative relaying system, there are in use two major modes: half-duplex (HD) and full-duplex (FD). Specifically, in HD mode, the relay is equipped with one antenna functioning so that the data re-transmission from the source is conducted in dedicated and orthogonal channels Laneman et al. (2004) . Meanwhile, in FD mode, a relay is equipped with two antennas to facilitate the data receiving and transmitting in the same time slot and bandwidth. Moreover, it is worth noting that the FD wireless network is praised owing to its ability to double the SE and improve considerably the network throughput in comparison with the HD one.
The combination of FD operating mode in EH relaying networks has been a debatable topic regarding the possibility to sustain themselves when operating FD mode and performing the relaying task. However, to the advancement of the antenna, battery technologies and signal processing capacity, it is reasonable to re-assess the FD-EH relaying networks for the promising benefit that they can offer, as in Zhong et al. (2014) , Liu et al. (2016) , Zeng and Zhang (2015) . Additionally, in Li et al. (2016), the utilization of energy storage can bring in zero diversity gain when the SNR level is high. Remarkably, Zhong et al. (2014) discussed intensively the constraints of FD-EH relaying networks and proved that the system performance in three different transmission modes can be boosted significantly.
To describe the outdoor wireless channel, Rayleigh, Rician and Nakagami-m fading channels have been widely accepted among the network designers, Zhang et al. (2015) . However, for indoor scenario, to characterize the shadowing effects caused by the building walls, obstacles and human movements, log-normal is a better choice Laourine et al. (2007) , Renzo et al. (2010) , Zhu et al. (2017) , making it a more suitable candidate for smart homes and Industrial Internet of Things (IIoTs) applications. Besides, it is reasonable to use the current advancement in the relaying network technology to further boost the system performance of the household networks. Indeed, this was proven to provide higher channel capacity and wider network coverage range as well as minimizing the shadowing effect, Zhang et al. (2009). Moreover, equipping more relays in a cooperative relaying system provides more degree of freedom (DoF), which enables the system to combine more independent fading signals from the several relays in operation, hence resulting in higher system performance Foschini (2002) .
The above studies have provided a background to develop a so-called low-power energy harvesting (LPEH) wireless sensor networks (WSN), which can counteract the high signal attenuation and noise in household scenarios Rubin et al. (2014) , Rabie et al. (2017) , Pu et al. (2019) .
Although the energy harvested from radio frequency (RF) is relatively low in comparison with other sources such as thermal, solar, etc., it is sufficient for operation of several devices and sensors Assogba et al. (2020) . Specifically, authors in Georgiou et al. (2016) attempted to measure the free ambient RF and found out that by densifying the Wi-Fi access points, it is possible to not only power the indoor devices (smoke detectors, wearable electronics, etc.) but also to extend their lifetime via trickle charging. Taking a step further into upgrading the indoor electrical grids, a namely power line communication (PLC) has been investigated, in which wireless devices can exploit the existing electricity cables for the improvement of data transmission and energy efficiency Wu (2015) . Regarding the security of the physical layer, the available techniques for wireless network are applicable for PLC as well. For example, a case study of how to utilize jamming technique to guard against eavesdroppers for cooperative PLC networks was presented in Salem et al. (2017) . In the household setup, it is highly recommended to utilize log-normal fading channels because other fading channels cannot describe efficiently the fading effects caused by walls, human movement and indoor obstacles Renzo et al. (2008) . A number of papers have extensively analyzed the performance of relay-aided EH wireless networks embedded in the PLC using different key parameters and proved that this combination is promising for the future of smart grids and indoor wireless communication Cheng et al. (2013) , Ezzine et al. (2015) , Rabien et al. (2016) , Rabie et al. (2018), Ramesh et al. (2020) , which is undeniably powered by the development of LPEH WSN.
Inspired by the aforementioned studies, this manuscript assesses the performance of a relay selection (RS) scheme so-called optimal loop interference relay selection (OPLIRS) in the context of LPEH WSN. Notably, the relays are equipped with batteries and operate with FD-AF protocol. The shadowing effect of the network is characterized by the log-normal fading channels.
2. System models
Fig. 1 below depicts a LPEH WSN including a source (S), an in-between cluster (C) of K cooperative relays
In addition, the carrier and symbol synchronization are assumed to be ideal. Each terminal knows beforehand its own channel state information (CSI). (S) is powered by a stable power source
In fact, the distances from (S) to
We consider the random variables (RVs) which are independently and identically distributed (i.i.d) as per log-normal distribution as
2.1. Standalone direct link
To serve as a foundation for further study, a direct transmission protocol, in which (S) transmits information directly to (D) without any assisting (R) in the LPEH WSNs is assumed and investigated.
Definition 1. In the context of direct transmission protocol, the direct (S)-(D) link is the unique option. Thus, it will use all the time slots from the signal block for data transmission.
Employing the direct transmission protocol, the overall (S)-(D) capacity can be obtained with zero-mean, circularly symmetric
where
As aforementioned, the ergodic OP is an indicator for evaluations of the system performance. This is the probability that the instantaneous capacity falls below a given threshold bits per channel use (BPCU) being
and
where
By utilizing the CDF of the log-normally distributed RV
where
2.2. Relay-aided cooperative protocol
As aforementioned, the relay-aided cooperative protocol is deployed to improve the LPEH WSN performance.
Definition 2. In the context of relay-aided cooperative protocol, all the relay links can alternatively transmit the data in place of the direct link. Specifically, if the direct link is severely attenuated, a relay will be chosen among
By this approach, more time slots are saved, and overhead information is reduced, because only the needed relay link is activated. Besides, in LPEH WSN, we can receive the maximal diversity gain equaling the relay nodes that are available in the network, as proven in Laneman et al. (2004) .
As described in Nguyen et al. (2018) , one transmission cycle from (S) to (D) realized within
Within
where the EH efficiency
As mentioned in Zhong et al. (2014) , as a relay can recognize its own signal in the FD multi-relay scenario, the interference cancellation can be applied to itself.
For
where the information signal
In a FD-AF system, after the signal is base-band processed at
where the relay gain,
Then, (8) is substituted into (7) and modified so that the end-to-end SNR of the
where
Additionally, the instantaneous capacity of the FD-AF-TSR system can be calculated.
From here, the RS scheme for the in-studied LPEH WSN so-called the optimal loop interference relay selection (OPLIRS) scheme is derived. In particular, the OPLIRS scheme chooses first the (R) having the best end-to-end link, then updates the SINR in the first branch. Thus, the selected
It should be noted that the OPLIRS scheme is established only if the full CSI is known.
2.3. Energy storage modeling at relay
The stationary stochastic process in Tutuncuoglu et al. (2017) states that the minimum energy needed to activate
where
In practice, however, the
where
Additionally, to formulate the energy buffer status as per the Markov stochastic process, we use the denotation
Subsequently, we can combine (12), (13) and the original PDF of
Lemma. 1 The
These two statuses are therefore used to characterize the flow of the energy that has been harvested. Accordingly, we proposed an on-off
Remarkably, (14) is not the same as the original PDF
Subsequently, an on
Remark 1. The relaying link in LPEH WSN can be activated if the direct link cannot perform the information transmission task and the available energy stored at the relay is greater than
3. Performance analysis
3.1. Formulating the problem
In practice, the relaying link over
At least one of the data packets cannot be successfully delivered during the information transmission from (S) to (D). This leads to the direct link’s end-to-end SNR below the threshold value of the system.
The energy harvested by
The relay
Having acknowledged the above constraints, for the herein study, we assume that
3. 2. Overall ergodic outage probability analysis
Regarding (10), the ergodic OP for S
where
Proposition 1.
The SNR in (11) is assumed to be high and identical. Thus, we can formulate the corresponding overall ergodic OP for the high SNR range under OPLIRS scheme as
were
Proof:
It is worth noting that the
Similarly, the SNR at (D) is given by.
Subsequently, we combine (18) and (19) then substitute them into (11) to obtain the ergodic OP in (16), considering
where
It should be noted that all the aforementioned channels means and variances are i.i.d. as per the log-normal distribution . Assuming that
where
Besides, the RV
As we substitute (22) and (23) into (21), the ergodic OP can be obtained as.
Consequently, (24) and (4) are substituted into (15) to obtain the overall ergodic OP in OPLIRS scheme, as given in (17).
4. Results and discussion
In this section, the Monte Carlo numerical simulation was conducted to investigate the overall ergodic OP of the in-studied system with OPLIRS scheme. The system parameters for the simulations are listed below in Table. 1. The results are calculated based on proposition 1 in (17), by means of MATLAB simulation.
Table 1 Simulation parameters.
| Primary Parameters | Description | Values |
|
|
energy-exhausted probability | 10-1 |
|
|
frequency bandwidth | 2(W) |
|
|
transmission rate threshold | 2(bps/Hz) |
|
|
traditional stabilized power source | 5(dB) |
|
|
overall AWGNs | 1 |
|
|
EH efficiency | 1 |
|
|
EH time fraction | 0.2 |
|
|
path-loss exponent | 2 |
|
|
(S)- ( |
5(m) |
|
|
( |
5(m) |
|
|
(S)-(D) distance | 10(m) |
|
|
(S)- ( |
4(dB) |
|
|
( |
4(dB) |
|
|
(S)--(D) channel mean | 4(dB) |
|
|
loop interference ( |
2(dB) |
|
|
(S)- ( |
3(dB) |
|
|
(S)--( |
3(dB) |
|
|
(S)-(D) channel variance | 3(dB) |
|
|
loop interference ( |
3(dB) |
Fig. 4 illustrates the overall ergodic OP versus the EH time switch
Fig. 5 depicts the relation between the overall ergodic OP of the LPEH WSN and the SNR. For comparison, we use three values of 0, 0.5 and 1 for the energy-exhausted probability
Fig. 6 plots the overall ergodic OP versus the SNR when changing the number of relays,
5. Conclusions
In general, the paper presents the performance analysis in terms of the overall ergodic OP of the OPLIRS scheme in the context of LPEH WSN. Because the simulations correlate well with the theory, the expressions that we derived show the potential to be applicable for other future studies. It is as well proven that the log-normal fading channel is appropriate for modelling such indoor scenarios. Future studies can consider different RS schemes and compare them with the herein studies to find the best one for the LPEH WSN setup.
