# Outage Performance Analysis of Non-Orthogonal Multiple Access with Time-Switching Energy Harvesting.

I. INTRODUCTIONRecently, thanks to the significant rise in the number of mobile devices and the advancement of wireless technologies, they lead to the sustainable demand for better connection [1]. As a result, much research interest has been attracted by fifth-generation (5G) networks because of data transfer and services from fourth generation (4G) networks. Thus, this advancement contributes to the information access at anytime and anywhere with more applications and mobile services [2]-[4].

In order to responding to the aforementioned demands, non-orthogonal multiple access (NOMA) has attracted much attention due to its ability to deal with massive connectivity, high latency, low throughput, and low reliability [5]. In particular, multiple users in NOMA systems can be served in a time slot, spreading code, or subcarrier [6]. However, NOMA is still in the beginning stage, and more works need to be done to pave the ways for future deployments.

Despite the advantages of using NOMA in future wireless systems, it also encounters some problems, such as the short lifetime of wireless nodes. Fortunately, although that factor prevents the potentials of NOMA systems, energy harvesting (EH), which is a promising technology, can be deployed to cope with the situation [7]. In practice, energy efficiency (EE) and spectrum efficiency (SE) are key objectives in most 5G systems. Therefore, a technique so-called simultaneous wireless information power transfer (SWIPT) can help EH systems harvest energy from radio frequency (RF) signals. Based on SWIPT, time switching (TS) and power splitting (PS) are two primary EH receiver architectures deployed at the relay node. In particular, thanks to time switching (TS) and power splitting (PS) protocols, the literature in [8] came up with two new relaying networks so-called time switching-based relaying (TSR) protocol and power splitting-based relaying (PSR) protocol to support EH and information processing at the relay node. In [9], the performance of relay selection (RS) schemes in networks with multiple relays was considered. In [10], the work designed a SWIPT NOMA network, where PS protocol is used with a strong channel condition, while NOMA with fixed power allocation and cognitive radio inspired NOMA with SWIPT were examined in [11].

In principle, NOMA allocates different powers to multiple users [12]--[15]. In [12], the study studied a full-duplex (FD) cooperative relaying NOMA (CR-NOMA) network, where a FD relay assists the communication between users with weak channel conditions. Meanwhile, the authors in [13] focused on a CR-NOMA adopting RS, and power allocation problems for half-duplex (HD) and FD in CR-NOMA systems were investigated in [14] to optimize the achievable data rate. In addition, the outage performance for CR-NOMA networks was considered in [15], in which closed-form expressions for outage probability were obtained.

Motivated from the aforementioned works, we design a CR-NOMA to improve the system performance. The contributions of the paper are summarized as follows:

--In this proposed NOMA system, we consider EH and information transmission (IT) time are important directly affect the system performance. Thus, we are going to optimize the IT time to drastically improve the system transmission rate.

--Next, we are going to obtain closed-form expressions for outage probability (OP) in exact and approximate forms to explore the advantages of NOMA.

--Lastly, simulation results are given to examine the impact of relay's placement, and we try to prove that the system performance in case of using NOMA outperforms traditional cooperative relaying networks (CRNs).

We divide this work into five sections. In particular, we present the system model in Section II. In Section III, we obtain the optimal IT time and closed-form expressions for the OP. In Section IV, simulation results are given. Lastly, Section V concludes the paper.

Notation: We denote the received signal-to-noise ratio (SNR) as [GAMMA]. Pr(.) stands for the probability distribution. E{[absolute value of (*)]} represents the expectation operator. The cumulative distribution function (CDF) and probability density function (PDF) of the random variable (RV) as [mathematical expression not reproducible], where [[OMEGA].sub.A] is the average power.

II. SYSTEM MODEL

In Fig. 1 we design a cooperative relaying network with non-orthogonal multiple access (CR-NOMA) which consists of a base station (BS) communicating with a NOMA destination (D) with the assistance of a half-duplex (HD) fixed decode-and-forward (DF) relay (R), it decodes the source data signal in one block and forward that signal in the following block to the destination node. Simultaneously, R cannot transmit and receive a data signal in HD mode. Interestingly, there is a direct connection between BS and D. Besides, R is deployed with strong channel conditions to assist D with worse channel conditions.

The addictive white Gaussian noise (AWGN) is assumed to have a negative impact on every node with zero mean [n.sub.0] and variance [N.sub.0]. In addition, g = [d.sub.Y]/[d.sub.X] is the distance ratio from BS [right arrow] R and from R [right arrow] D. It is noted that the distance between BS and D is [d.sub.Z], so we have:

[mathematical expression not reproducible] (1)

Time-switching protocol: In order to study EH, we use time-switching (TS) receiver architecture at R in Fig. 2. Specifically, T is denoted as the time block for a whole communication phase, in which (T-[delta]T) is referred to how much energy is harvested at R while [delta]T belongs to information transmission (IT) with half of that, [delta]/2 utilized for the link between BS and R, and the remaining part for the link between R and D. We define [delta] [member of] (0,1) as TS ratio. In the following sections, we are going to apply TS protocol in evaluating other system performance metrics.

Fading channels: This system consists of two consecutive time slots in the transmission process. In particular, BS transmits a data symbol denoted as [x.sub.1] to R and D in the first time slot with E([[absolute value of ([x.sub.1])].sup.2]) = 1, in which BS uses the transmit power, [P.sub.S]. Unlike the transmission in the first phase, we deploy power allocation at BS as a NOMA principle to differentiate two data symbols in the second time slot thanks to the characteristic of NOMA transceivers. In particular, BS forwards another data symbol, [x.sub.2] defined as E([[absolute value of ([x.sub.2])].sup.2]) = 1 to D with [P.sub.S], while R transmits [x.sub.1] with the transmit power at R, [P.sub.R] to D. Channel coefficients of the links between BS to R, R to D, and BS are presented by D x, Y, and Z, respectively. All channels are assumed to suffer from independent and identically distributed (i.i.d) quasi-static Rayleigh fading channel, so the channel power gain, [[absolute value of (A)].sup.2] with A [member of] {X, Y, Z} follows an exponential distribution with mean value, [[OMEGA].sub.A]. The path-loss exponent is m.

A. The First Time Slot's Transmission Process

We start by expressing the amount of signal received, [x.sub.1] at both R and D as

[mathematical expression not reproducible] (2)

and

[mathematical expression not reproducible] (3)

Then, the harvested energy, [E.sub.h] at R during [(1-[delta]).sup.T] is given by

[E.sub.h] = [eta][P.sub.S][[[absolute value of (X)].sup.2]/[d.sup.m.sub.X]] (1 - [delta])T, (4)

where the energy conversion efficiency is defined as 0 < [eta] < 1.

Because BS transmits the decoded signal using [E.sub.h] during [delta]T/ 2, we define the transmit power at R as

[P.sub.R] = [2[E.sub.h]/[delta]T] = [alpha][P.sub.S][[[absolute value of (X)].sup.2]/[d.sup.m.sub.X], (5)

where [alpha] = 2[eta](1 - [delta])/[delta].

B. The Second Time Slot's Transmission Process

Likewise, the received signal at D is basically presented as

[y.sub.D,2] = [square root of (([P.sub.R]/[d.sup.m.sub.Y])]Y[x.sub.1] + [square root of (([P.sub.S]/[d.sup.m.sub.Y])] Z[x.sub.2] + [n.sub.0]. (6)

Next, we compute D's received signal by replacing the obtained expression for [P.sub.R] from (5) into (6) as

[y.sub.D,2] = [square root of ([alpha][[P.sub.S]/[d.sup.m.sub.Y])]Y[x.sub.1] + [square root of ([alpha][[P.sub.S]/[d.sup.m.sub.Z])]Z[x.sub.2] + [n.sub.0]. (7)

III. PERFORMANCE ANALYSIS

In this part, we are going to optimize the IT time to achieve the optimal maximum transmission rate and obtain closed-form expressions for the outage probability (OP). Therefore, we now start with the received signal-to-noise ratio (SNR).

A. The Received Signal-to-Noise Ratio (SNR)

We define the received SNR as [GAMMA] = E{[[absolute value of signal)].sup.2]}/E{[[absolute value of (overallnoise)].sup.2]}. Thus, based on (2) and (3), the SNRs for, [x.sub.1] at R and D is expressed by

[mathematical expression not reproducible] (8)

and

[mathematical expression not reproducible] (9)

where the transmit SNR of BS is represented by [beta] = [[P.sub.S]/[N.sub.0]].

For simplicity, we decided to take advantage of successive interference cancellation (SIC) our system. In principle, D decodes [x.sub.1] by treating [x.sub.2] as a noise term which is later eliminated from [y.sub.D,2] to decode [x.sub.2]. Consequently, we derive the received SNRs at D for [x.sub.1] and [x.sub.2] as

[mathematical expression not reproducible] (10)

and

[mathematical expression not reproducible] (11)

Hence, we compute the end-to-end achievable data rate at D for [x.sub.1] and both [x.sub.1] and [x.sub.2] over the [delta]/2 time slot as

[mathematical expression not reproducible] (12)

and

[mathematical expression not reproducible] (13)

where [mathematical expression not reproducible] thanks to the deployment of fixed DF at the transceiver.

B. The Optimization of Information Transmission Time

In practice, the transmission rate is a function of [delta] of the end-to-end SNR. In this part, we are going to optimize the IT time, [[delta].sup.*] to achieve the maximum transmission rate in (12) with [delta] [member of] (0,1).

Due to the changes of the power level at R, the optimization of [delta] can be achieved by [mathematical expression not reproducible], (14)

where subject to [delta] [member of] (0,1).

As a result, the optimal TS [[delta].sup.*] is equivalent to the following

[mathematical expression not reproducible] (15)

In this work, because of the availability of the channel state information (CSI) at solely D. Base on (8) and (10), we can express the average optimal IT time after some manipulations as

[[delta].sup.*] = [[[B[[OMEGA].sub.Z][d.sup.m.sub.Y]/2[eta][[OMEGA].sub.Y][d.sup.m.sub.Z]] + [[d.sup.m.sub.Y]/ 2[eta][[OMEGA].sub.Y]] + 1].sup.-1]. (16)

Remark 1: The fading gain, Z of the BS [right arrow] D link is small than Y of the R [right arrow] D link due to the changes in distance. In addition, the stronger the BS [right arrow] R link becomes, the shorter the distance between BS and R is and shorter time required by R during (1-[delta]) to harvest more energy. This contributes to better the transmission rate.

C. Outage Performance of NOMA

In practice, OP is the probability that the information rate is less than the required threshold information rate, [[GAMMA].sub.0] which is defined as OP = Pr([GAMMA] < [[GAMMA].sub.0]) = [F.sub.[GAMMA]] ([[GAMMA].sub.0]). Besides, the threshold [mathematical expression not reproducible] is related to the target rate [R.sub.0] in HD mode. Thus, we have to evaluate the CDF first on the Proposition 1 before deriving OP later on.

Proposition 1. In this CR-NOMA, we compute the OPs, [mathematical expression not reproducible] for [x.sub.1] and [x.sub.2] respectively as

[mathematical expression not reproducible] (17)

and

[mathematical expression not reproducible] (18)

where [[upsilon].sub.1] = [[GAMMA].sub.0][d.sup.m.sub.Z]/[beta][[OMEGA].sub.Z], [[upsilon].sub.2] = [[GAMMA].sub.0][d.sup.m.sub.X]/[beta][[OMEGA].sub.X], and [mathematical expression not reproducible].

Proof:

with the CDF for [mathematical expression not reproducible] we have

[mathematical expression not reproducible] (19)

and

[mathematical expression not reproducible] (20)

As mentioned, the CDF of [mathematical expression not reproducible] should be evaluated first before the OP at D for [x.sub.1] is achieved. Thus, [mathematical expression not reproducible]([[GAMMA].sub.0]) is conditioned on [[absolute value of (Z)].sup.2] by

[mathematical expression not reproducible] (21)

where the desired expression is obtained following from [[integral].sup.[infinity].sub.0][e.sup.-[[beta]/4x]-[gamma]x] dx = [square root of ([beta]/[gamma])] [K.sub.1]([square root of ([beta][gamma])]) in [16, eq.(3.324.1)].

Therefore, we rewrite the CDF of [mathematical expression not reproducible], over [[absolute value of (Z)].sup.2] by

[mathematical expression not reproducible] (22)

If [x.sub.1] cannot be decoded by one of the links, an outage event may happen. However, using (19) and (24), the end-to-end SNR OP at D is written as

[mathematical expression not reproducible] (23)

Interestingly, the total value of OP of [x.sub.1] is computed by using selection combining technique at R as

[mathematical expression not reproducible] (24)

Replacing (20) and (23) into (24), (17) is obtained.

Furthermore, we achieve the OP of [x.sub.2] in the BS-D link, [mathematical expression not reproducible] as

[mathematical expression not reproducible] (25)

where [mathematical expression not reproducible]. Therefore, we derive the result following from (18).

This ends the proof for Proposition 1.

We see that although it is not easy to achieve a closedform expression in Proposition 1, we are going to express it in Proposition 2 due to using the integral item to reduce the computation complexity.

Proposition 2. In the asymptotic high SNR regime, we can easily approximate the result of Proposition 1 as

[mathematical expression not reproducible] (26)

and

[mathematical expression not reproducible] (27)

where [Y.sup.[infinity]] = [square root of (4[[GAMMA].sub.0][d.sup.- m.sub.Z][d.sup.m.sub.X][d.sup.m.sub.Y]x/[alpha][[OMEGA].sub.X][[OMEGA].sub.Y])] [K.sub.1] ([square root of (4[[GAMMA].sub.0][d.sup.-m.sub.Z][d.sup.m.sub.X][d.sup.m.sub.Y]x/[alpha][[OMEGA].sub.X][[OMEGA].sub.Y])]).

Proof:

Due to conducting the similar steps for the proof in Proposition 1, we upper bound the modified Bessel function of the second kind as x[K.sub.1](x) [right arrow] 1, when x [right arrow] 0. Therefore, [beta] [right arrow] [infinity], the CDF in (22) can be expressed at high SNR as

[mathematical expression not reproducible]. (28)

Finally, we can apply the approximations of [e.sup.-x] = 1 - x when x [right arrow] 0 on (17). After some algebraic manipulations, (26) can be obtained. Similarly, the approximate outage probability for [x.sub.2] in (27) can be obtained.

This ends the proof for Proposition 2.

IV. Numerical Results

In this section, the outage performance with the optimal IT time are simulated to give better insights into the system performance. In addition, the placement of relay regarding the distance allocation in this system is also illustrated. Note that the distance allocation ratio between [d.sub.X] and [d.sub.Y] is assumed to be equal, g = 1. In order to prove the robustness of the derived expressions, we compare with complementary Monte Carlo-simulated performance results. Without the loss of generality, we generate [10.sup.6] realizations of Rayleigh distribution RVs. The simulation systems follow some parameters summarized in Table I.

In Fig. 3, the considered CR-NOMA is compared with a traditional CRN without NOMA in terms of appropriate and exact OP with both data symbols, i.e., [x.sub.1] and [x.sub.2] versus the transmit SNR, [beta]. We can see that thanks to the principles of NOMA, data symbols, [x.sub.1] and [x.sub.2] can be decoded by using SIC technique. Both OPs decrease as the transmit SNR, [beta] rises. In addition, our CR-NOMA is outperforms the traditional CRN with [x.sub.1] due to its ability to combine signals of CRN and limit the performance of direct communication between BS and D.

In Fig. 4, we depict OP with different placements of R, including Case 1 (Close to BS with 3:7 ratio), Case 2 (In the middle with 1:1 ratio), and Case 3 (Far from BS with 7:3 ratio) based on the distance allocation between BS and D. Therefore, the impact of R's location degrades the OP when R and D is close together. As a result, this restricts the system transmission rate.

In Fig. 5, the transmission rate is depicted as a function of TS ratio, [delta]. It is noted that we set the transmit SNR to a fixed value of 5(dB). The existing CR-NOMA outperforms the traditional CR-OMA in terms of the transmission rate. It can be clearly seen that as TS ratio increases from 0.7 to 1, CR-OMA witnesses a significant drop in transmission rate. This phenomenon happens because SIC is deployed at D to make the transmission of data symbol possible in the second time slot. Besides that, with the assistance of R, the fading gain of data symbol can be mitigated by reducing the distance between R and D.

In Fig. 6, the OP with optimal IT time is shown as a function of the transmit SNR with the fixed IT time at [delta] = 0.7, [d.sub.Z] = 2, and g = ([d.sub.X] : [d.sub.Y]) = (1:1) ratio. It is evident that the OP of D using TS protocol experiences a steady decrease as the transmit SNR increases, because the optimal IT time ensures the decoding correctness of both data symbols, [x.sub.1] and [x.sub.2] at D.

V. CONCLUSIONS

In this work, owning to the benefits of NOMA systems, we decided to study an EH CR-NOMA using TS receiver architecture to study EH. In particular, we obtained the optimal IT time to boost the transmission rate. Furthermore, we achieved the closed-form expressions for OP at D in exact and approximate forms. Most importantly, the proposed CR-NOMA system is superior to conventional CRNs in terms of OP in the whole SNR regime.

http://dx.doi.org/10.5755/j01.eie.25.3.23682

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Hoang Thien Van (1), Hoang-Sy Nguyen (2,3), Thanh-Sang Nguyen (2), Van Van Huynh (4), Thanh-Long Nguyen (2,5), Lukas Sevcik (2), Miroslav Voznak (2)

(1) Faculty of Information Technology, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Vietnam

(2) IT4Innovations, VSB-Technical University of Ostrava, 17. listopadu 2172/15, Ostrava 708 00, Czech Republic

(3) Faculty of Information Technology, Robotics and Artificial Intelligence, Binh Duong University, Thu Dau Mot City, Binh Duong Province, Vietnam

(4) Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

(5) Center for Information Technology, Ho Chi Minh City University of Food Industry, Ho Chi Minh City, Vietnam

huynhvanvan@tdtu.edu.vn

Manuscript received 17 September, 2018; accepted 19 January, 2019.

This work was supported by The Ministry of Education, Youth and Sports from the Large Infrastructures for Research, Experimental Development and Innovations project "IT4Innovations National Supercomputing Center-LM2015070" and partially received a financial support from grant No. SGS SP2019/41 conducted at VSB-Technical University of Ostrava, Czech Republic.

Caption: Fig. 1. System model.

Caption: Fig. 2. Energy harvesting and information transmission protocol.

Caption: Fig. 3. Exact and approximate OP versus the transmit SNR.

Caption: Fig. 4. OP for [x.sub.1] versus the transmit SNR.

Caption: Fig. 5. OP as a function of the transmit SNR in case of optimal IT time and fixed IT time.

Caption: Fig. 6. OP as a function of the transmit SNR in case of optimal IT time and fixed IT time.

TABLE I. SIMULATION PARAMETERS. Parameter Value Parameter Value [R.sub.0] 1 (bps/Hz) m 2.7 [delta] 0.7 [d.sub.z] 1 [eta] 1 [[OMEGA].sub.A], A [member of] {X,Y,Z} 1

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Author: | Van, Hoang Thien; Nguyen, Hoang-Sy; Nguyen, Thanh-Sang; Van Huynh, Van; Nguyen, Thanh-Long; Sevcik, |
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Publication: | Elektronika ir Elektrotechnika |

Geographic Code: | 9VIET |

Date: | Jun 1, 2019 |

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