Outage performance analysis of non-orthogonal multiple access systems with RF energy harvesting

ABSTRACT


INTRODUCTION
NOMA technology is well-known because of its ability to serve multiple users exploiting the same resource block [1], [2]. Additionally, we can find in the existing literature the principal elements of NOMA, which have been well investigated, such as superposition coding, successive interference cancellation (SIC). Thus, it is needless to mention the convenience of deploying NOMA for the massive connectivity need of 5G and IoT applications, [3]- [8]. Besides, simultaneous wireless information and power transfer (SWIPT) systems, as the name suggests, exploit the radio frequency (RF) for EH and transferring data to power finitecapacity batteries in wireless relaying networks, [9]- [14]. Indeed, we can find a wide range of studies relating to EH relaying networks for outdoor scenarios in [15]- [24]. Specifically, in [15]- [17], the two relaying protocols namely power splitting-based (PS) and time switching-based (TS) and their hybrid version in cooperative relaying networks were studied. Additionally, two relay operation modes so-called amplify-andforward (AF) and decode-forward (DF) were investigated in [18]. Especially in [22]- [24], the authors analyzed the system performance of SWIPT networks in the context of NOMA. On the contrary, despite being excellent in modelling the indoor fading variations caused by building walls and moving objects [25]- [27], log-normal fading channels are not studied that intensively comparing to common fading channels

SYSTEM MODEL
Depicted in Figure 1(a) is the in-studied system model whereas a source ( ) attempts to transmit data to two user devices denoted as 1 and 2 . However, we can see that the → 2 communication link cannot be realized because of the in-between obstacle. Thereby, 1 is employed to relay the data transmitted from to 2 . It should be noted that 1 operates in DF mode and is energized by EH the signal that sends. The → 1 and 1 → 2 distances are denoted with 1 and 2 , and assigned with complex channel coefficients of ℎ 1 and ℎ 2 , respectively. Besides, there are two random variables (RVs) denoted as |ℎ 1 | 2 and |ℎ 2 | 2 . The two RVs are independently and identically distributed (i.i.d) over the time block in the log-normal distribution manner, with parameters ( ℎ 1 , ℎ 1 2 ) and ( ℎ 2 , ℎ 2 2 ), respectively. Additionally, we have ℎ 1 is the mean value of 10 log(|ℎ 1 | 2 ), and ℎ 2 is the standard deviation of 10 log(|ℎ | 2 ), ∈ {1,2}. With regard to Figure 1(b), we can see the PSR protocol that 1 employs in this study for EH and information transmission (IT) over the time block . Specifically, we have divided into two /2 blocks with details below.

In first time slot
During the first time slot /2, transmits data with a transmission power of to 1 . The second time slot, remaining /2, is used for IT from 1 to 2 . As aforementioned, PSR protocol 1 separates the to two portions for EH and IT purposes. We denote the power splitting (PS) ratio as , 0 < < 1. Thereby, at 1 , the energy amount from EH process is: 2 11 ( / 2), where 0 < < 1 is the EH efficiency at the energy receiver, determined by the rectifier and EH circuitry that 1 deploys. Employing the superposition property of S's transmit signal in NOMA scheme [1,2], the received signal at 1 is expressed as shown in (2).
( ) where we have 1 and 2 are, respectively, the power allocation coefficients of target signal 1 and 2 that attempts to send to 1 and 2 . Besides, we have the additive white Gaussian noise (AWGN) at 1 , which is 1 , with variance 0 . We assume that [ 1 2 ] = [ 2 2 ] = 1. Since 2 is further from S than 1 , it is allocated with more power. Thus, we have 2 > 1 > 0, which satisfies 1 + 2 = 1. Additionally, the 1 consumes a portion of the energy harvested for its operation while the rest is utilized for DF the received signal to 2 . Thereby, we can express the transmission power at 1 with regard to the harvested energy as shown in (3).
Considering (2), we have the received signal-to-interference-plus-noise ratio (SINR) at 1 for detecting the signal 2 of 2 formulated in (4). 12 2 The 1 receives then decodes the signal 1 and 2 from S with the help of SIC [23]. The received SNR that 1 exploits to identify its signal, 1 is formulated as (5). 11 2 ,

In second time slot
After decoding signal 2 , 1 forwards the signal to 2 . Hence, 2 receives the signal of: where 2 is denoted the additive white Gaussian noise (AWGN) at 2 , with variance 0 . We substitute (3) into (6) to obtain: Accordingly, the received SNR at 2 is expressed as

PERFORMANCE ANALYSIS 3.1. Outage performance at 1
In NOMA setup, 1 is not subject to any outage event on condition that both the 1 and 2 that it receives from are successfully decoded. Hence, with regard to (4) and (5), we can formulate the of 1 as shown in (9) where ℎ 1 = 2 2 1 − 1 and ℎ 2 = 2 2 2 − 1. To detect the 1 and 2 , the target rates 1 and 2 are deployed, respectively. The probability function is (. ). In general, the of 1 , deploying protocol, is expressed in the Theorem 1 as (10), Theorem 1.
we substitute (12) into (11) to prove the correctness of the Theorem 1. The proof ends here.

3.2.
Outage performance at 2 U Additionally, 2 experiences outage event either when 1 fails to detect 2 to forward to 2 or 2 is detected but cannot be recovered by 2 . Thus, with regard to (4) and (8), the of 2 is expressed as (14).

Total system throughput
It should be noted that for delay-limited transmission mode, the received signal is decoded by the destination node one block after another. Additionally, we have S transmit information with a constant rate of , ∈ (1,2), which is determined by the over log-normal fading channels. For protocol in the delaylimited transmission mode [21], we have the total system throughput as shown in (21).

UX and 22 ,
Ux are consecutively taken from Theorem 1 and 2. Besides, we have the target rates being 1 and 2 , which are respectively the target rates for 1 , 2 to detect 1 and 2 .

RESULTS AND DISCUSSION
This section presents the Monte Carlo simulation results of the derived expressions to show how the PS factor and the SNR affect the system performance in PSR NOMA scenario over log-normal fading channels. The simulation results are plotted in addition to the analytical results for comparison. For the simulations, we presume that = 1, = 2, 1 = 2 = 2 (m), ℎ 1 = ℎ 2 = 4 ( ), ℎ 1 = ℎ 2 = 3 ( ). Moreover, we use the power allocation coefficients of NOMA for 1 and 2 being 1 = 0.2 and 2 = 0.8, respectively. Last but not least, we set the target rates as 1 = 2 (bps/Hz) and 2 = 1 (bps/Hz). Figure 2 shows the versus the PS factor, . In general, we can see that the probability that the outage event happens to 1 is significantly higher than that of 2 . The raises constantly to the increase of the PS factor for 1 . However, for 2 , the first decreases to its minimum value as PS factor approaches (0.45), then rises to its maximum when the PS factor grows further. Figures 3 and 4 consecutively plot the and the throughput versus the SNR. Specifically, in Figure 3, it is obvious that the higher the SNR, the lower the O P. Besides, in Figure 4, we can observe that the throughput-SNR curve of 1 is remarkably better than that of 2 starting from SNR=2.5 (dB). Last but not least, we can see the impact of SNR on the with two different data transmission rates in Figure 5. In particular, for the lower 1 = 2 = 0 value, the system performs better indicated by the fact that the -SNR curve converges quicker to the zeroth floor, which indicates 100% success in data transmission. In closing, we can see that the simulation results fit well the analytical ones showing the accuracy of our derived expressions.

CONCLUSION
In a nutshell, we investigate the and the total throughput for delay-limited transmission mode of NOMA EH-HD-DF-PSR networks over log-normal fading channels. In general, we can conclude that the SNR increase will lead to better throughput, which subsequently makes the smaller. Furthermore, the network performs better with smaller data transmission rate and is more likely to experience outage event as the PS factor becomes higher.