Outage probability analysis for hybrid TSR-PSR based SWIPT systems over log-normal fading channels

Hoang Thien Van, Hoang-Phuong Van, Danh Hong Le, Ma Quoc Phu, Hoang-Sy Nguyen The Saigon International University (SIU), Ho Chi Minh City, Vietnam Faculty of Engineering and Technology, Thu Dau Mot University, Thu Dau Mot City, Binh Duong Province, Vietnam Van Hien University, Ho Chi Minh City, Vietnam Binh Duong University, Thu Dau Mot City, Binh Duong Province, Vietnam Eastern International University, Binh Duong Province, Vietnam


INTRODUCTION
For conventional energy-constrained wireless networks, it is occasionally hard or even impossible to recharge or replace batteries [1], [2]. Instead, we can exploit the natural resources (wind energy, solar energy) by EH modules to keep the networks energized, although with some limitations because of their fluctuating properties [3], [4]. Thereby, the research community has developed the simultaneous information and power transfer (SWIPT) technology to alter the renewable energy with radio frequency (RF), [5]- [8].
Rayleigh fading channels have been utilized for studies about the adaptive relaying protocol of twohop amplify-and-forward (AF) relaying networks with exceptional throughput performance [9], [10]. Besides, in [11] where the outage probability (OP) of decode-and-forward (DF) PSR system was analyzed, we can see that EH relaying network is more beneficial than conventional networks. Additionally, it is essential to deploy hybrid concepts to study and effectively improve system performance. For example, from the aspect of controlling cooperative multi-agent direct networks, a hybrid system is a mix of discrete-time and continuous-time systems [12]. For cooperative relaying networks, the hybrid concept is employed for either the combination of different relay selection schemes or different relaying protocols. Using hybrid fullduplex (FD) and half-duplex (HD) relay selection scheme, authors in [13], [14] discovered the upper and lower bounds for OP of DF systems. Additionally, we can find a so-called hybridized power-time splittingbased relaying (HPTSR) protocol in [15]- [17] where the OP and maximum throughput were studied. Moreover, in [18], [19], the OP and outage capacity of a so-called joint time allocation and power splitting (JTAPS) scheme over the Rayleigh fading channels were studied concerning the statistical and instantaneous channel state information (CSI). Additionally, in [20], [21], the system performance in terms of the average channel capacity was investigated. We can find some other studies such as [22]- [25], that used the instantaneous CSI to determine the PS factor for a namely dynamic power splitting scheme (DPSS). The OP and throughput for multi-user cooperative relaying networks over Nakagami fading channels were studied in [26], [27]. Last but not least, [28]-[30] investigated the performance of time switching relaying (TSR) and power splitting relaying (PSR) protocols for dual-hop relaying networks in the indoor scenario modelled by log-normal fading channels.
It is noted that several existing studies were conducted mainly over outdoor scenarios which are modelled by Rayleigh and Nakagami-m fading methods. Indeed, there is scarcely recent studies regarding the SWIPT systems for indoor scenarios modelled by log-normal fading channels. Among them, there are papers [28], [29] where the HD AF and DF SWIPT networks were analyzed. Moreover, log-normal fading fits better for modelling shadowing effect from indoor moving objects and human bodies, as mentioned in [31]- [33]. Besides, as in [34], log-normal fading can be employed to model the small-scale fading of indoor ultrawideband (UWB) communications, and in [35]- [37] to model the short and long-term fading of slowlyvarying indoor channels. To overcome all of these constraints, it is essential to deploy cooperative relays for indoor networks, especially for internet of things (IoT) applications [38].
Thereby, in this paper, we study the performance of a hybrid TSR-PSR scheme over log-normal fading channels in a cooperative AF relaying network. We evaluate the system performance in terms of its outage behaviour. It is proven that the proposed hybrid protocol can deliver significantly lower OP than the two separate protocols. Furthermore, we describe the system model in section 2. In section 3, we analyze the performance of the hybrid PSR-TSR AF system over log-normal fading channels. We report the simulation results and discuss them in section 4. The conclusion is in section 5.

SYSTEM MODEL
Illustrated in Figure 1(a) (see in appendix) is the system model of a dual-hop network including a base station (BS), a relay (R) and a destination (D). Assumed without direct link, the BS-to-D communication can only be realized via R, with BS's transmission power of . A part of the RF signal that BS sends is harvested by R for relaying task. We denote the BS-to-R, R-to-D distances, respectively, with 1 and 2 , and according channel coefficients of ℎ 1 and ℎ 2 . Additionally, we have two random variables (RVs) |ℎ 1 | 2 and |ℎ 2 | 2 which are independently and identically distributed (i.i.d.) over the block time following the log-normal distribution, respectively, with parameters ( ℎ1 , ℎ1 2 ) and ( ℎ2 , ℎ2 2 ). Moreover, we have the mean value of 10 log (|ℎ | 2 ) denoted as ℎ , and the standard deviation of 10 log (| ℎ | 2 ), ∈ {1,2}, denoted as ℎ 2 . BS-to-R and R-to-D have complex Gaussian background noise, and , the former has zero mean and the latter has variance 0 N . Last but not least, we have m which is the path-loss exponent.
Considering a hybrid PSR-TSR in Figure 1(b) (see in appendix), we have a two-time-slot block time, T , which is split by TS factor, 2 , to 2 and (1 − 2 ) given that 2 ∈ [0,1]. In 2 , R receives signal from BS. We divide this 1st time slot into two segments which are √ 1 and √1 − 1 , with the PS factor, 1 , given that 1 ∈ [0,1]. We use the segment √ 1 for RF EH, and the segment √1 − 1 for receiving information from BS. Then, within the 2nd time slot (1 − 2 ) , the harvested energy we have at R is used up to decode and forward the signal via the BS-to-D link. Besides, we assume that the processing power of R is neglected because it is relatively small in comparison with the transmission power of R-to-D [11], [39].

PERFORMANCE ANALYSIS HYBRID PSR-TSR SCHEME
Within the 1st time block, we have signal transmitted from BS to R for decoding given by (1).

 
Within the 2nd time slot, we have signal transmitted from R to D as (3).
After the base-band processing and amplifying processes at R, the R transmit signal is where we have the R gain, G of the HD-AF system as (5), From (5), we can formulate the received signal at D as (6).
Consequently, we substitute (3) and (5) into (6) then manipulate it to get the signal-to noise ratio (SNR) at D as (7), . We evaluate the system performance by analyzing the achievable date rate and the OP. Therefore, firstly, we derive the achievable data rate at D as (8).
where we have the HD relaying factor of 12.
The probability that the instantaneous data transmission rate declines below the source transmission rate of 0   ( bits/sec/Hz), with a pre-specified threshold value of 0  , is named OP.
We can obtain the OP at D for the AF hybrid PSR-TSR systems as (9)  Proof: With (7) and (9), we can formulate the OP for the HD-AF hybrid PSR-TSR network as (11). h is always a positive value, we can re-express the probability as (12).

RESULTS AND DISCUSSION
In this section, we investigate the impact of the TS factor, the PS factor and SNR on the OP of the hybrid PSR-TSR systems over the log-normal fading channel via the Monte Carlo simulation results of the previously derived expressions. We use the following system parameters in the simulations as shown in Table 1 unless specified otherwise.  Figures 2 and 3 depict the OP of the hybrid PSR-TSR systems versus, respectively, TS factor of 2 , and PS factor of 1 . As in Figure 2, if we fix 1 = 0.5 and vary 2 , we will obtain the lowest curve which yields the best system performance. It is interesting that all the curves in Figure 2 reach their optimal values at 2 = 0.25. On the other hand, as illustrated in Figure 3, for fixed 2 = 0.5 and varied 1 , the curve is the highest indicating the worst system performance. The optimal values for the curves in Figure 3 distributed 4237 from 1 = 0.7 0.9. Another obvious trait for both figures is that as TS and PS factors approach either zero or one, we have a 100% probability of system shutdown. This is because as 2 and 1 are too small or too large during the 1st time slot, the transmit power from EH process in the 2nd time slot becomes, respectively, insufficient or unnecessarily large leading to poor system capacity [28]. Besides, Figures 4 and 5 plot the OP versus the SNR, χ, with, respectively, three pairs of EH PS and TS factors, i.e., (α 2 = 0.3, α 1 = 0.5), (α 2 = 0.3, α 1 = 0.3), (α 2 = 0.5, α 1 = 0.3), and two data transmission rates, i.e., R 0 = 2 (bps/Hz), and R 0 = 4 (bps/Hz). In general, we can see that the OP decreases as the SNR increases. The hybrid PSR-TSR scheme with higher TS factor performs better. Additionally, the OP gets worse as the transmission rate grows because the power for EH and the transmission time decrease in the 2nd slot [11]. Generally speaking, the simulation results and theory agree well with each other. Thereby, we can use the derived expressions for further studies.

CONCLUSION
To summarize, we study a namely hybrid PSR-TSR protocol employed in a cooperative EH AF relaying network over log-normal fading channels by assessing the analytical expression of the OP. From the simulation results, we are able to conclude that the hybrid PSR-TSR scheme remarkably outperforms the standalone PSR and TSR schemes. Moreover, we prove that the system performance can be raised in association with the increase of EH TS factor and the decrease in data transmission rate.