Outage probability analysis of EH relay-assisted non-orthogonal multiple access (NOMA) systems over block rayleigh fading channel

ABSTRACT


INTRODUCTION
In the history of wireless communications from the first generation (1G) to 4G, the multiple access scheme has been the key technology to distinguish different wireless systems. It is well known that frequency-division multiple access (FDMA) for 1G, time-division multiple access (TDMA) mostly for 2G, code-division multiple access (CDMA) for 3G, and orthogonal frequency-division multiple access (OFDMA) for 4G are primarily orthogonal multiple access (OMA) schemes. In these conventional multiple access schemes, different users are allocated to orthogonal resources in either the time, frequency, or code domain in order to avoid or alleviate interfuse interference. In this way, multiplexing gain can be achieved with reasonable complexity. However, the fast growth of mobile Internet has propelled 1000-fold data traffic increase by 2020 for 5G. Hence, the spectral efficiency becomes one of the key challenges to handle such explosive data traffic. Moreover, due to the rapid development of the Internet of Things (IoT), 5G needs to support massive connectivity of users and/or devices to meet the demand for low latency, low-cost devices, and diverse service types. To satisfy these requirements, enhanced technologies are necessary. So far, some potential candidates have been proposed to address challenges of 5G, such as massive MIMO, millimeter wave communications, ultra-dense network, and non-orthogonal multiple access (NOMA). From that analysis, Non-orthogonal multiple access (NOMA) has been identified as a promising multiple access technique for the fifth generation (5G) mobile networks due to its superior spectral efficiency [1][2][3][4][5][6]. In contrast to traditional water-filling power allocation strategy, NOMA allocates more power to the users with worse channel conditions, which results in a better tradeoff between the system throughput and user fairness. From the previous researches, the impact of user pairing on downlink NOMA systems has been characterized in [7], the work in [8] has studied the power allocation with max-min fairness criterion. An uplink NOMA scheme with joint power and subcarrier allocations has been proposed in [9], where the performance of both link-level and system level has been investigated. In [10], a cooperation-based NOMA scheme for coordinated direct and relay transmissions has been introduced. A diversity-oriented detection mechanism for the cooperative relaying system using NOMA has been proposed in [11]. The performance of transmit antenna selection for NOMA assisted multiple-input-multiple-output (MIMO) relay networks have been examined in [12]. Inspired by user collaboration, a cooperative NOMA transmission scheme has been proposed in [13].
The main objective of this article is to propose and investigate a Non-Orthogonal Multiple Access (NOMA) EH relay assisted system over Block Rayleigh Fading Channel. Firstly, we proposed and investigated a Non-Orthogonal Multiple Access (NOMA) EH relay-assisted system over Block Rayleigh Fading Channel. In the analysis process, we analyze and derive the integral expression of the outage probability. Finally, the Monte Carlo Simulation is used for validating the analytical analysis in connection with all possible system parameters. The results show that the analytical and simulation results agree well with each other in contact with all possible system parameters. The main contributions of this research can be focused on as the followings: -We propose and investigate a Non-Orthogonal Multiple Access (NOMA) EH relay assisted system over Block Rayleigh Fading Channel. -The integral form expression of the outage probability is analyzed and derived. -The influence of all possible system parameters on the outage probability is investigated and discussed.
-All results are verified by the Monte Carlo simulation.
The rest of this manuscript is organized as follows. In section 2, we present the proposed system model and analysis of the outage probability of the proposed system model. Numerical results and some discussion are drawn in section 3. Section 4 concludes this manuscript.

SYSTEM MODEL AND OUTAGE PROBABILITY ANALYSIS
As shown in Figure 1, we proposed a simple cooperative network where a source node, communicates with a destination node, D, via the helping of a decode-and-forward (DF) relay node, R. Moreover, the source S can also directly communicate the destination D. Here, we assume that the systems operate in half-duplex mode, i.e,.., the relay cannot transmit and receive a symbol at the same time. We denote the channel coefficients  The fading gains in all involved links are assumed to follow the Rayleigh distribution with the probability density function (PDF) as in [14].
From (1) the cumulative distribution function (CDF) can be obtained as 2 ( ) 1 exp( the mean of the random variable 2 k h . As in many previous publications, we assume that the source and destination, as well as the relay, know the channel gains. The energy harvesting and information processing for this proposed model system as shown in Figure 2. In this protocol, the transmission is divided into blocks of length T, which consists of three time slots. In the first time slot αT (α is the time switching factor, 01   ), the relay harvests energy from the source node S n . In the second interval time (1-α) T/2, the source S transfers the information to R and D at the same time. Finally, the remaining time slot (1-α) T/2 is used for information transferring from the relay node to the destination.

Figure 2. EH and IT processes
The harvested energy at the relay can be expressed as in [ Where 01   is energy conversion efficiency, and 01   is a time-switching factor. The average transmit power at the relay can be given by The communication process for cooperative relay systems consists of the remaining two consecutive time slots. During the second time slot, the source S will transmit a symbol 1 a with the power P s to both the relay R and destination D. Therefore, the received signal at R and D can be expressed as, respectively.
Apply successive interference cancellation (SIC)-based NOMA scheme, D firstly decodes the symbol 1 a by disposing of the symbol 2 a as a noise term. Also, 1 a is rejected from y D by using SIC to decode 2 a . So, the received SNRs for symbol 1 a and 2 a are respectively obtained as Using the selecting combining (SC) technique at the receiver, so the total outage probability of 1 a is given by Where we denote Apply eq (3.324, 1) of the table of integral [15], (11) can be rewritten as the following Replace (12) Similarity, the end to end SNR for the transmitted symbol 2 a can be calculated as Therefore, the total outage probability of 2 a can be computed as In order to find the total outage probability of 2 a , we denote that   (17) Utilizing the result in [16], the CDF of V can be shown as the (18)

RESULTS AND DISCUSSION
For validation, the correctness of the derived system performance expressions, as well as investigation of the effect of various parameters on the system performance, a set of Monte Carlo simulations are conducted and presented in this section [17][18][19][20][21]. For each simulation, we first provide the graphs from the analytical formulas. Secondly, we plot the same curves that result from the Monte Carlo simulation. For this purpose, we generate 106 random samples of each channel gain, which are Rayleigh distributed. Finally, the analytical curve and the simulation one should match together to verify the correctness of our analysis.
The outage probability of the proposed system versus transmitting SNR γ 0 is plotted in Figure 3 with basic system parameters as R=0.5 bps, η=0.8, α=0.45 and 0.85. In this analysis, the transmit SNR γ 0 varies from -10 dB to 20 dB continuously. From the research results, we see that the outage probability of the proposed system decreases significantly with the increasing the transmit SNR γ 0 . It can be observed that the higher transmit SNR γ 0 causes a higher throughput of the proposed system. All the simulation and analytical curves matched well with each other. Furthermore, Figure 4 shows the connection between the system outage probability and time switching factor α with the main system parameters as R=0.5 bps, γ 0 = 10 dB and η=0.4, 0.8. As shown in Figure 4, we can see that the outage probability of the system model has a decrease when the time switching factor α varies from 0 to 1 in the connection with the fact that more power is used for harvesting energy at R than power is used for information transmission between D, R and S. Again all simulation and analytical results agree well with each other. Moreover, the function of the outage probability on the energy conversion efficiency η as shown in Figure 5. Here we set the main system parameters as R-0.5 bps, α=0.5 and γ 0 = 5, 10 dB. Similar to the above cases, the outage probability of the model system increases crucially while the energy conversion efficiency varies from 0 to 1. It can be observed that the more efficient energy conversion of the system the less outage probability. In addition, the analytical curve is the same as the simulation curve as shown in Figure 5.
Finally, the outage probability versus the source rate R as shown in Figure 6 with α=0.5, η=0.8 and γ 0 = 5, 10 dB. From the results, the outage probability increases significantly when the source rate increases from 0 to 7. We can see that the simulation and the analytical result are the same with all values of the source rate R. Figure 5. OP versus η Figure 6. OP versus R

CONCLUSION
In this paper, we introduce and investigate a Non-Orthogonal Multiple Access (NOMA) EH relay assisted system over Block Rayleigh Fading Channel. Firstly, we proposed and investigated a Non-Orthogonal Multiple Access (NOMA) EH relay-assisted system over Block Rayleigh Fading Channel. In the analysis process, we analyze and derive the integral expression of the outage probability. Finally, the Monte Carlo Simulation is used for validating the analytical analysis in connection with all possible system parameters. The results show that the analytical and simulation results agree well with each other in contact with all possible system parameters.